investigation of water treatment and steam generation

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2015-05-01

Investigation of Water Treatment and Steam

Generation Alternatives for SAGD Operations Using

Process Integration and Optimization

Dadashi Forshomi, Zainab

Dadashi Forshomi, Z. (2015). Investigation of Water Treatment and Steam Generation

Alternatives for SAGD Operations Using Process Integration and Optimization (Unpublished

master's thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/26666

http://hdl.handle.net/11023/2210

master thesis

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UNIVERSITY OF CALGARY

Investigation of Water Treatment and Steam Generation Alternatives for SAGD Operations

Using Process Integration and Optimization

by

Zainab Dadashi Forshomi

A THESIS

SUBMITTED TO THE FACULTY OF GRADUATE STUDIES

IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE

DEGREE OF MASTER OF SCIENCE

GRADUATE PROGRAM IN CHEMICAL AND PETROLEUM ENGINEERING

CALGARY, ALBERTA

APRIL, 2015

© Zainab Dadashi Forshomi 2015

Abstract

This thesis applies a combination of process integration tools and mathematical

optimization techniques to investigate opportunities to improve surface efficiencies in steam

assisted gravity drainage (SAGD) of oil sands operations.

The goal of the thesis is to design a distributed effluent treatment system based on the

concept of process integration and model this system using mathematical programming methods

to minimize cost and energy consumption. Different combinations of water treatment units and

steam generation options in SAGD operations are assessed and the tradeoffs between cost, energy,

water and GHG emissions within and across these combinations are explored. The results of the

thesis show that there are potential cost and electricity savings of up to 19.5% and 12% respectively

in the water treatment system of SAGD operations. Interesting tradeoffs have been identified

between cost, energy and water which can help oil sands operators make informed decisions about

investments in which water treatment technologies for SAGD operations.

i

Acknowledgements

I wish to express my sincere thanks and deep gratitude to my supervisor, Dr. Joule

Bergerson, for her invaluable guidance, helpfulness, inspiration and assistance throughout this

M.Sc. project. I am also deeply indebted to her for understanding and supporting me at demanding

situations.

I would like to give special thanks to my co-supervisor, Dr. Alberto Alva-Argáez, for his

continuous support throughout the course of my program. His fruitful advices have always helped

and encouraged me through different stages of work.

I am also grateful to my committee members Dr. Ian Gates, Dr. Milana Trifkovic and Dr.

Angus Chu for accepting to be in my defence committee.

I would like to thank our research group members, with whom I had the pleasure of

working. I specially thank Dr. Carlos Eduardo Carreon, Dr. Ganesh Doluweera and my dear friend

Nikou for their great help.

I gratefully acknowledge the financial support received from Canada School of Energy and

Environment, Carbon Management Canada (CMC), Natural Sciences and Engineering Research

Council of Canada (NSERC), and the Department of Chemical and Petroleum Engineering at the

University of Calgary.

Last but not least, I would like to offer my deep thanks, appreciations and gratitude to my

beloved family, my parents and siblings, who are always supportive, understanding, patient and

encouraging. Moreover, I would like to thank my dear husband, Kavan, for his continuous support

and being great sources of motivation and encouragement.

ii

Dedicated to my parents, brothers, and my husband

iii

Table of Contents

Abstract ................................................................................................................................ i Acknowledgements ............................................................................................................. ii Table of Contents ............................................................................................................... iv List of Tables ..................................................................................................................... vi List of Figures and Illustrations ....................................................................................... viii List of Symbols, Abbreviations and Nomenclature ........................................................... xi

CHAPTER ONE: INTRODUCTION ..................................................................................1

CHAPTER TWO: BACKGROUND AND LITERATURE REVIEW ...............................5 2.1 Background ................................................................................................................5

2.1.1 Overview of SAGD Operations .........................................................................5 2.1.1.1 Separation units ........................................................................................8 2.1.1.2 Water deoiling ..........................................................................................9 2.1.1.3 Water treatment ......................................................................................11 2.1.1.4 Steam generation ....................................................................................13 2.1.1.5 Waste disposal .......................................................................................14

2.2 Literature review ......................................................................................................15 2.2.1 Comparison of water treatment processes .......................................................15 2.2.2 Process Integration and Pinch Analysis ..........................................................18 2.2.3 Distributed effluent treatment system vs. centralized treatment system .........20

CHAPTER THREE: METHODS ......................................................................................31 3.1 Objective of the model .............................................................................................31 3.2 Operations Research and Mathematical Modeling ..................................................32

3.2.1 Objective function ...........................................................................................32 3.2.2 Decision variables ...........................................................................................33 3.2.3 Constraints .......................................................................................................33 3.2.4 Feasible region and optimal solution ...............................................................34 3.2.5 Linear and nonlinear models ...........................................................................34 3.2.6 Integer and non-integer models .......................................................................34 3.2.7 Convex and nonconvex sets ............................................................................34

3.3 Overview of the model ............................................................................................35 3.4 Problem description .................................................................................................36

3.4.1 Overview of the system components ...............................................................36 3.4.1.1 Contaminant mass load: .........................................................................40 3.4.1.2 Removal ratio: ........................................................................................40 3.4.1.3 Four cases for steam generation and waste disposal system in SAGD

operations ................................................................................................43 3.4.2 Developing the mathematical model ...............................................................46

3.4.2.1 Sets, parameters and variables ...............................................................48 3.4.2.2 Constraints .............................................................................................53 3.4.2.3 Objective function ..................................................................................59 3.4.2.4 Binary variables .....................................................................................61 3.4.2.5 Additional constraints (with binary variables) .......................................62

iv

3.5 Solution strategy ......................................................................................................64 3.5.1 The mixed-integer linear programming (MILP) problem ...............................65 3.5.2 The linear programming (LP) problem ...........................................................70

CHAPTER FOUR: RESULTS AND DISCUSSION ........................................................73 4.1 Optimized design for minimum total cost ...............................................................73 4.2 Cost minimization analysis for the treatment network ............................................78

4.2.1 Operating cost breakdown ...............................................................................79 4.2.2 Energy consumption analysis ..........................................................................85 4.2.3 GHG emissions analysis ..................................................................................90 4.2.4 Makeup water consumption and disposal water analysis ................................92 4.2.5 Makeup water and GHG emissions tradeoffs ..................................................94

4.3 Energy minimization analysis for the treatment network ........................................96 4.4 Sensitivity analysis ..................................................................................................97

4.4.1 Hardness requirement in the boiler ..................................................................97 4.4.2 Silica requirement in the boiler .......................................................................98 4.4.3 Capital cost of the treatment units ...................................................................99 4.4.4 Boiler blowdown recycle ratio in case 3 .......................................................100 4.4.5 Makeup water price .......................................................................................101 4.4.6 Makeup water composition ...........................................................................102 4.4.7 Inlet oil concentration limit for the oil removal filter ....................................102 4.4.8 Electricity emissions intensity .......................................................................103 4.4.9 Carbon tax .....................................................................................................104

CHAPTER FIVE: CONCLUSIONS AND RECOMMENDATIONS ............................107 5.1 Summary of results and principal insights .............................................................107 5.2 Future work ............................................................................................................109 5.3 Recommendations ..................................................................................................109

REFERENCES ................................................................................................................111 APPENDIX A ………………………………………………………………………... 122

APPENDIX B ………………………………………………………………………….128

v

List of Tables

Table 2-1 Concentration range for produced water contaminants .................................................. 6

Table 2-2 Concentration range for makeup water contaminants .................................................... 7

Table 2-3 Deoiling processes and their oil removal efficiency .................................................... 10

Table 2-4 Boiler feed water quality requirements for OTSG and drum boiler ............................. 14

Table 3-1 Contaminant concentrations of water and wastewater streams in the system used in the optimization model ......................................................................................................... 38

Table 3-2 Treatment processes and removable contaminants in SAGD operations ..................... 39

Table A-1 Capital, operating and total cost of the SAGD plant for current and optimized designs for the four cases (all costs are in $/year) .............................................................. 123

Table A-2 Capital, operating and total cost savings for the SAGD plant by optimization for the four cases (all costs are in $/year) ................................................................................. 123

Table A-3 Operating cost of the SAGD plant, broken down into electricity, chemicals and other costs for the four cases (all costs are in $/year) ......................................................... 124

Table A-4 Electricity, chemicals and other costs savings for the SAGD plant by optimization for the four cases (all costs are in $/year) ........................................................................... 124

Table A-5 Electricity and natural gas consumption of the SAGD plant for the four cases (MJ/year) ............................................................................................................................. 126

Table A-6 GHG emissions from electricity and natural gas consumption of the SAGD plant for the four cases (tCO2/year) ............................................................................................. 127

Table B-1 Capital, operating and total cost of the water treatment system for current and optimized designs for the four cases (all costs are in $/year) ............................................. 128

Table B-2 Capital, operating and total cost savings for the water treatment system by optimization for the four cases (all costs are in $/year) ...................................................... 128

Table B-3 Operating cost of the water treatment system, broken down into electricity, chemicals and other costs for the four cases (all costs are in $/year) ................................. 129

Table B-4 Electricity, chemicals and other costs savings for the water treatment system by optimization for the four cases (all costs are in $/year) ...................................................... 129

Table B-5 Operating cost of the water treatment system, broken down by treatment units for the four cases (all costs are in $/year) ................................................................................. 130

vi

Table B-6 Operating cost savings for the water treatment system, broken down by treatment units for the four cases (all costs are in $/year) .................................................................. 131

Table B-7 Capital cost of the water treatment system, broken down by treatment units for the four cases (all costs are in $/year) ....................................................................................... 132

Table B-8 Capital cost savings for the water treatment system, broken down by treatment unit for the four cases (all costs are in $/year) .................................................................... 133

Table B-9 Electricity consumption of the water treatment system for current and optimized designs for the four cases (MJ/year) ................................................................................... 134

Table B-10 Electricity savings of the water treatment system by optimization for the four cases (MJ/year) ................................................................................................................... 134

Table B-11 Electricity consumption of the water treatment system for current and optimized designs, broken down by treatment units for the four cases (MJ/year) .............................. 135

Table B-12 Electricity savings of the water treatment system, broken down by treatment units for the four cases (MJ/year) ................................................................................................ 136

Table B-13 GHG emissions from electricity consumption of the water treatment system for the four cases (tCO2/year) .................................................................................................. 137

Table B-14 GHG emissions reduction in the water treatment system by optimization for the four cases (tCO2/year) ........................................................................................................ 137

Table B-15 Makeup water consumption and disposal water generation in SAGD operations for the four cases (tonne/hr) ................................................................................................ 137

vii

List of Figures and Illustrations

Figure 2-1 Schematic diagram of SAGD operations ...................................................................... 8

Figure 2-2 Centralized treatment plant ......................................................................................... 20

Figure 2-3 Distributed effluent treatment system ......................................................................... 21

Figure 2-4 A wastewater stream and treatment line on concentration vs mass load diagram (C¬in=50 ppm, Ce=20 ppm, Cout=10 ppm, ΔmT=6 kg/hr) ................................................. 25

Figure 2-5 Example of partial bypass of water stream around a process unit .............................. 25

Figure 3-1 Examples of convex and nonconvex sets .................................................................... 35

Figure 3-2 Simplified scheme of water treatment and steam generation in SAGD operations .... 42

Figure 3-3 Four cases for steam generation and waste disposal in SAGD operations ................. 45

Figure 3-4 Superstructure of the system ....................................................................................... 47

Figure 3-5 Overall mass balance in the system ............................................................................ 54

Figure 3-6 Mass balance for the water source splitters................................................................. 54

Figure 3-7 Mass balance for the treatment unit mixers and splitters ............................................ 55

Figure 3-8 Mass balance for the discharge mixer ......................................................................... 56

Figure 4-1 Current design of water treatment network for case 1 (all stream flow rates are in tonne/hr) ................................................................................................................................ 74




Figure 4-5 Optimized design of case 1 for minimum cost (all stream flow rates are in tonne/hr) ................................................................................................................................ 76



viii


Figure 4-9 Annual cost of the water treatment system for cases 1-4, with operating cost breakdown ............................................................................................................................. 80

Figure 4-10 Annual costs of the water treatment system for cases 1-4, including operating cost breakdown, plus additional capital and operating costs in the boiler (differences between the costs of the OTSG and drum boiler) ................................................................. 82

Figure 4-11 Annual cost of the water treatment system for cases 1-4, with capital and operating cost broken down by treatment unit (CC=Capital cost- solid fill, OC=Operating cost- hashed fill) ........................................................................................... 83

Figure 4-12 Electricity consumed by the water treatment system for cases 1-4, brokendown by treatment units .................................................................................................................. 86

Figure 4-13 Energy consumption SAGD operations for cases 1-4 (electricity consumed in water treatment system and additional natural gas consumption in the OTSG above what is consumed in the drum boiler) ............................................................................................ 89

Figure 4-14 GHG emissions from electricity and use of additional natural gas in the OTSG ..... 91

Figure 4-15 Makeup water consumption and disposal water generation for all cases ................. 93

Figure 4-16 Make up water consumption and GHG emissions (from electricity consumption in water treatment system and additional natural gas consumption in OTSG) tradeoffs ..... 95

Figure 4-17 GHG emissions (from electricity consumption in water treatment system and additional natural gas consumption in OTSG) vs. make up water consumption .................. 95

Figure 4-18 Effect of boiler blowdown recycle ratio on makeup water consumption and disposal water generation in case 3 ..................................................................................... 100

Figure 4-19 Effect of the electricity emissions factor on the total GHG emission (from electricity consumption in water treatment system and additional natural gas in the OTSG) ................................................................................................................................. 103

Figure 4-20 Effect of the carbon tax on the total cost of SAGD water treatment and steam generation plant ................................................................................................................... 105

Figure A-1 Annual cost of the SAGD plant for cases 1-4, with operating cost breakdown ....... 122

Figure A-2 Annual cost of the SAGD plant for cases 1-4, with capital and operating cost broken down by treatment unit, steam generation and disposal sections (CC=Capital cost- solid fill, OC=Operating cost- hashed fill) ................................................................. 125

ix

Figure A-3 Energy consumed by the SAGD plant for cases 1-4, brokendown by electricity and natural gas .................................................................................................................... 126

Figure A-4 GHG emissions of the SAGD plant from electricity and natural gas ...................... 127

x

List of Symbols, Abbreviations and Nomenclature

Symbol Definition AF After filter BFW Boiler feed water BPCD Barrels per calendar day BPD Barrels per day C Concentration Ca(OH)2 Calcium hydroxide (lime) CC Capital cost CM Ceramic membrane CPF Central processing facility CPI Corrugated plate interceptor CSS Cyclic steam stimulation DGF Dissolved gas flotation DO Dissolved oxygen Evap Evaporator F Flowrate FWKO Free water knockout GHG Greenhouse gas HC Hydrocyclone HCl Hydrochloric acid HLS Hot lime softening IGF Induced gas flotation LP Linear programming MgO Magnesium oxide MILP Mixed-integer linear programming MINLP Mixed-integer nonlinear programming Na2CO3 Sodium carbonate (soda ash) NaOH Sodium hydroxide (caustic) NLP Nonlinear programming OC Operating cost OR Operations research ORF Oil removal filter OTSG Once-through steam generator ppm Parts per million RR Removal ratio SAGD Steam assisted gravity drainage ST Skim tank TDS Total dissolved solids TH Total hardness TOC Total organic carbon TP Treatment process TSS Total suspended solids TU Treatment unit WAC Weak acid cation exchanger

xi

WLS Warm lime softening ZLD Zero liquid discharge

xii

Chapter One: Introduction

World energy demand had significant growth over the past three decades; it has increased

about 84% in the period 1980 to 2012 and is forecast to increase by 33% to 41% between 2012

and 2035 [1]–[6]. Global crude oil demand, the major contributor to the total energy mix, is

anticipated to increase by 0.8% per year from 2014 to 2035 [2]. As conventional oil resources

continue to be depleted, unconventional resources have started to attract global attention and high

prices of oil over the past 35 years, have made the extraction of unconventional oil resources

economically viable [7]–[9]. Oil sands deposits in Alberta, Canada are an example of this trend in

development towards unconventional oil resources. Alberta’s oil sands are ranked the third largest

crude oil reserves in the world after Saudi Arabia and Venezuela [7]. The rapid development of

this resource brings substantial economic benefits but also a range of challenging environmental

issues including water contamination and treatment which force oil sands operators to improve the

efficiency of the extraction process (the rapid oil price decrease that started in mid-2014 has started

to threaten the unconventional oil industry. For example, an International Energy Agency (IEA)

report in October 2014 suggested that a quarter of proposed Canadian oil projects could be under

threat with oil prices lower than $80 U.S. per barrel for an extended period of time [10]).

Oil sands consist of a form of crude oil called bitumen that is a viscous and tar-like

substance, clay minerals, sand particles and water [8], [11], [12]. Two major methods for oil sands

extraction are surface mining and in situ extraction. Surface mining of oil sands ores includes

removal of the material (bitumen, sand, water, etc.) using large trucks and shovels. Once the

bitumen has been extracted from the earth it is separated from the other components (sand, water,

clay) using an alkaline hot water recovery process [13]. In situ techniques are used for oil sands

reserves that are too deep (more than 70 meters or 200 feet) below the ground such that mining

1

extraction techniques are not viable. In situ techniques involve extracting bitumen in situ (in place)

by drilling wells and injecting steam, air or solvent [12], [14].

Currently, the most largely deployed in situ recovery process (and the focus of this study)

is Steam Assisted Gravity Drainage (SAGD) (oil production using SAGD has surpassed oil

production using Cyclic Steam Stimulation (CSS) since 2009. In 2009 SAGD production rate in

Alberta was 244,507 BPD as opposed to 207,947 BPD production rate of CSS) [15], [16]. Since

80 percent of Alberta’s oil sands reserves are too deep underground to mine, in situ oil sands

production is growing more rapidly than mined oil sands production [7], [17]. Before 2012, the

majority of oil sands production was from surface mining, but for the first time in 2012 in situ

production overtook mining by representing 52% of the total oil sands production that year and its

share is expected to increase in the future [7], [17].

The important role anticipated for in situ extraction (and the SAGD operations specifically)

in Canada’s energy future, motivates oil producers to improve the efficiency of the extraction

process. Oil sands extraction processes are water intensive operations and environmental

regulations limit the ability to withdraw fresh water and even reduce brackish water removal.

Therefore, water use in oil sands extraction processes is important to oil sands operators and they

attempt to reduce the water use [18]–[20]. Moreover, although in situ oil extraction methods have

lower water intensity and land disturbance than mining operations, higher GHG intensity per barrel

of oil produced with in situ techniques motivates oil companies to explore more energy efficient

operations to reduce their overall environmental footprint [21]. Since energy inputs are the largest

cost in these operations, saving energy is of primary economic concern as well.

SAGD is a thermal oil recovery method applied to oil sands deposits. SAGD extraction

method includes high pressure (7,000-11,000 kPa), high temperature (about 300˚C), and 100%

2

quality steam [8], [22]. The steam to oil ratio for extra heavy oil or bitumen production in the

SAGD operations typically ranges between 2 and 4 barrels of cold water equivalent per day over

barrels of bitumen per day (i.e. to produce one barrel of bitumen, 2-4 barrels of cold water

equivalent of steam needs to be injected into the reservoir). Aside from the amount of steam that

is lost due to the reservoir retention (usually 5-10%), the remaining steam returns to the surface

together with the bitumen emulsion as hot water and is called produced water [8], [23]. Typical

SAGD projects have oil production capacity of ~10,000-100,000 BPD depending on the project

size. This means that water treatment of large volumes of produced water is required [8]. Oil

producers attempt to recycle as much produced water as possible for reuse in steam generation. In

order for the produced water to achieve quality requirements for recycle and use in boilers for

steam generation, the water must pass through a series of treatment processes. There are a number

of process alternatives for produced water treatment that are described later in this chapter.

Depending on the combination of treatment processes employed, between 87 to almost 99% of the

produced water can be recycled for steam generation [24]–[26].

A stream of makeup water is required to supplement the treated produced water volume

for steam generation that can be withdrawn from a fresh or saline water source based on their

availability and regulatory requirements [18]–[20] at each SAGD plant.

Environmental regulations for water disposal and withdrawal force oil sands producers to

recycle more produced water and use less makeup water [18]–[20]. On the other hand, the

treatment of water for recycle and reuse requires energy and capital. Increased energy consumption

leads to more GHG emissions which impose another environmental restriction facing the industry

[20], [27]. Therefore, there are tradeoffs between water and energy consumption, cost and GHG

emissions. These tradeoffs have yet to be explored in the literature but are needed to ensure

3

efficient design and operation of the wastewater treatment system and steam generation in SAGD

facilities. The focus of this thesis is to use process integration and mathematical optimization

techniques for the investigation of different technologies for wastewater treatment and steam

generation for a SAGD facility (process integration investigates diversion of flows and helps to

improve the wastewater treatment network design). The goal of the study is to develop a

framework that makes use of optimization to evaluate a set of water treatment and steam generation

networks for SAGD operations that are modeled using mathematical programming to evaluate

them in terms of total energy consumption, cost and makeup water consumption. The optimization

model is then used to define and quantify the tradeoffs involved in decisions about investment and

operation of water treatment processes.

In the second chapter of this thesis some background information about SAGD operations

and SAGD water treatment system are presented. Then the previous works on evaluating the

existing SAGD water treatment processes in the literature are investigated and the gaps in the

literature are discussed. Also, previous works on applying mathematical optimization techniques

to water networks are presented. Afterwards, in the third chapter the modeling and optimization

procedures for the system in this study are presented and four cases of water treatment and steam

generation are introduced. In the fourth chapter the results of the optimization and comparison

between different water treatment and steam generation cases are demonstrated. In the last chapter

the main insights of this work along with the future work and recommendations are presented.

4

Chapter Two: Background and Literature Review

2.1 Background

2.1.1 Overview of SAGD Operations

The SAGD operations consist of a pair of horizontal wells that are drilled into the reservoir;

an injection well (above) and a production well (below). Bitumen in the reservoir is highly viscous

(up to 5,000,000 cp) and will not flow at ambient conditions. Steam is produced at the surface of

the site with 100% quality at 7,000 – 11,000 kPa pressure and is injected into the reservoir through

the injection well. The injected steam heats the bitumen and reduces its viscosity. Then, the

bitumen emulsion (a mixture of oil, water, sand and clay minerals), is pumped to the surface

through the production well [8], [11], [14], [28], [29]. As bitumen is brought to the surface it enters

the central processing facility (CPF) constituting the SAGD plant and well pads. The SAGD CPF

consists of oil/water separation units, water treatment units and steam generation in addition to

storage units, pipelines, gas treatment units, oil treatment units and other utilities. In SAGD

facilities the objective is to treat the produced water after it is separated from the bitumen emulsion,

and increase water quality in order to meet boiler feed water requirements which in turn are

dictated by the type of boiler that is used (the details of the requirements and boiler options are

discussed later in this chapter). The objective is to recycle as much water as possible in this process

to reduce the amount of makeup water and wastewater disposal required to meet environmental

regulations. Boiler feed water quality is critical to prevent scaling and efficiency degradation. The

required treatment objectives to prevent scaling are different for the two types of boilers that are

commonly used in SAGD operations (drum boiler and once-through steam generator), these are

described in more detail later in this chapter. The major contaminants typically found in SAGD

5

produced water are oil, silica, metal ions (calcium, magnesium, etc. that are typically measured as

total hardness), total organic carbon (TOC), total suspended solids (TSS), total dissolved solids

(TDS) and dissolved oxygen (DO). The concentration of these contaminants might vary for

different projects in different fields. Table 2-1 shows the concentration range for the contaminants

in SAGD produced water after it is separated from the bitumen emulsion [11], [19], [23], [24],

[30]–[34]. Makeup water contains several contaminants as well, and needs treatment prior to

entering the boiler. Contaminant concentrations of fresh and brackish makeup water are shown in

Table 2-2 [25], [28], [30], [32].

Table 2-1 Concentration range for produced water contaminants

Contaminant Concentration range (ppm) Data Sources

Oil 1200-2000 [11], [30]–[32]

TDS 800-4000 [11], [23], [24], [30]–[32], [34]

Hardness 15-120 [19], [23], [24], [30]–[32], [34]

Silica 150-260 [19], [23], [24], [30]–[32]

TOC 200-400 [11], [19], [24], [30], [31]

TSS 25-150 [23], [30], [32]

6

Table 2-2 Concentration range for makeup water contaminants

Contaminant Concentration range (ppm)

Fresh makeup water References Saline or brackish

makeup water References

Oil < 1 [11], [30], [32] < 1 [30], [32]

TDS 2780 [11], [30], [32] 17708 [24], [30], [32]

Hardness 15-120 [30], [32] 2600 [24], [30], [32]

Silica 5 [30], [32] 8 [24], [30], [32]

TOC < 1 [11], [30], [32] 35 [24], [30], [32]

TSS < 2 [30] < 10 [30]

These contaminants can be removed from the produced water stream using various types

of treatment processes. Figure 2-1 shows SAGD operations schematically and the following is an

overview of the water treatment and steam generation system in SAGD operations, where the

system can be divided into 5 sections shown in Figure 2-1:

7

Figure 2-1 Schematic diagram of SAGD operations

2.1.1.1 Separation units

In the first step, the bitumen emulsion enters the inlet separator where vapors are removed.

After mixing with diluent, which enhances the oil-water separation, the diluted bitumen enters two

other process units named free water knockout (FWKO) and treaters to separate the water from

the oil. Oil is then sent to the upgrading facilities or is diluted and transported to refineries for

further processing. The produced water exiting the FWKO and treaters is directed to the water

treatment plant [29], [35].

8

2.1.1.2 Water deoiling

Deoiling is the first step in treating produced water. In the deoiling section of the plant the

remaining free oil that has not already been separated from the water in the separation units is

removed and the oil content in the produced water is reduced from between 1200 and 2000 ppm

to approximately 1 ppm. A variety of deoiling equipment can be employed for oil removal (e.g.,

dissolved or induced gas flotation, filters, membranes, etc.). Oil removal is usually performed in

three steps; primary, secondary and tertiary treatment. In primary treatment or bulk oil removal,

oil is removed from water via gravity separation. A skim tank is commonly used for bulk oil

removal in SAGD facilities, but other types of oil/water separators have been investigated (e.g.,

API separators and the corrugated plate interceptor (CPI) separator [23], [36]). In primary deoiling,

approximately 90% of the oil is separated from the water [23], [36]. Secondary treatment uses air

flotation technologies to separate smaller droplets of oil that are not separated in the first step.

Dissolved or induced gas flotation (DGF/IGF) are common unit operations for secondary oil

separation in SAGD operations. Deoiling hydrocyclones have recently been introduced to oil sands

water treatment activities as a replacement for part of the bulk oil removal and flotation process

[23], [33], [36]–[39]. Hydrocyclones are typically used as a pre-treatment process in conjunction

with other technologies. They do not require chemical inputs, have high tolerance for inlet oil

concentration and it is reported that they have long lifetimes (however, public literature does not

state the specifically this lifetime [39]). Tertiary treatment of oil removal is filtration. Oil removal

filters are used to remove the final traces of oil in the produced water. Walnut shell filters are

commonly used for this step.

9

All deoiling processes introduced above, are capable of removing suspended solids as well.

In primary deoiling, approximately 50% of suspended solids are removed via settling. Gas flotation

and filtration also remove roughly 70% and 90% of suspended solids respectively.

Ceramic membranes are a new deoiling technology that has been evaluated in different

studies to replace either the entire deoiling equipment or the secondary and tertiary oil removal

stages [36], [40]. A ceramic membrane is also capable of removing silica and suspended solids

from wastewater [8], [23], [29], [37], [41].

A summary of deoiling processes and their efficiency in oil removal is shown in Table 2-

3 (data sources [12], [27], [28], [30]).

Table 2-3 Deoiling processes and their oil removal efficiency

Process Separation technology

Oil droplet size

removal

Effluent oil concentration

(ppm)

Approximate removal ratio

Skim tank Gravity > 150 μm 200-400 85-90 %

API separator Gravity > 150 μm 200-400 50-99 %

CPI separator Gravity/Coalescence > 50 μm 100 -*

DGF/IGF Flotation > 20 μm 10-40 90-93 % Deoiling

hydrocyclone Centrifugal force > 10 μm 20-40 90-93%

Filtration Absorption < 2 μm 1-5 90 %

Membrane Barrier < 1 μm 0.5-4 -* *Accurate removal ratios could not be found in the literature.

10

2.1.1.3 Water treatment

Deoiled produced water is sent to the water treatment units to remove the water soluble

contaminants. Soluble contaminants in SAGD produced water include silica, hardness (calcium,

magnesium, iron, etc.), total dissolved solids, organic carbon and dissolved oxygen.

Warm or hot lime softening1 (WLS/HLS) and ion exchange are traditional processes for

silica and hardness removal that have been employed in SAGD operations for decades. These

processes are capable of removing silica and hardness via physical-chemical treatment.

WLS followed by a filtration system, removes silica and part of the hardness (there is a

debate about whether hardness is removed in the lime softening unit in the SAGD water treatment

process). It has been reported that part of the hardness (calcium and magnesium ions concentration)

(about 50%) is removed in the lime softening units [42], [43], but available water quality data for

industrial projects show no change or very small changes in hardness concentration after passing

through the lime softening unit (in this study a zero hardness removal in the lime softening unit is

assumed). The most widely used chemical compounds in this treatment process are calcium

hydroxide (lime, Ca(OH)2) and magnesium oxide (MgO). Sludge is produced during the softening

process and is separated from the treated water by a filter followed by dewatering in a centrifuge.

The sludge handling process is included as a part of the lime softening process in the present study.

The ion exchange unit is typically a weak acid cation exchanger (WAC) that reduces calcium,

magnesium and iron (hardness) content to meet the boiler specifications by using sodium carbonate

1 Warm and hot lime softening are similar regarding the configuration, water recycle, water quality and GHG emissions [24]. In this study WLS is used to represent both processes.

11

(soda ash: Na2CO3). The ion exchange system is regenerated with sodium hydroxide (caustic:

NaOH) and hydrochloric acid (HCl) regularly.

The water quality achieved by this approach meets the specifications for the OTSG but is

not clean enough to be used in a drum boiler. The recycle ratio of produced water using this

approach is approximately 80-90% depending on whether the boiler blowdown is recycled for

further treatment or is completely disposed of [30], [43], [44].

An evaporation method has recently been introduced to SAGD operations as a new water

treatment technology by employing vertical tube, falling film, vapor compression evaporators [45],

[46]. This process eliminates the sludge and some of chemicals required by the WLS or HLS units.

The chemicals required for the evaporative method are sodium hydroxide (caustic, NaOH),

antifoam and scale inhibitor. Caustic is added to increase pH for increasing the silica solubility in

order to avoid scaling in the evaporator. The heat transfer coefficient of vertical tube falling film

evaporators is the highest among all evaporator types. In this process, all dissolved solids are

removed to very low (below 1-2 ppm) concentrations and high quality distillate is generated for

use in the boiler. The quality of the effluent is compatible with standard drum boilers feed water

requirements. The contaminants are removed from the boiler feed water and separated in a waste

stream as evaporator blowdown which is about 1-2 wt% (weight percent) whereas the evaporator

recovers 98-99 wt% of the feed water [30], [43]. Dissolved oxygen is commonly removed from

the boiler feed by oxygen scavenger chemicals such as sodium sulphite or in a thermal deaerator

[8], [23], [47].

12

2.1.1.4 Steam generation

Treated produced water is then used for steam generation that is then injected into the wells.

Two types of boilers are currently used by SAGD operations for steam generation; once-through

steam generators (OTSG) and drum boilers.

OTSGs produce steam with 75-80% quality (not all the feed water vaporizes) and since

100% steam is required, a series of vapor-liquid separators (flash drum) are needed to separate the

water from the steam and produce 100% quality steam for injection. The separated water stream

that is not converted to steam is known as boiler blowdown. Removing this stream from the boiler

helps to control boiler water quality parameters within the required limits to avoid scaling,

corrosion and foaming issues. Boiler blowdown is either recycled back to the treatment system for

further treatment and reuse or sent to disposal (deep well injection or zero liquid discharge - ZLD

crystallizer) so that the contaminants exit the water treatment system [8], [19], [24].

Drum boilers are capable of producing 100% quality steam which eliminates the need for

vapor-liquid separators. Only 1-2% of the boiler feed water in this type of boiler is removed as

blowdown to control boiler water quality parameters. However, this comes at the cost of increased

capital costs and increased consumption of electricity. This is one of the tradeoffs that is explored

in this thesis.

Boiler feed water specifications for the OTSG and drum boiler are shown in Table 2-4 [8],

[19], [23], [32], [47]–[52]. Quality requirements for the OTSG that are reported across the studies

are quite different; therefore, the acceptable range for water quality shown in Table 2-4 is broad.

Drum boilers require lower contaminant concentrations and higher quality in the boiler feed water.

This is due to the higher quality of generated steam in this type of boiler.

13

Table 2-4 Boiler feed water quality requirements for OTSG and drum boiler

Parameter OTSG

requirement (ppm)

References Drum boiler requirement

(ppm) References

Oil 0.5-10 [8], [23], [32], [48], [52] 0.2 [23], [32]

TDS 7,000-12,000 [8], [23], [32], [48], [52] 5 [32]

TSS <1 [32], [52] <1 [32], [47], [49]

Hardness 0.5-1 [8], [19], [23], [32], [48], [52] 0.02-0.5 [19], [23], [32]

Silica 20-150 [8], [19], [23], [32], [48], [52] 0.1-2 [19], [23], [32]

TOC 200-600 [19], [32] 0.2 [19], [32]

DO 0.04 [8], [23], [52] 0.04 [23], [47], [49] Specific

conductance 2,000-10,000* [19] 150* [19], [23]

*Unit is μS/cm

2.1.1.5 Waste disposal

Boiler blowdown and evaporator blowdown are liquid waste streams in the system that are

recycled for treatment and reuse or are disposed of. The type of boiler used for steam generation

determines the amount of boiler blowdown that is generated. OTSG blowdown is approximately

20% of the boiler feed water volume that traditionally is disposed of via deep well injection. Drum

boiler blowdown is only 1-2% of boiler feed water that is disposed of in the same way. The other

method of wastewater disposal is the zero liquid discharge (ZLD) crystallizer which is usually

used in conjunction with an evaporator. ZLD crystallizers eliminate liquid waste completely via a

drying process and generate a distillate stream (pure distilled water) that is recycled back to the

boiler and a solid waste for disposal [43]. The solid waste is an easy-to-handle dry solid that can

be safely disposed of in a landfill [53], [54].

14

2.2 Literature review

2.2.1 Comparison of water treatment processes

Technical and economical comparisons of chemical treatment (i.e., lime softening and ion

exchange) and evaporative treatment methods have been conducted and presented in the academic

literature. Heins et al., Hill et al. and Perdicakis review both treatment methods in their studies and

suggest that there are some advantages of evaporation over the chemical treatment [24], [43], [44],

[55]:

• Using evaporators for water treatment increase process reliability.

• Boiler feed water quality is significantly improved with evaporators and makes the use of

drum boilers possible. Moreover, drum boilers allow for the use of alternate fuels which is

not an option with OTSGs. That is, OTSGs use natural gas to generate steam, but in drum

boilers other types of fuel (e.g., oil) can be used which adds flexibility to the process. Drum

boilers eliminate the need for vapor-liquid separators and reduce the volume of blowdown.

• The evaporative approach requires less chemicals.

• Sludge handling issues are eliminated with evaporators.

• Water recovery is improved and makeup water consumption is decreased.

• Economical evaluations show that the total installed costs for evaporators and drum boilers

are 8-10% lower than the conventional method (lime softening and OTSG).

• Operating costs for the evaporative approach are 1-6% lower than the conventional

approach.

Some advantages of traditional water treatment method from the aforementioned studies

are listed below:

• There is a risk of limiting steam production in case of severe fouling in evaporators.

15

• Cleaning process of drum boilers is more complicated than OTSGs. Drum boilers need

chemical cleaning.

• Boiler feed water quality requirement for drum boilers is higher than OTSGs.

• Energy consumption and GHG emissions in evaporation treatment are higher than

chemical treatment.

The advantages and disadvantages of using ZLD crystallizers have been investigated in

several previous studies. A Jacobs Consultancy report concludes that ZLD increases the produced

water recycle ratio, but at the same time increases energy use, GHG emissions and capital cost in

the process. This study also reports that the use of ZLD complicates the operation and may

decrease the reliability of the system [24]. Lozier et al. reached the same conclusion in their study

[56]. They concluded that the main advantage of using a ZLD system is increased recycle ratio of

the water and the main disadvantage of using such system is high capital and operating cost [56].

The results of a third study on brine-concentrate treatment and disposal options indicated that the

main advantages to a ZLD system is a high quality product water and proven history for use in

industrial applications (but not in the oil sands industry). They concur that the main disadvantages

are high capital, operating and maintenance cost, mechanical complexity of the system and the

need for frequent cleaning [57].

These studies investigate the technical and economic advantages of each approach, but the

potential improvements within each approach have not been considered. That is to say, most of

the studies found in the literature investigate the advantages and disadvantages associated with

replacing a treatment unit or a set of treatment processes with other treatment process alternatives.

This is not sufficient because there is also potential for the diversion of flows to reduce cost and

energy that have not to date been addressed in the literature. In addition, there are further

16

opportunities to explore the explicit evaluation of tradeoffs between decisions that affect energy,

water, cost and GHG emissions.

In Jacobs consultancy report by Hill et al. [24], the impact of increasing the water recycle

ratio and achieving zero liquid discharge (ZLD) on energy use, GHG emissions and waste

generation in SAGD operations is explored. The authors completed over 100 simulations to

evaluate nine different water treating configurations in terms of water use, water recycle, energy

consumption, GHG emissions and waste generation. They tried to keep balance between

environmental tradeoffs and economic returns by identifying the most promising water treatment

technologies. The results of this study revealed that blowdown evaporation best balance

environmental tradeoffs and economic returns. They also concluded that adding new technologies

(e.g., ZLD) that increase the produced water recycle ratio (by 1-2%), will result in an increased

energy use and GHG emissions (by 2-8%). However, the effect of other parameters such as the

performance of the water treatment processes, energy consumption and cost of the treatment units,

etc. (sensitivity analysis) are not investigated in Jacobs study.

It should be noted that the best technology depends on facility specific conditions (e.g.,

produced water and make-up water chemistry), power generation (power from grid vs. natural gas

cogeneration) and how GHG emissions are valued [25].

Process integration tools provide the opportunity to improve water treatment networks by

evaluating alternative configurations of the system without changing the treatment technologies

under consideration and only by rearranging the wastewater streams in the network. None of the

studies described above applied these tools.

Energy and water consumption, cost, waste production and GHG emissions are parameters

that are affected by the choice of treatment process, steam generation and waste disposal method.

17

In the present study, the design of distributed effluent treatment which is a subset of process

integration approaches and optimization techniques are used to provide insights about the

opportunities for improvement of the SAGD operations. In this study, we are interested in applying

a combination of water pinch analysis and optimization tools on the SAGD water treatment

network to investigate the tradeoffs between cost, energy, emissions and water as well as finding

the opportunities to divert wastewater flows around treatment units to improve the water treatment

network.

2.2.2 Process Integration and Pinch Analysis

Process integration is a set of techniques to study the process design and look for

inefficiencies in industrial processes. Process integration is used to assess modifications to

industrial processes to quantify the potential to reduce energy, water and raw material

consumption, GHG emissions and waste generation. Pinch analysis is the most common tool

among process integration techniques because of the simplicity of its primary concept and the

successful use of this method in different industrial projects around the world (e.g. up to 42%

reduction in water use in a refinery plant) [58]–[60]. Process integration, combined with other tools

such as process simulation and optimization, is an efficient (relatively simple to use and effective)

approach to analyze industrial processes and investigate the interactions between different parts of

a system [58], [61], [62].

Two main areas of pinch analysis applications are energy pinch and water pinch. The goal

of energy pinch is to minimize the total energy consumed by a process for heating and cooling by

modifying the heat exchanger network in the process based on process integration rules and

maximizing the heat recovered between process streams. An energy pinch analysis for the SAGD

18

operations suggests that water-energy tradeoffs exist [63], [64]. As a result, the focus of this

research is on analyzing the water network in the SAGD operations using water pinch concepts.

This will allow us to understand the correlation between water and energy and to identify

opportunities to optimize both water and energy use simultaneously by considering these tradeoffs

using specific criteria. Water pinch can be applied to build a water network to achieve two different

goals [65], [66]:

1. Minimizing wastewater generation by water reuse and recycle.

2. Designing a distributed effluent treatment system to treat generated wastewater.

The first application deals with water consuming operations in a facility. The idea is to

minimize fresh water consumption by optimizing water allocation to different operations and

maximizing water reuse or recycle based on the nature of the operations. The second application

evaluates a set of wastewater streams that could be treated for a number of contaminants in several

treatment units with the possibility of partial or total bypass for each unit, in order to reach the

environmental limit for all the contaminants (or any other performance goals).

In the SAGD water cycle, the only water consuming process is below the surface, inside

the reservoir. Since there is no other water consuming unit, there are not many opportunities for

reducing water consumption by using pinch analysis. Adding solvent to improve bitumen

extraction and reduce water consumption is possible, but it requires different types of analyses and

is outside the scope of pinch analysis (adding solvent can reduce water consumption by enhancing

the oil extraction, and is not related to pinch analysis). On the other hand, when water returns to

the surface and is separated from oil, it must be treated and recycled back into the process.

Therefore, the second approach within water pinch analysis can be used to investigate and optimize

water treatment as part of SAGD operations and is the main focus of this study.

19

2.2.3 Distributed effluent treatment system vs. centralized treatment system

Wastewater treatment in industrial plants is commonly carried out in a central treatment

facility where all the effluent streams from various processes that consume fresh water and produce

wastewater (e.g., desalting, washing operations, etc.) are collected in a common sewer and then

are sent through a series of treatment processes to reduce the concentration of different

contaminants to desired levels [66], [67]. Wastewater treatment in SAGD plants is conventionally

carried out in a centralized treatment system. Depending on the contaminant concentrations and

discharge limitations, the centralized treatment system might include primary, secondary and

tertiary treatment processes. A centralized treatment facility is illustrated schematically in Figure

2-2.

Figure 2-2 Centralized treatment plant

20

It has been noted that a distributed effluent treatment system (or segregated wastewater

treatment system) can have important advantages over centralized wastewater treatment [68]–[70].

This is due to the fact that streams can be treated separately and only combined if it is appropriate

according to certain rules that are presented later in this section. Other studies have shown that in

most wastewater treatment operations, the capital and operating costs are proportional to the total

flow rate of wastewater that flows through the treatment unit [66], [67], [71]. Therefore, by

designing a distributed system as shown in Figure 2-3, any wastewater stream can flow to any

treatment unit with the possibility of a partial bypass and with potentially reduced total system

costs/energy consumption.

Figure 2-3 Distributed effluent treatment system

21

Mishra et al. and Tyteca et al. review studies in the area of optimal design of water

treatment systems. Most of these studies that were conducted between 1974 and 1994 focused on

optimizing specific units or small groups of units with a single specific configuration [72], [73].

In these studies fundamental mechanisms that are the target of the wastewater treatment processes,

such as control of bacterial growth, oxygen supply, sedimentation, etc. are mathematically

modeled. Mathematical models are used to find optimal efficiency and cost (maximizing the

efficiency and minimizing the cost) of each unit by changing the size of treatment units or the

process parameters such as contaminant concentrations, water flow rate and temperature (which

are the decision variables of the mathematical model). Then the model is solved to optimize (e.g.

minimize cost or maximize efficiency) a specific system that consists of specific treatment units

arranged in a specific order. The maximum efficiency or the minimum cost is determined by

finding the proper size of treatment units as decision variables. Alternatively, a set of previously

dimensioned process units can be assumed and the optimal order of the units can be determined

via optimization techniques. In these studies only wastewater streams with specific contaminant

concentrations are investigated and they are not practical if the contaminant concentrations or any

of the other input parameters are changed. That is, if the input parameters are changed, the entire

model has to be rebuilt. Therefore, a general approach is needed to optimize water treatment

networks with different sets of input parameters. The suggested approach in the present study

allows for changing any of the input parameters (e.g. contaminant concentrations of the wastewater

streams) without the need to make any changes in the model. Since 1994, various new methods

have been proposed for optimal design of a wastewater treatment system [66], [74]–[77]. The two

main methods that are most applicable in this thesis can be categorized into graphical methods

based on the pinch analysis concept and mathematical modeling approaches.

22

Wang and Smith proposed a general conceptual graphical approach to design a distributed

effluent system for process industries based on the pinch analysis concept [66]. They assumed that

a set of wastewater streams containing specific contaminants are given with known flow rates and

concentrations. Moreover, the environmental concentration limits that must be achieved by the

treatment system are specified. Then, they assumed that a set of treatment processes were available

to remove the contaminants. Performance of the treatment processes were described by a fixed

removal ratio or a fixed outlet concentration for each contaminant in each treatment unit. Another

important assumption in this study is that the total cost of each treatment unit (capital and

operating) is proportionally related to the flow rate of the wastewater stream treated in that unit.

Although the relationship between cost and flow rate could be linear or nonlinear, Wang and Smith

assumed a linear relationship in their study. Therefore, total cost of the treatment system can be

minimized by minimizing the total flow rate of the streams going through the treatment units. To

achieve the optimal design of the system, a two-step method is suggested in this paper. First, the

minimum flow rate of effluent to be treated is set as the target (targeting step). Second, a network

is designed based on a set of design rules to achieve the target flow rate and concentration

requirements (design step).

A simplified description of the targeting and design steps discussed in Wang and Smith

study, for a single stream and single contaminant system is presented here. A wastewater stream

can be represented by considering the relationship between concentration and mass load of the

contaminant as seen in Figure 2-4. The horizontal and vertical axes are mass load and concentration

of the contaminant respectively. The goal of wastewater treatment processes is typically to reduce

the concentration of the contaminant in the waste stream from the inlet concentration (Cin) to the

desired concentration limit (Ce). The contaminant mass load to be removed from the waste stream

23

(ΔmT) is the production of stream flow rate (F) times the concentration difference within the

treatment unit (Cin - Ce) as shown in the equation below:

∆𝑚𝑚𝑇𝑇 = 𝐹𝐹 × (𝐶𝐶𝑖𝑖𝑖𝑖 − 𝐶𝐶𝑒𝑒)

This equation indicates that the stream flow rate is the inverse of the slope of the wastewater

line in a concentration vs mass load graph (Figure 2-4).

A treatment line can be represented on a concentration vs mass load graph as well. The treatment

line is an indicator of the stream passing through the treatment unit. The specifications of the

treatment unit (i.e. removal ratio of the treatment unit for the contaminant (RR) or the fixed outlet

concentration of the contaminant from the treatment unit (COUT)) determine the slope of the

treatment line. Once the slope is known, the treatment line can be drawn starting from the inlet

point of the wastewater line (i.e. (ΔmT, Cin) point on Figure 2-4). As mentioned earlier, the inverse

of the slope of these lines is the flow rate of the streams. A steeper slope for the treatment line

compared to the wastewater line shows that the flow rate of wastewater passing through the

treatment unit is smaller than the flow rate of the whole wastewater stream. This means that part

of the wastewater stream can be bypassed around the treatment unit. In other words, to reach the

desired limit for contaminant concentration (Ce) we only need a portion of the stream to be sent to

the treatment unit that has an outlet concentration of Cout. Figure 2-5 shows how the streams

presented in Figure 2-4 are translated into the treatment process arrangement is the design step.

24

Figure 2-4 A wastewater stream and treatment line on concentration vs mass load diagram

(Cin=50 ppm, Ce=20 ppm, Cout=10 ppm, ΔmT=6 kg/hr)

Figure 2-5 Example of partial bypass of water stream around a process unit

(For wastewater stream and treatment unit data shown in Figure 2-4)

Wang and Smith then expanded this approach to multiple streams and multiple

contaminants systems. They also addressed a case where a treatment unit has an inlet concentration

25

limit. Detailed information about these methods are found in [66]. Although the general approach

proposed by Wang and Smith offers valuable insights into the design of the distributed effluent

treatment system, there are shortcomings associated with this method. Because of the graphical

nature of the targeting step, this method is able to manage only simple design constraints and is

not an efficient approach for problems with a large number of treatment units and contaminants as

a result of interactions that occur between treatment processes and contaminants. In some cases,

this approach is not capable of predicting the lowest possible target flow rate in multiple-unit,

multi-contaminant problems. This is discussed further in the Kuo and Smith paper [67].

Additionally, to deal with systems involving two or more treatment units capable of removing a

specific contaminant, decisions need to be made about the mass load distribution of the

contaminant and the sequence of treatment units. These decisions might lead to suboptimal

network designs.

Kuo and Smith improved the earlier method by addressing the important features of

multiple treatment processes system design and existing interactions in an industrial water system

that were neglected in the previous study [78]. They proposed a staged graphical approach by

repeating the targeting and design steps. This method does not guarantee the minimum flow rate

but guides the designer towards the optimal design [67]. Kuo and Smith divided the water system

of an industrial plant into three subsystems: the water-using subsystem, the regeneration subsystem

and the effluent treatment subsystem. However, there are drawbacks associated with this method

as well. For example, although they addressed the design procedure of a distributed effluent

treatment for systems with three wastewater streams and three contaminants, because the

composite curves and network structure are constructed manually, this method is likely to fail

when used for systems with larger number of contaminants and treatment units (i.e. the method

26

might not be able to solve the problem or might give incorrect results). Also, because there are

strong interactions between these subsystems, Kuo and Smith method that divides the water system

into three separate subsystems, fails to explore all of the interactions. Furthermore, the final design

achieved by this method depends on the designer’s experience and may not be consistent. In other

words, one designer might make one set of decisions and another designer a different set of

decisions (i.e., when one contaminant is removed by more than one treatment unit, decisions must

be made about the load of contaminant in each treatment unit and the order of treatment units).

Another problem with this method and the method proposed by Wang and Smith is that they cannot

easily accommodate constraints to the design other than concentration and flow rate constraints,

such as limiting constraints for the distance between two treatment units, the size of treatment units

and avoiding uneconomically small flow rates between treatment units (it is not economic to set

up additional pipelines to transfer small flows. The proposed model in the present study is capable

of accepting constraints, e.g. a lower bound on the stream flow rates to avoid these small flows).

Mathematical optimization methods have gained attention in the past two decades [74]–

[76], [79]. Mathematical design techniques for the synthesis of distributed effluent treatment

networks usually depend on the solution of nonconvex mathematical models which lead to

multiple local optimal points and often cause local optimization techniques to fail [79]. In 1980,

Takama et al. developed an optimization approach and applied it in a petroleum refinery [80]. The

initial problem is a large dimensional and nonlinear problem with strict inequality constraints.

They transformed the model into a set of problems with no inequality constraints by applying a

penalty function. Then, the simplified models were solved using the “Complex” method [81]. In

this study which is one of the first studies investigating the optimal design of a water treatment

network with the aid of mathematical programming, optimization techniques are used to solve a

27

simple problem far from the real systems and it is not expanded to a general problem of optimal

water treatment network design. The expansion of the proposed method in Takama study will

require additional mathematical tools which make it impossible to expand the suggested solution

without making fundamental changes and rebuilding their model.

In 1988, Galan and Grossmann proposed a procedure based on linear underestimators that

was introduced by Quesada and Grossmann for bilinear terms within a branch and bound

algorithm, for solving the mixed integer nonlinear problem resulting from modeling a distributed

effluent treatment system [74], [82]. The proposed model in this paper gives rise to a nonconvex

nonlinear problem that usually causes convergence complications. Accordingly, the authors

successfully used linear underestimators to turn the initial nonlinear problem into a set of relaxed

linear models which provide initialization points for the original nonlinear problem [74]. This

method is useful in cases with the possibility of estimating tight linear relaxations for the bilinear

terms of the nonlinear problem. In cases similar to the present study where accurate linear

estimations cannot be made before solving the nonlinear problem, the use of linear relaxation

cannot help solving the initial nonlinear problem.

Hernández-Suárez et al. proposed a superstructure decomposition and parametric

optimization approach for the synthesis of a distributed wastewater treatment network [79]. In the

proposed method, the design search space is subdivided into smaller pieces by dividing the typical

complex network superstructure into a series of simple network superstructures. Then, the optimal

network design related to each simple superstructure is determined by solving a set of linear

programming models that is derived from the initial nonconvex model by fixing a number of

variables. This method is suitable for the systems with three treatment units or less.

28

Alva-Argáez et al. proposed an integrated approach based on the pinch analysis concept

for the design of industrial water systems within a mathematical programming model framework

[76], [83]. The proposed superstructure includes all possible reuse, recycle, regeneration and

treatment options in the system. A feasible solution of the original MINLP (mixed-integer

nonlinear programming) model is obtained by decomposing the MINLP model into a MILP and

LP problems and solving them iteratively. In the proposed method, the objective function of the

MILP model is augmented by an infeasibility term with an increasing coefficient that targets a

reduction of the problem infeasibilities. This method takes into account a more complete set of

constraints and treatment units which make it flexible to be used for a large number of treatment

units and contaminants. Therefore, a similar approach is used in the present study.

Liu et al. proposed a new heuristic procedure to obtain the optimal design of distributed

effluent treatment system by reducing unnecessary stream-mixing [77]. The proposed approach is

applied to multi-stream, multi-contaminant systems with more than two treatment units. Although

this approach addresses the problems of dealing with a large number of treatment units and

contaminants, the heuristic nature of the procedure could lead to different configurations of

streams in the final design depending on the designers’ judgement.

Process integration methods using mathematical programming tools have not been applied

to oil sands processes and specifically SAGD operations before. In this study, set of different

concepts and tools across the literature are incorporated and blended in order to develop a

comprehensive model that can handle a large set of possible process units, contaminants, etc. In

addition, different treatment options across a set of metrics (cost, energy, GHG emissions, etc.)

are compared. In this thesis, the details of the SAGD system (including the parameters of the

SAGD water treatment processes such as removal ratios, effluent concentration, cost, etc.) are

29

represented within a model that applies process integration techniques. Additionally, sensitivity

analysis is conducted to assess the impact of changing several input parameters on the output

parameters of the optimization model.

30

Chapter Three: Methods

3.1 Objective of the model

The mathematical model developed in this study is designed to minimize energy

consumption and cost of the water treatment network in SAGD operations. Environmental

regulations for water withdrawal, water disposal and GHG emissions [18], [27] challenge oil

producers to recycle as much produced water as possible in the extraction process and competition

in a global market encourages them to minimize energy consumption and cost per unit oil

produced. There are tradeoffs between cost, energy and water consumption in a water treatment

network. The model that is designed and implemented in this study uses optimization techniques

to evaluate all three factors simultaneously to explore these tradeoffs. In other words, the model is

designed to reach an optimal water treatment network, such that process constraints and

environmental limits are met at minimum cost and/or energy consumed.

One way to potentially reduce the cost and energy use in a treatment system is to design a

distributed effluent treatment system instead of a centralized treatment system. Several studies

applied in other industries have shown that distributed effluent treatment can have significant

advantages over centralized wastewater treatment [66], [80], [84]–[86]. These studies also reveal

that the capital cost of most wastewater treatment operations is proportional to the total flow of

wastewater through the system. Therefore, by designing a distributed system that can reduce flow

through particular units, there is potential to reduce the capital cost of the system.

Design of a distributed effluent system has been successfully applied in various industries

(e.g., petroleum refinery, pulp and paper industries, textile and dairy plants [67], [75], [80], [87]),

but has not been used in SAGD operations before. So, in this study cost, energy and water saving

31

opportunities in a SAGD water treatment network using process integration and optimization tools

are explored.

3.2 Operations Research and Mathematical Modeling

Operations research (OR) is a scientific tool and an interdisciplinary branch of applied

mathematics that helps researchers in the decision making process and uses mathematical

modeling, statistics and algorithms to find the best design of a system that is usually associated

with allocation of scarce resources. A “system” is defined as a set of interdependent components

that work together to reach the goal of the system. [88], [89].

A mathematical model is used to represent an actual system with mathematical equations.

The decision making process using the scientific approach of OR usually involves one or more

mathematical models. From a practical perspective, OR can be defined as an optimization process

that aims to find the minimum or maximum of an objective function. A general OR model can be

represented by the following general format:

Maximize or minimize Objective Function

Subject to

Constraints

3.2.1 Objective function

In most models there is a function we want to be maximized or minimized, this function is

called the objective function of the model. The most common objective functions in optimization

problems are profit, cost, energy, loss, time, yield and risk [88], [90], [91].

32

3.2.2 Decision variables

Decision variables are independent variables that are controlled by the user and influence

the constraints and the objective value [88].

3.2.3 Constraints

Constraints are the process model and describe the interrelationships of the key variables

of the system that are represented in the form of mathematical equations. Formulating the problem

is the main step in the optimization process and requires identifying the essential elements of a

system and present them mathematically [88], [91].

Constraints of a mathematical programming model can be an equality or inequality:

𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑒𝑒𝑐𝑐𝑒𝑒𝑒𝑒𝑐𝑐𝑒𝑒:𝑔𝑔(𝑥𝑥) = 0

𝑒𝑒𝑐𝑐𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑒𝑒𝑐𝑐𝑒𝑒𝑒𝑒𝑐𝑐𝑒𝑒:ℎ1(𝑥𝑥) ≥ 0 𝑐𝑐𝑐𝑐 ℎ2(𝑥𝑥) ≤ 0

In the standard form of a linear programming (LP) model, all constraints are equality

constraints. To convert inequality constraints to equality constraints, slack and surplus variables

are used.

ℎ1(𝑥𝑥) ≥ 0 → ℎ1(𝑥𝑥) − 𝑐𝑐1 = 0

ℎ2(𝑥𝑥) ≤ 0 → ℎ2(𝑥𝑥) + 𝑐𝑐2 = 0

𝑐𝑐1 is called a surplus variable and is a positive value. By subtracting a surplus variable a

“≥” constraint is converted into a “=” constraint. 𝑐𝑐2 is called a slack variable and is positive too.

By adding a slack variable, a “≤” constraint is converted into a “=” constraint.

33

3.2.4 Feasible region and optimal solution

A feasible solution of an optimization problem is a set of values for decision variables that

satisfies all the constraints of the model. The feasible region of a problem constitutes all possible

feasible solutions to that problem. An optimal solution of a problem is the feasible solution that

gives the best (minimum or maximum) value of the objective function among all feasible solutions

[88], [90].

3.2.5 Linear and nonlinear models

If all the constraints and the objective function of an optimization model are first degree

functions of decision variables, it is a linear model. If an optimization model is not linear, i.e. the

objective function of the model or one or more constraints of the model are second degree or higher

functions of decision variables, then it is a nonlinear programming problem.

3.2.6 Integer and non-integer models

If one or more decision variables assume integer values, the optimization model is an

integer model. If all the decision variables are continuous and free to have fractional values, the

optimization model is a non-integer model.

3.2.7 Convex and nonconvex sets

In optimization problems, the feasible region forms a convex set if the line segment

connecting any pair of distinct feasible points lies entirely inside the set. If a set is not convex, it

is a nonconvex set [88], [90], [91]. Simple examples of convex and nonconvex sets are shown in

Figure 3-1.

34

The feasible region of linear models are always convex sets, but nonlinear models can be

convex or nonconvex. Integer models are always nonconvex [88], [90].

3.3 Overview of the model

The proposed model explores different wastewater treatment and steam generation options

for SAGD operations. The conceptual design of the system is based on process integration and

pinch analysis concepts. Water treatment units and wastewater streams are the main components

of the system. The mathematical representation of the system is built based on the system

superstructure that is described in the next section and leads to a mixed-integer nonlinear

programming model (MINLP) with a cost/energy objective function. The MINLP problem is

divided into two simpler sub-models; mixed-integer linear programming (MILP) and linear

programming (LP) models, by introducing a penalty function and projection and relaxation

approaches. An iterative method is used to find the optimal solution of the MILP model, minimum

cost/energy and optimal flow rates. These results are then fed to the MINLP model to ensure the

decomposition has not missed major design features.

The model consists of mass balance equations for a set of treatment units and several

process constraints for treatment units and other components of the system such as splitters and

Convex set Nonconvex set

Figure 3-1 Examples of convex and nonconvex sets

35

mixers to ensure the feasibility of the system and satisfy the concentration and flow rate limits of

the treatment units. A number of different scenarios are investigated that will be explained in the

next section in detail. For each scenario, the model is solved to minimize both energy and cost

functions separately. Then all scenarios are compared in terms of cost, energy and water

consumption and the tradeoffs between them are investigated to determine the magnitude of the

divergence, the nature of the tradeoffs are explained, thresholds are determined, etc.

3.4 Problem description

3.4.1 Overview of the system components

The optimization model is designed as a system consisting of a set of wastewater streams

containing contaminants with known flow rates and concentrations and a number of treatment

units with known performance parameters (e.g., removal ratios), cost and energy consumption.

The performance of each treatment unit can either be specified by a fixed outlet concentration or

a fixed removal ratio for each contaminant. Each treatment unit is capable of removing one or

more contaminants from the wastewater stream. A general rule of thumb that is used throughout

industry [66] is that the cost of a treatment unit is a direct function of the flow rate of the wastewater

stream passing through that unit.

There are three main liquid streams in the system; one stream of wastewater (produced

water), a makeup water stream and boiler blowdown. Flow rate and contaminant concentrations

of these streams are different for different SAGD projects. However, for a specific SAGD plant

the flow rate and contaminant concentrations for each of these streams are known or can be

calculated from the parameters (e.g., quality of produced steam from steam generator and flow

losses in the treatment units) of the system. Produced water specifications are defined by the

36

production rate of the SAGD project and the reservoir characteristics and can be input by the user.

Flow rate and concentration of boiler blowdown vary based on the type of boiler used for steam

generation and the disposal method and is explained in detail later in this chapter. Makeup water

flow rate depends on the flow rate of produced water and boiler blowdown. Its contaminant

concentrations depend on the water source used to supply makeup water. The concentration of

contaminants in the makeup water stream is assumed to be known in my system.

The main contaminants in the waste streams of the system are oil, silica, metal ions

(Calcium, Magnesium, etc. that can be represented as total hardness (TH)), total organic carbon

(TOC), total suspended solids (TSS) and total dissolved solids (TDS). The aforementioned

contaminants can be removed from wastewater streams using various treatment processes

considered in this model. Some of the treatment processes are currently used by industry (e.g.,

skim tank, induced gas flotation, oil removal filter, warm/hot lime softening, ion exchange, and

evaporator) and some are being explored (e.g., ceramic membrane and hydrocyclone).

Contaminant concentrations of the produced water stream, fresh and brackish makeup

water that are used in the optimization model are shown in Table 3-1. Available treatment

processes along with the main contaminants they can remove are summarized in Table 3-2.

37

Table 3-1 Contaminant concentrations of water and wastewater streams in the system used in the

optimization model

Contaminant Produced water Fresh makeup water

Brackish makeup water

Oil (ppm) 2000 0 0

Silica (ppm) 350 15 15

TH (ppm) 20 245 2500

TSS (ppm) 50 0 5

Table 3-1 only shows the contaminants that are considered in the model. TDS and TOC are not

considered because they don’t significantly affect the choice of treatment processes in the system.

In other words, they are not the main contaminants to be removed in a treatment process and the

required concentrations for these contaminants are usually achieved regardless of the choice of the

treatment process. Their exclusion also helps to simplify the model.

38

Table 3-2 Treatment processes and removable contaminants in SAGD operations

Treatment process Contaminants

Skim tank (ST) Oil

Induced gas flotation (IGF) Oil

Oil removal filter (ORF) Oil

Hydrocyclone (HC) Oil

Warm/Hot lime softening (WLS/HLS) Silica, Hardness

Weak acid cation exchanger (WAC) Hardness

Evaporator (Evap) Silica, Hardness

Ceramic membrane (CM) Oil, Suspended solids, Silica

Table 3-2 shows some treatment processes can only remove one contaminant and some are

capable of removing more than one contaminant. All the treatment processes listed in Table 3-2

are considered in the model except hydrocyclone and ceramic membrane, since not enough

information about the performance of these treatment processes is available in the literature. More

importantly, these treatment processes have yet to be deployed by the SAGD industry. However

the methodology described in this work could incorporate these and other novel technologies as

data becomes available.

Performance parameters of the treatment units (i.e., fixed outlet concentration and fixed

removal ratio) are available in the literature [37], [42], [92]. The mathematical model can use either

of the parameters (fixed outlet concentration and fixed removal ratio) to solve the optimization

39

problem. Also, industry specific data were obtained and used in this study under a confidentiality

agreement.

Two key parameters of the system that are used in the mathematical representation of the

system, are defined and explained here to provide a better link between the treatment processes

introduced earlier with the parameters of the system:

3.4.1.1 Contaminant mass load:

Contaminant mass load (the amount of mass of the contaminant) in a wastewater stream is

the mass flow rate of that contaminant in the stream. Mass load of contaminant c in wastewater

stream i is defined as:

𝑀𝑀𝑐𝑐,𝑖𝑖 = 𝐹𝐹𝑖𝑖 ∗ 𝐶𝐶𝑐𝑐,𝑖𝑖 3.1

Where:

𝑀𝑀𝑐𝑐,𝑖𝑖 is the mass load of contaminant c in wastewater stream i,

𝐹𝐹𝑖𝑖 is the flow rate of wastewater stream i, and

𝐶𝐶𝑐𝑐,𝑖𝑖 is the concentration of contaminant c in wastewater stream i

3.4.1.2 Removal ratio:

Removal ratio is the percentage of a contaminant mass load in a wastewater stream that is

removed by a treatment unit and can be shown as:

𝑅𝑅𝑅𝑅𝑐𝑐,𝑡𝑡𝑡𝑡 =𝐹𝐹𝑡𝑡𝑡𝑡𝑖𝑖𝑖𝑖 ∗ 𝐶𝐶𝑐𝑐,𝑡𝑡𝑡𝑡

𝑖𝑖𝑖𝑖 − 𝐹𝐹𝑡𝑡𝑡𝑡𝑜𝑜𝑡𝑡𝑡𝑡 ∗ 𝐶𝐶𝑐𝑐,𝑡𝑡𝑡𝑡𝑜𝑜𝑡𝑡𝑡𝑡

𝐹𝐹𝑡𝑡𝑡𝑡𝑖𝑖𝑖𝑖 ∗ 𝐶𝐶𝑐𝑐,𝑡𝑡𝑡𝑡𝑖𝑖𝑖𝑖 =

𝑀𝑀𝑐𝑐,𝑡𝑡𝑡𝑡𝑖𝑖𝑖𝑖 − 𝑀𝑀𝑐𝑐,𝑡𝑡𝑡𝑡

𝑜𝑜𝑡𝑡𝑡𝑡 𝑀𝑀𝑐𝑐,𝑡𝑡𝑡𝑡𝑖𝑖𝑖𝑖 3.2

40

Where:

𝑅𝑅𝑅𝑅𝑐𝑐,𝑡𝑡𝑡𝑡 is the removal ratio of contaminant c in treatment unit tu,

𝐹𝐹𝑡𝑡𝑡𝑡𝑖𝑖𝑖𝑖 and 𝐹𝐹𝑡𝑡𝑡𝑡𝑜𝑜𝑡𝑡𝑡𝑡are the flow rates of inlet and outlet streams of treatment unit tu respectively,

𝐶𝐶𝑐𝑐,𝑡𝑡𝑡𝑡𝑖𝑖𝑖𝑖 and 𝐶𝐶𝑐𝑐,𝑡𝑡𝑡𝑡

𝑜𝑜𝑡𝑡𝑡𝑡 are the concentration of contaminant c in inlet and outlet streams of treatment unit

tu respectively,

𝑀𝑀𝑐𝑐,𝑡𝑡𝑡𝑡𝑖𝑖𝑖𝑖 and 𝑀𝑀𝑐𝑐,𝑡𝑡𝑡𝑡

𝑜𝑜𝑡𝑡𝑡𝑡 are the mass load of contaminant c entering and exiting the treatment unit tu

respectively.

The goal of a wastewater treatment system is to reach specific concentration limits for

various contaminants (e.g. environmental limits for wastewater disposal). All outlet streams from

treatment units within the central processing facility are combined at a discharge point and the

concentration of all contaminants in this combined stream should be within the required

concentration limits. In this work, the desired concentrations of the contaminants are determined

by boiler feed water requirements which in turn are defined by the type of boiler in operation. This

means that once the type of boiler is selected (between OTSG and drum boiler, before running the

optimization model) the target contaminant concentrations required for treated water are

established.

The goal of the optimization problem is to reach the optimal design of the treatment system.

The optimal design determines the treatment units that are selected, the streams that move through

each treatment unit and the streams that connect the treatment units to satisfy concentration

requirements at the final discharge point at the lowest cost and/or level of energy consumption.

The SAGD wastewater treatment and steam generation system is shown schematically in

Figure 3-2.

41

Figure 3-2 Simplified scheme of water treatment and steam generation in SAGD operations

There are different options available for treatment processes, steam generation and waste

disposal units in SAGD operations. The choice of steam generation and waste disposal systems

shown in Figure 3-2, affect the system parameters in different ways. First, the type of boiler defines

the boiler feed water quality requirements that sets the target concentration for the treatment system

(deoiling and soluble content removal in Figure 3-2). Second, the type of boiler and disposal

method (e.g., the use of zero liquid discharge (ZLD) crystallizers eliminate the liquid waste and

produce zero blowdown) define the amount of blowdown that will be produced. Third, the type of

steam generation and waste disposal systems affect the total cost and energy consumption of the

entire system.

Four different cases are considered for steam generation and waste disposal in this study

and are described below. For each case, the optimization problem is formulated and solved. Then,

the results of the optimization for all cases are compared. Below, these four cases are presented.

42

3.4.1.3 Four cases for steam generation and waste disposal system in SAGD operations

Four cases for the combination of steam generation and waste disposal methods in the

SAGD operations were analyzed in order to explore the energy/cost implications associated with

different technologies considered by industry.

Case 1- OTSG, no blowdown recycle: In the first case, an OTSG is assumed to be used

for steam generation. OTSGs generate approximately 75-80% quality steam2 [8] and OTSG

blowdown is assumed not to be recycled for further treatment and is disposed of via deep well

injection.

Case 2- OTSG, blowdown evaporation: In this case, again an OTSG is used for steam

generation and OTSG blowdown is sent to an evaporator for further treatment. Evaporator

distillate is then used as boiler feed water.

Case 3- OTSG, 30% blowdown recycle: In this case, again an OTSG is used for steam

generation. However, 30% of the OTSG blowdown is recycled back to the water treatment system

for further treatment and the remaining is disposed of via deep well injection.

Case 4- Drum boiler: In the fourth case, a drum boiler is assumed to be used for steam

generation. Drum boilers generate close to 100% quality steam and the amount of produced

blowdown is very small.

In both cases 2 and 3 OTSG blowdown is sent to treatment processes for further treatment,

but the difference between these two cases is that in case 2, the OTSG blowdown is forced to be

treated in an evaporator and the selection of the blowdown stream and blowdown evaporator are

not part of the optimization problem. In case 3 the blowdown stream is one of the wastewater

2 In this study I assumed 80% quality steam is generated in OTSG.

43

streams in the system and is part of the optimization problem. Therefore, the optimization routine

selects which treatment processes result in the minimum cost or energy.

In cases 2 and 4, the amount of blowdown in the system (boiler blowdown and evaporator

blowdown) is small and ZLD can be used for waste disposal. For these two cases deep well

injection is considered for waste disposal in the base case and a qualitative investigation of using

a ZLD crystallizer technology is considered in the sensitivity analysis.

A simplified diagram of all four cases are shown in Figure 3-3.

44

Figure 3-3 Four cases for steam generation and waste disposal in SAGD operations

45

3.4.2 Developing the mathematical model

The first step to mathematically model the system is to develop a general superstructure of

the network. The superstructure approach has been suggested in a number of studies [74], [76],

[86], [93]. The superstructure includes splitters, mixers, treatment units, wastewater streams, and

all the interconnections between treatment units as shown in Figure 3-4. Each water or wastewater

stream entering the system, first goes through a splitter (water source splitter) and can be divided

into smaller streams that go to different treatment units. There is a mixer ahead of each treatment

unit (treatment unit mixer) that mixes all the streams going through that treatment unit and there

is a splitter after each treatment unit (treatment unit splitter) which allows for the possibility of

redirecting the effluent of one treatment unit to other units or sending it to the discharge point.

Finally, there is a mixer at the discharge point (discharge mixer) where all discharge streams from

treatment units are gathered and sent to the boiler feed water tank.

46

Figure 3-4 Superstructure of the system

The focus of the optimization is on the configuration of the streams around the treatment

units. In other words, the optimization model focuses on investigating all possible interconnections

between treatment units and finding the optimal arrangement for the streams in the treatment

system. Therefore, before developing the superstructure of the system, the type of equipment for

steam generation and waste disposal in use is determined. In this way, all required input parameters

of the system are known.

47

The next step is defining the cost/energy relationships for each treatment unit as a function

of flow rate. In this study a linear correlation3 between cost/energy and flow rate is assumed.

𝐶𝐶𝑐𝑐𝑐𝑐𝑒𝑒/𝐸𝐸𝑐𝑐𝑒𝑒𝑐𝑐𝑔𝑔𝑒𝑒 = 𝑒𝑒 ∗ 𝐹𝐹𝑒𝑒𝑐𝑐𝐹𝐹𝑐𝑐𝑒𝑒𝑒𝑒𝑒𝑒 + 𝑏𝑏 3.3

Where “a” and “b” are fixed coefficients and are determined based on the type of the treatment

unit.

In the mathematical model, the objective function may be the total cost of the system, or

total energy consumption. Constraints in the model are mainly mass balance equations and some

additional constraints of the system that are explained later. Decision variables are stream flow

rates through each treatment unit. This means that the model will try to find the minimum possible

value for the objective function by exploring all possible combinations of flow rates through each

treatment unit, while all equality and inequality constraints are satisfied. Then, the system is

mathematically modeled based on the system superstructure shown in Figure 3-4. Before

representing the system in the form of mathematical equations, variables and parameters along

with the components of the system used in mathematical equations need to be defined. Sets,

variables and parameters of the model are presented below.

3.4.2.1 Sets, parameters and variables

Sets

C = {c | c is a contaminant}

c = O Oil,

3 The relationship between flow rate and cost/energy depends on the type of treatment process. Since there is very little information about this relationship for different treatment processes in the literature, a linear relationship is assumed based on the limited data we could gain access through our industrial partners.

48

S Silica,

TH Total hardness,

TDS Total dissolved solids,

TOC Total organic carbon

TU = {tu | tu is a treatment unit}

tu = ST Skim tank,

API API separator,

IGF Induced gas flotation,

DGF Dissolved gas flotation,

ORF Oil removal filter,

HCY Hydro-cyclone,

WLS Warm lime softener,

HLS Hot lime softener,

EVAP Evaporator,

WAC Weak acid cation exchanger,

CM Ceramic membrane

S = {s | s is a water source}

s = PW Produced water,

MUW Makeup water,

BBD Boiler blowdown

Parameters

Flow rates

𝐹𝐹𝑠𝑠 Flow rate of water source s ∈ S

49

𝐹𝐹𝑡𝑡𝑡𝑡𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠 Flow loss in treatment unit tu ∈ TU

𝐹𝐹𝐵𝐵𝐵𝐵𝐵𝐵 Boiler feed water flow rate

Concentrations

𝐶𝐶𝑠𝑠,𝑐𝑐 Concentration of contaminant c ∈ C in water stream s ∈ S

𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑜𝑜𝑡𝑡𝑡𝑡,𝑓𝑓𝑖𝑖𝑓𝑓 Fixed outlet concentration of contaminant c ∈ C from treatment unit tu ∈ TU

𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑖𝑖𝑖𝑖,𝑚𝑚𝑚𝑚𝑓𝑓 Maximum allowable inlet concentration of contaminant c ∈ C to treatment unit

tu ∈ TU

𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠 Contaminant c concentration of stream that is lost in treatment unit tu ∈ TU

𝐶𝐶𝑐𝑐𝑡𝑡𝑚𝑚𝑡𝑡𝑡𝑡𝑒𝑒𝑡𝑡 Target concentration required at discharge

𝐶𝐶𝑠𝑠,𝑡𝑡𝑡𝑡,𝑐𝑐 Concentration of contaminant c ∈ C in the stream between water source s ∈ S and

treatment unit tu ∈ TU

𝐶𝐶𝑐𝑐𝑚𝑚𝑎𝑎𝑒𝑒 Average concentration of contaminant c ∈ C in the system

Mass loads

𝑀𝑀𝑀𝑀𝑐𝑐𝑡𝑡𝑒𝑒𝑚𝑚 Mass load of contaminant c ∈ C to be removed from the system

𝑀𝑀𝑀𝑀𝑐𝑐𝑡𝑡𝑜𝑜𝑡𝑡 Total mass load of contaminant c ∈ C in the system

Cost parameters

𝐶𝐶𝑐𝑐𝑐𝑐𝑒𝑒𝑠𝑠𝑎𝑎𝑚𝑚𝑡𝑡 Variable cost of water stream s ∈ S

𝐶𝐶𝑐𝑐𝑐𝑐𝑒𝑒𝑠𝑠𝑓𝑓𝑖𝑖𝑓𝑓 Fixed cost of water stream s ∈ S

𝐶𝐶𝑐𝑐𝑐𝑐𝑒𝑒𝑡𝑡𝑡𝑡𝑎𝑎𝑚𝑚𝑡𝑡 Variable cost of treatment unit tu ∈ TU

50

𝐶𝐶𝑐𝑐𝑐𝑐𝑒𝑒𝑡𝑡𝑡𝑡𝑓𝑓𝑖𝑖𝑓𝑓 Fixed cost of treatment unit tu ∈ TU

Other parameters

𝑅𝑅𝑅𝑅𝑡𝑡𝑡𝑡,𝑐𝑐𝑓𝑓𝑖𝑖𝑓𝑓 Fixed value for the removal ratio of contaminant c ∈ C in treatment unit tu ∈ TU

𝑅𝑅𝑅𝑅𝑡𝑡𝑡𝑡,𝑐𝑐 Removal ratio of contaminant c ∈ C in treatment unit tu ∈ TU

𝐵𝐵𝑐𝑐𝑒𝑒𝑐𝑐𝐵𝐵𝑡𝑡𝑢𝑢 Upper bound for streams flow rate

𝐵𝐵𝑐𝑐𝑒𝑒𝑐𝑐𝐵𝐵𝑙𝑙𝑜𝑜𝑙𝑙 Lower bound for streams flow rate

𝑁𝑁𝑁𝑁𝑡𝑡𝑡𝑡𝑚𝑚𝑚𝑚𝑓𝑓 Maximum number of streams that can go through treatment unit tu ∈ TU

𝐻𝐻𝐻𝐻 Number of hours of operation per year

Variables

Flow rates

𝐹𝐹𝑠𝑠,𝑡𝑡𝑡𝑡 Flow rate of the stream from water source s ∈ S to treatment unit tu ∈ TU

𝐹𝐹𝑡𝑡𝑡𝑡,𝑡𝑡𝑡𝑡ˊ Flow rate of the stream from treatment unit tu ∈ TU to treatment unit tuʹ ∈ TU (tuʹ

≠ tu)

𝐹𝐹𝑡𝑡𝑡𝑡𝑒𝑒𝑓𝑓𝑖𝑖𝑡𝑡 Flow rate of the stream from treatment unit tu ∈ TU to discharge point

𝐹𝐹𝑡𝑡𝑡𝑡𝑖𝑖𝑖𝑖 Flow rate of inlet stream to treatment unit tu ∈ TU

𝐹𝐹𝑡𝑡𝑡𝑡𝑜𝑜𝑡𝑡𝑡𝑡 Flow rate of outlet stream from treatment unit tu ∈ TU

Concentration

𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑖𝑖𝑖𝑖 Concentration of contaminant c ∈ C in inlet stream to treatment unit tu ∈ TU

𝐶𝐶𝑡𝑡𝑡𝑡,𝑡𝑡𝑡𝑡´,𝑐𝑐 Concentration of contaminant c ∈ C in stream from treatment unit tu ∈ TU to

treatment unit tuʹ ∈ TU (tuʹ ≠ tu)

51

𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑒𝑒𝑓𝑓𝑖𝑖𝑡𝑡 Concentration of contaminant c ∈ C in the stream from treatment unit tu ∈ TU to

the discharge point

𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑜𝑜𝑡𝑡𝑡𝑡 Outlet concentration of contaminant c ∈ C from treatment unit tu ∈ TU

𝐶𝐶𝑐𝑐𝐵𝐵𝐵𝐵𝐵𝐵 Discharge concentration of contaminant c ∈ C (at discharge point)

Mass load

𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑡𝑡𝑒𝑒𝑚𝑚 Mass load of contaminant c ∈ C that is removed in treatment unit tu ∈ TU specified

with a fixed outlet concentration

𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑖𝑖𝑖𝑖 Mass load of contaminant c ∈ C entering the treatment unit tu ∈ TU

𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑜𝑜𝑡𝑡𝑡𝑡 Mass load of contaminant c ∈ C exiting the treatment unit tu ∈ TU

𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑡𝑡𝑚𝑚𝑖𝑖𝑖𝑖 Slack variable for mass load of contaminant c ∈ C in treatment unit tu ∈ TU

𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠 Surplus variable for mass load of contaminant c ∈ C in treatment unit tu ∈ TU

Cost and energy variables

𝐶𝐶𝑐𝑐𝑐𝑐𝑒𝑒𝑡𝑡𝑡𝑡𝑡𝑡𝑜𝑜𝑡𝑡 Total cost of treatment unit tu ∈ TU

𝐶𝐶𝑐𝑐𝑐𝑐𝑒𝑒𝑜𝑜𝑢𝑢 Operating cost of the system

𝐶𝐶𝑐𝑐𝑐𝑐𝑒𝑒𝑐𝑐𝑚𝑚𝑢𝑢 Capital cost of the system

𝐶𝐶𝑐𝑐𝑐𝑐𝑒𝑒𝑡𝑡𝑜𝑜𝑡𝑡 Total cost of the system

𝑒𝑒𝑐𝑐𝑒𝑒𝑐𝑐𝑔𝑔𝑒𝑒𝑡𝑡𝑡𝑡𝑎𝑎𝑚𝑚𝑡𝑡 Total energy consumption of the system

Some of the parameters such as the flow rate and concentration of water sources (except

the flow rate of the makeup water stream), performance parameters of treatment units (fixed outlet

concentration or removal ratio), maximum tolerable concentration entering treatment units, cost

52

parameters and target concentrations at the discharge point, are input manually from data sources

available in the literature or from industrial data sources. Other parameters (e.g., the flowrate of

makeup water stream, mass load of contaminant removed in each treatment unit, etc.) are

calculated from the known parameters that are input manually as mentioned above. The parameters

that are calculated are presented below and in the following section.

3.4.2.2 Constraints

Constraints of the problem are as follows:

Overall mass balance4

�𝐹𝐹𝑠𝑠𝑠𝑠

− 𝐹𝐹𝐵𝐵𝐵𝐵𝐵𝐵 = �𝐹𝐹𝑡𝑡𝑡𝑡𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠𝑡𝑡𝑡𝑡

3.4

(See Figure 3-5)

4 All mass balance equations are for water.

53

Figure 3-5 Overall mass balance in the system

Mass balance around splitters and mixers

𝐹𝐹𝑠𝑠 = �𝐹𝐹𝑠𝑠,𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡

∀ 𝑐𝑐 ∈ 𝑁𝑁 3.5

Equation 3.5 shows the mass balance for the water source splitters where each water source can

be sent to one or more treatment units. See Figure 3-6.

Figure 3-6 Mass balance for the water source splitters

54

�𝐹𝐹𝑠𝑠,𝑡𝑡𝑡𝑡 + �𝐹𝐹𝑡𝑡𝑡𝑡ʹ,𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡ʹ

= 𝐹𝐹𝑡𝑡𝑡𝑡𝑖𝑖𝑖𝑖𝑠𝑠

∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇 3.6

𝐹𝐹𝑡𝑡𝑡𝑡𝑜𝑜𝑡𝑡𝑡𝑡 = �𝐹𝐹𝑡𝑡𝑡𝑡,𝑡𝑡𝑡𝑡ʹ𝑡𝑡𝑡𝑡ʹ

+ 𝐹𝐹𝑡𝑡𝑡𝑡𝑒𝑒𝑓𝑓𝑖𝑖𝑡𝑡 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇 3.7

Equations 3.6 and 3.7 show the mass balance around the treatment unit mixer and splitter

respectively. As shown in Figure 3-7 the inlet stream to each treatment unit is the combination of

the water sources that are sent to the unit and the recycled streams from other treatment units to

that unit. The outlet stream from each treatment unit can be divided into recycled streams to other

treatment units and a discharge stream.

Figure 3-7 Mass balance for the treatment unit mixers and splitters

�𝐹𝐹𝑡𝑡𝑡𝑡𝑒𝑒𝑓𝑓𝑖𝑖𝑡𝑡𝑡𝑡𝑡𝑡

= 𝐹𝐹𝐵𝐵𝐵𝐵𝐵𝐵 3.8

Equation 3.8 shows the mass balance for the discharge mixer. All discharge streams are

collected together and mixed at the discharge point (see Figure 3-8).

55

Figure 3-8 Mass balance for the discharge mixer

Mass balance around treatment units

𝐹𝐹𝑡𝑡𝑡𝑡𝑖𝑖𝑖𝑖 − 𝐹𝐹𝑡𝑡𝑡𝑡𝑜𝑜𝑡𝑡𝑡𝑡 = 𝐹𝐹𝑡𝑡𝑡𝑡𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇 3.9

Equations 3.9 shows the mass balance for the total flow through each treatment unit (see

Figure 3-7, dashed boundary line).

Component mass balance in each treatment unit

�1 − 𝑅𝑅𝑅𝑅𝑡𝑡𝑡𝑡,𝑐𝑐� ∗ 𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑖𝑖𝑖𝑖 − 𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐

𝑜𝑜𝑡𝑡𝑡𝑡 − 𝐹𝐹𝑡𝑡𝑡𝑡𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠 ∗ 𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠 = 0 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇 , 𝑐𝑐 ∈ 𝐶𝐶 3.10

𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑖𝑖𝑖𝑖 − 𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐

𝑜𝑜𝑡𝑡𝑡𝑡 − 𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑡𝑡𝑒𝑒𝑚𝑚 − 𝐹𝐹𝑡𝑡𝑡𝑡𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠 ∗ 𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐

𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠 = 0 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇 , 𝑐𝑐 ∈ 𝐶𝐶 3.11

Equations 3.10 and 3.11 show the mass balance for each contaminant in each treatment

unit when the performance of the treatment unit is specified by a fixed removal ratio and a fixed

outlet concentration respectively.

56

Part of the inlet stream might be lost from the system during each treatment process. 𝐹𝐹𝑡𝑡𝑡𝑡𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠

and 𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠 are the flow rate and the concentration of the lost stream in each treatment unit

respectively. 𝐹𝐹𝑡𝑡𝑡𝑡𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠 is estimated for each treatment unit based on the nature of the process and 𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠

depends on the type of the process and can be estimated based on the type of the operation and

inlet and outlet concentrations.

Definition of inlet and outlet mass loads of contaminant c in treatment units

𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑖𝑖𝑖𝑖 and 𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐

𝑜𝑜𝑡𝑡𝑡𝑡 are the inlet and outlet mass loads of each contaminant for each

treatment unit respectively. These two terms are used in Equations 3.10 and 3.11 and are defined

as:

��𝐹𝐹𝑡𝑡𝑡𝑡ʹ,𝑡𝑡𝑡𝑡 ∗ 𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑜𝑜𝑡𝑡𝑡𝑡 �

𝑡𝑡𝑡𝑡ʹ

+ ��𝐹𝐹𝑠𝑠,𝑡𝑡𝑡𝑡 ∗ 𝐶𝐶𝑠𝑠,𝑐𝑐�𝑠𝑠

− 𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑖𝑖𝑖𝑖 = 0 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇 , 𝑐𝑐 ∈ 𝐶𝐶 3.12

𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑜𝑜𝑡𝑡𝑡𝑡 ∗ ��𝐹𝐹𝑡𝑡𝑡𝑡ʹ,𝑡𝑡𝑡𝑡

𝑡𝑡𝑡𝑡ʹ

+ �𝐹𝐹𝑠𝑠,𝑡𝑡𝑡𝑡𝑠𝑠

− 𝐹𝐹𝑡𝑡𝑡𝑡𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠� − 𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑜𝑜𝑡𝑡𝑡𝑡 = 0 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇, 𝑐𝑐 ∈ 𝐶𝐶 3.13

Concentration limit for inlet stream to treatment units

Some treatment units have specific limits for inlet concentration of contaminants and

cannot tolerate high concentrations of one or more contaminants. To avoid violating the

concentration limit Equation 3.14 is added as a constraint.

57

𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑖𝑖𝑖𝑖 ≤ 𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐

𝑖𝑖𝑖𝑖,𝑚𝑚𝑚𝑚𝑓𝑓 ∗ 𝐹𝐹𝑡𝑡𝑡𝑡𝑖𝑖𝑖𝑖 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇, 𝑐𝑐 ∈ 𝐶𝐶 3.14

Discharge concentration limit to meet boiler feed water quality requirements

Since the purpose of the treatment system is to reach final concentration requirements

(which is the boiler feed water requirements in my study) for all contaminants Equation 3.15 is

added to satisfy the concentration requirements.

��𝐹𝐹𝑡𝑡𝑡𝑡𝑒𝑒𝑓𝑓𝑖𝑖𝑡𝑡 ∗ 𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑜𝑜𝑡𝑡𝑡𝑡�

𝑡𝑡𝑡𝑡

≤ 𝐶𝐶𝑐𝑐𝑡𝑡𝑚𝑚𝑡𝑡𝑡𝑡𝑒𝑒𝑡𝑡 ∗ �𝐹𝐹𝑡𝑡𝑡𝑡𝑒𝑒𝑓𝑓𝑖𝑖𝑡𝑡

𝑡𝑡𝑡𝑡

∀ 𝑐𝑐 ∈ 𝐶𝐶 3.15

Total mass load of contaminant c to be removed from the system

Total mass load of each contaminant that is removed in all treatment units in the system

must be equal to or greater than the minimum mass load that is required to be removed from the

wastewater streams in order to reach the concentration requirements at the discharge point. This

constraint is shown in Equation 3.16.

�𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑡𝑡𝑒𝑒𝑚𝑚

𝑡𝑡𝑡𝑡

+ ��𝑅𝑅𝑅𝑅𝑡𝑡𝑡𝑡,𝑐𝑐 ∗ 𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑖𝑖𝑖𝑖 �

𝑡𝑡𝑡𝑡

≥ 𝑀𝑀𝑀𝑀𝑐𝑐𝑡𝑡𝑒𝑒𝑚𝑚 ∀ 𝑐𝑐 ∈ 𝐶𝐶 3.16

𝑀𝑀𝑀𝑀𝑐𝑐𝑡𝑡𝑒𝑒𝑚𝑚 is the total mass load of contaminant c that is required to be removed from the

system and is defined as:

𝑀𝑀𝑀𝑀𝑐𝑐𝑡𝑡𝑒𝑒𝑚𝑚 = �𝐹𝐹𝑠𝑠 ∗ (𝐶𝐶𝑠𝑠,𝑐𝑐 − 𝐶𝐶𝑐𝑐𝑡𝑡𝑚𝑚𝑡𝑡𝑡𝑡𝑒𝑒𝑡𝑡)

𝑠𝑠

∀ 𝑐𝑐 ∈ 𝐶𝐶 3.17

58

Cost of treatment units

The cost of each treatment unit consists of a fixed cost (that can be zero) and a variable

cost that is a function of flow rate as shown in Equation 3.18.

𝐶𝐶𝑐𝑐𝑐𝑐𝑒𝑒𝑡𝑡𝑡𝑡𝑡𝑡𝑜𝑜𝑡𝑡 = 𝐶𝐶𝑐𝑐𝑐𝑐𝑒𝑒𝑡𝑡𝑡𝑡𝑎𝑎𝑚𝑚𝑡𝑡 ∗ 𝐹𝐹𝑡𝑡𝑡𝑡𝑖𝑖𝑖𝑖 + 𝐶𝐶𝑐𝑐𝑐𝑐𝑒𝑒𝑡𝑡𝑡𝑡𝑓𝑓𝑖𝑖𝑓𝑓 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇 3.18

3.4.2.3 Objective function

The objective function of this problem is the total cost and/or total energy consumption of

the system and they are trying to be minimized. The total cost of the system includes capital cost

and operating cost. Capital cost is assumed to be the cost of treatment units and their installation.

Other expenses such as pumping, piping, etc. are not considered because they are assumed to be

roughly the same for all configurations considered. This assumption was supported through

consultation with industry experts [94]. The operating cost is the sum of treatment units’ expenses

during operation (e.g. electricity consumption of the treatment units, chemicals consumption, etc.)

and the cost of the makeup water stream. Since linear correlations are assumed for cost and energy,

the objective function is represented as a linear expression.

𝑂𝑂𝐹𝐹𝑐𝑐𝑜𝑜𝑠𝑠𝑡𝑡 = �𝐶𝐶𝑐𝑐𝑐𝑐𝑒𝑒𝑡𝑡𝑡𝑡𝑡𝑡𝑜𝑜𝑡𝑡𝑡𝑡𝑡𝑡

+ 𝐻𝐻𝐻𝐻 ∗ �(𝐹𝐹𝑠𝑠 ∗ 𝐶𝐶𝑐𝑐𝑐𝑐𝑒𝑒𝑠𝑠𝑎𝑎𝑚𝑚𝑡𝑡 )𝑠𝑠

3.19

𝑂𝑂𝐹𝐹𝑐𝑐𝑜𝑜𝑠𝑠𝑡𝑡 Objective function for total cost

59

The objective function for total energy consumed is similar to total cost, except energy is

only consumed during operation of the system and in treatment units. Energy consumed during

construction and any indirect or upstream energy consumption is neglected in this model.

𝑂𝑂𝐹𝐹𝑒𝑒𝑖𝑖𝑒𝑒𝑡𝑡𝑡𝑡𝑒𝑒 = ��𝑒𝑒𝑐𝑐𝑒𝑒𝑐𝑐𝑔𝑔𝑒𝑒𝑡𝑡𝑡𝑡𝑎𝑎𝑚𝑚𝑡𝑡 ∗ 𝐹𝐹𝑡𝑡𝑡𝑡𝑖𝑖𝑖𝑖�𝑡𝑡𝑡𝑡

3.20

Energy is consumed for steam generation and waste disposal as well, but since the steam

generator and waste handling equipment are not in the scope of the optimization and are considered

separately in the total cost calculations, these energy terms are not included in the objective

function. Similarly, the cost of the boiler and waste disposal are not considered in the cost objective

function.

For each steam generation and waste disposal combination (introduced earlier in this

chapter) cost and energy of steam generation and waste disposal are calculated separately and are

added to the final optimized cost and energy to arrive at a final total cost estimate for each

combination.

Hereafter, the cost objective function is used when describing the solution steps of the

optimization problem. However, the procedure is identical when the energy objective function is

selected.

The mathematical model described above is a nonlinear problem (NLP). Nonlinearities are

in the form of bilinear terms in equations 3.12, 3.13, and 3.15 where both flow rate and

concentration are unknown variables.

60

Binary variables can be used to show the existence or non-existence of water streams and

treatment units and to assign upper and lower bounds to the streams flow rates. When a treatment

unit is selected in the optimal design of the treatment system, the binary variable associated with

that treatment unit assumes the value of “1”, and if a treatment unit is not selected in the optimal

design, the binary variable associated with that treatment unit assumes the value of “0”. Similarly,

if the flow rate of a stream in the treatment network is nonzero, the binary variable associated with

that stream is “1” and if the flow rate of a stream in the treatment network is zero, the binary

variable associated with that stream is “0”.

By adding binary variables that are introduced below, the problem is converted to a mixed-

integer non-linear (MINLP) problem.

3.4.2.4 Binary variables

𝐵𝐵𝑠𝑠,𝑡𝑡𝑡𝑡 Binary variable to show the existence (value of 1) or non-existence (value of 0) of

the stream from water source s ∈ S to treatment unit tu ∈ TU

𝐵𝐵𝑡𝑡𝑡𝑡,𝑡𝑡𝑡𝑡ʹ Binary variable to show the existence (value of 1) or non-existence (value of 0) of

the stream from treatment unit tu ∈ TU to treatment unit tuʹ ∈ TU

𝐵𝐵𝑡𝑡𝑡𝑡𝑒𝑒𝑓𝑓𝑖𝑖𝑡𝑡 Binary variable to show the existence (value of 1) or non-existence (value of 0) of

the stream from treatment unit tu ∈ TU to discharge point

𝐵𝐵𝑡𝑡𝑡𝑡 Binary variable to show the existence (value of 1) or non-existence (value of 0) of

treatment unit tu ∈ TU

Additional constraints including binary variables are presented here. These constraints

control the reasonableness and practicality (e.g., eliminating the cycles between two treatment

units, avoiding very small flow rates, etc.) of the system.

61

3.4.2.5 Additional constraints (with binary variables)

Eliminating the cycles

This constraint is used to ensure that only one recycled stream exists between two particular

treatment units. In other words, if there is a stream recycled from treatment unit tu to treatment

unit tuʹ, there won’t be any stream recycled from treatment unit tuʹ to treatment unit tu.

𝐵𝐵𝑡𝑡𝑡𝑡,𝑡𝑡𝑡𝑡ʹ + 𝐵𝐵𝑡𝑡𝑡𝑡ʹ,𝑡𝑡𝑡𝑡 ≤ 1 ∀ 𝑒𝑒𝑒𝑒 𝑒𝑒𝑐𝑐𝐵𝐵 𝑒𝑒𝑒𝑒ʹ ∈ 𝑇𝑇𝑇𝑇 (𝑒𝑒𝑒𝑒 ≠ 𝑒𝑒𝑒𝑒ʹ) 3.21

Assigning upper bounds to the streams flow rate

A maximum flow rate can exist in the system and is the sum of all inlet streams (water

sources). The maximum possible flow rate and associated constraints for different streams in the

system are shown in Equations 3.22 to 3.26.

𝐵𝐵𝑐𝑐𝑒𝑒𝑐𝑐𝐵𝐵𝑡𝑡𝑢𝑢 = �𝐹𝐹𝑠𝑠𝑠𝑠

3.22

𝐹𝐹𝑠𝑠,𝑡𝑡𝑡𝑡 − 𝐵𝐵𝑠𝑠,𝑡𝑡𝑡𝑡 ∗ 𝐵𝐵𝑐𝑐𝑒𝑒𝑐𝑐𝐵𝐵𝑡𝑡𝑢𝑢 ≤ 0 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇, 𝑐𝑐 ∈ 𝑁𝑁 3.23

𝐹𝐹𝑡𝑡𝑡𝑡,𝑡𝑡𝑡𝑡ʹ − 𝐵𝐵𝑡𝑡𝑡𝑡,𝑡𝑡𝑡𝑡ʹ ∗ 𝐵𝐵𝑐𝑐𝑒𝑒𝑐𝑐𝐵𝐵𝑡𝑡𝑢𝑢 ≤ 0 ∀ 𝑒𝑒𝑒𝑒 𝑒𝑒𝑐𝑐𝐵𝐵 𝑒𝑒𝑒𝑒ʹ ∈ 𝑇𝑇𝑇𝑇 3.24

𝐹𝐹𝑡𝑡𝑡𝑡𝑒𝑒𝑓𝑓𝑖𝑖𝑡𝑡 − 𝐵𝐵𝑡𝑡𝑡𝑡𝑒𝑒𝑓𝑓𝑖𝑖𝑡𝑡 ∗ 𝐵𝐵𝑐𝑐𝑒𝑒𝑐𝑐𝐵𝐵𝑡𝑡𝑢𝑢 ≤ 0 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇 3.25

𝐹𝐹𝑡𝑡𝑡𝑡𝑖𝑖𝑖𝑖 − 𝐵𝐵𝑡𝑡𝑡𝑡 ∗ 𝐵𝐵𝑐𝑐𝑒𝑒𝑐𝑐𝐵𝐵𝑡𝑡𝑢𝑢 ≤ 0 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇 3.26

62

Assigning lower bounds to stream flow rate

To avoid unreasonably low flow rates (based on the experiences of industry experts [94])

in each stream, a minimum flow rate is defined based on the system specifications and used as the

lower bound of each stream flow rate in the system. The lower bound constraints are shown in

Equations 3.27 to 3.30.

𝐹𝐹𝑠𝑠,𝑡𝑡𝑡𝑡 − 𝐵𝐵𝑠𝑠,𝑡𝑡𝑡𝑡 ∗ 𝐵𝐵𝑐𝑐𝑒𝑒𝑐𝑐𝐵𝐵𝑙𝑙𝑜𝑜𝑙𝑙 ≥ 0 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇, 𝑐𝑐 ∈ 𝑁𝑁 3.27

𝐹𝐹𝑡𝑡𝑡𝑡,𝑡𝑡𝑡𝑡ʹ − 𝐵𝐵𝑡𝑡𝑡𝑡,𝑡𝑡𝑡𝑡ʹ ∗ 𝐵𝐵𝑐𝑐𝑒𝑒𝑐𝑐𝐵𝐵𝑙𝑙𝑜𝑜𝑙𝑙 ≥ 0 ∀ 𝑒𝑒𝑒𝑒 𝑒𝑒𝑐𝑐𝐵𝐵 𝑒𝑒𝑒𝑒ʹ ∈ 𝑇𝑇𝑇𝑇 3.28

𝐹𝐹𝑡𝑡𝑡𝑡𝑒𝑒𝑓𝑓𝑖𝑖𝑡𝑡 − 𝐵𝐵𝑡𝑡𝑡𝑡𝑒𝑒𝑓𝑓𝑖𝑖𝑡𝑡 ∗ 𝐵𝐵𝑐𝑐𝑒𝑒𝑐𝑐𝐵𝐵𝑙𝑙𝑜𝑜𝑙𝑙 ≥ 0 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇 3.29

𝐹𝐹𝑡𝑡𝑡𝑡𝑖𝑖𝑖𝑖 − 𝐵𝐵𝑡𝑡𝑡𝑡 ∗ 𝐵𝐵𝑐𝑐𝑒𝑒𝑐𝑐𝐵𝐵𝑙𝑙𝑜𝑜𝑙𝑙 ≥ 0 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇 3.30

Bounding constraints (3.23 to 3.30) help simplify the optimization problem by directing

the model to search through a smaller range of values for the flow rates throughout the system.

Maximum number of streams going through a treatment unit

�𝐵𝐵𝑠𝑠,𝑡𝑡𝑡𝑡𝑠𝑠

+ �𝐵𝐵𝑡𝑡𝑡𝑡ʹ,𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡ʹ

≤ 𝑁𝑁𝑁𝑁𝑡𝑡𝑡𝑡𝑚𝑚𝑚𝑚𝑓𝑓 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇 3.31

63

Constraint 3.31 limits the number of wastewater streams that can go through each treatment

unit. This constraint helps simplify the final configuration and makes the final optimal design more

applicable in the industrial plants.

The MINLP model is a non-convex nonlinear optimization problem that is similar to the

formulation presented by Quesada and Grossmann [82]. In this type of problem, the use of MINLP

solvers can lead to erroneous results and global optimality is not guaranteed. In addition, results

of the optimization are highly dependent on the initialization of variables [82], [84], [95], [96].

Therefore, proper initial values are essential to find the global optimum. For this reason a two-step

iterative approach is used to solve the problem. This is described in the next section.

3.5 Solution strategy

Conceptual approaches presented in various studies and mathematical optimization tools

form the basis of the solution strategy in this study [65]–[67], [76], [86], [97]. Quesada and

Grossmann proposed a branch and bound algorithm to solve the optimization problem related to a

contaminant separation network (similar to the problem in this study). The proposed method uses

linear underestimators5 for the bilinear terms to find the global optimum [82]. Galan and

Grossmann introduced a relaxation approach along with linear underestimators that was mentioned

above to solve a distributed effluent treatment problem [74]. They proposed a linear relaxation of

the initial nonlinear problem based on linear underestimators of the nonconvex constraints that

provides a valid lower bound for the global optimum of the initial problem. The relaxed LP is then

solved to minimize the flow rate through a specific treatment unit and the result is used as an initial

5 They used linear functions that were a lower bound for the actual nonlinear constraints in the model.

64

point for the nonlinear problem. This procedure is repeated for each treatment unit and the best

solution (minimum value for the objective function) for the nonlinear problem is selected as the

optimal design. This method is extended to a procedure for the selection of treatment technologies

where the contaminants are removed by mutually exclusive technologies (where a particular

contaminant can be removed in one particular treatment unit). Alva-Argaez proposed a more

general approach where the treatment units are not mutually exclusive, i.e. a particular contaminant

can be removed in more than one treatment unit [93].

The solution strategy in the present study consists of a decomposition approach that was

initially proposed by Alva-Argaez [76], [93]. In this approach the initial MINLP problem is

divided into MILP and LP problems that are solved iteratively to reach an optimal solution which

is then used as an initial point for MINLP problem.

3.5.1 The mixed-integer linear programming (MILP) problem

The nonlinearity of the initial problem is due to bilinear terms in the mass balance

equations, 3.12, 3.13 and 3.15, where two unknown variables, concentration and flow rate, are

multiplied by each other. To remove the nonlinearity, aforementioned constraints are projected

onto the concentration space. This means that 𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑜𝑜𝑡𝑡𝑡𝑡 will be assumed to be a known parameter in

those constraints (it was initially an unknown variable); 𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑜𝑜𝑡𝑡𝑡𝑡.𝑢𝑢𝑚𝑚𝑡𝑡. Therefore, this parameter must

be initialized before the solution procedure starts. As a starting point, all treatment processes are

assumed to be perfect treatment units that can remove 100% of all the contaminants (i.e., all outlet

concentrations are zero), except when the removal ratio or the fixed outlet concentration of a

contaminant in a treatment unit is known. So, there are two groups for the combination of a

contaminant and a treatment units (tu,c); the first group consists of contaminants (e.g., contaminant

65

O (O ∈ C) that can be partially removed in a treatment unit, e.g. ST (ST ∈ TU). For this group, the

mass load of contaminant O will change after passing through treatment unit ST and the outlet

concentration of O is different from the inlet stream concentration of this contaminant. Therefore,

𝐶𝐶𝑆𝑆𝑇𝑇,𝑂𝑂𝑜𝑜𝑡𝑡𝑡𝑡 ≠ 𝐶𝐶𝑆𝑆𝑇𝑇,𝑂𝑂

𝑖𝑖𝑖𝑖

The second group consists of the contaminants, e.g. S (S ∈ C) the mass load of which will

not change in a treatment unit, e.g. ST (ST ∈ TU). This means that the concentration of S is the

same for inlet and outlet streams of treatment unit ST. For this group,

𝐶𝐶𝑆𝑆𝑇𝑇,𝑆𝑆𝑜𝑜𝑡𝑡𝑡𝑡 = 𝐶𝐶𝑆𝑆𝑇𝑇,𝑆𝑆

𝑖𝑖𝑖𝑖

For the first group, the performance of the treatment unit is known for the desired

contaminant in the form of a fixed outlet concentration or a fixed removal ratio.

The initial values for parameter 𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑜𝑜𝑡𝑡𝑡𝑡 are assigned directly as stated below:

• For the first group when the input data are available in the form of fixed outlet concentration

𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑜𝑜𝑡𝑡𝑡𝑡,𝑢𝑢𝑚𝑚𝑡𝑡 = 𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐

𝑜𝑜𝑡𝑡𝑡𝑡,𝑓𝑓𝑖𝑖𝑓𝑓 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇, 𝑐𝑐 ∈ 𝐶𝐶 3.32

𝑅𝑅𝑅𝑅𝑡𝑡𝑡𝑡,𝑐𝑐 = 0 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇, 𝑐𝑐 ∈ 𝐶𝐶 3.33

• For the first group when the input data are available in the form of fixed removal ratio

𝑅𝑅𝑅𝑅𝑡𝑡𝑡𝑡,𝑐𝑐 = 𝑅𝑅𝑅𝑅𝑡𝑡𝑡𝑡,𝑐𝑐𝑓𝑓𝑖𝑖𝑓𝑓 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇, 𝑐𝑐 ∈ 𝐶𝐶 3.34

𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑜𝑜𝑡𝑡𝑡𝑡,𝑢𝑢𝑚𝑚𝑡𝑡 = 0 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇, 𝑐𝑐 ∈ 𝐶𝐶 3.35

66

• For the second group:

𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑜𝑜𝑡𝑡𝑡𝑡,𝑢𝑢𝑚𝑚𝑡𝑡 = 0 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇, 𝑐𝑐 ∈ 𝐶𝐶 3.36

𝑅𝑅𝑅𝑅𝑡𝑡𝑡𝑡,𝑐𝑐 = 0 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇, 𝑐𝑐 ∈ 𝐶𝐶 3.37

A number of constraints are changed to a different form to simplify the optimization

procedure. New forms of equations 3.12 and 3.13, after projection onto concentration space, are

shown below:

��𝐹𝐹𝑡𝑡𝑡𝑡ʹ,𝑡𝑡𝑡𝑡 ∗ 𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑜𝑜𝑡𝑡𝑡𝑡,𝑢𝑢𝑚𝑚𝑡𝑡 �

𝑡𝑡𝑡𝑡ʹ

+ ��𝐹𝐹𝑠𝑠,𝑡𝑡𝑡𝑡 ∗ 𝐶𝐶𝑠𝑠,𝑐𝑐�𝑠𝑠

− 𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑖𝑖𝑖𝑖 = 0 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇 , 𝑐𝑐 ∈ 𝐶𝐶 3.12ʹ

𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑜𝑜𝑡𝑡𝑡𝑡,𝑢𝑢𝑚𝑚𝑡𝑡 ∗ ��𝐹𝐹𝑡𝑡𝑡𝑡ʹ,𝑡𝑡𝑡𝑡

𝑡𝑡𝑡𝑡ʹ

+ �𝐹𝐹𝑠𝑠,𝑡𝑡𝑡𝑡𝑠𝑠

− 𝐹𝐹𝑡𝑡𝑡𝑡𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠� − 𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑜𝑜𝑡𝑡𝑡𝑡 = 0 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇, 𝑐𝑐 ∈ 𝐶𝐶 3.13ʹ

Constraint 3.15 is converted into an equality constraint and relaxed6 using slack and surplus

variables as:

��𝐹𝐹𝑡𝑡𝑡𝑡𝑒𝑒𝑓𝑓𝑖𝑖𝑡𝑡 ∗ 𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑜𝑜𝑡𝑡𝑡𝑡,𝑢𝑢𝑚𝑚𝑡𝑡�

𝑡𝑡𝑡𝑡

+ 𝑐𝑐𝑐𝑐2 − 𝑐𝑐𝑐𝑐5 = 𝐶𝐶𝑐𝑐𝑡𝑡𝑚𝑚𝑡𝑡𝑡𝑡𝑒𝑒𝑡𝑡 ∗ �𝐹𝐹𝑡𝑡𝑡𝑡𝑒𝑒𝑓𝑓𝑖𝑖𝑡𝑡

𝑡𝑡𝑡𝑡

∀ 𝑐𝑐 ∈ 𝐶𝐶 3.15ʹ

6 Relaxation means adding an infeasibility term to the equation (𝑐𝑐𝑐𝑐5 in this equation) that helps keep the model feasible.

67

Variable 𝑐𝑐𝑐𝑐2 is used to change the inequality constraint to an equality and variable 𝑐𝑐𝑐𝑐5 is

used to relax the constraint and maintain feasibility. This variable is an infeasibility term and the

model attempts to reduce the term to zero during the optimization procedure.

Constraints 3.10 and 3.11 can be presented together in one equation. The relaxed form of

this constraint is shown as:

�1 − 𝑅𝑅𝑅𝑅𝑡𝑡𝑡𝑡,𝑐𝑐� ∗ 𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑖𝑖𝑖𝑖 − 𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐

𝑜𝑜𝑡𝑡𝑡𝑡 − 𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑡𝑡𝑒𝑒𝑚𝑚 − ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇 , 𝑐𝑐 ∈ 𝐶𝐶 3.10ʹ

𝐹𝐹𝑡𝑡𝑡𝑡𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠 ∗ 𝐶𝐶𝑡𝑡𝑡𝑡𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠 + 𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑡𝑡𝑚𝑚𝑖𝑖𝑖𝑖 − 𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐

𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠 = 0

𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑡𝑡𝑚𝑚𝑖𝑖𝑖𝑖 and 𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐

𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠 are slack and surplus variables that help maintain feasibility of the

problem and are considered as infeasibility terms which the procedure will aim to reduce to zero.

Equation 3.14 is converted to an equality constraint:

𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑖𝑖𝑖𝑖 + 𝑐𝑐𝑡𝑡𝑡𝑡,𝑐𝑐

1 = 𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑖𝑖𝑖𝑖,𝑚𝑚𝑚𝑚𝑓𝑓 ∗ 𝐹𝐹𝑡𝑡𝑡𝑡𝑖𝑖𝑖𝑖 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇, 𝑐𝑐 ∈ 𝐶𝐶 3.14ʹ

Equation 3.16 is converted to an equality constraint and relaxed as:

�𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑡𝑡𝑒𝑒𝑚𝑚

𝑡𝑡𝑡𝑡

+ ��𝑅𝑅𝑅𝑅𝑡𝑡𝑡𝑡,𝑐𝑐 ∗ 𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑖𝑖𝑖𝑖 �

𝑡𝑡𝑡𝑡

∀ 𝑐𝑐 ∈ 𝐶𝐶 3.16ʹ

− 𝑐𝑐𝑐𝑐4 + 𝑐𝑐𝑐𝑐3 = 𝑀𝑀𝑀𝑀𝑐𝑐𝑡𝑡𝑒𝑒𝑚𝑚

68

Variable 𝑐𝑐𝑐𝑐3 is an infeasibility term as well. So, we have the sum of infeasibilities in the

equation below:

𝐼𝐼 = ��𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑡𝑡𝑚𝑚𝑖𝑖𝑖𝑖

𝑐𝑐𝑡𝑡𝑡𝑡

+ ��𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠


+ �𝑐𝑐𝑐𝑐3𝑐𝑐

+ �𝑐𝑐𝑐𝑐5𝑐𝑐

3.38

The sum of infeasibilities should be minimized along with the objective function during

the optimization procedure. For this reason this term is added with a weighting factor to the

objective function. Attaching a weight to the infeasibility term was suggested by Alva-Argaez

[93]. The updated objective function is then:

𝑂𝑂𝐹𝐹𝑐𝑐𝑜𝑜𝑠𝑠𝑡𝑡 = �𝐶𝐶𝑐𝑐𝑐𝑐𝑒𝑒𝑡𝑡𝑡𝑡𝑡𝑡𝑜𝑜𝑡𝑡𝑡𝑡𝑡𝑡

+ 𝐻𝐻𝐻𝐻 ∗ �(𝐹𝐹𝑠𝑠 ∗ 𝐶𝐶𝑐𝑐𝑐𝑐𝑒𝑒𝑠𝑠𝑎𝑎𝑚𝑚𝑡𝑡 )𝑠𝑠

+ 𝑃𝑃𝐼𝐼 3.39

𝑃𝑃 is the weighting factor for infeasibilities that is updated in each iteration. It starts with

10-5 and is increased by one order of magnitude in each iteration step while I gets closer to zero.

The purpose of applying this factor is to not allow the PI term to become negligible compared to

the rest of the terms on the same side of the equation and force the model to continue the iteration

until I becomes zero. The choice of weights for the infeasibility term was suggested by Palacios-

Gomez et al. and Takama et al. [80], [98].

So, the MILP problem consists of constraints 3.4 to 3.9, 3.10ʹ, 3.12ʹ, 3.13ʹ, 3.14ʹ, 3.15ʹ, 3.16ʹ,

3.18, 3.19, 3.21, 3.23 to 3.31, and 3.38. The objective function is equation 3.39.

69

3.5.2 The linear programming (LP) problem

The constraints of the LP problem include equation 3.10ʹ, and equations 3.12 and 3.13

projected onto the 𝐹𝐹𝑡𝑡𝑡𝑡ʹ,𝑡𝑡𝑡𝑡 and 𝐹𝐹𝑠𝑠,𝑡𝑡𝑡𝑡 space. Initial values for 𝐹𝐹𝑡𝑡𝑡𝑡ʹ,𝑡𝑡𝑡𝑡 and 𝐹𝐹𝑠𝑠,𝑡𝑡𝑡𝑡 are available from the

results of the MILP problem. Using the new constraints, the outlet concentration, 𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑜𝑜𝑡𝑡𝑡𝑡 is an

unknown variable and stream flow rates, 𝐹𝐹𝑡𝑡𝑡𝑡ʹ,𝑡𝑡𝑡𝑡 and 𝐹𝐹𝑠𝑠,𝑡𝑡𝑡𝑡 from equations 3.12 and 3.13 are assumed

to be known parameters and are written in the form of 𝐹𝐹𝑡𝑡𝑡𝑡ʹ,𝑡𝑡𝑡𝑡𝑢𝑢𝑚𝑚𝑡𝑡 and 𝐹𝐹𝑠𝑠,𝑡𝑡𝑡𝑡

𝑢𝑢𝑚𝑚𝑡𝑡 respectively.

��𝐹𝐹𝑡𝑡𝑡𝑡ʹ,𝑡𝑡𝑡𝑡𝑢𝑢𝑚𝑚𝑡𝑡 ∗ 𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐

𝑜𝑜𝑡𝑡𝑡𝑡 �𝑡𝑡𝑡𝑡ʹ

+ ��𝐹𝐹𝑠𝑠,𝑡𝑡𝑡𝑡𝑢𝑢𝑚𝑚𝑡𝑡 ∗ 𝐶𝐶𝑠𝑠,𝑐𝑐�

𝑠𝑠

− 𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑖𝑖𝑖𝑖 = 0 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇 , 𝑐𝑐 ∈ 𝐶𝐶 3.12ʹʹ

𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑜𝑜𝑡𝑡𝑡𝑡 ∗ ��𝐹𝐹𝑡𝑡𝑡𝑡ʹ,𝑡𝑡𝑡𝑡

𝑢𝑢𝑚𝑚𝑡𝑡

𝑡𝑡𝑡𝑡ʹ

+ �𝐹𝐹𝑠𝑠,𝑡𝑡𝑡𝑡𝑢𝑢𝑚𝑚𝑡𝑡

𝑠𝑠

− 𝐹𝐹𝑡𝑡𝑡𝑡𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠� − 𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑜𝑜𝑡𝑡𝑡𝑡 = 0 ∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇, 𝑐𝑐 ∈ 𝐶𝐶 3.13ʹʹ

In the LP problem the goal is to minimize the sum of infeasibilities that appear in the

problem constraints. The objective function of the LP problem is named M and is in the form of:

𝑀𝑀 = ��𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑡𝑡𝑚𝑚𝑖𝑖𝑖𝑖


+ ��𝑀𝑀𝑀𝑀𝑡𝑡𝑡𝑡,𝑐𝑐𝑙𝑙𝑜𝑜𝑠𝑠𝑠𝑠


∀ 𝑒𝑒𝑒𝑒 ∈ 𝑇𝑇𝑇𝑇, 𝑐𝑐 ∈ 𝐶𝐶 3.40

Let MILPk and LPk be the mixed-integer linear problem and the linear problem at iteration

k. The approach to solve this, is described in the following steps:

1. Set k=1. Outlet contaminants concentration and removal ratios are initialized as described in

equations 3.32 to 3.37 for the first iteration.

70

2. The MILPk is solved to minimize the objective function and optimal values of flow rates are

found: 𝐹𝐹𝑠𝑠,𝑡𝑡𝑡𝑡∗, 𝐹𝐹𝑡𝑡𝑡𝑡,𝑡𝑡𝑡𝑡ˊ

∗, 𝐹𝐹𝑡𝑡𝑡𝑡𝑒𝑒𝑓𝑓𝑖𝑖𝑡𝑡∗, 𝐹𝐹𝑡𝑡𝑡𝑡𝑖𝑖𝑖𝑖

∗, 𝐹𝐹𝑡𝑡𝑡𝑡𝑜𝑜𝑡𝑡𝑡𝑡∗.

3. Set 𝐹𝐹𝑠𝑠,𝑡𝑡𝑡𝑡𝑢𝑢𝑚𝑚𝑡𝑡,𝑘𝑘 = 𝐹𝐹𝑠𝑠,𝑡𝑡𝑡𝑡

∗ and 𝐹𝐹𝑡𝑡𝑡𝑡ʹ,𝑡𝑡𝑡𝑡𝑢𝑢𝑚𝑚𝑡𝑡,𝑘𝑘 = 𝐹𝐹𝑡𝑡𝑡𝑡,𝑡𝑡𝑡𝑡ˊ

∗ and solve the LPk to find a new outlet

concentration vector 𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑜𝑜𝑡𝑡𝑡𝑡∗.

4. Increase the iteration number by one unit: k=k+1. Set 𝑃𝑃𝑘𝑘+1 = 𝑃𝑃𝑘𝑘 ∗ 10 and 𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑜𝑜𝑡𝑡𝑡𝑡,𝑘𝑘+1 =

𝐶𝐶𝑡𝑡𝑡𝑡,𝑐𝑐𝑜𝑜𝑡𝑡𝑡𝑡∗. Then solve the MILPk to find new values for the stream flow rates.

5. If 𝐼𝐼 ≤ 𝜀𝜀 stop. Otherwise repeat the procedure from step 3.

This procedure iterates between the two problems (MILP and LP) until the sum of

infeasibilities is close to zero (𝜀𝜀 = 10−5). The optimal values of the objective function and flow

rates from the last iteration when feasibility is reached can then be used as the initial point for the

MINLP problem. In most cases the results of the last iteration are similar to the results of the

MINLP problem, but in some case the MINLP problem improves (gives a smaller value for the

objective function) the results of the iteration.

In this procedure a penalty term (sum of infeasibilities) is added to the objective function

of the MINLP problem to account for the infeasibilities that are imposed on the model by the initial

assumption of perfect treatment performance. This assumption is essential to remove the nonlinear

terms and converts the feasible region of the problem to a convex set. The iterative approach helps

decrease the infeasibility term step by step until it converges to zero.

CPLEX solver is used for the linear models and BARON is used for the nonlinear models

in the study. CPLEX is a high performance solver for LP and MIP problems and is the most widely

used commercial MIP solver. This solver uses the primal or dual simplex algorithm, the barrier

algorithm or the network algorithm to solve the problems [99]. The Branch-And-Reduce

71

Optimization Navigator (BARON) is designed to find globally optimal solutions for nonconvex

optimization model types. Purely continuous, purely integer, and mixed-integer nonlinear model

types can be solved using this solver. While traditional NLP and MINLP algorithms are guaranteed

to provide global optima only under certain convexity assumptions, BARON implements

deterministic global optimization algorithms of branch-and-bound type that are guaranteed to

provide global optima under fairly general assumptions (e.g. the existence of finite lower and upper

bound on nonlinear expressions in the NLP or MINLP) [100], [101]. BONMIN is another solver

that was used to solve MINLP problems to compare the results with the results of BARON. In

roughly 90% of cases considered in this thesis, both solvers give the same results. In all other cases

the variation is less than 2% in the final costs estimated.

The four cases described above are run in the optimization model to explore the energy/cost

implications and the tradeoffs that are created by optimizing the designs. The analysis is based on

a typical SAGD operation that requires 500 tonnes/hour of steam and produces 20,000 BPCD

(barrels per calendar day) bitumen. Reservoir retention (water loss inside the reservoir) is assumed

to be 5% for all cases. Boiler blowdown for the OTSG and drum boiler are assumed to be 20%

and 2% of the boiler feed water respectively. Evaporator blowdown is 5% of the evaporator feed.

Total cost of the SAGD operations and total cost of the water treatment system of the SAGD

operations are compared across four cases. Also, electricity consumed within the water treatment

system and additional natural gas consumed in the OTSG boiler (compared to that consumed in

the drum boiler) and GHG emissions associated with the electricity and natural gas consumption

are compared across all cases. Total makeup water consumption is the other metric evaluated to

compare the four cases.

72

Chapter Four: Results and Discussion

The optimization of the water treatment network of SAGD operations for four different

configuration scenarios (case 1 to case 4) is explored and presented in this chapter. For each case,

the current and optimized designs are compared across a set of metrics (cost, energy, GHG

emissions, etc.). Additionally, four cases are compared to each other in order to explore

cost/energy/water/GHG emissions tradeoffs within and across different cases. The analysis is

based on a typical SAGD operation that requires 500 tonnes/hour of steam and produces 20,000

BPCD (barrels per calendar day) bitumen.

4.1 Optimized design for minimum total cost

The optimized designs resulting from the optimization of 4 cases for minimized cost (i.e.

by deploying the cost objective function) are presented here. Figure 4-1 to Figure 4-4 show the

current designs for the SAGD water treatment network for four cases. Optimized designs for case

1 to 4 are shown in Figure 4-5 to Figure 4-8.

73

Figure 4-1 Current design of water treatment network for case 1 (all stream flow rates are in

tonne/hr)


tonne/hr)

74


tonne/hr)


tonne/hr)

75

Figure 4-5 Optimized design of case 1 for minimum cost (all stream flow rates are in tonne/hr)


76



77

In all cases parts of the streams are bypassed around one or more treatment units in the

optimized design. In cases 1, 2 and 3, makeup water goes directly to the ion exchange unit (WAC)

in the optimized design, while in the current design it goes to the lime softening unit (WLS/HLS)

first and then to the ion exchange unit. This is because the main contaminant in the makeup water

stream is hardness (that is removed in the ion exchange unit) and the silica concentration in this

stream is not high (less than 15 ppm) and therefore, it doesn’t need to go to the lime softener for

silica removal.

In the optimized design of case 3, the recycled boiler blowdown stream is divided into two

streams, one stream is mixed with the inlet stream to the gas flotation unit (IGF) and the other

stream goes to the WAC. However, in the current design the recycled boiler blowdown goes to the

WLS and WAC.

In case 4, a small part of the produced water stream (2 tonne/hr, 0.4% of the produced

water stream) is bypassed around the oil removal filter (ORF) in the optimized design. In addition,

in the optimized design of case 4, the makeup water stream is sent to the WAC for hardness

removal, while in the current design makeup water is treated in the evaporator and no ion exchange

unit is used in the current design. Therefore, it is cheaper to have a small ion exchange unit for

makeup water hardness removal and an evaporator for treating only the produced water (as the

result of optimization of case 4 suggests) than having a larger evaporator that treats both produced

water and the makeup water streams.

4.2 Cost minimization analysis for the treatment network

In this section the results of the optimization model (cost, energy, etc.) when cost is

minimized for all cases are considered. The optimization model focuses on providing guidance on

78

decisions related to the water treatment system. Therefore, results include comparisons of different

water treatment technologies and the remainder of the SAGD operation (e.g., steam generation

and waste disposal) is not presented. Of specific note, the impact of the difference in the boiler

costs (difference between OTSG and drum boiler costs) and the difference in natural gas

combustion in different types of boiler (OTSG and drum boiler) are considered in results presented

in this chapter, not the entire steam production section (i.e. the results get dwarfed since the cost

of the water treatment system is about 12.5-25% of the total cost of the plant for different

configurations. We acknowledge that the emissions and costs are relatively small when compared

to the total plant, however, they are still on the order of millions of dollars per year and therefore

are important to investigate.). However, the results in the context of the entire facility are presented

in Appendix A.

4.2.1 Operating cost breakdown

The total cost of the water treatment system for current and optimized designs for the four

cases are shown in Figure 4-9. In this figure, the operating cost of the water treatment system

(WTS) is divided into the electricity cost, chemicals cost and other costs (e.g. maintenance cost,

manpower cost, etc.).

79

Figure 4-9 Annual cost of the water treatment system for cases 1-4, with operating cost

breakdown

For each case, costs of the current and optimized designs are shown in Figure 4-9.

According to this figure, the cost of the water treatment system decreases due to the improvements

that are recommended through the optimization model (that are shown in Figure 4-1 to Figure 4-

8). In the optimized design of all the four cases, stream flow rates passing all or some of the

treatment units are reduced. Smaller flow rate results in smaller treatment units, which means

lower cost of treatment unit. Cases 1 and 3 show the highest potential for cost savings with 19.5%

and 15.8% cost savings respectively. Cases 2 and 4 show the lowest with 7% and 9% potential

cost savings. However, all optimized cases result in lower costs than the corresponding “current”

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Case 1 Case 2 Case 3 Case 4

Annu

al c

ost (

$1E6

/yr)

Chemicals CostNatural Gas CostElectricity CostOther CostsCapital Cost

Operating Cost:

80

cases. The contribution of operating cost to the total cost savings is about 15-30% higher than the

contribution of capital cost for all cases. This means that operating cost has a more significant

share of the potential savings than capital cost especially in the treatment units making larger

contributions to the cost savings.

Electricity represents a small share of the total operating cost in cases 1 and 3 (16% and

14% respectively). In cases 2 and 4 where the evaporator is used for water treatment, the share of

electricity in total operating cost is more significant (36% and 63% respectively). Optimizing the

flow of the streams also leads to savings in electricity. These savings are relatively small for cases

1, 2 and 3 (from 5.8% to 6.3% of the total operating cost savings) but are more significant for case

4 (60% of total operating cost savings). This is due to the use of evaporators in case 4. That is,

more than 95% of total electricity consumption of case 4, is used in the evaporator and this case

consumes 3.5-13 times more electricity than cases 1, 2 and 3. Therefore, bypassing wastewater

streams around the evaporator where possible will result in a reduction in the electricity used in

case 4 more than other components of the operating cost.

The results also show that case 1 has the lowest cost of water treatment system and cases

3, 2 and 4 rank next respectively. The higher cost of cases 2 and 4 is due to the use of evaporators

that are more expensive than other treatment units. All the detailed cost results are presented in

Appendix B, Table B-1 to Table B-4.

To include the impact of the steam generation component of the water treatment system,

the total cost of the water treatment system plus the additional capital and operating cost associated

with the steam generation system, for current and optimized designs for the four cases are shown

in Figure 4-10 (total capital cost of drum boiler used in case 4 is higher than OTSG used in cases

1, 2 and 3, while total operating cost of OTSG is higher than drum boiler). Only the cost differences

81

between the two types of boiler are considered in Figure 4-10, and are referred to as “Additional

Capital Cost” and “Additional Operating Cost” respectively.). Electricity, natural gas and

chemicals costs account for 15%, 68% and 17% respectively of the additional operating cost in the

OTSG boiler.

Figure 4-10 Annual costs of the water treatment system for cases 1-4, including operating cost

breakdown, plus additional capital and operating costs in the boiler (differences between the

costs of the OTSG and drum boiler)

As shown in Figure 4-10, with the additional costs of the steam generation system

included in the cost analysis, the results of the comparison between the four cases don’t change;

02468

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Annu

al c

ost (

$1E6

/yr)

Chemicals Cost

Natural Gas Cost

Electricity Cost

Other Costs

Additional Operating Cost (boiler)

Capital Cost- Water treatment system

Additional Capital Cost (boiler)

Operating Cost- water treatmenr system:

82

case 4 is still the most expensive case and cases 2, 3 and 1 are increasingly less costly. This

means the additional costs for the steam generation system are not significant in the cost analysis

of the four cases and therefore are not included in the results presented in the remaining of the

chapter.

Capital and operating cost breakdown by treatment unit

Figure 4-11 shows the total cost of the water treatment system including capital and

operating cost broken down by treatment unit.

Figure 4-11 Annual cost of the water treatment system for cases 1-4, with capital and operating

cost broken down by treatment unit (CC=Capital cost- solid fill, OC=Operating cost- hashed fill)

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28


Annu

al c

ost (

$1E6

/yr)

Makeup Water

Evaporator

WAC

WLS

ORF

IGF

Skim Tank

CC

OC

83

According to Figure 4-11, in cases 1 and 3 the lime softener contributes the largest share

of both capital and operating cost. In case 2, the lime softener and evaporator constitute more than

90% of the total operating cost and about 50% of the total capital cost. In case 4, the evaporator is

the major contributor to the total capital (about 70%) and operating cost (more than 90%) of the

water treatment system.

Cost savings associated with each treatment unit are also investigated here. The results

show that in cases 1 to 3 the lime softener accounts for more than 90% of both capital and operating

cost savings in the water treatment system. In case 4, the evaporator accounts for almost all the

savings in the capital and operating cost. This suggests that to minimize cost via process

modifications, it is better to start by improving the lime softening unit and the evaporator efficiency

rather than other treatment units. Detailed cost results for treatment units are shown in Appendix

B, Table B-5 to Table B-8.

In some cases negative values are reported for the cost savings in a treatment unit, e.g. ion

exchange in case 4 (Appendix B, Table B-8). This is due to the use of treatment units in the

optimized design that are not used in the current design. In other words, when a unit is not part of

the current treatment system design like the ion exchange unit in case 4, the cost of that unit is zero

in the current design. Then, if that unit is selected in the optimized design, it will result in a negative

value for savings for that specific unit (i.e., a cost). In case 4 the ion exchange unit is part of the

optimized design, because the use of the ion exchange unit can reduce the contaminant load on the

evaporator and therefore reduce its size. This consequently leads to a lower total cost.

According to the results of the cost analysis for the entire plant (presented in Appendix A),

the total cost of the whole SAGD process (water treatment, steam generation, steam injection,

waste disposal, etc.) is estimated to be between $11.9 and $14.4 per barrel of bitumen produced.

84

4.2.2 Energy consumption analysis

The energy consumption associated with cases 1 through 4 are presented here. It should be

noted that these are the same cases presented above (i.e., the optimization model is run using the

cost minimization objective function). Later in this chapter, the impacts of running the

optimization model to minimize energy consumption are explored.

Figure 4-12 shows the electricity consumption7 in the water treatment system for the four

cases in the current and optimized design broken down by treatment unit.

7 In SAGD operations, NG is used for steam generation in the boilers and is not used directly in the water treatment system. Electricity is therefore the only form of energy that is used in the treatment system and this can be generated using natural gas or purchased from the Alberta electricity grid.

85

Figure 4-12 Electricity consumed by the water treatment system for cases 1-4, brokendown by

treatment units

Electricity consumption in case 4 is one order of magnitude higher than the other 3 cases

because it uses evaporators which account for more than 95% of the total electricity consumed.

Case 2 uses evaporators as well, but the flow rate of the wastewater stream that is treated in the

evaporator in case 2 (OTSG blowdown) is about 4 times smaller than the flow rate of the

wastewater stream treated in the evaporator in case 4 (produced water is the water stream that is

treated in the evaporator in case 4). This means the evaporator in case 2 is approximately 4 time

smaller and consumes less electricity than the evaporator in case 4 (about one quarter of the

020406080

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Elec

tric

ity (1

E6 M

J/yr

)

Makeup Water

Evaporator

WAC

WLS

ORF

IGF

Skim Tank

86

electricity consumed in case 4). Evaporators account for about 80% of the total electricity use in

case 2. Lime softening, induced gas flotation and makeup water equipment are three major

sources of electricity consumption in cases 1 and 3.

Electricity savings potential (between the corresponding current and optimized cases) for

case 2 is lower than other cases and is about 1.5% of total electricity consumption. This is because

in case 2 there are no electricity consumption savings in the evaporator (because of the structure

of the treatment network in case 2 where stream bypassing the evaporator is not allowed) and this

unit accounts for more than 90% of total electricity consumption in this case. In other words, less

than 10% of the total amount of electricity consumption in case 2 is affected by the optimization

process which results in 1.5% savings in total electricity consumption.

In cases 1-3, the lime softening unit accounts for more than 90% of the savings in electricity

(which is between 1.5-12%). In case 4, the evaporator accounts for almost all the electricity

reduction (which is about 11%) in the system.

The results indicate that to reduce electricity consumption in the system, we should focus

on the lime softening and evaporation units (whichever is used in the treatment system), i.e.

improve their efficiencies. Electricity consumption for other treatment units is not significant.

Figure 4-12 shows the energy consumption (or the electricity consumption) in the water

treatment system of SAGD operations. The energy consumption in the steam generation section is

not included. In order to investigate the impacts of both steam generation technology and water

treatment system decisions, natural gas consumption in the boiler should be considered as well.

Figure 4-13 shows the electricity consumption in the treatment system plus the additional natural

gas consumed in the OTSG over and above what is consumed in the drum boiler. Additional

natural gas refers to the difference between the amount of natural gas consumed in the OTSG

87

(cases 1, 2 and 3) and the natural gas consumed in the drum boiler (case 4). The amount of natural

gas consumed per cubic meter of boiler feed water is a little higher for drum boilers than that for

OTSGs (based on the data we have). However, because for the same amount of required steam,

the drum boiler needs less boiler feed water (the drum boiler generates only 1-2% blowdown from

the boiler feed water while the OTSG generates about 20% blowdown), total natural gas

consumption for cases 1-3 that use OTSG is higher that case 4 that uses drum boiler. The reason

for presenting the difference between natural gas consumption in the two types of boiler instead

of presenting the total amount of natural gas consumption for each type of boiler is to show the

differences between the energy consumption in four cases in a more visually distinguishable

manner. It should be noted that since the optimization doesn’t affect the steam generation section

of the plant, natural gas consumed in the current and optimized designs of each case are equal.

Therefore, only the results of the optimized designs are shown in Figure 4-13.

88

Figure 4-13 Energy consumption SAGD operations for cases 1-4 (electricity consumed in water

treatment system and additional natural gas consumption in the OTSG above what is consumed

in the drum boiler)

Cases 1-3 all consume more natural gas than Case 4 because they all employ an OTSG.

However, when the total energy consumed is included (both additional natural gas and electricity),

the results of energy consumption are similar (only a 20% difference between the lowest and

highest energy consumption (cases 1 and 2) compared to the 92% difference between the lowest

and highest electricity consumption (cases 1 and 4) in Figure 4-12). However, Case 2 has the

highest total energy consumption among all four cases. Since the type of energy is different for

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Optimized DesignCase 1




Ener

gy C

onsu

mpt

ion

(1E6

MJ/

yr)

Additonal NG

Electricity

89

each case, the environmental implications of the different systems will be quite different. Detailed

results of energy consumption are presented in Appendix A, Table A-5 and Appendix B, Table B-

9 to Table B-12.

4.2.3 GHG emissions analysis

GHG emissions associated with the water treatment system (that come from the electricity

consumption in the water treatment system) are proportionally related to the electricity

consumption shown in Figure 4-12. GHG emissions from electricity are much higher for case 4

(3.5-13 time higher than cases 1, 2 and 3) due to the significant consumption of electricity in the

evaporator (8.5E07 kWh/year). However, if we also include the emissions associated with the

natural gas burned to compensate for the increased energy requirements of the OTSG (compared

with the drum boiler), the GHG emissions difference between cases narrows somewhat (for

example case 4 has 1.8-3.2 more GHG emissions than cases 1, 2 and 3 rather than 3.5-13 more

GHG emissions if only electricity is considered). GHG emissions from electricity and additional

natural gas consumption in the OTSG are shown in Figure 4-14.

90

Figure 4-14 GHG emissions from electricity and use of additional natural gas in the OTSG

According to Figure 4-14, case 4 still has the largest GHG emissions, even though the total

energy consumed in case 4 is lower than case 2 (energy consumption of cases 2 and 4 are 3.8E08

MJ/year and 3.2E08 MJ/year respectively. GHG emissions of case 2 and 4 are 3.6E04 tCO2/year

and 6.5E04 tCO2/year respectively). The reason is that natural gas has a lower GHG intensity (per

MJ) than electricity (the electricity emissions factor assumed in this analysis for Alberta’s

electricity grid is 0.75 tCO2 per MWh [102]), and since the majority of the energy used in case 2

is natural gas, total GHG emissions in this case is lower than case 4. The electricity emissions

factor is an important factor in determining the relative GHG emissions of cases 2 and 4. However,

the emissions intensity of electricity from Alberta grid varies greatly from year to year. It would

take a low carbon source of electricity (e.g., from renewable or nuclear), for the total emissions of

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91

case 4 to be lower than case 2 (the impact of different emissions intensities is further investigated

in the sensitivity analysis section). The results of GHG emissions are presented in Appendix A,

Table A-6 and Appendix B, Table B-13 and Table B-14.

Adding a cogeneration unit to SAGD facilities provides the opportunity to simultaneously

produce steam and electricity and help to reduce the GHG emissions produced in SAGD operations

[103]. I investigated the impacts of using a cogeneration system which produces required

electricity for the entire SAGD operations on total GHG emissions. Cogeneration could reduce

GHG emissions by 17-30% from electricity and natural gas consumption for the four cases

investigated in this study.

4.2.4 Makeup water consumption and disposal water analysis

Makeup water consumption and disposal water generation are fixed by the type of boiler

and disposal method selected and are not affected by the optimization. Therefore, for each case the

amount of makeup water and disposal water are equal for the current and optimized design. Figure

4-15 shows the amount of makeup water requirements and the amount of wastewater generated in

each case.

92

Figure 4-15 Makeup water consumption and disposal water generation for all cases

According to Figure 4-15, there is a direct relationship between the amount of disposal

water and the amount of required makeup water. The more disposal water generated, the more

makeup water required. Cases 2 and 4 have the lowest makeup water consumption and disposal

water generation because of the high level of water recovered in the evaporator. In the base case

for all 4 cases (for each case, the base case is the initial optimized case to which the results of

sensitivity analysis are compared later in this chapter), the cost of makeup water regardless of the

equipment used for its transportation is assumed to be zero. In the sensitivity analysis section, the

effect of makeup water price on the total cost of the treatment system is investigated. More detailed

estimates of makeup water consumption and disposal water generation are presented in Appendix

B, Table B-15.

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All results reported thus far assume that wastewater disposal undergoes deep well injection.

However, in cases 2 and 4, ZLD crystallizers are another option for the disposal that recovers more

water compared to deep well injection. If the ZLD system is used, the amount of makeup water

required would be lower than the values shown in Figure 4-15. On the other hand, cost, energy

and GHG emissions would also be higher than what is shown in Figure 4-9 to Figure 4-14. More

detailed analysis using the method developed in this thesis would likely provide additional insights

about the potential and tradeoffs associated with this technology.

4.2.5 Makeup water and GHG emissions tradeoffs

There is a tradeoff between makeup water consumption and GHG emissions in SAGD

water treatment and steam generation systems. Higher recycle ratios for the boiler blowdown leads

to lower makeup water requirements. On the other hand, higher recycle ratios result in higher

energy requirements to treat the recycled water which leads to higher GHG emissions. Figure 4-

16 and Figure 4-17 show the tradeoffs between the makeup water requirements and GHG

emissions (emissions from electricity and the additional natural gas used in the OTSG) for the four

cases in the optimized design.

94

Figure 4-16 Make up water consumption and GHG emissions (from electricity consumption in

water treatment system and additional natural gas consumption in OTSG) tradeoffs

Figure 4-17 GHG emissions (from electricity consumption in water treatment system and

additional natural gas consumption in OTSG) vs. make up water consumption

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95

Cases 1 and 3 have high makeup water requirements and low GHG emissions, while case

4 has low makeup water consumption and high GHG emissions. However, in case 2 both makeup

water consumption and GHG emissions are relatively low (although GHG emissions in case 2 are

higher than cases 1 and 3, they are still relatively low).

Figure 4-17 shows the water-emission tradeoffs even more clearly. As shown in this figure,

cases 1 and 3 are low in emissions and case 4 is low in water use and case 2 is in-between. We are

aiming towards the lower left quadrant of the figure. None of the options really fit in this quadrant

so the decision is really between cases 2 and 3 if these are the only two metrics that we care about.

Case 2 is recommended if makeup water is the priority whereas case 3 is recommended if GHG

emissions are your priority.

As shown in Figure 4-16 and Figure 4-17, the makeup water consumption in case 3 is

reduced by 25% compared to case 1 by recycling 30% of the OTSG blowdown to the treatment

system, and GHG emissions are only increased by 7%. The effect of the blowdown recycle ratio

on water consumption and GHG emissions is further investigated in the sensitivity analysis

section.

4.3 Energy minimization analysis for the treatment network

The model can also be run to minimize energy (instead of cost). The results of the energy

minimization runs show that the same amount of electricity is consumed regardless of which

objective function is selected. This means that the electricity savings achieved by cost optimization

is the maximum amount of savings that can be reached in the system using optimization techniques

and the current configuration of the model. Further electricity savings require process

modifications or switching to other water treatment processes.

96

Since the results of energy minimization are similar to the results of cost minimization (less

than 1% difference in the cost, energy consumption, GHG emissions, etc.), they are not presented

here.

4.4 Sensitivity analysis

There is a high degree of uncertainty in the data in this thesis (e.g., performance and

limitations of the treatment units, source of electricity, cost data, etc.). Therefore, a sensitivity

analysis is conducted to better understand the parameters that have the largest impact on estimates

of cost, energy and emissions for the different cases considered. The impacts of many parameters

have been investigated in the model and the most interesting results are presented here.

4.4.1 Hardness requirement in the boiler

The hardness requirement in the OTSG feed water is assumed to be 3 ppm in the base case

(for cases 1, 2 and 3), that is the most common value for hardness requirement in the OTSG

reported in the literature [8], [23]. In the sensitivity analysis, 1 ppm and 10 ppm are investigated

as hardness requirements in the boiler based on consultation with experts [94]. The results are

similar for all three cases (1, 2, and 3).

The current design doesn’t change by changing the hardness requirement in the boiler,

because in the current design all produced water passes through all of the treatment units regardless

of the performance of the treatment units and the concentration requirements in the boiler. The

results show that the hardness concentration required for the boiler feed water doesn’t have a

significant effect on the total cost of the water treatment system and the cost savings potential via

optimization. The total cost of the treatment system slightly reduces (less than 1%) as the hardness

97

concentration required in the boiler increases. According to the results, the small reduction in costs

is due to a reduction in chemical costs rather than the electricity and other costs. The reason is that

the ion exchange unit that is responsible for hardness removal, uses chemicals (Na2CO3, NaOH,

HCl) to remove the hardness and chemical costs are the most significant contributor (99% of the

total operating cost of the ion exchange unit) to the total operating cost of this treatment unit.

Therefore, when the hardness concentration requirement is lower or higher compared to the base

case, more or less flow needs to go through this treatment unit respectively which affects the

chemicals requirements and chemicals cost (by about 4%) and consequently the total operating

cost (by less than 1%). Similar results are obtained for the capital cost and the capital cost savings.

The effect of hardness requirements in the boiler on the electricity consumption and GHG

emissions are negligible (i.e., < 0.5%).

4.4.2 Silica requirement in the boiler

The required silica concentration in the OTSG is 50 ppm in the base case (the most common

value reported in the literature for silica requirement in the OTSG [8], [23]). In the sensitivity

analysis, 30 ppm and 70 ppm are tested based on consultation with experts (for cases 1, 2 and 3).

The total cost of the treatment system changed by about -4% to +5% for case 1, -5% to +7% for

case 2 and -3% to +6% for case 3 (the total cost decreases when the silica requirements increase

and the total cost increases when the silica requirements decreases). The changes in the cost

savings is due to the different flow rates of the inlet stream to the lime softening unit (the treatment

unit that removes silica from the wastewater).

98

Since the lime softening unit is more expensive than the ion exchange unit, changing the

silica requirements in the boiler has a greater effect on the cost of the treatment system than

changing the hardness requirements (in the previous section).

In all three cases 28 ppm is approximately the lowest silica concentration that can be

reached by the lime softener with the data used in the model. By lowering the silica requirement

beyond this point in the OTSG, the optimization model chooses the evaporator instead of the lime

softener. Therefore, 28 ppm can be considered the transition point for the silica concentration to

switch from the lime softener to the evaporator.

4.4.3 Capital cost of the treatment units

To study the effect of uncertain and variable capital costs of the treatment units on the

optimal design and the total cost of the water treatment system, for the capital cost of the treatment

units in the base case, multipliers are used that range from 0.5 to 1.5 (steps of 0.1: 0.5, 0.6, etc.).

This is because capital cost may be affected by the geographical location where the project is being

executed (due to different equipment prices in different regions and countries. For example, in

Alberta higher prices exist because of the high labor cost).The optimal design and the total cost of

the treatment system are obtained for each multiplier for all four cases.

The results show that applying a multiplier for the capital cost increases the total cost of

the treatment system linearly. Although the cost savings increases for the larger multipliers

(between 2-9% in each step), there is not a significant change in the percentage of cost savings

(about 2%). The results of the optimization show that the optimal design of the treatment system

(the treatment system configuration and flow rates) doesn’t change due to any multiplier

considered.

99

4.4.4 Boiler blowdown recycle ratio in case 3

In the base case of case 3, 30% of the boiler blowdown is recycled back to the treatment

system for further treatment and reuse in the boiler. The effect of changing the boiler blowdown

recycle ratio to 20% and 50% on the total cost of the treatment system and makeup water

consumption is investigated.

The recycling ratio also raises further tradeoffs between the cost/electricity use/GHG

emissions and water use. Makeup water requirements and disposal water generated for different

boiler blowdown recycle ratios are shown in Figure 4-18.

Figure 4-18 Effect of boiler blowdown recycle ratio on makeup water consumption and disposal

water generation in case 3

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Recycling 50% of boiler blowdown, reduces the need for makeup water (reductions on the

order of 10-22% below the cases where 30% is assumed). On the other hand, recycling more

blowdown requires more treatment which increases energy use, GHG emissions and cost. The total

optimal cost of the treatment system, electricity consumption and GHG emissions slightly increase

(1.6-3.5%) by increasing the boiler blowdown recycle ratio from 30 to 50%.

A sensitivity analysis was done on the makeup water cost. By comparing the 50% recycle

case to the base case (30% recycle), it is seen that by assigning a 2.3 ($/tonne of water) price to

the makeup water, the cost of the two cases will be the same. In other words, at costs below 2.3

$/tonnes of water, 50% recycle is more expensive than 30% recycle and at costs above 2.3 $/tonnes

of water, 50% recycle is cheaper than 30% recycle.

4.4.5 Makeup water price

The total cost of the water treatment system in case 3 is relatively low and the amount of

makeup water consumption is high. On the other hand, the total cost of the water treatment system

in case 4 is high and the makeup water consumption in this case is low (total cost of the water

treatment system in cases 3 and 4 are $1.1E07/year and $2.5E07/year respectively and makeup

water consumption in cases 3 and 4 are 112.5 tonne/hr and 59 tonne/hr respectively). Therefore, I

performed a sensitivity analysis on the cost of makeup water for these two cases.

The results of the sensitivity analysis show that if the price of makeup water was $30.5 per

tonne of water or $0.035 per litre of water, the total cost of the treatment system for these two

cases would be the same. In other words, at costs below $0.035 per litre of water, case 4 is more

expensive than case 3 and at costs above $0.035 per litre of water, case 3 is more expensive.

Generally, the average fresh water consumption in SAGD operations is approximately 0.5 barrels

101

of fresh water per barrel of oil produced [29]. The calculated price for the makeup water ($0.035

per litre of water) results in an additional cost of $1.47 per barrel oil produced.

Under some reservoir conditions, excess water is produced in the SAGD process that will

reduce the makeup water requirements and the total cost of the system. The model is capable of

incorporating this situation and the amount of excess water produced can be specified in the model

as an input variable.

4.4.6 Makeup water composition

The effect of changing the makeup water composition on the optimized design and total

cost of the water treatment system is investigated here. Makeup water required in the SAGD

operations can be from fresh or brackish (saline) water sources (brackish water has higher hardness

concentrations (about 10 times higher than fresh water). In the base case of all the four cases,

makeup water is assumed to be from a fresh water source. In the sensitivity analysis brackish water

is considered as the source of makeup water. The results show that the total cost increases by less

than 1% when brackish water is used. The cost increase is due to a 2-8% increase in the flow rate

of the inlet stream to the WAC unit which is responsible for hardness removal in the water

treatment system.

4.4.7 Inlet oil concentration limit for the oil removal filter

The effect of different inlet oil concentration limits for the oil removal filter has been

investigated. The results show that the optimal design doesn’t change by changing the inlet oil

limit of ORF and this parameter is not a significant parameter affecting the total cost of the water

treatment system (total cost of the water treatment system changes less than 1%).

102

4.4.8 Electricity emissions intensity

In the base case, the electricity emissions factor is assumed to be 0.75 tCO2/MWh for the

Alberta grid [102]. However, this value changes greatly from year to year. In addition, the future

Alberta electricity grid could employ very different generation types. A sensitivity analysis to

investigate the effect of the electricity emissions factor on the total GHG emissions (from

electricity and additional natural gas in the OTSG) over a range of 0-1 tCO2/MWh for the

electricity emissions factor is conducted (0 represents electricity production from renewable

sources that are close to 0 tCO2/MWh and 1 refers to electricity production from coal).

Figure 4-19 Effect of the electricity emissions factor on the total GHG emission (from electricity

consumption in water treatment system and additional natural gas in the OTSG)

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103

As shown in Figure 4-19, for lower values of electricity emissions factor, case 4 has lower

GHG emissions, but by increasing this value, the total GHG emissions of case 4 increases more

rapidly than the three other cases. The reason is the electricity consumption of case 4 is

significantly higher than other cases and total GHG emissions in this case is affected more

significantly by increasing the electricity emission factor. According to Figure 4-19, at emissions

factor of approximately 0.26 tCO2/MWh, the total emissions of case 4 is equal to case 2. Before

this point case 2 has higher emissions and after this point emissions in case 4 overtake case 2 which

means that when electricity is generated from clean sources of energy (e.g., renewable and nuclear

energy), case 4 has the lowest GHG emissions among all four cases, but with electricity generated

from emission intensive sources (e.g., coal, natural gas, etc.), case 4 has higher GHG emissions

than the other three cases.

4.4.9 Carbon tax

Environmental regulations are trying to push industries towards lower carbon emissions

[104]. A carbon tax which is usually defined as placing a fee on GHG emissions is one of the

solutions that can incentivize industries to reduce their emissions [105]. To investigate the impact

of a carbon tax on decision making about the water treatment technologies used in a SAGD water

treatment system, a sensitivity analysis is done to assess the effect of carbon price on the total cost

of a SAGD plant. In the base case, the carbon tax is considered to be zero. The sensitivity analysis

is done by increasing the carbon tax from $0 to $150/tonneCO2. The results are shown in Figure

4-20.

104

Figure 4-20 Effect of the carbon tax on the total cost of SAGD water treatment and steam

generation plant

Applying the carbon tax increases the operating cost and consequently the total cost of the

system for all cases but to different degrees. The increase in the operating cost and the total cost is

more significant when GHG emissions are higher. The results show the total cost of case 4 is

significantly increased (about 10% increase as opposed to 2-6% increase in cases 1, 2 and 3) by

applying the carbon price, because the GHG emissions for this case are higher than other cases.

In all cases the difference between the optimized and the current design cost increases after

applying the carbon tax on the GHG emissions. The reason is that the emissions in the current

design are slightly higher than the optimized design. Therefore, the total price paid for carbon is

higher for the current design than the optimized design. For example, GHG emissions in the

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105

optimized design of case 3 are 5.5E02 tCO2/year lower than the current design. Total cost of the

plant for current and optimized designs of case 3 are $8.7E07/year and $8.5E07/year respectively

with zero carbon tax and $9.0E07/year and $8.7E07/year with $150/tonneCO2 carbon tax. This

means that the cost difference of the plant between the current and optimized designs has increased

by 4% when the carbon tax is $150/tonneCO2 compared to zero carbon tax.

106

Chapter Five: Conclusions and Recommendations

5.1 Summary of results and principal insights

This study shows that process integration techniques can demonstrate potential cost and

energy savings in the water treatment system of SAGD operations. Results of the study show up

to 19.5% cost savings (for water treatment system cost in case 1) and up to 12% electricity savings

(for electricity consumption in water treatment system in case 1) only by diverting flows in

wastewater streams. According to the results, lime softening and evaporator units have the most

significant contribution to the cost and energy savings.

In this study the effect of using treatment alternatives in the SAGD water treatment system

is also investigated by considering four different cases for water treatment and steam generation

system in SAGD operations. According to the results, from a cost perspective, cases 1 and 3 (with

no evaporator) are the most attractive cases. Case 4 (produced water evaporation) is the most

expensive case and case 2 (blowdown evaporation) lies in-between. From an energy consumption

and GHG emissions perspective, again cases 1 and 3 are the best cases with the lowest energy

consumption and GHG emissions. Although case 4 consumed the most electricity, total energy

consumption (electricity and natural gas in boiler) of case 2 is about 18% higher than the total

energy consumption of case 4. However, total GHG emissions from case 4 is higher than case 2

because of the significant share of electricity in total energy consumption (electricity emission

factor is calculated from Alberta’s electricity grid and is much higher than that of natural gas).

From a water consumption perspective, case 2 is the most favourable case having the lowest water

consumption. Cases 1 and 3 have the highest water consumption and case 4 lies in-between.

107

There are tradeoffs between cost, energy, emissions and water. Choosing the best case

depends on how water, energy and GHG emissions are valued. For example, when the price of

makeup water is zero, case 2 is more expensive than cases 1 and 3, but if the makeup water price

is greater than 0.7 ¢/litre, case 2 becomes cheaper than cases 1 and 3. Also, total GHG emissions

of case 2 are higher than cases 1 and 3 in the base case (where electricity emission factor is

calculated for Alberta’s electricity grid- 0.75 tCO2/MWh electricity), but when lower carbon

sources of electricity are used, the difference between the total emissions of case 2 and cases 1 and

3 is very small and for zero carbon electricity, the total emissions of cases 1, 2 and 3 are the same.

That is to say, the choice of the best configuration for the water treatment system of SAGD

operations depends on several factors such as makeup water price, carbon intensity of the

electricity, etc. It also depends on the importance placed on minimizing water, GHG emissions

and cost for decision makers, based on which the suitableness of an option can be determined, and

there is no single treatment configuration that consistently gives the best results.

Currently, water is highly undervalued and oil sands producers pay negligible prices for

withdrawing water for extraction purposes. Placing a price on water could move the SAGD

projects towards less water intensive options (e.g., use of evaporators). However, in several cases

the price would have to be potentially prohibitively high (e.g., $1.47/bbl of oil produced) in order

to see a change in investment decision towards a less water intensive option. In addition, the use

of technologies such as evaporators come with important tradeoffs between cost, water, and GHG

emissions. In the face of these tradeoffs, a range of policy alternatives (e.g., price on water,

withdrawal and disposal requirements) should be explored to find the best balance between cost,

energy, GHG emissions and water.

108

5.2 Future work

There are several options to expand the current study into a more comprehensive work. For

instance, this work can be blended with energy integration studies and expanded to a simultaneous

water and energy minimization model using process integration tools. Linear cost functions are

assumed in this study, but the model is capable of using nonlinear cost functions as well. Nonlinear

cost functions may better represent the costs of some of the treatment units, and improve the

accuracy of the results of the study. Additionally, although piping costs and the distances between

the treatment units are not considered in this study (required data were not available), if the data

related to piping costs and distances between the treatment units are available, they can be

incorporated in the model to improve the accuracy of the results.

There are many treatment processes (membranes, hydrocyclones, etc.) that can be used for

water treatment in SAGD facilities and have not yet been investigated. These treatment processes

need to be further investigated by oil sands producers to determine their suitability for use in the

SAGD operations. The proposed model in this study can help investigate new water treatment

technologies and find the tradeoffs between water, energy, emissions and cost associated with

various groups of technologies and help the oil sands operators gain a better understanding of the

advantages and disadvantages of their possible choices.

5.3 Recommendations

The framework developed in this study can help oil sands operators make informed

decisions about which water treatment technologies to choose for SAGD operations. For example,

if cost is the most determinative factor, conventional treatment technologies, lime softening and

ion exchange, are better choices compared to evaporators. But if reducing water consumption is

109

the most important factor in the decision making process, the use of evaporators would be a better

option to reduce water consumption and disposal. If reducing GHG emissions is more important

than cost and water consumption, each of four different cases could be the best choice depending

on the electricity emission factor, and conducting sensitivity analysis can help the operators find

the best option in various circumstances.

110

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121

APPENDIX A: COST, ENERGY AND GHG EMISSIONS ESTIMATES FOR THE SAGD

PLANT

Figure A-1 Annual cost of the SAGD plant for cases 1-4, with operating cost breakdown

0

10

20

30

40

50

60

70

80

90

100

110


Annu

al c

ost (

$1E6

/yr)

Natural Gas Cost

Chemicals Cost

Electricity Cost

Other Costs

Capital Cost

Operating Cost

122

Table A-1 Capital, operating and total cost of the SAGD plant for current and optimized designs for the four cases (all costs are in $/year)


Current Design

Capital Cost 2.49E+07 2.53E+07 2.47E+07 3.28E+07

Operating Cost 6.11E+07 6.33E+07 6.10E+07 6.87E+07

Total Cost 8.60E+07 8.86E+07 8.56E+07 1.02E+08

Optimized Design



Total Cost 8.35E+07 8.74E+07 8.36E+07 9.90E+07

Table A-2 Capital, operating and total cost savings for the SAGD plant by optimization for the four cases (all costs are in $/year)


Total Cost Total Cost Difference 2.53E+06 1.18E+06 2.04E+06 2.49E+06

Total Cost Savings 2.95% 1.33% 2.38% 2.46%

Capital Cost

Capital Cost Difference 9.46E+05 4.99E+05 7.30E+05 8.28E+05

Capital Cost Savings 3.79% 1.97% 2.96% 2.53%

Contribution to total savings 37.30% 42.41% 35.76% 33.23%

Operating Cost

Operating Cost Difference 1.59E+06 6.78E+05 1.31E+06 1.66E+06

Operating Cost Savings 2.60% 1.07% 2.15% 2.42%


123

Table A-3 Operating cost of the SAGD plant, broken down into electricity, chemicals and other costs for the four cases (all costs are in $/year)


Current Design

Electricity Cost 4.75E+06 6.56E+06 4.64E+06 1.34E+07

Chemicals Cost 3.58E+06 3.61E+06 3.57E+06 2.92E+06

Other Costs 3.20E+06 3.53E+06 3.20E+06 4.25E+06

Optimized Design



Other Costs 2.46E+06 3.24E+06 2.59E+06 3.88E+06

Table A-4 Electricity, chemicals and other costs savings for the SAGD plant by optimization for the four cases (all costs are in $/year)


Electricity

Electricity Cost Difference 9.99E+04 4.22E+04 7.56E+04 1.05E+06

Electricity Cost Savings 2.10% 0.64% 1.63% 7.84%

Contribution in total savings 6.28% 6.23% 5.76% 63.05%

Chemicals

Chemicals Cost Difference 7.53E+05 3.39E+05 6.26E+05 2.40E+05

Chemicals Cost Savings 21.04% 9.41% 17.55% 8.22%


Other Costs

Other Costs Difference 7.37E+05 2.96E+05 6.09E+05 3.75E+05

Other Costs Savings 23.05% 8.39% 19.06% 8.82%


124

Figure A-2 Annual cost of the SAGD plant for cases 1-4, with capital and operating cost broken down by treatment unit, steam generation and disposal sections (CC=Capital cost- solid fill,

OC=Operating cost- hashed fill)

0

10

20

30

40

50

60

70

80

90

100

110


Annu

al c

ost (

$1E6

/yr)

Disposasl

Boiler

Makeup Water

Evaporator

WAC

WLS

ORF

IGF

Skim Tank

CC

OC

125

Figure A-3 Energy consumed by the SAGD plant for cases 1-4, brokendown by electricity and natural gas

Table A-5 Electricity and natural gas consumption of the SAGD plant for the four cases (MJ/year)


Current Design Natural gas 9.91E+09 9.91E+09 9.91E+09 9.64E+09

Electricity 1.71E+08 2.36E+08 1.67E+08 4.82E+08

Optimized Design Natural gas 9.91E+09 9.91E+09 9.91E+09 9.64E+09

Electricity 1.68E+08 2.35E+08 1.64E+08 4.44E+08

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000


Ener

gy C

onsu

mpt

ion

(1E6

MJ/

yr)

Electricity

Natural Gas

126

Figure A-4 GHG emissions of the SAGD plant from electricity and natural gas

Table A-6 GHG emissions from electricity and natural gas consumption of the SAGD plant for the four cases (tCO2/year)


Current Design GHG emissions- Natural gas 5.61E+05 5.61E+05 5.61E+05 5.46E+05

GHG emissions- Electricity 3.47E+04 4.79E+04 3.39E+04 9.78E+04

Optimized Design GHG emissions- Natural gas 5.61E+05 5.61E+05 5.61E+05 5.46E+05

GHG emissions- Electricity 3.40E+04 4.76E+04 3.33E+04 9.01E+04

050

100150200250300350400450500550600650


GHG

Emiss

ions

(1E3

tCO

2/yr

)

GHG Emissions-Electricity

GHG Emissions-Natural Gas

127

APPENDIX B: DETAILED COST, ENERGY AND GHG EMISSIONS RESULTS

ESTIMATES FOR THE WATER TREATMENT SYSTEM

Table B-1 Capital, operating and total cost of the water treatment system for current and optimized designs for the four cases (all costs are in $/year)


Current Design



Total Cost 1.30E+07 1.65E+07 1.29E+07 2.72E+07

Optimized Design



Total Cost 1.05E+07 1.53E+07 1.09E+07 2.47E+07

Table B-2 Capital, operating and total cost savings for the water treatment system by optimization for the four cases (all costs are in $/year)


Total cost Total Cost Difference 2.53E+06 1.18E+06 2.04E+06 2.49E+06

Total Cost Savings 19.47% 7.13% 15.79% 9.18%

Capital Cost

Capital Cost Difference 9.46E+05 4.99E+05 7.30E+05 8.28E+05

Capital Cost Savings 13.40% 6.15% 10.42% 7.25%


Operating Cost

Operating Cost Difference 1.59E+06 6.78E+05 1.31E+06 1.66E+06

Operating Cost Savings 26.64% 8.09% 22.15% 10.58%


128

Table B-3 Operating cost of the water treatment system, broken down into electricity, chemicals and other costs for the four cases (all costs are in $/year)


Current Design



Other Costs 2.43E+06 2.77E+06 2.43E+06 3.41E+06

Optimized Design



Other Costs 1.70E+06 2.47E+06 1.82E+06 3.03E+06

Table B-4 Electricity, chemicals and other costs savings for the water treatment system by optimization for the four cases (all costs are in $/year)


Electricity

Electricity Cost Difference 9.99E+04 4.22E+04 7.56E+04 1.05E+06

Electricity Cost Savings 12.71% 1.50% 10.20% 10.61%


Chemicals

Chemicals Cost Difference 7.53E+05 3.39E+05 6.26E+05 2.40E+05

Chemicals Cost Savings 27.40% 12.14% 22.81% 9.83%


Other Costs

Other Costs Difference 7.37E+05 2.96E+05 6.09E+05 3.75E+05

Other Costs Savings 30.29% 10.70% 25.04% 11.01%


129

Table B-5 Operating cost of the water treatment system, broken down by treatment units for the four cases (all costs are in $/year)


Current Design

Skim Tank 5.19E+04 5.19E+04 5.19E+04 5.19E+04

IGF 2.29E+05 2.29E+05 2.29E+05 2.29E+05

ORF 0.00E+00 0.00E+00 0.00E+00 0.00E+00

WLS 5.19E+06 4.21E+06 5.19E+06 0.00E+00

WAC 3.09E+05 2.50E+05 3.09E+05 0.00E+00

Evaporator 0.00E+00 3.60E+06 0.00E+00 1.54E+07

Makeup Water 1.81E+05 3.77E+04 1.36E+05 7.09E+04

Optimized Design

Skim Tank 5.19E+04 5.19E+04 5.19E+04 5.19E+04

IGF 2.27E+05 2.27E+05 2.34E+05 2.29E+05

ORF 0.00E+00 0.00E+00 0.00E+00 0.00E+00

WLS 3.62E+06 3.57E+06 3.89E+06 0.00E+00

WAC 2.95E+05 2.08E+05 2.93E+05 2.90E+04

Evaporator 0.00E+00 3.60E+06 0.00E+00 1.37E+07


130

Table B-6 Operating cost savings for the water treatment system, broken down by treatment units for the four cases (all costs are in $/year)


Skim Tank

Skim Tank Cost Difference 0.00E+00 0.00E+00 0.00E+00 0.00E+00

Skim Tank Cost Savings 0.00% 0.00% 0.00% 0.00%

Contribution to Total Operating Cost Savings 0.00% 0.00% 0.00% 0.00%

IGF

IGF Cost Difference 2.73E+03 2.81E+03 -4.78E+03 0.00E+00

IGF Cost Savings 1.19% 1.23% -2.09% 0.00%

Contribution to Total Operating Cost Savings 0.17% 0.41% -0.36% 0.00%

ORF

ORF Cost Difference 0.00E+00 0.00E+00 0.00E+00 0.00E+00

ORF Cost Savings - - - -


WLS

WLS Cost Difference 1.57E+06 6.33E+05 1.30E+06 0.00E+00

WLS Cost Savings 30.29% 15.04% 25.04% -


WAC

WAC Cost Difference 1.35E+04 4.25E+04 1.56E+04 -2.90E+04

WAC Cost Savings 4.36% 16.98% 5.04% -

Contribution to Total Operating Cost Savings 0.85% 6.26% 1.19% -1.74%

Evaporator

Evaporator Cost Difference 0.00E+00 0.00E+00 0.00E+00 1.69E+06

Evaporator Cost Savings - 0.00% - 11.01%


Makeup Water

Makeup Water Cost Difference 0.00E+00 0.00E+00 0.00E+00 0.00E+00

Makeup Water Cost Savings 0.00% 0.00% 0.00% 0.00%


131

Table B-7 Capital cost of the water treatment system, broken down by treatment units for the four cases (all costs are in $/year)


Current Design

Skim Tank 1.42E+06 1.42E+06 1.42E+06 1.42E+06

IGF 9.18E+05 9.18E+05 9.18E+05 9.18E+05

ORF 5.93E+05 5.93E+05 5.93E+05 5.93E+05

WLS 2.88E+06 2.33E+06 2.88E+06 0.00E+00

WAC 9.69E+05 7.85E+05 9.69E+05 0.00E+00

Evaporator 0.00E+00 1.95E+06 0.00E+00 8.33E+06


Optimized Design

Skim Tank 1.42E+06 1.42E+06 1.42E+06 1.42E+06

IGF 9.07E+05 9.06E+05 9.37E+05 9.18E+05

ORF 5.72E+05 5.88E+05 6.13E+05 5.90E+05

WLS 2.01E+06 1.98E+06 2.16E+06 0.00E+00

WAC 9.26E+05 6.51E+05 9.20E+05 9.11E+04

Evaporator 0.00E+00 1.95E+06 0.00E+00 7.41E+06


132

Table B-8 Capital cost savings for the water treatment system, broken down by treatment unit for the four cases (all costs are in $/year)


Skim Tank

Skim Tank Cost Difference 0.00E+00 0.00E+00 0.00E+00 0.00E+00

Skim Tank Cost Savings 0.00% 0.00% 0.00% 0.00%

Contribution to Total Capital Cost Savings 0.00% 0.00% 0.00% 0.00%

IGF

IGF Cost Difference 1.09E+04 1.12E+04 -1.91E+04 0.00E+00

IGF Cost Savings 1.19% 1.23% -2.09% 0.00%

Contribution to Total Capital Cost Savings 1.16% 2.25% -2.62% 0.00%

ORF

ORF Cost Difference 2.08E+04 4.33E+03 -2.03E+04 2.84E+03

ORF Cost Savings 3.51% 0.73% -3.42% 0.48%

Contribution to Total Capital Cost Savings 2.20% 0.87% -2.78% 0.34%

WLS

WLS Cost Difference 8.72E+05 3.51E+05 7.21E+05 0.00E+00

WLS Cost Savings 30.29% 15.04% 25.04% -


WAC

WAC Cost Difference 4.22E+04 1.33E+05 4.88E+04 -9.11E+04

WAC Cost Savings 4.36% 16.98% 5.04% -

Contribution to Total Capital Cost Savings 4.47% 26.68% 6.69% -10.99%

Evaporator

Evaporator Cost Difference 0.00E+00 0.00E+00 0.00E+00 9.17E+05

Evaporator Cost Savings - 0.00% - 11.01%


Makeup Water

Makeup Water Cost Difference 0.00E+00 0.00E+00 0.00E+00 0.00E+00

Makeup Water Cost Savings 0.00% 0.00% 0.00% 0.00%


133

Table B-9 Electricity consumption of the water treatment system for current and optimized designs for the four cases (MJ/year)


Current Design 2.83E+07 1.01E+08 2.67E+07 3.56E+08

Optimized Design 2.47E+07 9.98E+07 2.39E+07 3.18E+08

Table B-10 Electricity savings of the water treatment system by optimization for the four cases (MJ/year)


Electricity Difference 3.59E+06 1.52E+06 2.72E+06 3.78E+07

Electricity Savings 12.71% 1.50% 10.20% 10.61%

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Table B-11 Electricity consumption of the water treatment system for current and optimized designs, broken down by treatment units for the four cases (MJ/year)


Current Design

Skim Tank 1.87E+06 1.87E+06 1.87E+06 1.87E+06

IGF 8.26E+06 8.26E+06 8.26E+06 8.26E+06

ORF 0.00E+00 0.00E+00 0.00E+00 0.00E+00

WLS 1.15E+07 9.34E+06 1.15E+07 0.00E+00

WAC 1.13E+05 9.19E+04 1.13E+05 0.00E+00

Evaporator 0.00E+00 8.04E+07 0.00E+00 3.43E+08


Optimized Design

Skim Tank 1.87E+06 1.87E+06 1.87E+06 1.87E+06

IGF 8.16E+06 8.16E+06 8.43E+06 8.26E+06

ORF 0.00E+00 0.00E+00 0.00E+00 0.00E+00

WLS 8.04E+06 7.93E+06 8.64E+06 0.00E+00

WAC 1.08E+05 7.63E+04 1.08E+05 1.07E+04

Evaporator 0.00E+00 8.04E+07 0.00E+00 3.06E+08


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Table B-12 Electricity savings of the water treatment system, broken down by treatment units for the four cases (MJ/year)


Skim Tank

Skim Tank Electricity Consumption Difference 0.00E+00 0.00E+00 0.00E+00 0.00E+00

Skim Tank Electricity Savings 0.00% 0.00% 0.00% 0.00%

Contribution to Total Electricity Savings 0.00% 0.00% 0.00% 0.00%

IGF

IGF Electricity Consumption Difference 9.84E+04 1.01E+05 -1.72E+05 0.00E+00

IGF Electricity Savings 1.19% 1.23% -2.09% 0.00%

Contribution to Total Electricity Savings 2.74% 6.66% -6.33% 0.00%

ORF

ORF Electricity Consumption Difference 0.00E+00 0.00E+00 0.00E+00 0.00E+00

ORF Electricity Savings - - - -


WLS

WLS Electricity Consumption Difference 3.49E+06 1.40E+06 2.89E+06 0.00E+00

WLS Electricity Savings 30.29% 15.04% 25.04% -


WAC

WAC Electricity Consumption Difference 4.94E+03 1.56E+04 5.71E+03 -1.07E+04

WAC Electricity Savings 4.36% 16.98% 5.04% -

Contribution to Total Electricity Savings 0.14% 1.03% 0.21% -0.03%

Evaporator

Evaporator Electricity Consumption Difference 0.00E+00 0.00E+00 0.00E+00 3.78E+07

Evaporator Electricity Savings - 0.00% - 11.01%


Makeup Water

Makeup Water Electricity Consumption Difference 0.00E+00 0.00E+00 0.00E+00 0.00E+00

Makeup Water Electricity Savings 0.00% 0.00% 0.00% 0.00%


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Table B-13 GHG emissions from electricity consumption of the water treatment system for the four cases (tCO2/year)


Current Design 5.74E+03 2.06E+04 5.41E+03 7.22E+04

Optimized Design 5.01E+03 2.02E+04 4.86E+03 6.46E+04

Table B-14 GHG emissions reduction in the water treatment system by optimization for the four cases (tCO2/year)


GHG Emissions Difference 7.29E+02 3.09E+02 5.52E+02 7.67E+03

GHG Emissions Reduction 12.71% 1.50% 10.20% 10.61%

Table B-15 Makeup water consumption and disposal water generation in SAGD operations for the four cases (tonne/hr)


Makeup Water Consumed 150 31.25 112.5 58.75

Disposal Water Generated 125 6.227 87.5 33.95

137