development of novel refrigeration cycles for small scale

Development of novel refrigeration cycles for small scale

LNG processes

A thesis submitted to The University of Manchester for the degree of

Master of Philosophy

in the Faculty of Engineering and Physical Sciences

2016

Héctor Fernando Almeida Trasviña

School of Chemical Engineering and Analytical Science

2

List of Contents

List of Figures ....................................................................................................................... 5

List of Tables ........................................................................................................................ 9

Abstract ............................................................................................................................... 11

Declaration .......................................................................................................................... 12

Copyright Statement .......................................................................................................... 13

Acknowledgements ............................................................................................................. 14

Chapter 1 – Introduction ................................................................................................... 15

1.1 LNG production at small scale .............................................................................. 16

1.2 Challenges in design and optimisation of refrigeration cycles for LNG at

small scale ............................................................................................................. 17

1.3 Motivation and research objectives ....................................................................... 21

1.4 Overview of this Thesis ......................................................................................... 22

Chapter 2 – Technology Background and Literature Review ....................................... 24

2.1 Introduction ........................................................................................................... 24

2.2 Modelling of refrigeration cycles for LNG processes ........................................... 26

2.2.1 Modelling of pure refrigerant cycles .............................................................. 29

2.2.2 Modelling of mixed refrigerant cycles ........................................................... 30

2.2.3 Modelling of cascade cycles .......................................................................... 33

2.3 Research literature on refrigeration cycles for LNG processes ............................. 35

2.3.1 Modelling and design of mixed refrigerant cycles ......................................... 36

2.3.2 Optimisation of mixed refrigerant cycles ....................................................... 42

2.3.3 Design of refrigeration cycles for small scale LNG processes ...................... 47

2.3.4 Design and optimisation of the CryoMan process ......................................... 51

2.3.5 WORK software ............................................................................................. 55

2.3.6 Example of refrigeration cycle simulation in WORK software ..................... 56

2.4 Conclusions ........................................................................................................... 59

Chapter 3 – Development and Design of Novel Refrigeration Cycles ........................... 61

3.1 Introduction ........................................................................................................... 61

3.1.1 Benchmark processes ..................................................................................... 63

3.1.2 Performance evaluation .................................................................................. 64

3.1.3 Operating cost estimation ............................................................................... 64

3.2 Further development of the CryoMan process ...................................................... 64

3

3.2.1 Analysis of the CryoMan process .................................................................. 65

3.2.2 Generation of structural options ..................................................................... 69

3.2.3 Proposal of novel designs .............................................................................. 71

3.3 Process modelling .................................................................................................. 73

3.3.1 Modelling of the Bypass design ..................................................................... 73

3.3.2 Modelling of the Two Flash Levels design .................................................... 80

3.3.3 Modelling of the Mixing After Precooling design ......................................... 83

3.3.4 Example of mixed refrigerant cycle modelling .............................................. 86

3.4 Strategy for the evaluation of the novel designs ................................................... 89

3.4.1 Simulation and analysis ................................................................................. 90

3.4.2 Optimisation of promising designs ................................................................ 90

3.5 Conclusions ........................................................................................................... 91

Chapter 4 – Evaluation of the Novel Refrigeration Cycles ............................................ 93

4.1 Introduction ........................................................................................................... 93

4.2 Determination of the natural gas conditions .......................................................... 93

4.3 Sensitivity analyses: Manipulation of the degrees of freedom in the novel

refrigeration cycles ................................................................................................ 99

4.3.1 Manipulation of the refrigerant composition ............................................... 100

4.4 Evaluation of the Bypass design ......................................................................... 102

4.4.1 Bypass design: Initial simulation ................................................................. 102

4.4.2 Bypass design: Sensitivity studies and discussion ....................................... 103

4.4.3 Bypass design: Manipulation of its degrees of freedom .............................. 110

4.5 Evaluation of the Two Flash Levels design ........................................................ 112

4.5.1 Two Flash Levels design: Initial simulation ................................................ 112

4.5.2 Two Flash Levels design: Sensitivity studies and discussion ...................... 114

4.6 Evaluation of the Mixing After Precooling design.............................................. 120

4.6.1 Mixing After Precooling design: Initial simulation ..................................... 120

4.6.2 Mixing After Precooling design: Sensitivity studies and discussion ........... 121

4.7 Selection of the novel designs for optimisation .................................................. 126

4.8 Conclusions ......................................................................................................... 127

Chapter 5 – Case Study: Optimisation of Novel Refrigeration Cycles ....................... 128

5.1 Introduction ......................................................................................................... 128

5.2 Optimisation criteria ............................................................................................ 129

4

5.3 Problem statement ............................................................................................... 131

5.4 Bypass design: Optimisation and discussion ....................................................... 132

5.5 Two Flash Levels design: Optimisation and discussion ..................................... 136

5.6 Operating costs comparison between the novel refrigeration cycles and

the benchmark processes ..................................................................................... 140

5.7 Conclusions ......................................................................................................... 142

Chapter 6 – Conclusions and Future Work ................................................................... 144

6.1 Conclusions ......................................................................................................... 144

6.2 Future work ......................................................................................................... 147

Appendix 1 – Determination of the Natural Gas Stream Conditions ......................... 149

Appendix 2 – Bypass design and Two Flash Levels design: Optimisation Results .... 159

A2.1 Optimisation results of the Bypass design ....................................................... 159

A2.2 Optimisation results of the Two Flash Levels design ...................................... 162

Appendix 3 – Optimisation of the CryoMan Process with Six Compression Stages . 166

A3.1 Introduction ...................................................................................................... 166

A3.2 Problem formulation ........................................................................................ 167

A3.3 Problem statement............................................................................................ 168

A3.4 Optimisation of the CryoMan process ............................................................. 169

References ......................................................................................................................... 172

5

List of Figures

Figure 1. 1. World energy demand according to the New Policies Scenario:

a) 2015 and b) 2035 [adapted from IEA (2012)]. ................................................ 16

Figure 1. 2. The PRICO cycle (Swenson, 1977). ..................................................................... 18

Figure 1. 3. Complexity of commercial refrigeration cycles increases as efficiency

increases [adapted from (Air Products and Chemicals Inc., 2013)]. .................... 19

Figure 1. 4. The CryoMan configuration (Zheng, 2009). ........................................................ 21

Figure 2. 1. Ideal refrigeration cycle: a) configuration; b) P–H diagram

[adapted from (Smith, 2005b, Ch. 24.6)]. ............................................................. 24

Figure 2. 2. Configuration options to reduce shaft power demand of a simple cycle:

a) multistage expansion; b) intercooling: c) multilevel refrigeration

[adapted from (Smith, 2005b, Ch. 24.6)]. ............................................................ 26

Figure 2. 3. Refrigerant evaporating profile (at constant pressure): a) pure component;

b) mixed refrigerant [adapted from (Radermacher, 1989)]. ................................. 30

Figure 2. 4. Temperature–enthalpy profile calculation for a mixed refrigerant stream

(ΔP = 0 in the evaporator). ................................................................................... 31

Figure 2. 5. PRICO refrigeration cycle (Swenson, 1977). ....................................................... 33

Figure 2. 6. Cascade refrigeration cycle with two temperature levels of refrigeration. ........... 34

Figure 2. 7. Commercial cascade cycles: a) Phillips cascade cycle; b) Propane precooled

mixed refrigerant cycle; c) Dual mixed refrigerant cycle. .................................... 35

Figure 2. 8. Two temperature levels refrigeration cycle using a presaturator

(Shelton and Grossmann, 1986). ........................................................................... 36

Figure 2. 9. Design methodology for low temperature processes presented by Linnhoff

and Dhole (1992)................................................................................................... 38

Figure 2. 10. Generation of the ‘ideal’ cold composite curve (Lee, 2001, Ch. 4). .................. 38

Figure 2. 11. Multistage refrigeration cycle. ............................................................................ 41

Figure 2. 12. a) The PRICO cycle; b) “Pre-flash” design; c) the CryoMan process

[adapted from (Zheng, 2009)]. ............................................................................ 52

Figure 2. 13. Operating conditions of the PRICO cycle for the simulation example

problem. ............................................................................................................. 57

Figure 2. 14. Natural gas temperature–enthalpy data for the simulation example in

WORK software. ................................................................................................. 58

Figure 3. 1. Multistage centrifugal compressor [adapted from (Ludwig, 2001, Ch. 12)]. ....... 62

Figure 3. 2. Multi-stream heat exchanger for five streams [reproduced from (ESDU

International plc, 2006)]. ....................................................................................... 63

Figure 3. 3. Refrigeration cycles presented by Zheng (2009): a) “Pre-flash” design, and

b) the CryoMan process. ...................................................................................... 65

Figure 3. 4. Ternary refrigerant after flash separation: a) composition distribution; and

b) shaft work for compression of 1 kmol·s-1

from 1.2 bar and 30°C to 20 bar. ... 66

Figure 3. 5. Shaft work demand of LP Stream in the “Pre-flash” and in the CryoMan

process for different outlet pressures at constant inlet pressure (1.2 bar). ........... 68

6

Figure 3. 6. Compression trends with actual flow rates (Zheng, 2009): a) LP Streams

at constant inlet pressure (1.2 bar); and b) overall refrigerant streams at

constant outlet pressure (48.3 bar). ...................................................................... 69

Figure 3. 7. A refrigerant stream bypassing the flash unit. ...................................................... 70

Figure 3. 8. Multiple flash separation of the refrigerant stream (liquid from first flash

unit is further expanded). ..................................................................................... 70

Figure 3. 9. Partial mixing of refrigerant stream after precooling in the MSHE. .................... 71

Figure 3. 10. Novel refrigeration cycle 1: Bypass design. ....................................................... 71

Figure 3. 11. Novel refrigeration cycle 2: Two Flash Levels design. ...................................... 72

Figure 3. 12. Novel refrigeration cycle 3: Mixing After Precooling design. ........................... 73

Figure 3. 13. Bypass design: degrees of freedom. ................................................................... 74

Figure 3. 14. Multistage compression. ..................................................................................... 78

Figure 3. 15. Two Flash Levels design: degrees of freedom. .................................................. 81

Figure 3. 16. Mixing After Precooling design: degrees of freedom. ....................................... 84

Figure 3. 17. Natural gas temperature–enthalpy data (from HYSYS, 1 kmol·s-1

) for the

modelling example. ............................................................................................. 87

Figure 4. 1. Temperature–enthalpy profile according to data from Remeljej and Hoadley

(2006) compared to that published by Lee (2001). ............................................... 95

Figure 4. 2. Determination of the natural gas stream conditions through minimisation of

the sum of squared difference of the enthalpy profiles against the data

provided by Lee (2001, Ch. 4). ............................................................................ 96

Figure 4. 3. Temperature–enthalpy profile of the optimised stream compared to the data

provided by Lee (2001). ....................................................................................... 97

Figure 4. 4. The CryoMan process. .......................................................................................... 99

Figure 4. 5. Example of composition manipulation: propane mole percentage is

increased; the mole percentage proportion between the remaining

components remains the same. ........................................................................... 102

Figure 4. 6. The Bypass design showing the new degrees of freedom and initial values. ..... 102

Figure 4. 7. Effect of increasing the Bypass Stream flow rate fraction: a) shaft power

demand and minimum driving force in the MSHE; b) the composite

curves in the MSHE. .......................................................................................... 103

Figure 4. 8. Effect of increasing the pressure level of the Bypass Stream: a) shaft power

demand and minimum driving force in the MSHE; b) P–H diagram. ............... 104

Figure 4. 9. Effect of increasing the compressor discharge pressure: a) power demand

and minimum driving force; b) the vapour fraction of the refrigerant. .............. 105

Figure 4. 10. Effect of increasing the flow rate fraction of liquid from the flash unit (f Liq

):

a) shaft power demand and minimum driving force in the MSHE; b) flow

rates of Stream 1 and Stream 2. ....................................................................... 106

Figure 4. 11. a) Increasing the value of f Liq

increases the heat of vaporisation of Stream 1;

b) heat of vaporisation of the refrigerant is increased as heavy components

in the composition are increased. ..................................................................... 107

Figure 4. 12. Effect of composition on power demand and minimum driving force in

the Bypass design: a) methane; b) ethane; c) propane; d) n-butane;

e) nitrogen ........................................................................................................ 108

7

Figure 4. 13. As the overall refrigerant composition becomes lighter: a) its vapour

fraction increases; and b) its evaporating temperatures decreases. .................. 110

Figure 4. 14. Manipulation of the operating variables in the Bypass design: a) Bypass

Stream flow rate fraction is varied; b) the liquid mixing fraction (f Liq

)

is varied. ........................................................................................................... 111

Figure 4. 15. The Two Flash Levels design showing the new degrees of freedom

and initial values. ............................................................................................. 112

Figure 4. 16. Streams arrangement in the multistage compressor: a) CryoMan

process; b) Two Flash Levels design ............................................................... 114

Figure 4. 17. Effect of increasing the flow rate fraction of liquid fed to the second

flash unit (f 2nd

): a) shaft power demand and minimum driving force

in the MSHE; b) flow rate of Stream 2. ........................................................... 115

Figure 4. 18. Effect of increasing the pressure of the second flash unit (P2nd

):

a) power demand and minimum driving force in the MSHE; b) heat

of vaporisation and flow rate of Stream 3. ....................................................... 116

Figure 4. 19. Effect of increasing the precooling temperature of Stream 3: a) power

demand and minimum driving force in the MSHE; b) evaporating

temperature; c) infeasible heat transfer in the MSHE. ..................................... 117


the Two Flash Levels design: a) methane; b) ethane; c) propane;

d) n-butane; e) nitrogen. ................................................................................... 118

Figure 4. 21. The Mixing After Precooling design showing the new degrees of freedom

and initial values. ............................................................................................. 121

Figure 4. 22. Effect of increasing flow rate fraction α: a) shaft power demand and

minimum driving force in the MSHE; b) heat of vaporisation of Stream 5. ... 122

Figure 4. 23. a) Evaporating temperature of Stream 5 increases as flow rate fraction α

increases; b) infeasible heat transfer as a result of the increased evaporating

temperature of Stream 5. .................................................................................. 122

Figure 4. 24. Effect of increasing flow rate fraction β on: a) shaft power demand and

minimum driving force in the MSHE; b) the composite curves in the

MSHE. .............................................................................................................. 123


the Mixing After Precooling design: a) methane; b) ethane; c) propane;

d) n-butane; e) nitrogen. ................................................................................... 124

Figure 5. 1. Objective function progression in the optimisation of the operating variables

of the Bypass design. ......................................................................................... 132

Figure 5. 2. Bypass design. .................................................................................................... 133

Figure 5. 3. Composite curves in the MSHE: a) the Bypass design; b) the CryoMan

process. ............................................................................................................... 135

Figure 5. 4. Objective function progression in the optimisation of the operating variables

of the Two Flash Levels design. ........................................................................ 136

Figure 5. 5. Two Flash Levels design. ................................................................................... 137

Figure 5. 6. Composite curves in the MSHE of the optimised Two Flash Levels design. .... 138

8

Figure A1. 1. Temperature–enthalpy profile of the natural gas stream (Lee, 2001). ............. 150

Figure A1. 2. Temperature–enthalpy profile comparison between the data provided by

Lee (2001) and that according Remeljej and Hoadley (2006). ....................... 151

Figure A1. 3. a) Constructed profile (squares, Starting Point 16) failing to fully cover

the condensing zone; b) condensing enthalpy change increases as

pressure of the stream decreases ..................................................................... 155

Figure A1. 4. Sum of squared errors (SSE) of enthalpy values for each starting point

and for each pressure drop profile assumption. .............................................. 156

Figure A1. 5. Temperature–enthalpy profiles comparison between data published by

Lee (2001) and the stream constructed by optimisation. ................................ 158

Figure A2. 1. Bypass refrigeration cycle. .............................................................................. 159

Figure A2. 2. Optimisation progression of the Bypass design (run 1). .................................. 159



Figure A2. 5. Two Flash Levels refrigeration cycle. ............................................................. 162

Figure A2. 6. Optimisation progression of the Two Flash Levels design (run 1).................. 163



Figure A3. 1. Objective function progression in the optimisation of the operating

variables of the CryoMan process. .................................................................. 169

Figure A3. 2. The CryoMan refrigeration cycle. ................................................................... 170

9

List of Tables

Table 2. 1. Suggested working temperatures for common refrigerants [adapted from

(Lee, 2001, Ch. 1)]. ................................................................................................ 30

Table 2. 2. Cascade refrigeration cycles in the LNG industry [adapted from

(Mokhatab et al., 2014b, Ch. 3.2)]. ........................................................................ 35

Table 2. 3. Models for simulation of refrigeration cycles. ....................................................... 42

Table 2. 4. Mixed refrigerant cycles studied in the open research literature for LNG

production at small scale. ....................................................................................... 50

Table 2. 5. Natural gas and mixed refrigerant compositions [mole %] for the simulation

example in WORK software. ................................................................................. 58

Table 2. 6. Natural gas temperature–enthalpy data for the simulation example in

WORK software. .................................................................................................... 58

Table 2. 7. Comparison of the PRICO cycle simulation between WORK software and

Aspen HYSYS. ...................................................................................................... 59

Table 3. 1. Natural gas and mixed refrigerant composition [mole %] for the modelling

example. ................................................................................................................. 87

Table 3. 2. Natural gas temperature–enthalpy data (from HYSYS, 1 kmol·s-1

) for the

modelling example. ................................................................................................ 87

Table 3. 3. Results comparison of the Two Flash Levels design simulation example. ........... 88

Table 3. 4. Temperature–enthalpy profile of the natural gas stream published by

Lee (2001). ............................................................................................................ 89

Table 4. 1. Natural gas stream data presented by Lee (2001), Del Nogal (2006) and

Zheng (2009). ......................................................................................................... 94

Table 4. 2. Natural gas stream conditions resulted from the optimisation (zero pressure

drop in the MSHE). ................................................................................................ 96

Table 4. 3. Composition of optimised natural gas stream compared to that of Remeljej

and Hoadley (2006). ............................................................................................... 97

Table 4. 4. The CryoMan process (Zheng, 2009): inputs to HYSYS using the natural

gas stream of Table 4.2. ......................................................................................... 99

Table 4. 5. Assumptions in the novel refrigeration cycles to maintain consistency with

Zheng (2009). ....................................................................................................... 100

Table 4. 6. Composition ranges for feasible heat transfer in the Bypass design. ................... 108

Table 4. 7. Operating variables of the Bypass design after the sensitivity analyses. ............. 111

Table 4. 8. Composition ranges for feasible heat transfer in the Two Flash Levels design. . 118

Table 4. 9. Operating variables of the Two Flash Levels design after the sensitivity

analyses. ............................................................................................................... 119

Table 4. 10. Composition ranges for feasible heat transfer in the Mixing After

Precooling design. .............................................................................................. 124

Table 4. 11. Operating variables of the Mixing After Precooling design after the

sensitivity analyses. ............................................................................................ 125

Table 5. 1. Genetic Algorithm parameters for the optimisation of the novel

refrigeration cycles. .............................................................................................. 131

10

Table 5. 2. Temperature–enthalpy profile of the natural gas stream to be liquefied

(Lee, 2001). .......................................................................................................... 132

Table 5. 3. Optimised operating variables of the Bypass design. .......................................... 133

Table 5. 4. Optimised operating variables of the Two Flash Levels design. ......................... 137

Table 5. 5. Operating cost savings comparison (relative to the CryoMan process)

between the novel refrigeration cycles and benchmark processes. ..................... 141

Table A1. 1. Temperature–enthalpy profile of the natural gas stream (Lee, 2001;

Del Nogal, 2006; Zheng, 2009). ....................................................................... 150

Table A1. 2. Natural gas stream profile according to Remeljej and Hoadley (2006)

compared to Lee (2001). ................................................................................... 151

Table A1. 3. Starting points for the natural gas stream optimisation. .................................... 154

Table A1. 4. Optimised values of the vector x* for the natural gas stream (zero

pressure drop in the MSHE). ............................................................................. 157

Table A1. 5. Composition of the optimised natural gas stream and that of Remeljej

and Hoadley (2006). .......................................................................................... 157

Table A1. 6. Temperature–enthalpy data comparison between the optimised stream

and the published data. ...................................................................................... 158

Table A2. 1. Optimised operating variables of the Bypass design (run 1). ........................... 160



Table A2. 4. Optimised operating variables of the Two Flash Levels design (run 1). .......... 163



Table A3. 1. Genetic Algorithm parameters for optimisation of the CryoMan process. ....... 168

Table A3. 2. Natural gas stream data (temperature–enthalpy profile). .................................. 169

Table A3. 3. Operating variables of the optimised CryoMan process with six and four

compression stages. ........................................................................................... 170

11

Development of Novel Refrigeration Cycles for Small Scale LNG Processes


The University of Manchester

2016

Abstract – MPhil Thesis

Demand for liquefied natural gas (LNG) is continuously increasing. Commercial

exploitation of small gas reserves is thus becoming accordingly attractive. Natural gas

liquefaction processes are both capital- and energy-intensive. Refrigeration cycles are used

to liquefy the natural gas to temperatures around –160°C; the shaft power demand for

refrigerant compression dominates operating costs. Energy efficiency is usually achieved

in large-scale commercial processes with complex configurations. However, the

complexity of refrigeration cycles in small-scale LNG processes (where production rate is

up to 1 million t per annum) should be low to keep the capital costs relatively low. A trade-

off exists between energy efficiency and capital costs in the design of refrigeration cycles.

In addition, optimisation of the operating variables of the refrigeration cycle is difficult.

Optimisation aims to find the combination of operating variables (including mixed

refrigerant composition) that minimises the shaft power demand for refrigerant

compression in a process with a given configuration and a given liquefaction duty.

However, because of the relatively large number of degrees of freedom available in the

refrigeration cycle and the complex interactions between the operating variables, the

optimisation becomes challenging.

A limited range of refrigeration cycles is studied in the open research literature for the

production of LNG at small scales. Single mixed refrigerant cycles are commonly studied

because they have ‘simple configurations’, although ‘complexity’ of refrigerant cycle

configurations has not been clearly defined. The PRICO cycle is the simplest commercial

refrigeration cycle for LNG production. The so-called ‘CryoMan’ process, developed at

the University of Manchester, modified the structure of the PRICO cycle and achieved

significant shaft power savings (around 8%), compared to the PRICO cycle.

In this work, further structural modifications to the CryoMan process are proposed,

resulting in three novel refrigeration cycles (namely the ‘Bypass’ design, the ‘Two Flash

Levels’ design and the ‘Mixing After Precooling’ design). Design constraints, related to

the number of refrigerant compression stages and the number of streams in the multi-

stream heat exchanger, are defined in this work to limit the complexity of the novel cycles.

To illustrate the benefits of the structural modifications, the configurations are optimised in

an industrially-relevant case study. Sensitivity studies and optimisation are employed to

explore thoroughly the complex interactions between operating variables; a Genetic

Algorithm is applied, to search the solution space and to avoid local optima. The case

study demonstrates that the structural modifications proposed can bring shaft power

savings of up to 3.2% in the case of the Bypass configuration (equivalent to operating cost

savings of £0.69 million per annum for a natural gas feed of 0.75 million t per annum) with

relatively minor increases in the complexity of the refrigeration cycles.

12

Declaration

No portion of the work referred to in the thesis has been submitted in support of an

application for another degree or qualification of this or any other university or other

institute of learning.


13

Copyright Statement

i. The author of this thesis (including any appendices and/or schedules to this thesis)

owns certain copyright or related rights in it (the “Copyright”) and s/he has given

The University of Manchester certain rights to use such Copyright, including for

administrative purposes.

ii. Copies of this thesis, either in full or in extracts and whether in hard or electronic

copy, may be made only in accordance with the Copyright, Designs and Patents

Act 1988 (as amended) and regulations issued under it or, where appropriate, in

accordance with licensing agreements which the University has from time to time.

This page must form part of any such copies made.

iii. The ownership of certain Copyright, patents, designs, trade marks and other

intellectual property (the “Intellectual Property”) and any reproductions of

copyright works in the thesis, for example graphs and tables (“Reproductions”),

which may be described in this thesis, may not be owned by the author and may be

owned by third parties. Such Intellectual Property and Reproductions cannot and

must not be made available for use without the prior written permission of the

owner(s) of the relevant Intellectual Property and/or Reproductions.

iv. Further information on the conditions under which disclosure, publication and

commercialisation of this thesis, the Copyright and any Intellectual Property

University IP Policy (see

http://documents.manchester.ac.uk/display.aspx?DocID=24420), in any relevant

Thesis restriction declarations deposited in the University Library, The University

Library’s regulations (see http://www.library.manchester.ac.uk/about/regulations/)

and in The University’s policy on Presentation of Theses.

14

Acknowledgements

Firstly, I want to acknowledge my supervisors. I would like to thank very much to Dr.

Megan Jobson for her constant patience, support, supervision and feedback throughout the

completion of my research. Many thanks to Prof. Robin Smith for sharing his knowledge

and for giving me great advices and suggestions for my project. Thanks to both for giving

me the opportunity to study under your supervision.

I would like to thank Steve Doyle for his help during the coding and programming stage in

my project. Thanks to my friends and colleagues at the Centre for Process Integration

(CPI) – the best group! – for their help and good advices (and for all the good moments!).

I also want to acknowledge the Mexican National Council of Science and Technology

(CONACyT) for the financial support provided during my studies.

Thanks to my family and friends for all their support.

Chapter 1 Introduction

15

Chapter 1 – Introduction

Natural gas, along with coal and oil, is one of the major sources of energy all around the

world; natural gas currently supplies 22% of the total energy demand globally (IEA, 2012).

Also, natural gas represents the cleanest form of fuel in terms of carbon dioxide emissions,

compared to coal and oil. When oil and coal are used as fuel, emissions of carbon dioxide

and other pollutants such as nitrogen oxides, which are greenhouse gases related to global

warming, are over 40% greater than those produced when natural gas is employed as the

fuel (Kidnay and Parrish, 2006a, Ch. 1.1). The demand for natural gas is likely to increase

in the next decades as a result of the increasing concern on environmental regulations,

because the natural gas would be less affected by economic penalties for CO2 emissions

compared to coal and oil (IEA, 2012).

Natural gas is usually transported from the gas wells using a pipeline network. However,

when the gas reservoirs are located in remote areas or when long distance transportation is

required (i.e. over 3,500 km), natural gas transportation as liquefied natural gas (LNG) via

cargo ships or trucks becomes more profitable, compared to gas pipelines transportation

(Mokhatab et al., 2014a, Ch. 1.2).

Worldwide LNG production in 2014 – around 330 billion m3 – accounted for nearly 10%

of the total natural gas production, according to a report from BP (BP Global, 2015). In

total, 3,400 billion m3 of natural gas were produced globally during the year 2014. Nearly

1,000 billion m3 of natural gas was traded as exports in the same year, 33% from which

was traded as LNG (BP Global, 2015). Furthermore, over two thirds of the total LNG

produced was exported to the Asian market, especially to Japan and South Korea. Qatar is

the world largest LNG producer as it exported around 103 billion m3 of LNG worldwide

during the year of 2014 – exporting mainly to Japan, South Korea and India –, i.e. over

30% of the total LNG production (BP Global, 2015). Australia is also one of the major

contributors to LNG production – nearly 32 billion m3 exported in the same year – and its

production capacity is expected to increase by around 75 billion m3 per year since seven

LNG projects would be starting operation in the next five years (IEA, 2012).

Unconventional gas resources (e.g. shale gas) are becoming increasingly important for

natural gas production, and potentially for LNG production as well. For example, the sharp

increase of natural gas production in the US during the second half of the past decade,


16

coming from the exploitation of shale gas by hydraulic fracturing the shale rock (process

also known as ‘fracking’), could lead to the US exporting natural gas as LNG to Asian

markets, especially to Japan (IEA, 2012). Production and trade of LNG is expected to

increase in the next decades.

1.1 LNG production at small scale

Natural gas will play an important role as a main source of fuel according to the increasing

trend in energy demand (Kumar et al., 2011) and the demand for natural gas is projected to

increase up to 24% of the total energy share in the next two decades according to the New

Policies Scenario presented by the International Energy Agency (IEA, 2012) – see Figure

1.1. Proven gas reserves considered as technically and economically feasible (187 trillion

m3) would allow natural gas production for 50 years if the production rate is assumed

constant (BP Global, 2015). Remaining gas reserves (including proven reserves and

estimated undiscovered resources) that are technically recoverable are calculated as 790

trillion m3 (IEA, 2012).

However, unprocessed gas wells are estimated to account for nearly half of overall natural

gas reserves around the world; many of these reserves are considered as ‘stranded

reservoirs’ due to the limited access for commercial exploitation (Castillo and Dorao,

2010). Since energy demand is continuously increasing (IEA, 2012), small reserves of

natural gas are gaining attention for commercial exploitation as LNG to help meeting the

global energy demand (small scale production rate is up to 1 million t per annum compared

to large scale in which production rate is above 2.5 million t per annum (Mokhatab et al.,

2014b, Ch. 3.3)).

a) b)

Figure 1. 1. World energy demand according to the New Policies Scenario: a) 2015 and b) 2035 [adapted

from IEA (2012)].

Around 50% of the increase in natural gas production is expected to come from

unconventional gas resources, especially from shale gas (IEA, 2012). However, in Europe

Natural

Gas

22%

Coal

28%

Oil

31%

Nuclear

5% Other

14%

2015

(162.7 million GW·h)

Natural

Gas

24%

Coal

24%

Oil

27%

Nuclear

7%

Other

18%

2035

(200.0 million GW·h)


17

and especially in UK, the development of projects for exploiting shale gas resources is still

uncertain as a result of public opinion on potential social and environmental risks that

‘fracking’ processes may produce, e.g. groundwater contamination and exposure to

particulate matter (Reap, 2015), in spite of the energy security and economic growth that

shale gas would bring compared to coal and oil. Even though public opinion might be

influenced by factors such as lack of knowledge of shale gas as a source of energy

(Whitmarsh et al., 2015), the development of shale gas is still dependent on public

acceptance, and on creation of policies and regulations (IEA, 2012). These concerns on

shale gas development also encourage the exploitation of small gas reserves for production

of LNG at small scale to meet the growing energy demand.

1.2 Challenges in design and optimisation of refrigeration cycles for LNG at small

scale

Since natural gas is mostly methane, which has a normal boiling point of –161°C (112 K),

very low temperatures are needed in order to fully liquefy a natural gas stream. In this

liquefaction process, temperatures down to –161°C are reached by employing refrigeration

cycles that provide the cooling needed by the natural gas stream. In vapour compression

refrigeration cycles, widely employed in the LNG industry (Smith, 2005b, Ch. 24.6), a

refrigerant fluid at a low pressure level continuously removes heat from the process stream

and rejects it to a heat sink (e.g. cooling water) after compression at a high pressure level.

In LNG commercial refrigeration cycles, for example the PRICO cycle (Swenson, 1977)

which is the simplest commercial refrigeration cycle in the LNG industry – shown in

Figure 1.2 –, the refrigerant stream at low pressure removes heat not only from the natural

gas stream but also from the refrigerant stream at high pressure level, in order to precool or

fully condense the refrigerant at high pressure (i.e. self-cooling or self-condensing) and

reach very low temperatures (e.g. –161°C) once expanded. Liquefaction of natural gas is a

highly energy consuming process; the shaft power demand for refrigerant compression in

the refrigeration cycle dominates operating costs (Mokhatab et al., 2014b, Ch. 3.2).


18

Figure 1. 2. The PRICO cycle (Swenson, 1977).

The design of the refrigeration cycles should then be energy-efficient in order to minimise

the shaft power demand for compression and hence operating costs. Any savings in power

demand that can be achieved in the refrigeration cycle significantly reduce the operating

costs. For example, Montanez-Morantes (2015, Ch. 3) presented a case study in which the

operating variables (refrigerant flow rate, pressure levels and compressors rotational speed)

of the precooling stage of a propane precooled mixed refrigerant cycle (commercially

dominant refrigeration cycle in the LNG industry) are optimised in order to minimise the

shaft power demand. Shaft power consumption is reduced by 3% compared to the initial

conditions, and such improvements would represent operating cost savings of nearly £0.9

million per annum by only adjusting the operating variables of the refrigeration cycle.

In commercial liquefaction processes, as the efficiency of the refrigeration cycle increases,

its complexity usually increases as well (as illustrated in Figure 1.3), in order to increase

the number of degrees of freedom in the refrigeration cycles (i.e. the operating variables

that can be manipulated by the designer, such as refrigerant flow rate, composition,

pressure levels) to help reducing the overall energy consumption of the refrigeration cycle

while satisfying the natural gas liquefaction demand. For instance, the propane precooled

mixed refrigerant cycle (0.29 kWh·kg-1

of LNG) is more efficient than the PRICO cycle

(0.40 kWh·kg-1

of LNG) (Castillo and Dorao, 2010) because the propane precooling stage

helps reducing the cooling duty of the mixed refrigerant cycle, which can be adjusted to

liquefy the natural gas stream with a lower overall shaft power consumption compared to

that of the PRICO cycle.

However, the increase in efficiency of the propane precooled mixed refrigerant cycle,

compared to the PRICO cycle, is at the expense of increase in the complexity of its

configuration. The propane cycle comprises four heat exchangers for the precooling stage


19

and its own multistage compressor, which are in addition to the multi-stream heat

exchanger (MSHE) and multistage compressor for the mixed refrigerant cycle. Thus, the

increase in complexity also increases significantly the capital costs of the propane

precooled mixed refrigerant cycle compared to those in the PRICO cycle. Low complexity

and compactness of the refrigeration cycle are especially important in small scale LNG

processes. For example, capital investment has to be low when small projects are intended

for short operating periods (Li and Ju, 2010), in order to maintain profitability.

Additionally, since one of the main purposes of such refrigeration cycles is for offshore

liquefaction, there would be a limited plot area for the plant to be built, and weight can also

be a limiting factor as the LNG plant would be built on a platform or on top of a ship

(Castillo and Dorao, 2010).

Figure 1. 3. Complexity of commercial refrigeration cycles increases as efficiency increases [adapted from

(Air Products and Chemicals Inc., 2013)].

Therefore, an economic trade-off exists in the design of refrigeration cycles for small scale

LNG processes between a refrigeration cycle with high efficiency (for energy savings) and

a cycle with a low-complexity configuration (to keep relatively low capital investment);

the refrigeration cycle should then be designed to take advantage of this economic trade-

off.


20

Another challenge is the modelling of mixed refrigerant cycles because of the non-

isothermal nature of mixed refrigerants. The composition of the mixed refrigerant streams

determines the temperature profile and temperature range in which the refrigerant

evaporates for a fixed evaporating pressure (Mokhatab et al., 2014c, Ch. 5.1). Thus,

although the temperatures of the mixed refrigerant at the inlet and outlet of the MSHE

indicate that heat transfer is feasible (i.e. heat transfer with a minimum temperature

approach), intermediate temperatures may lead to infeasible heat transfer as a result of the

continuously-changing temperature of the refrigerant. Therefore, the composite curves

inside the MSHE need to be checked at intermediate temperatures in order to guarantee

feasible heat transfer. There exist models proposed in the open literature, for example (Del

Nogal et al., 2008), in which a user-specified number of intermediate temperatures are

calculated for the hot composite curve and compared to those of the cold composite at the

same enthalpy values. The composite curves are more detailed as the number of

intermediate temperatures increases but at the expense of increased computational time

that is needed for the calculations.

The optimisation of the operating variables of the refrigeration cycle is also challenging.

The optimisation of the operating variables in mixed refrigerant cycles aims to find a

combination of the operating variables (i.e. values of refrigerant flow rate, composition,

pressure levels, etc.) that yields the lowest total shaft power demand for refrigerant

compression. However, the optimisation is difficult because of a relatively large number of

degrees of freedom and also because complex interactions exist between the operating

variables of the refrigeration cycles; a robust optimisation method is needed in order to

fully explore the possible combinations of the operating variables to achieve the minimum

shaft power.

The results obtained from a deterministic optimisation (known as local optima) are

strongly dependent on the initial conditions selected and thus the optimisation should be

performed from different initial conditions to find the global minimum (Edgar et al., 2001,

Ch. 10.1). Different approaches have been proposed in the research open literature for the

optimisation of LNG refrigeration cycles. For example, in the publication of Del Nogal et

al. (2008), a Genetic Algorithm optimisation technique is used to help avoiding local

optima.


21

1.3 Motivation and research objectives

As mentioned in Section 1.2, shaft power demand in refrigeration cycles for LNG

production has a great impact in process economics. Thus, the design of refrigeration

cycles for small scale LNG production should be aimed at minimising shaft power demand

while keeping low complexity.

Only limited refrigeration cycles have been studied in the open research literature. The

“CryoMan” process (Zheng, 2009, Ch. 3) – shown in Figure 1.4 –, a single mixed

refrigerant cycle developed through structural modifications to the PRICO cycle,

demonstrated significant power savings (nearly 8%) compared to the PRICO cycle. The

structural modifications in the CryoMan process include a flash unit after the partial

condenser; the CryoMan process takes advantage from flashing the mixed refrigerant into

vapour and liquid, and partially mixing these flashed streams to create two refrigerant

streams with different compositions. Each refrigerant stream can be expanded to an

independent pressure level. Thus, the CryoMan process takes advantage of creating new

refrigerant streams from a single mixed refrigerant stream. Yet, the configuration of the

CryoMan process remains with relatively low complexity. However, the ‘complexity’ of

the refrigeration cycles has not been clearly defined in the open research literature.

Figure 1. 4. The CryoMan configuration (Zheng, 2009).

The CryoMan process thus might be further structurally modified to develop novel

refrigeration cycles that bring further shaft power savings while keeping the configuration

with relatively low complexity. Hence, the novel refrigeration cycles would exploit the

trade-off between energy-efficiency of the refrigeration cycle and the complexity of its

design.


22

Therefore, this thesis aims to:

Clearly establish criteria to define ‘complexity’ in a refrigeration cycle design.

Develop novel refrigeration cycles, by structurally modifying the CryoMan

process, that bring shaft power savings compared to the CryoMan process. The

novel configurations are of low complex design according to the previous bullet

point. In order to propose meaningful structural modifications to the refrigeration

cycle, the CryoMan process is analysed in detail to identify key operating variables

that could be exploited.

Model and simulate the novel refrigeration cycles. Models available in the open

research literature are used; the models are consistent with those employed in the

CryoMan process in order to perform meaningful comparisons.

Assess and screen the novel refrigeration cycles. Sensitivity studies are performed

to evaluate the novel refrigeration cycles, using the shaft power demand as the

performance indicator. Only the promising designs are selected for optimisation of

their corresponding operating variables.

Optimise the operating variables (e.g. refrigerant flow rate, composition and

streams pressure levels) of the promising novel refrigeration cycles in an

industrially-relevant case study to liquefy a given natural gas stream. The total shaft

power consumption of the novel refrigeration cycles is compared against both the

CryoMan process and the PRICO cycle, and illustrated on an annual operating

costs basis.

1.4 Overview of this Thesis

This thesis is structured in six chapters and three appendixes. In Chapter 1, the current

status and relevance of natural gas as a source of energy is exposed, as well as the

importance of liquefied natural gas (LNG) processes at small scale (i.e. up to 1 million t

per annum). The main challenges in the design of refrigeration cycles for small scale LNG

processes are discussed. The research objectives of this thesis are presented.

In Chapter 2, refrigeration cycles for LNG processes are introduced as well as modelling

for both single component and mixed refrigerant cycles. The research in the open literature


23

regarding modelling and optimisation of refrigeration cycles for LNG processes, and

design of refrigeration cycles for LNG processes at small scale, is critically reviewed also

in Chapter 2. Additionally, the CryoMan process is introduced in this chapter.

The development of the novel refrigeration cycles is presented in Chapter 3. The criteria to

account for ‘complexity’ in the design of a refrigeration cycle is discussed and clearly

defined. The CryoMan process is analysed; options for structural modifications to the

CryoMan process are identified. The modelling of the novel refrigeration cycles is

presented in detailed.

The novel designs are simulated and assessed in Chapter 4 (see also Appendix 1). The

novel refrigeration cycles are evaluated through sensitivity studies performed in their

corresponding degrees of freedom (e.g. refrigerant composition, streams pressure level) in

order to identify promising designs.

A case study is presented in Chapter 5 (see also Appendixes 2 and 3) to illustrate the

benefits from the structural modifications in the novel refrigeration cycles. The operating

variables of the promising novel refrigeration cycles are optimised in order to fully liquefy

a natural gas stream while minimising the total shaft power consumption. The shaft power

demand of the novel cycles is compared against that of the CryoMan process and the

PRICO cycle. The resulting shaft power savings from the optimised novel cycles are

illustrated on an annual operating cost savings basis.

Finally, conclusions on the development of novel refrigeration cycles for small scale LNG

production, and suggestions for extending this research (future work) are presented in

Chapter 6.

Chapter 2 Technology Background and Literature Review

24

Chapter 2 – Technology Background and Literature Review

2.1 Introduction

A simple refrigeration cycle is composed of four elements: an evaporator, a compressor, a

condenser and an expansion device. Figure 2.1 shows the schematic of this cycle, where an

ideal process is described and no pressure drop is assumed through the evaporator and

condenser. The liquid refrigerant provides cooling to the process stream in the evaporator

at the low-pressure level (PLow) while vaporising, following the path 1 to 2 in Figure 2.1a.

The refrigerant vapour is returned to the high-pressure level (PHigh) in the compressor (path

2 to 3). Compression of superheated vapour (i.e. vapour above its dew temperature at the

inlet pressure) is desired since any presence of liquid might produce damages to the

compression equipment (Lee et al., 2002). The compression increases the temperature of

the refrigerant. Isentropic compression (ΔS = 0), also known as adiabatic compression, is

assumed since no heat losses are considered inside the compressor (Dincer and Kanoglu,

2010, Ch. 3.5). The superheated vapour refrigerant rejects heat in the condenser (path 3 to

4) to an external heat sink, e.g. cooling water or another process stream. The refrigerant is

desuperheated and condensed. Finally, the pressure of the liquid refrigerant is released

from PHigh to PLow through an expansion device, e.g. a throttle valve, and its temperature

decreases accordingly. This is represented by the path 4 to 1. Isentropic (ideal) expansion

is also assumed. The refrigerant is partially vaporised as a consequence of the pressure let

down. Figure 2.1b illustrates the refrigeration cycle in a pressure–enthalpy diagram.

Isentropic compression is represented as the solid line from PLow to PHigh. Isentropic

expansion is the solid line from PHigh to PLow.

Figure 2. 1. Ideal refrigeration cycle: a) configuration; b) P–H diagram [adapted from (Smith, 2005b, Ch.

24.6)].


25

In practice, neither compression nor expansion is actually ideal and deviations from these

theoretical paths are observed, as shown in dashed lines in the P–H diagram of Figure 2.1b.

Deviation from isentropic compression incurs a higher change of enthalpy of the

refrigerant (dashed line from PLow to PHigh in Figure 2.1b) which increases its temperature

accordingly. Higher duties of the heat sink are therefore required in the condenser to

convert vapour refrigerant into liquid compared to the ideal compression. Non-isentropic

expansion leads to a refrigerant stream with a greater vapour fraction compared to

isentropic expansion, and now isenthalpic expansion can be assumed (Dincer and Kanoglu,

2010, Ch. 3.8) as shown with a vertical dashed line in Figure 2.1b. As a result, there is less

liquid refrigerant for providing cooling; higher flow rates of the refrigerant are then needed

in the evaporator to provide cooling to the process stream compared to the ideal expansion.

Both non-ideal processes increase of the volumetric flow rate of the refrigerant, leading to

an increase of the shaft power required for refrigerant compression.

The simple cycle can be modified to reduce the power consumption. Three examples are

presented in Figure 2.2. Figure 2.2a shows a refrigeration cycle with two expansion levels.

A flash unit (known as economiser) separates vapour and liquid phases of the refrigerant

stream after the first expansion. The liquid phase is further expanded and provides cooling

to the process stream whilst the vapour is sent directly to the compressor. As can be seen

from Figure 2.2a, multistage compression is used; the vapour from the first expansion goes

to the high pressure compression stage. The flowrate in the low pressure compressor is

reduced and thus, savings in shaft power are achieved (Borgnakke and Sonntag, 2009, Ch.

11.12). Intercooling, e.g. with cooling water, can be used after the compression of the low

pressure refrigerant, before mixing with the vapour at intermediate pressure, as illustrated

in Figure 2.2b. The intercooling reduces the volumetric flow rate at the inlet of the high

pressure compressor, leading to shaft power savings (Borgnakke and Sonntag, 2009, Ch.

11.12). Alternatively, a multilevel refrigeration cycle can be used. This is displayed in

Figure 2.2c with a two-level refrigeration cycle, in which a portion of the liquid after the

first expansion can be used to provide cooling to the process stream at a warmer

temperature, whilst the remaining liquid is further expanded and provides cooling at a

colder temperature. Shaft power savings comes from the reduced flow rate in the low

pressure compressor (Smith, 2005b, Ch. 24.6).


26

Figure 2. 2. Configuration options to reduce shaft power demand of a simple cycle: a) multistage expansion;

b) intercooling: c) multilevel refrigeration [adapted from (Smith, 2005b, Ch. 24.6)].

LNG processes are highly energy-intensive; the operating costs are dominated by the shaft

power requirement for refrigerant compression in the refrigeration cycle (Mokhatab et al.,

2014b, Ch. 3.2). Therefore, minimising the shaft power consumption in the refrigeration

cycle significantly reduces the operating costs. The ‘efficiency’ of the refrigeration cycle

can thus be defined as the shaft power consumption per unit mass flow rate of LNG

produced (i.e. specific shaft power consumption, kWh·kg-1

of LNG) and be used as a

performance indicator for comparison against other refrigeration cycles (Mokhatab et al.,

2014b, Ch. 3.2). A refrigeration cycle with a low specific shaft power consumption value is

more efficient than a refrigeration cycle with a high specific shaft power consumption

value because the former requires less energy input to liquefy a fixed flow rate of natural

gas compared to the latter.

To determine the shaft power consumption of a refrigeration cycle and relative savings

achieved with different configurations and operating conditions, mathematical modelling is

required. The following Section 2.2 addresses the modelling of refrigeration cycles. Pure

component and mixed refrigerant cycles are considered separately in Section 2.2.1 and

Section 2.2.2, respectively, and cascade cycles are also introduced in Section 2.2.3. Where

appropriate, commercial refrigeration cycles for LNG processes are also presented.

2.2 Modelling of refrigeration cycles for LNG processes

Modelling is used to represent a process configuration through mathematical equations

allowing data to be collected from the simulations, including flow rates, temperatures or


27

energy needs (Smith, 2005a, Ch. 1.3). Thus, different operating variables or process

configurations can be evaluated and screened. To simulate a refrigeration cycle, enthalpy

calculations are required to perform energy balances and entropy calculations are needed

because isentropic compression models are employed. Equations of state can predict

pressure-volume-temperature relations, which allow calculating enthalpy and entropy

values, and vapour-liquid equilibrium (Elliot and Lira, 1999, Ch. 6.5).

The Peng–Robinson equation of state (Equation 2.1) is shown to calculate such volumetric

relations with good accuracy for hydrocarbons and light gases, as a function of their

critical properties – temperature and pressure – and acentric factor (ω). Calculated enthalpy

values and vapour pressures of these components have also been shown in good agreement

with experimental data in a wide range of temperatures and pressures: enthalpy values are

calculated in ranges from –157°C to 10°C and from 14 bar to above 130 bar, vapour

pressures are shown to have a relative error of < 1%, and (Peng and Robinson, 1976).

These components – including C1 to C4 and nitrogen – are common in LNG processes

since they are the major constituents of the natural gas streams to be liquefied, and also the

main components of the refrigerant mixtures employed in the refrigeration cycles. The

Peng–Robinson equation can be thus considered as a reliable equation for calculating

physical and thermodynamic properties of the refrigerant fluid in refrigeration cycles – and

natural gas stream – for LNG processes.

Enthalpy calculations can be performed with the Peng–Robinson equation, when combined

with the thermodynamic relation in Equation 2.2. Vapour-liquid equilibrium calculations

can be carried out when combined with Equation 2.3. For mixtures, the parameters a and b

are calculated with Equations 2.4 and 2.5, according to the corresponding mole fraction of

the ith and jth component in the mixture (Peng and Robinson, 1976).

𝑃 = 𝑅𝑇

𝜐−𝑏−

𝑎(𝑇)

𝜐2+2𝑏𝜐−𝑏2 (2.1a)

𝑎(𝑇) = 0.45724𝑅2𝑇𝑐

2

𝑃𝑐∙ [1 + 𝜅(1 − 𝑇𝑟

1/2)]

2 (2.1b)

𝑏 = 0.07780𝑅𝑇𝑐

𝑃𝑐 (2.1c)

𝜅 = 0.37464 + 1.54226𝜔 − 0.26992𝜔2 (2.1d)


28

𝐻 − 𝐻∗ = 𝑅𝑇(𝑍 − 1) + ∫ [𝑇 (𝜕𝑃

𝜕𝑇)

𝜐− 𝑃] 𝑑𝜐

𝜐

∞ (2.2)

𝑙𝑛𝑓

𝑃= ∫ (

𝑣

𝑅𝑇−

1

𝑃) 𝑑𝑃

𝑃

0 (2.3)

𝑎 = ∑ ∑ 𝑥𝑖𝑥𝑗(1 − 𝛿𝑖𝑗)√𝑎𝑖𝑎𝑗𝑗𝑖 (2.4)

𝑏 = ∑ 𝑥𝑖𝑏𝑖𝑖 (2.5)

The enthalpy and entropy of a stream of known composition (pure or mixed refrigerant)

can be calculated if its pressure and temperature are known. Alternatively, the temperature

or pressure of a stream can be obtained if any two of the remaining values (temperature,

pressure, enthalpy, entropy) are known.

For example, assuming that the pressure levels in the refrigeration cycle of Figure 2.1 and

the refrigerant composition are known (either pure or mixed refrigerant) for the ideal

refrigeration cycle, the enthalpy of the refrigerant leaving the condenser can be calculated

at PHigh and the temperature of the condenser. Similarly, the temperature of the refrigerant

after the expansion can be obtained with PLow and the same enthalpy value if isenthalpic

expansion is assumed.

The shaft power required for compression in the ideal refrigeration cycle of Figure 2.1

(either pure or mixed refrigerant) can be calculated with an energy balance around the

compressor, according to Equation 2.6 (Dincer and Kanoglu, 2010, Ch. 3.5):

𝑊 = 𝑚 ∙ (𝐻𝐶𝑜𝑚𝑝𝑜𝑢𝑡 − 𝐻𝐶𝑜𝑚𝑝

𝑖𝑛 ) (2.6)

where HCompin

and HCompout

are the enthalpies at the inlet and outlet of the compressor,

respectively. HCompin

can be obtained with PLow and the temperature after the evaporator,

whilst HCompout

can be determined with PHigh and the entropy at the compressor inlet as

isentropic compression is assumed.

Alternatively, the shaft work can be estimated using the following Equation 2.7 (Kyle,

1999b, Ch. 15.1):

𝑊 = 𝛾 ∙ 𝐹𝑖𝑛 ∙ 𝑃𝑖𝑛

𝛾 − 1[1 − (

𝑃𝑜𝑢𝑡

𝑃𝑖𝑛)

𝛾 − 1

𝛾] (2.7)

where W = Compression shaft work [W]

γ = Heat capacity ratio of inlet stream (Cp·Cv-1

)

Fin = Inlet volumetric flow rate [m3·s

-1]

Pin, out = Inlet and outlet pressure [Pa]


29

In an isentropic compression is assumed an ideal gas in a compression path PVγ = constant,

and no heat is transferred to or from the refrigerant (Kyle, 1999a, Ch. 3.3). As stated in

Section 2.1, however, the compression in non-ideal refrigeration cycles deviates from the

isentropic path. An efficiency term of the compression can then be considered, which can

be included into the model for calculating the shaft power demand, as in Equation 2.8

(Kyle, 1999b, Ch. 15.1):

𝑊 = (𝛾

𝛾−1)

𝐹𝑖𝑛 ∙ 𝑃𝑖𝑛

𝜂𝐼𝑆[1 − (

𝑃𝑜𝑢𝑡

𝑃𝑖𝑛)

𝛾−1

𝛾] (2.8)

ηIS is the isentropic efficiency of the compression, that is the ratio of the shaft work of an

isentropic compression to the actual shaft work needed for compression, and accounts for

losses of power energy including friction in the compressor.

The modelling of the composite curves in the evaporator depends on the type of refrigerant

used in the refrigeration cycle, i.e. pure component or mixed refrigerant. Pure components

evaporate at constant temperature (if a zero pressure drop is assumed) and thus, the

pressure is calculated according to the temperature needed in the evaporator (which should

be lower than the outlet temperature of the process stream by a minimum temperature

difference, to guarantee feasible heat transfer). On the other hand, mixed refrigerants

evaporate over a wide temperature range and their evaporating profile depends on their

corresponding composition (with ΔP = 0); thus, calculation of intermediate temperatures is

required to evaluate feasible heat transfer considering a minimum temperature difference.

In Section 2.2.1, modelling of evaporators with pure refrigerants is briefly described,

whilst modelling for mixed refrigerants is presented in detail in Section 2.2.2. In Section

2.2.3, cascade cycles are introduced.

2.2.1 Modelling of pure refrigerant cycles

In pure refrigerant cycles, cooling is delivered by a refrigerant which is a single

component. When a pure component refrigerant evaporates at a fixed pressure, its

temperature remains constant. Therefore the selection of the refrigerant is influenced by

the final temperature that is needed by the process stream. Table 2.1 shows some common

refrigerants with their suggested working temperatures. For each component, the upper

limit temperature (TMAX) is either ambient or a temperature in which the latent heat of

vaporisation is 50% of that at atmospheric pressure, and the lower limit temperature (TMIN)

is the normal boiling point (Lee, 2001, Ch. 1).


30

Table 2. 1. Suggested working temperatures for common refrigerants [adapted from (Lee, 2001, Ch. 1)].

Nitrogen Methane Ethane Propane* i-Butane* n-Butane*

TMIN [K] 75 120 187 232 264 274

TMAX [K] 120 163 273 310 310 310

*denotes refrigerants that can reject heat to an ambient utility (e.g. cooling water).

The pressure in the evaporator is calculated so that the temperature of the vaporising

refrigerant (saturation temperature) is lower than the final temperature of the process

stream by a minimum temperature difference (ΔTMIN). The Antoine correlation or an

equation of state (e.g. Peng–Robinson) can be used to calculate the pressures in the

evaporator and in the condenser.

However, from Table 2.1 it can be deducted that the temperature provided by simple

refrigeration cycles using single component refrigerants is limited to around –40°C (232

K) since only propane, i-butane and n-butane can reject heat to an ambient utility, e.g.

cooling water. Lower temperatures (e.g. –161°C for LNG processes) can be achieved by

pure component refrigeration cycles when cascade configurations are used (Borgnakke and

Sonntag, 2009, Ch. 11.12).

2.2.2 Modelling of mixed refrigerant cycles

In mixed refrigerant cycles, the refrigerant is a mixture: light hydrocarbons (C1 to C4) and

nitrogen are commonly used in LNG processes (Mokhatab et al., 2014b, Ch. 3.2). Unlike

with single components, the temperature of mixed refrigerants continuously changes as the

evaporation takes place (see Figure 2.3). The composition of the refrigerant determines the

profile and the temperature range in which the refrigerant evaporates for a fixed

evaporating pressure (Radermacher, 1989).

Figure 2. 3. Refrigerant evaporating profile (at constant pressure): a) pure component; b) mixed refrigerant

[adapted from (Radermacher, 1989)].


31

The composition of the refrigerant is selected to have close temperature approaches to the

ΔTMIN in the composite curves, which represent shaft power consumption reduction. Since

the temperature of both the process stream and the mixed refrigerant are continuously

changing, feasible heat exchange (i.e. heat transfer between hot and cold streams with a

minimum temperature difference) needs to be checked at intermediate temperatures and

included into the modelling of the evaporator. In order to evaluate the feasibility of heat

transfer at intermediate temperatures, the overall enthalpy change in the mixed refrigerant

stream can be divided into a user-specified number of intervals, as shown in Figure 2.4,

and the temperature for each interval can be then calculated with an equation of state (e.g.

Peng–Robinson) using each enthalpy value, the refrigerant composition and the pressure of

the evaporator (zero pressure drop assumed). Similarly, intermediate temperatures of the

process stream can be calculated at the same enthalpy values.

Figure 2. 4. Temperature–enthalpy profile calculation for a mixed refrigerant stream (ΔP = 0 in the

evaporator).

The difference between the calculated temperatures of the mixed refrigerant stream and the

process stream, at the ith interval (ΔTi), is compared against the ΔTMIN value selected in

order to check feasible heat transfer. If all the ΔTi’s are greater than or equal to the value of

ΔTMIN then the design is feasible (in terms of heat transfer). If any temperature difference

is less than the specified minimum temperature difference, however, the design is

infeasible and a degree of freedom would need to be manipulated, such as increasing the

flow rate of the mixed refrigerant, increasing the pressure ratio (i.e. ratio of outlet to inlet

compression pressure) or changing the composition of the mixed refrigerant (Lee, 2001,

Ch. 4). After a degree of freedom is manipulated, the calculation of the temperature–

enthalpy of the mixed refrigerant stream would need to be performed again in order to

compare its evaporating temperature, at each ith interval, against the corresponding

condensing temperature of the process stream and thus, checking that heat transfer is


32

feasible (i.e. a positive minimum temperature difference value between the condensing

temperature of the process stream and the evaporating temperature of the mixed

refrigerant).

Very low temperatures are needed in LNG processes (e.g. –161°C); the mixed refrigerant

can be cooled by an external utility (i.e. another refrigeration cycle) or self-cooled to

achieve such low temperatures. In self-cooling, the low pressure refrigerant provides

cooling to the process stream and also to the high pressure refrigerant (as shown in Figure

2.5), allowing the mixed refrigerant to achieve a colder temperature before the expansion

compared to the case without self-cooling. After the expansion, the mixed refrigerant can

thus achieve a very low temperature (e.g. –161°C). In addition, the mixed refrigerant

stream might be fully condensed during self-cooling and, once expanded, the liquid

fraction of the refrigerant would be greater, compared to without self-cooling, which helps

reducing the refrigerant flow rate needed for providing cooling.

Multi-stream heat exchangers (MSHE) are commonly used in the LNG industry to

accommodate several streams in the same equipment unit, e.g. when refrigerant self-

cooling is employed. To model an MSHE as the evaporator in which a mixed refrigerant is

self-cooled, the calculation of the T–H curves is needed for both cold and hot composite

curves each time the degrees of freedom of the refrigeration cycle are manipulated since

the conditions of the refrigerant (pressure and temperature) and its composition will affect

both composite curves.

The simplest commercially established mixed refrigerant cycle for LNG processes is the

PRICO (Poly Refrigerated Integrated Cycle Operation) process, developed and patented by

Black & Veatch (Swenson, 1977). Figure 2.5 shows the configuration of the PRICO

process. It consists only of a single mixed refrigerant stream with two pressure levels. The

refrigerant is a mixture that can be composed of C1 to C5 and N2 (Swenson, 1977). The

high pressure refrigerant and the natural gas stream are condensed by the low pressure

refrigerant stream in a single MSHE unit.


33

Figure 2. 5. PRICO refrigeration cycle (Swenson, 1977).

This process shows low efficiency (0.40 kWh·kg-1

of LNG) when compared to more

complex cycles such as the APCI C3MR cycle, which is a cascade cycle (0.29 kWh·kg-1

of

LNG) (Castillo and Dorao, 2010).

2.2.3 Modelling of cascade cycles

As mentioned in Section 2.2.1, cascade cycles are employed when very low temperatures

are required (e.g. –161°C in the LNG industry). In cascade cycles, two or more cycles

operate at different temperature levels. The refrigerant cycle at the coldest temperature

liquefies the natural gas stream, and rejects heat to a warmer refrigeration cycle; the

refrigeration cycle at the warmest temperature rejects heat to an ambient heat sink (e.g.

cooling water). For example, Figure 2.6 presents a cascade cycle consisting of two simple

refrigeration cycles. Cycle 1 in Figure 2.6 provides cooling to the process stream and

rejects heat to Cycle 2; Cycle 2 rejects heat to an ambient utility (e.g. cooling water). Each

cycle has an independent refrigerant and, therefore, an independent compressor. The

refrigerant in each cycle can be either pure component or mixed refrigerant.

MSHE units can also be employed in cascade cycles. Cascade cycles in the LNG industry

use MSHEs for precooling both the natural gas stream as well as the lower temperature

refrigerant. The calculation of the composite curves in MSHEs as evaporators for cascade

cycles can be performed as detailed in Section 2.2.1 and Section 2.2.2, depending if pure or

mixed refrigerants are used.


34

Figure 2. 6. Cascade refrigeration cycle with two temperature levels of refrigeration.

In cascade cycles, each refrigeration cycle can use a single component refrigerant or a

mixed refrigerant; alternatively, the cascade cycle can combine a pure refrigerant cycle and

a mixed refrigerant cycle. Table 2.2 compares the refrigerants and the relative efficiency of

three commercial cascade cycles applied to LNG processes; Figure 2.7 shows a simplified

schematic of each cascade process presented in Table 2.2. The Phillips optimized cascade

cycle, illustrated in Figure 2.7a, consists of three pure refrigerant cycles (propane, ethylene

and methane) for the liquefaction of the natural gas stream (Hughes, 1971). The propane

precooled mixed refrigerant cycle (C3MR), developed by Air Products and Chemicals Inc.

(Figure 2.7b), uses a propane cycle and a mixed refrigerant cycle; the propane cycle

precools the natural gas stream and the mixed refrigerant, whereas the mixed refrigerant

fully liquefies the natural gas stream (Gaumer and Newton, 1973). The dual mixed

refrigerant (DMR), developed by Shell (Figure 2.7c), consists of two mixed refrigerant

cycles in cascade; in the first mixed refrigerant cycle, both the natural gas and the second

mixed refrigerant are precooled, whilst in the second mixed refrigerant cycle the natural

gas is fully liquefied (Grootjans et al., 2002).

In Table 2.2, the Phillips optimized cascade cycle shows a higher efficiency than the C3MR

and the DMR cycle, but at the expense of higher complexity and associated initial capital

investment (Mokhatab et al., 2014b, Ch. 3.2). The APCI C3MR cycle is the dominant

refrigeration technology in the LNG industry as over 70% of the installed plants in the

world use this cascade cycle (Mortazavi et al., 2012).


35

Table 2. 2. Cascade refrigeration cycles in the LNG industry [adapted from (Mokhatab et al., 2014b, Ch.

3.2)].

No. Cycles

Precooling

Stage Liquefaction Stage

Efficiency relative to

cascade cycle

Phillips optimized

cascade cycle 3

Propane (C3)

Ethylene (C2=)

Methane (C1) 1.00

Propane precooled

mixed refrigerant 2 Propane (C3) MR (C1 to C3 + N2) 1.15

Dual mixed

refrigerant 2 MR (C2 + C3) MR (C1 to C3 + N2) 1.05

Figure 2. 7. Commercial cascade cycles: a) Phillips cascade cycle; b) Propane precooled mixed refrigerant

cycle; c) Dual mixed refrigerant cycle.

2.3 Research literature on refrigeration cycles for LNG processes

The research literature is reviewed and organised as follows: in Section 2.3.1

methodologies for systematic design of refrigeration cycles are presented and the

modelling approach is analysed. Most of these design methodologies include a case study

or an example problem in which a refrigeration cycle is designed and optimised using their

corresponding modelling approach. These case studies and the optimisation methods

selected in each methodology are discussed in Section 2.3.2. In Section 2.3.3 a review on

the design of refrigeration cycles for small scale LNG processes is presented. Section 2.3.4

provides an introduction to the “CryoMan” process (Zheng, 2009, Ch. 3), which is an

single mixed refrigerant cycle developed by structural modifications to the PRICO cycle.

In Section 2.3.5 WORK software is presented and tested to simulate refrigeration cycles.


36

WORK is in-house software developed in the Centre for Process Integration at the

University of Manchester for modelling, simulation and optimisation of refrigeration

cycles (see Section 2.3.5). WORK software is used to simulate and optimise the CryoMan

process (Zheng, 2009, Ch. 3).

2.3.1 Modelling and design of mixed refrigerant cycles

The use of mathematical programming and thermodynamic-based approaches has been

proposed to design refrigeration cycles systematically. For instance, Shelton and

Grossmann (1986) developed a mathematic model for the systematic design of pure

component multilevel refrigeration cycles. The model is based on a superstructure, which

is a conceptual configuration of a refrigeration cycle with multiple discrete temperature

levels. Refrigeration at two different temperature levels are connected using a presaturator

in which the liquid refrigerant from the upper temperature level is contacted with the

vapour compressed from the lower temperature level (see Figure 2.8). According to

Shelton and Grossmann (1986), the use of presaturators yields only linear relations

between power demand, and evaporating and condensing duties in the refrigeration levels

(because the refrigerant vapour is always saturated at the inlet of the compressor;

otherwise, the degree of superheating is dependent on the duty in the intercooler). To

evaluate the refrigeration cycle with different combinations of temperature levels, binary

variables are introduced to activate or deactivate a temperature level. The resulting

mathematical model is a Mixed Integer Linear Programming (MILP) problem.

Figure 2. 8. Two temperature levels refrigeration cycle using a presaturator (Shelton and Grossmann, 1986).


37

The methodology presented by Shelton and Grossmann (1986) considers only refrigeration

cycles using pure component refrigerants. Further, the selection of the refrigerant is not

explicitly included into the design methodology. To create the superstructure for the

multilevel refrigeration cycle, the number and temperatures of the levels are chosen by the

designer, so the final results are likely to depend on the temperatures selected. Because of

the linear relations assumed, the model only applies for refrigeration cycles using

presaturators. The shaft power demand in the refrigeration cycles is calculated using

correlations from the pressure–enthalpy diagram, between the heat of vaporisation of the

selected pure refrigerant and the refrigeration cycle working temperatures (Shelton and

Grossmann, 1985). An isentropic efficiency factor is considered in the correlations for

calculating the shaft power demand; however, the correlations only hold when assuming

compression of saturated vapour of single component refrigerants.

Linnhoff and Dhole (1992) proposed an approach to design pure component refrigeration

cycles integrated with the heat exchanger network (HEN) for sub-ambient processes.

Conventional composite curves (T–H profiles) shows the heat loads in the process but

ignore energy in the form of power; thus Linnhoff and Dhole (1992) replaced the

temperature axis of the T–H diagram in the conventional pinch analysis with the Carnot

factor 𝜂𝐶 = (1 −𝑇0

𝑇), and allowed for including shaft work in the diagram. In the Carnot

factor, T0 is the ambient temperature and T is the temperature at which energy (heat and

shaft work) is available. The area between the resulting composite curves (σTHEN) is

demonstrated to be proportional to the shaft work input in the refrigeration cycle. Once a

refrigeration cycle is modelled and represented in the T–H diagram, changes in the

refrigeration cycle (such as number of refrigeration levels or the temperature of each level)

can be suggested to reduce the area between the composite curves (as shown in Figure 2.9)

in order to reduce the total shaft power demand. The main strength of the methodology is

to investigate potential shaft power savings with different configurations without the need

of modelling each possible design but rather calculating the area between the composite

curves and comparing it to a base case design. Linnhoff and Dhole (1992) presented a case

study for the design of a refrigeration cycle and a HEN in an ethylene recovery process

(discussed in Section 2.3.2).


38

Figure 2. 9. Design methodology for low temperature processes presented by Linnhoff and Dhole (1992).

The methodology, however, is limited to refrigeration cycles using pure components and

the selection of the refrigerant is not included. The choice of a different configuration of

the refrigeration cycle (e.g. including an additional refrigeration level, changing the

temperature level of an existing refrigeration level) does not follows an optimisation-based

approach but is rather guided only by judgement.

Lee et al. (2002) proposed a design methodology for mixed refrigerant cycles for LNG

processes in which the composition of the refrigerant is optimised. The PRICO single

mixed refrigerant cycle is used in the design methodology. Initial conditions (refrigerant

composition, condensing and evaporating pressure, and refrigerant flow rate) are first

selected and the hot composite curve is generated. The hot composite curve is created by

combining the T–H profiles of the natural gas stream and the self-cooled refrigerant, as in

the conventional pinch analysis. For each stream, the T–H profile is obtained by dividing

its corresponding overall enthalpy change into a user-specified number of intervals for

which the temperature is calculated according to the corresponding stream pressure and

composition. An ‘ideal’ cold composite is generated as a duplicate of the hot composite but

colder by a minimum temperature difference (ΔTMIN), as illustrated in Figure 2.10. In

Lee’s work, a minimum temperature difference of 5°C is assumed.

Figure 2. 10. Generation of the ‘ideal’ cold composite curve (Lee, 2001, Ch. 4).


39

The composition of the mixed refrigerant is optimised as a non-linear programming (NLP)

problem using a deterministic algorithm, and three options of objective function are

defined: i) minimisation of the largest negative difference between the evaporating

temperatures of the ‘ideal’ cold composite curve and those of the cold refrigerant stream

(because in the PRICO cycle there is only one cold refrigerant stream in the MSHE, the

evaporating profile of the cold refrigerant stream is equivalent to the evaporating profile of

the cold composite curve); ii) minimisation of the sum of the negative differences between

the evaporating temperatures of the ‘ideal’ cold composite curve and those of the cold

refrigerant stream; and iii) minimisation of shaft power demand for refrigerant

compression. The cold refrigerant composition is only constrained to have evaporating

temperatures less than those of the hot composite at each interval, in order to have feasible

heat transfer. That is, the evaporating temperatures of the cold composite curve should be

colder than those of the hot composite at each interval, but not necessarily colder by a

minimum temperature difference.

The composite curves are updated as the refrigerant composition changes. When the

refrigerant composition optimisation is completed, either the refrigerant flow rate or the

pressure levels in the refrigeration cycle is decreased (by judgement or optimisation,

although no details are provided regarding the mathematical formulation for the

optimisation) in order to reduce the shaft power demand for refrigerant compression. This

decrease of the refrigerant flow rate, or pressure levels, changes the composite curves.

Thus, the optimisation of the refrigerant composition is performed again. This procedure is

repeated until no further minimisation of the shaft power can be obtained from reducing

the refrigerant flow rate, or reducing the pressure levels, and with feasible heat transfer.

The proposed methodology allows manipulating the operating variables of the mixed

refrigerant cycle, including the refrigerant composition, using an optimisation approach.

Also, the model provides an approach to consider the non-isothermal evaporation of mixed

refrigerants by evaluating intermediate temperatures of the cold refrigerant stream for

feasible heat transfer in the MSHE. However, the operating variables of the refrigeration

cycle (refrigerant composition, refrigerant flow rate and pressure levels) are not

manipulated simultaneously; that is, interactions between the operating variables are not

considered, leading to results that are likely to be non-optimal. Moreover, even though the

refrigerant composition is optimised to minimise the differences between the evaporating

temperature of cold refrigerant and that of the ‘ideal’ cold composite curve (created to be


40

colder than the hot composite curve by a minimum temperature difference), feasible heat

transfer is defined in the model only as a positive temperature difference at each interval

between the hot composite and the cold composite curves, but not a positive difference by

a minimum temperature approach. Furthermore, no details of the compressor model

employed are provided or discussed. Single stage compression is assumed.

Vaidyaraman and Maranas (2002) implemented a mathematical approach to model and

design systematically cascade refrigeration cycles using mixed refrigerants with multistage

refrigeration. Unlike conventional cascade refrigeration cycles in which each different

refrigerant stream has its own compression system, the multistage refrigeration cycles

proposed by Vaidyaraman and Maranas (2002) (see Figure 2.11) consist of a single mixed

refrigerant stream with only one compression system. When partially condensed and

flashed, the mixed refrigerant creates two streams (vapour and liquid) with different

compositions. The number of levels in the cascade refrigeration cycle and the number of

refrigeration stages in each refrigeration level are user-specified. It is assumed that the hot

refrigerant stream at each MSHE leaves as saturated liquid, and the cold refrigerant stream

at each MSHE leaves as saturated vapour.

Vaidyaraman and Maranas (2002) presented a case study for the design of a cascade cycle

with multistage refrigeration to cool a methane-rich process stream down to –58 °C (215

K). The design variables of the refrigeration cycle include pressure levels, refrigerant

composition and quality of the refrigerant after each partial condensation.

The model employed by Vaidyaraman and Maranas (2002) allows exploiting the

composition of mixed refrigerants, to create two streams with different compositions after

partial condensing and flashing a single mixed refrigerant. The model is thus useful for

designing single- and multiple-stage mixed refrigerant cycles, including cascade cycles.

However, in the model, the constraint of minimum driving force for feasible heat transfer

(ΔTMIN) between hot and cold streams is only applied at the inlet and outlet of the heat

exchangers and thus, feasible heat transfer at intermediate temperatures inside each MSHE

is not guaranteed. Additionally, as with Lee et al. (2002), the model considers only single

stage compression of the refrigerant, and also ideal (isentropic) compression is assumed.

Similarly, Del Nogal et al. (2008) presented a systematic methodology for the design and

optimisation of refrigeration cycles using mixed refrigerants for processes such as the

liquefaction of natural gas. Multistage refrigeration (Figure 2.11) and cascade cycles with


41

multistage refrigeration are considered in the proposed methodology. For the case of

multistage refrigeration cycles, it is considered that the process stream is liquefied as it is

fed through a series of MSHEs, as in the designs proposed by Vaidyaraman and Maranas

(2002), so the cooling duty of the process stream is divided into the selected number of

refrigeration stages (user-defined). The high pressure refrigerant is partially condensed and

flashed to generate a vapour and a liquid stream of different composition. However, this

time the liquid can be subcooled in the subsequent heat exchanger stage. Additionally, the

cold refrigerant leaving any heat exchanger can be superheated (to avoid wetness at the

inlet of the compression system).

Figure 2. 11. Multistage refrigeration cycle.

Compared to the methodology presented by Vaidyaraman and Maranas (2002), the

compression is no longer considered isentropic as the isentropic efficiency is introduced.

Multistage compression with intercooling is also adopted in the methodology developed by

Del Nogal et al. (2008). The maximum ratio of outlet to inlet compression pressures (PRAT)

is set to 5, which is an industrial common practice according to the authors. Additionally,

feasible heat transfer checks between the hot and cold streams are included in the

modelling of the MSHEs. Once both composite curves are constructed, a user-specified

number of intermediate temperatures are compared between the hot and cold composite

curves. The design has feasible heat transfer when a positive difference of temperatures is

equal to or greater than a minimum temperature approach (ΔTMIN), which is specified by

the designer.

Table 2.3 summarises the modelling approaches reviewed in the open literature for the

design of refrigeration cycles highlighting the main assumptions (e.g. consideration of

feasible heat transfer at intermediate temperatures).


42

Table 2. 3. Models for simulation of refrigeration cycles.

Refrigeration cycle

Isentropic

efficiency

Multistage

compression

Feasible heat

transfer

Shelton and Grossmann (1986) Pure refrigerant N/A

Linnhoff and Dhole (1992) Pure refrigerant N/A

Lee et al. (2002) SMR - Partially covered

Vaidyaraman and Maranas (2002) Mixed refrigerants

and Cascade cycles

Only at the ends of

the heat exchangers

Del Nogal et al. (2008) Mixed refrigerants

and Cascade cycles Fully covered

- no details provided

SMR = Single Mixed Refrigerant

N/A = Not applicable

2.3.2 Optimisation of mixed refrigerant cycles

When optimisation is applied to the design or the operating variables of a refrigeration

cycle, commonly the objective function is to minimise the total shaft power for refrigerant

compression as it represents the major energy-consuming operation in the LNG plant and

dominates operating costs (Mokhatab et al., 2014b, Ch. 3.2). The conditions obtained as

optimal depend on the modelling assumptions as well as on the optimisation technique that

is selected. This section reviews the case studies from the design methodologies presented

in Section 2.3.1, and the optimisation methods selected in each case study are discussed.

Shelton and Grossmann (1986) presented a case study to design a refrigeration cycle that

operates between 240 K and 320 K. A minimum temperature approach (ΔTMIN) of 10 K is

considered in the evaporators and condensers. Also, is assumed a temperature level each

10 K for the refrigeration cycle. The MILP problem is solved with branch and bound

optimisation algorithm. With this method, different combinations of temperature levels are

evaluated according to the activated binary variables. For each combination of temperature

levels, the work coefficient, defined as the ratio of shaft work input to heat removed from

the process stream, is evaluated. The objective function is either to minimise the total

utility cost, the capital cost (only compressors are evaluated) or the total annualised cost.

The three objective functions are tested in the case study. Results showed that minimising

the capital cost resulted in the simplest refrigeration cycle configuration. When the

objective function is to minimise the total utility cost, the optimal refrigeration cycle yields

the highest capital costs because of the increased number of temperature levels (and

corresponding compressors, although the number is not explicit) compared to the optimal

design when minimising capital cost or total annualised cost. Minimising the total

annualised cost is a trade-off between utility and capital costs.


43

As discussed by Shelton and Grossmann (1986), the main disadvantage of the MILP

problem formulation is the computational time needed according to the number of

temperature levels selected. On the one hand, if a large number of temperatures are

explored then a high computational effort is required to solve the problem. On the other

hand, a simpler problem formulation would not represent any computational inconvenience

but the temperature levels would not be thoroughly explored to find an optimum solution

to the problem.

For the modelling approach developed by Linnhoff and Dhole (1992), an example problem

is studied to design a refrigeration cycle integrated with the HEN in an ethylene production

process. Refrigeration is provided using propylene and ethylene at multiple temperature

levels. A base case is established using a single level of propylene (at 229 K) and three

levels of ethylene (at 212.5 K, 189 K and 173 K). The shaft power consumption is

calculated as 12.9 MW using modelling and simulation (models are not explicit in the

paper). Their approach is then used to calculate the shaft power input required for a

refrigeration cycle consisting of three levels of propylene (at 282 K, 257 K and 238 K) and

three levels of ethylene (at 209 K, 189 K and 173 K). Savings in shaft power are predicted

to be 3.83 MW. The proposed design is simulated (models are not explicit in the paper),

and the calculated shaft power savings are in good agreement (3.76 MW) as compared to

the predicted value using their approach.

However, since changes in the configuration of the refrigeration cycle are based on

judgement, the methodology to design the integrated refrigeration cycles is not systematic.

Thus, no optimisation technique is adopted by Linnhoff and Dhole (1992) in their work.

Three case studies are presented by Lee et al. (2002) for the design of a PRICO process

using their systematic design methodology for refrigeration cycles based on refrigerant

composition optimisation. The composition optimisation is formulated as an NLP problem.

In the first case study, the objective function of the optimisation is to minimise the

difference of the evaporating temperatures between the cold refrigerant stream and the

‘ideal’ cold composite curve (a duplicate of the hot composite curve but colder by a

minimum temperature difference, 5°C). The refrigerant can be composed of C1 – C4 and

nitrogen. The operating conditions are specified (flow rate, pressure levels and

composition), and the composition is optimised while the pressure levels and the

refrigerant flow rate are held constant. After the initial composition optimisation, either the


44

pressure levels or the flow rate are decreased to reduce the compression shaft power

demand. Then, the composition optimisation is reinitiated to minimise possible

temperature crossovers between the composite curves, resulting from the modifications in

the refrigerant flow rate or pressure levels. This iterative process is continued until shaft

power savings are no longer possible. Results showed that shaft power savings of 21% are

achieved with the PRICO process designed with the presented methodology, compared to

the commercial PRICO process (1.49 MJ·kg-1

of LNG).

In the second case study, the composition optimisation is performed in two stages. In the

first stage, the refrigerant composition is optimised to minimise the sum of negative

differences between the evaporating temperatures of the ‘ideal’ cold composite curve and

those of the cold refrigerant stream, whilst in the second stage the composition is optimised

only to reduce the shaft power consumption. According to Lee et al. (2002), the second

stage begins when the refrigerant flow rate is decreased enough to avoid wetness at the

inlet of the compressor. The total shaft power is reduced 3.6% further in the second case

study, leading to a shaft power consumption of 1.13 MJ·kg-1

of LNG. In the third case

study, the effect of the ΔTMIN (from 3 K to 8 K) in the shaft power consumption is

investigated. As expected, the power demand is accordingly increased as the minimum

temperature approach is increased (from 1.14 to 1.32 MJ·kg-1

of LNG).

Although significant shaft power savings are achieved compared to the commercial PRICO

process, the degrees of freedom are not manipulated simultaneously during the

optimisation. Instead, the pressure levels, or the refrigerant flow rate, is adjusted (by

judgement or optimisation, although no details of the mathematical formulation are

provided for the optimisation) only after each composition optimisation. Thus, the degrees

of freedom are not fully exploited. Moreover, no criterion is explicitly discussed for the

manipulation of the flow rate and the pressure levels. Additionally, during the second stage

of the second case study, the optimisation is likely to lead to temperature crossover as the

ΔTMIN is no longer being considered.

Another shortcoming in the methodology followed by Lee et al. (2002) is that the results

obtained from an NLP optimisation strongly depend on the initial conditions selected

(Edgar et al., 2001, Ch. 10.1). Therefore, results presented by Lee et al. (2002) are likely to

be trapped in local optima. Optimisation approaches that helps avoiding local optima


45

include multistart-point procedures and stochastic models, such as Genetic Algorithm and

Scatter Search (Edgar et al., 2001, Ch. 10).

The methodology for systematic design of cascade refrigeration cycles presented by

Vaidyaraman and Maranas (2002) is evaluated with an example problem to cool down a

methane-rich process stream from 20°C to –58°C. A minimum temperature difference of

2.5°C for feasible heat transfer is assumed. The optimisation is formulated as an NLP

problem, where the objective is to minimise the compression shaft power demand. The

degrees of freedom of the optimisation include the condensing and evaporating pressures,

the share of the process stream cooling duty in each MSHE, the vapour fraction of the

refrigerant after each partial condensation and the composition of the refrigerant. The

components of the refrigerant are ethane, propane and n-butane. The problem is solved for

various configurations: a cascade cycle of two refrigeration levels with different number of

refrigeration stages in each level. The results are expressed as the coefficient of

performance, COP, defined by Vaidyaraman and Maranas (2002) as the ratio of shaft work

input to heat rejected (thus, low COP values represent low values of shaft power demand

for a fixed heat load). The minimum COP is found with a configuration consisting in two

refrigeration stages in the upper cycle and three refrigeration stages in the lower cycle

(COP = 0.3957). According to Vaidyaraman and Maranas (2002), the optimum cascade

cycle design solution (COP = 0.3957) is a trade-off between a close temperature approach

in the composite curves (because of multiple streams with different compositions coming

from successive partial condensation) and an increasing flow rate, as the number of

refrigeration stages increases.

Unlike in the case studies presented by Lee et al. (2002), each configuration is optimised

by Vaidyaraman and Maranas (2002) from different starting points in order to avoid local

optima in the NLP problem. However, the number of optimisations per configuration is not

stated and the criteria for the selection of the different starting points are not discussed

either.

Del Nogal et al. (2008) selected two previously published case studies to illustrate their

proposed design methodology. Firstly, the case study presented by Lee et al. (2002) is

considered to design a PRICO process to liquefy a natural gas stream. The refrigerant

mixture is composed of C1 – C4 and nitrogen. Secondly, the case study of Vaidyaraman

and Maranas (2002) is studied for the design of cascade refrigeration cycles. Ethane,


46

propane and n-butane are available to select the composition of the refrigerant. In both

cases, the degrees of freedom in the refrigeration cycles are manipulated simultaneously. A

Genetic Algorithm optimisation method is used to help avoid local optima.

In the Genetic Algorithm optimisation method, a user-specified number of initial

conditions (initial values of a vector that contains all the degrees of freedom), called

population, are generated randomly and thus, the optimisation is performed from different

starting points to help avoid local optima. That is, a set with a user-specified number of

vectors is generated (each vector is called member of the population). As the optimisation

progresses, one or more values of each member are changed (mutation) or replaced with

the value of the same variable from another member (crossover) (Edgar et al., 2001, Ch.

10.5), according to a probability factor ranging from 0 to 1. The new members (offspring)

are simulated and ranked according to the shaft power demand, in order to update the

population with those members with best performance (lowest shaft power consumption).

A penalty function is used to reject members that violate constraints (e.g. leading to

infeasible heat transfer inside the MSHE). An iteration (called generation) of the

optimisation is completed after all the members of the population are evaluated and the

population is updated. The optimisation is terminated when the maximum number of

generations (also user-defined) is reached. The member that yields the lowest specific

shaft power demand after the optimisation terminates, is considered as the optimum

solution.

Compared to deterministic optimisation methods (e.g. Sequential Quadratic Programming),

in which the result obtained from the optimisation depends on the initial conditions

selected, Genetic Algorithm explores the combination of the values of the variables more

thoroughly. Thus, Genetic Algorithm helps to avoid local optima, although the results

obtained with Genetic Algorithm are not guarantee to be optimal (Edgar et al., 2001, Ch.

10.1).

In the first case study presented by Del Nogal et al. (2008), the conditions obtained by Lee

et al. (2002) are specified and resulted in a ΔTMIN of 1.2°C between the composite curves.

Using this minimum temperature approach, to compare with the results found by Lee et al.

(2002), 8% in shaft work savings are achieved with the simultaneous optimisation of the

degrees of freedom. In the second case study, the same designs presented by Vaidyaraman

and Maranas (2002) are reproduced (considering the same minimum temperature approach


47

of 2.5°C) and ΔTMIN violations are observed at intermediate temperatures inside the

MSHEs. The same refrigeration cycle designs are optimised with the Genetic Algorithm

method, and using Del Nogal’s modelling approach. The COP values increased up to 15%

for some of the configurations when compared to those in Vaidyaraman and Maranas

(2002). This time, however, the minimum temperature difference of 2.5°C between the

composite curves is guaranteed at intermediate temperatures inside the MSHEs.

In summary, optimisation of refrigeration cycles is commonly applied to minimise the total

shaft power for refrigerant compression (and therefore, to minimise operating costs).

Moreover, interactions between operating variables in the refrigeration cycles (e.g.

refrigerant composition, pressure levels, etc.) are exploited by simultaneous manipulation

of the degrees of freedom. Further, optimisation of the operating variables of refrigeration

cycles using stochastic methods (e.g. Genetic Algorithm) helps avoiding local optima

compared to NLP algorithms (e.g. Sequential Quadratic Programming).

2.3.3 Design of refrigeration cycles for small scale LNG processes

The research of refrigeration cycles for LNG processes at small scale, i.e. LNG production

up to 1 million t per annum according to Mokhatab et al. (2014b, Ch. 3.3), can be classified

in two groups: firstly, technology selection (especially between single mixed refrigerant

cycles and nitrogen expander cycles) based on performance indicators such as the

compression shaft power input; the operating conditions of the refrigeration cycles are not

optimised. Secondly, optimisation of the operating variables (e.g. refrigerant composition,

flow rate, etc.) of a refrigeration cycle to minimise the shaft power consumption is the aim

of research. The publications regarding technology selection are first reviewed.

Exergy is defined as a measure of the maximum work that can be obtained from a stream

when it reaches equilibrium with the surroundings (Querol et al., 2013, Ch. 2.1). Exergy

can be thus used to measure the minimum work input that needs to be supplied to a stream

to reach the specified conditions of temperature and pressure. Remeljej and Hoadley

(2006) published an exergy study of refrigeration cycles for LNG processes at small scale.

The LNG production rate is 0.700 million t per annum. A single mixed refrigerant cycle

(the PRICO cycle) and a nitrogen expander cycle are selected for the evaluation as well as

two open loop systems (“New LNG Scheme” and “GCL”) in which part of the feed gas is

used as the refrigerant mixture. The aim is to compare the exergetic ratio (i.e. the ratio of

actual work input to theoretical minimum work) of the refrigeration cycles for the same


48

liquefaction task. The PRICO cycle showed an exergetic ratio of 2.8, which represented the

lowest shaft work consumption (0.3440 kWh·kg-1

of LNG) of the four refrigeration cycles.

The nitrogen expander cycle showed an exergetic ratio of 3.5 (shaft work is 0.4119

kWh·kg-1

of LNG), i.e. the shaft work is higher by 20% compared to the PRICO cycle.

Cao et al. (2006) evaluated a single mixed refrigerant cycle (with two refrigeration stages)

and a N2–CH4 expander cycle (with two refrigeration stages) for LNG production at small

scale (690 t per annum of LNG) by comparing the shaft power consumption of each

refrigeration cycle. Liquefaction is performed in two refrigeration stages (two heat

exchangers) and the natural gas stream is cooled down to a final temperature of –152°C.

The results indicated that the N2–CH4 cycle is about 24% less energy-consuming (1.3141

kWh·kg-1

of LNG) compared to the single mixed refrigerant cycle (1.7244 kWh·kg-1

of

LNG).

Yin et al. (2008) also compared the power consumption of a single mixed refrigerant cycle

and a nitrogen expander cycle. Both refrigeration cycles consisted of four stages of cooling

to liquefy the natural gas stream (down to –146°C). The LNG production rate is 0.006

million t per annum. The specific shaft work demand is estimated as 0.6715 kWh·kg-1

of

LNG for the nitrogen expander cycle and 0.3042 kWh·kg-1

of LNG for the single mixed

refrigerant cycle (i.e. 55% lower than that of the nitrogen expander cycle).

Li and Ju (2010) assessed the shaft power consumption of a nitrogen expander cycle, a

single mixed refrigerant cycle and a C3MR cycle for offshore LNG production according

to natural gas conditions (composition, working temperature and pressure) in South China

Sea. The LNG production rate is 0.061 million t per annum. The liquefaction is achieved

with four cooling stages in the C3MR cycle, three cooling stages in the single mixed

refrigerant cycle and three cooling stages in the nitrogen expander cycle. The nitrogen

cycle power consumption (0.5064 kWh·kg-1

of LNG) is 52% and 68% higher than that of

the single mixed refrigerant cycle (0.3330 kWh·kg-1

of LNG) and that of the C3MR cycle

(0.3013 kWh·kg-1

of LNG), respectively.

Castillo and Dorao (2010) proposed an economic model for refrigeration technology

selection in which the area for building the liquefaction plant is included in the capital

costs as installation costs. The LNG production rate is assumed as 0.500 million t per

annum. Mixed refrigerant technology (the specific mixed refrigerant cycle is not stated) is

compared against nitrogen expander technology (the specific cycle configuration is not


49

specified). The shaft power consumption of the mixed refrigerant technology is assumed as

0.35 kWh·kg-1

of LNG and that of the nitrogen technology is assumed as 0.70 kWh·kg-1

of

LNG. The area needed for installation is estimated as a linear function of the LNG

production rate. An analysis for three different installation areas of the mixed refrigerant

technology (data not shown explicitly), showed that the installation area of the mixed

refrigerant significantly impacts on overall profit (including revenues, operating costs and

capital costs), as profit of the mixed refrigerant technology decreased up to 5 times

compared to that of the nitrogen expander. However, the authors suggested that more

accurate data should be used to correlate the installation area to the LNG production rate.

Shirazi and Mowla (2010) performed an optimisation of a PRICO cycle for small scale

LNG production (0.028 million t per annum). The case study addressed is similar to that

studied by Lee et al. (2002), and discussed in Section 2.3.1 and Section 2.3.2, but the

composition of the natural gas stream is different. Two-stage compression is assumed with

intercooling at 30 °C. The minimum temperature approach in the MSHE is 1.5°C. Genetic

Algorithm is adopted as the optimisation method to avoid local optima. The degrees of

freedom are manipulated simultaneously. The objective is to minimise the compression

shaft power. Shaft power savings of 3% (0.3034 kWh·kg-1

of LNG) are achieved compared

to the results published by Lee et al. (2002) (0.3130 kWh·kg-1

of LNG). The authors

concluded that the implementation of multistage compression with intercooling, compared

to single compression stage without intercooling in Lee (2001), led to the power savings.

He and Ju (2014b) presented a nitrogen expander cycle enhanced with a precooling stage

for LNG production at small scale (LNG production rate is 160 t per annum); either a

propane cycle or a cycle in which the refrigerant is a mixture of difluoromethane (CH2F2)

and pentafluoroethane (C2HF5), is used as the precooling stage. The refrigeration cycles,

including a conventional nitrogen expander cycle (as the base case), the nitrogen cycle

precooled with a propane cycle, and the nitrogen cycle precooled with the mixture of

difluoromethane and pentafluoroethane, are modelled in HYSYS. The NLP optimiser

within HYSYS is employed to optimise their corresponding operating variables.

Optimisations are performed for the conventional nitrogen cycle (base case) and for the

two precooled refrigeration cycles, to evaluate the precooling stage influence on the overall

shaft power demand (objective function). Compared to the base case, which consumes

0.6032 kWh·kg-1

of LNG, the propane precooling stage reduced the shaft power

consumption by 20% (0.4824 kWh·kg-1

of LNG) whilst the precooling stage with the


50

mixture of difluoromethane and pentafluoroethane showed shaft power savings of 23%

(0.4660 kWh·kg-1

of LNG).

Hwang et al. (2013) considered the optimisation of a cascade of two mixed refrigerant

cycles (dual mixed refrigerant cycle) for the production of 380 t per annum of LNG. A

hybrid optimisation approach is used, consisting of a Genetic Algorithm method with SQP

(Sequential Quadratic Programming). For both mixed refrigerant cycles of the cascade, the

refrigerant flow rate, refrigerant composition, streams pressure level and refrigerant

precooling temperatures are optimised. The objective function is to minimise the shaft

work power for refrigerant compression. The optimum shaft power consumption of the

dual mixed refrigerant cycle is 0.2721 kWh·kg-1

of LNG.

He and Ju (2014a) presented a single mixed refrigerant cycle for LNG production at small

scale (0.009 million t per annum). The refrigeration cycle consists of two refrigeration

stages. Two-stage compression with intercooling is adopted. The refrigeration cycle is

modelled in HYSYS and optimised employing a Genetic Algorithm method. The

refrigerant flow rate, refrigerant composition, streams pressure levels and compressor

discharge pressure are the optimisation variables. The objective function is to minimise the

shaft power demand for refrigerant compression. The shaft power consumption of the

optimised refrigeration cycle is 0.3158 kWh·kg-1

of LNG.

From this review it is clear that single mixed refrigerant cycles are commonly studied for

LNG production at small scale. Table 2.4 summarises the mixed refrigerant cycles that are

being studied in the open research literature for production of LNG at small scale (i.e. up to

1 million t per annum), and also provides the efficiency reported for each mixed refrigerant

cycle (i.e. the specific shaft power consumption).

Table 2. 4. Mixed refrigerant cycles studied in the open research literature for LNG production at small scale.

Author(s) Mixed refrigerant

cycle

LNG production

[million t per annum]

Shaft power consumption

[kWh·kg-1

of LNG]

Remeljej and Hoadley (2006) PRICO cycle 0.7000 0.3440

Cao et al. (2006) 2 MSHE stages 0.0007 1.7284

Yin et al. (2008) 4 MSHE stages 0.0061 0.3042

Li and Ju (2010) 3 MSHE stages 0.0610 0.3330

Castillo and Dorao (2010) MR Technology* 0.5000 0.3500

Shirazi and Mowla (2010) PRICO cycle 0.0280 0.3035

He and Ju (2014a) 2 MSHE stages 0.0095 0.4175

*Not specified


51

Moreover, from Table 2.4, is evident that limited refrigerant cycle configurations are being

studied in the open research literature for LNG production at small scale. The following

Section 2.3.4 describes the work of Zheng (2009), on the development of single mixed

refrigerant cycles for LNG processes, especially the “CryoMan” refrigeration cycle, which

is developed based on configurational modifications to the PRICO cycle.

2.3.4 Design and optimisation of the CryoMan process

The so-called “CryoMan” process is a single mixed refrigerant cycle for LNG processes.

The CryoMan process is developed by Zheng (2009) and later patented by the University

of Manchester (Kim and Zheng, 2011).

Zheng (2009) first presented a refrigeration cycle design, also resulting from structural

modifying the PRICO cycle, that consists on a flash unit after the condenser, so the vapour

and liquid phases of the partially condensed single mixed refrigerant are separated (this

refrigeration cycle is called “Pre-flash” design). The CryoMan process is developed by

further structurally modifying the “Pre-flash” design. Thus, the PRICO refrigeration cycle

is first explained, followed by the “Pre-flash” design and the CryoMan process.

In the PRICO cycle (Figure 2.12a), the mixed refrigerant is compressed to the compressor

discharge pressure and partially condensed using an ambient utility (e.g. cooling water).

The refrigerant stream is fed to the MSHE where is fully condensed. The refrigerant stream

is throttled to the low pressure level and returned to the MSHE where is vaporised to

provide cooling both to the natural gas stream and the high-pressure refrigerant stream.

The vaporised refrigerant stream is fed to the compressor where is recompressed to the

compressor discharge pressure, completing the refrigeration cycle. The composition of the

refrigerant stream strongly impacts on the compression shaft power demand of the

refrigeration cycle.

Regarding the “Pre-flash” design (Figure 2.12b), the structural modifications include a

flash unit attached after the partial condenser. Once the mixed refrigerant stream is

compressed to the compressor discharge pressure and partially condensed with the ambient

utility (e.g. cooling water), the refrigerant stream is fed to the flash unit where the vapour

and liquid phases are separated. The vapour and liquid streams have different composition.

Thus, two refrigerant streams with different composition are created from the single mixed

refrigerant stream. These two refrigerant streams are precooled in the MSHE to


52

independent temperature levels, and are expanded to independent pressure levels using

throttle valves. The two refrigerant streams thus vaporise at different temperature levels to

provide the cooling duty needed in the MSHE for the liquefaction of the natural gas stream

and the self-cooling of the high-pressure refrigerant streams. Each refrigerant stream is fed

to the compressor at its corresponding pressure level.

In the CryoMan process (Figure 2.12c), similar to the “Pre-flash” design, the structural

modifications include a flash unit after the partial condenser; additionally, the product

streams from the flash unit are split and partially re-mixed to create the two actual

refrigerant streams. Compared to the “Pre-flash” design in which the composition and flow

rate of the refrigerant streams are those directly obtained from the flash separation, in the

CryoMan process, partially mixing of the vapour and liquid streams leaving the flash unit

allows manipulating the composition and flow rate of the two refrigerant streams. The two

refrigerant streams in the CryoMan process are also precooled to independent temperature

levels in the MSHE, throttled to independent pressure levels and vaporised at different

temperature levels (in the MSHE) to provide the cooling needed for liquefying the natural

gas stream and self-cooling the high-pressure refrigerant streams. The vaporised refrigerant

streams are fed to the compressor at their corresponding pressure levels. LP Stream is

compressed from the lowest pressure level; HP Stream is fed to the compressor at its

corresponding pressure level, where is mixed with LP Stream. The re-mixed refrigerant

stream is further compressed to the compressor discharge pressure.

Figure 2. 12. a) The PRICO cycle; b) “Pre-flash” design; c) the CryoMan process [adapted from (Zheng,

2009)].


53

Thus, the degrees of freedom (i.e. the operating variables manipulated by the designer) in

the CryoMan process are the refrigerant composition, the compressor discharge pressure,

the flow rate fraction of the vapour stream leaving the flash unit fed to LP Stream, the flow

rate fraction of the liquid stream leaving the flash unit fed to LP Stream, the precooling

temperature, pressure level and MSHE outlet temperature of both LP Stream and HP

Stream.

In the model used to simulate the CryoMan process, the hot and cold composite curves in

the MSHE are calculated; enthalpy values are calculated for a predefined number of

intermediate temperatures, as the composition of the refrigerant streams and their

corresponding pressure levels are known (zero pressure drop in the MSHE is assumed).

Thus, feasible heat transfer at intermediate temperatures is checked by comparing a

predefined number of intermediate temperature differences between the hot and cold

composite curves against the ΔTMIN value (user-defined). Physical and thermodynamic

properties of the refrigerant streams (e.g. temperatures, enthalpies) are calculated with the

Peng–Robinson equation of state in Aspen Properties.

The composition of the two refrigerant streams, resulting from the partial mixing of liquid

and vapour streams, are calculated by mass balance of each component of the refrigerant

mixture. The overall refrigerant stream is composed of hydrocarbons C1 to C4 and

nitrogen.

Multistage compression model is adopted for calculating the shaft power demand of the

compressor; intercooling with an ambient heat sink (e.g. cooling water) after each

compression stage is assumed. Zero pressure drop of the refrigerant stream is assumed in

the intercoolers and the refrigerant stream is assumed to be cooled down to 30°C. The shaft

power demand for each compression stage is calculated with an energy balance over the

compressor, with the enthalpy values of the refrigerant stream at the inlet and outlet of

each compression stage under isentropic compression assumption. The enthalpy values are

calculated using Peng–Robinson equation of state, and an isentropic efficiency of 80% is

assumed.

To obtain the temperature of the overall refrigerant stream at the inlet of the intermediate

compression stage in which LP Stream and HP Stream are mixed, the enthalpy after

mixing is calculated with an energy balance over the mixing point. The enthalpy of HP

Stream is calculated at its MSHE outlet temperature (refrigerant composition and pressure


54

level are known); the enthalpy of LP Stream is calculated at the intermediate pressure level

and the outlet temperature from the previous compression stage (refrigerant composition is

known).

Regarding the optimisation of the CryoMan process, the shaft power consumption is the

performance indicator. Therefore, the minimisation of the total compression shaft power

demand (the sum of the compression power demand of each compression stage) is defined

as the objective function. In order to optimise CryoMan process, i.e. to find the set of

values of its degrees of freedom that yield the minimum compression power input, a

Genetic Algorithm method is selected as the optimisation algorithm. The Genetic

Algorithm is implemented in WORK software (described in Section 2.3.5).

The case study first published by Lee et al. (2002) (see Section 2.3.2) is considered in

order to evaluate the performance (i.e. total shaft power consumption of the refrigeration

cycle) of the PRICO cycle, the “Pre-flash” design and the CryoMan process, when their

corresponding degrees of freedom are optimised to fully liquefy a natural gas stream.

According to Zheng (2009), the shaft power demand for the PRICO cycle is 28.27 MW;

the “Pre-flash” design achieved shaft power consumption of 26.60 MW, whereas the shaft

power demand in the CryoMan process is 26.05 MW. That is, the “Pre-flash” design and

the CryoMan process yielded shaft power savings of 6% and 8%, respectively, compared

to the PRICO cycle.

As discussed by Zheng (2009), the “Pre-flash” design benefits from an additional

refrigerant stream, compared to the PRICO cycle, created from the structural modification

applied (i.e. a flash unit attached). The additional refrigerant stream has independent

precooling temperature level and evaporating pressure level; the “Pre-flash” design also

benefits from refrigerant streams with different compositions that help reducing the total

shaft power demand. In the case of the CryoMan process, the structural changes

implemented in the configuration allows manipulating the flow rate and composition of the

refrigerant streams in order to minimise the shaft power consumption, by partially mixing

the vapour and liquid streams leaving the flash unit. Furthermore, the configuration of both

the “Pre-flash” design and the CryoMan process remained with relatively low complexity

(Zheng, 2009).

According to Zheng (2009), the benefits (shaft power savings compared to the PRICO

cycle) resulting from both the “Pre-flash” design and the CryoMan process is that the


55

different composition of the refrigerant streams helped reducing the area between the

composite curves in the MSHE because of their corresponding evaporating profiles (but

keeping a minimum temperature difference between the composite curves for feasible heat

transfer). However, no numerical data of the area between the composite curves is

provided in order to compare and quantify the area reduction between the PRICO cycle,

the “Pre-flash” design and the CryoMan process. A comparison and analysis between the

composition of the refrigerant streams of the “Pre-flash” design and the CryoMan process

is not provided, in order to assess the impact of the refrigerant composition in the

performance of the refrigeration cycle. Additionally, although the configuration of both

refrigeration cycles (the “Pre-flash” design and the CryoMan process) is considered as a

low complex design, the ‘complexity’ of the refrigeration cycle design is not quantified or

clearly defined.

Thus, by analysing and taking advantage of key degrees of freedom in the configuration of

the CryoMan process, novel refrigeration cycles could be developed by further structurally

modifying the CryoMan process in order to bring further shaft power savings and hence,

operating cost savings. Moreover, because the novel refrigeration cycles developed from

structural modifications would be for LNG production at small scale, they should maintain

a design with low complexity in order to keep capital costs low. The ‘complexity’ of the

refrigeration cycle design should then be clearly defined.

2.3.5 WORK software

WORK software is in-house software of the Centre for Process Integration at the

University of Manchester. WORK software capabilities include modelling, simulation and

optimisation of refrigeration cycles, based on the research carried out in the Centre by Lee

(2001), Del Nogal (2006), and Zheng (2009).

Simple refrigeration cycles and cascade refrigeration cycles can be simulated in WORK

software. To check feasible heat transfer at intermediate temperatures inside the MSHEs,

the minimum temperature approach and the number of intermediate temperature

differences between the composite curves that are compared, are user-defined. Multistage

refrigerant compression with intercooling can also be simulated; the isentropic

compression efficiency, the maximum pressure ratio in a compression stage and the

temperature of the refrigerant stream after intercooling are user-supplied. Pure component

refrigerants as well as mixed refrigerants can also be simulated; physical and


56

thermodynamic properties (e.g. temperatures, enthalpies) of the refrigerants can be

calculated through the use of coded equations of state (i.e. Peng–Robinson and Soave–

Redlich–Kwong) or, alternatively, by interfacing with other commercial software

packages, such as Aspen HYSYS or Aspen Properties.

Optimisation of operating variables of refrigeration cycles in WORK can be performed

using an NLP algorithm (Sequential Quadratic Programming) or with stochastic algorithms

(i.e. Genetic Algorithm and Simulated Annealing). Further, WORK is capable of

optimising the composition of a mixed refrigerant, given its constituent components. The

objective function can be the minimisation of the total shaft power consumption for

refrigerant compression.

The process stream (the stream that needs to be cooled or liquefied) is represented in

WORK using only its T–H profile. That is, composition, pressure levels and flow rate of

the process stream are not required. So, for example, the cooling/condensing profile (T–H

profile) of any process stream can be obtained from a simulation in Aspen HYSYS and

input directly in WORK software as the T–H profile of the process stream. However, a

process stream that is represented in WORK cannot be directly input in Aspen HYSYS as

the T–H profile only, because the full conditions of the process stream (composition, flow

rate, inlet and outlet pressures, and pressure drop profile in the heat exchanger) are

required in Aspen HYSYS.

However, despite the difference in the method for specifying the process stream that needs

to be cooled or liquefied, the results obtained from simulation of refrigeration cycles in

WORK software are in good agreement compared to those obtained from Aspen HYSYS

(see Section 2.3.6). Moreover, compared to Aspen HYSYS, WORK software is capable of

optimising the composition of mixed refrigerants. Furthermore, WORK can perform

stochastic optimisations (using either Genetic Algorithm or Simulated Annealing) to help

avoiding local optima.

2.3.6 Example of refrigeration cycle simulation in WORK software

In order to validate the simulations performed in WORK software (in the absence of

experimental data), an example problem is next presented and the results are compared to

those obtained from the simulation in Aspen HYSYS for the same example. Thus, the

results of Aspen HYSYS are assumed to represent real operational data accurately.


57

The problem is taken from Morosuk et al. (2015), and consists of liquefying a natural gas

stream using a PRICO cycle. The flow rate of the natural gas stream is 50 kg·s-1

whilst that

of the mixed refrigerant stream is 475 kg·s-1

. The compositions of the natural gas and the

refrigerant mixture are displayed in Table 2.5. The natural gas stream enters the MSHE at

67 bar and 38°C and leaves as LNG at 64 bar and –159°C. The high-pressure mixed

refrigerant enters the MSHE at 22 bar and 30°C, and leaves at 19 bar and –159°C. The

precooled mixed refrigerant is then throttled to the low-pressure level (6 bar, –163°C). The

cold (low-pressure) refrigerant stream provides the cooling needed by the natural gas

stream and the high-pressure refrigerant stream, and leaves the MSHE at 3 bar. The

vaporised cold refrigerant is compressed to the compressor discharge pressure in two

compression stages; the intercooler and the condenser cool the refrigerant down to 30°C.

Figure 2.13 shows the schematic of the example problem.

Figure 2. 13. Operating conditions of the PRICO cycle for the simulation example problem.

According to the example problem, there is a pressure drop of 3 bar for each stream inside

the MSHE, but because the pressure drop profile is not stated, is assumed as linearly

dependent on the heat that each stream rejects or absorbs, in order to simulate the pressure

drop profile in Aspen HYSYS.

Physical and thermodynamic properties of the refrigerant (e.g. temperatures, enthalpies)

are calculated using Peng–Robinson. In WORK software, physical and thermodynamic

properties of the refrigerant stream are calculated using Peng–Robinson equation by

interfacing with Aspen HYSYS. It is assumed that the minimum temperature difference

between the composite curves in the MSHE is 3°C for feasible heat transfer; also,

isentropic efficiency for refrigerant compression is assumed as 80%.


58

Table 2. 5. Natural gas and mixed refrigerant compositions [mole %] for the simulation example in WORK

software.

C1 C2 C3 C4 N2

Natural Gas 0.88 0.08 0.02 - 0.02

Mixed Refrigerant 0.30 0.30 - 0.25 0.15

Once the natural gas stream is simulated in Aspen HYSYS, its T–H profile is generated

and is fed to the simulation in WORK software (see Table 2.6 and Figure 2.14). Also,

because the flow rate of the mixed refrigerant has to be supplied to WORK on a molar

basis, the reported mass flow rate of the refrigerant is converted to molar flow rate

according to the composition in Table 2.5 and then fed to WORK software.

Table 2. 6. Natural gas temperature–enthalpy data for the simulation example in WORK software.

Segment Supply Temperature [K] Target Temperature [K] ΔH [kW] CP [kW·K-1

]

1.1 311.15 290.84 2701.3 133.0

1.2 290.84 270.53 2835.3 139.6

1.3 270.53 252.92 2691.0 152.8

1.4 252.92 237.91 2691.0 179.2

1.5 237.91 226.55 2691.0 236.8

1.6 226.55 219.12 2691.0 362.5

1.7 219.12 213.93 2691.0 518.3

1.8 213.93 208.74 2466.1 474.9

1.9 208.74 200.95 2723.1 349.5

1.10 200.95 190.70 2723.1 265.8

1.11 190.70 178.27 2723.1 219.1

1.12 178.27 164.05 2723.1 191.5

1.13 164.05 149.83 2483.8 174.6

1.14 149.83 133.55 2663.6 163.6

1.15 133.55 114.15 3022.0 155.8

Figure 2. 14. Natural gas temperature–enthalpy data for the simulation example in WORK software.


59

Table 2.7 compares the results obtained with WORK against those obtained with Aspen

HYSYS; there is an error of less than 0.1% in the calculation of the shaft power demand

for compression. The minimum driving force for heat exchange (ΔTMIN) is different

compared to that in HYSYS by only 0.1°C. The calculations of the refrigeration cycle

performed in WORK are in good agreement compared to those obtained from the

simulation in Aspen HYSYS, and are thus considered successfully validated.

Table 2. 7. Comparison of the PRICO cycle simulation between WORK software and Aspen HYSYS.

WORK HYSYS Difference

Input Data

Refrigerant flow rate [kg·s-1

] 475a 475

Refrigerant high-pressure level [bar] 22 22

Refrigerant low-pressure level [bar] 6 6

Refrigerant precooling temperature [°C] –159 –159

Maximum compression ratio 3 3

Output Data

Number of compression stages 2 2 -

ΔTMIN [°C] 4.0 4.1 0.1°C

Shaft power [MW] 91.15 91.09 < 0.1 % aRefrigerant flow rate fed in WORK software as 14.6 kmol·s

-1

2.4 Conclusions

The literature review revealed that single mixed refrigerant cycles are commonly studied in

the open research for the production of LNG at small scale (up to 1 million t per annum).

Moreover, the literature review also revealed that there is only limited refrigeration cycle

configurations studied.

The CryoMan process (Zheng, 2009) is a single mixed refrigerant cycle that is developed

by structurally modifying the PRICO cycle (which is the simplest commercial refrigeration

cycles for LNG processes). Significant shaft power savings (nearly 8%) are achieved by

the CryoMan process compared to the PRICO cycle (which required 28.27 MW of shaft

power). Additionally, the design of the CryoMan process remained with relatively low

complexity.

Novel refrigeration cycles could be developed by analysing and further modifying the

structure of the CryoMan process, in order to bring shaft power savings and, therefore,

operating cost savings. The design of the novel refrigeration cycles should also remain

with low complexity to help keeping low capital costs, as they are intended for LNG

production at small scale. Thus, the ‘complexity’ of the refrigeration cycles has to be

clearly defined in order to develop novel designs with low complexity.


60

Additionally, there are useful models in the open research literature for simulating mixed

refrigerant cycles. Because of the non-isothermal evaporation and condensation of mixed

refrigerants, feasible heat transfer needs to be checked inside the MSHE by calculating

intermediate temperatures of the composite curves. Introducing an isentropic efficiency for

refrigerant compression allows considering energy losses in compression (e.g. because of

friction in the compressor); modelling multistage compression with intercooling is useful

to represent commonly-practised industrial scenarios compared to single stage refrigerant

compression without intercooling.

Furthermore, optimisation of the operating variables of refrigeration cycles for LNG

processes, in the open research literature, is commonly aimed at minimising the total shaft

power demand for refrigerant compression since shaft power demand dominates operating

cost of refrigeration cycles. Simultaneous manipulation of the degrees of freedom in the

refrigeration cycles (e.g. refrigerant composition, pressure levels, etc.) allows exploiting

complex interactions between the operating variables. Stochastic optimisation methods

(e.g. Genetic Algorithm) helped avoiding local optima.

The accuracy of WORK software for the simulation of mixed refrigerant cycles, compared

to commercial software (i.e. Aspen HYSYS), was illustrated with an example problem.

The results obtained from WORK software were in good agreement compared to those

from the simulation in the commercial software. The calculation of the total shaft power

demand showed a relative difference of less than 0.1%, whereas the minimum temperature

approach was calculated with a difference of only 0.1°C between the two simulations.

Chapter 3 Development and Design of Novel Refrigeration Cycles

61

Chapter 3 – Development and Design of Novel Refrigeration

Cycles

3.1 Introduction

An important aim in the development of novel refrigeration cycles for small scale LNG

processes (i.e. LNG production is up to 1 million t per annum), is to keep the designs with

low complexity. Low complexity of the refrigeration cycles is especially important in LNG

processes at small scale, because of the capital costs associated with the design. For

instance, capital costs have to be low when small LNG projects are intended to operate for

short periods of time (Li and Ju, 2010) in order to keep profitability. Additionally, when

the refrigeration cycles are for offshore LNG production, the LNG plant would be built in a

platform or on top of a ship, and so the area or weight of the plant would be constrained

(Castillo and Dorao, 2010).

On the other hand, high energy-efficiency is important as operating costs dominates

economics in refrigeration cycles for LNG processes and shaft power consumption

represents the major energy-consuming stage of the refrigeration cycle (Mokhatab et al.,

2014b, Ch. 3.2). Large scale commercial refrigeration processes (e.g. propane precooled

mixed refrigerant cycle and dual mixed refrigerant cycle) yield high efficiencies by

introducing more equipment in order to increase the number of degrees of freedom in the

refrigeration cycle. The resulting operating variables are adjusted to reduce the overall

power consumption. However, this also results in large and complex configurations. For

example, the propane precooled mixed refrigerant cycle is reported to have a greater

efficiency (0.29 kWh·kg-1

of LNG) compared to the PRICO cycle (0.40 kWh·kg-1

of LNG)

(Castillo and Dorao, 2010); the multilevel propane precooling cycle reduces the heat load

of the natural gas stream in the mixed refrigerant cycle, and the operating variables of the

mixed refrigerant cycle (e.g. refrigerant composition, pressure levels, etc.) can be adjusted

to liquefy the natural gas stream with a lower overall energy consumption compared to the

PRICO cycle. However, the complexity and the capital costs of the propane precooled

mixed refrigerant cycle significantly increase since four heat exchangers and the multistage

compressor are needed for the multilevel propane precooling stage, which is in addition to

the mixed refrigerant cycle that includes the multi-stream heat exchanger (MSHE) as well

as its own compressor.


62

Therefore, an economic trade-off exists between a refrigeration cycle with high energy-

efficiency (low operating costs) and a cycle with a low complexity configuration (low

capital investment). In order to limit of the complexity of a refrigeration cycle, equipment

design constraints are defined in this work for the design of the novel refrigeration cycles.

Compressors represent the most capital-intensive equipment in the refrigeration cycle and

also the most energy-consuming (Mokhatab et al., 2014b, Ch. 3.2). Centrifugal

compressors are commonly used in the LNG industry (Hanlon, 2001, Ch. 3.11). These

compressors can be designed with multiple compression stages in a single casing (usually

up to 8 compression stages) as well as with nozzles at intermediate pressures, for example,

to send the partially compressed refrigerant to an intercooler or to admit side streams at

intermediate pressure levels (see Figure 3.1) (Ludwig, 2001, Ch. 12). Each compression

stage is usually designed for a maximum pressure ratio of 3 (Hanlon, 2001, Ch. 3.5). Thus,

in this work, as a limit for complexity, only one centrifugal multistage compressor is

considered, and is constrained to a single casing with up to 8 compression stages, in which

the maximum pressure ratio of each individual compression stage is 3.

Figure 3. 1. Multistage centrifugal compressor [adapted from (Ludwig, 2001, Ch. 12)].

Regarding the main heat exchanger, plate-fin heat exchangers are one type of MSHEs that

are commonly used in the LNG industry. The plate-fin heat exchangers can be designed to

accommodate up to 12 streams in a single piece of equipment (Hesselgreaves, 2001, Ch.

2), which is defined in this work as the design constraint for the limit for complexity in the

MSHE. Figure 3.2 shows an example of an MSHE in which 5 streams are simultaneously

involved in heat exchange.


63

Figure 3. 2. Multi-stream heat exchanger for five streams [reproduced from (ESDU International plc, 2006)].

Thus, a single casing centrifugal compressor with a maximum of 8 compression stages,

and a maximum pressure ratio of 3 in each compression stage, plus a single MSHE with a

maximum of 12 streams, are the criteria defined as the boundary for complexity. In this

thesis, beyond this boundary, any refrigeration cycle is considered as a complex design.

The design constraints defined in this thesis as the limits for complexity would help

keeping the capital costs of the novel refrigeration cycles relatively low.

Capital cost estimation is difficult because of scarce data available in the open literature.

For instance, even though the methodology presented in (ESDU International plc, 2006)

allows obtaining a general estimate of the cost of a MSHE, based on the volume of the unit

and the number of streams involved in heat exchange, cost correlations are limited to

MSHE units with a maximum of six streams. Additionally, correlation models for

equipment cost estimation based on energy consumption (e.g. for compressors) do not

always reflect the complexity of the equipment. For example, the shaft power consumption

– and hence cost – of a multistage compressor would be reduced as the number of

compression stages (with their corresponding intercooling stages) is increased; however,

the complexity of the multistage compressor design would be increased and its cost would

be expected to increase accordingly. Capital costs estimation is thus not considered in this

thesis.

3.1.1 Benchmark processes

As mentioned in Section 2.3.3, single mixed refrigerant cycles are commonly considered

for LNG processes at small scale. Amongst the single mixed refrigerant cycles, the PRICO

cycle is the leading refrigeration technology for small and medium scale liquefied natural


64

gas production (Mokhatab et al., 2014b, Ch. 3.3). Also, the CryoMan process is used as the

starting point for the development of novel refrigeration cycles. Therefore, in order to

evaluate the performance of the novel refrigeration cycles, the results obtained (i.e. shaft

power consumption, operating costs) are compared against these two benchmark processes,

i.e. the PRICO cycle and the CryoMan process.

3.1.2 Performance evaluation

The shaft power requirement for refrigerant compression of each novel design is firstly

evaluated (as a preliminary assessment) through sensitivity analyses, and compared to the

shaft power demanded in the CryoMan process. Simulation and sensitivity studies are

performed on each degree of freedom (e.g. refrigerant composition, pressure levels, etc.) of

the novel designs using Aspen HYSYS v8.2 (Aspen Technology Inc., 2013). The novel

refrigeration cycles that show shaft power savings in the preliminary assessment, compared

to the CryoMan process, are optimised in WORK software by means of a Genetic

Algorithm method. The results obtained from the optimisation are compared and evaluated

against the benchmark processes.

3.1.3 Operating cost estimation

As mentioned in Section 3.1, refrigerant compression is the most energy-consuming stage

in the refrigeration cycle and thus, is used to estimate the operating costs of the novel

refrigeration cycles. The operating costs are calculated on an annual basis and the unit

power energy cost is assumed as £0.0955·kWh-1

for extra-large scale industrial consumers

(U.K. Department of Energy & Climate Change, 2015). Thus, the operating costs of the

novel refrigeration cycles are estimated from the total shaft power demand by the

compressor annually and the unit power energy cost.

3.2 Further development of the CryoMan process

As mentioned in Section 3.1.1, the CryoMan process is used as the starting point design for

developing novel refrigeration cycles based on structural modifications. In order to make

meaningful structural modifications, the CryoMan process is first analysed in detail

(Section 3.2.1) to identify and take advantage of key degrees of freedom in its design. As a

result of the analysis, possible structural modifications that can bring shaft power savings

in the liquefaction process are then presented in Section 3.2.2. Finally, in Section 3.2.3, the

configuration modifications are proposed and the novel refrigeration cycles are designed.


65

3.2.1 Analysis of the CryoMan process

Zheng (2009) presented two refrigeration cycle designs, resulting from structural

modifications to the PRICO cycle, in which two independent refrigerant streams are

obtained, i.e. their corresponding inlet and outlet temperatures of the MSHE, pressure

levels and composition are different from each other (see Figure 3.3). One of those

refrigeration cycles consists of a flash unit after the partial condenser (named “Pre-flash”

design; see Figure 3.3a). Thus, the vapour and liquid phases (LP Stream and HP Stream in

Figure 3.3a, respectively) are generated and used as the refrigerant streams. The two

streams have different composition. Nearly 6% in shaft power savings are achieved with

this configuration (0.3075 kWh·kg-1

of LNG), compared to the PRICO cycle (0.3268

kWh·kg-1

of LNG), for the natural gas liquefaction case study first presented by Lee (2001)

(see Section 2.3.4).

In the CryoMan process (Figure 3.3b), the vapour and liquid phases from the flash unit are

partially mixed (isobaric mixing is assumed), which allows manipulating the composition

of the actual refrigerant streams (LP Stream and HP Stream). The CryoMan process

showed shaft power consumption of 0.3011 kWh·kg-1

of LNG, i.e. savings in shaft power

demand of nearly 8% compared to the PRICO cycle.

Figure 3. 3. Refrigeration cycles presented by Zheng (2009): a) “Pre-flash” design, and b) the CryoMan

process.

To illustrate how the composition of the refrigerant streams (LP Stream and HP Stream)

changes when the overall refrigerant stream is flashed and partially mixed, consider, as an

example, the flash separation of a ternary refrigerant (mixture of 50% ethane, 30% propane

and 20% n-butane) at 20 bar and 30°C. The resulting compositions are shown in Figure

3.4a. The square represents the composition of the liquid phase resulting from the flash

unit, whereas the diamond is the composition of the vapour phase, and the triangle stands


66

for the composition of the refrigerant that is being flashed. The circles represent the

compositions obtained when the vapour and liquid phases are partially mixed at different

proportions (proportions are shown in Figure 3.4b as Case 1 to Case 7). As the proportions

of vapour and liquid partially mixed increase, the resulting composition moves towards the

triangle (the overall refrigerant composition) because the overall refrigerant is obtained

when all the vapour and liquid is mixed.

Figure 3.4b shows the shaft power demand for compression of 1 kmol·s-1

of the refrigerant

mixtures in Figure 3.4a from 1.2 bar and 30°C to 20 bar. A refrigerant flow rate on a molar

basis (1 kmol·s-1

assumed) would allow comparing the compression shaft power demand

of streams with the same number of molecules, and so changes in shaft power can be

related to the differences in composition (i.e. different proportions of the components) of

the streams.

According to Figure 3.4b, as the composition moves towards that of the vapour phase, the

shaft power required for compression increases. The vapour phase is highly composed of

the ‘light components’ in the refrigerant mixture, i.e. molecules with relatively small size

(72% of the vapour stream is ethane compared to only 6% of n-butane). In the liquid

stream, on the other hand, 41% is ethane compared to 26% of n-butane. More power is

required to compress and increase the pressure of a refrigerant stream as the mole fraction

of the ‘light components’ increases. Thus, the compression power required is sensitive to

the composition of the refrigerant mixture and increases as the mole fraction of ethane (the

smallest molecule in the mixture compared to propane and n-butane) increases. This

ternary mixture example can be extended to a refrigerant with five or more components.

Figure 3. 4. Ternary refrigerant after flash separation: a) composition distribution; and b) shaft work for

compression of 1 kmol·s-1

from 1.2 bar and 30°C to 20 bar.


67

In the “Pre-flash” design (Figure 3.3a), the streams leaving the flash unit are used as the

refrigerant streams. Zheng’s results suggested that different compositions in the two

refrigerant streams bring benefits since shaft power savings of 6% are achieved in the

refrigeration cycle, compared to the PRICO cycle. In the CryoMan process, the flash unit

product streams are partially mixed. This partial mixing of vapour and liquid phases

yielded a further 2% savings in shaft power, i.e. a total of 8% savings in shaft power

demand compared to the PRICO cycle.

Thus, according to the example illustrated with Figure 3.4, partial mixing of the vapour

and liquid phases helps reducing the mole fraction of light components (i.e. small

molecules) in LP Stream in the CryoMan process, resulting in a refrigerant stream with a

composition that requires less power for compression compared to that of LP Stream in the

“Pre-flash” design.

The compositions of the streams obtained with the “Pre-flash” design and with the

CryoMan process are compared (see Figure 3.5) in terms of the shaft power required for

compression of 1 kmol·s-1

of refrigerant in LP Stream. The shaft work is calculated for

different outlet pressures, at a constant inlet pressure (1.2 bar, which is the pressure level of

LP Stream in both designs), to create a compression power trend for the “Pre-flash” design

(diamonds) and for the CryoMan process (squares). As can be seen from Figure 3.5, the

partial mixing of streams leaving the flash unit yielded a composition that requires less

power, per unit flow rate, to be compressed at the same outlet pressure, compared to LP

Stream in the “Pre-flash” design. This is in agreement with the previous example of the

ternary mixture in which as the composition moves away from that of the flash unit vapour

stream (i.e. as the mole fraction of the light components decreases), the compression power

decreases.


68

Figure 3. 5. Shaft work demand of LP Stream in the “Pre-flash” and in the CryoMan process for different

outlet pressures at constant inlet pressure (1.2 bar).

However, if the actual flow rates of LP Stream and HP Stream are considered, then the

compression power trend of LP Stream in the CryoMan process is higher compared to that

in the “Pre-flash” design (see Figure 3.6a). This is also true for the compression of the

overall refrigerant from their corresponding intermediate pressure level to the compressor

discharge pressure (48.3 bar, which is the same in both designs) (Figure 3.6b). Since the

CryoMan process achieved greater shaft power savings than those achieved with the “Pre-

flash” design, the increased compression power trends of the CryoMan process thus

suggests that a trade-off exists between the shaft power savings achieved with intermediate

compositions compared to those obtained from simple flash separation, and the increase in

flow rate.

LP Stream in the CryoMan process is compressed to 9.6 bar, whereas in the “Pre-flash”

design the corresponding stream is compressed to 6.9 bar. This leads to a total power

consumption of 3 MW higher than that in the “Pre-flash” design. Nevertheless, the

compression of the overall refrigerant stream (when LP Stream and HP Stream are mixed

in the compressor) yields total shaft power savings of 3.6 MW in the CryoMan process,

compared to the “Pre-flash” design, since the compression starts from a higher inlet

pressure (9.6 bar) compared to that in the “Pre-flash” design (6.9 bar) . Therefore, the

overall resulting shaft power demand is reduced by 0.6 MW in the CryoMan process

compared to the “Pre-flash” design.

7

8

9

10

8 10 12 14 16

Sh

aft

Po

wer

[M

J·k

mo

l-1]

Outlet Pressure [bar]

PreFlash = 1 kmol/s

CryoMan = 1 kmol/s


69

Figure 3. 6. Compression trends with actual flow rates (Zheng, 2009): a) LP Streams at constant inlet

pressure (1.2 bar); and b) overall refrigerant streams at constant outlet pressure (48.3 bar).

Thus, the partial mixing of vapour and liquid not only benefits from having intermediate

compositions with less compression power requirement per unit flow rate compared to the

vapour stream obtained from the flash unit, but also exploits a trade-off existing between

the flow rate of each stream and the compression level at which each stream is compressed.

Therefore, the design of the novel refrigeration cycles should be aimed at exploiting these

trade-offs in complex interactions. Creating different refrigerant streams can result in

compositions that require less power for compression, compared to only flash product

streams. This new compositions show a trade-off with the flow rate of each stream. On the

other hand, there is also a trade-off between the flow rate of each refrigerant stream and the

pressure levels at which the stream is expanded and compressed.

3.2.2 Generation of structural options

Different modifications of the structure of the refrigeration cycle can be performed to

exploit the trade-offs identified and discussed in Section 3.2.1, in order to reduce the shaft

power demand. For example, since refrigerant streams with different compositions can

bring shaft power savings, one option is to introduce a bypass stream before the flash unit

(see Figure 3.7). This stream would have an intermediate composition (the overall

composition) compared to those obtained with the flash unit, with or without partial

mixing. The trade-off between stream flow rate and pressure level could also be exploited

since the bypass stream would help reducing the flow rate of the stream at the lowest

pressure level (LP Stream).

6.9 bar

9.6 bar

8

9

10

11

12

13

14

15

5 7 9 11 13

Sh

aft

Po

wer

[M

W]

Outlet Pressure [bar]

PreFlash = 1.64 kmol/sCryoMan = 1.79 kmol/s

Power

Savings:

-3 MW

Inlet pressure = 1.2

6.9 bar

9.6 bar

10

12

14

16

18

20

22

6 8 10 12

Sh

aft

Po

wer

[M

W]

Inlet Pressure [bar]

PreFlash = 3.08 kmol/sCryoMan = 3.21 kmol/s

Power

Savings:

+3.6 MW

Outlet pressure = 48.3


70

Figure 3. 7. A refrigerant stream bypassing the flash unit.

Another modification to create intermediate compositions is to flash repeatedly the main

refrigerant stream to obtain multiple streams with different compositions. Each flash

separation would require either an additional partial condensation of the vapour from the

previous flash unit or an expansion of the liquid stream prior to entering the MSHE (see

Figure 3.8). Furthermore, if each of the multiple streams generated has an independent

pressure level, the trade-off between the streams flow rate and their corresponding pressure

level could be exploited as the flow rate in the low pressure compression stages might be

reduced.

Figure 3. 8. Multiple flash separation of the refrigerant stream (liquid from first flash unit is further

expanded).

The above structural modification concepts (a bypass stream and multiple flash

separations) focus on modifying the refrigeration cycle before the refrigerant enters the

MSHE. Another option is partial mixing the refrigerant streams after precooled in the

MSHE and expanded to their corresponding pressure levels. That is, a flow rate fraction α

from LP Stream can be mixed with a flow rate fraction β from HP Stream to create a new

stream with intermediate composition (see Figure 3.9). Because the partial mixing of the

refrigerant streams is after expansion, the new refrigerant stream would be constrained to

have the same pressure level of the stream at the lowest pressure level. However, by

creating a new refrigerant stream with intermediate composition, the trade-off between

refrigerant flow rate and composition would be exploited in order to help reducing the

overall refrigerant flow rate and potentially bring shaft power savings.


71

Figure 3. 9. Partial mixing of refrigerant stream after precooling in the MSHE.

3.2.3 Proposal of novel designs

Based on the conceptual modifications that can be implemented in the CryoMan process,

as discussed in Section 3.2.2, the configuration of the novel refrigeration cycles can be

then designed.

Firstly, the Bypass design is shown in Figure 3.10. In this design, before the main

refrigerant stream is flashed into vapour and liquid, a portion of the stream bypasses the

flash unit. This additional third stream has an intermediate composition compared to those

obtained from the flash unit. Moreover, the bypass stream has its own pressure level.

Figure 3. 10. Novel refrigeration cycle 1: Bypass design.

To create several streams with different compositions, a refrigeration cycle design with a

double flash separation is introduced (Two Flash Levels design; see Figure 3.11). The

liquid phase from the first flash unit is divided in three streams: two are partially mixed

with the vapour from the same flash unit (as in the conventional CryoMan process),

whereas the remainder is expanded to a second pressure level and further flashed in a

second flash unit. The resulting vapour and liquid phases from the second flash unit are


72

allowed to be partially mixed with each other. In addition, each stream has its own

independent pressure level.

Figure 3. 11. Novel refrigeration cycle 2: Two Flash Levels design.

Finally, in a third refrigeration cycle – Mixing After Precooling design in Figure 3.12 –, a

new cold stream is created from the streams partially mixed after the flash unit. However,

the new stream is created after the two partially mixed streams have been precooled in the

MSHE and expanded to their corresponding pressure levels. According to Figure 3.12, a

flow rate fraction α from Stream 1 is mixed with a flow rate fraction β from Stream 2, to

create Stream 5. The resulting new stream has an intermediate composition and would take

advantage of the trade-off between composition and refrigerant flow rate to potentially

bring shaft power savings. Also, as discussed in Section 3.2.2, the new refrigerant stream

(Stream 5) would be constrained to have the same pressure level as Stream 4, i.e. the

lowest pressure level.


73

Figure 3. 12. Novel refrigeration cycle 3: Mixing After Precooling design.

3.3 Process modelling

In order to simulate and evaluate the performance of each novel refrigeration cycle,

process modelling is required. The Bypass design model is described in Section 3.3.1,

whereas the Two Flash Levels design is in Section 3.3.2 and the Mixing After Precooling

design model is in Section 3.3.3. In all three cases, the starting point of the refrigeration

cycle simulation is at the outlet of the condenser; it is firstly assumed a refrigerant flow

rate of 1 kmol·s-1

.

The models of the novel refrigeration cycles are implemented in WORK software. Physical

and thermodynamic properties of the refrigerant (such as temperatures, enthalpies, phase

equilibrium, etc.) are calculated using the Peng–Robinson equation of state by interfacing

with Aspen HYSYS v8.2. These calculations are expressed in this thesis as ‘Relations’,

using the notation of Example Relation E3.1, in which the specific enthalpy of a refrigerant

stream is calculated at temperature level 1 (TLevel 1) and pressure level 2 (PLevel 2), provided

that the refrigerant composition (XRef

) is known.

ℎ𝑅𝑒𝑓 → 𝑋𝑅𝑒𝑓 , 𝑇𝐿𝑒𝑣𝑒𝑙 1, 𝑃𝐿𝑒𝑣𝑒𝑙 2 (E3.1)

3.3.1 Modelling of the Bypass design

Figure 3.13 shows the Bypass design refrigeration cycle with its degrees of freedom (i.e.

the variables that are independently manipulated by the designer). Once a set of values for

the degrees of freedom are specified, the molar flow rate of the bypass stream is obtained

with Equation 3.1, where FMR

is the molar flow rate of the overall refrigerant stream, and α

is the flow rate fraction that bypasses the flash unit.


74

𝐹𝐵𝑦𝑝𝑎𝑠𝑠 = 𝛼 ∙ 𝐹𝑀𝑅 (3.1)

where F Bypass

= Molar flow rate of Bypass Stream

F MR

= Molar flow rate of the overall refrigerant stream

α = Flow rate fraction of the overall refrigerant stream that bypasses the flash unit

Figure 3. 13. Bypass design: degrees of freedom.

The vapour fraction of the mixed refrigerant (with known composition, XMR

) is obtained

with Relation 3.2 at the condenser temperature and compressor discharge pressure, which

are user-specified. The remainder of the refrigerant is flashed and the composition of each

of the phases is calculated using Relation 3.3 and Relation 3.4. The flow rate of each flash

product stream is calculated with Equation 3.5 and Equation 3.6.

𝑉𝐹𝑀𝑅 → 𝑋𝑀𝑅 , 𝑇𝐶𝑜𝑛𝑑, 𝑃𝐻𝑖𝑔ℎ (3.2)

𝑋𝑉𝑎𝑝 → 𝑋𝑀𝑅 , 𝑇𝐶𝑜𝑛𝑑, 𝑃𝐻𝑖𝑔ℎ (3.3)

𝑋𝐿𝑖𝑞 → 𝑋𝑀𝑅 , 𝑇𝐶𝑜𝑛𝑑, 𝑃𝐻𝑖𝑔ℎ (3.4)

𝐹𝑉𝑎𝑝 = 𝑉𝐹𝑀𝑅 ∙ (𝐹𝑀𝑅 − 𝐹𝐵𝑦𝑝𝑎𝑠𝑠) (3.5)

𝐹𝐿𝑖𝑞 = (1 − 𝑉𝐹𝑀𝑅) ∙ (𝐹𝑀𝑅 − 𝐹𝐵𝑦𝑝𝑎𝑠𝑠) (3.6)

where VF MR

= Vapour fraction of the overall refrigerant stream

X MR

= Vector for the composition of the overall refrigerant stream

X Vap,Liq

= Vector for the composition of the vapour and liquid streams leaving the flash unit

TCond = Temperature of the refrigerant stream after the condenser

PHigh = Compressor discharge pressure

F Vap

= Molar flow rate of the vapour stream leaving the flash unit

F Liq

= Molar flow rate of the liquid stream leaving the flash unit


75

After the partial mixing of vapour and liquid (isobaric mixing is assumed), the composition

of Stream 1 and Stream 2 is calculated with a mass balance for each component (xi)

according to the flow rate fraction of vapour (f Vap

) and liquid (f Liq

) to be mixed in each

stream (Equations 3.7 and 3.8). f Vap

is the flow rate fraction of the vapour stream leaving

the flash unit, that is mixed with f Liq

to create Stream 1; f Liq

is the flow rate fraction of the

liquid stream leaving the flash unit, that is mixed with f Vap

to create Stream 1. The flow

rate of Stream 1 and Stream 2 are obtained with Equations 3.9 and 3.10. The composition

of Bypass Stream is the same as the overall refrigerant stream composition.

𝑥𝑖𝑆1 = [

(𝑉𝐹𝑀𝑅∙𝑓𝑉𝑎𝑝∙𝑥𝑖𝑉𝑎𝑝

) + ((1−𝑉𝐹𝑀𝑅)∙𝑓𝐿𝑖𝑞∙𝑥𝑖𝐿𝑖𝑞

)

(𝑉𝐹𝑀𝑅∙𝑓𝑉𝑎𝑝) + ((1−𝑉𝐹𝑀𝑅)∙𝑓𝐿𝑖𝑞)]; 𝑥𝑖

𝑆1 ∈ 𝑋𝑆1 (3.7)

𝑥𝑖𝑆2 = [

(𝑉𝐹𝑀𝑅∙(1−𝑓𝑉𝑎𝑝)∙𝑥𝑖𝑉𝑎𝑝

) + ((1−𝑉𝐹𝑀𝑅)∙(1−𝑓𝐿𝑖𝑞)∙𝑥𝑖𝐿𝑖𝑞

)

(𝑉𝐹𝑀𝑅∙(1−𝑓𝑉𝑎𝑝)) + ((1−𝑉𝐹𝑀𝑅)∙(1−𝑓𝐿𝑖𝑞))]; 𝑥𝑖

𝑆2 ∈ 𝑋𝑆2 (3.8)

𝐹𝑆1 = [(𝐹𝑉𝑎𝑝 ∙ 𝑓𝑉𝑎𝑝) + (𝐹𝐿𝑖𝑞 ∙ 𝑓𝐿𝑖𝑞)] (3.9)

𝐹𝑆2 = [(𝐹𝑉𝑎𝑝 ∙ (1 − 𝑓𝑉𝑎𝑝)) + (𝐹𝐿𝑖𝑞 ∙ (1 − 𝑓𝐿𝑖𝑞))] (3.10)

where xiS1,S2

= Mole fraction of the ith component in Stream 1 and Stream 2

xiVap,Liq

= Mole fraction of the ith component in the vapour and liquid streams from the flash unit

X S1,S2

= Vector for the composition of Stream 1 and Stream 2

f Vap

= Flow rate fraction of the vapour leaving the flash unit, mixed with f Liq

to create Stream 1

f Liq

= Flow rate fraction of the liquid leaving the flash unit, mixed with f Vap

to create Stream 1

F S1,S2

= Molar flow rate of Stream 1 and Stream 2

S1,S2 = Stream 1, Stream 2

All the three hot streams are precooled to their user-specified temperature and expanded to

their corresponding pressure level. The specific enthalpy after the precooling of each hot

stream (hAP) is thus obtained with Relation 3.11 according to their corresponding

composition. The superscripts ‘Ref’, ‘Ref1’, ‘Ref2’ and ‘Ref3’ are employed in this section

to refer to generic refrigerant streams. The temperature after the expansion of each stream

is determined with Relation 3.12 under the assumption of isenthalpic expansion (hAP is

therefore employed for calculating the temperature after expansion). The specific enthalpy

of the cold streams at the outlet of the MSHE is then calculated using Relation 3.13

according to their user-specified outlet temperatures. The amount of heat transferred by

each hot stream and absorbed by each cold stream in the MSHE is then determined with

Equations 3.14 and 3.15, respectively (zero pressure drop is assumed). The overall

refrigerant flow rate is then obtained from an energy balance around the MSHE according


76

to Equation 3.16, considering the heat load of the natural gas to be liquefied, which is user-

specified.

ℎ𝐴𝑃 → 𝑋𝑅𝑒𝑓 , 𝑇𝐴𝑃, 𝑃𝐻𝑖𝑔ℎ (3.11)

𝑇𝐴𝐸 → 𝑋𝑅𝑒𝑓 , 𝑃𝐴𝐸 , ℎ𝐴𝑃 (3.12)

ℎ𝑜𝑢𝑡 → 𝑋𝑅𝑒𝑓, 𝑇𝑜𝑢𝑡, 𝑃𝐴𝐸 (3.13)

∆ℎℎ𝑜𝑡 = (ℎ𝑖𝑛 − ℎ𝐴𝑃) (3.14)

∆ℎ𝑐𝑜𝑙𝑑 = (ℎ𝑜𝑢𝑡 − ℎ𝐴𝑃) (3.15)

𝐹𝑀𝑅 = [𝑄𝑁𝐺

(∆ℎ𝑐𝑜𝑙𝑑𝑆1 +∆ℎ𝑐𝑜𝑙𝑑

𝑆2 +∆ℎ𝑐𝑜𝑙𝑑𝐵𝑦𝑝𝑎𝑠𝑠

) − (∆ℎℎ𝑜𝑡𝑆1 +∆ℎℎ𝑜𝑡

𝑆2 +∆ℎℎ𝑜𝑡𝐵𝑦𝑝𝑎𝑠𝑠

)] (3.16)

where hAP = Specific enthalpy of a hot refrigerant stream after precooling in the MSHE

hin = Specific enthalpy of a hot refrigerant stream prior to entering the MSHE

TAP = Temperature of a hot refrigerant stream after precooling in the MSHE

TAE = Temperature of a cold refrigerant stream after expanded with the throttle valve

PAE = Pressure level of a cold refrigerant stream after expended with the throttle valve

Tout = Temperature of a cold refrigerant stream at the outlet of the MSHE

hout = Specific enthalpy of a cold refrigerant stream at the outlet of the MSHE

QNG

= Heat load of the natural gas that is liquefied

Heat transfer feasibility is then checked inside the MSHE based on a minimum

temperature difference between the composite curves. The T–H profile for each refrigerant

stream is first generated. A user-specified number of intermediate temperatures is selected,

and these intermediate temperatures are evenly distributed in the range between the inlet

and outlet temperatures of each stream, according to Equation 3.17. The corresponding

enthalpy is calculated for each intermediate temperature, using Relation 3.18, where the

specific enthalpy is first determined and is then multiplied by the stream flow rate,

provided that the composition of the stream is known. The pressure of the stream remains

constant as zero pressure drop is assumed.

𝑇𝑖𝑛𝑡𝑅𝑒𝑓

= 𝑇𝑖𝑛𝑙𝑒𝑡 + [(𝑇𝑜𝑢𝑡𝑙𝑒𝑡−𝑇𝑖𝑛𝑙𝑒𝑡)

𝑁𝑖𝑛𝑡∙ 𝑖𝑛𝑡]; 𝑖𝑛𝑡 = 1, 2, 3, … 𝑁𝑖𝑛𝑡 (3.17)

𝐻𝑖𝑛𝑡𝑅𝑒𝑓

→ [𝑋𝑅𝑒𝑓 , 𝑇𝑖𝑛𝑡𝑅𝑒𝑓

, 𝑃𝑅𝑒𝑓] ∙ 𝐹𝑅𝑒𝑓 (3.18)

where Tint = Temperature of the refrigerant stream at the corresponding interval

Hint = Enthalpy of the refrigerant stream at Tint

Nint = Number of intermediate temperatures for calculating the T–H profile of the refrigerant stream


77

The hot composite curve is generated by summing the enthalpy differences of the

individual hot streams (natural gas and hot refrigerants self-cooling) for each intermediate

temperature interval. Similarly, the cold composite curve is generated by summing the

enthalpy differences of the individual cold streams (evaporating refrigerant streams) in

each intermediate temperature interval.

A user-defined number of intermediate temperatures of the hot composite curve are then

compared against those of the cold composite curve at the same enthalpy values. The

resulting temperature difference is compared to the specified minimum temperature

difference for feasible heat transfer (ΔTMIN), according to Equation 3.19. Feasible heat

transfer is only considered when the temperature difference between the hot and cold

composite curves is greater than or equal to the specified minimum temperature difference,

in all the intervals evaluated.

∆𝑇𝑀𝐼𝑁 ≤ (𝑇𝑖𝑛𝑡𝐻𝑂𝑇 − 𝑇𝑖𝑛𝑡

𝐶𝑂𝐿𝐷) (3.19)

After the cold refrigerant streams have absorbed heat in the MSHE, they are recompressed

to the compressor discharge pressure. A multistage compression model is adopted for the

refrigerant compression (Figure 3.14). Each of the three refrigerant streams has a different

pressure level and, therefore, enters the multistage compressor at a different compression

stage accordingly. The refrigerant stream at the lowest pressure level enters the low-

pressure stage of the compressor, where it is partially compressed to an intermediate

pressure. Then, the stream is cooled down with an intercooler and mixed with the second

refrigerant stream (at the same pressure). The resulting stream is further compressed,

cooled in an intercooler and mixed isobarically with the remaining stream. Finally, the

total refrigerant is compressed to the compressor discharge pressure and cooled down in

the condenser. A zero pressure drop is assumed in the intercoolers, and it is also assumed

that the refrigerant is cooled to the same temperature as in the condenser (TCond).


78

Figure 3. 14. Multistage compression.

Using Equation 3.20, the integer number of compression stages is determined iteratively in

order to have a pressure ratio equal to or less than 3. The pressure ratio is first calculated

assuming a single compression stage; if the resulting pressure ratio is greater than 3, then

the number of compression stages is increased by one, and the pressure ratio is calculated

again. The outlet pressure of each compression stage is calculated by Equation 3.21.

𝑃𝑅𝐴𝑇 = √𝑃𝑜𝑢𝑡

𝑃𝑖𝑛

𝑆𝑡𝑔𝑠 𝑃𝑅𝐴𝑇 ≤ 3 (3.20)

𝑃𝑆𝑡𝑔,𝑜𝑢𝑡𝑅𝑒𝑓1

= 𝑃𝑅𝐴𝑇 ∙ 𝑃𝑆𝑡𝑔,𝑖𝑛𝑅𝑒𝑓1

(3.21)

where PRAT = Ratio of outlet to inlet pressure of each compression stage

Stgs = Number of compression stages

PStg = Pressure of the refrigerant stream at the inlet and outlet of the compression stage

For each compression stage, the shaft power required is calculated using an isentropic

model. The specific entropy and enthalpy values of the stream at the inlet of the

compression stage are calculated using Relation 3.22 at the corresponding stage inlet

temperature and inlet pressure. Since isentropic compression is assumed (sStg,in = sStg,out),

the outlet specific enthalpy and outlet temperature can be obtained from Relation 3.23 at

the compression stage outlet pressure. The isentropic efficiency (ηIS, user-specified) is then

introduced to account for compression inefficiencies, and the shaft power is calculated

with an energy balance around the compressor, considering the corresponding refrigerant

flow rate, using Equation 3.24.

𝑠𝑆𝑡𝑔,𝑖𝑛𝑅𝑒𝑓1

, ℎ𝑆𝑡𝑔,𝑖𝑛𝑅𝑒𝑓1

→ 𝑋𝑅𝑒𝑓1, 𝑇𝑆𝑡𝑔,𝑖𝑛𝑅𝑒𝑓1

, 𝑃𝑆𝑡𝑔,𝑖𝑛𝑅𝑒𝑓1

(3.22)

ℎ𝑆𝑡𝑔,𝑜𝑢𝑡𝑅𝑒𝑓1

, 𝑇𝑆𝑡𝑔,𝑜𝑢𝑡𝑅𝑒𝑓1

→ 𝑋𝑅𝑒𝑓1, 𝑃𝑆𝑡𝑔,𝑜𝑢𝑡𝑅𝑒𝑓1

, 𝑠𝑆𝑡𝑔,𝑖𝑛𝑅𝑒𝑓1

(3.23)


79

𝑊𝑆𝑡𝑔 = 𝐹𝑅𝑒𝑓1 ∙ (ℎ𝑆𝑡𝑔,𝑜𝑢𝑡

𝑅𝑒𝑓1−ℎ𝑆𝑡𝑔,𝑖𝑛

𝑅𝑒𝑓1

𝜂𝐼𝑆) (3.24)

where sStg,in = Specific entropy of the refrigerant stream at the inlet of the compression stage

hStg,in = Specific enthalpy of the refrigerant stream at the inlet of the compression stage

hStg,out = Specific enthalpy of the refrigerant stream at the outlet of the compression stage

TStg,in = Temperature of the refrigerant stream at the inlet of the compression stage

TStg,out = Temperature of the refrigerant stream at the outlet of the compression stage

ηIS = Compression isentropic efficiency

WStg = Shaft power demand of the compression stage

After a refrigerant stream has been compressed, it is cooled down by an intercooler, which

is in between two compression stages (see Figure 3.14). The duty in the intercooler is

calculated from the change in enthalpy of the refrigerant stream that is cooled from its inlet

temperature to TCond. The inlet and outlet enthalpies of the refrigerant in the intercooler are

obtained with Relations 3.25 and 3.26, respectively. The duty in the intercooler is

calculated by Equation 3.27.

ℎ𝑐𝑜𝑜𝑙,𝑖𝑛𝑅𝑒𝑓1

→ 𝑋𝑅𝑒𝑓1, 𝑇𝑆𝑡𝑔,𝑜𝑢𝑡𝑅𝑒𝑓1

, 𝑃𝑆𝑡𝑔,𝑜𝑢𝑡𝑅𝑒𝑓1

(3.25)

ℎ𝑐𝑜𝑜𝑙,𝑜𝑢𝑡𝑅𝑒𝑓1

→ 𝑋𝑅𝑒𝑓1, 𝑇𝐶𝑜𝑛𝑑, 𝑃𝑆𝑡𝑔,𝑜𝑢𝑡𝑅𝑒𝑓1

(3.26)

𝑄𝑐𝑜𝑜𝑙 = 𝐹𝑅𝑒𝑓1 ∙ (ℎ𝑐𝑜𝑜𝑙,𝑖𝑛𝑅𝑒𝑓1

− ℎ𝑐𝑜𝑜𝑙,𝑜𝑢𝑡𝑅𝑒𝑓1

) (3.27)

where hcool = Specific enthalpy of the refrigerant at the inlet and outlet of the intercooler

Qcool

= Heat load in the intercooler

If the refrigerant stream is partially condensed after being cooled in the intercooler, the

liquid formed is separated in a flash unit and then pumped to the compressor discharge

pressure. An isentropic model is considered for the pump, including an isentropic

efficiency, to calculate the power consumption. The vapour fraction of the refrigerant after

the intercooler and the composition of the liquid phase are obtained with Relation 3.28.

The flow rate of the condensed liquid is obtained with Equation 3.29. The specific enthalpy

and entropy of the liquid at the inlet of the pump is obtained with Relation 3.30. The

specific outlet enthalpy and the outlet temperature of the liquid are calculated using

Relation 3.31. The shaft power of the pump is calculated with an energy balance using the

isentropic efficiency (Equation 3.32).

𝑉𝐹𝑐𝑜𝑜𝑙𝑅𝑒𝑓1

, 𝑋𝑐𝑜𝑜𝑙𝐿𝑖𝑞 → 𝑋𝑅𝑒𝑓1, 𝑇𝐶𝑜𝑛𝑑 , 𝑃𝑆𝑡𝑔,𝑜𝑢𝑡

𝑅𝑒𝑓1 (3.28)


80

𝐹𝑃𝑢𝑚𝑝 = [𝐹𝑅𝑒𝑓1 ∙ (1 − 𝑉𝐹𝑐𝑜𝑜𝑙𝑅𝑒𝑓1

)] (3.29)

ℎ𝑖𝑛𝑃𝑢𝑚𝑝, 𝑠𝑖𝑛

𝑃𝑢𝑚𝑝 → 𝑋𝑐𝑜𝑜𝑙𝐿𝑖𝑞 , 𝑇𝐶𝑜𝑛𝑑, 𝑃𝑆𝑡𝑔,𝑜𝑢𝑡

𝑅𝑒𝑓1 (3.30)

ℎ𝑜𝑢𝑡𝑃𝑢𝑚𝑝, 𝑇𝑜𝑢𝑡

𝑃𝑢𝑚𝑝 → 𝑋𝑐𝑜𝑜𝑙𝐿𝑖𝑞 , 𝑃𝐻𝑖𝑔ℎ, 𝑠𝑖𝑛

𝑃𝑢𝑚𝑝 (3.31)

𝑊𝑃𝑢𝑚𝑝 = 𝐹𝑃𝑢𝑚𝑝 ∙ (ℎ𝑜𝑢𝑡

𝑃𝑢𝑚𝑝−ℎ𝑖𝑛

𝑃𝑢𝑚𝑝

𝜂𝐼𝑆) (3.32)

where VFcool = Vapour fraction of the refrigerant stream after the intercooler

XcoolLiq

= Vector for the composition of the liquid condensed after refrigerant intercooling

FPump

= Molar flow rate of the refrigerant stream entering the pump

sinPump

= Specific entropy of the refrigerant stream at the inlet of the pump

hin,outPump

= Specific enthalpy of the refrigerant stream at the inlet and outlet of the pump

ToutPump

= Temperature of the refrigerant stream at the outlet of the pump

WPump

= Shaft power demand of the pump

When two refrigerant streams are mixed at an intermediate pressure level, the temperature

of the resulting stream has to be calculated to determine the inlet conditions of the

refrigerant (temperature and pressure) to the next compression stage. An energy balance is

used to obtain the specific enthalpy of the resulting stream after mixing (Equation 3.33)

and the temperature of the resulting stream is then calculated using Relation 3.34.

ℎ𝑀𝑖𝑥𝑅𝑒𝑓3

= [(𝐹𝑅𝑒𝑓1∙ℎ𝑅𝑒𝑓1)+(𝐹𝑅𝑒𝑓2∙ℎ𝑅𝑒𝑓2)

(𝐹𝑅𝑒𝑓1+𝐹𝑅𝑒𝑓2)] (3.33)

𝑇𝑀𝑖𝑥𝑅𝑒𝑓3

→ 𝑋𝑀𝑖𝑥𝑅𝑒𝑓3

, 𝑃𝑆𝑡𝑔𝑅𝑒𝑓3

, ℎ𝑀𝑖𝑥𝑅𝑒𝑓3

(3.34)

where hMix = Specific enthalpy of the stream resulting from mixing Ref1 and Ref2 in the compressor

TMix = Temperature of the streams resulting from mixing Ref1 and Ref2 in the compressor

The total compression shaft power is calculated as the sum of the power required by each

compressor stage plus the power consumed by the pumps (Equation 3.35):

𝑊𝑇𝑜𝑡𝑎𝑙 = ∑ 𝑊𝑖𝑆𝑡𝑔

+ ∑ 𝑊𝑖𝑃𝑢𝑚𝑝

(3.35)

3.3.2 Modelling of the Two Flash Levels design

The Two Flash Levels refrigeration cycle is displayed in Figure 3.15. The values for the

degrees of freedom are specified, and then the vapour fraction of the refrigerant is obtained

with Relation 3.36. The compositions of the flash unit product streams are obtained with

Relations 3.37 and 3.38, and their corresponding flow rates are calculated with Equations

3.39 and 3.40. The flow rate fed to the second flash unit (F2nd

) is calculated with Equation


81

3.41, given the flow rate fraction of the liquid phase (f 2nd

) that is expanded to the second

pressure level.




𝐹𝑉𝑎𝑝 = 𝑉𝐹𝑀𝑅 ∙ 𝐹𝑀𝑅 (3.39)

𝐹𝐿𝑖𝑞 = (1 − 𝑉𝐹𝑀𝑅) ∙ 𝐹𝑀𝑅 (3.40)

𝐹2𝑛𝑑 = 𝑓2𝑛𝑑 ∙ 𝐹𝐿𝑖𝑞 (3.41)

Figure 3. 15. Two Flash Levels design: degrees of freedom.

The temperature and vapour fraction of the stream that is expanded to the second pressure

level is obtained with Relation 3.42, assuming isenthalpic expansion of the liquid from the

first flash unit. The resulting two-phase refrigerant mixture is separated into vapour and

liquid in the second flash unit. The compositions of the product streams from the second

flash unit are determined with Relations 3.43 and 3.44, whilst the flow rate of each phase is

calculated with Equations 3.45 and 3.46.

𝑇2𝑛𝑑 , 𝑉𝐹2𝑛𝑑 → 𝑋𝐿𝑖𝑞 , 𝑃2𝑛𝑑 , ℎ𝐿𝑖𝑞 (3.42)

𝑋𝑉𝑎𝑝2 → 𝑋𝐿𝑖𝑞 , 𝑇2𝑛𝑑 , 𝑃2𝑛𝑑 (3.43)

𝑋𝐿𝑖𝑞2 → 𝑋𝐿𝑖𝑞 , 𝑇2𝑛𝑑 , 𝑃2𝑛𝑑 (3.44)


82

𝐹𝑉𝑎𝑝2 = 𝑉𝐹2𝑛𝑑 ∙ 𝐹2𝑛𝑑 (3.45)

𝐹𝐿𝑖𝑞2 = (1 − 𝑉𝐹2𝑛𝑑) ∙ 𝐹2𝑛𝑑 (3.46)

where T 2nd

= Temperature of the refrigerant stream entering the second flash unit

VF 2nd

= Vapour fraction of the refrigerant stream entering the second flash unit

X Vap2,Liq2

= Vector for the composition of the vapour and liquid streams from the second flash unit

F Vap2,Liq2

= Molar flow rate of the vapour and liquid streams leaving the second flash unit

The vapour and liquid of the second flash unit are partially mixed (isobarically), and the

resulting composition of Streams 3 and Stream 4 are calculated with Equations 3.47 and

3.48 for each component (xi) in the refrigerant mixture. Equations 3.49 and 3.50 calculate

the flow rate of Stream 3 and Stream 4, respectively.

𝑥𝑖𝑆3 = [

(𝑉𝐹2𝑛𝑑∙𝑓𝑉𝑎𝑝2∙𝑥𝑖𝑉𝑎𝑝2

) + ((1−𝑉𝐹2𝑛𝑑)∙𝑓𝐿𝑖𝑞2∙𝑥𝑖𝐿𝑖𝑞2

)

(𝑉𝐹2𝑛𝑑∙𝑓𝑉𝑎𝑝2) + ((1−𝑉𝐹2𝑛𝑑)∙𝑓𝐿𝑖𝑞2)]; 𝑥𝑖

𝑆3 ∈ 𝑋𝑆3 (3.47)

𝑥𝑖𝑆4 = [

(𝑉𝐹2𝑛𝑑∙(1−𝑓𝑉𝑎𝑝2)∙𝑥𝑖𝑉𝑎𝑝2

) + ((1−𝑉𝐹2𝑛𝑑)∙(1−𝑓𝐿𝑖𝑞2)∙𝑥𝑖𝐿𝑖𝑞2

)

(𝑉𝐹2𝑛𝑑∙(1−𝑓𝑉𝑎𝑝2)) + ((1−𝑉𝐹2𝑛𝑑)∙(1−𝑓𝐿𝑖𝑞2))];

𝑥𝑖𝑆4 ∈ 𝑋𝑆4 (3.48)

𝐹𝑆3 = (𝐹𝑉𝑎𝑝2 ∙ 𝑓𝑉𝑎𝑝2) + (𝐹𝐿𝑖𝑞2 ∙ 𝑓𝐿𝑖𝑞2) (3.49)

𝐹𝑆4 = (𝐹𝑉𝑎𝑝2 ∙ (1 − 𝑓𝑉𝑎𝑝2)) + (𝐹𝐿𝑖𝑞2 ∙ (1 − 𝑓𝐿𝑖𝑞2)) (3.50)

where xiS3,S4

= Mole fraction of the ith component in Stream 3 and Stream 4

xiVap2,Liq2

= Mole fraction of the ith component in the vapour and liquid streams from 2nd flash unit

X S3,S4

= Vector for the composition of Stream 3 and Stream 4

f Vap2

= Flow rate fraction of vapour from the second flash unit, mixed with f Liq2

to create Stream 3

f Liq2

= Flow rate fraction of liquid from the second flash unit, mixed with f Vap2

to create Stream 3

F S3,S4

= Molar flow rate of Stream 3 and Stream 4

S3,S4 = Stream 3, Stream 4

The hot streams (Stream 1 to Stream 4) enter the MSHE and are precooled to their

specified temperature and their specific enthalpy is calculated with Relation 3.51 (Stream 1

and Stream 2) and Relation 3.52 (Stream 3 and Stream 4). After expansion to their

corresponding pressure level, the temperature of each stream is calculated using Relation

3.53 under the assumption of isenthalpic expansion.


ℎ𝐴𝑃 → 𝑋𝑅𝑒𝑓 , 𝑇𝐴𝑃, 𝑃2𝑛𝑑 (3.52)



83

The specific enthalpy of each cold stream at the outlet of the MSHE is calculated with

Relation 3.54. Heat rejected by each hot stream is then calculated with Equation 3.55,

whereas heat absorbed by each cold stream is obtained with Equation 3.56. The overall

refrigerant flow rate is then calculated (Equation 3.57) with an energy balance around the

MSHE.


∆ℎℎ𝑜𝑡 = (ℎ𝑖𝑛 − ℎ𝐴𝑃) (3.55)




𝑆2 +∆ℎ𝑐𝑜𝑙𝑑𝑆3 +∆ℎ𝑐𝑜𝑙𝑑

𝑆4 ) − (∆ℎℎ𝑜𝑡𝑆1 +∆ℎℎ𝑜𝑡

𝑆2 +∆ℎℎ𝑜𝑡𝑆3 +∆ℎℎ𝑜𝑡

𝑆4 )] (3.57)

Feasible heat transfer is checked as described in Section 3.3.1. Similarly, after the cold

streams have absorbed heat from the hot streams (refrigerants self-cooling and natural gas

condensing), the cold streams are returned to the high pressure level (i.e. the compressor

discharge pressure) and shaft power calculations are performed as described in Section

3.3.1.

3.3.3 Modelling of the Mixing After Precooling design

The Mixing After Precooling refrigeration cycle is shown in Figure 3.16. The values for

the degrees of freedom are first specified. The vapour fraction of the mixed refrigerant is

obtained with Relation 3.58. The refrigerant is flashed and the compositions of the product

streams are obtained with Relations 3.59 and 3.60 for the vapour and liquid phase,

respectively. The flow rate of each stream (vapour and liquid) is calculated using

Equations 3.61 and 3.62.




𝐹𝑉𝑎𝑝 = 𝑉𝐹𝑀𝑅 ∙ 𝐹𝑀𝑅 (3.61)

𝐹𝐿𝑖𝑞 = (1 − 𝑉𝐹𝑀𝑅) ∙ 𝐹𝑀𝑅 (3.62)


84

Figure 3. 16. Mixing After Precooling design: degrees of freedom.

The composition of the hot refrigerants Stream 1 and Stream 2 (XS1

and XS2

) is calculated

with Equations 3.63 and 3.64, respectively, with a mass balance of each component (xi) in

the mixture after partial mixing of vapour and liquid phases from the flash unit (isobaric

mixing is assumed). The flow rate for each hot refrigerant stream is calculated with

Equations 3.65 and 3.66.

𝑥𝑖𝑆1 = [



)


𝑆1 ∈ 𝑋𝑆1 (3.63)

𝑥𝑖𝑆2 = [



)


𝑆2 ∈ 𝑋𝑆2 (3.64)

𝐹𝑆1 = (𝐹𝑉𝑎𝑝 ∙ 𝑓𝑉𝑎𝑝) + (𝐹𝐿𝑖𝑞 ∙ 𝑓𝐿𝑖𝑞) (3.65)

𝐹𝑆2 = (𝐹𝑉𝑎𝑝 ∙ (1 − 𝑓𝑉𝑎𝑝)) + (𝐹𝐿𝑖𝑞 ∙ (1 − 𝑓𝐿𝑖𝑞)) (3.66)

The hot refrigerant streams are precooled in the MSHE and then expanded with throttle

valves. The specific enthalpy after precooling is calculated with Relation 3.67. The

temperature of Stream 1 and Stream 2 after expansion is calculated using Relation 3.68,

respectively, assuming isenthalpic expansion. Once expanded, a flow rate fraction ‘α’ from

Stream 1 is mixed with a flow rate fraction ‘β’ from Stream 2 (isobaric mixing is

assumed), in order to create a new cold stream with a different composition (i.e. Stream 5).

In order to partially mix both streams, the refrigerant flow rate fraction α from Stream 1

has to be expanded to the same pressure level of Stream 2. The flow rate fraction α from

Stream 1 is mixed with the flow rate fraction β from Stream 2. The temperature of the


85

refrigerant fraction α, once expanded, is obtained with Relation 3.69. The flow rates of the

three cold streams (Stream 3, Stream 4 and Stream 5) are calculated by Equations 3.70 to

3.72. The composition of the new stream (Stream 5) is calculated similarly as with Stream

1 and Stream 2 (Equation 3.73). The temperature of Stream 5, after flow rate fractions α

and β are mixed, is obtained with Relation 3.75 after obtaining its specific enthalpy value

resulting from the mixing process (Equation 3.74).



𝑇𝐴𝐸𝛼 → 𝑋𝑆1, 𝑃𝐴𝐸

𝑆2, ℎ𝐴𝑃𝑆1 (3.69)

𝐹𝑆3 = 𝐹𝑆1 ∙ (1 − 𝛼) (3.70)

𝐹𝑆4 = 𝐹𝑆2 ∙ (1 − 𝛽) (3.71)

𝐹𝑆5 = (𝐹𝑆1 ∙ 𝛼) + (𝐹𝑆2 ∙ 𝛽) (3.72)

𝑥𝑖𝑆5 = [

(𝐹𝑆1∙ 𝛼 ∙ 𝑥𝑖𝑆1) + (𝐹𝑆2∙ 𝛽 ∙ 𝑥𝑖

𝑆2)

(𝐹𝑆1∙ 𝛼) + (𝐹𝑆2∙ 𝛽)]; 𝑥𝑖

𝑆5 ∈ 𝑋𝑆5 (3.73)

ℎ𝑀𝑖𝑥𝑆5 = [

(𝐹𝑆1∙ 𝛼 ∙ ℎ𝐴𝑃𝑆1 )+(𝐹𝑆2∙ 𝛽 ∙ ℎ𝐴𝑃

𝑆2 )

(𝐹𝑆1∙ 𝛼)+(𝐹𝑆2∙ 𝛽)] (3.74)

𝑇𝑀𝑖𝑥𝑆5 → 𝑋𝑆5, 𝑃𝐴𝐸

𝑆2, ℎ𝑀𝑖𝑥𝑆5 (3.75)

where α = Flow rate fraction from Stream 1, mixed to create Stream 5

β = Flow rate fraction from Stream 2, mixed to create Stream 5

xiS5

= Mole fraction of the ith component in Stream 5

XS5

= Vector for the composition of Stream 5

hMixS5

= Specific enthalpy of Stream 5, resulting from mixing α and β

TMixS5

= Temperature of Stream 5, after mixing α and β

S1,S2,S3,S4,S5 = Stream1, Stream 2, Stream 3, Stream 4, Stream 5

The specific enthalpy of the cold streams at the outlet of the MSHE is then calculated with

Relation 3.76. The heat rejected by each hot stream and the heat absorbed by each cold

stream can thus be calculated by Equations 3.77 and 3.78, respectively. The overall

refrigerant flow rate is calculated from an energy balance around the MSHE (Equation

3.79).


∆ℎℎ𝑜𝑡 = (ℎ𝑖𝑛 − ℎ𝐴𝑃) (3.77)



86



𝑆4 +∆ℎ𝑐𝑜𝑙𝑑𝑆5 )−(∆ℎℎ𝑜𝑡

𝑆1 +∆ℎℎ𝑜𝑡𝑆2 )

] (3.79)

Feasible heat transfer is then checked at intermediate temperatures in the MSHE as

described in Section 3.3.1. The cold refrigerant streams leaving the MSHE are then

compressed to the compressor discharge pressure. Stream 4 and Stream 5 enter at the same

compression stage since both have the same pressure level. The multistage compression

model, described in Section 3.3.1, is then used to calculate the shaft power demand of the

refrigeration cycle.

3.3.4 Example of mixed refrigerant cycle modelling

In order to evaluate the accuracy of the models of the novel refrigeration cycles (and in the

absence of experimental data), the model of the Two Flash Levels design is simulated in

WORK software and compared to a simulation of the same refrigeration cycle in Aspen

HYSYS v8.2. That is, it is assumed that the results in Aspen HYSYS are an accurate

representation of the real data.

The natural gas stream in WORK software is entered as a T–H profile, whereas in HYSYS,

the full conditions of the natural gas stream are required, i.e. the composition, flow rate,

MSHE inlet and outlet temperatures as well as inlet and outlet pressures. The model in

WORK takes the temperatures of the cold refrigerants at the outlet of the MSHE as input,

and calculates the overall flow rate of the refrigerant with an energy balance. HYSYS, on

the other hand, takes the flow rate of the refrigerant and n–1 outlet temperatures of the cold

streams (n is the total number of cold streams leaving the MSHE) as input and calculates

the temperature of the remaining cold stream at the outlet of the MSHE.

The natural gas stream is first specified (i.e. composition, inlet and outlet temperatures,

etc.) in HYSYS. The MSHE model in HYSYS generates the temperature–enthalpy profiles

of each stream in the MSHE by calculating a user-specified number of intermediate

temperatures (relative to inlet and outlet temperatures of each stream). Thus, the T–H

profile of the natural gas stream is obtained. The natural gas T–H profile is then entered in

WORK software and the parameters for the mixed refrigerant cycle are specified (e.g.

refrigerant composition, streams pressure levels, etc.), allowing calculating the refrigerant

flow rate. The flow rate obtained in WORK is then input to HYSYS to run the simulation.


87

For this example, a natural gas stream (1 kmol·s-1

) is to be liquefied at –163°C (110 K)

from 25°C (298 K). The natural gas is assumed to be at a pressure of 45 bar and to leave

the MSHE at 40 bar. The composition of the natural gas stream is taken from Cao et al.

(2006) and is on Table 3.1. The mixed refrigerant is composed of C1 – C4 and nitrogen (see

Table 3.1). The T–H data of the natural gas stream is provided in Table 3.2 and Figure

3.17.

Table 3. 1. Natural gas and mixed refrigerant composition [mole %] for the modelling example.

C1 C2 C3 n-C4 i-C4 N2

Natural gas* 82.0 11.2 4.0 0.9 1.2 0.7

Mixed refrigerant 20.0 40.0 10.0 20.0 0.0 10.0

*Composition obtained from Cao et al. (2006).

Table 3. 2. Natural gas temperature–enthalpy data (from HYSYS, 1 kmol·s-1

) for the modelling example.

Segment Supply Temperature [K] Target Temperature [K] ΔH [kW] CP [kW·K-1

]

1.1 298.1 276.7 1051.2 49.0

1.2 276.7 261.8 754.9 50.8

1.3 261.8 258.4 296.3 85.1

1.4 258.4 246.1 1051.2 86.0

1.5 246.1 233.9 1102.5 90.2

1.6 233.9 222.3 1147.5 98.9

1.7 222.3 213.3 1036.4 115.0

1.8 213.3 206.2 1036.4 145.3

1.9 206.2 201.1 1036.4 202.6

1.10 201.1 197.5 1036.4 290.1

1.11 197.5 195.6 695.5 367.4

1.12 195.6 191.6 340.9 85.5

1.13 191.6 178.1 1036.4 76.6

1.14 178.1 162.8 1036.4 67.8

1.15 162.8 147.5 954.9 62.5

1.16 147.5 130.3 1016.8 59.0

1.17 130.3 110.1 1137.5 56.5

Figure 3. 17. Natural gas temperature–enthalpy data (from HYSYS, 1 kmol·s-1

) for the modelling example.

100

130

160

190

220

250

280

310

0 3 6 9 12 15 18

Tem

per

atu

re [

K]

ΔH [MW]


88

For the simulation it is assumed that the maximum pressure ratio for each compression

stage is 3. The compression isentropic efficiency is considered as 80%. Physical and

thermodynamic properties of the mixed refrigerant are calculated using Peng–Robinson

equation of state. In WORK software, the fluid properties of the mixed refrigerant are

calculated using Peng–Robinson equation by interfacing with Aspen HYSYS.

Table 3.3 compares the simulation in WORK with that in Aspen HYSYS v8.2. The results

obtained with the model of the Two Flash Levels design simulated in WORK are in good

agreement compared to those obtained in HYSYS since there is a difference of only 0.1%

in the shaft power calculated using HYSYS compared to the power demand calculated in

WORK. The main discrepancy in the calculation of the shaft power demand comes from

the pump model. The minimum temperature driving force in the simulation on WORK is

different by only 0.2°C compared to the simulation in HYSYS.

Table 3. 3. Results comparison of the Two Flash Levels design simulation example.

HYSYS v8.2 WORK Difference

Refrigerant flow rate [kmol·s-1

] 2.5a 2.5 -

Outlet pressure of compressor [bar] 45a 45

b -

Pressure second flash unit [bar] 15a 15

b -

Fraction of liquid to the second flash unit 0.6a 0.6

b -

Flow rate fraction of vapour for partial mixing (f Vap

):

- Stream 1

- Stream 2

- Stream 3

- Stream 4

0.75a

0.25a

0.70a

0.30a

0.75b

0.25b

0.70b

0.30b

-

-

-

-

Flow rate fraction of liquid for partial mixing (f Liq

):

- Stream 1

- Stream 2

- Stream 3

- Stream 4

0.17a

0.23a

0.25a

0.75a

0.17b

0.23b

0.25b

0.75b

-

-

-

-

Expansion pressure [bar]

- Stream 1

- Stream 2

- Stream 3

- Stream 4

1.2a

6.0a

11.5a

3.6a

1.2b

6.0b

11.5b

3.6b

-

-

-

-

MSHE outlet temperature [K]:

- Stream 1

- Stream 2

- Stream 3

- Stream 4

296.0a

297.0a

295.0a

284.4

296.0b

297.0b

295.0b

285.2b

-

-

-

0.8°C

Intercooling duty [MW] 35.06 36.07 2.8%

Number of compression stages 5 5 -

ΔTMIN [K] 2.1 1.9 0.2°C

Compression shaft power [MW] 20.00 20.02 0.1% aDenotes input data to HYSYS.

bDenotes input to WORK.


89

3.4 Strategy for the evaluation of the novel designs

To evaluate the novel refrigeration cycles, the same natural gas stream employed in the

CryoMan process is used as the liquefaction duty. The natural gas stream data is provided

only as a T–H profile in a tabular form (see Table 3.4) and was first published by Lee

(2001).

The evaluation of the novel refrigeration cycles is divided in two stages. Firstly, the novel

refrigeration cycles are simulated in Aspen HYSYS v8.2 to evaluate their shaft power

consumption through sensitivity analyses on each degree of freedom (e.g. refrigerant

composition, pressure levels, etc.). Because the natural gas stream is only provided as a T–

H profile, its full conditions (e.g. composition, inlet and outlet pressure, etc.) have to be

determined in order to be simulated in HYSYS for the assessment of the novel

refrigeration cycles on the same liquefaction duty basis as the CryoMan process. An

optimisation approach is employed to find a combination of values for the natural gas

stream conditions that minimises the sum of squared difference of the enthalpies between

the T–H profile of the optimised stream and that in Table 3.4.

In the second stage of the evaluation, only the refrigeration cycles that show shaft power

savings in the sensitivity analyses, compared to the shaft power consumption of the

CryoMan process, are considered for optimisation in WORK software. The degrees of

freedom (e.g. refrigerant composition, pressure levels, etc.) of each novel refrigeration

cycle are optimised and the resulting performance indicators (including shaft power

demand and the ΔTMIN) are compared against those in the CryoMan process as well as

those in the PRICO cycle.

Table 3. 4. Temperature–enthalpy profile of the natural gas stream published by Lee (2001).

Segment Supply

Temperature [°C]

Target

Temperature [°C] ΔH [kW] CP [kW·K

-1]

1.1 25.00 –06.03 –1861.5 60

1.2 –06.03 –34.09 –1964.3 70

1.3 –34.09 –57.65 –1885.0 80

1.4 –57.65 –70.10 –2490.0 200

1.5 –70.10 –74.55 –1780.0 400

1.6 –74.55 –82.26 –3084.0 400

1.7 –82.26 –96.50 –1424.0 100

1.8 –96.50 –115.00 –1850.0 100

1.9 –115.00 –163.00 –3840.0 80


90

3.4.1 Simulation and analysis

The novel refrigeration cycles are built in Aspen HYSYS v8.2 and sensitivity analyses are

implemented around each of their corresponding degrees of freedom (such as the

refrigerant composition, pressure levels, etc.). Each sensitivity analysis involves the

manipulation of only one degree of freedom.

The sensitivity analyses are performed as a preliminary study in order to investigate the

refrigeration cycle designs that show results towards reducing shaft power consumption for

refrigerant compression in the liquefaction of a natural gas stream, compared to the shaft

power required in the CryoMan process. Only designs that show shaft power savings are

considered for optimisation of their operating variables. Chapter 4 provides details of the

results obtained from the sensitivity studies in each of the novel refrigeration cycles.

3.4.2 Optimisation of promising designs

The promising refrigeration cycles are optimised in WORK software in Chapter 5. A

Genetic Algorithm is used as the optimisation method to find a set of values of the

operating variables (e.g. refrigerant composition, evaporating pressures, etc.) that yield the

lowest shaft power consumption of the novel refrigeration cycle. As defined in Section 3.1,

the design of novel refrigeration cycles is constrained to a single MSHE with up to 12

refrigerant streams involved in heat exchange and a single multistage centrifugal

compressor; also, the novel refrigeration are constrained to refrigerant compression with a

maximum pressure ratio (i.e. ratio of outlet to inlet pressure) of 3 in each compression

stage, and up to a maximum of 8 compression stages in the compressor.

Chapter 5 presents a case study for the liquefaction of the natural gas stream (presented in

Table 3.4), in which the operating variables of the novel refrigeration cycles are optimised

to minimise the shaft power consumption of the refrigeration cycle. Results are compared

against the CryoMan process and against the PRICO cycle. A detailed analysis of the

results obtained and an economic comparison (based on operating costs) between the novel

refrigeration cycles and the benchmark processes (i.e. the CryoMan process and the

PRICO cycle) is presented in Chapter 5 as well.


91

3.5 Conclusions

The CryoMan process was analysed and the manipulation of the composition, by partial

mixing of the product streams of the flash unit, was identified as a key degree of freedom.

As a result of the composition manipulation, in the CryoMan process, LP Stream required

less shaft power for compression than LP Stream in the “Pre-flash” design. Moreover, a

trade-off was identified between the flow rate of each refrigerant stream and its pressure

level. The CryoMan process reduced the shaft power consumption, compared to the “Pre-

flash” design, by increasing the flow rate of LP Stream but reducing the pressure

difference between the intermediate pressure level (i.e. the pressure level of HP Stream)

and the compressor discharge pressure.

Conceptual modifications to the structure of the refrigeration cycle were suggested based

on the analysis performed to the CryoMan process and the trade-offs identified between

the operating conditions (e.g. flow rates, pressure levels, compositions, etc.), with the aim

of reducing the overall shaft power demand of the refrigeration cycle. To account for the

low complexity and compactness required in small scale LNG processes, the design of the

novel refrigeration cycles was constrained to use only one multistage compressor in which

the pressure ratio of each stage was not greater than 3, plus only one MSHE with a

maximum of 12 streams involved in heat exchange.

Three novel refrigeration cycles were developed (namely the Bypass design, the Two Flash

Levels design and the Mixing After Precooling design) with the suggested structural

modifications and under the limits defined for complexity. The novel refrigeration cycles

were successfully modelled as it was demonstrated through an example.

In the following Chapter 4, the novel refrigeration cycles are simulated in Aspen HYSYS

v8.2 in order to assess their performance (i.e. shaft power consumption) through sensitivity

analyses towards potential shaft power savings compared to the CryoMan process. Also,

the full conditions the natural gas stream (e.g. composition, inlet and outlet pressure, etc.)

are determined; details of the optimisation approach for the determination of the natural

gas conditions are in Appendix 1. Moreover, Chapter 5 presents a case study for the

liquefaction of the natural gas stream, in which the operating variables of the promising

novel refrigeration cycles are optimised, in order to minimise the total shaft power

consumption for refrigerant compression. Results of the optimised novel refrigeration


92

cycles are compared to those of the CryoMan process and the PRICO cycle (see also

Appendixes 2 and 3). The optimisation is performed in WORK software by means of a

Genetic Algorithm.

Chapter 4 Evaluation of the Novel Refrigeration Cycles

93

Chapter 4 – Evaluation of the Novel Refrigeration Cycles

4.1 Introduction

As mentioned in Section 3.4, the novel refrigeration cycles are evaluated in two stages: a

preliminary assessment using Aspen HYSYS v8.2 (Aspen Technology Inc., 2013) through

sensitivity analyses, and the optimisation of the operating variables in WORK software of

the refrigeration cycles that show shaft power savings compared to the CryoMan process.

This chapter is focused on the first stage of the evaluation.

Aspen HYSYS is used to perform a preliminary study of the novel refrigeration cycles

through sensitivity analyses. An initial simulation of the novel refrigeration cycle is first

performed. Then, sensitivity studies explore the performance of each refrigeration cycle,

using the shaft power consumption and the minimum temperature approach in the multi-

stream heat exchanger (MSHE) as the performance indicators, when each degree of

freedom in their corresponding designs is varied (e.g. the bypass stream flow rate fraction,

the fraction of the streams partially mixed after a second flash separator, etc.). The

compression shaft power demand is compared to that of the reference case – the CryoMan

process – for the same liquefaction duty; therefore, the same natural gas stream employed

with the CryoMan process, provided only as a T–H profile, is used in the preliminary

assessment of the novel refrigeration cycles (see Section 4.2).

The novel refrigeration cycles are modelled in HYSYS as described in Section 3.3. In the

sensitivity analyses, the degrees of freedom of each novel refrigeration cycle are

manipulated, one variable at the time, in order to assess their impact on the shaft power

demand for refrigerant compression. The novel designs that show shaft power savings,

compared to the CryoMan process, are selected for optimisation of their corresponding

operating variables using WORK software. The optimisation of the novel refrigeration

cycles is presented with a case study in Chapter 5.

4.2 Determination of the natural gas conditions

The procedure for obtaining the conditions of the natural gas stream is briefly described in

this section and the detailed procedure is provided in Appendix 1.

The natural gas stream, first published by Lee (2001, Ch. 4), and later employed by Del

Nogal (2006, Ch. 2) and Zheng (2009, Ch. 3), is provided only as a temperature–enthalpy


94

profile in a tabulated form, as shown in Table 4.1. Remeljej and Hoadley (2006) provided a

composition and mass flow rate for the same natural gas stream in the evaluation of four

different refrigeration cycles, including the PRICO cycle.

Additional information in Lee (2001, Ch. 4) is that the natural gas stream enters the MSHE

at 55 bar and leaves at 50 bar, i.e. there is a pressure drop of 5 bar, although the pressure

drop profile inside the MSHE is not specified. The flow rate of the liquefied natural gas is

not mentioned either.

Table 4. 1. Natural gas stream data presented by Lee (2001), Del Nogal (2006) and Zheng (2009).

Segment Supply

Temperature [°C]

Target


-1]

1.1 25.00 –06.03 –1861.5 60

1.2 –06.03 –34.09 –1964.3 70

1.3 –34.09 –57.65 –1885.0 80

1.4 –57.65 –70.10 –2490.0 200

1.5 –70.10 –74.55 –1780.0 400

1.6 –74.55 –82.26 –3084.0 400

1.7 –82.26 –96.50 –1424.0 100

1.8 –96.50 –115.00 –1850.0 100

1.9 –115.00 –163.00 –3840.0 80

To simulate in HYSYS the natural gas stream that Zheng (2009) employed to optimise the

CryoMan process (see Table 4.1), the full conditions of the stream are required, i.e. the

flow rate, composition, inlet and outlet pressures and temperatures, as well as the pressure

drop profile across the MSHE.

However, the pressure drop profile of the natural gas stream in the MSHE is not provided

in any of the publications previously mentioned. Moreover, the molar flow rate of the

natural gas obtained according to Remeljej and Hoadley (2006) (1.37 kmol·s-1

) is

conflicting when compared to 1 kmol·s-1

used by Zheng (2009) [stated explicitly in Zheng

(2007)] to optimise the CryoMan process. In addition, the T–H profile obtained from the

natural gas stream according to the conditions employed by Remeljej and Hoadley (2006)

does not match that originally presented by Lee (2001), as shown in Figure 4.1. The

conditions of the natural gas stream (composition, flow rate, inlet and outlet pressure, and

pressure drop profile in the MSHE) are thus unclear.


95

Figure 4. 1. Temperature–enthalpy profile according to data from Remeljej and Hoadley (2006) compared to

that published by Lee (2001).

In order to model the natural gas stream in HYSYS, this work determines the conditions of

the stream (composition, flow rate, inlet and outlet pressures, etc.) through an optimisation

approach that minimises the sum of squared enthalpy differences in the T–H profile

generated with the optimised stream and that provided in Table 4.1, as illustrated in Figure

4.2. The objective function to minimise is that in Equation 4.1. The stream T–H profile is

affected by the composition of the stream, the flow rate and the inlet and outlet pressures.

Thus, the variables to optimise are the natural gas mass flow rate, the molar composition,

and the inlet pressure (represented in Equation 4.1 as the vector x*). The optimisation is

performed with three different pressure drop profiles in the MSHE: i) linear dependence on

the temperature change; ii) linear dependence on the heat rejected by the natural gas stream

(enthalpy change); and iii) zero pressure drop assumed inside the MSHE (i.e. Pin = Pout).

The natural gas is assumed to be composed of methane, ethane, propane, n-butane, i-

butane and nitrogen.

𝑓(𝐱∗) = ∑ (∆𝐻𝑖 − ∆𝐻𝑐𝑎𝑙𝑐)29𝑖=1 𝑖 = 1,2, … ,9 (4.1)

where x* = [x1, x2, x3, x4, x5, m, Pin]

ΔHi = Enthalpy change value of Lee’s natural gas stream at the ith temperature segment

ΔHcalc = Enthalpy change value of the optimised stream at the ith temperature segment

xj = Mole fraction of the jth component in the optimised natural gas stream

m = Normalised value for the mass flow rate of the optimised natural gas stream

Pin = Normalised value for the inlet pressure of the optimised natural gas stream

-200

-150

-100

-50

0

50

0 5 10 15 20 25

Tem

per

atu

re [

°C]

ΔH [MW]

Remeljej and Hoadley (2006)

Lee (2001)


96

Figure 4. 2. Determination of the natural gas stream conditions through minimisation of the sum of squared

difference of the enthalpy profiles against the data provided by Lee (2001, Ch. 4).

Because the T–H profile of the natural gas depends on the interactions between its

components, and on the overall composition, pressures and flow rate, the optimisation is

performed using fmincon solver in MATLAB for nonlinear problems (The MathWorks

Inc., 2013). Table 4.2 shows the conditions of the natural gas stream that are obtained from

the optimisation. The optimisation in which zero pressure drop is assumed inside the

MSHE resulted in the closest match of the T–H profiles between the optimised stream and

the data originally presented by Lee (2001), as shown in Figure 4.3. According to the flow

rate of the natural gas obtained (24.03 kg·s-1

), the LNG production is 0.75 million t per

annum.

Table 4. 2. Natural gas stream conditions resulted from the optimisation (zero pressure drop in the MSHE).

Composition [mole fraction] Flow rate Inlet pressure

C1 C2 C3 n-C4 N2 i-C4 [kg·s-1

] [bar]

0.9000 0.0940 0.0047 0.0013 0.0000 0.0000 24.03 43.86


97

Figure 4. 3. Temperature–enthalpy profile of the optimised stream compared to the data provided by Lee

(2001).

The resulting molar flow rate of the optimised natural gas stream is 1.37 kmol·s-1

, which is

higher than that stated by Zheng (2009) (1 kmol·s-1

). Although the value of molar flow rate

is the same as that obtained from Remeljej and Hoadley (2006), the corresponding mass

flow rate is nearly 6% greater in the optimised natural gas stream (i.e. 24.03 kg·s-1

compared to 22.60 kg·s-1

), as a result of the difference in composition,. The composition of

the optimised natural gas stream is compared to that provided by Remeljej and Hoadley

(2006) in Table 4.3. The ethane and propane mole fractions are increased by nearly 0.065

and 0.004, respectively, in the optimised stream compared to that from Remeljej and

Hoadley (2006); the mole fraction of methane, on the other hand, is decreased by nearly

0.070 in the optimised natural gas stream.

Table 4. 3. Composition of optimised natural gas stream compared to that of Remeljej and Hoadley (2006).

Natural gas composition [mole fraction]

C1 C2 C3 n-C4 N2 i-C4

Optimised natural gas stream 0.9000 0.0940 0.0047 0.0013 0.0000 0.0000

Remeljej and Hoadley (2006) 0.9693 0.0294 0.0006 0.0001 0.0006 0.0000

The CryoMan process is simulated in HYSYS using the ‘reconstructed’ natural gas stream

obtained by optimisation (Table 4.2), and the conditions of the CryoMan process reported

in Zheng (2007) – shown in Table 4.4 and Figure 4.4 –, in order to compare the

refrigeration cycle simulation results against those reported by Zheng (2009). The ‘Label’

column in Table 4.4 refers to the letters in the CryoMan process shown in Figure 4.4.

-200

-150

-100

-50

0

50

0 5 10 15 20 25

Tem

per

atu

re [

°C]

ΔH [MW]

OptimisationLee (2001)


98

Also, in the simulation in HYSYS, the pressure drop of the refrigerant streams in the

MSHE is assumed to be negligible and the T–H profile of each stream is calculated at

equally-spaced intermediate temperatures between their corresponding MSHE inlet and

outlet temperatures. Physical and thermodynamic properties of the refrigerant streams (e.g.

temperatures, enthalpies, etc.) are calculated using the Peng–Robinson equation of state.

The refrigerant compression is performed with 4 compression stages, assuming refrigerant

intercooling to 30°C between compression stages.

The main results of the CryoMan process simulation (performance indicators) are also

presented in Table 4.4. The shaft power consumption of the CryoMan process is expressed

as the total shaft power (MW) needed for the liquefaction of the natural gas stream, and is

also expressed as specific shaft power consumption (kWh·kg-1

of LNG). The specific shaft

power demand is used for comparisons of the novel refrigeration cycles against the

CryoMan process, and can also be used for comparisons against refrigeration cycles for

LNG processes reported in the literature.

According to the simulation in HYSYS, the total shaft power demand is 25.93 MW, which

is within 0.5% of the value reported, 26.05 MW (Zheng, 2009). The shaft power demand in

the CryoMan process, obtained from the simulation in HYSYS, represents a specific shaft

power consumption of 0.2997 kWh·kg-1

of LNG. The minimum temperature approach in

the MSHE is 4.9°C in the simulation, compared to 5.0°C reported by Zheng (2009). The

simulation of the CryoMan process in HYSYS may thus be seen to be in good agreement

with the reported data, and the natural gas stream is used to evaluate the novel refrigeration

cycles.

Total shaft power for compression (MW) is used during the sensitivity analyses and

examples in this chapter; the specific shaft power demand (kWh·kg-1

of LNG) is used to

compare the novel refrigeration cycles at the best conditions found through sensitivity

analyses.


99

Table 4. 4. The CryoMan process (Zheng, 2009): inputs to HYSYS using the natural gas stream of Table 4.2.

Label in Figure 4.4 Degree of freedom Input Value

A Refrigerant flow rate [kmol·s-1

] 3.2

A Composition [mole fraction]

- Methane 0.2288

- Ethane 0.3703

- Propane 0.1684

- n-Butane 0.1517

- Nitrogen 0.0808

A Discharge pressure [bar] 48.3

B Vapour flow rate fraction 0.883

C Liquid flow rate fraction 0.223

LP Stream HP Stream

D Precooling temperature [°C] –164.6 –79.0

E Expansion pressure [bar] 1.2 9.6

F MSHE outlet temperature [°C] 21.2 24.3

Performance indicators

Number of compression stages 4

ΔTMIN [°C] 4.9

Total shaft power [MW] 25.93

Specific shaft work [kWh·kg-1

LNG] 0.2997

Figure 4. 4. The CryoMan process.

4.3 Sensitivity analyses: Manipulation of the degrees of freedom in the novel

refrigeration cycles

Each novel refrigeration cycle is initially simulated with the same values of the operating

variables as those in the CryoMan process (see Table 4.4 and Figure 4.4). The values of the

new degrees of freedom for the initial simulations are presented in Section 4.4.1 for the

Bypass design, in Section 4.5.1 for the Two Flash Levels design, and in Section 4.6.1 for

the Mixing After Precooling design.

In order to keep consistency with the CryoMan process, a minimum temperature approach

of 5°C in the MSHE is defined for feasible heat transfer between hot and cold streams; the

values for the new degrees of freedom in each novel design are thus selected to achieve a


100

feasible simulation. Table 4.5 summarises other modelling assumptions and constraints

which are considered in this work in order to maintain consistency with Zheng (2009). The

Peng–Robinson equation of state is used to calculate physical and thermodynamic

properties of the refrigerant mixture (such as enthalpies, entropies, temperatures, phase

equilibrium, etc.).

Table 4. 5. Assumptions in the novel refrigeration cycles to maintain consistency with Zheng (2009).

Compressor MSHE Throttle Valves Condenser Flash Unit Streams

Mixing

Multistage

centrifugal ΔTMIN = 5°C

Isenthalpic

expansion

Refrigerant leaves

at 30°C

Zero pressure

drop Isobaric

Efficiency

ηIS = 80% Zero pressure drop - Zero pressure drop - -

Intercooling

at 30°C - - - - -

As the operating variables of the novel refrigeration cycles are manipulated, the minimum

temperature approach in the MSHE is calculated in HYSYS by comparing a user-specified

number of intermediate temperature values from the hot composite curve against the

corresponding values in the cold composite curve; each temperature comparison between

the hot and cold composite curves is evaluated at the same enthalpy value. Because each

variable is manipulated independently of the remaining variables (i.e. interactions between

the variables are not considered), the constraint of 5°C as minimum temperature difference

between hot and cold streams in the MSHE would reduce significantly the range in which

each variable can be manipulated. Thus, a minimum temperature approach range of

5±0.3°C is considered during the sensitivity analyses.

Sensitivity analyses are performed within HYSYS for the novel refrigeration cycles for

each degree of freedom except for the refrigerant composition, which is manipulated using

MATLAB (see Section 4.3.1). While the selected operating variable is varied, the

remaining degrees of freedom are held constant.

4.3.1 Manipulation of the refrigerant composition

The composition of the refrigerant is complicated to manipulate and to analyse in the

sensitivity analyses. For example, if the mole fraction of a component in the mixture is

decreased, the remaining mole fractions must also be modified to ensure the sum of mole

fractions is unity. Different approaches can be used to manipulate the composition. For

instance, when increasing the mole fraction of one of the components, the reduction of the

remaining proportion can be distributed on an equal share among the other components, or


101

the mole fraction of the remaining components can be changed while keeping their initial

proportions constant. The resulting compositions for the sensitivity analyses, and their

corresponding impact on the refrigeration cycle performance, depend on the method of

adjusting the composition.

The method selected to vary the composition of the refrigerant during the sensitivity

analyses is to vary the mole fraction of one component while keeping constant the initial

proportions of the remaining components in the refrigerant mixture. This method ensures

that when a component, for example propane, is increased, only its mole faction is

increased and the relative contributions of the remaining components stay constant (see

Figure 4.5). A code was developed in MATLAB (The MathWorks Inc., 2013) to calculate

the refrigerant composition, and linked to Aspen HYSYS to input the refrigerant

composition to the simulation. The initial mole fraction of the components is first input in

the code. Equation 4.2 is employed to calculate the initial proportion of the ith component

in the refrigerant mixture. The reference component in the refrigerant mixture is varied

from 0.05 to 0.95 on a mole fraction basis (xref). As the mole fraction of xref is manipulated,

the mole fraction of the remaining components (xi) is calculated with Equation 4.3

according to their corresponding proportion in the initial composition. The composition of

the optimised CryoMan process (see Table 4.4) is used to calculate the initial proportions

of the components in the refrigerant mixture, which allow calculating the overall

composition of the refrigerant while each component is manipulated.

φ𝑖 =𝑥𝑖

𝑖𝑛𝑖𝑡𝑖𝑎𝑙

1−𝑥𝑟𝑒𝑓𝑖𝑛𝑖𝑡𝑖𝑎𝑙 ; 𝑥𝑖 , 𝑥𝑟𝑒𝑓 ∈ 𝑋𝑀𝑅 (4.2)

𝑥𝑖𝑐𝑎𝑙𝑐 = [1 − 𝑥𝑟𝑒𝑓

𝑣𝑎𝑟𝑖𝑒𝑑] ∙ φ𝑖 (4.3)

where φi = Proportion of the ith component in the initial refrigerant composition

xref = Mole fraction of the reference component

xi = Mole fraction of the ith component

XMR

= Vector for the composition of the overall refrigerant composition

initial = Indicates that the mole fraction of a component is from the initial composition

calc = Indicates the mole fraction of a component, calculated after the reference component is varied

varied = Indicates the mole fraction of the reference component as is varied from 0.05 to 0.95


102

Figure 4. 5. Example of composition manipulation: propane mole percentage is increased; the mole

percentage proportion between the remaining components remains the same.

4.4 Evaluation of the Bypass design

4.4.1 Bypass design: Initial simulation

The Bypass design, together with the values of the new degrees of freedom is shown in

Figure 4.6. As mentioned in Section 4.3, the values of the remaining degrees of freedom

are those of the optimised CryoMan process, and are shown in Table 4.4. The values of the

new degrees of freedom are chosen in order to achieve a feasible simulation, i.e. a

minimum temperature approach of 5°C between the composite curves in the MSHE. As

shown in Figure 4.6, the flow rate of the refrigerant is increased (3.75 kmol·s-1

), compared

to 3.21 kmol·s-1

in the CryoMan process, because the Bypass Stream reduces by 15% the

flow rate fed to the flash unit. These values are the initial conditions used to evaluate the

Bypass design through sensitivity analyses.

Figure 4. 6. The Bypass design showing the new degrees of freedom and initial values.

23.6%

37.9%

15.0%

15.4%

8.2%

Methane Ethane Propane n-Butane Nitrogen

22.2%

35.7%

20.0%

14.5%

7.7%


103

The initial simulation resulted in shaft power demand of 26.81 MW (0.3099 kWh·kg-1

of

LNG) for refrigerant compression, which is 3.4% higher than that of the CryoMan process.

The minimum temperature approach between the composite curves in the MSHE is 5.3°C.

4.4.2 Bypass design: Sensitivity studies and discussion

The bypass flow rate fraction is varied and the effect on the shaft power demand

(diamonds) as well as on the minimum driving force in the MSHE (squares) is displayed in

Figure 4.7a. The shaft power demand decreases from 29 MW to 26 MW as the bypass flow

ratio is varied from 0.05 to 0.19.

As the flow rate in the Bypass Stream increases, the flow rate fed to the flash unit

decreases. Thus, increasing the Bypass Stream (which is compressed from 20 bar) implies

reducing the flow rate of Stream 1, which is compressed from 1.2 bar. A greater flow is

compressed from only 20 bar to 48.3 bar as the bypass flow rate fraction increases, and the

shaft power consumption decreases accordingly. However, Stream 1 is the only cold

stream that provides cooling in the temperature range from –170°C to –95°C (see Figure

4.7b), and as the flow rate fraction of the Bypass Stream is increased further (above 0.17),

the flow rate of Stream 1 (1.73 kmol·s-1

) fails to provide cooling to the hot streams in the

MSHE while maintaining a minimum temperature difference of 5°C. Thus, increasing the

bypass flow rate fraction reduces the flow rate of Stream 1 to bring shaft power savings but

decreasing the flow rate of Stream 1 may also result in infeasible heat transfer inside the

MSHE (i.e. minimum temperature approach between hot and cold streams less than 5°C).

Figure 4. 7. Effect of increasing the Bypass Stream flow rate fraction: a) shaft power demand and minimum

driving force in the MSHE; b) the composite curves in the MSHE.

Increasing the pressure level of the Bypass Stream also reduces the shaft power

consumption of the refrigeration cycle (see diamonds in Figure 4.8a). As the pressure level

of the Bypass Stream is increased from 15 bar to 25 bar, the shaft power demand decreases


104

from 28.1 MW to 26.3 MW. This decreasing trend in the shaft power demand is expected

because, as illustrated in the pressure–enthalpy diagram of a refrigeration cycle of Figure

4.8b, the shaft power required for refrigerant compression decreases as the expansion

pressure (refrigerant pressure level) increases, for a fixed compressor discharge pressure

considering the same flow rate and composition of the refrigerant and the same

compression efficiency. The minimum temperature difference between the composite

curves in the MSHE is unaffected by the variation of the pressure level of the Bypass

Stream (squares in Figure 4.8a). This null effect on the minimum driving force indicates

that the minimum temperature approach of the composite curves in the MSHE is not within

the temperature range in which the Bypass Stream provides cooling (i.e. between –95°C

and 7°C according to Figure 4.6). According to the sensitivity analyses, higher pressure

levels of the Bypass Stream (compared to the initial pressure level, 20 bar) would help to

reduce the shaft power demand in the refrigeration cycle.

Figure 4. 8. Effect of increasing the pressure level of the Bypass Stream: a) shaft power demand and

minimum driving force in the MSHE; b) P–H diagram.

The effect of the compressor discharge pressure on the shaft power for refrigerant

compression (diamonds) and minimum driving force in the MSHE (squares) is shown in

Figure 4.9a. The shaft power required for refrigerant compression hardly changes (increase

from 26.76 MW to 26.81 MW) as the discharge pressure increases from 43 bar to 49 bar.

As the discharge pressure is increased further, from 49 bar to 52 bar in Figure 4.9a

(diamonds), the shaft power consumption decreases to 26.79 MW. Increasing the

compressor discharge pressure significantly reduces the minimum driving force in the

MSHE (squares in Figure 4.9a). As the compressor discharge pressure increases, more

liquid refrigerant is obtained after the condenser; this effect of pressure on the vapour

fraction of the refrigerant at the condenser temperature is illustrated with an isotherm in a

P–H diagram in Figure 4.9b. Increasing the pressure reduces the vapour fraction of the


105

refrigerant, i.e. the liquid fraction of the refrigerant increases. The flow rate of Stream 1 is

consequently reduced. Beyond 50 bar, the flow rate of Stream 1 (1.71 kmol·s-1

) is not able

to provide cooling to the hot streams in the MSHE while meeting the minimum

temperature difference constraint (see squares in Figure 4.9a). The sensitivity analyses thus

suggest that the compressor outlet pressure should decrease, compared to the base case

(48.3 bar), to avoid infeasible heat transfer in the MSHE.

Figure 4. 9. Effect of increasing the compressor discharge pressure: a) power demand and minimum driving

force; b) the vapour fraction of the refrigerant.

The flow rates of Stream 1 and Stream 2 are also controlled by the flow rate fractions of

the vapour (f Vap

) and liquid (f Liq

) that are partially mixed after the flash unit (labelled ‘B’

and ‘C’ in Figure 4.6, respectively). Both variables indicate the fraction of their

corresponding flow rates that is mixed to create Stream 1. Figure 4.10 shows how the flow

rates of Stream 1 and Stream 2 (diamonds and squares in Figure 4.10b, respectively)

change as f Liq

is increased from 0.15 to 0.35, which leads to increasing the shaft power

demanded by the refrigeration cycle (diamonds in Figure 4.10a). As the liquid flow rate

fraction increases from 0.15 to 0.35, the shaft power demand increases from 26 MW to

28.2 MW. Increasing f Liq

increases the flow rate of Stream 1 (which is at the lowest

pressure level), leading to increase in the shaft power demand. As the value of f Liq

is

decreased below 0.19, the flow rate of Stream 1 (1.68 kmol·s-1

) cannot provide cooling to

the hot streams in the MSHE with a minimum temperature difference of at least 5°C (see

squares in Figure 4.10a).


106

Figure 4. 10. Effect of increasing the flow rate fraction of liquid from the flash unit (f

Liq): a) shaft power

demand and minimum driving force in the MSHE; b) flow rates of Stream 1 and Stream 2.

Additionally, as f Liq

increases, the composition of Stream 1 yields a higher specific heat of

vaporisation (see Figure 4.11a). That is, the heat required to fully vaporise 1 kmol of the

refrigerant increases as the amount of liquid that is fed to Stream 1 increases. The heat of

vaporisation is a function of the composition of the refrigerant, at a fixed pressure, and

increases as the composition of the stream becomes richer in ‘heavy’ components (i.e.

propane and n-butane), which have greater heat of vaporisations compared to ‘light’

components (nitrogen, methane and ethane), as exemplified in Figure 4.11b.

Figure 4.11b shows the heat of vaporisation of the streams involved in a flash separation in

order to have three streams (inlet refrigerant, vapour phase and liquid phase) with different

compositions. According to Figure 4.11b, less refrigerant flow would be required, to

provide the same cooling duty, with the liquid phase stream since its heat of vaporisation is

greater than that of the inlet refrigerant and of the vapour phase stream. Thus, increasing

the heat of vaporisation of Stream 1 may help to reduce the overall refrigerant flow rate.

Reducing the overall refrigerant flow rate would reduce the shaft power consumption.

Consequently, a trade-off exists between decreasing the value of f Liq

to reduce of flow rate

of Stream 1, which would bring shaft power savings, and increasing the value of f Liq

to

modify the composition of Stream 1, increasing its heat of vaporisation and reducing the

overall refrigerant flow rate to bring shaft power savings. The sensitivity analyses suggest

that decreasing f Liq

would rather take advantage of reducing the flow rate of Stream 1,

leading to shaft power savings in the refrigeration cycle (see diamonds in Figure 4.10a).


107

Figure 4. 11. a) Increasing the value of f

Liq increases the heat of vaporisation of Stream 1; b) heat of

vaporisation of the refrigerant is increased as heavy components in the composition are increased.

The effect of the overall composition of the refrigerant on the power demand is shown for

each component in Figure 4.12 as the line with diamonds in each plot. The descending

trends of the power demand observed as the proportion of propane (Figure 4.12c) and n-

butane (Figure 4.12d) increases agrees with the discussion in Section 3.2.1; in this section

it was seen that the shaft power for compression decreases as the mole fraction of the

heavier components (i.e. propane and n-butane, compared to ethane, methane and nitrogen)

increases. As the mole fraction of methane (Figure 4.12a), ethane (Figure 4.12b) and

nitrogen (Figure 4.12e) increases, the shaft power for compression increases accordingly,

although the shaft power demand is less sensitive to changes in the mole fraction of ethane.

For example, the power demand increases by 2 MW as the mole fraction of methane

increases by 0.05, whereas the shaft power increases by only 0.1 MW as the mole fraction

of ethane increases by 0.05. However, the mole fraction of each component can be varied

only within a limited range, in order to meet the constraint of minimum temperature

approach inside the MSHE.

The minimum temperature approach between the composite curves inside the MSHE is

also represented in each plot of Figure 4.12 (squares). As can be seen in Figure 4.12, the

range of compositions for which heat transfer is feasible (i.e. minimum temperature

approach inside the MSHE of 5°C) is highly constrained. For example, in Figure 4.12a

feasible heat transfer is potentially achieved only with the compositions obtained when the

mole fraction of methane in the refrigerant mixture is greater than 0.20 but less than 0.30.

Table 4.6 shows the mole fraction ranges of each component in which the composition

could result in feasible heat transfer according to the sensitivity analyses.

The composition of the overall refrigerant stream determines the flow rate and composition

of the flash unit product streams (at fixed compressor discharge pressure and condenser


108

temperature). Because the mixing flow rate fractions of vapour and liquid, and the flow

rate fed to the flash unit are held constant, the overall composition determines the actual

molar flow rates and compositions of Stream 1 and Stream 2. Increasing the flow rate of

Stream 1 reduces the flow rate of Stream 2, and vice versa. Thus, as the composition of the

overall refrigerant stream is varied, infeasible heat transfer comes from reducing either

Stream 1 or Stream 2.

Figure 4. 12. Effect of composition on power demand and minimum driving force in the Bypass design:

a) methane; b) ethane; c) propane; d) n-butane; e) nitrogen.

Table 4. 6. Composition ranges for feasible heat transfer in the Bypass design.

Lower bound [mole fraction] Upper bound [mole fraction]

Methane 0.20 0.30

Ethane 0.30 0.40

Propane 0.10 0.20

n-Butane 0.05 0.20

Nitrogen 0.05 0.15

As the mole fraction of the light components (methane, ethane and nitrogen) increases, two

effects take place: i) the vapour fraction of the refrigerant mixture at the condenser


109

temperature increases (illustrated in Figure 4.13a), and ii) the heat of vaporisation of the

refrigerant decreases (previously illustrated with Figure 4.11b). As the mole fraction of the

light components increases, the molar flow rate of vapour leaving the flash unit increases,

which leads to increasing the flow rate of Stream 1 and reducing the molar flow rate of

Stream 2 (since the flow rate fed to the flash unit and the vapour and liquid flow rate

fractions partially mixed are constant). Increasing the molar flow rate of Stream 1 leads to

increasing compression shaft power. Additionally, for example, when methane represents

over 30% mole of the refrigerant mixture, the molar flow rate of Stream 2 is not able to

provide cooling to the hot streams in the MSHE with a minimum temperature difference of

5°C (according to Table 4.6).

As the mole fraction of methane increases, the specific heat of vaporisation of the overall

refrigerant stream decreases. Thus, a refrigerant with a low specific heat of vaporisation

would require a greater molar flow rate to provide the same cooling duty compared to a

refrigerant with a high heat of vaporisation, as previously discussed and illustrated with

Figure 4.11b. However, a refrigerant with light components can provide cooling at colder

temperatures than a refrigerant with heavy components, at the same pressure level, because

light components evaporate at lower temperatures (see Figure 4.13b).

On the other hand, as mole fraction of the heavy components (propane, n-butane) increase

in the refrigerant mixture, the opposite effects occur compared to the increase of light

components mole fraction: for instance, when n-butane represents over 20% mole of the

refrigerant mixture (according to Table 4.6), the liquid condensed and separated in the

flash unit increases; the flow rate of Stream 1 decreases to bring shaft power savings but is

not able to provide cooling in the MSHE with a minimum driving force of 5°C. This

infeasible heat transfer occurs despite the increase of the specific heat of vaporisation in

the refrigerant stream.

Thus, a complex trade-off exists in the selection of the overall refrigerant composition:

heavy components can provide larger cooling duties per unit mole than light components,

which would reduce the overall refrigerant flow rate and bring shaft power savings;

however, light components provide cooling at colder temperatures (compared to heavy

components) at the same pressure level, but at the expense of increasing the shaft power

demand since light compositions require more shaft power for compression than heavy

compositions (see Section 3.2.1).


110

Figure 4. 13. As the overall refrigerant composition becomes lighter: a) its vapour fraction increases; and

b) its evaporating temperature decreases.

4.4.3 Bypass design: Manipulation of its degrees of freedom

According to the trends and trade-offs observed in the sensitivity analyses previously

discussed, the degrees of freedom in the Bypass design are then manipulated in order to

reduce the shaft power consumption for refrigerant compression. The initial values of the

degrees of freedom are those of the initial simulation (see Section 4.4.1). As mentioned in

Section 4.3, a minimum temperature approach of 5±0.3°C is considered for feasible heat

transfer during the manipulation of the degrees of freedom.

For example, Figure 4.14a shows the manipulation of the Bypass Stream flow rate fraction,

which is increased from 0.15, in the initial simulation, to 0.17, and the shaft power demand

is reduced from 26.8 MW to 26.4 MW while the minimum temperature difference in the

MSHE is reduced from 5.3°C to 4.8°C. Increasing the Bypass Stream flow rate fraction

takes advantage of reducing the flow rate of Stream 1 from 1.77 kmol·s-1

to 1.73 kmol·s-1

.

In Figure 4.14b, the fraction of the liquid stream leaving the flash unit and mixed to create

Stream 1 (f Liq

) is manipulated after the value of the Bypass Stream flow rate fraction is

changed. The value of f Liq

is decreased from 0.22 to 0.20, which further reduces the flow

rate of Stream 1 (to 1.69 kmol·s-1

) and the shaft power demand (to 26.1 MW). The

minimum temperature approach in the MSHE remains as 4.8°C.


111

Figure 4. 14. Manipulation of the operating variables in the Bypass design: a) Bypass Stream flow rate

fraction is varied; b) the liquid mixing fraction (f Liq

) is varied.

Each of the operating variables of the Bypass design is manipulated in order to reduce the

shaft power demand, as illustrated with Figure 4.14, and the values that yield the lowest

shaft power demand are shown in Table 4.7. The ‘Label’ column in Table 4.7 refers to the

letters in the Bypass design shown in Figure 4.6. The shaft power demand is 25.68 MW

(0.2968 kWh·kg-1

of LNG), i.e. a reduction of 1% compared to the CryoMan process. The

minimum temperature approach between the composite curves in the MSHE is 5.1°C.

Table 4. 7. Operating variables of the Bypass design after the sensitivity analyses.

Label in Figure 4.6 Process variable Value


] 3.65

A Composition [mole fraction]:

- Methane 0.2569

- Ethane 0.3552

- Propane 0.1650

- n-Butane 0.1547

- Nitrogen 0.0682

A Discharge pressure [bar] 41

A Bypass fraction 0.13



Stream 1 Stream 2 Bypass

D Precooling temperature [°C] –163 –68 –73

E Expansion pressure [bar] 1.2 7.5 20

F MSHE outlet temperature [°C] 15 25 24

Performance indicators


ΔTMIN [°C] 5.1


Specific shaft power [kWh·kg-1

LNG] 0.2968

Shaft power savings (%) 1.0

Even though the mole fraction of methane (light component) in the overall refrigerant

stream is increased, the results in Table 4.7 suggest that the Bypass design takes advantage

of reducing the flow rate of Stream 1 by creating the Bypass Stream to bring shaft power

savings. The overall refrigerant flow rate is reduced (3.75 kmol·s-1

in the initial simulation

compared to 3.65 kmol·s-1

in Table 4.7); the flow rate fraction of the liquid stream leaving


112

the flash unit (f Liq

), mixed to create Stream 1, is decreased from 0.22 (in the initial

simulation) to 0.08, while the bypass flow rate fraction is also decreased from 0.15 (initial

simulation) to 0.13. The Bypass design appears to offer advantages compared to the

CryoMan process.

Further power savings are likely to be achieved in the Bypass design if its operating

variables are optimised. Therefore, the Bypass design is considered for optimisation using

WORK software, as presented in Chapter 5.

4.5 Evaluation of the Two Flash Levels design

4.5.1 Two Flash Levels design: Initial simulation

The Two Flash Levels design and the initial values of the new degrees of freedom are

shown in Figure 4.15. These initial values are chosen in order to achieve a feasible

simulation (i.e. the minimum temperature difference between hot and cold streams inside

the MSHE is 5°C). The values of the remaining degrees of freedom are those of the

CryoMan process (see Section 4.3).

Note that the order in which the refrigerant streams are fed to the compressor, according to

Figure 4.15, does not represent the actual arrangement of the refrigerant streams in the

compressor. The order of the refrigerant streams shown in Figure 4.15 is only for clarity in

labelling the streams and values of the operating variables of the new degrees of freedom

in the Two Flash Levels design.

Figure 4. 15. The Two Flash Levels design showing the new degrees of freedom and initial values.


113

According to the initial simulation of the Two Flash Levels design, the resulting shaft

power demand is 26.78 MW (0.3096 kWh·kg-1

of LNG), which is 3.3% greater than that of

the CryoMan process; the minimum driving force for heat transfer in the MSHE is 5.2°C.

Similar to the Bypass design, the refrigerant flow rate increases compared to the CryoMan

process (by nearly 1.3%, to 3.25 kmol·s-1

) since 30% of the liquid produced from the first

flash unit is fed to the second flash separator (initial value for the simulation) and

consequently the minimum temperature approach in the MSHE would be less than 5°C for

the initial flow rate.

Note that, in the CryoMan process (Figure 4.4), the LP Stream (at 1.2 bar) is compressed in

two compression stages to the pressure level of the HP Stream (9.6 bar) (the maximum

pressure ratio is 3), which leads to one intermediate pressure level between the pressure

levels of the LP Stream and the HP Stream (see Figure 4.16a). In the initial conditions of

the Two Flash Levels design, the pressure level of the new two streams (2.4 bar for Stream

3 and 4.8 bar for Stream 4) are accommodated between the pressure levels of Stream 1 and

Stream 2 (1.2 bar and 9.6 bar, respectively), as illustrated in Figure 4.16b. Consequently,

the compression of Stream 1 (at 1.2 bar) to the pressure level of Stream 2 (9.6 bar) in the

Two Flash Levels design is performed in three compression stages. Therefore, the overall

compression of the refrigerant takes place with 5 compression stages, compared to 4

compression stages in the CryoMan process. Since after each compression stage the

refrigerant is cooled down to 30°C with an intercooler (as illustrated in Figure 4.16) that

helps reducing the shaft power demand, the Two Flash Levels design would take

advantage of the additional compression stage and associated intercooling stage. However,

this additional compression stage would also increase the capital costs of the Two Flash

Levels design.


114

Figure 4. 16. Streams arrangement in the multistage compressor: a) CryoMan process;

b) Two Flash Levels design.

4.5.2 Two Flash Levels design: Sensitivity studies and discussion

Similar to the Bypass design, the variables of the Two Flash Levels design are evaluated in

terms of their effect on shaft power demand and minimum temperature approach between

the composite curves in the MSHE. Trends of the operating variables are presented and

discussed, where the aim is to reduce the shaft power demand in the novel refrigeration

cycle.

The effect of the flow rate fraction that is fed to the second flash unit (f 2nd

), on the shaft

power demand (diamonds) of the refrigeration cycle and minimum temperature approach

in the MSHE (squares), is shown in Figure 4.17a. The shaft power demand increases from

26 MW to 27.9 MW as the flow rate fraction fed to the second flash unit increases from

0.15 to 0.50 (Figure 4.17a). Since the flow rate fraction of liquid from the first flash unit (f

Liq), mixed to create Stream 1, is held constant, increasing f

2nd reduces the flow rate of

Stream 2 to create the new streams after the second flash unit (Stream 3 and Stream 4) (see

Figure 4.17b). The pressure levels of Stream 3 and Stream 4 are 2.4 bar and 4.8 bar,

respectively, whereas the pressure level of Stream 2 is 9.6 bar. Thus, as fraction f 2nd

is

increased, the refrigerant flow rate at lower pressure levels than that of Stream 2 (9.6 bar)

is increased accordingly. As previously illustrated in Figure 4.8b, the shaft power demand

is increased as the difference between the refrigerant pressure level and the compressor


115

discharge pressure is increased. Thus, reducing f 2nd

would decrease the shaft power for

refrigerant compression. However, as f 2nd

is decreased below 0.20, the cold streams in the

MSHE fail to provide cooling to the hot streams with a minimum temperature difference of

5°C in the MSHE (Figure 4.17a), which indicates that the minimum temperature difference

between the composite curves in the MSHE is in the temperature range in which Stream 3

and Stream 4 provide cooling (i.e. from –63°C to 7°C). So, reducing f 2nd

(below 0.30)

would help reducing the total shaft power demand because the flow rate at a high pressure

level (Stream 1 at 9.6 bar) is increased compared to that at pressure levels of Stream 3 and

Stream 4 (2.4 bar and 4.8 bar, respectively), but values below 0.20 may lead to infeasible

heat transfer within the MSHE.

Figure 4. 17. Effect of increasing the flow rate fraction of liquid fed to the second flash unit (f

2nd): a) shaft

power demand and minimum driving force in the MSHE; b) flow rate of Stream 2.

The pressure in the second flash unit (P2nd

in Figure 4.15) is varied from 15 bar to 35 bar;

the effect on the power demand (diamonds) and minimum temperature approach in the

MSHE (squares) is presented in Figure 4.18a. The variation of the shaft power demand is

negligible (diamonds in Figure 4.18a), decreasing by 0.05 MW over the whole pressure

range. The minimum temperature difference between hot and cold streams in the MSHE

(squares in Figure 4.18a) decreases as the pressure in the second flash unit is increased.

The pressure in the second flash unit determines the vapour-liquid equilibrium of the

refrigerant; the temperature of the refrigerant before the throttle valve of the second flash

unit is assumed to be that of the condenser, and the pressure and composition of the

refrigerant before the throttle valve are held constant. The pressure in the second flash unit

thus determines the flow rate of vapour and liquid leaving the second flash unit and their

corresponding composition.

Because Stream 3 and Stream 4 are created by partially mixing the vapour and liquid from

the second flash unit, the pressure of the second flash unit would then affect the flow rate


116

of Stream 3 and Stream 4 and their corresponding composition. For example, Figure 4.18b

shows the effect of the pressure in the second flash unit on the flow rate (diamonds) and

heat of vaporisation, ΔHvap (squares, related to the composition), of Stream 3. As the

pressure increases from 15 bar to 35 bar, the heat of vaporisation of Stream 3 is increased

by 1.6% and, according to the discussion of Figure 4.11b in Section 4.4.2, would help to

reduce the overall flow rate fed to the second flash unit to bring shaft power savings. On

the other hand, as P2nd

is increased, the vapour fraction of the refrigerant stream fed to the

second flash is reduced, decreasing the flow rate of Stream 3 by 8%. Consequently, the

minimum temperature approach in the MSHE is decreased from 5.3°C to 5.0°C (squares in

Figure 4.18a). Thus, as P2nd

increases, there is a trade-off between increasing the heat of

vaporisation of Stream 3 or Stream 4 to reduce the refrigerant flow rate in the second flash

unit, and reducing the flow rate of Stream 3 or Stream 4 leading to infeasible heat transfer.

Figure 4. 18. Effect of increasing the pressure of the second flash unit (P

2nd): a) power demand and minimum

driving force in the MSHE; b) heat of vaporisation and flow rate of Stream 3.

Figure 4.19a shows the effect of the precooling temperature of Stream 3 on the power

demand (diamonds) and minimum temperature approach in the MSHE (squares). As the

precooling temperature of Stream 3 is decreased, the flow rate of the refrigerant would be

expected to increase because the cooling duty in the MSHE would increase (and so would

the shaft power demand) in order to maintain a constant minimum temperature difference

between hot and cold streams in the MSHE. However, the flow rate of the refrigerant is

held constant during the sensitivity analyses and therefore, the minimum temperature

difference in the MSHE would vary and indicate the temperature range in which Stream 3

can be precooled with the current refrigerant flow rate (3.25 kmol·s-1

) with feasible heat

transfer, and the shaft power demand would remain constant.

In Figure 4.19a (squares), the minimum temperature approach in the MSHE remains

constant at 5.2°C as the precooling temperature of Stream 3 increases from –93° to –63°C;


117

the minimum temperature approach then decreases when the precooling temperature of

Stream 3 is further increased. As illustrated in Figure 4.19b, as the precooling temperature

of the mixed refrigerant stream decreases, at fixed pressure, the temperature at which the

stream provides cooling, once expanded at the throttle valve outlet pressure, decreases

accordingly. Thus, the evaporating temperature of Stream 3 increases as its precooling

temperature increases. At precooling temperatures above –55°C, Stream 3 evaporates at

temperatures above –75°C, resulting in infeasible heat transfer at around –80°C, (see

Figure 4.19c). To avoid infeasible heat transfer inside the MSHE, Stream 3 then would

have to be precooled to temperatures below –55°C to help provide cooling at colder

temperatures. The shaft power demand (diamonds in Figure 4.19a), as previously

discussed, remain constant.

Figure 4. 19. Effect of increasing the precooling temperature of Stream 3: a) power demand and minimum

driving force in the MSHE; b) evaporating temperature; c) infeasible heat transfer in the MSHE.

The overall refrigerant composition in the Two Flash Levels design is explored according

to Section 4.3.1. Figure 4.20 displays the effect of the refrigerant composition on the shaft

power demand of the refrigeration cycle as well as on the minimum temperature approach


118

in the MSHE. Similar to the Bypass design, Figure 4.20 shows that the shaft power

demand increases when the mole fraction of the light components (i.e. methane, ethane and

nitrogen) increases, and decreases as the mole fraction of the heavy components (i.e.

propane and n-butane) increases. According to the trends of the minimum temperature

difference inside the MSHE in Figure 4.20, heat transfer is feasible potentially only within

the composition ranges shown in Table 4.8.

Figure 4. 20. Effect of composition on power demand and minimum driving force in the Two Flash Levels

design: a) methane; b) ethane; c) propane; d) n-butane; e) nitrogen.

Table 4. 8. Composition ranges for feasible heat transfer in the Two Flash Levels design.

Lower bound [mole fraction] Upper bound [mole fraction]

Methane 0.20 0.30

Ethane 0.30 0.40

Propane 0.10 0.20

n-Butane 0.10 0.20

Nitrogen 0.05 0.10

The operating variables of the Two Flash Levels design are manipulated, one variable at

the time, as exemplified in Section 4.4.2 for the Bypass design, according to the sensitivity


119

analyses and trends observed. As mentioned in Section 4.3, the minimum temperature

approach for heat transfer between hot and cold streams inside the MSHE is considered

between 4.7°C and 5.3°C. After the operating variables are manipulated in the Two Flash

Levels design, the values of the variables that result in the lowest shaft power demand for

refrigerant compression are shown in Table 4.9. The ‘Label’ column in Table 4.9 refers to

the letters in the Two Flash Levels design shown in Figure 4.15. The shaft power obtained

is 25.93 MW (0.2997 kWh·kg-1

of LNG), which is the same as that in the CryoMan

process. The minimum temperature approach in the MSHE is 4.8°C.

Table 4. 9. Operating variables of the Two Flash Levels design after the sensitivity analyses.



] 3.45


- Methane 0.2332

- Ethane 0.4000

- Propane 0.0503

- n-Butane 0.2397

- Nitrogen 0.0768

A Discharge pressure [bar] 41

H Pressure 2nd flash unit [bar] 30

G Liquid fraction to 2nd flash unit 0.224

Stream 1 Stream 2 Stream 3 Stream 4

D Precooling temperature [°C] –163 –78 –43 –53

E Expansion pressure [bar] 1.2 7.5 5 18.5

F MSHE outlet temperature [°C] 17 25 25 20

B, I Vapour flow rate fraction 0.74 0.26 0.10 0.90

C, J Liquid flow rate fraction 0.25 0.526 0.20 0.80

Performance indicator


ΔTMIN [°C] 4.8



LNG] 0.2997

Shaft power savings (%) 0.0

The Two Flash Levels design thus, according to the results shown in Table 4.9, takes

advantage of decreasing the flow rate fraction fed to the second flash unit and increasing

the pressure of the second flash unit to manipulate the heat of vaporisation of Stream 3 and

Stream 4. Moreover, the pressure level of Stream 4 is increased from 4.8 bar to 18.5 bar, to

help reduce the refrigerant flow rate that is compressed at low pressure levels (i.e. 1.2 bar

of Stream 1 and 5 bar of Stream 3). Also, note that despite the increase in the pressure level

of Stream 4 from 4.8 bar to 18.5 bar, the overall refrigerant in the Two Flash Levels design

is still compressed in 5 compression stages. As discussed in Section 4.5.1, the additional

compression stage, compared to the CryoMan process, helps to reduce the shaft power

demand because of the associated intercooling stage, although at the expense of increasing

the capital costs.


120

Thus, according to Table 4.9, the Two Flash Levels design is very likely to achieve shaft

power savings, compared to the CryoMan process, once its operating variables are

optimised. Therefore, the Two Flash Levels design is considered for optimisation in

Chapter 5.

4.6 Evaluation of the Mixing After Precooling design

4.6.1 Mixing After Precooling design: Initial simulation

The Mixing After Precooling design and the values of the new degrees of freedom are

shown in Figure 4.21. The values of the remaining degrees of freedom are those of the

CryoMan process (see Section 4.3). Similar to the initial simulation of the previous novel

refrigeration cycles, the initial values of the new degrees of freedom in the Mixing After

Precooling design are chosen in order to achieve a feasible simulation.

Note that, according to Figure 4.21, Stream 1 is expanded to an intermediate pressure

(shown in Figure 4.21 as Stream 3) whereas Stream 2 is expanded to the lowest pressure

level (shown in Figure 4.21 as Stream 4). Thus, Stream 1 in the Mixing After Precooling

design is simulated with the conditions (pressure level, precooling temperature,

composition, etc.) of the HP Stream in the CryoMan process, and Stream 2 is simulated

with the conditions of the LP Stream in the CryoMan process. That is, Stream 1 and

Stream 2 in the Mixing After Precooling design are in the opposite pressure order

compared to Stream 1 and Stream 2 in the Bypass design and in the Two Flash Levels

design.

Stream 5 is created from the mixing of the flow rate fraction α (from Stream 1) and the

flow rate fraction β (from Stream 2). Because the mixing of the flow rate fractions α and β

is assumed to be isobaric, Stream 5 is constrained to have the same pressure level as

Stream 4, as illustrated in Figure 4.21.


121

Figure 4. 21. The Mixing After Precooling design showing the new degrees of freedom and initial values.

For the initial simulation, the overall refrigerant flow rate is increased to 3.65 kmol·s-1

(+13.7%), compared to 3.21 kmol·s-1

in the CryoMan process; the shaft power demand is

increased accordingly, to 30.48 MW (0.3523 kWh·kg-1

of LNG), i.e. 17.6% greater than

that of the CryoMan process. The minimum temperature approach in the MSHE is 5.0°C.

4.6.2 Mixing After Precooling design: Sensitivity studies and discussion

The effect of the flow rate fraction α (from Stream 1) on the shaft power demand and

minimum temperature approach between hot and cold streams in the MSHE, is shown in

Figure 4.22a. The heat of vaporisation of Stream 5 increases as the flow rate fraction α

increases (Figure 4.22b) which indicates that the mole fraction of heavy components (i.e.

propane and n-butane) in Stream 5 increases, as previously illustrated with Figure 4.11b.

As discussed in Section 4.4.2, as the heat of vaporisation increases, the flow rate needed

for the same cooling duty decreases. Increasing the heat of vaporisation of Stream 5 helps

to reduce the overall refrigerant flow rate to decrease the shaft power demand for

compression. On the other hand, however, increasing the heat of vaporisation of Stream 5

(by increasing flow rate fraction α) implies also increasing its flow rate. Consequently, the

shaft power demand of the refrigeration cycle (diamonds in Figure 4.22a) increases

accordingly from 29.1 MW to 31 MW because the refrigerant flow rate in the lowest

pressure level increases as the flow rate of Stream 5 increases.

Furthermore, as seen in Figure 4.22a, increasing flow rate fraction α beyond 0.15 also

leads to infeasible heat transfer. As the mole fraction of the heavy components in Stream 5

increases, its evaporating temperature increases accordingly (see Figure 4.23a), at a fixed

pressure. Consequently, when the value of flow rate fraction α is increased above 0.15,


122

Stream 5 evaporates from –129°C (compared to –132°C in the initial simulation) and the

flow rate of Stream 4 fails to provide cooling in the temperature range of –171°C to –

132°C to the hot streams in the MSHE with a minimum temperature difference of 5°C (see

Figure 4.23b). Thus, a trade-off exists, as the flow rate fraction α increases, between

increasing the heat of vaporisation of Stream 5 to reduce the overall flow rate, and

increasing the flow rate in the lowest pressure level. According to the sensitivity study in

Figure 4.22a, values below 0.15 for the flow rate fraction α would help reducing the shaft

power demand, compared to the initial values of the simulation of the Mixing After

Precooling design, and would also avoid infeasible heat transfer in the MSHE.

Figure 4. 22. Effect of increasing flow rate fraction α: a) shaft power demand and minimum driving force in

the MSHE; b) heat of vaporisation of Stream 5.

Figure 4. 23. a) Evaporating temperature of Stream 5 increases as flow rate fraction α increases; b) infeasible

heat transfer as a result of the increased evaporating temperature of Stream 5.

According to the Mixing After Precooling design shown in Figure 4.21, once hot Stream 2

is precooled in the MSHE and expanded, it is split to create cold Stream 4, and cold Stream

5 with the flow rate fraction β. As the flow rate fraction β from Stream 2 is increased, the

shaft power demand (Figure 4.24a) remains constant while the minimum temperature

difference between hot and cold streams in the MSHE continuously decreases. Because

Stream 5 and Stream 4 are at the same pressure level (the lowest pressure level, 1.2 bar),


123

both are fed to the compressor at the first compression stage. The flow rate fed to the

compressor at the first compression stage would remain constant, regardless of the

refrigerant flow rate in Stream 4 and Stream 5, because the flow rate fraction α is held

constant. Further, the composition of the stream at the inlet of the compressor would also

remain unaffected because the flow rate fraction α is held constant, even though the

composition of Stream 4 and Stream 5 might be different. Thus, as the flow rate fraction β

from Stream 2 increases, the flow rate and composition resulting from mixing Stream 4

and Stream 5 at the inlet of the compressor, after providing cooling in the MSHE, remains

the same and therefore leads to a constant shaft power demand for refrigerant compression.

However, as the flow rate fraction β is increased above 0.13, the hot and cold streams in

the MSHE are not able to transfer heat with a minimum temperature difference of 5°C (see

squares in Figure 4.24a). As the flow rate fraction β increases above 0.13, the flow rate of

Stream 4 decreases and is no longer able to provide cooling with a minimum temperature

difference of 5°C, in the temperature range between –171°C and –137°C as shown in

Figure 4.24b. Values of the flow rate fraction β lower than 0.13 would then avoid

infeasible heat transfer in the MSHE.

Figure 4. 24. Effect of increasing flow rate fraction β on: a) shaft power demand and minimum driving force

in the MSHE; b) the composite curves in the MSHE.

Regarding the effect of the overall composition of the refrigerant, Figure 4.25 shows the

trends of the shaft power demand and of the minimum temperature approach in the MSHE

as each component is manipulated, as described in Section 4.3.1. The shaft power demand

increases as the mole fraction of methane or nitrogen increases, and decreases as the mole

fraction of propane or n-butane increases. According to the minimum temperature

approach trends (Figure 4.25), the mole fraction ranges of each component in which heat

transfer is potentially feasible are those listed in Table 4.10.


124

Figure 4. 25. Effect of composition on power demand and minimum driving force in the Mixing After

Precooling design: a) methane; b) ethane; c) propane; d) n-butane; e) nitrogen.

Table 4. 10. Composition ranges for feasible heat transfer in the Mixing After Precooling design. Lower bound [mole fraction] Upper bound [mole fraction]

Methane 0.20 0.30

Ethane 0.20 0.40

Propane 0.10 0.20

n-Butane 0.05 0.20

Nitrogen 0.05 0.15

The operating variables of the Mixing After Precooling design are manipulated according

to the trends and trade-offs observed in the sensitivity analyses. As mentioned in Section

4.3, during the manipulation of the operating variables of the Mixing After Precooling

design, the range for feasible heat transfer is from 4.7°C to 5.3°C. The values of the

operating variables that yield the lowest shaft power are shown in Table 4.11. The ‘Label’

column in Table 4.11 refers to the letters in the Mixing After Precooling design shown in

Figure 4.21. The shaft power is 26.58 MW (0.3073 kWh·kg-1

of LNG, 2.5% greater than


125

that of the CryoMan process) with a minimum temperature approach of 4.8°C for heat

transfer in the MSHE.

Table 4. 11. Operating variables of the Mixing After Precooling design after the sensitivity analyses.



] 3.27


- Methane 0.2373

- Ethane 0.3500

- Propane 0.1754

- n-Butane 0.1548

- Nitrogen 0.0825


G Fraction α of Stream 1 0.02

H Fraction β of Stream 2 0.01

Stream 1 Stream 2 Stream 3 Stream 4 Stream 5

D Precooling temperature [°C] –93 –166 - - -

E Expansion pressure [bar] - - 10.8 1.2 1.2

F MSHE outlet temperature [°C] - - 25 25 5

B Vapour flow rate fraction 0.16 0.84 - - -

C Liquid flow rate fraction 0.67 0.33 - - -

Performance indicator


ΔTMIN [°C] 4.8



LNG] 0.3073

Shaft power savings (%) –2.5

The values of the new degrees of freedom in Table 4.11 are in agreement with the trends

observed during the sensitivity analyses. Reducing both flow rate fractions α and β help to

reduce the total shaft power demand of the refrigeration cycle from 30.48 MW (in the

initial simulation) to 26.58 MW. However, Table 4.11 also suggests that the trade-offs of

the operating variables in the Mixing After Precooling design are moving towards

minimising the flow rate of Stream 5, rather than increasing the heat of vaporisation of

Stream 5 to reduce the overall refrigerant flow rate. Even though Stream 5 might benefit

from the increased heat of vaporisation (by increasing both flow rate fractions α and β), the

total shaft power would increase because the compressor would receive an increased flow

rate of refrigerant at the lowest pressure level (1.2 bar) since Stream 5 is constrained to

have the same pressure level as Stream 4.

Consequently, according to Table 4.11, the structural modification in the refrigeration

cycle shows no effect towards bringing shaft power savings to the refrigeration cycle since

the values of the flow rate fractions α and β are close to zero (0.02 and 0.01, respectively).

Therefore, the Mixing After Precooling Design is not further considered for optimisation.


126

4.7 Selection of the novel designs for optimisation

According to the sensitivity studies, the Bypass design achieved shaft power savings of

1%, compared to the CryoMan process, through the manipulation of the variables. The

Bypass design benefits from reducing the flow rate of the stream in the lowest pressure

level (Stream 1 at 1.2 bar) by creating the Bypass Stream. The total shaft power demand

achieved with the Bypass design is 25.68 MW (0.2968 kWh·kg-1

of LNG).

The sensitivity analyses also show that the Two Flash Levels design benefits from an

additional compression stage (and associated intercooling stage), compared to the

CryoMan process. Manipulating the heat of vaporisation of Stream 3 and Stream 4 allows

a reduction in the refrigerant the flow rate fed to the second flash level compared to the

initial simulation. Additionally, because the pressure level of Stream 4 is increased from

4.8 bar to 18.5 bar, the refrigerant flow rate at the lowest pressure levels of the compressor

is also reduced (Stream 1 at 1.2 bar and Stream 3 at 5 bar). The Two Flash Levels design

achieved the same shaft power demand as that in the CryoMan process, i.e. 25.93 MW of

total shaft power consumption (0.2997 kWh·kg-1

of LNG).

Based on the sensitivity studies, the minimum total shaft power achieved with the Mixing

After Precooling design is 26.58 MW (0.3073 kWh·kg-1

of LNG), which is 2.5% higher

than that in the CryoMan process. The sensitivity analyses on the Mixing After Precooling

design suggest that the structural modifications proposed in the novel refrigeration cycle

(two streams partially mixed, after precooled in the MSHE, to create a new stream with

intermediate composition) would not have a significant effect on the performance of the

refrigeration cycle in order to bring shaft power savings, compared to the CryoMan

process.

Thus, the Bypass design already achieved shaft power savings of 1%, compared to the

CryoMan process, during the sensitivity analyses and is therefore considered for

optimisation of its operating variables. The Two Flash Levels design showed the same

shaft power demand as that of the CryoMan process during the sensitivity analyses.

However, in the sensitivity analyses, the operating variables are manipulated one at the

time. That is, the interactions between the operating variables are not considered. Thus, it

was concluded that the Two Flash Levels design is very likely to show shaft power

savings, compared to the CryoMan process, if its operating variables are simultaneously

optimised. Therefore, the Two Flash Levels design is considered for optimisation. The


127

Mixing After Precooling design, on the other hand, showed no shaft power savings

compared to the CryoMan process. Moreover, the sensitivity analyses suggest that the

structural modification in the Mixing After Precooling design has no significant effect in

the performance of the refrigeration cycle, compared to the CryoMan process. The Mixing

After Precooling design is not further considered for optimisation.

4.8 Conclusions

The natural gas stream provided by Lee (2001, Ch. 4) only as a T–H profile was simulated

in Aspen HYSYS v8.2. The natural gas stream was reconstructed using an optimisation

approach that consisted in minimising the sum of the squared difference of the enthalpy

profiles between the data provided and the optimised stream, at the intermediate

temperatures indicated in Table 4.1. This regression of the natural gas stream data allowed

a robust evaluation of the novel refrigeration cycles, comparing their performance (shaft

power demand) against that of the CryoMan process. The novel refrigeration cycles were

successfully modelled and simulated in Aspen HYSYS v8.2.

The sensitivity analyses showed that the Bypass design and the Two Flash Levels design

are refrigeration cycles that can bring shaft power savings, compared to the CryoMan

process, as they benefit from the structural modifications implemented. The Bypass design

already showed shaft power savings of 1% compared to the CryoMan process, whilst the

Two Flash Levels design yielded the same shaft power consumption as that of the

CryoMan process (0.2997 kWh·kg-1

of LNG). On the other hand, the sensitivity analyses

on the Mixing After Precooling design suggested that the structural modification would not

impact significantly in the performance of the refrigeration cycle and, therefore, would not

bring shaft power savings compared to the CryoMan process.

Consequently, the Bypass design and the Two Flash Levels design are taken into account

for optimisation of their corresponding operating variables, whereas the Mixing After

Precooling design is not further considered for optimisation.

In the following Chapter 5, the operating variables of the Bypass design and the Two Flash

Levels design are optimised in a case study for the liquefaction of the natural gas stream.

Chapter 5 Case Study: Optimisation of Novel Refrigeration Cycles

128

Chapter 5 – Case Study: Optimisation of Novel Refrigeration

Cycles

5.1 Introduction

According to the assessment performed on the novel refrigeration cycles in Chapter 4, the

Bypass design and the Two Flash Levels design are selected to optimise their

corresponding operating variables. The Mixing After Precooling design, on the other hand,

is discarded as the sensitivity analyses suggested that the structural modification proposed

would not bring shaft power savings to the refrigeration cycle, compared to the CryoMan

process.

In the case of the Bypass design, the sensitivity analyses revealed that the Bypass Stream

allowed reducing the flow rate of Stream 1 (1.62 kmol·s-1

) which is at the lowest pressure

level (1.2 bar), compared to LP Stream in the CryoMan process (1.79 kmol·s-1

at 1.2 bar),

to bring shaft power savings in spite the increase of methane in the composition of the

overall refrigerant stream. The specific shaft power is reduced to 0.2968 kWh·kg-1

LNG,

which represents shaft power savings of 1% compared to the CryoMan process.

Regarding the Two Flash Levels design, the sensitivity studies suggested that the trade-off

between refrigerant flow rate and heat of vaporisation (related to the refrigerant

composition) of Stream 3 and Stream 4 is being exploited, to reduce the refrigerant flow

rate fed to the second flash unit, in order to bring shaft power savings. Additionally, the

Two Flash Levels design would also benefit from an additional compression stage and its

corresponding intercooling stage, although the extra compression stage would increase the

capital costs relative to the CryoMan process. Therefore, the operating cost savings that

can be achieved with the Two Flash Levels design would have to justify the increase in

capital costs. The specific shaft power demand of the Two Flash Levels design, achieved

only with sensitivity studies, is 0.2997 kWh·kg-1

LNG.

The corresponding operating variables of these two novel refrigeration cycles are

optimised in a case study – presented in this chapter – using WORK software. Compared

to HYSYS, regarding the optimisation capabilities for refrigeration cycles, WORK

software is able to optimise the composition of the mixed refrigerant. Further, WORK is

also capable to use stochastic optimisation techniques (e.g. Genetic Algorithm). Even


129

though MATLAB can be used to perform stochastic optimisations and input the values of

the operating variables to the simulation in HYSYS (including the composition of the

mixed refrigerant) at each iteration of the optimisation, the flowsheet in HYSYS would

have to be well robust to include, for example, scenarios in which the pressure level of the

refrigerant streams are changed and thus, the refrigerant streams need to be fed to the

compressor at different compression stages.

The novel refrigeration cycles are optimised in order to find the combination of the values

of their corresponding operating variables that yield the lowest power consumption for the

liquefaction of a given natural gas stream. The optimisation is performed in WORK

software by means of a Genetic Algorithm method. The resulting shaft power demand of

the optimised designs is compared to that of the CryoMan process and the PRICO cycle;

the power savings achieved are also illustrated on an economic basis by comparing the

annual operating costs and savings obtained relative to the CryoMan process.

5.2 Optimisation criteria

The operating variables of the novel refrigeration cycles are optimised to minimise the

total shaft power demand for refrigerant compression. Thus, the objective function is

formulated as in Equation 5.1, and the mathematical formulation for the optimisation,

according to the modelling described in Chapter 3, is as follows:

Minimise: 𝑊𝑇𝑜𝑡𝑎𝑙 = ∑ 𝑊𝑖𝑆𝑡𝑔(Φ)𝑛

𝑖=1 𝑖 = 1,2, … , 𝑛 (5.1)

Subject to: Equations 3.1 to 3.35 (for the Bypass design)

Equations 3.17 to 3.57 (for the Two Flash Levels design)

Δ𝑇𝑀𝐼𝑁 ≥ 5℃ (5.2)

𝑃𝑅𝐴𝑇 ≤ 3 (5.3)

∑ 𝑥𝑗 = 1𝑚𝑗=1 𝑥𝑗 ∈ 𝑋𝑀𝑅 𝑗 = 1,2, … , 𝑚 (5.4)

𝑙𝑏 ≤ Φ ≤ 𝑢𝑏 (5.5)

where Φ = [𝑋𝑀𝑅 , 𝑃𝐻𝑖𝑔ℎ, 𝑓𝑉𝑎𝑝, 𝑓𝐿𝑖𝑞 , 𝑇𝐴𝑃𝑘 , 𝑃𝐴𝐸

𝑘 , 𝑇𝑜𝑢𝑡𝑘 , 𝛼]

𝑘 = 𝑆𝑡𝑟𝑒𝑎𝑚 1, 𝑆𝑡𝑟𝑒𝑎𝑚 2, 𝐵𝑦𝑝𝑎𝑠𝑠 (5.6a)

Φ = [𝑋𝑀𝑅 , 𝑃𝐻𝑖𝑔ℎ, 𝑃2𝑛𝑑 , 𝑓𝑉𝑎𝑝, 𝑓𝐿𝑖𝑞 , 𝑓𝑉𝑎𝑝2, 𝑓𝐿𝑖𝑞2, 𝑓2𝑛𝑑 , 𝑇𝐴𝑃𝑘 , 𝑃𝐴𝐸

𝑘 , 𝑇𝑜𝑢𝑡𝑘 ]

𝑘 = 𝑆𝑡𝑟𝑒𝑎𝑚 1, … , 𝑆𝑡𝑟𝑒𝑎𝑚 4 (5.6b)


130

Thus, Φ is a vector that includes the values of all the operating variables to be optimised in

each design, including compressor discharge pressure, refrigerant streams pressure level,

precooling temperatures and MSHE outlet temperatures, vapour and liquid flow rate

fractions, and refrigerant composition. Note that Φ includes the operating variables of the

Bypass design (bypass flow rate fraction; bypass stream pressure level, precooling

temperature and MSHE outlet temperature) only when the Bypass design is optimised

(Equation 5.6a), and includes the operating variables of the Two Flash Levels design (flow

rate fraction fed to the second flash unit; pressure in the second flash level; pressure levels,

precooling temperatures and MSHE outlet temperatures of the streams resulting from the

second flash level) only when the Two Flash Levels design is optimised (Equation 5.6b).

Equations 3.1 to 3.35 represent the mass and energy balances in the Bypass design and

Equations 3.17 to 3.57 are those for the Two Flash Levels design (detailed in Section 3.3.1

and 3.3.2, respectively); Equation 5.2 ensures that the minimum temperature difference

across the length of the composite curves in the MSHE is at least 5°C for feasible heat

transfer between hot and cold streams. With Equation 5.3, the pressure ratio in any

compression stage is limited to a maximum of 3. Equation 5.4 states that the sum of the

mole fractions of the components in the refrigerant mixture must be unity. During the

optimisation, each value in vector Φ is varied within a range that is limited by lower and

upper bounds; the lower bound for each variable is included in vector lb, and the upper

bound for each variable is included in vector ub (Equation 5.5).

The optimisation parameters for the optimisation of both the Bypass design and the Two

Flash Levels design are displayed in Table 5.1. The population size is 250 whereas the

maximum number of generations is 400. That is, the optimisation is performed from 250

different starting points in order to help avoiding local optima. Crossover is usually the

parameter with highest probability for producing new members in the population,

compared to mutation (Bäck et al., 1997, Ch. B1.1). Crossover probability is often around

0.90, whereas mutation rate usually has a probability of 0.01 (Poli et al., 2008, Ch. 2.4).

Alternatively, the values of both the crossover probability and mutation rate can be finely

adjusted – e.g. by performing sensitivity analyses – as they might have an impact on the

optimum solution found or in the computational time needed for the optimisation. The

values for crossover probability and mutation rate in this work – shown in Table 5.1 – are

selected according to the recommended values previously discussed.


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Table 5. 1. Genetic Algorithm parameters for the optimisation of the novel refrigeration cycles.

Parameter Population Size Maximum Generations Crossover Probability Mutation Rate

Value 250 400 0.85 0.01

5.3 Problem statement

The operating variables of the novel refrigeration cycles are optimised in order to fully

liquefy a natural gas stream. The case study is that first published by Lee (2001), and later

used by Zheng (2009) to optimise the PRICO cycle and the CryoMan process.

The case study optimises the operating variables of the refrigeration cycle for liquefying a

given natural gas stream, where the objective is to minimise the shaft power consumption

of the refrigeration cycle. The natural gas stream is provided as a temperature–enthalpy

profile (shown in Table 5.2). WORK software is employed to perform the optimisation

and, as mentioned in Section 4.2 and also described in Appendix 1, the natural gas stream

is input directly as the T–H profile. According to the case study, the natural gas stream

enters the multi-stream heat exchanger (MSHE) at 25°C and 55 bar and leaves the MSHE

at –163°C and 50 bar as liquefied natural gas. The operating variables that are optimised

are the refrigerant composition, the compressor discharge pressure, the pressure level of

the refrigerant streams, the flow rate fraction of vapour and liquid streams to be split after

each flash separation unit, the precooling temperature of the refrigerant streams in the

MSHE and the MSHE outlet temperature of the refrigerant streams. The bypass flow rate

fraction is a variable only in the Bypass design, and the flow rate fraction of liquid fed to

the second flash unit and the pressure of the second flash unit are variables only in the Two

Flash Levels design.

In order to maintain consistency with the optimisation of the CryoMan process (Zheng,

2009), the following assumptions are made: the refrigerant mixture comprises methane,

ethane, propane, n-butane and nitrogen. The isentropic efficiency of the refrigerant

compression is assumed to be 80%. The maximum pressure ratio of each compression

stage is 3. The minimum temperature approach between the composite curves in the

MSHE is 5°C. During the optimisation, physical and thermodynamic properties of the

refrigerant mixture (e.g. temperatures, enthalpies) are calculated using Peng–Robinson

equation of state by interfacing with Aspen HYSYS v8.2 (Aspen Technology Inc., 2013).


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Table 5. 2. Temperature–enthalpy profile of the natural gas stream to be liquefied (Lee, 2001).

Segment Supply

Temperature [°C]

Target


-1]

1.1 25.00 –06.03 –1861.5 60

1.2 –06.03 –34.09 –1964.3 70

1.3 –34.09 –57.65 –1885.0 80

1.4 –57.65 –70.10 –2490.0 200

1.5 –70.10 –74.55 –1780.0 400

1.6 –74.55 –82.26 –3084.0 400

1.7 –82.26 –96.50 –1424.0 100

1.8 –96.50 –115.00 –1850.0 100

1.9 –115.00 –163.00 –3840.0 80

5.4 Bypass design: Optimisation and discussion

Figure 5.1 shows the objective function of the optimisation (i.e. total shaft power demand)

plotted as a function of the generation (iteration) number, as the optimisation of the Bypass

design progresses. According to Figure 5.1, the optimisation reaches a steady objective

function value (i.e. total shaft power demand) of 25.22 MW. Further, the optimisation is

performed three times to gain confidence in the optimum solution found (on average, the

total shaft power demand varies only within a range of ±0.4%, see Appendix 2). The

optimisation takes 4,490 minutes – on average – using an Intel Core i5-4570 processor

with 3.20 GHz and 8.00 GB of RAM memory, resulting from the relatively large

population size and number of iterations of the optimisation.

Figure 5. 1. Objective function progression in the optimisation of the operating variables of the Bypass

design.

The resulting values of the operating variables of the optimised Bypass design are

displayed in Table 5.3 (the ‘Label’ column refers to the letters in Figure 5.2). The total

shaft power demand obtained is 25.22 MW (0.2915 kWh·kg-1

LNG). This shaft power


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value represents shaft power savings of 3.2% when compared to 26.05 MW of shaft power

demand in the CryoMan process (0.3011 kWh·kg-1

LNG) and 10.8% in power savings

when compared to 28.27 MW of shaft power consumption in the PRICO cycle (0.3268

kWh·kg-1

LNG) as reported by Zheng (2009), who employed the same models,

assumptions, equation of state and optimisation approach.

Table 5. 3. Optimised operating variables of the Bypass design.

Label in Figure 5.2 Process variable Value A Refrigerant flow rate [kmol·s

-1] 3.43

A Composition [mole fraction]: - Methane 0.2250 - Ethane 0.3743 - Propane 0.1770 - n-Butane 0.1509 - Nitrogen 0.0728 A Discharge pressure [bar] 39.4 A Bypass fraction 0.0868 B Vapour flow rate fraction 0.8527 C Liquid flow rate fraction 0.1106 Stream 1 Stream 2 Bypass D Precooling temperature [°C] –166.3 –97.2 –99.8 E Expansion pressure [bar] 1.21 7.48 20.2 F MSHE outlet temperature [°C] 22.1 25.0 25.0 Performance indicators Value

Number of compression stages 4 ΔT

MIN [°C] 5.0



LNG] 0.2915 Shaft power savings (%)* 3.2

*compared to the CryoMan process (Zheng, 2009).

Figure 5. 2. Bypass design.


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According to the optimised values of the operating variables displayed in Table 5.3, the

bypass flow rate fraction is decreased from 0.13 (see Table 4.7 in Section 4.4.3 for results

of the sensitivity analyses) to 0.08, even though the sensitivity analyses suggested that

increasing the flow rate of Bypass Stream would bring shaft power savings as a result of

decreasing the flow rate of Stream 1 (which is at the lowest pressure level). However, the

overall refrigerant flow rate is decreased from 3.65 kmol·s-1

(after the sensitivity analyses)

to 3.43 kmol·s-1

, which also leads to decreasing the flow rate of Stream 1. The compressor

discharge pressure is decreased from 41 bar to 39.4 bar, which is in agreement with the

trend shown in the sensitivity analyses (presented in Section 4.4.2) to avoid infeasible heat

transfer that would otherwise occur as a consequence of decreasing the vapour fraction of

the overall refrigerant stream (i.e. decreasing the vapour flow rate obtained in the flash

unit).

The flow rate fraction of the liquid from the flash unit (f Liq

) that is partially mixed to create

Stream 1 is increased from 0.08 (after the sensitivity analyses; see Table 4.7) to 0.11 after

the optimisation. As discussed in Section 4.4.2, increasing the value of f Liq

increases the

total shaft power demand of the refrigeration cycle (because the flow rate of Stream 1

would be increased, which is at the lowest pressure level). However, increasing the value

of f Liq

also increases the heat of vaporisation of Stream 1, which can help to reduce the

overall refrigerant flow rate to bring shaft power savings. On the other hand, decreasing the

flow rate of Stream 1 might also lead to infeasible heat transfer between hot and cold

streams in the MSHE. The optimised Bypass design thus exploits the trade-off between

increasing the heat of vaporisation of Stream 1 to reduce the overall refrigerant flow rate

and bring shaft power savings, and increasing the power consumption as a result of

increasing the flow rate of Stream 1 (at the lowest pressure level, 1.21 bar).

The Bypass Stream is 8.7% of the overall refrigerant stream. Introducing the Bypass

Stream allows to reduce the flow rate of the stream at the lowest pressure level in the

Bypass design (Stream 1) to bring shaft power savings. Figure 5.3 compares the flow rate

and heat load of Stream 1 in the optimised Bypass design (Figure 5.3a) against those of LP

Stream in the CryoMan process (Figure 5.3b) using the composite curves in the MSHE.

The flow rate of LP Stream in the CryoMan process is 1.8 kmol·s-1

compared to 1.7

kmol·s-1

of Stream 1 in the Bypass design. The heat duty of LP Stream in the CryoMan

process is 39.7 MW, whereas Stream 1 in the Bypass design has a heat load of 37.6 MW.

Note that the composite curves shown in Figure 5.3 represent an ideal scenario in terms of


135

heat transfer inside the MSHE; the actual composite curves might be affected if, for

example, the actual arrangement of the refrigerant streams inside the MSHE is considered.

However, determination of the actual arrangement of the refrigerant streams inside the

MSHE is beyond the scope of this work.

Reducing the heat load of Stream 1 in the Bypass design, compared to LP Stream in the

CryoMan process, resulted in shortening the length (x axis) of its T–H profile (Figure

5.3a), which would produce infeasible heat transfer at –83°C because the minimum

temperature approach between hot and cold composite curves would be less than 5°C.

Such a minimum driving force violation is avoided since both the Bypass Stream and

Stream 2 provide cooling to the hot streams from temperatures near –100°C, compared to

HP Stream in the CryoMan process which evaporates at –80°C. Thus, the Bypass Stream

allowed a reduction in the flow rate of Stream 1 by providing cooling at the necessary

temperature (–100°C) to avoid a minimum temperature approach violation, but at a higher

pressure level (20.2 bar) than Stream 1 (1.21 bar) to bring shaft power savings.

Figure 5. 3. Composite curves in the MSHE: a) the Bypass design; b) the CryoMan process.

Regarding the composition of the overall refrigerant stream, the optimised mole fraction

values of the components (in Table 5.3) are in agreement with the ranges obtained with the

sensitivity analyses (Table 4.5) in which heat transfer is feasible.

Furthermore, the mole fraction of methane in the overall composition of the refrigerant is

reduced to 0.2250, compared to 0.2288 in the CryoMan process; the mole fraction of

nitrogen is reduced to 0.0728 (compared to 0.0808 in the CryoMan process). Decreasing

the mole fraction of the light components in the refrigerant mixture helps reducing the total


136

shaft power demand of the refrigeration cycle, as previously discussed and illustrated in

Section 4.4.2.

The Bypass design achieves 3.2% savings in shaft power demand, compared to the

CryoMan process, by creating a new refrigerant stream that bypasses the flash unit (Bypass

Stream). In the optimised Bypass design, the compression of the overall refrigerant stream

takes place in 4 compression stages, i.e. with the same number of compression stages as

that in the CryoMan process. Thus, compared to the CryoMan process, the increase in

complexity of the Bypass design is only reflected with two additional refrigerant streams in

the MSHE (i.e. hot and cold Bypass Stream).

5.5 Two Flash Levels design: Optimisation and discussion

Figure 5.4 shows the minimisation of the objective function (i.e. total shaft power demand)

plotted as the optimisation of the Two Flash Levels design progresses, i.e. increasing the

number of generations (iterations). The optimisation reaches a steady objective function

value of 25.40 MW. Similar to the Bypass design, the optimisation is performed three

times in order to gain confidence in the optimum solution obtained (on average, the

objective function varies only within a range of ±0.4%, see Appendix 2). The optimisation

takes around 6,592 minutes – on average – with an Intel Core i5-4570 processor with 3.20

GHz and 8.00 GB of RAM memory.

Figure 5. 4. Objective function progression in the optimisation of the operating variables of the Two Flash

Levels design.

The optimised values of the operating variables in the Two Flash Levels design are shown

in Table 5.4 (where the ‘Label’ column refers to the letters in Figure 5.5). The total shaft


137

power consumption is 22.40 MW (0.2936 kWh·kg-1

LNG), which is 2.5% in shaft power

savings compared to 26.05 MW of shaft power demand in the CryoMan process (0.3011

kWh·kg-1

LNG), and 10.2% savings in shaft power compared to 28.27 MW of shaft power

demand in the PRICO cycle (0.3268 kWh·kg-1

LNG) according to Zheng (2009).

Table 5. 4. Optimised operating variables of the Two Flash Levels design.

Label in Figure 5.5 Process variable Value A Refrigerant flow rate [kmol·s

-1] 3.42

A Composition [mole fraction]: - Methane 0.2372 - Ethane 0.4013 - Propane 0.0587 - n-Butane 0.2285 - Nitrogen 0.0743 A Discharge pressure [bar] 41.1 H Pressure 2nd flash unit [bar] 26.7 G Liquid fraction to 2nd flash unit 0.2082 Stream 1 Stream 2 Stream 3 Stream 4 D Precooling temperature [°C] –162.3 –110.2 –96.5 –56.3 E Expansion pressure [bar] 1.2 7.8 4.7 11.2 F MSHE outlet temperature [°C] 19.6 24.0 18.9 25.0

B, I Vapour flow rate fraction 0.7506 0.2494 0.2975 0.7025 C, J Liquid flow rate fraction 0.2193 0.5725 0.2559 0.7441

Performance indicators Value


MIN [°C] 5.0



LNG] 0.2936 Shaft power savings (%)* 2.5

*compared to the CryoMan process (Zheng, 2009).

Figure 5. 5. Two Flash Levels design.


138

The compression of the overall refrigerant stream is achieved with six compression stages.

As discussed in Section 4.5.1, additional compression stages, compared to the CryoMan

process, could help with shaft power savings in the refrigeration cycle because of their

corresponding intercooling stages. In Section 4.5.1, the compression of the overall

refrigerant in the initial simulation of the Two Flash Levels design is achieved with five

compression stages. After the optimisation, because of the design constraint of a maximum

pressure ratio of 3 in each compression stage, the resulting pressure level of the refrigerant

streams (shown in Table 5.4) lead to a compression of the overall refrigerant stream that is

achieved with six compression stages. Nevertheless, because of the two extra compression

stages and associated intercooling stages relative to the CryoMan process, the capital costs

of the Two Flash Levels design would increase accordingly (see Section 5.6 and Appendix

3 for further discussion).

According to the values in Table 5.4, the flow rate fraction of liquid from the first flash

unit that is fed to the second flash unit (f 2nd

) is decreased from 0.2240 (after the sensitivity

analyses, see Table 4.9) to 0.2082. The optimised value of f 2nd

is in agreement with the

discussion in Section 4.5.2, in which reducing the value of f

2nd decreases the shaft power

demand (as a consequence of reducing the flow rate of the streams leaving the second flash

unit). On the other hand, values of f 2nd

below 0.20 would lead to infeasible heat transfer in

the temperature range in which Stream 3 and Stream 4 (resulting from the second flash

unit) provide cooling in the MSHE, i.e. from –96°C to 25°C for the optimised conditions

(see Figure 5.6).

Figure 5. 6. Composite curves in the MSHE of the optimised Two Flash Levels design.


139

The pressure in the second flash unit (P2nd

), according to the optimised values in Table 5.4,

is decreased to 26.7 bar (from 30 bar after the sensitivity analyses, see Table 4.9).

According to the sensitivity analyses in Section 4.5.2 and Figure 4.17, more vapour is

produced in the second flash unit as its pressure level is decreased.

Also, the optimised values of the vapour and liquid flow rate fractions in Table 5.4,

indicates that Stream 4 has above 70% of the flow rate fed to the second flash unit. The

pressure level of Stream 4 is 11.2 bar, which is the highest pressure level amongst the

refrigerant streams. Thus, over 70% of the flow rate fed to the second flash unit is

compressed from a relatively high pressure level. According to a previous discussion in

Section 4.4.2 (illustrated with Figure 4.7b for the Bypass design), the shaft power demand

for compression decreases as the pressure level of the refrigerant streams increases, for a

fixed compressor discharge pressure.

Regarding the optimised composition of the overall refrigerant stream in the Two Flash

Levels design, the mole fraction of n-butane is increased from 0.1517, in the CryoMan

process, to 0.2285. Increasing the mole fraction of n-butane in the composition of the

overall refrigerant stream reduces the total shaft power consumption for refrigerant

compression (see discussion in Section 4.4.2). However, the increase in the mole fraction

of n-butane is at the expense of decreasing the mole fraction of propane to 0.0587

(compared to 0.1684 in the CryoMan process), which increases the shaft power demand.

The mole fraction of ethane is increased to 0.4013 from 0.3703 in the CryoMan process,

which also increases the shaft power demand; although the overall shaft power

consumption is less sensitive to changes in the mole fraction of ethane compared to

changes in the mole fraction of the remaining components in the refrigerant mixture (see

Section 4.4.2).

Also, note that the mole fraction values of ethane, propane and n-butane are outside of the

ranges provided in Table 4.7 (see Section 4.5.2) in which heat transfer is feasible according

to the sensitivity analyses. For example, the optimised mole fraction value for propane is

0.0587 (see Table 5.4), whereas the range in which the mole fraction of propane would

lead to feasible heat transfer in the MSHE, according to the sensitivity analyses in Section

4.5.2, is between 0.10 and 0.20. After the optimisation (where the operating variables are

manipulated simultaneously), the complex interactions and trade-offs between the

operating variables in the refrigeration cycle (e.g. pressure levels, stream flow rates,


140

compositions from flash separations) allowed the mole fraction of the components in the

overall refrigerant stream to be outside the ranges obtained through sensitivity analyses

(provided in Table 4.7, Section 4.5.2), in which only the composition is manipulated whilst

the remaining degrees of freedom (e.g. refrigerant flow rate, stream pressure levels) are

held constant.

The optimised Two Flash Levels design thus exploits the complex interactions and trade-

offs between refrigerant flow rate, composition and pressure levels of the new streams in

the refrigeration cycle (Stream 3 and Stream 4). The design constraint of maximum

pressure ratio in a compression stage is also exploited, leading to a compression of the

overall refrigerant stream achieved with six compression stages. On the other hand, as

mentioned before, the two extra compression stages would significantly increase the

capital costs of the Two Flash Levels design.

Overall, the Two Flash Levels design achieves shaft power savings of 2.5% relative to the

CryoMan process. The structural modification proposed in the Two Flash Levels design

consists in throttling and flashing a portion of the liquid from the first flash unit, to a lower

pressure level. Two new refrigerant streams (Stream 3 and Stream 4) result from partially

mixing the product streams of the second flash unit. The compression of the overall

refrigerant stream is achieved with six compression stages. Thus, compared to the

CryoMan process, the increase in the complexity of the Two Flash Levels design is

reflected with four additional refrigerant streams in the MSHE (two hot and two cold

streams), and also with two extra compression stages.

5.6 Operating costs comparison between the novel refrigeration cycles and the

benchmark processes

The refrigerant compression in the refrigeration cycles is the most energy-consuming stage

in the liquefaction process, and hence, dominates operating costs of LNG plants (Mokhatab

et al., 2014b, Ch. 3.2). In this section, the total shaft power achieved with the novel

refrigeration cycles is compared against those in the benchmark processes (i.e. the PRICO

cycle and the CryoMan process) on an annual operating cost basis, in order to illustrate

operating cost savings as a result of the shaft power savings.

According to the results shown in Table 5.3 and Table 5.4, shaft power savings of 3.2%

and 2.5% are achieved with the Bypass design and with the Two Flash Levels design,

respectively, compared to the CryoMan process. The unit shaft power energy cost is


141

assumed to be £0.0955·kWh-1

for extra-large scale industrial consumers (U.K. Department

of Energy & Climate Change, 2015). Table 5.5 presents the annual operating costs of the

novel refrigeration cycles as well as those of the benchmark processes, and compares the

operating cost savings relative to the CryoMan process.

According to Table 5.5, the shaft power demand achieved with the Bypass design (0.2915

kWh·kg-1

LNG) would lead to operating cost savings of nearly £0.70 million per annum

compared to the CryoMan process and over £2.5 million per annum compared to the

PRICO cycle. The optimised Two Flash Levels design yielded a specific shaft power

consumption of 0.2936 kWh·kg-1

LNG, which represents operating cost savings of £0.54

million per annum relative to the CryoMan process and £2.4 million per annum when

compared to the PRICO cycle. Thus, significant operating cost savings are achieved with

the novel refrigeration cycles, according to the shaft power savings obtained, compared to

the benchmark processes.

Table 5. 5. Operating cost savings comparison (relative to the CryoMan process) between the novel

refrigeration cycles and benchmark processes.

PRICO cycle CryoMan process Bypass design Two Flash Levels design

Total shaft power

[MW] 28.27 26.05 25.22 25.40

Specific shaft power

[kWh·kg-1

LNG] 0.3268 0.3011 0.2915 0.2936

Shaft power savings

[%] – 8.5 - + 3.2 + 2.5

Number of

compression stages 4 4 4 6

Operating costs

[£ million per annum] 23.65 21.79 21.10 21.25

Operating cost savings

[£ million per annum] – 1.86 - + 0.69 + 0.54

However, the optimised Two Flash Levels design is impacted by the design constraint of

maximum compression ratio in a single compression stage (Equation 5.3): the overall

refrigerant stream is compressed to the compressor discharge pressure with six

compression stages. Thus, the capital costs of the Two Flash Levels design would

significantly increase as a consequence of the two extra compression stages compared to

the CryoMan process.


142

In order to compare the Two Flash Levels design and the CryoMan process on the same

basis, the CryoMan process is optimised for the case that the compression of the overall

refrigerant stream is achieved with six compression stages. The optimisation of the

CryoMan process is presented in Appendix 3. The total shaft power demand of the

CryoMan process optimised with six compression stages is 24.94 MW (0.2883 kWh·kg-1

of LNG), which is 1.8% lower than that of the optimised Two Flash Levels design.

That is, the comparison on a basis of equal number of compression stages suggests that the

Two Flash Levels design mainly benefits from the extra compression stages, rather than

from the structural modification proposed. Thus, the shaft power savings and the

corresponding operating cost savings achieved by the Two Flash Levels design – shown in

Table 5.5 – would not justify the increase in capital costs.

5.7 Conclusions

The operating variables of the novel refrigeration cycles (the Bypass design and the Two

Flash Levels design) were successfully optimised to evaluate their performance in the LNG

production case study (0.75 million t per annum) that was employed by Zheng (2009) to

optimise the CryoMan process and the PRICO cycle. The optimisation was performed

using WORK software.

Genetic Algorithm was employed as the optimisation method in order to help avoiding

local optima. The objective function to minimise was the total shaft power demand for

refrigerant compression. The Genetic Algorithm method demonstrated to be a robust

optimisation method, allowing explore thoroughly the combination of values of the

operating variables of the novel refrigeration cycles to minimise the objective function.

The optimisation was performed three times on each novel refrigeration cycle. The similar

solutions resulting from their corresponding optimisations, gives confidence in the optimal

results obtained.

The structural modification in the Bypass design allowed a reduction of the flow rate of the

refrigerant stream at the lowest pressure level (Stream 1 at 1.21 bar) to bring shaft power

savings. The optimised Bypass design achieved a shaft power consumption of 25.22 MW

(0.2915 kWh·kg-1

LNG), i.e. shaft power savings of 3.2% compared to the CryoMan

process and 10.8% compared to the PRICO cycle. The shaft power savings achieved with

the Bypass design would be equivalent to savings of £0.69 million per annum in operating


143

costs, compared to the CryoMan process and £2.55 million per annum compared to the

PRICO cycle. Furthermore, the compression of the overall refrigerant stream in the Bypass

design was achieved with four compression stages, i.e. the same number of compression

stages as that in the CryoMan process. Thus, the shaft power savings (and corresponding

operating cost savings) offered by the Bypass design, compared to the CryoMan process,

are at the expense of only minor increase in the structure complexity of the refrigeration

cycle design, that is an additional refrigerant stream that bypasses the flash unit.

The optimised Two Flash Levels design yielded a total shaft power demand of 25.40 MW

(0.2936 kWh·kg-1

LNG), which is 2.5% in shaft power savings compared to the CryoMan

process and 10.2% compared to the PRICO cycle. The shaft power savings are equivalent

to operating cost savings of £0.54 million per annum, compared to the CryoMan process.

However, the compression of the overall refrigerant stream, in the optimised Two Flash

Levels design, resulted with six compression stages, i.e. two additional compression stages

compared the CryoMan process. It was concluded – in Appendix 3 – that the Two Flash

Levels design was mainly benefited from the intercooling associated with the additional

compression stages, rather than from the structural modification proposed (i.e. two new

refrigerant streams from a second flash unit). Thus, the operating cost savings achieved

would not justify the increase in complexity and associated capital costs.

As previously discussed in Section 3.1, an important trade-off exists in the design of

refrigeration cycles for small scale LNG processes; on the one hand, the refrigeration cycle

should be of low complexity to help keeping the capital costs low. On the other hand, the

energy-efficiency of the refrigeration cycle should be high to minimise the shaft power

consumption in the refrigeration cycle, which dominates operating costs in LNG processes.

The novel refrigeration cycles in this work, developed by modifying the configuration of

the CryoMan process, showed that the Bypass design exploited this trade-off as it was

benefited from the structural modification proposed (a stream bypasses the flash unit).

Significant shaft power savings and, therefore, significant operating cost savings were

achieved, compared to the CryoMan process, with minor increase in design complexity. In

the case of the Two Flash Levels design, even though shaft power savings were achieved,

the operating cost savings achieved does not justify the increase in capital costs associated

with two additional compression stages compared to the CryoMan process.

Chapter 6 Conclusions and Future Work

144

Chapter 6 – Conclusions and Future Work

6.1 Conclusions

In the current scenario on global energy demand and supply, natural gas is a major source

of energy. Trends project that the production and market of natural gas will continue

growing in the next two decades. Thus, small natural gas reserves are likely to become

increasingly attractive for commercial exploitation as liquefied natural gas (LNG) at small

scale production, i.e. up to 1 million t per annum (Mokhatab et al., 2014b, Ch. 3.3).

LNG processes are both capital- and energy-intensive. The design of refrigeration cycles

for LNG process at small scale is challenging: high energy-efficiency of the refrigeration

cycle is important to minimise the shaft power demand for refrigerant compression (which

dominates operating costs). However, energy savings are usually at the expense of

increasing the complexity of the design and associated capital costs. In small scale LNG

processes, complexity of the refrigerant cycle design should be kept low to help keep

capital costs relatively low.

The literature review – presented in Chapter 2 – revealed that a limited range of mixed

refrigerant cycles have been studied for the production of LNG at small scale. The

CryoMan process (Zheng, 2009; Kim and Zheng, 2011), developed by structurally

modifying the simplest commercial mixed refrigerant cycle (the PRICO cycle), showed

significant shaft power savings (nearly 8%) compared to the PRICO cycle. The structural

modifications consisted on a flash unit after the partial condenser to separate the overall

refrigerant stream into vapour and liquid phases (that have different composition); these

vapour and liquid phases are partially mixed to create the two actual refrigerant streams.

The flow rate and composition of the refrigerant streams can thus be manipulated. The

shaft power savings in the CryoMan process resulted from the exploitation of the trade-offs

between refrigerant flow rate, refrigerant composition and pressure level of the refrigerant

streams.

Further structural modifications in the CryoMan process were explored in this work, in

order to explore and exploit the trade-off in the design of refrigeration cycles for LNG at

small scale: complexity (which can be related to capital costs) against energy-efficiency (in

particular shaft power demand for refrigerant compression, to account for operating costs).

However, the complexity of a refrigeration cycle has not been clearly defined in the open


145

research literature. Thus, in this work, design constraints in the refrigerant compressor and

in the multi-stream heat exchanger (MSHE) were defined to impose a limit of how

‘complex’ the novel refrigeration cycles can be.

In this thesis, three novel mixed refrigerant cycles were proposed – in Chapter 3 –, namely

the Bypass design, the Two Flash Levels design, and the Mixing After Precooling design.

The novel refrigeration cycles were developed by exploring structural modifications

applied to the base case refrigeration cycle (i.e. the CryoMan process). The modification

proposed for the Bypass design consisted of a stream that bypasses the flash unit, with an

independent pressure level. In the Two Flash Levels design, a portion of the liquid stream

obtained from the first flash unit is expanded to a second pressure level and flashed; two

new refrigerant streams are created by partially mixing the resulting vapour and liquid

phases from the second flash unit. In the Mixing After Precooling design, a new refrigerant

stream is created by partially mixing the two hot refrigerant streams once precooled in the

MSHE and expanded; the new refrigerant stream is constrained to have the same pressure

level as that of the refrigerant stream at the lowest pressure level.

The structural modifications aimed to exploit trade-offs between the operating variables of

the refrigerant streams (refrigerant flow rate, composition, pressure level, etc.) to bring

further shaft power savings to the refrigeration cycles, with relatively minor increase in the

complexity of the design to help keep capital costs low.

The three novel refrigeration cycles were first assessed and screened – in Chapter 4 –

through sensitivity analyses, in commercial simulator software (i.e. Aspen HYSYS), for

the liquefaction of the same natural gas stream as in the CryoMan process. The promising

designs were further considered for optimisation of their corresponding operating

variables. Because the natural gas stream is provided as a temperature–enthalpy profile

only, its conditions (flow rate, composition, etc.) were determined – in Appendix 1 – with

an optimisation approach that minimises the sum of squared enthalpy differences between

the published data and the optimised stream.

The preliminary assessment showed that the Bypass design could achieve shaft power

savings of 1% compared to the CryoMan process. The new stream in the Bypass design

allowed a reduction of the flow rate of the refrigerant stream at the lowest pressure level,

by providing cooling at the necessary temperature (–100°C) but at a higher pressure (20.2

bar). Additionally, the new stream impacted the composition of the overall refrigerant


146

stream by reducing the mole fraction of the light components in the mixture, resulting in

shaft power savings. The Two Flash Levels design demonstrated potential for shaft power

savings; this novel design was benefited from reducing the flow rate of the new refrigerant

streams and increasing their corresponding pressure level, and also from the intercooling

associated with an additional compression stage. The extra compression stage would,

however, increase the capital costs of the refrigeration cycle. In the Mixing After

Precooling design, on the other hand, the structural modification showed no effect towards

bringing shaft power savings to the refrigeration cycle. The studies suggested that, as the

flow rate of the new stream increases, its composition would help to reduce the overall

refrigerant flow rate. However, because the new stream is constrained to have the lowest

pressure level, increasing its flow rate resulted in increasing the shaft power demand.

Only the Bypass design and the Two Flash Levels design were optimised – in Chapter 5 –:

the benefits obtained from their corresponding structural modifications were illustrated

with an industrially-relevant case study that has been studied in several research

publications. The case study consists in the liquefaction of a given natural gas stream while

minimising the shaft power consumption in the refrigeration cycle. An optimisation using

Genetic Algorithm was performed to the novel refrigeration cycles. The optimisation

considered the simultaneous manipulation of the degrees of freedom of each novel

refrigeration cycle (e.g. refrigerant flow rate and composition, streams pressure level) and

explored the complex interactions between their corresponding operating variables, thus

avoiding local optima.

The optimised Bypass design yielded 3.2% savings in shaft power compared to the

CryoMan process. That is, power savings equivalent to operating cost savings of £0.69

million per annum were possible. Furthermore, the compression of the overall refrigerant

stream was achieved with only four compression stages, i.e. the same number of

compression stages as that in the CryoMan process. Therefore, the shaft power savings

(and corresponding operating cost savings) achieved by the Bypass design come at the

expense of only minor increase in complexity, i.e. an additional refrigerant stream that

bypasses the flash unit, compared to the CryoMan process.

In the case of the optimised Two Flash Levels design, 2.5% savings in shaft power

consumption were achieved, which are equivalent to operating cost savings of £0.54

million per annum. However, the compression of the overall refrigerant stream was


147

achieved with two additional compression stages compared to the CryoMan process. It was

concluded – in Appendix 3 – that the novel refrigeration cycle was mainly benefited from

the intercooling associated with the extra compression stages, rather than the structural

modification proposed. The additional compression stages would increase the capital costs

of this novel design; the operating cost savings achieved in the case study would not justify

the increase in complexity and associated capital costs.

The Genetic Algorithm optimisation method was shown to be a robust optimisation

approach to thoroughly explore the complex interactions between the operating variables

in the novel refrigeration cycles. Moreover, the optimisation was performed three times for

each novel refrigeration cycle; the similar results obtained allowed gaining confidence in

the optimal solutions found.

The structural modifications proposed in this work allowed the novel designs to bring shaft

power savings with relatively minor increase in the complexity of the refrigeration cycles.

Shaft power savings achieved with the novel refrigeration cycles yielded up to 3.2% in the

case of the Bypass design (equivalent to operating cost savings of £0.69 million per

annum) compared to the CryoMan process. Compared to the PRICO cycle, the shaft power

savings achieved by the novel refrigeration cycles yielded up to 10.8% (equivalent to

operating cost savings of £2.55 million per annum).

6.2 Future work

The constraints for complexity defined in this work may be different from those considered

in industrial practice, and thus other criteria for the complexity could be established in the

development of refrigeration cycles for LNG processes at small scale. For example, the

constraint of the number of streams inside the MSHE could be replaced with a constraint

for a maximum heat transfer area. Alternatively, the criteria could be combined to include

both constraints in the MSHE.

Also, the evaluation of structural modifications in the liquefaction process could be

strengthened by including an assessment of the capital cost of the novel refrigeration

cycles. For example, even though the design constraints were defined to include only one

compressor, its cost would be expected to increase not only as the shaft power demand

increases, but also as the number of compression stages increases (i.e. as the compressor

becomes more complex). The same would be expected for the cost of the MSHE as the


148

total heat transfer area increases, or as the number of streams in a single MSHE increases

and the equipment design becomes more complicated. The objective function of the

optimisation could thus be the minimisation of the total annualised costs in order to

account for both shaft power and complexity of the refrigeration cycle design.

The scope of structural modifications for the development of novel refrigeration cycles

should be extended to cascade cycles and, therefore, should be applied to larger scale LNG

processes (e.g. LNG production above 2.5 million t per annum). Thus, novel cascade

refrigerant cycles could be developed, in which the modifications applied would improve

further the high energy-efficiencies achieved with commercial cascade cycles, and bring

significant operating cost savings.

Furthermore, a robust integrated design methodology, e.g. that includes power systems

design and driver selection to run the refrigerant compressors, such as that proposed by Del

Nogal (2006, Ch. 4 and 5), could be developed to include the novel refrigeration cycles.

The benefits of structural modifications in the refrigeration cycles, presented in this thesis,

could be further explored and extended by exploiting the interactions between the

refrigeration cycles and the power systems (e.g. steam turbines, gas turbines, electric

motors) in the production of LNG.

Regarding the optimisation, the values of the Genetic Algorithm parameters (e.g. crossover

probability, mutation rate) could be further studied in order to investigate potential benefits

on the optimisation performance, both on the final solution obtained (objective function)

and on the computational time needed. Finally, although the stochastic optimisation

approach employed in this work (i.e. Genetic Algorithm) gives confidence that the

solutions found are closer to a global optimum compared to those from deterministic

methods, the results obtained are not guaranteed to be optimal. Thus, a different

optimisation approach could be studied. For instance, a combination of stochastic and

deterministic optimisation methods could be implemented to explore thoroughly the

solution space and also to guarantee optimality of the final results obtained.

Appendix 1 Determination of the Natural Gas Stream Conditions

149

Appendix 1 – Determination of the Natural Gas Stream

Conditions

The temperature–enthalpy profile of a natural gas stream first published by Lee (2001, Ch.

4), presented in Table A1.1 and Figure A1.1, has been employed in the open research

literature by Lee (2001, Ch. 4), Del Nogal (2006, Ch. 2), Remeljej and Hoadley (2006),

and Zheng (2009, Ch. 3), to assess the shaft power consumption of a refrigeration cycle to

liquefy the natural gas stream.

Lee (2001), also in (Lee et al., 2002), presented the natural gas data (T–H profile) in a case

study in which the composition of the mixed refrigerant in the PRICO cycle is optimised in

order to minimise the shaft power demand for refrigerant compression. Similarly, Del

Nogal (2006), also in (Del Nogal et al., 2008), employed the natural gas T–H data in a case

study to optimise the operating variables of the PRICO cycle to minimise the total

compression shaft power demand, but considering simultaneous manipulation of the

degrees of freedom (refrigerant composition, pressure levels, refrigerant flow rate).

Remeljej and Hoadley (2006) used the natural gas stream to simulate and compare the

performance (using the shaft power demand as the performance indicator) of four different

refrigeration cycles, including the PRICO cycle, in the liquefaction of the natural gas

stream for small scale LNG processes. Zheng (2009) employed the natural gas data to

optimise the operating variables of five refrigeration cycle designs, including the PRICO

cycle and the CryoMan process, to minimise the total shaft power demand in order to

explore structural modifications to the PRICO refrigeration cycle.

Since Zheng (2009) employed the previously mentioned natural gas stream to evaluate the

performance of the CryoMan process, this natural gas stream is also used to assess the

novel refrigeration cycles developed in this work. The evaluation of the novel refrigeration

cycles is performed in two stages: a preliminary assessment using Aspen HYSYS v8.2

(Aspen Technology Inc., 2013) (see Chapter 4), and a case study in which the operating

variables of the novel refrigeration cycles are optimised to minimise the total shaft power

demand and the resulting specific shaft power consumption is compared to the benchmark

processes, i.e. the PRICO cycle and the CryoMan process (see Chapter 5).

The natural gas T–H profile data is used by Zheng (2009) to optimise the CryoMan process

in WORK software; no details of the composition of the natural gas stream, flow rate or


150

pressure drop profile are needed. On the other hand, to simulate the natural gas stream in

HYSYS, the full conditions of the stream are needed, i.e. flow rate, composition,

temperatures at the inlet and outlet of the multi-stream heat exchanger (MSHE), inlet and

outlet pressures as well as the pressure drop profile.

Table A1. 1. Temperature–enthalpy profile of the natural gas stream (Lee, 2001; Del Nogal, 2006; Zheng,

2009).

Segment Supply Temperature

[°C]

Target Temperature

[°C] ΔH [kW] CP [kW·K

-1]

1.1 25.00 –06.03 –1861.5 60

1.2 –06.03 –34.09 –1964.3 70

1.3 –34.09 –57.65 –1885.0 80

1.4 –57.65 –70.10 –2490.0 200

1.5 –70.10 –74.55 –1780.0 400

1.6 –74.55 –82.26 –3084.0 400

1.7 –82.26 –96.50 –1424.0 100

1.8 –96.50 –115.00 –1850.0 100

1.9 –115.00 –163.00 –3840.0 80

Figure A1. 1. Temperature–enthalpy profile of the natural gas stream (Lee, 2001).

In Lee (2001), the data available for the natural gas stream is the T–H profile, the inlet

pressure (55 bar) and outlet pressure (50 bar). In Del Nogal (2006), only the T–H profile

data of the natural gas stream are shown, but details of its inlet and outlet pressures are

omitted, and the flow rate is not stated. Moreover, even though Remeljej and Hoadley

(2006) provide a composition and mass flow rate (22.60 kg·s-1

) of the natural gas stream,

in addition to the inlet and outlet pressure, the resulting molar flow rate (1.37 kmol·s-1

) is

different to that stated by Zheng (2007) (1 kmol·s-1

). Additionally, the T–H profile

-200

-150

-100

-50

0

50

0 5 10 15 20 25

Tem

per

atu

re [

°C]

ΔH [MW]


151

obtained according to the natural gas stream conditions used by Remeljej and Hoadley

(2006) does not match that originally published by Lee (2001), as shown in Table A1.2 and

Figure A1.2. In Zheng (2009), the inlet and outlet pressures of the natural gas are omitted.

Furthermore, the pressure drop profile of the natural gas in the MSHE is not reported in

any of the previously mentioned publications. Consequently, the conditions of the natural

gas stream (composition, flow rate, inlet and outlet pressure, and pressure drop profile in

the MSHE) are unclear.

Table A1. 2. Natural gas stream profile according to Remeljej and Hoadley (2006) compared to Lee (2001).

Segment Supply

Temperature [°C]

Target

Temperature [°C]

Cumulative ΔH [kW] (Lee, 2001)

Cumulative ΔH [kW]

(Remeljej and Hoadley, 2006) Difference

[%]

1.1 25.00 –06.03 20178.8 18972.9 6.0

1.2 –06.03 –34.09 18317.3 17119.6 6.5

1.3 –34.09 –57.65 16353 15313.1 6.4

1.4 –57.65 –70.10 14468 13467.6 6.9

1.5 –70.10 –74.55 11978 11891.1 0.7

1.6 –74.55 –82.26 10198 10263.7 –0.6

1.7 –82.26 –96.50 7114 7692.4 –8.1

1.8 –96.50 –115.00 5690 5722.0 –0.6

1.9 –115.00 –163.00 3840 3871.3 –0.8

Figure A1. 2. Temperature–enthalpy profile comparison between the data provided by Lee (2001) and that

according Remeljej and Hoadley (2006).

Thus, an optimisation is undertaken in order to find a stream with the same T–H profile as

that provided in Table A1.1. The objective function of the optimisation is to minimise the

sum of squared difference of the enthalpies compared to the data in Table A1.1, at the

fixed intermediate target temperatures shown in Table A1.1. Squares of differences of

enthalpy values account for both positive and negative differences against the published

-200

-150

-100

-50

0

50

0 5 10 15 20 25

Tem

per

atu

re [

°C]

ΔH [MW]

Remeljej and Hoadley (2006)Lee (2001)


152

data. The degrees of freedom optimised, i.e. the variables to be varied, are the molar

fraction of (n – 1) components, the overall mass flow rate as well as the inlet pressure of

the natural gas stream.

The overall pressure drop of the natural gas streams is assumed as 5 bar (Lee, 2001).

Because the pressure drop profile across the MSHE is not reported, the optimisation is

performed with three different pressure drop profile assumptions: i) linear dependence on

the overall temperature change of the stream (Equation A1.1); ii) linear dependence on the

heat that the natural gas stream rejects during the liquefaction process (Equation A1.2); iii)

zero pressure drop is also assumed, i.e. the natural gas stream is liquefied at constant

pressure and, therefore, its inlet and outlet pressures are the same (Equation A1.3).

𝑃𝑖 = 𝑃𝑖𝑛 − [𝑇𝑖𝑛−𝑇𝑖

𝑇𝑖𝑛−𝑇𝑜𝑢𝑡∙ ∆𝑃𝑇𝑜𝑡𝑎𝑙]; 𝑖 = 1, 2, … , 9 (A1.1)

𝑃𝑖 = 𝑃𝑖𝑛 − [∆𝐻𝑖𝑛−∆𝐻𝑖

∆𝐻𝑖𝑛−∆𝐻𝑜𝑢𝑡∙ ∆𝑃𝑇𝑜𝑡𝑎𝑙]; 𝑖 = 1, 2, … , 9 (A1.2)

∆𝑃𝑇𝑜𝑡𝑎𝑙 = 0 (A1.3)

where ΔPTotal = Overall pressure drop of the natural gas stream across the MSHE

Pin = Pressure of the natural gas stream at the inlet of the MSHE

Pi = Pressure of the natural gas stream at the ith temperature segment

Tin = Temperature of the natural gas stream at the inlet of the MSHE

Tout = Temperature of the natural gas stream at the outlet of the MSHE

Ti = Temperature of the natural gas stream at the ith segment

ΔHin = Cumulative enthalpy change value of the natural gas stream at the inlet of the MSHE

ΔHout = Cumulative enthalpy change value of the natural gas stream at the outlet of the MSHE

ΔHi = Cumulative enthalpy change value of the natural gas stream at the ith temperature segment

The optimisation is performed for each pressure drop profile assumption. It is assumed that

the natural gas stream is composed of methane, ethane, propane, n-butane, i-butane and

nitrogen, because those are the components commonly found in natural gas to be liquefied

(Mokhatab et al., 2014a, Ch. 1.3). The mathematical formulation of the objective function

is as in Equation A1.4:


153

Minimise: 𝑓(𝐱∗) = ∑ (∆𝐻𝑖 − ∆𝐻𝑐𝑎𝑙𝑐)29𝑖=1 𝑖 = 1, 2, … , 9 (A1.4)

Subject to: ∑ 𝑥𝑗6𝑗=1 = 1 (A1.5)

0 ≤ 𝑥𝑗 ≤ 1; 𝑗 = 1, 2, … , 5 (A1.6)

0.67 ≤ 𝑚 ≤ 1 (A1.7)

0.73 ≤ 𝑃𝑖𝑛 ≤ 1 (A1.8)

where x* = [x1, x2, x3, x4, x5, m, Pin]

ΔHi = Enthalpy change value of the natural gas stream in Table A1.1 at the ith temperature segment

ΔHcalc = Enthalpy change value of the optimised natural gas stream at the ith temperature segment

xj = Mole fraction of the jth component in the optimised natural gas stream

m = Normalised value of the mass flow rate of the optimised natural gas stream

Pin = Normalised value of the inlet pressure of the optimised natural gas stream

Equation A1.5 states that the sum of the components in the natural gas stream must yield

unity. During the optimisation, the mole fraction of five components in the natural gas

stream (x1 to x5) is varied from 0 to 1 (Equation A1.6).

Based on the mass flow rate reported by Remeljej and Hoadley (2006) (22.60 kg·s-1

), the

mass flow rate of the natural gas stream is allowed to vary between 20 kg·s-1

and 30 kg·s-1

.

The inlet pressure of the natural gas stream is varied from 55 bar to 40 bar during the

optimisation for each pressure drop profile assumption. The mass flow rate (m) and inlet

pressure (Pin) ranges are normalised by dividing by their corresponding upper bound (i.e.

30 kg·s-1

and 55 bar, respectively) as stated by Equation A1.7 and Equation A1.8. The

optimum combination of composition, flow rate, inlet pressure and pressure drop profile

would present minimum difference of enthalpy change with the published data.

The temperature–enthalpy profile of the natural gas depends on the interactions between

the components in the mixture, and on the overall composition, pressures and flow rate.

The optimisation is thus performed using fmincon solver within MATLAB for nonlinear

problems (The MathWorks Inc., 2013). The solution obtained (values of vector x*) in

nonlinear problems is likely to depend on the initial conditions (starting point) of the

optimisation (Edgar et al., 2001, Ch. 10.1). Thus, a set of different starting points is

proposed to explore thoroughly the possible solutions achieved by optimisation, as shown

in Table A1.3.


154

Since the main component of the natural gas is methane, the compositions selected as the

starting points are composed of methane ranging from 88% to 98%. Ethane is varied from

2% to 10%. For each starting point it is assumed that the portions of methane and ethane in

the mixture do not exceed 98% of the total composition of the natural gas stream (except in

Starting Point 1 where the summed fractions yield 99.50%). For each value of the methane

mole fraction, there is a number of starting points as the ethane fraction is varied in order

to yield up to 98% of the overall composition (see Table A1.3). The proportions between

the components in the composition of the natural gas stream are thus also modified. The

remainder of the stream is composed of propane, n-butane, nitrogen and i-butane in

proportions of 50%, 16%, 24% and 10%, respectively.

Table A1. 3. Starting points for the natural gas stream optimisation.

Composition - Mole fraction

Starting

point C1 C2 C3 n-C4 N2 i-C4

Normalised

flow rate

Normalised

inlet pressure

1 0.98 0.0150 0.0025 0.0008 0.0012 0.0005

0.78 0.83

2 0.89 0.92

3 0.96 0.0200 0.0100 0.0032 0.0048 0.0020

0.78 0.83

4 0.89 0.92

5

0.94

0.0200 0.0200 0.0064 0.0096 0.0040 0.78 0.83

6 0.89 0.92

7 0.0400 0.0100 0.0032 0.0048 0.0020

0.78 0.83

8 0.89 0.92

9

0.92

0.0200 0.0300 0.0096 0.0144 0.0060 0.78 0.83

10 0.89 0.92

11 0.0400 0.0200 0.0064 0.0096 0.0040

0.78 0.83

12 0.89 0.92

13 0.0600 0.0100 0.0032 0.0048 0.0020

0.78 0.83

14 0.89 0.92

15

0.90

0.0200 0.0400 0.0128 0.0192 0.0080 0.78 0.83

16 0.89 0.92

17 0.0400 0.0300 0.0096 0.0144 0.0060

0.78 0.83

18 0.89 0.92

19 0.0600 0.0200 0.0064 0.0096 0.0040

0.78 0.83

20 0.89 0.92

21 0.0800 0.0100 0.0032 0.0048 0.0020

0.78 0.83

22 0.89 0.92

23

0.88

0.0200 0.0500 0.0160 0.0240 0.0100 0.78 0.83

24 0.89 0.92

25 0.0400 0.0400 0.0128 0.0192 0.0080

0.78 0.83

26 0.89 0.92

27 0.0600 0.0300 0.0096 0.0144 0.0060

0.78 0.83

28 0.89 0.92

29 0.0800 0.0200 0.0064 0.0096 0.0040

0.78 0.83

30 0.89 0.92

31 0.1000 0.0100 0.0032 0.0048 0.0020

0.78 0.83

32 0.89 0.92


155

For each initial composition of the natural gas stream, there are two values of the

normalised mass flow rate and two values of the normalised inlet pressure (see Table

A1.3). The two normalised values selected for these variables, are equally-spaced values

between their corresponding upper and lower bounds.

In the optimisations, when the pressure drop profile of the natural gas stream is assumed

linearly dependent on the temperature change (Equation A1.1) and also when the pressure

drop profile is assumed linearly dependent on the heat rejected (Equation A1.2), the inlet

pressure of the natural gas stream was initially varied between 50 bar and 55 bar (i.e.

between normalised values 0.90 and 1.0) in order to represent a similar scenario to that

stated by Lee (2001). However, as shown in Figure A1.3a, the resulting natural gas stream

was not fully covering the condensing zone (indicated by the change of slope) of the

original T–H profile. The condensing enthalpy change (ΔHCond) of the natural gas stream

increases as its pressure level decreases, as illustrated with two isobars in a temperature–

enthalpy diagram in Figure A1.3b. Thus, during the optimisations, the lower bound of the

natural gas inlet pressure was decreased to 40 bar (i.e. normalised value of 0.73) to allow

the condensing enthalpy change in the constructed natural gas stream to increase.

Figure A1. 3. a) Constructed profile (squares, Starting Point 16) failing to fully cover the condensing zone;

b) condensing enthalpy change increases as pressure of the stream decreases.

After the optimisation, the selected combination of stream composition, inlet pressure,

overall mass flow rate and pressure drop profile, is that with the lowest sum of squared

errors (SSE) between the enthalpy values of the optimised T–H profile and the published

data. Figure A1.4 shows the SSE values plotted for each of the starting points after the

optimisation and for each of the three pressure drop profiles assumed for the natural gas

stream across the MSHE. SSE values when the pressure drop profile is assumed as linearly


156

dependent on the temperature change (ΔP/ΔT = k) are displayed in squares; SSE values

when the pressure drop profile is assumed as linearly dependent on the heat rejected

(ΔP/ΔH = k) are shown in triangles; SSE values when zero pressure drop in the MSHE is

assumed (ΔP = 0) are displayed in diamonds.

The approach assuming constant pressure during the liquefaction of the natural gas stream

(i.e. a zero pressure drop across the MSHE) resulted in lower values of SSE compared to

those achieved when pressure drop was modelled based either on temperature change or

heat rejection dependence. Multiple starting points (2-6, 10-12, 15, 18-20, 22, 25, 28 and

32) yielded the lowest SSE value (68×103), and also resulted in the same x* vector of

values for stream composition, normalised flow rate and normalised inlet pressure. The

optimisation is considered successful since a wide range of starting points with different

initial values ended up with the same solution.

Figure A1. 4. Sum of squared errors (SSE) of enthalpy values for each starting point and for each pressure

drop profile assumption.

The values of the vector x* that achieved the closest match to the published T–H profile

are those presented in Table A1.4. The values of normalised flow rate and normalised inlet

pressure represent a mass flow rate of 24.03 kg·s-1

and an inlet pressure of 43.86 bar,

respectively, of the natural gas stream. The mass flow rate obtained (24.03 kg·s-1

) is

equivalent to LNG production of 0.75 million t per annum, which is within the production

limits of liquefied natural gas at small scale, i.e. up to 1 million t per annum (Mokhatab et

al., 2014b, Ch. 3.3).

65×10³

70×10³

75×10³

80×10³

85×10³

90×10³

0 5 10 15 20 25 30 35

SS

E

Starting Point Number

ΔP = 0

ΔP/ΔT = k

ΔP/ΔH = k


157

Table A1. 4. Optimised values of the vector x* for the natural gas stream (zero pressure drop in the MSHE).

C1 C2 C3 n-C4 N2 i-C4 Normalised

flow rate

Normalised

inlet pressure

0.9000 0.0940 0.0047 0.0013 0.0000 0.0000 0.8009 0.7975

The molar flow rate of the optimised natural gas is 1.37 kmol·s-1

, which is greater than that

stated by Zheng (2009) (1 kmol·s-1

). The mass flow rate of the optimised natural gas

stream (24.03 kg·s-1

) is higher than the mass flow rate employed by Remeljej and Hoadley

(2006) (22.60 kg·s-1

) by around 6%. Regarding the composition, Table A1.5 shows the

composition of the optimised natural gas stream and that provided by Remeljej and

Hoadley (2006). The molar fraction of methane is decreased by nearly 0.070, in the

optimised natural gas stream, whereas the mole fractions of ethane and propane are

increased by 0.065 and 0.004, respectively. In the optimised natural gas stream, the low

fraction of n-butane (0.0013) and i-butane (0.0000) is expected since the natural gas stream

undergoes a series of separation processes including heavy hydrocarbons (C4+) removal

prior to liquefaction; the low mole fraction of nitrogen (0.0000) is also expected, as

nitrogen is usually in low concentrations (mole fraction < 0.0100) in natural gas to be

liquefied (Kidnay and Parrish, 2006b, Ch. 13.2).

Table A1. 5. Composition of the optimised natural gas stream and that of Remeljej and Hoadley (2006).

Natural gas composition [mole fraction]

C1 C2 C3 n-C4 N2 i-C4

Optimised natural gas stream 0.9000 0.0940 0.0047 0.0013 0.0000 0.0000

Remeljej and Hoadley (2006) 0.9693 0.0294 0.0006 0.0001 0.0006 0.0000

Table A1.6 compares the T–H profile of the natural gas stream obtained from the

optimisation against that originally published by Lee (2001) and later used by Zheng

(2009) to optimise the CryoMan process. The largest deviation in the T–H profile of the

optimised natural gas stream occurs at –82°C (the difference is 3% compared to the

published data). Figure A1.5 displays the T–H profile obtained with the optimisation

(squares) as compared to the published data (line with diamonds). Figure A1.5

demonstrates that a good agreement between the T–H curves is achieved.


158

Table A1. 6. Temperature–enthalpy data comparison between the optimised stream and the published data.

Segment Supply

Temperature [°C]

Target

Temperature [°C]

Cumulative ΔH [kW] (Lee, 2001)

Cumulative ΔH [kW]

(optimisation) Difference

[%]

1.1 25.00 –06.03 20178.8 20147.6 0.2

1.2 –06.03 –34.09 18317.3 18255.9 0.3

1.3 –34.09 –57.65 16353 16427.2 –0.5

1.4 –57.65 –70.10 14468 14448.0 0.1

1.5 –70.10 –74.55 11978 11911.7 0.6

1.6 –74.55 –82.26 10198 10225.2 –0.3

1.7 –82.26 –96.50 7114 7330.0 –3.0

1.8 –96.50 –115.00 5690 5616.2 1.3

1.9 –115.00 –163.00 3840 3846.2 –0.2

Figure A1. 5. Temperature–enthalpy profiles comparison between data published by Lee (2001) and the

stream constructed by optimisation.

The values of the composition, flow rate and inlet pressure obtained from the optimisation,

are employed in HYSYS to simulate the natural gas stream used by Zheng (2009) to

optimise the CryoMan process. This back-calculation allowed the natural gas stream to be

defined and so evaluate the novel refrigeration cycles with the same production rate (0.75

million t per annum), and compare their performance (especially specific shaft power

demand) against that of the CryoMan process (see Chapter 4).

-200

-150

-100

-50

0

50

0 5 10 15 20 25

Tem

per

atu

re [

°C]

ΔH [MW]

Optimisation

Lee (2001)

Appendix 2 Bypass design and Two Flash Levels design: Optimisation Results

159

Appendix 2 – Bypass design and Two Flash Levels design:

Optimisation Results

A2.1 Optimisation results of the Bypass design

Figure A2. 1. Bypass refrigeration cycle.

Figure A2. 2. Optimisation progression of the Bypass design (run 1).


160

Table A2. 1. Optimised operating variables of the Bypass design (run 1).

Label in Figure A2.1 Process variable Value A Refrigerant flow rate [kmol·s

-1] 3.43

A Composition [mole fraction]: - Methane 0.2250 - Ethane 0.3743 - Propane 0.1770 - n-Butane 0.1509 - Nitrogen 0.0728 A Discharge pressure [bar] 39.4 A Bypass fraction 0.0868 B Vapour flow rate fraction 0.8527 C Liquid flow rate fraction 0.1106 Stream 1 Stream 2 Bypass D Precooling temperature [°C] –166.3 –97.2 –99.8 E Expansion pressure [bar] 1.21 7.48 20.20 F MSHE outlet temperature [°C] 22.1 25.0 25.0 Performance indicators Value


MIN [°C] 5.0




161



-1] 3.56

A Composition [mole fraction]: - Methane 0.2239

- Ethane 0.3797

- Propane 0.1897

- n-Butane 0.1295

- Nitrogen 0.0772





Stream 1 Stream 2 Bypass D Precooling temperature [°C] –167.5 –66.5 –72.9

E Expansion pressure [bar] 1.32 8.12 22.04

F MSHE outlet temperature [°C] 23.9 21.5 24.7



MIN [°C] 5.0




162



-1] 3.66

A Composition [mole fraction]: - Methane 0.2495

- Ethane 0.3697

- Propane 0.1565

- n-Butane 0.1502

- Nitrogen 0.0741





Stream 1 Stream 2 Bypass D Precooling temperature [°C] –163.6 –96.6 –90.8

E Expansion pressure [bar] 1.23 9.52 22.94

F MSHE outlet temperature [°C] 24.7 23.5 24.9



MIN [°C] 5.0


A2.2 Optimisation results of the Two Flash Levels design

Figure A2. 5. Two Flash Levels refrigeration cycle.


163

Figure A2. 6. Optimisation progression of the Two Flash Levels design (run 1).

Table A2. 4. Optimised operating variables of the Two Flash Levels design (run 1).


-1] 3.42

A Composition [mole fraction]: - Methane 0.2372 - Ethane 0.4013 - Propane 0.0587 - n-Butane 0.2285 - Nitrogen 0.0743 A Discharge pressure [bar] 41.1 H Pressure 2nd flash unit [bar] 26.7 G Liquid fraction to 2nd flash unit 0.2082 Stream 1 Stream 2 Stream 3 Stream 4 D Precooling temperature [°C] –162.3 –110.2 –96.5 –56.3 E Expansion pressure [bar] 1.2 7.8 4.7 11.2 F MSHE outlet temperature [°C] 19.6 24.0 18.9 25.0

B, I Vapour flow rate fraction 0.7506 0.2494 0.2975 0.7025 C, J Liquid flow rate fraction 0.2193 0.5725 0.2559 0.7441



MIN [°C] 5.0



164




-1] 3.38


- Methane 0.2569

- Ethane 0.3536

- Propane 0.1271

- n-Butane 0.1792

- Nitrogen 0.0832


H Pressure 2nd flash unit [bar] 33.4


Stream 1 Stream 2 Stream 3 Stream 4 D Precooling temperature [°C] –162.8 –106.3 –74.7 –54.2

E Expansion pressure [bar] 1.3 8.6 4.9 13.3

F MSHE outlet temperature [°C] 24.9 25.0 25.0 24.9





MIN [°C] 5.0



165




-1] 3.41


- Methane 0.2327

- Ethane 0.4000

- Propane 0.0537

- n-Butane 0.2377

- Nitrogen 0.0759


H Pressure 2nd flash unit [bar] 33.67


Stream 1 Stream 2 Stream 3 Stream 4 D Precooling temperature [°C] –162.2 –109.6 –44.4 –47.3







MIN [°C] 5.0


Appendix 3 Optimisation of the CryoMan Process with Six Compression Stages

166

Appendix 3 – Optimisation of the CryoMan Process with Six

Compression Stages

A3.1 Introduction

The optimised Two Flash Levels design – presented in the case study in Chapter 5 –

showed that operating cost savings (from its corresponding shaft power savings) of £0.54

million per annum are achieved, compared to the CryoMan process (Zheng, 2009). In the

Two Flash Levels design, the compression of the overall refrigerant stream is performed

with six compression stages, i.e. two additional compression stages compared to the

CryoMan process. There is an intercooling stage after each compression stage (according

to the model described in Section 3.3.1), that helps reducing the shaft power demand by

decreasing the temperature and volumetric flow rate of the refrigerant stream at the inlet of

the next compression stage. The Two Flash Levels thus takes advantage of the intercooling

associated with the two additional compression stages.

However, the two extra compression stages (compared to four in the CryoMan process)

would be expected to significantly increase the capital investment of the Two Flash Levels

design because the compressors are the most expensive equipment in the refrigeration

cycle (Mokhatab et al., 2014b, Ch. 3.2).

The Two Flash Levels design is thus compared – in this appendix – to the CryoMan

process optimised to have also six compression stages with their corresponding

intercooling stages. This comparison is in order to evaluate whether the operating cost

savings achieved by the Two Flash Levels design (see Section 5.6) can offset the increase

in capital investment resulting from additional compression stages.

The rationale for this study is as follows: the optimised Two Flash Levels design, which

has six compression stages, is compared to the CryoMan process optimised with six

compression stages. This study would allow comparing both designs in the same basis of

complexity of the compressor. Thus, any shaft power savings yielded by the Two Flash

Levels design, relative to the CryoMan process with six compression stages, would now

represent operating cost savings that can be achieved as a result of the structural

modification proposed (two new streams from a second flash unit), regardless of the

intercooling stages. That is, the operating cost savings achieved by the Two Flash Levels


167

design (see Section 5.6) would justify the increase in capital investment associated with the

additional compression stages.

A3.2 Problem formulation

First, to model the CryoMan process with additional compression stages, either the Bypass

design model (Section 3.3.1) or the Two Flash Levels design model (Section 3.3.2) can be

used. If the Bypass design model is used, then Equation 3.1 (calculation of the flow rate in

the Bypass Stream) is forced to be zero. If the Two Flash Levels design model is selected,

Equation 3.41 (calculation of the flow rate fed to the second flash unit) is forced to be zero.

Similar to the Bypass design and the Two Flash Levels design, the objective function of

the optimisation is the minimisation of the total shaft power demand for refrigerant

compression. The model of the Bypass configuration is used to simulate the CryoMan

process. Thus, the objective function (Equation A3.1) and the mathematical formulation

for the optimisation of the CryoMan process are as follows:

Minimise: 𝑊𝑇𝑜𝑡𝑎𝑙 = ∑ 𝑊𝑖𝑆𝑡𝑔(Φ)𝑛

𝑖=1 𝑖 = 1,2, … , 𝑛 (A3.1)

Subject to: Equations 3.1 to 3.35 (for the Bypass design)

α = 0 (Bypass flow rate fraction) (A3.2)

Δ𝑇𝑀𝐼𝑁 ≥ 5℃ (A3.3)

𝑃𝑅𝐴𝑇 ≤ 2 (A3.4)

∑ 𝑥𝑗 = 1𝑚𝑗=1 𝑥𝑗 ∈ 𝑋𝑀𝑅 𝑗 = 1,2, … , 𝑚 (A3.5)

𝑙𝑏 ≤ Φ ≤ 𝑢𝑏 (A3.6)

where

Φ = [𝑋𝑀𝑅 , 𝑃𝐻𝑖𝑔ℎ, 𝑓𝑉𝑎𝑝, 𝑓𝐿𝑖𝑞, 𝑇𝐴𝑃𝑘 , 𝑃𝐴𝐸

𝑘 , 𝑇𝑜𝑢𝑡𝑘 ]

𝑘 = 𝐿𝑃 𝑆𝑡𝑟𝑒𝑎𝑚, 𝐻𝑃 𝑆𝑡𝑟𝑒𝑎𝑚 (A3.7)

Φ is a vector that includes the values of the operating variables to be optimised, i.e.

refrigerant composition, refrigerant streams pressure level, precooling temperatures and

outlet temperatures from the multi-stream heat exchanger (MSHE), vapour and liquid flow

rate fractions, and compressor discharge pressure (Equation A3.7).


168

Note that, this time, the maximum pressure ratio for each compression stage (Equation

A3.4) is 2, in order to achieve the compression of the overall refrigerant stream with six

compression stages.

Equation A3.2 ensures that the flow rate of the Bypass Stream is zero and, therefore, the

adapted CryoMan process is modelled. Equation A3.3 guarantees feasible heat transfer

inside the MSHE, i.e. heat transfer between hot and cold streams with a minimum

temperature difference of 5°C. Equation A3.5 states that the sum of mole fractions of the

components, in the refrigerant mixture, is unity. Each operating variable (e.g. refrigerant

composition, streams pressure level) is varied within a lower and upper bounds (Equation

A3.6).

The CryoMan process is optimised using WORK software. The Genetic Algorithm method

is used for the optimisation. The values of the optimisation parameters (shown in Table

A3.1), which are employed in the optimisation of both the Bypass design and the Two

Flash Levels design (see Section 5.2), are also employed in the optimisation of the

CryoMan process.

Table A3. 1. Genetic Algorithm parameters for optimisation of the CryoMan process.

Parameter Population Size Maximum Generations Crossover Probability Mutation Rate

Value 250 400 0.85 0.01

A3.3 Problem statement

The optimisation is aimed at minimising the total shaft power demand needed for

refrigerant compression in the liquefaction of a given natural gas stream. The case study is

that first published by Lee (2001), and later employed by Zheng (2009) to optimise the

CryoMan process (in which refrigerant compression is achieved with four compression

stages). The natural gas stream enters the MSHE at 25°C and leaves as LNG at –163°C

(the LNG production is assumed as 0.75 million t per annum). The data of the natural gas

stream is provided in Table A3.2 as a temperature–enthalpy profile.

In order to keep consistency with the optimisation performed by Zheng (2009), the

following assumptions are adopted: the refrigerant stream mixture comprises methane,

ethane, propane, n-butane and nitrogen. The compressor isentropic efficiency is assumed

as 80%. Zero pressure drop of the refrigerant streams inside of the MSHE is assumed. The

minimum temperature approach inside the MSHE for feasible heat transfer is 5°C. Physical


169

and thermodynamic properties of the refrigerant streams (e.g. temperatures, enthalpies) are

calculated using Peng–Robinson equation of state by interfacing with Aspen HYSYS v8.2

(Aspen Technology Inc., 2013).

Table A3. 2. Natural gas stream data (temperature–enthalpy profile).

Segment Supply

Temperature [°C]

Target


-1]

1.1 25.00 –06.03 –1861.5 60

1.2 –06.03 –34.09 –1964.3 70

1.3 –34.09 –57.65 –1885.0 80

1.4 –57.65 –70.10 –2490.0 200

1.5 –70.10 –74.55 –1780.0 400

1.6 –74.55 –82.26 –3084.0 400

1.7 –82.26 –96.50 –1424.0 100

1.8 –96.50 –115.00 –1850.0 100

1.9 –115.00 –163.00 –3840.0 80

A3.4 Optimisation of the CryoMan process

Figure A3.1 shows the minimisation of the objective function (i.e. total shaft power

demand) as the optimisation progresses. According to Figure A3.1, the objective function

reaches a steady value of 24.94 MW of total shaft power demand.

Figure A3. 1. Objective function progression in the optimisation of the operating variables of the CryoMan

process.

The optimised values of the operating variables in the CryoMan process are shown in

Table A3.3 (the ‘Label’ column in Table A3.3 refers to the letters in Figure A3.2). The

total shaft power demand is 24.94 MW, i.e. 0.2883 kWh·kg-1

of LNG.


170

Compared to the CryoMan process in which refrigerant compression is achieved with four

compression stages (26.05 MW), the two additional compression stages allowed a

reduction in the total shaft power demand of 4.3%.

Table A3. 3. Operating variables of the optimised CryoMan process with six and four compression stages.

Six compression stages Four compression stages

Label in Figure A3.2 Process variable Value Value


] 3.15 3.21


- Methane 0.2362 0.2288

- Ethane 0.3739 0.3703

- Propane 0.1640 0.1684

- n-Butane 0.1407 0.1517

- Nitrogen 0.0852 0.0808

A Discharge pressure [bar] 47.7 48.3

B Vapour flow rate fraction 0.8640 0.8830

C Liquid flow rate fraction 0.2020 0.2230

LP Stream HP Stream LP Stream HP Stream

D Precooling temperature [°C] –162.6 –88.7 –164.6 –79.0



Performance indicators Value Value

Number of compression stages 6 4

ΔTMIN

[°C] 5.0 5.0

Total shaft power [MW] 24.94 26.05


LNG] 0.2883 0.3011

Figure A3. 2. The CryoMan refrigeration cycle.

In the CryoMan process with six compression stages, the pressure level of LP Stream is

increased from 1.2 bar to 1.3 bar (which helps reduce the shaft power demand, see Section

4.4.2) at the expense of increasing the mole fraction of the light components (mole fraction


171

of methane is increased from 0.2288 to 0.2362; mole fraction of nitrogen is increased from

0.0808 to 0.0852) which increases the shaft power demand (as discussed in Section 4.4.2).

However, because of the design constraint of maximum pressure ratio (Equation A3.4), the

pressure level of the refrigerant streams lead to compression of the overall refrigerant

stream with six compression stages and thus, take advantage of the intercooling associated

with the two additional compression stages.

The Two Flash Levels design can now be compared to the CryoMan process on the basis

of equal number of compression stages and equal number of intercooling stages. The total

shaft power demand achieved by the CryoMan process, when compression of the overall

refrigerant stream is performed with six compression stages, is 24.94 MW; the total shaft

power demand of the Two Flash Levels design (also with six compression stages, see

Section 5.5) is 25.40 MW. That is, the power demand in the Two Flash Levels design is

1.8% higher than that of the CryoMan process. Therefore, shaft power savings are no

longer achieved with the Two Flash Levels design (relative to the CryoMan process with

six compression stages).

It can be then concluded that the shaft power demand achieved by the optimised Two Flash

Levels design – 25.40 MW – in the case study presented in Chapter 5, is significantly

affected by the intercooling associated with the two additional compression stages,

compared to the CryoMan process with four compression stages.

The comparison suggests that the shaft power savings and corresponding operating cost

savings achieved by the Two Flash Levels design, compared to the CryoMan process with

four compression stages, are achieved mainly as a result of cooling the refrigerant stream

after each compression stage. The structural modification proposed, i.e. two new

refrigerant streams created from a second flash unit, does not show a significant effect

towards bringing shaft power demand savings. Thus, the operating cost savings achieved

by the Two Flash Levels design – shown in Chapter 5 – would not justify the increase in

capital costs that the two additional compression stages represent.

References

172

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