equilibrium and non-equilibrium thermodynamics of natural gas processing measurement and modelling...

Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing

Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas

Processing

Measurement and Modelling of Absorption of Carbon Dioxide into Methyldiethanolamine Solutions at High Pressures

Ph.D Dissertation Even Solbraa14.February 2003


What has been done ?

• A high pressure experimental equipment has been built and new high pressure experimental data are presented

• Equilibrium and kinetic limitations related to CO2 removal at high pressures in MDEA solutions are identified

• NeqSim - a general simulation program for natural gas processing operations has been developed. It is based on equilibrium and non-equilibrium models developed in this work. Many types of processes can now be solved effectively using a general non- equilibrium two-fluid model


How are the results used today?

• Capacity and kinetic limits of high pressure absorption processes of CO2 in MDEA-solutions are estimated

• The simulation program developed is used to solve and teach thermodynamics and mass transfer processes

• High pressure equilibrium (e.g. dew point) and non-equilibrium (e.g. drying) processes are solved in an effective way


1. Introduction to Natural Gas Processing and Transport

2. Equilibrium and Non-Equilibrium Model Development

3. Presentation of the Simulation Program Developed

4. Modelling and Regression to Experimental Data

5. Experimental Work and Results

6. Conclusions

Outline


The Natural Gas Chain


Natural Gas Processing

Natural Gas + CO2

Natural Gas

Lean Amine

Rich Amine

CO2 Gas


Lean Amine Solution

Rich Amine Solution

Acid Natural Gas

Sweet Gas

Random and structured packings:

Film Flow


CO2 removal with physical and chemical solvents

PCO2

xCO2

Physical

Solvents

Chemica

l

Solvents

CO2

Water+CO2

Physical Solvent (water):

CO2

Water

Chemical Solvent(MDEA):

MDEA

CO2HCO3

-

CO32-


Two Illustrative and Case Studies

Problem to reach design specification in high pressure (100 bar) CO2 absorption plant operating at 70-80°C using MDEA

Condensation of Liquid Water in Sub Sea Dry Gas Pipeline operating between 100-200 bar

1. Erroneous predictions of water dew-point with standard equations of state in high pressure natural gas systems

1. Almost all models developed are low pressure models (GE-models).

2. High pressure equilibrium and mass transfer data not available

2. Non-equilibrium models for two-phase pipe flow not available







6. Conclusions

Outline


The Non-Equilibrium Two Fluid Model

The Non-Equilibrium Two Fluid Model

Closure Relations

Thermodynamic Models

Mass Transfer / Kinetic Models

Physical Property Models


Weak Electrolyte Calculation Procedure

2 2 3MDEA H O CO HCO MDEA

Reactive/Non-reactive TP-flash algorithm


Thermodynamic Modelling of Amine Thermodynamic Modelling of Amine SolutionsSolutions

Polynoms(Kent and Eisenberg, 1976)

Electrolyte GE-modelsAustgen (1989), Li and Mather (1994)

State of the Art

Future

Electrolyte Equations of StateFurst and Renon (1993), this work

+ Easy and fast- Too simple, no physics

+ Relatively easy and fast- Problematic to add supercritical components- Low pressure model

+ Generally applicable

- Computational demanding


Thermodynamic ModelsThermodynamic Models

Type of FluidType of Fluid

ElectrolyteElectrolyteNon-PolarNon-Polar PolarPolar PolymersPolymers

GE-ModelsGE-Models19501950

19801980

EoS-ModelsEoS-Models


19901990

GE-ModelsGE-Models

Debye-Debye-HuckelHuckel

EoS-ModelsEoS-Models EoS-ModelsEoS-Models


20002000


Empirical Empirical modelsmodels

Empirical Empirical modelsmodels

otherother

EoS-ModelsEoS-Models EoS-ModelsEoS-Models EoS-ModelsEoS-Models EoS-ModelsEoS-Models

YearYear


Definition and Calculation of Thermodynamic Equilibrium

Equation of Statesi i i ix P y P

Parameters:

• Critical Temperature and Pressure

• Accentric Factor

GE-models ,

, xpi sat i

i i sat i i i

v P Px P e y P

RT

Molecular Parameters:

• Vapour Pressure of Pure Components

• Molar Volumes in solution


Development of Two New Electrolyte Equations of State

BORNLRSRSRRFRT

AA

RT

AA

RT

AA

RT

AA

RT

AA

RT

AA

00

2

0

1

000

,

, ,r

T P

A T V nRTP

V V

nGeneral Equation of State

Contributions to the Helmholtz Energy

The Modelling Procedure

Find Best Molecular EoS

Find Best Electrolyte Terms


Development of Two New Electrolyte Equations of State


Equations of State Considered

• RK (Redlich Kwong, 1949)

• SRK (Soave, 1971)

• PR (Peng and Robinson, 1979)

• ScRK (Scwartzentruber and Renon, 1989)

• CPA (Kontegorgios, 1999)

Equations of State Mixing Rules

• no

• Classic (Van der Waals, 1905)

• Huron Vidal (Huron-Vidal, 1979)

• Wong-Sandler (Wong and Sandler, 1993)

Electrolyte Extensions

• Debye-Huckel (Debye-Huckel, 1952)

• MSA (Blum and Høye, 1982)

• Furst and Renon (Furst and Renon, 1993)


Molecular Terms of Electrolyte Equations of State

Absolute average relative deviation1) [%] between experimental and calculated vapour pressures and densities with different equation of states

Component RK SRK PR ScRK2) CPA3) Experimental Data Methane vapour pressure: liquid density: gas density:

15.6 5.8 17.7

2.8 6.5 3.9

0.9 8.1 1.5

2.8 6.5 4.6

- - -

Perry (1998), Borgnakke et. al (1997)

Nitrogen vapour pressure: liquid density: gas density:

10.1 4.5 11.8

1.7 4.2 3.3

0.5 4.5 2.3

2.2 4.1 3.8

- - -


CO2 vapour pressure: liquid density: gas density:

21.4 14.9 24.9

0.3

11.6 3.2

0.8 4.0 2.5

0.2

11.5 3.5

2.2 1.9 1.9


MDEA vapour pressure: liquid density: gas density:

>>100 20.8

-

83.3 13.3

-

67.2 3.16

-

5.1

14.4 -

4.2 1.1 -

Noll et.al. (1998)

Water vapour pressure: liquid density: gas density:

>>100 30.7

>>100

11.5 27.8 15.5

6.9

18.8 10.6

0.3

27.8 5.9

1.2 1.1 1.7


1) Deviation (%) = 100 x (experimental-calculated)/experimental 2) The polar coefficients in the ScRK-EOS coefficients were fitted for water, CO2 and MDEA 3) The coefficients in the CPA-EOS were fitted to experimental data


Mixing Rules for Molecular Terms

Absolute average deviations (%) between experimental data and different models for the calculation of solubility of gasses in water and water in gas.

Gas No.points used for fitting1)

SRK + classic

SRK- HV2)

ScRK-HV

PR-HV

SRK-WS

CPA + classic

Number of Fitted Parameters

1 4 4 4 5 1

Nitrogen nitrogen in water water in nitrogen

13 78

>>100 32.2

3.0 8.1

7.1

17.6

4.3 10.0

8.7

11.6

29.7 28.2

CO2 CO2 in water water in CO2

43 57

>>100 45.0

6.0

13.5

6.1

10.6

5.8 11.8

7.6

15.4

12.0 22.5

Methane methane in water water in methane

176 215

>>100 52.2

6.4

13.1

5.5

10.6

5.9 10.1

7.6

10.4

31.8 14.1

1) See chapter 8 for references to the actual experimental data used in the fitting 2) The parameter in the Huron Vidal and Wong Sandler mixing rule was not fitted


Electrolyte Terms

0

321k l kl

k lSR

A A n nW

RT V

i i

iiLR

LRN

VZn

RT

AA

314

3220

20 2

*0

11

4i i

is iBORN

n ZA A Ne

RT RT D

Osmotic coefficients of salt solutions calculated using the electrolyte ScRK-EOS


Evaluation of Electrolyte Terms

Evaluation of different electrolyte models for the calculation osmotic coefficient and mean ionic coefficient for 28 halide salt solutions1)

Model No. of experimental points used in fitting

Osmotic coefficient abs.avg.rel.dev [%]

Mean ionic activity abs.avg.rel.dev [%]

Experimental data

Electrolyte ScRK-EOS

230 2.1 5.5 Robinson (1952)

Electrolyte CPA-EOS

230 2.3 4.9 Robinson (1952)

1) Salt concentrations: 0.1-6.0 molal. Salt solutions: NH4Cl, LiCl, LiBr, LiI, NaCl, NaBr, NaI, KCl, KBr, KI, KBr, KI, RbCl, RbBr, RbI, CsCl, CsBr, CsI, MgCl2, MgBr2, MgI2, CaCl2, CaBr2, MgI2, CaCl2, CaBr2, CaI2, SrCl2, SrBr2, SrI2, BaCl2, BaBr2, BaI2


Predictions With the Electrolyte Model

Calculated and experimental density of an aqueous NaCl solution

Calculation of mean ionic activity coefficients of salt solutions using the electrolyte ScRK-EOS.

Density of Ionic Solution Mean Ionic Activity Coefficient


Non-Equilibrium Modelling

1900:

1920:

1950:

1970:

1980:

1990:

2000:

Fick’s law for diffusion

Fourier law of heat transfer

Kinetic Theory of Gasses

Multicomponent Mass Transfer

Non-Equilibrium Thermodynamics

Molecular Simulation

Resistance at Interface

Scientific Work Simulation Tools

Equilibrium Models

Stage Efficiencies

Simple Maxwell Stefan

General Maxwell Stefan

OLGA

Software

HYSYS

ASPEN PLUS

Fick’s law

Simple Maxwell Stefan

General Maxwell StefanThis work


Generalized Maxwell Stefan Equations

,1

n

t k k T P k k k k jj

c RTd c P

k jF F

1

tJ c B d

1`

1 1, 1,2,..., 1

ni k

iikin iki k

ij iij in

x xB

D D

B x i j and i j nD D

Multicomponent Maxwell Stefan Equation:

Generalized Driving Force:

+ General model

- Relatively complicated- Need thermodynamic model


The Enhancement Factor

CO2 Water

xCO2

yCO2

CO2Water MDEACO2

HCO3-

MDEA+xCO2

yCO2

2 2 3MDEA H O CO HCO MDEA

,

,

i reactivei

i non reactive

JE

J


Calculation of the Enhancement Factor

Two Ways to Estimate the Enhancement Factor:

• Analytical Expressions (for simple reactions, e.g reversible first order reactions)

• Numerical Solutions of Film (for coupled and reversible reactions)

This work:

2

2

2

2 ,

2,

1t CO eff

COCO eff

k MDEA DE

k analytical

2 2

* *, ,( )t CO i CO bJ c E k x x

2

*,CO bx CO2 fraction at chemical equilibrium in liquid bulk


The Generalized Non-Equilibrium Two Fluid Model

• Conservation of total mass

• Conservation of components

• Conservation of momentum

• Conservation of energy







6. Conclusions

Outline


NeqSim – a General Non-Equilibrium Simulator

• General modelling tool for non-equilibrium and equilibrium processes

• Based on rigorous thermodynamic models

• Fluid mechanics based the on the one- or two fluid model

• Implemented in an object oriented language (Java/Python object oriented design where everything is an object)

• Suitable for being used as a modelling tool (general parameter fitting routines implemented)

• Validated against experimental data (equilibrium/non-equilibrium)


NeqSim – a General Non-Equilibrium Simulator


NeqSim - Examples of use

• Multiphase flash calculation

• Construction of phase envelopes

• Weak electrolyte calculations

• Process plant simulation


Parameter Fitting Routines

2

2

1

;( )

Ni i

i i

y y x

aa

Shi-Square Fitting

Minimized using the Levenberg- Marquardt Method







6. Conclusions

Outline


Thermodynamic Properties of Mixtures

ScRK-EOS + Huron Vidal CPA-EOS + ClassicMutual solubility of Water+CO2:

Freezing points of MDEA+Water: Mutual solubility of Methane+Water:

Mutual solubility of Water+CO2:


Solubility of CO2 in water+MDEA solutions

Electrolyte ScRK-EoS

20.5 wt % MDEA : 50 wt% MDEA

Ref. MDEA (wt%) Temperature (K) Loading range (mol CO2/mol

amine)

Number of points

AAD (%)

Jou et.al. (1993) 35 313, 373 0.005-0.795 35 26.5

Jou et.al. (1982) 23.448.9

298,313,343,373,393298,313,343,373,393

0.0009-1.8330.0001-1.381

5455

29.628.4

Austgen et.al. (1991)

23.448.9

313313

0.006-0.8420.04-0.671

95

21.021.0

Chakma and Meisen (1987)

19.8, 48.9 373 0.04-1.304 17 18.8

Bahiri (1984) 20.0 311, 339 0.157-1.336 44 12.8

Kuranov (1996) 18.8-19.232.1

313, 333, 373, 393313, 333, 373, 393

0.209-1.3160.195-1.157

3334

16.323.2

Rho et.al. (1997) 5.020.5

323, 348, 373323, 348, 373

0.03-0.6840.026-0.847

1931

16.411.3

Mac Gregor and Mather (1991)

23.4 313 0.124-1.203 5 31.4

Average Deviation

26%


High pressure solubility of CO2 and methane in water+MDEA solutions

Electrolyte ScRK-EoSEstimated bubble point pressure30 wt % MDEA

Estimated PCO2:30 wt% MDEA


High pressure solubility of methane in CO2+water+MDEA solutions

Electrolyte ScRK-EoSEstimated methane solubility30 wt % MDEA


Capacity Loss of Amine Solution at 100 bar and 70C







6. Conclusions

Outline


The High-Pressure Wetted Wall Column


Experiments Done in This Work

Experiment Type

Number of Experiments

Comments Temperature [ C]

Pressure [bar]

Purpose

Water-CO2-nitrogen

12 Low pressure experiments

25, 40 20 Study physical mass transfer – compare to exciting low pressure data

Water-CO2-nitrogen

35 High pressure experiments

25, 40 50, 100,150

Measure new high pressure data

MDEA-water-CO2-nitrogen

48 High pressure experiments

25, 40 50, 100,150

High pressure absorption data of CO2 in MDEA solutions


Experimental Results – Reference Data CO2 +Water

Reference Reynolds Number K a b Abs.rel.dev. [%]

Yih et.al. (1982) 300<Re<1600 2.99510-2 0.2134 0.50 13.0 This work 230<Re<1750 3.10110-2 0.2201 0.50 10.5

1/32* Rea bLL

kk K Sc

D g

Reference Reynolds Number K a b Abs.rel.dev. [%]

Yih et.al. (1982) 300<Re<1600 2.99510-2 0.2134 0.50 13.0 This work 230<Re<1750 3.10110-2 0.2201 0.50 10.5


Experimental Results – Reference Data CO2, MDEA and water

2

2

2

2 ,

2,

1 t CO eff

COCO eff

k MDEA DE

k 2 2 313

1 1exp

313a

t t T K

Ek k

R T K

0

50

100

150

200

250

300

270 290 310 330 350 370 390

Temperature [K]

k2 [

m/k

mo

l sec]

Pacheco (1998) -low pressure

This work - highpressure

3

2 313.15 6.45 /

50.0

t T K

a

k m kmol s

kJE mol


Conclusions

A high pressure wetted wall column was designed and constructed New mass transfer data were obtained for absorption of CO2 into MDEA-solutions at

pressures between 50 and 150 bar An electrolyte EOS (electrolyte ScRK-EOS) was used to model the thermodynamics

of the CO2-MDEA-water systems The electrolyte EOS was able to represent the experimental data for the systems CH4-

CO2-MDEA-water with good accuracy A general non-equilibrium mass transfer model was developed A non-equilibrium simulator – NeqSim – was implemented in a Java code Examples of how to do non-equilibrium process simulations were presented The non-equilibrium model developed is able to represent the experimental mass

transfer data of this work with a good precision.


Conclusions

For a given partial pressure CO2, the capacity of MDEA solutions is lowered at increasing pressures. The capacity can be reduced up to 40% at 200 bar total pressure (inert gas methane)

For a specified natural gas, the capacity of MDEA solutions will increase with increasing gas stream pressures. This increase is not as high as we would expect from only consideration of the increased partial pressure of CO2

The reaction kinetics is not considerable affected by the total pressure (up to 150 bar with nitrogen as inert gas)


Operation Chart 100 bar, 70-80C

0.0

2.0

4.0

6.0

8.0

10.0

12.0

0 0.2 0.4 0.6 0.8 1

Loading

CO

2 P

art

ial P

res

su

re

Hysys

Operationline

Ideal Electrolyte EOS

Real Electrolyte EOS

Case 1: Case 2: Condensation of Liquid Water in Sub Sea Dry Gas Pipeline operating between 100-200 bar

Case 1: Problem to reach design specification in high pressure (100 bar) CO2 absorption plant operating at 70-80°C using MDEA


Case 2: Case 2: Condensation of Liquid Water in Sub Sea Dry Gas Pipeline operating between 100-200 bar

Solubility of water in methane:


Thanks

• Institute for Energy- and Process Technology

• Statoil

• Norwegian Research Council

equilibrium and non-equilibrium thermodynamics of natural gas processing measurement and modelling...

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