A Dissertation Entitled Membrane Process Design for Post

Home , Partial pressure

A Dissertation

entitled

Membrane Process Design for Post-Combustion Carbon Dioxide Capture

Norfamila Che Mat

Submitted to the Graduate Faculty as partial fulfillment of the requirements for the

Doctor of Philosophy Degree in

Chemical Engineering

______Dr. Glenn Lipscomb, Committee Chair

______Dr. Maria Coleman, Committee Member

______Dr. Yakov Lapitsky, Committee Member

______Dr. Constance Schall, Committee Member

______Dr. Matthew Franchetti, Committee Member

______

Dr. Amanda Bryant-Friedrich, Dean College of Graduate Studies

The University of Toledo December 2016

Membrane Process Design for Post-Combustion Carbon Dioxide Capture

Norfamila Che Mat

Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Doctor of Philosophy Degree in Chemical Engineering

The University of Toledo

December 2016

Concerns over the effects of anthropogenic carbon dioxide (CO2) emissions from fossil-fuel electric power plants has led to significant efforts in the development of processes for CO2 capture from flue gas. Options under consideration include absorption, adsorption, membrane, and hybrid processes.

The US Department of Energy (DOE) has set goals of 90% CO2 capture at 95% purity followed by compression to 140 bar for transport and storage. Ideally, the

Levelized Cost of Electricity (LCOE) would increase by no more than 35%.

Because of the relatively low CO2 concentration in post-combustion flue gas, most of the reported process configurations for membrane systems have sought to generate affordable CO2 partial pressure driving forces for permeation. Membrane

Technology and Research, Inc. (MTR) proposed the use of an air feed sweep system to increase the CO2 concentration in flue gas. This process utilizes a two-stage membrane process in which the feed air to the furnace sweeps the flue gas in the second stage to

iii

reduce the flow of CO2 in the effluent to 10% of that leaving the furnace. Such a design significantly reduces capture costs but leads to a detrimental reduction in the oxygen concentration of the feed air to the boiler.

In this dissertation, the economic viability of combined cryogenic-membrane separation is evaluated. The work incorporates the tradeoff between CO2/N2 selectivity and CO2 permeability that exists when considering the broad range of potential membrane materials.

Of particular interest is the use of lower selectivity, higher permeability materials such as polydimethylsiloxane (PDMS). Additional enriching stages are required in a membrane-cryogenic air feed sweep configuration to enable use of these materials and achieve the 90% CO2 recovery and 95% purity targets. The higher CO2 permeance of

PDMS significantly reduces the total module membrane area requirement and associated capital cost (CAPEX). However, the lower selectivity increases the parasitic plant load required to produce the desired CO2 purity due the need for an additional membrane stage and the associated recycle loops; this increases operating cost (OPEX).

Multistage membrane-cryogenic air feed sweep configurations are optimized using the Robeson upper bound relation to relate membrane permeability to selectivity.

Membrane selectivity is varied over a broad range encompassing the values considered by MTR. Permeability is varied with selectivity according to the variation anticipated by the upper bound of the Robeson plot for CO2 and N2. Membrane permeance is calculated assuming membranes can be fabricated with an effective thickness of 0.1 micron.

Additionally, the two stages may utilize different membrane materials. The feed and

permeate pressures also are varied over ranges encompassing the values proposed by

MTR.

The optimization space of membrane properties and operating conditions is scanned globally to determine the process design that minimizes LCOE. The oxygen concentration to the boiler is evaluated during the optimization process and can be used to constrain viable alternatives. The results indicate a fairly broad range of membrane properties can yield comparable LCOE near the minimum. The optimal operating pressure range is somewhat narrower. The minimum allowable oxygen concentration can constrain viable designs significantly and is critical to process economics.

Membrane separation system shows a rapid response as the incoming flow flue gas flow rate changes due to the small time constant value. High pressure ratio and low CO2/N2 shows the fastest response due to the smaller residence time.

Considering the fixed membrane area, compressor and vacuum power, step changes of incoming flue gas flow rate results in the variation effect of feed compression pressure and also vacuum permeate pressure. This leads to selectivity dependent changes in permeate flow that affect CO2 recovery.

Acknowledgements

I would like to extend my sincerest thanks and appreciation my advisor Dr. Glenn

Lipscomb for his support, patience, guidance and mentorship over the past 4 years. Thank you for instilling in me an interest in this area; and always challenging me to think in ways I had never imagined possible. Special thanks to Dr. Coleman, Dr. Lapitsky, Dr.

Schall and Dr. Franchetti for agreeing to serve on my dissertation committee.

My heartfelt thanks to my parents, family and partner(s) in crime for the never ending support, prayers and encouragement throughout my studies. Thank you for all the joy and laughter that has helped me a lot throughout tough times.

Last but not least, financial support from Ministry of Higher Education Malaysia

(PhD Fellowship) and University Malaysia Sarawak (study leave) is gratefully acknowledged.

Table of Contents

Abstract ...... iii

Acknowledgements ...... vi

Table of Contents ...... vii

List of Figures ...... xii

List of Tables ...... xviii

List of Abbreviations ...... xix

List of Symbols ...... xxi

1. Introduction ...... 1

1.1 Membrane Separation Processes for Post-Combustion ...... 1

1.2 Membrane Air Feed Sweep Configurations ...... 3

1.3 Research Objectives ...... 7

1.4 Research Significance ...... 9

1.5 Structure of Dissertation ...... 12

2. Literature Review ...... 15

2.1 CO2 Emissions from Electricity Power Generation Sources ...... 15

2.2 CO2 Emissions Mitigations Options from Electricity Power Generation ...... 17

2.3 Carbon Capture and Storage (CCS) ...... 17

2.3.1 Pre-Combustion ...... 18 vii

2.3.2 Oxyfuel Combustions ...... 18

2.3.3 Post-Combustion ...... 18

2.4 Carbon Capture and Storage (CCS) Economic Evaluations ...... 19

2.4.1 Levelized Cost of Electricity (LCOE) ...... 20

2.4.2 Cost of CO2 Avoided ...... 22

2.4.3 Cost of CO2 Captured ...... 23

2.5 Membrane Process Design for Post-Combustions Applications ...... 23

2.5.1 Hollow Fiber Membrane Module ...... 23

2.5.2 Gas Permeation Model ...... 24

2.5.3 Single-Stage Membrane Design Configuration Feasibility Studies for Post-Combustion

Applications ...... 29

2.5.4 Affordable CO2 Driving Force Generation Strategies in Membrane Processes for Post-

Combustions Applications ...... 33

2.6 Optimization for Membrane Post-Combustion Application ...... 37

2.6.1 Gradient Based Optimization Method in Membrane Separations ...... 39

2.6.2 Non-Gradient Based Optimization Method in Membrane Separations (Stochastic

Algorithm) ...... 41

3. Modelling Multicomponent Hollow Fiber Membrane Gas Separation Modules and Study of Single Stage Membrane Processes for Post-Combustion CO2 Capture...... 43

3.1 Introduction ...... 43

viii

3.2 Cross-Flow Solution Strategies for Isothermal Operation and Constant Permeance ...... 45

3.3 Counter-Current Solution Strategies for Isothermal Operation and Constant Permeance ... 47

3.4 Counter-Current Configuration Solution Strategies for Non-Isothermal Conditions and

Temperature Dependent Permeance ...... 51

3.5 Multicomponent Gas Membrane Permeator Isothermal Model Validations ...... 56

3.6 Multicomponent Gas Membrane Permeator at Non-Isothermal Conditions ...... 57

3.7 Parametric Study for Single Stage Membrane CO2 Enrichment Stage for Post-Combustion

Application ...... 59

3.8 Area and CO2/N2 Variation Study at Fixed Feed and Permeate Pressure for Single Stage

Membrane CO2 Enrichment Process...... 61

3.9 Pressure Ratio and CO2/N2 Variation Study at Fixed Membrane Area for Single Stage

Membrane as CO2 Enrichment Step...... 63

3.10 CO2 Mole Fraction Feed and CO2/N2 Variation Study at Fixed Membrane Area for Single

Stage Membrane as CO2 Enrichment Step...... 65

3.11 Conclusions ...... 66

4. Staged Membrane Configurations for Post-Combustion CO2 Capture ...... 68

4.1 Introduction ...... 68

4.2 Process Descriptions and Economic Evaluations ...... 69

4.3 Boiler CO2 Recycle Loop Configuration ...... 73

4.4 Post-Boiler CO2 Recycle Loop Configuration ...... 76

4.5 Stage Cut Impact Variation Impact for Air Feed Sweep System Configuration ...... 77

4.6 Stage Cut Impact Variation of Air Feed Sweep System Configuration Towards LCOE .... 80

4.7 Stage Cut Impact Variation Impact for Post-Boiler CO2 Recycle Loop Configuration ...... 83

4.8 Stage Cut Impact Variation of Post-Boiler CO2 Recycle Loop Configuration Towards LCOE

...... 86

4.9 Process Facilities Cost (PFC), Variable Operating and Maintenance Cost (VOM) and LCOE

Breakdown ...... 88

4.10 Conclusions ...... 91

5. Membrane Process Optimization for Carbon Capture ...... 94

5.1 Introduction ...... 94

5.2 Methodology ...... 96

5.3 Impact of Enriching and Stripping Module Area Variation at Constant Feed and Permeate

Pressure ...... 101

5.4 Impact of Enriching and Stripping Module Area Variation for Various Feed and Permeate

Pressures ...... 105

5.5 Influence of Feed and Permeate Pressure Variation at Fixed Selectivity And Boiler O2 Mole

Faction on LCOE ...... 108

5.6 Influence of Feed Pressure, Permeate Pressure, and CO2/N2 Selectivity on LCOE for Fixed

Boiler O2 Mole Faction ...... 112

5.7 Conclusions ...... 115

6. Dynamic Simulations of Membrane Separation for Post-Combustion Applications ...... 118

6.1 Introduction ...... 118

6.2 Multi-Component Membrane Dynamic Simulations for Isothermal Operation and Constant

Permeance ...... 119

6.3 Linearization of Non-Linear Multicomponent Membrane Permeator Models...... 122

6.4 Dynamic Simulations of CO2 Capture from Flue Gas ...... 124 x

6.5 Dynamic Process Descriptions ...... 125

6.6 Feed and Permeate Pressure Changes Resulting from a Step Change in Flue Gas Flow Rate

...... 126

6.7 Composition and Flow Changes Resulting from a Step Change in Flue Gas Flow Rate .. 132

6.8 Conclusions ...... 144

7. Conclusions and Future Work ...... 145

7.1 Conclusions ...... 145

7.2 Future work ...... 148

References ...... 150

Appendices ...... 161

A.Net Permeation Directions for Each Gas Component in Membrane Module According

to Component Permeability...... 161

B. Example on LCOE Calculations (Membrane with CO2/N2 Selectivity of 75 with CO2

Permeance of 1180 GPU) ...... 162

C. Simplified Flow Diagram and Stream Table for MTR Air Feed System (Membrane with

CO2/N2 Selectivity of 75 with CO2 Permeance of 1180 GPU ...... 162

List of Figures

[3] Figure 1-1: Robeson plot of selectivity versus permeability for the CO2/N2 gas pair ...... 2

Figure 1-2: Air feed sweep configuration proposed by MTR [4]...... 5

Figure 2- 1 Sources of USA electricity generation in 2015 [15]...... 16

Figure 2-2: Cut–away view of a typical hollow fiber membrane module with a lumen feed and shell sweep operating in counter-current contacting mode [24]...... 24

Figure 2-3: Enrichment air multistage membrane cryogenic configurations proposed by Scholes et al. [9] ...... 37

Figure 3-1 Cross- flow module configurations divided into N stages...... 46

Figure 3-2: Counter-current module configurations divided into N stages...... 47

Figure 3-3: Solution procedure for counter-current configurations at isothermal conditions...... 50

Figure 3- 4 Temperature and enthalpy variation for stage j...... 52

Figure 3-5:Solution procedure for non-isothermal counter-current flow configurations ...... 55

Figure 3-6: Model validation with Pan [29] work. The lines represent model simulation result while all the markers represent the experimental data from Pan. Feed pressure is 35.28 bar with the permeate pressure of 0.93 bar Feed composition is 48.5% CO2, 27.9 CH4, 16.26% C2H6 and

7.34% C3H8. Gas permeances (GPU) are: 40.05 CO2, 1.11 CH4, 0.31 C2H6 and 0.06 C2H8 ...... 57

Figure 3-7 Model validation with Coker work [36]. Feed binary composition comprised of 40%

CO2 and 60% CH4.Multicomponent mixture comprised of 40.00% CO2, 55.89% CH4, 1.72%

C2H6 and 0.65% C3H8. The feed temperature is 50° C; feed pressure is 850 psig with permeate pressure of 10 psig. Permeances (GPU): 22.7 CO2, 0.7 CH4, 4.4 N2 0.75, C2H6 and 0.0009 C3H8 respectively...... 58

xii

Figure 3-8:Single stage membrane process with feed compression (B1), expander (B4) and permeate vacuum (B5) prior to integration with other separation unit operations. Membrane separation is considered as CO2 enrichment prior sending to other CO2 capture method to complete separation target of 90% CO2 recovery with 95% purity...... 59

Figure 3-9:Impact of membrane area and CO2/N2 selectivity for the single stage process in Figure

3-8 on (a) CO2 permeate purity (b) CO2 permeate recovery (c) stage cut (permeate stream flow rate S5/ feed flow rate S2), and (d) parasitic load. Feed pressure is fixed at 2 bar with fixed permeate pressure of 0.2 bar. CO2 permeance is calculated based on Robeson upper bound relation by assuming membrane effective thickness of 0.1 microns...... 62

Figure 3-10: Impact of feed pressure and CO2/N2 for the single stage counter-current stage in

Figure 3-8 on (a) CO2 permeate purity (b) CO2 permeate recovery (c) stage cut (permeate stream flow rate S5/ feed flow rate S2) (d) parasitic load. Membrane area is fixe fixed at 100,000 m2 with fixed permeate pressure of 0.2 bar. CO2 permeance is calculated based on Robeson upper bound relation by assuming membrane effective thickness of 0.1 microns...... 64

Figure 3-11: Impact of feed CO2 mole fraction and CO2/N2 selectivity for the single stage counter-current stage in Figure 3-8 on (a) CO2 permeate purity (b) CO2 permeate recovery (c) stage cut (permeate stream flow rate S5/ feed flow rate S2) (d) parasitic load. Membrane area is

2 fixed at 100,000 m with fixed feed pressure of 2 bar and permeate pressure of 0.2 bar. CO2 permeance is calculated based on Robeson upper bound relation by assuming membrane effective thickness of 0.1 microns...... 65

Figure 4-1: Staged membrane-cryogenic process with air feed sweep system (Boiler CO2 recycle loop). The additional enriching module ensures low CO2/N2 membrane meet the target recovery of 90% with 95+ CO2 purity ...... 75

xiii

Figure 4-2: Staged membrane-cryogenic process without air feed sweep system (Post-boiler CO2 recycle loop). Stripping stage is eliminated to prevent boiler O2 loss. The additional enriching module ensures low CO2/N2 membrane meet the target recovery of 90% with 995+ CO2 purity . 77

Figure 4-3: Impact of 1st enriching stage cut (permeate stream flow rate S9 /feed flow rate S8) and 2nd enriching stage cut (permeate stream flow rate S18 /feed flow rate S16) on total module area (m2) for (a) PDMS (b) Polaris in the configuration of Figure 4-1...... 79

Figure 4-4: Impact of 1st enriching stage cut (permeate stream flow rate S9 /feed flow rate S8) and 2nd enriching stage cut (permeate stream flow rate S18 /feed flow rate S16) on total plant parasitic load (%) for (a) PDMS (b) Polaris in the configuration of ...... 80

Figure 4-5: Impact of 1st enriching stage cut (permeate stream flow rate S9 /feed flow rate S8) and 2nd enriching stage cut (permeate stream flow rate S18 /feed flow rate S16) on LCOE (dash line) and boiler O2 concentration (dot line) for (a) PDMS (b) Polaris in the configuration of

Figure 4-1 ...... 82

Figure 4-6: Impact of 1st enriching stage cut (permeate stream flow rate S10/feed flow rate S8) and 2nd enriching stage cut (permeate stream flow rate S16 /feed flow rate S1) on total required module area (m2) for (a) PDMS (b) Polaris in the configuration of Figure 4-2 ...... 84

Figure 4-7: Impact of 1st enriching stage cut (permeate stream flow rate S10 /feed flow rate S8) and 2nd enriching stage cut (permeate stream flow rate S16 /feed flow rate S14) on total plant parasitic load (%) for (a) PDMS (b) Polaris in the configuration of Figure 4-2 ...... 86

Figure 4-8: Impact of 1st enriching stage cut (permeate stream flow rate S10/feed flow rate S8) and 2nd enriching stage cut (permeate stream flow rate S16/feed flow rate S14) on LCOE for a)

PDMS (b) Polaris in the configuration of Figure 4-2. The base electricity price without LCOE is assumed at $53.96/MWh...... 87

Figure 4-9: Process Facilities Cost (PFC) breakdown comparison between Polaris and PDMS for

Figure 4-1 and Figure 4-2...... 89 xiv

Figure 4-10: Operating Cost (VOM) breakdown comparison between Polaris and PDMS for

Figure 4-1 and Figure 4-2 ...... 90

Figure 4-11: LCOE breakdown comparison between Polaris and PDMS for Figure 4-1 and

Figure 4-2 ...... 91

Figure 5-1: MTR Membrane-Cryogenic Air Feed Sweep Configuration [4] ...... 95

Figure 5-2: Flowchart for optimization of membrane-cryogenic for post-combustions ...... 101

Figure 5-3: Impact of stage area for α(CO2/N2) =75, feed pressure=2 bar, and permeate pressure=0.2 bar: (a) CO2 recovery (dash) and purity (solid), (b) LCOE (yellow dash), boiler O2 concentration (solid), CO2 recovery (black dash)...... 103

Figure 5-4: LCOE variation with boiler O2 mole fraction as a function of α (CO2/N2) for 90%

CO2 recovery, feed pressure=2 bar, and permeate pressure=0.2 bar. Base electric price without

CCS is assumed to be $53.96 /MWh...... 104

Figure 5-5: Impact of stage area for α(CO2/N2) =75, feed pressure=4 bar, and permeate pressure=0.5 bar: (a) CO2 recovery (dash) and purity (solid), (b) LCOE (yellow solid), boiler O2 concentration (black solid), CO2 recovery (dash)...... 105

Figure 5-6: LCOE variation with boiler O2 mole fraction as a function of operating pressures for

90% CO2 recovery and α(CO2/N2) =75. Base electric price without CCS is assumed to be $53.96

/MWh...... 107

Figure 5-7: LCOE dependence on feed and permeate pressure for boiler oxygen feed concentrations = 17, 18, and 19% and for αCO2/N2) = 75. CO2 recovery is fixed at 90%. Base electric price is assumed to be $ 53.96 /MWh...... 110

Figure 5-8: LCOE dependence on feed and permeate pressure for boiler oxygen feed concentrations = 17, 18, and 19% and for α(CO2/N2) = 100 (a-c) and 45 (d-f). CO2 recovery is fixed at 90%. Base electric price is assumed to be $ 53.96 /MWh...... 112

Figure 5-9: LCOE variation with feed and permeate pressure for various combinations of enriching and stripping stage selectivity and a fixed boiler oxygen concentration of 18% and 90%

CO2 recovery. Base electric price without CCS system is assumed at $53.96 /MWh...... 114

Figure 6-1: Counter-current module configurations divided into N stages ...... 120

Figure 6-2: Modified Process Diagram for Installed 1 Ton per day CO2 Capture MTR

Membrane separation system at NCCC [12]...... 125

Figure 6-3: Outlet compressor (B2) pressure changes for a 10% increase, (a) and (b), and 10% decrease, (c) and (d) in flue gas flow rate. Values of selectivity and feed pressure (bar) are indicated ...... 129

Figure 6-4: Inlet vacuum pump (B6) pressure changes for a 10% increase, (a) and (b), and 10% decrease, (c) and (d) in flue gas flow rate. Values of selectivity and feed pressure are indicated in each sub-figure...... 131

Figure 6-5:CO2 Permeate mole fraction transients for various selectivities and pressure ratios in response to a 10% feed flow rate increase. The arrow indicates apparent time constant () .... 133

Figure 6-6:CO2 Permeate mole fraction transients for various selectivities and pressure ratios in response to a 10% feed flow rate decrease. The arrow indicates apparent time constant () .... 134

Figure 6-7:CO2 recovery transients for various selectivities and pressure ratios in response to a

10% feed flow rate increase. The arrow indicates apparent time constant (τp) ...... 136

Figure 6-8:CO2 recovery transients for various selectivities and pressure ratios in response to a

10% feed flow rate decrease. The arrow indicates apparent time constant () ...... 137

Figure 6-9: Inlet vacuum pump (B6) pressure changes for a 10% increase, (a) and (b), and 10% decrease, (c) and (d) in flue gas flow rate. Values of selectivity and feed pressure are indicated in each sub-figure. The arrow indicates apparent time constant (τp) ...... 139

xvi

Figure 6-10: O2 concentration transients for various selectivities and pressure ratios in response to a 10% feed flow rate decrease. The arrow indicates apparent time constant (τp) ...... 140

Figure 6- 11: Comparison of time constants for CO2 obtained from the simulations at various

CO2/N2 ...... 142

Figure 6- 12: Comparison of time constants for O2 obtained from the simulations at various

CO2/N2 selectivities and pressure ratios to values calculated from Equation (6-25). The solid line represents the values from Equation (6-25) while the symbols represents the value evaluated from the simulations...... 143

xvii

List of Tables

Table 2.1 Air feed sweep system key findings [4] ...... 35

Table 3.1: Flue gas conditions considered in this study ...... 61

Table 4.1: Base power plant basic data and flue gas conditions considered in this study ...... 72

Table 4.2:Economic viability comparison between PDMS and Polaris for air feed system configurations...... 83

Table 4.3:Economic viability comparison between PDMS and Polaris for post boiler CO2 recycle system configuration in Figure 4-2 ...... 88

[3] Table 5.1: CO2 permeance calculated from Robeson upper bound relation ...... 99

Table 5.2: Decision variables used for optimization...... 99

Table 6.1: Base Flue Gas Feed in MTR field test [12] ...... 124

xviii

List of Abbreviations

ACM Aspen Custom Modeler AT Present Value of an annuity payment BEC Bare Erected Cost CAPEX Capital Expenditure CF Plant Capacity Factor CCS Carbon Capture and Storage COE Cost of electricity DOE Department of Energy EPA Environmental Protection Agency EPC Engineering, Procurement & Construction Cost FCF Fixed charge factor FC Fuel Cost per unit of Energy FOM Fixed Operating and Maintenance Cost GA Genetic Algorithm GPU Gas permeation unit

HR Net power plant heat rate IGCC Integrated gasification combined cycle IVP Initial value problem KWH Kilowatt-hours LCOE Levelized Cost of Electricity MINLP Mixed Integer Non Linear Programming mMMT Million metric tons MTR Membrane Technology Research NCCC National Carbon Capture Center NLP Non-Linear Programming NSGa-11 Nondominated Sorting Genetic Algorithm II O&M Operating and Maintenance Cost opex Operating and Maintenance Expenditure PC Pulverized coal PDMS Polydimethylsiloxane

xix

PFC Process Facilities Cost PVT Pressure-volume-temperature R Interest rate SA Simulated Annealing T Economic Life of the plant T&S Transport and storage TOC Total Overnight Cost TPC Total Plant Cost VOM Variable Operating and Maintenance Cot

List of Symbols

Ni Flux across the membrane (kmol/s)

Pi Membrane permeability value for component i (kmol.m/(s.m2.bar)) l Membrane thickness (m) 2 Am Membrane area (m )

xi Retentate mole fractions,

yi Permeate mole fractions

Pf Feed pressures (Pa)

Pp Permeate pressures (Pa)

/ Membrane selectivity (ratio of gas permeability or permeances for two components A and B)

mi,j Molar permeation rate for component i leaving j stage, mi,j in (kmol/s) i 2 , Membrane permeance (kmol/s.m .Pa) of component I at stage j L Active (or permeating length) of the hollow fibers(m)

Number of fiber

Ro Hollow fiber outer radius (m)

, Arrhenius pre-exponential factor

, Permeation activation energy for component I (kJ/mol)

, Temperature of at stage j(K) at the retentate side

Feed flow rate (kmol/s)

Rs Sweep flow rate (kmol/s)

Ts Sweep temperature (K) z Distance along the module (m) η Gas mixture viscosity (Pa.s)

Rg Ideal gas constant ( J/mol.K)

ri Fiber inner radius (m) R H j-1 Enthalpy of the retentate entering stage j from stage j- 1(J/kmol) R H j i Enthalpy of the retentate leaving stage j (J/kmol)

xxi

Qmem Net rate of conductive heat flow across the hollow fiber membrane(J/kmol) P H j+1 Permeate enthalpy entering stage j from stage j+1(J/kmol) P H j Permeate enthalpy leaving stage j (J/kmol) ideal,P H j+1 Ideal gas enthalpies of the permeate streams entering (J/kmol) ideal,P H j Ideal gas enthalpies of the permeate streams leaving (J/kmol) ideal,R H j-1 Ideal gas enthalpies of the retentate streams entering(J/kmol) ideal,R H j Ideal gas enthalpies of the retentate streams leaving (J/kmol) εP j+1 Enthalpy departure functions of the permeate streams entering stage j (J/kmol) εP j Enthalpy departure functions of the permeate streams leaving stage j (J/kmol) εR j-1 Enthalpy departure functions of the retentate streams entering stage j (J/kmol) εR j Enthalpy departure functions of the retentate streams leaving stage j (J/kmol) , Average ideal gas heat capacities for the permeate stream leaving stage j+1 and entering stage j (J/kmolK) , Average ideal gas heat capacities for the permeate stream leaving stage j (J/kmolK) , Average ideal gas heat capacities for the retentate stream leaving stage j (J/kmolK) R V j-1 Specific volumes of the retentate streams entering stage j (m3) R V j Specific volumes of the retentate streams leaving stage j (m3) P V j Specific volumes of the permeate streams leaving stage j (m3) P V j-+1 Specific volumes of the permeate streams entering stage j (m3)

/ Ratio of Carbon Dioxide permeability to Nitrogen permeability

xxii

/ Ratio of Oxygen permeability to Nitrogen permeability

PCO2 CO2 permeability (barrer)

O2 permeability (barrer)

N2 permeability (barrer)

LCOEβ LCOE at given O2 boiler concentration ($/MWh)

β O2 level difference

LCOEθ LCOE at the given CO2 recovery rate ($/MWh)

θ CO2 recovery rate differences 3 VP Permeate side tank volume (m ) 3 VR Retentate side tank volume (m ) OD Fiber outer diameter (μm) ID Fiber inner diameter (μm)

Lf Fiber length (m)

Ashell Area on the module shell side (m2)

Amodule Module area (m2)

ID module Module inner diameter (m).

Permeate side time constant (s)

Retentate side time constant (s)

Qref, j Reference gas permeance for stage -j

Pcomp Compressors power requirement (kW)

Pvac Vacuum pump power requirement (kW) Molar flow rate through equipment (mol/s)

Tin Compressors/Vacuum pump operating temperature (K)

Equipment efficiency γ Adiabatic expansion factor

Pout Out-coming compressors pressure(bar)

Pin Incoming vacuum pressure (bar)

xxiii

Chapter 1

1. Introduction

Anthropogenic emissions of carbon dioxide (CO2) from fossil-fuel electric power plants potentially can lead to undesirable global climate change [1]. Consequently, significant research effort has focused in reducing the carbon intensity of fossil fuel through post-combustion capture technology. In comparison with pre-combustion and oxy-fuel combustion capture technique, post-combustion has the lowest CO2 content in the flue gas stream due to the large nitrogen (N2) presence in air. Because of the low CO2 feed partial pressure driving force, this technology suffers from a severe energy efficiency penalty. Therefore, the key to achieve the stringent capture of 90% recovery and 95% purity, without increasing the cost of electricity (COE) by more than 35% [2], is to generate affordable CO2 feed partial pressure driving force. Membrane processes are one of many options under development.

1.1 Membrane Separation Processes for Post-Combustion

There are few major barriers to make membrane process work effectively in post- combustion applications. The first is the availability of the membrane material to fulfill the capture target criteria. Membranes that permeate CO2 as quickly as possible are desired to reduce the membrane area required to perform the separation and associated

capital cost. Membranes that possess the highest selectivity for CO2 (i.e., the highest ratio of CO2 permeability to N2 permeability) also are desired to reduce energy requirement and associated operating cost. However, changes in polymer primary (compositional) and secondary (conformational) structure that increase CO2 membrane permeability are accompanied by a decrease in CO2/N2 selectivity. The trade-off between CO2

[3] permeability and CO2/N2 selectivity is shown by the Robeson plot in Figure 1-1. All known rubbery and glassy polymers possess permeability and selectivity combinations that lie below the indicated upper bound line; the symbols represent values reported in the literature. In the context of carbon capture application, this plot also reflects the tradeoff between total module area and energy requirement. Therefore, to move above the upper bound line, most of the reported CO2 membrane material development work has sought to improve both CO2 permeability and CO2/N2 selectivity by using non-polymeric membranes or mixed matrix membranes that are polymer-inorganic composites.

[3] Figure 1-1: Robeson plot of selectivity versus permeability for the CO2/N2 gas pair

Because of the low CO2 feed partial pressure driving force in flue gas, it is impossible for a single stage-membrane process to achieve CO2 recovery and purity targets (even for

[4] high CO2/N2 selectivity materials) due to pressure ratio limitations . Thus, implementing multi-stage designs is required to increase the CO2 feed partial pressure by creating an internal gas recycle loop in the systems. Additionally, economically viable multi-stage membrane process design depends strongly on two important process parameters: 1) pressure ratio and 2) operating stage-cut. However, most of the reported work has not thoroughly addressed the impact of these parameters on the Levelized Cost of Electricity (LCOE).

To date, most of the reported process configurations for membrane systems have sought to generate affordable CO2 partial pressure driving forces for permeation by a combination of: feed compression, vacuum permeation, internal gas recycles and feed-air sweep system [4-6] . Combining membranes with other separation techniques, such as

[7, 8] cryogenic and absorption, also potentially could reduce CO2 capture cost .

1.2 Membrane Air Feed Sweep Configurations

Recently, Membrane Technology Research (MTR) proposed an innovative way to

[4] generate affordable CO2 partial pressures . This process used MTR’s Polaris membrane that has a high CO2 performance of 1000 GPU with a CO2/N2 selectivity of 50. The high selectivity value allows preferential permeation and concentration of CO2 relative to other gas components. The proposed design configuration combines a two-stage membrane system with a final cryogenic separation. The air feed sweep configuration is shown in Figure 1-2.

In this scheme, flue gas stream S1, containing about 11.6% CO2 from the boiler, is sent through multiple pre-treatment steps, compressed to 2 bar, and cooled to 35 °C prior to sending it as S8 to the first enriching membrane unit (B2). The vacuum pump

(B4) maintains a vacuum of 0.2 bar on the permeate side of the first enriching module to increase the CO2 permeation driving force. The enriched CO2 permeate stream (S9) contains a significant amount of CO2 from S6. This stream is pressurized before sending to flash B5 where liquid water is removed. The top product (S17) contains about 83%

CO2 and is sent to a multistage compression and cooling system after which the captured

CO2 is removed as a liquid in stream S20 from the flash B6. The flash overhead product is sent to the smallest membrane unit that is denoted as cryogenic module (B7) to create another small CO2 recycle loop in S23. The permeate stream from the cryogenic module

(S23) is recycled to the compression unit to recycle some CO2 while the retentate stream

(S24) is sent to an expander for energy recovery and then to the first enriching stage feed as S25 to create another CO2 recirculation loop.

The CO2 lean retentate(S10) leaving the enriching stage contains about 7% CO2 and is fed to a counter-current sweep stripping stage (B3) to achieve the desired 90% CO2 recovery target. Utilization of the boiler feed air as a sweep in the module dramatically improves module performance by increasing the partial pressure driving force (i.e., chemical potential) for permeation. The exiting sweep stream (S12) contains about 8.7%

CO2 and is sent to the boiler as the feed air. This creates a large CO2 recirculation loop that increases the CO2 concentration in the flue gas stream (S8) fed to the enriching stage from 11.6% to 20.3%. The exiting retentate stream (S11) from the stripping stage (B3)

contains about 1.8% CO2 and is vented to the atmosphere. The vented CO2 is 10% of the

CO2 produced in the boiler.

Unfortunately, the air feed used as a sweep in the CO2 stripping stage loses oxygen in the stage. The oxygen concentration decreases from 21% to 18%. The use of this oxygen deficient boiler feed is of concern as discussed later. The CO2 capture cost reported in this work was $23/ton CO2, which is more affordable than other proposed post- combustion methods.

O2 deficient air (S12) B1 S5 S6 B3 S10 Air feed S1 S3 S7 S8 S11 Lean-CO2 vent S4 B2 S2 Enriched CO2 Coal permeate (S9) S13 S14 S23 B4 S17

S22 S21

S18 S15 S19 B5 B6 S25 S24

Liq CO2 S20 S16

Figure 1-2: Air feed sweep configuration proposed by MTR [4].

Merkel et al. [4] also emphasized that in order to reduce the capture cost in the future, it is important to develop materials with high CO2 permeability and moderate selectivity since it would further reduce total membrane area requirement. Furthermore, the separation capability of higher selectivity materials cannot be exploited fully with the low permeate-to-feed pressure ratios being considered for the process. The Robeson upper-bound indicates that increasing permeability must lead to lower selectivity but the impact of this trade-off was not investigated. In summary, this study suggests that use of the boiler feed air to sweep a second CO2 stripping stage can improve process economics significantly in two ways:

a) Increasing CO2 concentration in the feed to the first CO2 enriching stage by

recirculating CO2 through the boiler, and

b) Utilizing the “free” additional driving force for CO2 permeation in the stripping

stage afforded by the feed air sweep.

However, although CO2-boiler recycle loop has been identified as the most viable method to increase CO2 feed partial pressure driving force in affordable way, the impact

[9] of boiler oxygen (O2) reduction on LCOE remains unclear. Scholes et al. note that sufficiently high O2 partial pressure in the boiler is vital to control adiabatic flame

[10] temperature. Franz et al. also report that a reduction in O2 partial pressure will affect boiler temperature – a decrease in adiabatic temperature is expected with increasing CO2 recovery as O2 partial pressure decreases which in turn will reduce boiler efficiency.

With that in mind, a new super-structure for staged membrane capture processes with final cryogenic concentration is proposed in this work which accommodates a broad 6

range of membrane permeability and selectivity combinations as dictated by the Robeson upper bound [3]. Materials with high permeability and low selectivity reduce membrane capital cost at the expense of greater energy consumption. There are two types of CO2 recycle loops considered: one through the boiler and the other after the boiler. The post- boiler recycle loop avoids undesirable reductions in oxygen concentration. The tradeoff relation between capital and operating costs is evaluated by determining the LCOE for various embodiment to identify the optimal design.

1.3 Research Objectives

The overarching objective of the proposed research is to evaluate the economic viability of combined cryogenic-membrane separation processes-for post-combustion carbon dioxide (CO2) applications. A staged membrane superstructure network is evaluated that specifically accommodates the use of high permeability/low selectivity membrane materials. This superstructure builds upon previously reported cryogenic- membrane processes that utilize an air-feed sweep configuration [4]. Such a configuration produces oxygen deficient feed air that potentially could impact boiler performance, but the proposed superstructure incorporates a post-boiler CO2 recycle loop that avoids this problem. The tradeoff relation between area and energy requirement will be evaluated as function of process configuration and membrane material. Specific tasks include:

 Develop robust and reliable mathematical models for non-isothermal

multicomponent gas separation in hollow fiber membrane module.

 Integrate the developed membrane unit operation model with a commercial

process-simulator 7

 Simulate and design various membrane-cryogenic hybrid process configurations

for post-combustion application using a commercial process-simulator.

 Evaluate the impact of pressure ratio and enriching stage cut on the total

membrane area requirement, power plant parasitic load, and Levelized Cost of

Electricity (LCOE) and oxygen boiler concentration.

 Evaluate the Levelized Cost of Electricity (LCOE) associated with CO2 capture.

 Examine the impact of CO2/N2 selectivity towards total module area requirement,

power plant parasitic load, CO2 avoidance cost, and oxygen boiler concentration.

 Assess economic impacts in terms of LCOE and boiler oxygen concentration for

air feed sweep system

The second research objective is to develop a rigorous optimization for the above mentioned developed super-structure membrane-cryogenic design. The specific tasks are mentioned as follow:

 Develop Systematic Global Search algorithm to minimize LCOE by simultaneous

optimization of superstructure membrane-cryogenic configurations, operating

parameters, membrane material properties and also considering O2 boiler

consideration as variable constraint

 Evaluate the effect of transient behavior of membrane modules used for post-

combustion applications due to the fluctuations of flue gas flow rate and CO2 feed

concentration in the flue gas stream. The effect of membrane properties and

operating pressure ratio for multistage membrane configurations on transient

response upon the step changes of flow rate is discussed. 8

1.4 Research Significance

The proposed research seeks to evaluate novel cryogenic-membrane processes for post-combustion CO2 capture. Process configurations that permit the use of membrane materials with high CO2 permeance, low CO2 /N2 selectivity are considered in addition to higher selectivity materials. The low CO2 partial pressure in the feed gas is the major barrier to any capture process. The preferred process will be the one that incurs the lowest capture cost and leads to the lowest Levelized Cost of Electricity (LCOE).

Membrane separation processes for post-combustion application have been widely studied in recent years. The majority of the reported work is devoted to the development and evaluation of membrane materials with high CO2 permeability and CO2/N2 selectivity. Increasing CO2 permeability reduces the required membrane area and associated capital cost while increasing CO2/N2 selectivity reduces the process energy requirements and associated operating cost. Unfortunately, the literature suggests that material changes which increase CO2 permeability will lead to a concomitant decrease in

[3] CO2/N2 selectivity. This relationship commonly is referred to as the Robeson plot and arises from the physics of the solution-diffusion process that governs transport in polymeric materials.

The use of membrane processes requires the generation of affordable CO2 partial pressure driving forces for permeation. However, the literature reports result primarily for higher selectivity materials. Moreover, one expects higher selectivity may not be desirable if process economics dictate the use of low pressure ratios due to the energy required to produce the partial pressure driving force. Additionally, because of pressure ratio limitations, it may not be possible for a single stage-membrane process to achieve recovery 9

and purity targets despite high CO2/N2 selectivity. The proposed staged membrane superstructure design will help increase the CO2 feed partial pressure and achieve capture targets through internal gas recycle in the system. The economics of the staged configurations will depend strongly on two process parameters, pressure ratio and stage- cut. The proposed work will evaluate the effect of these variables on LCOE.

To increase the CO2 partial pressure driving forces for permeation, one may use feed compression, vacuum permeation, and hybrid systems with cryogenic condensation.

Recently, Membrane Technology and Research (MTR) proposed a new scheme to increase CO2 partial pressure driving force in an affordable manner by incorporating an air-feed sweep in a staged membrane system. Although this scheme has been successfully demonstrated to reduce capture cost, it produces an oxygen deficient feed air stream that could potentially reduce the boiler adiabatic temperature. The higher CO2 concentration in the feed stream may also reduce boiler temperature. The impact of boiler oxygen (O2) concentration on LCOE is unclear.

The proposed work seeks to build upon the past literature to evaluate a broader range of membrane materials and processes for carbon dioxide capture. The entire range of known membrane materials will be examined in addition to staged processes that permit the achievement of target CO2 capture rates and purities. Of particular interest is the tradeoff between reduced capital costs with increased membrane permeability and increased operating costs to perform the separation. In addition, many studies have focused on the binary separation of CO2 and N2, this neglects the important impact of O2 and water on transport.

The optimization of staged membrane processes for CO2 capture requires simultaneous evaluation of several design variables on LCOE. Recent work on optimization for membrane gas separation applications has utilized gradient based method such as Mixed Integer Non Linear Programming (MINLP) and Non-Linear

Programming (NLP). Because of the non-linear constraints that exist, both MINLP and

NLP models are non-convex problem for which solutions correspond to a local optimum near the starting point for the optimization search. Although non-gradient methods such as Genetic Algorithm (GA) are relatively straightforward and potentially can identify non-local optimum with sufficient accuracy, they commonly require longer computational times and might be impractical in this work.

While past work with gradient based optimization has included membrane selectivity and permeability as decision variables and even multicomponent permeators, the case studies considered were for small scale systems which are not representative of utility scale power plants. Moreover, past work neglects the initialization strategies in both

MINLP and NLP models. The convergence processes in gradient based methods are extremely sensitive to the initial points in the model. Thus, a poor initial guess may lead to suboptimal configurations and process parameters.

In this study, the multistage membrane-cryogenic air feed sweep configuration in

Figure 1-2 is optimized according to the Robeson upper bound relation. Systematic

Global Search is used to determine the membrane properties and operating conditions that minimize LCOE. The O2 concentration to the boiler is evaluated during the optimization process and the optimization is performed for a range of fixed O2 concentrations to determine sensitivity to this important design variable. 11

Understanding the transient and thermal behavior of membrane gas separation processes for post combustion CO2 capture is crucial because these processes must accommodate plant start-up, shut down, and variation of flue gas flow rate and composition due to daily electricity demand fluctuations. The literature on dynamic membrane gas permeator models is limited and suggests membrane separations have a negligible effect on process dynamics because of their fast response [11] . However, the impact of variation of operating pressure ratio as well as membrane properties has not been addressed. Variation of CO2/N2 selectivity reveals a trade-off between CO2 purity and recovery in addition to a variation in process energy requirements when disturbances are introduced into the system.

1.5 Structure of Dissertation

Chapter 1: Introduction

This chapter provides an introduction to membrane separation system in post-combustion applications. The objectives and anticipated knowledge contributions of this work are discussed in this chapter.

Chapter 2: Literature Review

This chapter gives a general review of the relevant literature related to the membrane separation system in post combustion applications with emphasis on process economics in multistage membrane configurations systems. This chapter also summarizes the published works relevant to the solution approach for multicomponent hollow fiber membrane permeator modelling as well as membrane separation system optimization.

Chapter 3: Modelling Multicomponent Hollow Fiber Membrane Gas Separation Modules and Study for Single Stage Membrane for Post- Combustion CO2 Capture

This chapter investigates the trade-off between CO2/N2 selectivity and CO2 permeability in a single stage membrane configuration prior to combining it with other stages in a CO2 capture system to achieve the target CO2 recovery of 90% with 95%+ purity. The first part of this chapter describes the solution method for the proposed multicomponent membrane gas permeator model which incorporates Joule-Thompson thermal effects.

Chapter 4: Staged Membrane Configurations for Post-Combustions CO2 Capture

This chapter discusses the super-structure for staged membrane configurations with a final cryogenic polishing stage that accommodate a broad range of CO2/N2 selectivity according to the Robeson plot. The superstructures considered here incorporate two types of CO2 recycle loops: one through the boiler and one after the boiler. The post-boiler recycle loops avoids undesirable reductions in O2 concentration. The tradeoff between capital and operating costs is evaluated by determining the LCOE of various embodiments of the superstructure to identify the optimal design.

Chapter 5: Membrane Process Optimization for Carbon Capture

This chapter discusses the optimization method for the MTR multistage hybrid membrane-cryogenic air-feed sweep configuration in Figure 1-2. Membrane transport properties are varied according to the Robeson upper bound relation for CO2 and N2.

Previously reported operating conditions [4] and membrane separation properties are used to set establish an initial reference state for the optimization.

Chapter 6: Dynamic Simulation of Membrane Separations for Post-Combustion

Applications 13

This chapter reports a dynamic simulation for multi-stage membrane systems used in post-combustion carbon capture processes. The simulations are based on a field test

[12] conducted by MTR to capture 1 ton per day of CO2 at a membrane based pilot plant .

The impact of membrane CO2/N2 selectivity and operating feed to permeate pressure ratio is discussed.

Chapter 7: Conclusions and Future Work

This chapter presents the conclusions obtained from this work and the recommendations for future work.

Chapter 2

2. Literature Review

2.1 CO2 Emissions from Electricity Power Generation Sources

Anthropogenic emissions of carbon dioxide (CO2) from fossil-fuel electric power plants potentially can lead to undesirable global climate change. According to the Energy

Information (EIA), global carbon emissions from fossil fuel have increased from 5,355

[13] million metric tons (MMmt) in 2013 to 5,406 MMmt in 2014 . Accumulation of CO2 in the atmosphere could lead to irreversible climate change for up to 1000 years [1].

Moreover, Environmental Protection Agency (EPA) studies predict that continuation of this trend will increase the rate of global average temperature rise to twice that of the last

100 years[14].

The United States’ production of electricity in 2014 was estimated at 4,093 billion kilowatt-hours (kWh). Figure 2-1 shows the breakdown of electricity generation by sources. Fossil fuel such as coal and natural gas account for more than 60% of the electricity generation.

Although renewable and non-fossil energy sources have grown dramatically, coal- fired power plants will continue to play a vital role in meeting our growing electricity demand [15]. Several studies suggest that fossil fuel sources will remain the primary sources for electricity generation until at least 2050 [16]. In view of this, the US

Department of Energy (DOE) has challenged researchers to develop separations processes capable of 90% CO2 capture at 95% purity and subsequent compression to 140 bar for transport and storage, without increasing the cost of electricity (COE) by more than 35% [2].

Petroleum , Others , 0.8% 0.2%

Natural gas , 28.0%

Coal, 71.0%

Figure 2- 1 Sources of USA electricity generation in 2015 [15].

2.2 CO2 Emissions Mitigations Options from Electricity Power Generation

A wide variety of technological options have been identified to mitigate the CO2 emissions. These options include [17]:

 Energy conservation implementation

 Improve power supply and distribution efficiency

 Energy efficiency improvement

 Using less fossil fuel sources by switching to nuclear and renewable energy and

also use less carbon intensive fuel

 Incorporating Carbon Capture and Storage (CCS) technology in the power plant.

By 2020, electricity generation from coal is predicted to grow twice as much as from renewable sources. Thus, it is impossible for existing coal fired power plants to meet stringent emission regulations without CCS technology. Additionally, CCS technology will enable dependency on the relatively cheap fossil fuel, thus it could potentially reduce

[18] CO2 emissions at a lower cost per ton than other above proposed mitigation options .

2.3 Carbon Capture and Storage (CCS)

Generally, there are three major components of the CCS process: capture, transport and storage. The CCS process begins with CO2 capture by separation from electrical and industrial sources. There are three options to capture CO2: pre-combustion, oxy-fuel and post combustion. All the captured CO2 is then compressed to a high density before transport to the storage location and underground sequestration for a long period

of time. Captured CO2 could potentially be stored by underground injection, confinement in geological formations, and deep ocean injections and also be used to produce organic carbonate[19].

2.3.1 Pre-Combustion

This process involves reaction of the primary fuel in a shift reactor with steam and air or oxygen (O2) to produce syngas which is comprised of carbon monoxide (CO) and hydrogen (H2). Steam is then added to syngas to convert CO to CO2 and produce additional H2. Because the reaction is conducted at high pressure, shift reactors could produce to up to 60% CO2. CO2 is removed and captured from the syngas product through some separation process. This leaves an enriched H2 stream that can be used for electricity generation. Pre-combustion could only be used in an integrated gasification combined cycle (IGCC) power plant [19].

2.3.2 Oxyfuel Combustions

This process uses O2 instead of air for combustion. Fuel combustion in pure oxygen results in the absence of N2 in the flue gas stream and a higher CO2 concentration. The major drawback of this process is that it requires significant energy for upstream separation of oxygen from air with a purity of 95-99% [19].

2.3.3 Post-Combustion

In this process, fossil fuel is combusted with air in a boiler. The heat of combustion is used to produce steam for electricity generation. The exhaust flue gas is cooled and treated to remove all particulate matter before entering the capture system.

The advantage of this method is that it can be retrofitted into existing pulverized coal

(PC) power plants without substantial changes in the boiler [19]. Currently, amine solvent based absorption is the most well established post-combustion capture technology because of its high separation efficiency. This high separation efficiency is attributed primarily to the large enthalpy change upon CO2 absorption. However, the concomitant energy consumption required for solvent regeneration is the major barrier to achieving the CO2 capture target cost. This can increase the cost of electricity (COE) by up to 70-

80% [20]. Additionally, amine capture systems could potentially double plant water consumption since a substantial amount of water is required to support the absorption and regeneration unit [21] . Furthermore, amine solvent consumption and disposal could lead to unintentional human health and environment hazards [22].

In comparison with pre-combustion and oxy-fuel combustion capture techniques, post-combustion starts with the lowest CO2 content in the flue gas stream due to the N2 in the atmospheric air feed. Because of the low CO2 feed partial pressure driving force, this technology suffers from a severe energy efficiency penalty [19]. Therefore, the key to achieving the stringent requirements of 90% recovery and 95% purity, without increasing

COE by more than 35%, is to generate affordable CO2 feed partial pressure driving forces. Membrane processes are one of many options under development.

2.4 Carbon Capture and Storage (CCS) Economic Evaluations

Several cost metrics can be used in CCS studies. These include the Levelized Cost of Electricity (LCOE), the cost of CO2 avoided, cost of electricity (COE) or first year cost

[23] of electricity and the cost of CO2 captured .

2.4.1 Levelized Cost of Electricity (LCOE)

According to Rubin et al.[23] , LCOE can be defined as “cost of electricity generation” ($/MWh) that incorporates all associated expenses for building and operating a power plant over its economic life with an expected rate of return on invested capital that is normalized over the total net electricity generated. Therefore, it represents the cost of electricity per MWh that the customer must be charged to recoup all expenses plus the desired rate of return. The LCOE varies between power plants because of the different technologies used, different types of fuel used, different capital expenditure paths, different annual operating costs (such as operating, maintenance, taxes, carbon process), different net outputs and different economic lifetimes. The LCOE can be calculated as follows

( ) & () = ∑ ( ) (2-1) ∑ () where (Electricity sold)t is the net electricity produced and sold in year t in MWh, r represents the annual rate used to discount values, which usually is taken to be a pre- defined rate of return (also called the interest rate of weighted cost of capital) required to cover equity and debt costs, (Capital expenditure)t is expenditure in year t associated with construction of the plant, O&Mt is the total non-fuel operating and maintenance

[23] costs in year t, and Fuel t is the total fuel costs in year t .

Assuming the net electricity produced and sold each year is constant over the life of plant and O&M and fuel costs are constant (i.e., escalation and inflation rates are zero), the above equation can be simplified to:

()() = + +()() (2-2) ()(∗)

where TCR represents Total Capital Requirement in $ (that include Bare Erected Cost

(BEC), Engineering, Procurement & Construction Cost (EPC), Total Plant Cost (TPC),

Total Overnight Cost (TOC), Contingencies and other associated owners’ costs), FCF is the fixed charge factor, FOM ($/year) stands for Fixed O&M , VOM ($/MWh) stands for

Variable O&M, MW is net power output of the plant (MW), CF is plant capacity factor,

HR is net power plant heat rate (MJ/MWh), and FC is fuel cost per unit of energy ($/MJ).

Equation (2-2) also gives the “first year cost of electricity” or COE [23].

Fixed charge factor (FCF) is used to levelize the plant Total Capital Requirements. This factors converts the total capital value to a uniform annual amount. FCF can be calculated as follows:

() = (2-3) () Where r is the interest rate or discount rate and T is the economic life of the plant.

To include the effects of fuel and O&M cost increases as well as plant output variation with time, Equation (2-1) may be written as:

()() = + + ()() (2-4) ()(∗) where l1, l2 and l3 are levelization factors applied to the first year of fixed and variable

O&M and total fuel costs, respectively. These factors convert all first year O&M and fuel costs to annuity values over the plant lifetime and are given by:

= (2-5) () Where

() = (2-6) = , (2-7)

And

, = 1+ ,1+ −1 (2-8) where AT represent the present value of an annuity payment, and ea,i is the apparent escalation rate of the relevant cost component, i, resulting from a real annual escalation rate, er,i and a general inflation rate, einf. If the calculation is made at constant dollar value with no real cost escalations, the value of eai is zero and the levelization factors are equal to 1.0.

Additionally, if the power plant capacity factor varies from year to year, a

[23] levelized plant capacity factor CFL value must be calculated. Rubin suggests a power plant will have lower CF values in the first and second year of operation before higher values can be realized. Based on this assumption, the levelized plant capacity factor can be calculated as:

() () = ∑ (2-9) () ()

2.4.2 Cost of CO2 Avoided

The cost of CO2 avoided ($/tonne CO2 avoided) on the other hand represents a cost comparison between a plant with CCS systems to a reference plant without CCS system. This method is used to quantify the average cost of avoiding CO2 emissions. The reference plant and CCS plant are usually assumed to be the same type and approximate size. In this regard, the CO2 avoidance cost also is equivalent to the price or tax on CO2 emissions that would equalize the cost of electricity production for the plants with and

[20] without CCS. The CO2 avoidance cost can be calculated as follows :

( ) 2 = (2-10) () 22

Where COE is the cost of electricity for the reference and CCS plants ($/MWh) and ER is the CO2 emissions intensity for the reference and CCS plants (tonne/MWh).

2.4.3 Cost of CO2 Captured

This method is used to quantify only the cost of capturing and producing CO2 as a chemical commodity sought by commercial markets. According to Rubin et al. [23], this cost metric is suitable for commercial considerations rather than climate change mitigation. Additionally, it excludes any cost for transporting or sequestering the captured CO2 products. The cost of CO2 captured ($/tonne CO2 captured) can be calculated as difference in COE of plants with and without capture divided by tons CO2 captured per MWh [20].

2.5 Membrane Process Design for Post-Combustions Applications

2.5.1 Hollow Fiber Membrane Module

Hollow fiber membranes are used in a wide range of separation applications especially for gas separations. Modules made from hollow fiber membranes are the mass transfer equivalent of a shell and tube heat exchanger. As such they consist of a hollow fiber bundle the ends of which are embedded in a tube sheet. The feed can be introduced to either the fiber lumen or the space external to the fibers (the shell) [24].

Gas mixture components permeate at various rates from the high pressure feed across the membrane. The portion of the feed that does not permeate is referred to as the retentate while the fraction that does is referred to as the permeate. A permeate sweep also may be fed to the module. The sweep mixes with the permeate and can dramatically

improve the separation performance by increasing the chemical potential difference across the membrane. In comparison to co-current or cross-flow configurations, counter- current operation is more efficient and reduces the membrane area required to perform a separation [24].

Figure 2-2: Cut–away view of a typical hollow fiber membrane module with a lumen feed and shell sweep operating in counter-current contacting mode [24]

2.5.2 Gas Permeation Model

A gas permeation model can be used to predict hollow fiber module performance.

Module performance commonly is predicted by assuming all fibers possess identical geometry and transport properties. Additionally, lumen flow rates are assumed to be identical for each fiber and the shell flow is assumed to be uniform plug flow [24].

Stern and Wang compared the method of analysis for cocurrent and countercurrent operation for binary gas mixtures [25]. Unlike countercurrent mode, the

cocurrent flow model solution is relatively straightforward because the governing mass balance equations can be integrated directly from feed inlet to retentate outlet. This is due to the fact that the boundary conditions for both the retentate and permeate are specified at the inlet. However, for counter-current configurations, the governing equations are complicated by split boundary conditions. Boundary conditions for the retentate side mass balances are specified at the feed inlet (permeate outlet) while boundary conditions for permeate-side mass balances are specified at the opposing feed outlet (permeate inlet). Such boundary conditions necessitate the use of an iterative procedure to solve the coupled non-linear differential equations. With that in mind, over the past few years several authors have proposed various numerical methods to deal with the split boundary value problem in the counter-current flow configurations.

Shindo extended the binary model to multicomponent model in five different flow configurations-one side mixing, perfect mixing, cross flow, cocurrent and counter-current

[26]. Iterations are made until satisfactory mass balances are achieved with the assumptions of negligible pressure drop for both the lumen and shell flows. The major drawback of any iterative method is that it can be extremely sensitive to the initial guess and convergence issues arise when a poor initial guess is made.

An averaging method also has been used as an alternate approach to overcome computational complexity in counter-current gas permeation model. Pettersen and Lien applied the concept of logarithmic mean of driving force that is analogous to counter- current heat exchanger [27]. Chen et al. [28] on the other hand improved the Shindo model by using an approximate average driving force that is constant along the fiber length.

Although the algorithm could handle multicomponent gas permeation at reasonable 25

computational time, it could not deal with pressure drop variation and may be inapplicable for high stage cut separations.

The simulation of multicomponent membrane gas separation modules can be complicated further by a dependence of gas permeation rates on membrane structure in addition to permeability and selectivity. While symmetric membrane (i.e., a uniform dense membrane) module performance depends on the feed and permeate flow pattern, the supporting porous layers in asymmetric membrane (i.e., a thin dense discriminating layer on a porous support) modules can prevent the permeate mixing that is required to achieve true counter-current operation. To address this problem, Pan`s model assumes the permeation driving force is not altered by the permeate mixing that occurs in the shell as the permeate flows counter-current to the retentate and uses the driving force for a cross- flow configuration instead [29]. This model also considered the permeate pressure variation inside the fiber. Initial estimates of permeate pressure profile, area and compositions are required in order to solve this problem. The new permeate flux and area can be obtained by using a trial and error shooting method to converge on the solution.

To reduce the computational effort to solve Pan`s model, Kovvali [30]assumed an approximate linear relation between feed and permeate compositions for certain intervals along the fiber length. However, the accuracy of the solution depends on the number of intervals along the fiber length. This eventually leads to significant computational effort especially when a larger number of intervals are used for multicomponent systems.

Khalilpour et al. [31] converted Pan`s model into a non-linear differential equation system and adopted a combination of backward differentiation and Gauss-Siedel solution 26

methodologies. Because Pan`s models are extremely sensitive to the initial guess for concentration profiles, several attempts have been made to reduce this sensitivity. Kaldis et al. [32] used collocation methods to solve Pan`s model. Although this method is less sensitive to initial values of retentate concentration and permeate pressure, solution accuracy and computational effort depends on the number of collocation points.

[8] Chowdhury et al. transformed Pan`s model into an initial value problem (IVP). They used Adam`s Moulton or Gear backward differentiation method to solve Pan`s equation.

Makaruk and Harasek [33] developed a Gauss-Siedel based finite difference algorithm to solve the multicomponent gas permeation problem. While convergence could be stabilized by adapting appropriate relaxation factors, computational effort increases significantly for systems with high gas selectivities. Davis [34] proposed a simpler approach to transform the gas permeator model equations into an implicit function for the stage cut variable which can be solved by damped successive substitution. However, convergence was obtained only for stage cuts less than 60%.

Coker et al. [35] used an iterative finite difference method to solve the multicomponent gas permeator problem. They introduced the concept of well-mixed tanks in series. In this approach, the module is approximated by a set of well-mixed tanks in series that allow transformation of the differential mass balances into a set of non- linear algebraic equations. The equation set can be written in a tridiagonal matrix form that can be solved using the Thomas algorithm. The iterative method exhibited poor convergence when a poor initial guess was made, so they proposed using the concentration profiles from a cross-flow model as initial guesses. The major drawback of

this method is the need to use a large number of tanks to adequately approximate the governing equations. As a result, this significantly increases the computation time.

In the later publications, Coker et al. [36] extended the model by incorporating temperature variation effects. Scholz et al. [37]incorporated non-ideal effects such as concentration polarization, temperature variation, pressure losses and real gas behavior into the permeation model. The model was programmed in Aspen Custom Modeler

(ACM). Boutan et al [38] used similar approach to solve binary component membrane permeator model in a transient state.

Katoh et al. [39] on the other hand considered nonideal mixing in the permeate and retentate using the tanks in series method. They applied relaxation methods to approximate the governing equations under transient conditions for multicomponent gas mixtures. Kao and Yan[40] solved dynamic binary component membrane permeator models by orthogonal collocation method based on the quasi-steady-state assumption.

Konda et al [41] introduced a transfer function methodology to stimulate membrane models in transient states.

Recently, Binns et al. [42] solved the tank in series model by using Newton-

Raphson approach, where initial fiber concentration profile is generated by a relaxation simulation. While this method results in feasible and stable solutions for single stage systems, the computational efforts may increase significantly when considering superstructure membrane network configurations. Moreover, Jacobian derivatives using numerical derivatives necessitate longer computational times

2.5.3 Single-Stage Membrane Design Configuration Feasibility Studies for Post-

Combustion Applications

Because of the potential environmental and economic impact associated with amine absorption processes, researchers and policy makers are considering membrane technology in post-combustion applications. Membrane technology has been used widely for gas separations because of compactness, light weight, modularity, high energy efficiency and ease of operation. Therefore, it can be easily retrofitted at the tail end of power-plant flue gas without complicated process integration [43].

Gas permeation through the glassy and rubbery polymers used to make high performance commercial membranes follows a solution and diffusion mechanism. The driving force for permeation is provided by maintaining a chemical potential (e.g., pressure) difference between the retentate and permeate through a combination of feed gas compression and permeate vacuum. Assuming gas sorption follows Henry’s law and diffusion is Fickian, the permeation rate across the membrane is given by [44, 45]:

= − (2-11)

Where Ni is the flux across the membrane (kmol/s), Pi is the membrane permeability

2 value for component i (kmol.m/(s.m .bar)) , l is the membrane thickness (m) , Am is the

2 membrane area (m ) , xi and yi are the retentate and permeate mole fractions, respectively, and Pf and Pp are the feed and permeate pressures, respectively, in bar. The gas permeability commonly is reported in Barrer where 1 Barrer = 3.348 x 10-12 kmol.m/(s.m2.bar)). Industrial membranes typically are characterized by thickness normalized permeability or permeance JA since the selective layer cannot be determined

easily. Permeance JA commonly is reported in GPUs (gas permeation unit), where 1 GPU

= 10-6 cm3(STP)/cm2/cm Hg/s [45]

= (2-12)

Membrane selectivity / is the parameter used to compare membrane separation performance for two components, A and B. Membrane selectivity is defined as ratio of gas permeability or permeances [45]

/ = = (2-13) High membrane selectivity is desired to produce a high purity permeate but is accompanied by lower intrinsic permeability, as seen in the Robeson plot, which increases the membrane area and capital cost required for a separation. According to Lin

[46], optimal membrane separation performance requires high selectivity to produce a high purity permeate but also the ability to form thin supported membrane structures to overcome the lower permeability of high selectivity polymers.

Because gas permeation requires the application of a pressure difference, the feed to permeate pressure ratio has a significant impact on overall membrane gas separation performance. Component i permeates from the retentate to the permeate only when the feed partial pressure is greater than the permeate partial pressure [4, 44, 46, 47]:

> (2-14) where xi and yi are the retentate and permeate mole fractions, respectively. Equation (2-

14) can be rewritten to give the minimum feed-to-permeate pressure ratio required to perform a desired separation as:

≥ (2-15)

Equation (2-15) indicates the feed-to-permeate pressure ratio is always greater than the ratio of permeate-to-feed concentration regardless of membrane permeability and selectivity. Because of the pressure ratio limitation, Merkel et al. [4] concluded that a single membrane stage is an economically viable option only for low CO2 product purity

(<50%). Therefore, a single stage membrane system appears unviable to achieve the targets of 90% CO2 capture at 95% purity regardless of membrane permeability and selectivity, especially given the tradeoff between membrane area and energy requirements as selectivity increases [4].

[48] Van Der Sluijs et al. explored the feasibility of polymeric membranes for CO2 capture from flue gas by comparing single stage and two-stage cascade configurations at various CO2/N2 selectivity and pressure ratio values. The single stage configurations are economically feasible only for low purity (<70%) CO2 product streams. For a membrane process to compete with other conventional CO2 capture technologies at high CO2 purity and recovery, the two-stage cascade system requires a selectivity of at least 200 and compressors/expanders with isentropic efficiency of 90%.

Favre [49] studied the potential for membrane separation processes in post- combustion applications by conducting a systematic analysis for a selectivity range of 40 to 200 for binary separations between CO2 and N2 in a single stage membrane module.

The analysis revealed that for high CO2 recovery and purity (>80%) module performance is extremely sensitive to inlet CO2 feed concentration, CO2/N2 selectivity and pressure ratio. For a 10% CO2 feed stream, target performance of 90% recovery and purity could not be met in a single stage configuration in the selectivity and pressure ratio ranges considered in the study. For membrane processes to be economically viable for post- 31

combustion applications at the aforementioned target levels, the inlet CO2 feed concentration must be higher than 20% and permeate vacuum used to increase the partial pressure driving force. Additionally, the target membrane selectivity should be around

60. However, even for a higher CO2 feed concentration, increasing membrane selectivity does not simply reduce the total energy requirement. Although vacuum permeation results in a lower total energy requirement, membrane area is significantly larger in comparison to feed compression configurations [50].

Recently, Brunetti et al. [51] developed a general procedure to evaluate the tradeoff relationship between CO2 recovery and purity for binary separations between CO2 and

N2 in a single stage membrane configuration. Their analysis examined a range of membrane selectivities as well as feed and operating conditions. While higher feed to permeate pressure ratio and higher CO2/N2 selectivity increases CO2 permeate purity and recovery, the effect is smaller for lower CO2 feed concentrations. This is due to the fact that the CO2 feed concentration is critical to produce the driving force required to meet the target values of CO2 recovery and purity. Thus, the authors concluded that for dilute

CO2 feeds a single stage membrane configuration is not viable; multistage configurations are essential to meet the separation target. Moreover, the advantages of both high permeability and high selectivity membranes can be easily realized in multi-stage configurations [52].

2.5.4 Affordable CO2 Driving Force Generation Strategies in Membrane Processes for

Post-Combustions Applications

Higher-pressure ratio operation can be achieved by either using a larger feed compressor to increase the feed pressure or a vacuum pump to reduce the permeate pressure. Ho et al. [5] compared the economic benefits of permeate vacuum versus feed compression to generate the required feed-to-permeate pressure ratio across the membrane. Feed compression requires compression of both CO2 and the other flue gas components (primarily N2). The energy put into the other components is lost upon expansion of the retentate as it leaves the module. The use of a turbo-expander to recover the energy of expansion can reduce the energy loss. Conversely, permeate vacuum puts energy in to the gas that permeates across the membrane, which primarily is CO2, and reduces the energy put into the other flue gas components during separation. This can reduce the total energy requirement. However, the required membrane area goes up relative to the use of feed compression as gas fluxes (permeation rate per unit membrane area) are directly proportional to feed pressure. To maximize the economic benefits of permeate vacuum, Merkel et al. [4] proposed using a permeate pressure of 0.2 bar – the lowest practical pressure due to vacuum pump design constraints.

According to Ho et al. [5], even for very high pressure ratios, increasing membrane permeability and selectivity only slightly reduces the overall capture cost. While they proposed that affordable capture cost can be achieved by reducing the pressure driving force as membrane module costs account for less than 10% of the total capture cost, this is true only for higher CO2/N2 selectivities. As pointed out previously, the Robeson plot

[3] indicates use of a higher CO2/N2 selectivity membrane results in a concomitant decrease in CO2 permeability which increases the required membrane area and associated capital cost. Hence, increasing CO2/N2 selectivity and implementing vacuum system may not lead to the desired capture cost; unless CO2 feed partial pressure also is increased in an affordable way.

Membrane separation processes alone may not offer an economically viable option to achieve the desired targets of 90% CO2 recovery and 95% purity from post- combustion flue gas due to energy and membrane costs. Moreover, membrane systems due not produce directly the CO2 product in the compressed or liquefied state desired for transportation and storage. However, membrane processes can be used in hybrid configurations to pre-concentrate the CO2 beforehand and potentially reduce overall sequestration costs. Hybrid membrane-cryogenic process are of particular interest because of their lower energy requirements relative to amine absorption processes.

Belaissaoui et al. [7] conclude that for hybrid membrane-cryogenic in a single stage- configuration to be competitive with amine absorption technology, increasing the input

CO2 feed partial pressure is preferred over use of higher selectivity membrane materials.

This could be accomplished with internal gas recirculation in a multi-stage design configuration. Several other investigators have addressed the analysis of multi-stage membrane configurations and performed economic feasibility studies for post- combustion applications [6, 53-58].

As described previously, Membrane Technology and Research (MTR) proposed an innovative way to increase CO2 partial pressure driving force in an affordable manner by incorporating an air-feed sweep system which results in a multi-stage CO2 34

recirculation loop [4]. This process utilizes MTR’s Polaris membrane which possesses a high CO2 permeance of 1000 GPU and a CO2/N2 selectivity of 50. The high selectivity values allow production of the desired permeate CO2 purity while the high permeance reduces the required membrane area to achieve the CO2 recovery and purity targets. The proposed design is a hybrid configuration which utilizes a cryogenic liquefaction step to yield the CO2 product in the desired purity and liquid state. As shown in Figure 1-2, majority of CO2 re-circulation loop arises from the CO2-rich stream produced by sweeping the second stripping stage with the boiler feed air.

Unfortunately, use of the feed air as a sweep also leads to loss of oxygen in the stripping stage and a decrease in boiler feed oxygen concentration. Key process design variables associated with this configuration are summarized in Table 2.1.

Table 2.1 Air feed sweep system key findings [4]

Parameters Value Total module area (m2) 1,300,000 Total Parasitic Load (%) 16

Cost of Capture ($/ton CO2) 23 Oxygen concentration to boiler (%) 18

Merkel et al. [4] also emphasized that to reduce capture costs, it would be desirable to develop higher permeance materials with moderate selectivity since it would further reduce the total module area requirement; higher selectivity materials could not be utilized fully with the low pressure ratios considered for use in the process. This study

demonstrates that a two stage, air sweep hybrid system can improve process economics in two ways:

1. The CO2 recirculation loop created by the stripping stage increases the

enriching stage feed CO2 concentration without energy input through

compression or vacuum.

2. Use of the boiler feed air as a sweep in the stripping stage increases the

driving force for permeation thereby reducing the enriching stage area

requirement

Oxygen deficient combustion air could potentially reduce power plant efficiency as the adiabatic combustion temperature will decrease [10]. In order to address this problem, Scholes et al [9] proposed adding an air enrichment membrane (using Air

Products’ Prism technology) to the MTR configuration as shown in Figure 2-3. The proposed configuration compensates for loss of oxygen in the boiler feed air by increasing the feed air oxygen concentration before it is fed to the stripping stage. They report the process may be affordable with a 33% CO2 sweep concentration.

Figure 2-3: Enrichment air multistage membrane cryogenic configurations proposed by

Scholes et al. [9]

However, there are some major drawbacks associated with this configuration. The

O2/N2 selectivity is relatively low which may require excessive energy input (higher compression/vacuum operating costs) to produce the required oxygen-enriched air [59].

This cost in addition to the module area cost and increased process footprint are undesirable.

2.6 Optimization for Membrane Post-Combustion Application

The low CO2 concentration in flue gas is the major barrier to use of membrane processes in post-combustion applications. The economic viability of these processes is highly dependent on the energy required to produce the driving force for permeation

[5] through a combination of feed compression and permeate vacuum . Increasing CO2 membrane permeance reduces the required membrane area and associated capital cost while increasing CO2/N2 selectivity reduces the process energy requirement and

associated operating cost [4, 22]. However, it is not possible to increase both selectivity and permeability simultaneously due to the trade-off relationship embodied in the Robeson plot [3]. For current commercial membrane products, compression and vacuum energy costs account for the majority of the capture cost [5]. Thus, based on the existing material literature, commercialization of materials with higher CO2 permeability and moderate

[4, 60] CO2/N2 selectivity could potentially reduce the capture cost .

Apart from development of novel membrane materials with improved separation properties, improving existing process design also is essential to reduce capture costs.

According to Huang et al. [60], it is crucial for membrane developers to address the balance between operating pressure ratio and selectivity. Commercial membrane separation processes are operated with feed-to-permeate pressure ratios of 5 to 15. Within this range, higher CO2 selectivities are not expected to reduce capture costs because CO2 capture and purity are limited by the pressure ratio as discussed previously. Additionally, the optimum membrane selectivity is expected to depend on CO2 feed concentration. Due to the pressure-ratio limitation, low CO2 feed concentrations in the 10-20 mol% range will require moderate selectivities of 50-100. Higher selectivity materials may be economically viable for CO2 feed concentrations above 30 mol%.

An economically viable process design is crucially dependent on two important factors: (1) selection of optimal unit operation configuration, and (2) selection of optimal operating parameters [61]. For membrane gas separations, the selection of feasible configurations and operating parameters are subject to separation property, environmental

(i.e., CO2 capture targets) and financial constraints. Although the separation targets can be met with various staged module networks, the associated costs of these designs must 38

be determined to identify the most favorable configuration [62]. In addition to stage configuration, the tradeoff between selectivity and permeability embodied in the Robeson plot[3] necessitates a systematic optimization technique.

2.6.1 Gradient Based Optimization Method in Membrane Separations

The optimization of staged membrane processes for post combustion CO2 capture requires systematic evaluation of a number design variables on LCOE. Recent work on optimization for membrane separation applications has utilized gradient based method such as Nonlinear Programming (NLP) and Mixed Integer Non Linear Programming

(MINLP).

Bhide and Stern[63-66] adapted grid search methods to optimize membrane separations system performance in various configurations for natural gas treatment and oxygen enrichment of air. Qi and Henson [67] used NLP approaches to determine optimal operating conditions that fulfill the requirements for binary CO2/CH4 separation in natural gas treatment and enhanced oil recovery while minimizing annual processing cost. The developed membrane superstructure consists of continuous variables that represent operating conditions, as well as processing units and their interconnections.

They also assume constant membrane selectivity and permeability in their work.

In a subsequent publication, Qi and Henson[68] used a multicomponent gas permeator model to simulate membrane network superstructures in a MINLP problem to minimize the total annual processing cost for acid gas (CO2 and H2S) separations from crude natural gas mixtures. Unlike previous work, they assumed membrane area was a discrete instead of a continuous variable. Purnomo and Alpay [62] employed a successive

quadratic programming approach to optimize a membrane process for bulk air separations.

Kookos [69] introduced a novel approach to simultaneously optimize membrane properties, membrane network structure and operating parameters. In this study the membrane stage superstructure for binary air separation is formulated as a NLP problem and the Robeson upper bound is used to evaluate the trade-off between O2/N2 selectivity and O2 permeability for polymeric membrane materials. This approach identifies the optimal membrane configuration and operating parameters as well as the ideal O2/N2 selectivity and O2 permeability for specific binary air separation process application.

Recently, Scholz et al. [70] implemented MINLP algorithm to identify the most profitable membrane based biogas upgrading superstructure network. They also considered the trade-off between CO2/CH4 selectivity and CO2 permeability according to

[3] the Robeson upper bound . For this particular binary separation, the optimum CO2/CH4 selectivity is approximately 120. Ohs et al. [71] took a similar approach to evaluate optimal process configuration and operating parameters for N2 removal from gas with various feed configurations. Significant processing cost savings were identified.

[72] For post-combustion CO2 capture applications, Chowdhury et al. used a NLP approach to investigate total power requirement for multicomponent flue gas separation in hybrid membrane-absorption networks. They evaluated two possible superstructures with two different types of membrane modules with fixed CO2 permeance and CO2/N2 selectivity. Only membrane pressure ratio and total module area were considered as decision variables.

Because of the non-linear constraints that exist in multicomponent membrane permeator models with mixed boundary conditions, gradient based optimization solutions often converge to a local optimum near the starting point for the optimization search [68].

Unlike gradient based methods that require numerical derivative information, non- gradient methods such as Genetic Algorithm (GA) are relatively straightforward and potentially can identify global optimum [73].

2.6.2 Non-Gradient Based Optimization Method in Membrane Separations (Stochastic

Algorithm)

Stochastic optimization algorithms follow a stochastic path to determine the minimum or maximum of an objective function. Unlike gradient based methods, stochastic methods perform global searches of the solution space and can handle non- linear constraints flexibly. Therefore, this method could potentially generate a large number of possible solutions within the solution domain, though at the expense of longer computational times [73, 74]. Simulated Annealing (SA) and Genetic Algorithm (GA) are two common approaches to stochastic optimization.

Several investigators report the use of stochastic methods to optimize the membrane network superstructure. Uppaluri et al. [74] used the SA algorithm to optimize enriched oxygen production and hydrogen recovery from synthesis gas membrane networks. Marriott and Sorensen [73] used GA for pervaporation membrane superstructure network optimization. Chang and Hou [75] applied multi-objective GA to optimize a membrane network for oxygen enrichment. Corriou et al. [76] conducted GA optimization studies of pulsed cyclic membrane operation for CO2/H2 separation system. 41

[77] Recently, Yuan et al. evaluated N2 selective metallic membrane potential in post-combustion application for a 650-MW coal fired power plant by performing multi- objective optimization using nondominated sorting genetic algorithm II (NSGA-11) for a binary CO2 and N2 system. Total membrane area and energy consumption were considered as objective functions. Although CO2 separation targets of 90% recovery and

95% purity could be easily achieved in a single stage N2 selective membrane due to the high N2/CO2 selectivity and N2 permeability, the parasitic plant load was significant. The majority of the load came from feed compression and heating required by the high operating temperature of the N2 selective membrane. Using a CO2 selective membrane in the CO2 enriching stage of a two stage configuration reduced costs. This work did not consider the impact of other flue gas component such as O2 and water nor did it perform an economic assessment in terms of LCOE.

Chapter 3

3. Modelling Multicomponent Hollow Fiber Membrane

Gas Separation Modules and Study of Single Stage

Membrane Processes for Post-Combustion CO2

Capture.

3.1 Introduction

The greatest challenge in simulation of multicomponent hollow fiber membrane gas separation modules in a counter-current flow configuration is development of a robust and stable algorithm for solution of the governing mass balance equations. In counter- current flow, the boundary conditions for these differential equations are specified at both ends of the module. Such split boundary conditions necessitate the use of an iterative procedure to obtain a solution. While significant efforts have been reported to overcome this challenge, an approach with general applicability remains elusive especially for separations involving gas mixtures with a broad range of selectivity. Such problems often lead to large concentration gradients that are difficult to resolve numerically. Therefore, in this chapter a new methodology is proposed to solve the mass balances. The effect of module non-idealities such as temperature drop, pressure drop and temperature dependence of permeation will be incorporated. The model will be solved based on the following assumptions:

1) Gas mixtures behave ideally

2) Steady-state operation

3) Lumen pressure drop is calculated using the Hagen-Poiseuille equation for

compressible flows

4) For non-isothermal operation, temperature of the permeate and retentate are

identical, due to high heat transfer rates across hollow fibers, but the temperature

can vary along the length of the module due to Joule-Thomson effects

5) Gas permeability follows an Arrhenius temperature dependence

6) Gas permeability is independent of gas pressure, i.e., dual mode effects are

negligible

7) Negligible axial diffusion

8) All fibers possess identical physical and transport properties

9) Concentration polarization is negligible

The solution method in this work is similar to that of Coker et al. [35] which is based on a stages in series approximation to transform the governing differential mass balances into set a of coupled non-linear algebraic equations. Unlike Coker, a direct substitution algorithm is used to solve the equations instead of the Thomas algorithm.

Past experience indicates this has the potential to make convergence less sensitive to the initial guess and reduce computational times. Additionally, to improve convergence, the cross-flow configuration solution is used as the initial guess for the counter-current simulation.

In the second part of this chapter, the developed multicomponent membrane gas

permeator is used to study a single stage membrane process for carbon capture. While

a single stage membrane separation process may not offer an economically viable

option to achieve the desired targets of 90% CO2 recovery and 95% purity from post-

combustion flue gas due to energy and membrane costs[4], it can be used in hybrid

configurations with other separation techniques such as absorption and cryogenics to

pre-concentrate the CO2 beforehand and potentially reduce overall sequestration

[7] costs . In this work, the flue gas is taken to be a multicomponent mixture of CO2, N2,

O2 and water. Membrane properties are taken from the Robeson upper bound

relationship describing the tradeoff relation between CO2/N2 selectivity and CO2

permeability. The effect of CO2/N2 selectivity and other process variables such as

membrane area, feed pressure and CO2 feed mole fraction in the flue gas is evaluated

for carbon capture from a 550 MWh coal fired power plant.

3.2 Cross-Flow Solution Strategies for Isothermal Operation and Constant

Permeance

The lumen-side mass balances are solved by dividing each fiber into N perfectly mixed stages as shown in Figure 3-1. The molar permeation rate for component i leaving j stage, mi,j in (kmol/s) is given by Equation (3-1):

, = , (,, − ,, ) (3-1) 2 Where Qi,i is the membrane permeance (kmol/s.m .Pa) of component i, PR is the retentate pressure (Pa), PP is the permeate pressure (Pa), xi,j is the retentate mole fraction, yi,j is the permeate mole fraction and ΔAm is the active area per stage given by:

= (3-2)

Where L is the active (or permeating length) of the hollow fibers in the module, Nf is the

number of fibers, and Ro is the hollow fiber outer radius (m). For non-isothermal

conditions, the temperature dependence of the permeance is calculated from the

Arrhenius relationship:

, , =, − (3-3) ,

where Qo,i is Arrhenius pre-exponential factor, Eact, i is the permeation activation energy

for component i and TR,j is the temperature of at stage j which is identical for the permeate

and retentate.

Feed:Rf, xf ,i,Pf ,Tf Rj ,xi,j RN-1,x i,N-1 RN,x i,N R1, xi,1 R j-1, xi,j-1 1 … j N …

P1, yi,1 Pj,yi,j PN, yi,N Figure 3-1 Cross- flow module configurations divided into N stages.

The retentate and permeate flow rates of component i leaving stage j (kmol/s) are

given by R i,j and Pi,j, respectively. Species mole fractions, component flow rate and total

rates are related as follows:

, =, (3-4)

, =, (3-5)

Hence, the total retentate and permeate flow rates (kmol/s) leaving stage j are the sum of

component flow rates:

= ∑ , (3-6)

= ∑ , = − (3-7) Where NC is the number of components. The permeate mole fraction in cross flow is given by [26]:

, (,,, ) , = (3-8) ∑ , (,,, ) Using the relation in Equation (3-5), component molar flow rates in the permeate can be determined from:

, = , (,, −, ) (3-9)

In cross-flow, the retentate flow rate of component i leaving stage j is given by:

, =, −, (3-10)

3.3 Counter-Current Solution Strategies for Isothermal Operation and Constant

Permeance

Similar to cross-flow the lumen-side mass balances are solved by dividing each fiber into N perfectly mixed stages as shown in Figure 3-2.

Figure 3-2: Counter-current module configurations divided into N stages

The initialization method begins at stage j=1 with the following expressions:

= (3-11)

, = (3-12)

= (3-13)

= (3-14)

, = (3-15)

= (3-16)

Where Rf is the feed flow rate (kmol/s), Pf is the feed pressure (Pa), Tf is the feed temperature, Rs is the sweep flow rate (kmol/s) and Ts is the sweep temperature. In counter-current flow, the component flow rates leaving stage j are given by Equations (3-

17) and (3-18), respectively.

, = ,+, (,, − , ) (3-17)

, = , −(, − ,) (3-18)

The total flow rate for permeate and retentate sides is shown in equations (3-19) and (3-

20) respectively.

= + ∑ , (,, − ,, ) (3-19)

= − ∑ , (,, − ,, ) (3-20)

Molar compositions and flows obtained from the cross flow configuration are used as the initial guess for Equations (3-17) - (3-20). The solution procedure for counter-current model at isothermal conditions and constant permeance is illustrated in Figure 3-3. A direct substitution iterative algorithm is used to solve Equations (3-1) to (3-20) and

(3-17)-(3-20) for each stage. The iterative procedure is stopped when the difference between old and new values is less than some prescribed tolerance

Figure 3-3: Solution procedure for counter-current configurations at isothermal conditions

The lumen pressure drop is calculated using the Hagen-Poiseuille equation [78] by substituting the product of molar flow rate and molar density for the volumetric flow rate and using the ideal gas law to calculate molar density

, =− (3-21)

Where z is the distance along the module, η is the gas mixture viscosity, Rg is the ideal gas constant, T is the gas mixture temperature, ri is the fiber inner radius and Nf is the number of fibers. The integral of this equation for a single stage is given by [79]:

, = , − (3-22) Where L is the length of the stage (i.e., active fiber length/N).

3.4 Counter-Current Configuration Solution Strategies for Non-Isothermal

Conditions and Temperature Dependent Permeance

Joule-Thompson effects which result in non-isothermal operation are included in the simulation following the approach of Coker et al. [36]. During the Joule-Thompson expansion that occurs upon gas permeation from high to low pressure, gas pressure and specific volume change but enthalpy remains constant. The following assumptions are used to calculate thermal changes:

1) Pressure-volume-temperature (PVT) properties are described by the Redlich-

Kwong equation of state [80]

2) The module operates adiabatically

3) Axial convective heat transfer dominates axial conductive heat transfer except at

the sealed end of the hollow fibers (if a sweep is not used)

4) Effects of viscous dissipation and reversible work are negligible

5) No condensation occurs in the expansion-driven cooling process

The direct substitution iterative procedure described for isothermal operation is readily adapted for non-isothermal operation. To address convergence issues with non-isothermal operation, a damping factor is introduced to control the temperature change that occurs during each iteration. The energy balance for the retentate-side of stage j is given by

Equation (3-23) and illustrated in Figure 3-4

Figure 3- 4 Temperature and enthalpy variation for stage j.

= + ∑ ,∆,, −,, − (3-23)

R R Where H j-1 is the enthalpy of the retentate entering stage j from stage j-1, H j is the enthalpy of the retentate leaving stage j and Qmem is the net rate of conductive heat flow across the hollow fiber membrane into the stage j. Writing the permeate-side energy balance and adding to the retentate balance gives:

+ = + (3-24)

P P Where H j+1 is the permeate enthalpy entering stage j from stage j+1, and H j is the permeate enthalpy leaving stage j. The enthalpies can be calculated as follows:

, = − (3-25)

, = − (3-26)

, = − (3-27)

, = − (3-28)

ideal,P ideal,P ideal,R ideal,R Where H j+1, H j, H j-1 and H j are the ideal gas enthalpies (J/kmol) of the permeate streams entering and leaving stage j and the retentate streams entering and

εP εP εR εR leaving stage j, respectively. j+1, j, j-1 and j and are enthalpy departure functions (J/kmol) of the permeate streams entering and leaving stage j and retentate streams entering and leaving stage j, respectively, Using the inlet retentate temperature as the reference state, the enthalpies can be calculated from:

= 0− (3-29)

= , − − (3-30)

= , − − (3-31)

= , − − (3-32)

Where the average ideal gas heat capacities of the gas mixture (J/(kmol K)) are represented by CP and the subscripts indicate the stage and stream (i.e., retentate or permeate). The heat capacities for the permeate stream leaving stage j+1 and entering

P [81] stage j , C P,,j+1, can be calculated from the following

, , , = ∑ ∑ − (3-33)

Where A l,i is the lth coefficient in the power-series representation of the ideal gas heat capacity of component i. The Redlich-Kwong equation of state will be used to calculate the enthalpy departure functions.

= − + . 1+ (3-34)

= − + . 1+ (3-35)

= − + . 1+ (3-36)

= − + . 1+ (3-37)

R R P P Where V j-1, V j, V j+1, and V j are the specific volumes of the retentate streams entering and leaving stage j and the specific volumes of the permeate streams entering and leaving stage j respectively, The Redlich-Kwong mixture coefficient for each stream is represented by a and b.

By combining and rearranging the above equations, the temperature of stage j can be determined as:

, , = + (3-38) ,,,,

The solution for non-isothermal counter-current configuration is illustrated in Figure 3-5.

Figure 3-5:Solution procedure for non-isothermal counter-current flow configurations

3.5 Multicomponent Gas Membrane Permeator Isothermal Model Validations

In order to demonstrate the applicability of the developed model for multicomponent gas separations in membrane-based post combustion applications, the

[29] model is validated with the experimental data reported by Pan for CO2 recovery from sour natural gas. Stage cut is defined as ratio of permeate flow rate to total feed flow rate.

Figure 3-6 illustrates the how the composition of each component in the permeate stream depends on stage cut. The results illustrate the typical tradeoff between stage cut and purity in membrane enrichment: the concentration of the most permeable species (the desired product) asymptotically approaches a maximum at low stage cuts and decreases monotonically as stage cut increases. As can be seen, the simulation results agree reasonably well with experimental results. The CO2 purity decreases from a maximum of

~0.95 with increasing stage cut, so increasing CO2 permeate concentration comes at the expense of lower CO2 recovery.

1.00 0.30 Target Component Remaining Component CO2 0.95 0.25

CH4 0.90 0.20 0.85 0.15

0.80 permeate molefraction 8 H 0.10 3 permeate molefraction ,C 2 0.75 6

C2H6 CO ,CH 0.70 0.05 4 CH C3H8 0.65 0.00 0.35 0.45 0.55 0.65 Stage Cut

Figure 3-6: Model validation with Pan [29] work. The lines represent model simulation result while all the markers represent the experimental data from Pan. Feed pressure is

35.28 bar with the permeate pressure of 0.93 bar Feed composition is 48.5% CO2, 27.9

CH4, 16.26% C2H6 and 7.34% C3H8. Gas permeances (GPU) are: 40.05 CO2, 1.11 CH4,

0.31 C2H6 and 0.06 C2H8

3.6 Multicomponent Gas Membrane Permeator at Non-Isothermal Conditions

The non-isothermal model also was validated with the results reported by Coker

[36] et al. for CO2 recovery from natural gas separations. The temperature changes from the feed to the retentate product end for binary and multicomponent scenarios as a function of stage cut (the ratio of permeate product flow rate to feed flow rate) are presented in Figure 3-7. The temperature changes result from Joule-Thompson cooling as this process is conducted at high feed to permeate pressure ratio. The temperature

changes increase with the CO2 recovery rate. The simulation results are in good agreement with the reported values. The differences between the multicomponent and pseudo binary simulations are small suggesting a full multicomponent simulation is not necessary for this application. This conclusion is not true in general especially when components are present that could condense upon cooling. Since lower feed to permeate pressure ratios are used in membrane post-combustion CO2 capture processes, temperature drops between retentate and feed are negligible in this work.

40 Cokers

35 Binary Composition (K) 30 Multicomponent Composition retentate 25 -T

feed 20 T

5 0.1 0.2 0.3 0.4 0.5 0.6 Stage cut

Figure 3-7 Model validation with Coker work [36]. Feed binary composition comprised of

40% CO2 and 60% CH4.Multicomponent mixture comprised of 40.00% CO2, 55.89%

CH4, 1.72% C2H6 and 0.65% C3H8. The feed temperature is 50° C; feed pressure is 850 psig with permeate pressure of 10 psig. Permeances (GPU): 22.7 CO2, 0.7 CH4, 4.4 N2

0.75, C2H6 and 0.0009 C3H8 respectively.

3.7 Parametric Study for Single Stage Membrane CO2 Enrichment Stage for Post-

Combustion Application

This section evaluates the effect of CO2/N2 selectivity on CO2 recovery from flue gas in a single stage configuration as shown Figure 3-8. The relationships between

CO2/N2 selectivity and other process variables such as area, feed pressure and CO2 feed mole fraction in flue gas on CO2 capture are discussed. The key performances metrics are CO2 permeate recovery, CO2 purity, and plant parasitic load. While such a configuration is unlikely to meet economic targets, it might be combined with separation unit operations to do so.

Enriched CO2 permeate S1 S6 S7 Flue gas feed S2 (S5) CO2 Capture B2 System B6 B1 B3 B5

B4 S3 Lean CO2-vent (S4)

Figure 3-8: Single stage membrane process with feed compression (B1), expander (B4) and permeate vacuum (B5) prior to integration with other separation unit operations.

Membrane separation is considered as CO2 enrichment prior sending to other CO2 capture method to complete separation target of 90% CO2 recovery with 95% purity.

In this process, the incoming flue gas feed stream is assumed to be comprised of a multicomponent mixture of CO2, N2, O2 and water at atmospheric pressure. It is sent to 59

compressor (B1) prior to entering the membrane separation unit (B3). The flue gas feed stream conditions are reported in Table 3.1. A vacuum pump (B5) is used to reduce the permeate pressure to 0.2 bar to increase the CO2 permeation driving force. The retentate stream (S3) is sent through expander (B4) for energy recovery before venting to the atmosphere. The product CO2 purity is obtained from the CO2 concentration in permeate stream (S5) while CO2 recovery is calculated as the flow rate of CO2 in S5 divided by the flow rate of CO2 in the feed gas. Because of the trade-off relation between CO2/N2 selectivity and CO2 permeance, the CO2 permeance used in the simulations is calculated from the CO2/N2 selectivity using the Robeson upper bound relationship. The details of this calculation are discussed in Chapter 5.Net permeation direction for each gas component in membrane module according to component permeabilty is illustrated in

Appendix A. The total power requirement is calculated by adding the feed compressor

(B1) and permeate vacuum (B5) energy requirements and subtracting the energy recovered in the expander (B4). Plant parasitic load is calculated as the ratio of the energy requirement to the total plant output of 550 MWh.

Table 3.1: Flue gas conditions considered in this study

Variable Value Flue gas flow rate (MMSCFD) 1514 Flue gas temperature (°C) 51.67 Flue gas pressure (bar) 1.01 Flue gas composition (mol %)

CO2 13.9

N2 73.7

O2 3.1 Water 9.0

3.8 Area and CO2/N2 Variation Study at Fixed Feed and Permeate Pressure for

Single Stage Membrane CO2 Enrichment Process.

Figure 3-9(a) and (b) represents the membrane area and CO2/N2 variation with the CO2 permeate purity and recovery at fixed pressure of 2 bar and permeate pressure of

0.2 bar. Because of the tradeoff relation between CO2/N2 selectivity and CO2 permeance,

CO2 recovery decreases as CO2/N2 selectivity increases for a fixed membrane area.

Conversely, increasing membrane area increases CO2 recovery. Although using a low

CO2/N2 selectivity membrane (from 10-25) results in high CO2 recovery, because of the high CO2 permeance, the permeate is of low purity which will entail the use of additional separation steps to reach the target purity.

The highest possible CO2 purity achievable for the range of membrane area and selectivity considered is ~40-44% for a moderate CO2/N2 selectivity of 35-60. The associated CO2 recovery ranges broadly from ~20-70%. Additionally, the parasitic plant 61

load ranges from ~5-10%. These observations suggest that while a single stage may not be able to achieve carbon capture targets, significant concentration enhancement and recovery can be achieved in a single stage which could be used in combination with another stage or other separation unit operation to reach the targets.

5 4 . . 4 0 . 9 0 . 8 0 . 4 0 . 0 0 ) ) 2 2 1 .3 0 1 Area (m Area 5 Area (m .3 5 0

. 5 .2 2 0 . 0 0 .7 .6 .5 0 0 0

8 5 6 3 2

. . .4 . . .

0 0 0 0 0 0

0 ) ) 0.7 2 2

0 .1 0

2 6 . . 0 Area (m Area

Area Area (m 0

Figure 3-9:Impact of membrane area and CO2/N2 selectivity for the single stage process in Figure 3-8 on (a) CO2 permeate purity (b) CO2 permeate recovery (c) stage cut

(permeate stream flow rate S5/ feed flow rate S2), and (d) parasitic load. Feed pressure is fixed at 2 bar with fixed permeate pressure of 0.2 bar. CO2 permeance is calculated based on Robeson upper bound relation by assuming membrane effective thickness of 0.1 microns. 62

3.9 Pressure Ratio and CO2/N2 Variation Study at Fixed Membrane Area for

Single Stage Membrane as CO2 Enrichment Step.

Figure 3-10 (a) and (b) illustrate how CO2 purity and recovery change with feed

2 pressure and CO2/N2 selectivity for a fixed membrane area of 100,000 m and permeate pressure of 0.2 bar. Use of a higher feed pressure has a relatively small effect on CO2 purity for low to moderate CO2/N2 selectivities although CO2 recovery can increase significantly. For moderate to high CO2/N2 selectivities, increasing the feed pressure can reduce purity slightly, especially for the highest values considered, while increasing recovery.

The highest permeate purities of 40-45% are accompanied by CO2 recovery values of ~20-70% and parasitic loads of 5-15% similar to the results in Figure 3-9. This provides further evidence of the viability of using a single stage with one or more additional separation unit operations to achieve carbon capture targets.

3 5

5 4 0. 9 8 7 . 4 6 5 4 3 ......

0 0 0 0 0 0 0 0 0 2 0 .

. 0

5 5

1 1 2 5 . . 3 4 . . 3 . 0

0 0.2 0 . Feed Pressure Feed (bar) Pressure 0 0

Feed Pressure Feed (bar) Pressure 3 0 0.

.1 5 6 0 . 2 5 4 3 2 2 . 5 . . . . . 0 0 0 1 0 0 0 0 . 0

0 . 6

1 0. .1

0 Feed (bar) Pressure Feed Pressure Feed (bar) Pressure

Figure 3-10: Impact of feed pressure and CO2/N2 for the single stage counter-current stage in Figure 3-8 on (a) CO2 permeate purity (b) CO2 permeate recovery (c) stage cut

(permeate stream flow rate S5/ feed flow rate S2) (d) parasitic load. Membrane area is

2 fixe fixed at 100,000 m with fixed permeate pressure of 0.2 bar. CO2 permeance is calculated based on Robeson upper bound relation by assuming membrane effective thickness of 0.1 microns.

3.10 CO2 Mole Fraction Feed and CO2/N2 Variation Study at Fixed Membrane

Area for Single Stage Membrane as CO2 Enrichment Step.

5 5 5 5 . . 9 8 7 6 5 4 3 2 4 . 0 0 ...... 0 .4 0 0 0 0 0 0 0 0 0

35 0 0. .

4 0 0 5 0 . . . 3 2 3 5 5 0

mole fraction mole feed fraction . 4 feed mole fraction 2 2 0 0 .1 0.2 .1 5 CO CO

. 5 4 3 2 1 8 6 4 2 1 8 6 2 0 . . . . . 0 1 1 1 1 0 0 . 0 0 0. 0 . . . . 0 . . 6 0 0 0 0 0 0 mole fraction mole feed fraction mole fraction feed mole fraction 2 2 CO CO

Membrane area is fixed at 100,000 m2 with fixed feed pressure of 2 bar and permeate pressure of 0.2 bar. CO2 permeance is calculated based on Robeson upper bound relation by assuming membrane effective thickness of 0.1 microns.

Figure 3-11 (a) indicates how CO2 permeate purity depends on feed CO2 mole

2 fraction and CO2/N2 selectivity for a fixed membrane area of 100,000 m , feed pressure of 2 bar, and permeate pressure of 0.2 bar. Increasing the CO2 mole fraction results in significant improvement of CO2 purity in all cases. The greatest change occurs for moderate CO2/N2 selectivity values of 40-75. Increasing CO2 mole fraction has little effect on CO2 recovery.

Plant parasitic load is relatively insensitive to feed concentration at low selectivity values. However, at higher values, the load can increase significantly as stage cut also increases. The highest permeate purities are produced with recoveries of ~40-70% and parasitic loads of 8-15% similar to the results in the previous two sections

3.11 Conclusions

In this section, a non-isothermal hollow fiber membrane module model is presented. A procedure for solving the model equations based on dividing the module into a series of well-mixed tanks is described which relies upon a direct substitution algorithm to solve the resulting non-linear algebraic equations

The model is validated by comparing predictions with previously reported experimental and simulations results. In all cases, agreement is good. Although thermal effects arising from Joule-Thompson cooling are captured well, thermal changes are not expected to be significant in post-combustion carbon capture as the pressure differences are small enough to assume isothermal operation.

A parametric study of the operation of a single stage is reported to provide an indication of the effect of module design and operating variables on performance. While

high CO2 recovery is possible with a low CO2/N2 selectivity membrane, CO2 permeate purity is unacceptably low. Higher selectivity membranes increase the purity but the target of 95% CO2 cannot be reached. Thus, while a single stage cannot achieve capture targets, it could be a useful step in a multi-stage membrane system or in combination with other separation unit operations. Of particular importance is the significant enhancement in performance that accompanies an increase in the CO2 feed partial pressure which can be accomplished by recycling CO2 in the separation train as described in the next chapter.

The highest possible CO2 maximum purity depends on the operating pressure ratio, stage cut and CO2 feed partial pressure. The analysis reported in this chapter indicates that the most significant concentration and recovery is found with a CO2/N2 selectivity in the range of 40-75. However, determination of the optimum selectivity, as well as process operating conditions, will require optimization with one or more additional separation unit operations to achieve capture targets. Such an optimization is described in Chapter 5 for membrane-cryogenic hybrid.

Chapter 4

4. Staged Membrane Configurations for Post-

Combustion CO2 Capture

4.1 Introduction

The major challenge for membranes in post-combustion CO2 capture is the low

CO2 partial pressure and high flow rate of the flue gas. Use of high CO2 /N2 selectivity membranes can increase the CO2 permeate purity with lower energy costs. However, the

[3] Robeson upper bound dictates that use of a higher CO2/N2 selectivity membrane will lead to a concomitant decrease in CO2 permeability which increases the required membrane area and associated capital cost. Conversely, the usage of high CO2 permeance membranes with low CO2/N2 selectivity will reduce the associated membrane capital cost at the expense of higher energy costs. To overcome the permeate purity constraints that exist for a single stage membrane process as described in the previous chapter, a multistage design is essential which increases the CO2 feed partial pressure driving force by

[4] creating a CO2 recycle loop . Designing an economically viable stage configuration is strongly dependent on the selection of appropriate pressure ratio and stage-cut. The stage- cut and pressure ratio are the most important parameters towards affordable driving force generation.

In this chapter, two super-structures for staged membrane capture processes with final cryogenic purification that accommodate a wide range of CO2/N2 selectivity along the Robeson upper bound are discussed. The superstructures possess two types of CO2 recycle loops: 1) through the boiler and 2) after the boiler. The post-boiler recycle loop avoids undesirable reduction in O2 concentration. The tradeoff between capital and operating costs is evaluated by determined the LCOE of various embodiments of the superstructure to identify the optimal design.

4.2 Process Descriptions and Economic Evaluations

This section describes the performance and economic evaluation of novel multistage hybrid membrane - cryogenic configurations retrofitted for an existing 550 MW

(net) subcritical pulverized coal-fired power plant. The base plant derating due to inefficiency and internal power consumption is assumed to be approximately 22 MW.

The new configurations are designed to achieve 90% CO2 recovery and produce a 95% purity (or greater) liquid CO2 stream to meet US DOE CCS requirements.

It is assumed that trace components such as particulate matter and SO2 are removed from the flue gas through an electrostatic precipitator (ESP) and lime-based

[82] desulfurization (FGD) prior to entering the CO2 capture system . Thus, the entering flue gas is comprised of four major components: CO2, N2, O2 and water. The base cost of electricity (COE) price without CCS system is assumed at $ 53.96/MWh-net.

The economic metric used in this work is LCOE, which is defined as cost of electricity per MWh that must be charged to recoup all expenses plus a desired rate of return[23]. The LCOE calculation used here is based on the guidelines proposed in the

literature [20, 23]. The plant life is 25 years with a capacity of 85% and interest rate of

10.30%. Membrane module costs are assumed to be $50/m2. The compressor and expander efficiencies are assumed to be0.85 while the vacuum pump efficiency is assumed to be 0.75. Furthermore, the net electricity produced and sold each year is assumed constant over the life of the plant as well as constant FCF, fuel and O&M costs.

General inflation and real escalation rates also are assumed zero. Labor costs are calculated assuming a 5 day and 10 hours per day work week. With these assumptions, the LCOE is given by:

()() = + +()() (4-1) ()(∗) where TCR represents Total Capital Requirement (including Bare Erected Cost (BEC),

Engineering, Procurement & Construction Cost (EPC), Total Plant Cost (TPC), Total

Overnight Cost (TOC), Contingencies and other associated owner’s costs), FCF is the fixed charge factor, FOM ($/year) is Fixed O&M, VOM ($/MWh) is Variable O&M, MW is net plant power output (MW), CF is plant capacity factor, HR is net power plant heat rate (MJ/MWh), and FC is fuel cost per unit of energy ($/MJ).

TCR in this system consists of all costs associated with the Process Facilities

Capacities (PFC) as well as indirect expenses such as the general facilities cost, engineering and home office fees, contingencies and other associated owner costs. The

PFC is comprised of all direct costs from purchasing and installing process equipment such as membrane modules and frames, compressors, expanders, vacuum pump, heat exchangers, CO2 compression cost and CO2 liquefaction facilities. All other indirect costs are assumed to be given as a percent of PFC. FOM consists of operating labor,

maintenance cost as well as administrative and support labor cost while VOM consists of membrane replacement cost, electricity and other utilities annually. Membrane replacement cost is assumed to be $10/m2 with a five-year lifetime. FCF is the parameter that converts the total capital value to a uniform annual amount [23] and can be calculated as:

() = (4-2) () Where r is the interest rate or discount rate and T is the economic life of the plant.

Additionally, since the LCOE calculation includes all costs incurred by the CCS facilities investment, CO2 product transport and storage (T&S) is assumed $3/ton CO2 in this work. All other treated flue gas conditions and base plant basic data are summarized in

Table 4.1. A sample on LCOE calculation is provided in Appendix B.

Table 4.1: Base power plant basic data and flue gas conditions considered in this study

Variable Value Plant type Subcritical pulverized coal Coal type Mid-western bituminous coal Cooling type Wet tower Gross/Net electrical output (MW) 571.54/550.00 Net plant efficiency (%) 35.01 Operating time (hour/year) 7446 Coal cost ($/MMBtu) 1.80 Main steam pressure (bar) 175 Main steam temperature (°C) 538 Air feed sweep flow rate (MMSCFD) 1300 Flue gas flow rate (MMSCFD) 1514 Flue gas temperature (°C) 51.67 Flue gas pressure (bar) 1.01 Flue gas composition (mol %)

CO2 13.9

N2 73.7

O2 3.1 Water 9.0

The simulation work is made at steady-state and isothermal conditions. The simulations are conducted using the Aspen Plus simulation software version 8.4. The

Soave-Redlich-Kwong (SRK)[80] equation of state is used to evaluate the multiphase system over the wide range of temperature and pressure in the process. The developed gas permeation model in the previous section is interfaced into the Aspen Plus user unit operation model[83].

Two membrane polymeric materials are considered for the membrane CO2 capture system which span a broad range permeance and selectivity:

a) Polydimethylsiloxane (PDMS) membrane with permeance of 15,000 GPU and

CO2/N2 selectivity of 15. The permeance of PDMS is calculated based on an

intrinsic permeability of 3250 barrer[84] and the assumption that a membrane can

be fabricated with a 0.2 µm effective skin thickness. The O2/N2 on the other hand

is assumed to be 2.

b) Polaris membrane with permeance of 1,000 GPU and CO2/N2 selectivity of 50.

The O2 permeance value used in assumed 50 GPU.

The water permeance in both membranes is assumed to be 10,000 GPU.

4.3 Boiler CO2 Recycle Loop Configuration

The first configuration considered here is based on the air feed sweep system

[4] proposed by MTR (described previously in Chapter 1) which results in elevated CO2 feed partial pressure in the feed to the first enriching stage. The air feed sweep system results in an internal CO2 recycle loop. The boiler CO2 recycle loop configuration comprised of a multi-stage membrane with final cryogenic process is depicted in Figure

4-1. The process is operated under the same conditions as the MTR process where feed pressure is 2 bar and permeate pressure is 0.2 bar in the first enriching module [4].

However, unlike the MTR configuration, an additional enriching module (B14) is used.

The second enriching module will enable use of lower CO2/N2 selectivity membranes to achieve the 90% CO2 recovery and 95%+ purity target.

In this scheme, the boiler air feed stream is used as a permeate sweep in the counter-current module (B8) that serves as a CO2 stripping stage. The exiting permeate is a mixture of the air feed and the permeate from the stripping stage (stream S12) and is sent to the boiler. This results in an elevation of the CO2 partial pressure (from 13% to

22%) in the feed to the first enriching stage. The feed air unfortunately loses oxygen in the stripping stage so the stream sent to the boiler is oxygen deficient. While this is of concern, some reduction in oxygen concentration is considered acceptable.

The first CO2 recycle loop is the permeate stream (S12) from the stripping stage that passes through the boiler and returns as the feed to the first enriching stage. The retentate stream from the stripping module (S11) on the other hand is sent through an expander for energy recovery before venting out to the atmosphere. This stream must contain no more than 10% of the CO2 produced by combustion in the boiler to meet capture targets. A permeate vacuum of 0.2 bar is maintained in both enriching stages to increase the permeation driving force. The CO2 enriched permeate from the second enriching stage (S18) passes through a flash separator to remove water in S22 and enters the multistage compressors trains (B20 and B22) required to pressurize the stream before cooling to -25 °C to produce a liquid of the target purity. The liquid CO2 is removed in flash B25.

The retentate stream from the second enriching module (S17) is recycled back to the first enriching stage feed to create an additional internal CO2 recirculation loop. The overhead product from the cryogenic flash (S32) is sent to the smallest cryogenic membrane module(B28). The permeate (S34) from this module is sent to the start of the compressor train to create another internal CO2 recirculation. The retentate stream from 74

this membrane stage expanded for energy recovery before being sent back to the feed for the first enriching stage along with the retentate from the second enriching stage.

O2 deficient air (S12)

B2 B3 S5

B4 S1 S3 S6 S10 Air feed

B1 S2 B8 S4 S7 S8 Coal B5 B6 B7 Enriched B9 2 CO S11 Lean CO2-vent permeate (S9) S14 S13 S15 S16 S37 B10 B11 B12 B13 S17 Enriched CO2 permeate B14 (S18) S19 S20 S21 S34 B19 S24 B28 B15 B16 B17

S33 S32 B30 B27 S25 S22 S30 S29 S28 S27 S26 S35 S36 B24 B23 B22 B21 B20 B29 B25 B18 Liq CO2 S31 S23

B26

4.4 Post-Boiler CO2 Recycle Loop Configuration

While boiler-CO2 recycle loop configurations elevate CO2 partial pressure with no additional compression cost, the accompanying loss of oxygen could potentially reduce boiler efficiency in the long term. Thus, another option to make hybrid multistage membrane cryogenic processes viable in post-combustion applications is to eliminate the stripping stage as shown in Figure 4-2. The most striking difference in this design is that the retentate stream from the second enriching module (B13) is vented to the atmosphere in S15 instead of re-circulating to the first enriching stage feed to reduce the amount of

N2 circulation. It is anticipated that N2 reduction in S16 will lower downstream compression energy requirement. Hence, this configuration leads to lower CO2 feed partial pressures in the first enriching stage since the CO2 recycle to the first enriching stage consists only of the relatively low flow retentate stream from the cryogenic membrane module (B28) in S35.

Air feed

B2 B3 S5

B4 S1 S3 S6 S9 Lean CO2-vent B8 B1 S2 S4 S7 S8 Coal B5 B6 B7 Enriched CO2 S15 Lean CO2-vent permeate (S10) S11 S12 S13 S14 B14 B9 B10 B11 B12 B13 S35 Enriched CO2 permeate (S16) S17 S18 S19 B16 B15 B17

B19 S32 S22

S31 S30 B30 S23 B28 B27 S20 S28 S27 S26 S25 S24 S34 S33 B24 B23 B22 B21 B20 B18 B25 Liq CO2 S29 S21 B29 B26

Figure 4-2: Staged membrane-cryogenic process without air feed sweep system (Post- boiler CO2 recycle loop). Stripping stage is eliminated to prevent boiler O2 loss. The additional enriching module ensures low CO2/N2 membrane meet the target recovery of

90% with 995+ CO2 purity

4.5 Stage Cut Impact Variation Impact for Air Feed Sweep System Configuration

The impact of enriching module stage cut, the ratio of permeate flow rate from each enriching module of M1 and M3 to feed flow rate, on total required module area for

PDMS (CO2/N2 selectivity 15) and Polaris (CO2/N2 selectivity 50) membranes in the stage configuration of Figure 4-1 is illustrated in Figure 4-3(a) and (b) respectively. The stage cut ranges shown correspond to ranges required to achieve 90% CO2 capture and

95% purity.

Stage cut values for the first enriching stage (M1) are much smaller for the Polaris membrane than the PDMS membrane. This reflects the higher purity permeate produced by the Polaris membrane which allows 90% recovery with a lower flow rate. The stage cut values for the second enriching stage are much higher for the Polaris membrane than for the PDMS membrane. Since the Polaris membrane produces a relatively high purity permeate in the first stage, less enrichment is need in the second so stage cuts can be higher. The need for significant additional enrichment in the second stage with the PDMS membrane necessitates operating with lower stage cuts. Since the Polaris membrane has a much lower CO2 permeance than PDMS, the total required module area (1.4 to 3.6 million m2) is approximately 10 times larger than for the PDMS membrane.

Figure 4-4 (a) and (b) illustrates the impact of enriching stage cut on total plant parasitic load for PDMS and Polaris, respectively. While higher CO2 permeance and lower CO2/N2 selectivity for PDMS reduce the total module membrane area requirement, the minimum plant parasitic load is 38% at the lowest operating stage cut which is approximately double the value for the Polaris membrane (as well as the value for the MTR air feed sweep configuration). This increase is due to a higher feed flow rate to the second stage which requires recompression of the permeate from the first stage. Because of the additional compression required for the second enriching stage, the parasitic load for the

Polaris membrane is slightly higher than that reported for the MTR air feed sweep configuration [4].

Figure 4-1

4.6 Stage Cut Impact Variation of Air Feed Sweep System Configuration Towards

LCOE

Although the air feed sweep configuration increases the CO2 feed partial with virtually no additional energy costs, the increase comes at the cost of a reduction in the oxygen content of the boiler feed air in stream S12 which potentially can reduce the boiler adiabatic temperature and boiler efficiency. The boiler oxygen concentration variation and LCOE for both the PDMS and Polaris membranes are illustrated in Figure

4.5 (a) and (b) respectively. The dashed line is the LCOE required while the dotted line is the boiler feed oxygen concentration. While higher operating enriching stage cut 80

results in higher O2 concentration for both membranes (the dependence on second enriching stage cut is minimal for the Polaris membrane), LCOE increases as well. The range of boiler O2 concentration for both membranes is17 to 19 % Furthermore, for

Polaris, the maximum boiler O2 concentration is slightly higher than for PDMS. Since

PDMS has slightly lower CO2 in the permeate stream due to its lower selectivity, the stripping staged is relied upon more heavily to remove CO2 which simultaneously leads to greater O2 loss. Additionally, the increase in CO2 recycling in stream S12 increases power requirements. The results presented here are for a fixed feed pressure of 2 bar. It may be possible increase the oxygen concentration further if the feed pressure is increased.

Figure 4-1

The comparison performance between PDMS and Polaris membrane for this configuration in Figure 4-1 is summarized in Table 4.2. The viable operating stage cut for Polaris ranges from 17 to 19% while for PDMS it is much higher. The boiler oxygen concentration on the other hand lies similar ranges from 17 to 18%. Higher CO2 permeance of PDMS results in much lower area requirement. However, since PDMS has the lower CO2/N2 selectivity, it results in greater CO2 recycling and this eventually results in higher energy expenditure to achieve separation targets. Although higher CO2/N2 selectivity and lower of CO2 permeance for Polaris significantly reduce the plant parasitic load in comparison with PDMS, it comes at the expense of much higher total module area requirement. Figure 4.5 indicates the capital-operating expense tradeoff results in lower

LCOE for the Polaris membrane than the PDMS membrane. 82

Table 4.2: Economic viability comparison between PDMS and Polaris for air feed system configurations.

Parameters PDMS Polaris

1st enriching operating stage cut (%) 33 to 35 17 to 19

2nd enriching operating stage cut (%) 47 to 50 88 to 90

Oxygen concentration to boiler (%) 17.2 17.4 to 18

Total parasitic load (%) 38 to 39 23 to 25

Total module area (m2) 90,000 to 94,000 1,400,000 to 1,600,000

Levelized cost of electricity ($/MWh) 94 to 96 80 to 85

*Base electricity price without CCS system is assumed $53.96/MWh

4.7 Stage Cut Impact Variation Impact for Post-Boiler CO2 Recycle Loop

Configuration

The impact of enriching module stage cut on total module area for PDMS and

Polaris membranes in the configuration Figure 4-2 is illustrated in Figure 4-6 (a) and (b) respectively. As for the previous configuration (Figure 4-1), increasing stage cut leads to an increase in CO2 recovery in that stage and requires greater membrane area. As stage cut increases, though, CO2 purity will decrease so a combination of stage cuts that meets capture targets must be determined. The stage cut ranges shown in Figure 4-6 corresponds to values required to meet the separation targets of 90% CO2 recovery rate and 95+ CO2 purity target.

The configuration of Figure 4-2 does not contain an air swept stripping stage so no boiler air oxygen loss occurs. However, this also leads to lower CO2 feed partial pressures to the enriching stages. Despite the lower CO2 feed partial pressure, the second enriching stage (B13) enables both membranes to meet the separation targets. Unlike the previous configuration which has a higher CO2 feed partial pressure, enriching stage cut for both membranes is much higher, especially in the first enriching stage cut. This is required because of the lower CO2 purity in the feed and indicates the required operating stage cuts depend on both CO2/N2 selectivity and CO2 feed concentration. In case of

PDMS, the total module area required is slightly higher than the previous configuration.

However, due to the lower CO2 permeance, the total module area requirement for Polaris is double that of the previous configuration (Figure 4-1).

Figure 4-6: Impact of 1st enriching stage cut (permeate stream flow rate S10/feed flow rate S8) and 2nd enriching stage cut (permeate stream flow rate S16 /feed flow rate S1)

on total required module area (m2) for (a) PDMS (b) Polaris in the configuration of

Figure 4-2

The lower CO2 feed partial pressures and higher stage cuts in the configuration of

Figure 4-2 also impacts the total parasitic load as energy requirements increase with stage cut. The plant parasitic load for PDMS and Polaris is illustrated in Figure 4-7 (a) and (b). Although Polaris has the higher CO2/N2 selectivity that could potentially reduce energy requirements, the minimum plant parasitic load is about 32% which is higher than for the configuration of Figure 4-1. The minimum parasitic load for PDMS is 62% - twice that for the Polaris membrane. This is mainly due to higher N2 content in the permeate for PDMS. The observed parasitic load value difference between PDMS and

Polaris in both configurations (Figure 4-1) and (Figure 4-2) indicates the effect of

CO2/N2 selectivity on energy requirements is greater for lower CO2 feed partial pressures.

4-2

4.8 Stage Cut Impact Variation of Post-Boiler CO2 Recycle Loop Configuration

Towards LCOE

The variation of LCOE with stage cut for PDMS and Polaris is illustrated in

Figure 4.8 (a) and (b) respectively. The LCOE values are higher than for the previous configuration of Figure 4-1 because of the increase in stage cut (and associated module area) and parasitic load discussed previously. The highest LCOE is found for the highest stage cuts as expected. These results suggest that to achieve lower LCOE, it is essential to increase the CO2 feed partial pressure by creating an affordable CO2 recirculation loop

Figure 4-8: Impact of 1st enriching stage cut (permeate stream flow rate S10/feed flow rate S8) and 2nd enriching stage cut (permeate stream flow rate S16/feed flow rate S14) on LCOE for a) PDMS (b) Polaris in the configuration of Figure 4-2. The base electricity price without LCOE is assumed at $53.96/MWh.

The performance of the PDMS and Polaris membranes in this particular configuration is summarized in Table 4.3. Due to the lower CO2 feed partial pressure, stage cuts are higher than in the previous configuration and the increase is especially dramatic for the Polaris membrane despite its higher CO2/N2 selectivity value. The lower

CO2 feed partial also results in higher total membrane module area, plant parasitic load and overall LCOE.

Table 4.3: Economic viability comparison between PDMS and Polaris for post boiler

CO2 recycle system configuration in Figure 4-2

Parameters PDMS Polaris

st 1 enriching operating stage cut (%) 44 to 47 28 to 32

nd 2 enriching operating stage cut (%) 60 to 67 68 to 74

Total parasitic load (%) 61 to 70 31 to 39

2 Total module area (m ) 100,000 to 130,000 2,200,000 to 3,400,000

Levelized cost of electricity 160 to 210 93 to 114

($/MWh) *

*Base electricity price without CCS system is assumed $53.96/MWh

4.9 Process Facilities Cost (PFC), Variable Operating and Maintenance Cost (VOM) and LCOE Breakdown

A comparison of the PFC for the PDMS and Polaris membranes in the configurations of Figure 4-1 and Figure 4-2 is provided in Figure 4-9. As can be seen, the cost associated with downstream CO2 liquefaction is less than 5% of the total.

Because of high CO2 permeance of PDMS, membrane costs do not significantly impact

PFC as they account for less than 10% of the total. The major cost components for PDMS are the compression, vacuum, and expander systems used to increase the CO2 permeation driving force. Increasing CO2 permeance by reducing membrane thickness and reducing membrane price per unit area will reduce the membrane cost contribution significantly 88

only for the Polaris membrane.

100.00% Process Facilities Cost ( PFC) Breakdown 93.60% 90.00% 84.30% 80.00% 70.00% 59.67% 60.00% 55.47% 50.00% 37.74% 40.00% 35.71% 30.00% 20.00% 6.39% 10.00% 3.69% 3.10% 5.01%4.31% 2.61% 2.91% 3.47% 2.02% 0.02% 0.00% Polaris (Fig 4-1) PDMS (Fig 4-1) Polaris (Fig 4-2) PDMS (Fig 4-2) Membrane Membrane compression & Vac system Liquefecation Heat exchanger

Figure 4-9: Process Facilities Cost (PFC) breakdown comparison between Polaris and

PDMS for Figure 4-1 and Figure 4-2.

Figure 4-10 shows the estimated Variable Operating & Maintenance (VOM) comparison for the Polaris and PDMS membranes in the configurations of Figure 4-1 and Figure 4-2. The VOM calculated here is based on the guidelines published by Zhai et al [20]. It constitutes electricity consumption as well as other utilities such as refrigerant, cooling water and process steam that are used to service the heat exchangers and expanders and membrane replacement cost. For both membranes, the largest VOM contributions are associated with the electricity required for gas compression to generate the driving force for CO2 permeation; especially for the lower CO2 feed concentrations in the configuration of Figure 4-2. Since this work is conducted at fixed feed and permeate pressure, detailed optimization might decrease electricity consumption.

Variable Operating Cost (VOM) breakdown

Membrane replacement cost Electricity consumption Cooling water Liquefaction Process steam 98.13% 100.00% 96.41% 92.24% 90.26% 90.00% 80.00% 70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 4.98% 6.77% 10.00% 1.92% 1.54% 1.66% 0.22%0.65% 0.24% 0.14% 1.31% 1.50% 0.18% 0.75%0.09%0.85% 0.00% 0.16% Polaris (Figure 4-1) PDMS (Figure 4-1) Polaris (Figure 4-2) PDMS (Figure 4-2)

Figure 4-10: Operating Cost (VOM) breakdown comparison between Polaris and PDMS for Figure 4-1 and Figure 4-2

Figure 4-11 illustrates the total Capital Expenditure (CAPEX) and Operating and

Maintenance (OPEX) contribution to the LCOE. As discussed previously, increasing membrane CO2 permeance by reducing membrane effective thickness will reduce membrane contribution towards overall LCOE. Compression costs dominate the LCOE especially as the CO2/N2 selectivity is reduced. The electricity power requirement estimated here comes primarily from the membrane compression system. Because of the larger flow rates with lower CO2 purity obtained with PDMS, greater compression costs are incurred. Detailed integration and optimization of the downstream CO2 liquefaction step may lead to reduced separation costs if the required purity of the membrane product required for liquefaction can be reduced.

LCOE Cost Breakdown Annual CAPEX Annual OPEX 90.00% 84.04% 84.46%

80.00% 73.44% 71.42% 70.00%

60.00%

50.00%

40.00% 28.58% 30.00% 26.56%

20.00% 15.96% 15.54%

10.00%

0.00% Polaris (Figure 4-1) PDMS (Figure 4-1) Polaris (Figure 4-2) PDMS (Figure 4-2)

Figure 4-11: LCOE breakdown comparison between Polaris and PDMS for Figure 4-1 and Figure 4-2

4.10 Conclusions

The use of membrane processes in post-combustion requires generation of affordable CO2 feed partial pressure driving forces for permeation. Multi-stage membrane processes can generate the required driving forces to meet capture targets by creating

CO2 recycle loops and allowing enrichment beyond that achievable in a single stage.

Key process design variables for a membrane system are the transport properties of the membrane material (CO2 permeance and CO2/N2 selectivity), operating pressures, and stage cut (or equivalently area). While high permeance and selectivity are desired, available materials show a tradeoff between the two: as the permeance increases the selectivity decreases and vice versa.

Two configurations and two materials are considered in this chapter. The two configurations are: 1) two enriching stages and a stripping stage which uses the boiler air feed as a sweep and 2) two enriching stages. Both configurations rely upon a final cryogenic polishing step. The second enriching stage is needed to allow operation with the lower selectivity membranes of interest here.

In all cases, compression energy is the dominant contribution to LCOE. The higher selectivity Polaris membrane had lower energy costs for both configurations despite a significant increase in membrane fixed cost; membrane fixed costs for PDMS were insignificant relative to other costs.

The process configuration with the boiler air swept stripping stage led to the lowest LCOE for both membranes. The air sweep increases the driving force for CO2 permeation without additional compression or vacuum energy costs. Additionally, the

Polaris membrane gave the lowest LCOE for both configurations. The tradeoff between membrane CAPEX costs and compression/vacuum energy OPEX costs favor the use of the membrane with the higher selectivity (lower OPEX) and lower permeance (higher

CAPEX).

The lower LCOE associated with use of an air swept stripping stage comes at the cost of a reduction in boiler feed oxygen concentration as some oxygen is lost in the stripping stage. If this reduction is sufficiently low, boiler operation may not be affected significantly. Alternatively, on-site O2 generation might be considered to reduce the loss but the cost must be included in the LCOE calculation.

Because of the superior performance of the air swept stripping stage configuration, a systematic optimization of this configuration is considered in the next 92

chapter. Membrane properties and operating conditions are optimized to produce the lowest LCOE. The dependence of this optimum on oxygen reduction in the boiler feed area is quantified.

Chapter 5

5. Membrane Process Optimization for Carbon Capture

5.1 Introduction

Optimization of multi-stage membrane processes for post combustion CO2 capture requires systematic evaluation of a number design variables on LCOE. While increasing CO2 membrane permeability results in significant savings in capital cost, it comes with the major tradeoff of lower CO2/N2 selectivity which eventually results in larger plant parasitic loads. Therefore, to determine the optimum operating conditions and membrane separation properties for post-combustion application, one should not only consider the balance between required feed to permeate pressure ratio and CO2/N2 selectivity [60], but also the trade-off relationship between selectivity and permeability as shown in Robeson plot previously.

In this chapter, the MTR proposed multistage hybrid membrane-cryogenic air- feed sweep configuration in Figure 5-1 is optimized according to Robeson upper bound relation. All previously reported operations conditions and membrane separation properties are used to establish a base condition [4]. In this study, membrane properties and operating pressures of the membrane stages are optimized. CO2 permeability is varied with selectivity according to the upper bound proposed by Robeson for CO2 and

N2. The enriching feed (B1) and permeate pressure (B4) are also varied over ranges 94

encompassing the values proposed by MTR. Simplified flow diagram and stream table is provided in Appendix C. Systematic Global Search is used to determine the membrane properties and operating conditions that minimize LCOE. Because reduction of boiler O2 concentration boiler in stream 12 may reduce boiler efficiency, the O2 concentration to the boiler is evaluated during the optimization process and results are presented for a range of fixed feed concentrations. Since the CO2 liquefaction unit operation accounts for only ~10% of overall capture cost [9] , cryogenic process design variables are held constant in this work.

O2 deficient air (S12) B1 S5 S6 B3 S10 Air feed S1 S3 S7 S8 S11 Lean-CO2 vent S4 B2 S2 Enriched CO2 Coal permeate (S9) S13 S14 S23 B4 S17

S22 S21

S18 S15 S19 B5 B7 B6 S25 S24

Liq CO2 S20 S16

Figure 5-1: MTR Membrane-Cryogenic Air Feed Sweep Configuration [4]

5.2 Methodology

The objective function for Figure 5-1 superstructure network is defined as LCOE and the problem can be stated as follows:

For a given flue gas feed condition and oxygen concentration to the boiler, determine the lowest LCOE and operating conditions that fulfill the capture target of 90% CO2 recovery and 95% purity. The cost related parameters are assumed to be known while the membrane separation properties such as optimal selectivity and permeability are determined by the Robeson upper-bound empirical relationship. Previously reported results are [4] used to establish a base case for comparisons. The optimization approach used in this work also is based on the following assumptions:

1) The flue gas feed streams contain multicomponent gas mixture at known

conditions

2) The pressure drops in both lumen and shell are negligible

3) The process is conducted at steady and isothermal conditions

4) Membrane permeability is calculated using CO2/N2 selectivity values from the

upper bound line of the Robeson plot

5) Water permeance in every membrane is assumed constant at the value of

10,000 GPU. Water permeance is typically so high that permeation is limited

by the pressure ratio and the specific value of permeance does not affect the

results

Optimization variables are the total module area for each stage, CO2/N2 selectivity in B2,

B3, and B5, feed compressor outlet pressure in B1 and vacuum pump operating pressure 96

in B4. The Robeson upper bound is used to determine the membrane permeability. CO2,

O2 and N2 permeability, (PCO2, PO2 and PN2 respectively) are calculated from the following upper bound relationships:

. = 30,967,000/ barrer (5-1)

Where / is the CO2/N2 selectivity:

/ = (5-2)

. = 1,396,000/ barrer (5-3)

Where / is the O2/N2 selectivity:

/ = (5-4)

For a specified selectivity, PCO2 is calculated from Equation (5-1) and PN2 from Equation

(5-2). Combining Equations (5-3) and (5-4) yields Equation (5-5) which can be used to calculate the O2/N2 selectivity from PN2:

,, . / = (5-5)

PO2 then can be calculated from Equation (5-3). Assuming membranes can be fabricated with an effective thickness of 0.1 micron, the permeance in GPU for each component can

[3] be calculated from each permeability value. The calculated CO2 permeance from the upper bound relation at the given selectivity is provided in Table 5.1. The Polaris membrane possesses a permeance and selectivity of 1000 GPU and 50, respectively.

Table 5.1 indicates a selectivity of 50 corresponds to a higher CO2 permeance than that reported for the Polaris module. A selectivity of 75 with a CO2 permeance of 1180 GPU

is used as base comparison value since it will provide performance slightly better than the

Polaris case.

[3] Table 5.1: CO2 permeance calculated from Robeson upper bound relation

Selectivity Permeance (CO2/N2) (GPU) 150 160 100 519 85 830 75 1180 65 1800 50 3790 45 4840 35 10700

The optimization variables are provided in Table 5.2. Constraints for this problem are as follows:

1) CO2 capture from the membrane hybrid system must be ≥ 90%

2) CO2 purity in the liquefied CO2 must be ≥ 95%

Table 5.2: Decision variables used for optimization.

Decision variable Lower and upper limits Enriching module (I) feed pressure (B1) 2-7.5 (bar) Enriching module (I) permeate pressure 0.2 -0.5 (B4) (bar)

Module CO2/N2 selectivity (B2, B3 & 35-100 B5) Module area (m2) (B2, B3 & B5) 0-10,000,000

Module CO2 permeance (GPU) 150-12,000

Figure 5-2 illustrates the optimization procedure that were used in this study. Prior to staring the optimization procedure, at the given feed pressure, permeate pressure and

CO2/N2selectivity, a series of simulations were performed to determine approximate membrane areas that meet or exceed the CO2 recovery and purity target. These values are used as initial guesses for determining the area that satisfies the separations target of exactly 90% CO2 recovery and 95%+ CO2 purity as well as a fixed boiler feed O2 concentration. Interior point optimizer is used to determine the minimum membrane area required that meet the separations target, interior point optimizer starting from the area estimates obtained previously. This area is used to determine the LCOE. The procedure is repeated for the range of feed pressures, permeate pressures, and CO2/N2 selectivities considered in this work.

100

Figure 5-2: Flowchart for optimization of membrane-cryogenic for post-combustions

5.3 Impact of Enriching and Stripping Module Area Variation at Constant Feed and

Permeate Pressure

As described previously, one of the key observations from Merkel et al.[4] is that use of boiler feed air as a sweep in the CO2 stripping stage can significantly improve process economics. This sweep increases the CO2 concentration in the feed to the first

CO2 enriching stage by recirculating CO2 through the boiler with minimum energy input.

[9] [6] According to Scholes et al. and Ramasubramanian et al. , the amount of CO2 recirculation can have a substantial impact on overall capture cost due to the tradeoff between enriching and stripping stage module area in stage 1 and stage 2 respectively, as 101

well as overall compression power requirement . In this work, initially the impact of both enriching and module area variation on CO2 recovery and purity was determined at process conditions similar to those used by Merkel et al. [4] : feed pressure = 2 bar, permeate pressure =0.2 bar,CO2/N2 selectivity = 75, and CO2 permeance = 1180 GPU.

The results are shown in Figure 5-3(a). As can be seen, the liquid CO2 purity constraint is met over the entire range of stage areas considered. However, the recovery of CO2 is highly dependent on both enriching and stripping stage module area. For a given CO2 recovery, increasing stripping module area increases the CO2 recirculation rate to the boiler which increases the driving force for membrane separation and results in higher

CO2 concentration in the permeate stream S9. Therefore, minimizing enriching module area is desirable and results in a slight increase in liquefied CO2 purity.

102

α Figure 5-3: Impact of stage area for (CO2/N2) =75, feed pressure=2 bar, and permeate pressure=0.2 bar: (a) CO2 recovery (dash) and purity (solid), (b) LCOE (yellow dash), boiler O2 concentration (solid), CO2 recovery (black dash).

The impact of enriching and stripping module area on CO2 recovery, LCOE and boiler O2 mole fraction is shown in Figure 5-3 (b). Increasing both enriching and stripping module area lead to higher LCOE. For 90% CO2 recovery, there are various possible enriching and stripping module area combinations that meet this minimum separation target. However, LCOE and O2 boiler concentration can vary dramatically.

While maximizing stripping module area and minimizing enriching module area results in lower LCOE O2 mole fraction decreases undesirably. Reducing the desired CO2 recovery can reduce LCOE while maintaining boiler feed oxygen concentration as expected.

While increasing CO2/N2 selectivity reduces the enriching compression power requirement [56], it concomitantly leads to an increase in the membrane area requirement

[3] because of a lower CO2 permeance . The effect of CO2/N2 selectivity on LCOE and 103

boiler O2 mole fraction for exactly 90% CO2 recovery is illustrated in Figure 5-4. For all values of selectivity, LCOE decreases as boiler O2 concentration decreases as the CO2 concentration in the feed to the enriching stage increases. A minimum is not observed as the boiler concentration decreases – LCOE appears to decrease asymptotically to a minimum instead. For a given boiler O2 concentration, LCOE passes through an apparent broad minimum for low selectivity and increase dramatically as selectivity increases above 75. This behavior reflects the decrease in permeance that accompanies an increase in selectivity and the associated increase in membrane area capital expense.

CO2/N2=100 85 CO2/N2=75 CO2/N2=45

CO2/N2=35 80

($/MWh) 75

LCOE 70

60 0.14 0.16 0.18 0.2 Boiler O2 mole fraction

α Figure 5-4: LCOE variation with boiler O2 mole fraction as a function of (CO2/N2) for 90% CO2 recovery, feed pressure=2 bar, and permeate pressure=0.2 bar. Base electric price without CCS is assumed to be $53.96 /MWh.

104

5.4 Impact of Enriching and Stripping Module Area Variation for Various Feed and

Permeate Pressures

Although higher CO2/N2 selectivity potentially can minimize boiler O2 concentration reduction, it could not be exploited economically at the lower pressure ratio

[4] due to the large area requirement needed to meet the CO2 recovery target . To address this issue, Figure 5-5 (a) illustrates the enriching and stripping module area variation for a CO2/N2 selectivity of 75 at a lower pressure ratio: feed pressure = 4 bar and permeate pressure=0.5 bar. Similar to the results in Figure 5-3, CO2 recovery increases with enriching and striping module area. Because of the higher feed pressure, the enriching and stripping area requirements are dramatically lower. Liquefied CO2 purity also increases slightly with the higher feed pressure.

α Figure 5-5: Impact of stage area for (CO2/N2) =75, feed pressure=4 bar, and permeate pressure=0.5 bar: (a) CO2 recovery (dash) and purity (solid), (b) LCOE (yellow solid), boiler O2 concentration (black solid), CO2 recovery (dash).

The impact of enriching and stripping area on LCOE, CO2 recovery and boiler O2 concentration for a feed pressure = 4 bar and permeate pressure = 0.5 bar is illustrated in 105

Figure 5-5 (b). For each CO2 recovery fraction, maximizing stripping stage area and minimizing enriching stage area reduces LCOE but also reduces boiler O2 mole concentration. This is consistent with the results presented previously for a higher pressure ratio. Despite the higher compression costs to reach higher feed pressures,

LCOE is considerably lower for a fixed CO2 and boiler feed oxygen concentration relative to the results in Figure 5-3. This is due primarily to the lower membrane area requirement for higher feed pressures.

Figure 5-6 illustrates the effect of pressure ratio on the relationship between

LCOE and feed oxygen concentration for exactly 90% CO2 recovery with a CO2/N2 selectivity of 75. The lowest LCOE is found for a feed: permeate pressure ratio of 4:0.5.

Increasing both pressures relative to base case of 2:02 is beneficial as the higher feed pressure reduces the membrane area requirement and the higher permeate pressure does not a significant adverse effect on CO2 recovery and purity; gas liquefaction is robust in its ability to meet the purity requirement from a broad range of initial concentrations.

106

76 75 Feed:Permeate=2:0.2 74 Feed:Permeate=2:0.4 73 Feed:Permeate=4:0.25 72 Feed:Permeate=4:0.5 71 70 69 LCOE ($/MWh) 68 67 66 65 0.14 0.16 0.18 0.20

Boiler O2 mole fraction

Figure 5-6: LCOE variation with boiler O2 mole fraction as a function of operating α pressures for 90% CO2 recovery and (CO2/N2) =75. Base electric price without CCS is assumed to be $53.96 /MWh.

Note that the maximum feed oxygen concentration that can be achieved is a function of the pressure ratio as indicated by where the symbols end in Figure 5-6. As the feed pressure increases, the maximum possible oxygen concentration also increase.

The highest possible oxygen concentration was achieved with a pressure ratio of 4:2.5 but this is accompanied by an increase in LCOE. These results suggest that for a given

CO2/N2 selectivity the use of higher feed and permeate pressures, relative to the base case of 2:0.2, may reduce LCOE will maintaining boiler feed oxygen concentration.

107

5.5 Influence of Feed and Permeate Pressure Variation at Fixed Selectivity And

Boiler O2 Mole Faction on LCOE

The effect of feed and permeate pressure on LCOE for a CO2/N2 selectivity of 75 is illustrated in Figure 5-7 (a)-(c) for fixed boiler O2 mole fractions ranging from 17 to

19%. The results in Figure 5-7 exactly satisfy the 90% CO2 recovery target and give liquid CO2 purities of at least 95%. Lines of constant LCOE are indicated numerically and by color. Over the range of pressures considered, it was not possible to determine enriching and stripping stage areas to exactly reach the desired oxygen level. In those cases, an artificial cost was added to the LCOE calculation based on the formula below:

= +(rβ) (5-6)

Where LCOEβ is the LCOE at given O2 level, r is the interest rate and β is the boiler O2 difference between given O2 level with the desired O2 level.

The point where this additional cost was added is indicated in the figure. Additionally, over the range of pressures considered, it was not possible to determine enriching and stripping stage areas to exactly reach the 90% CO2 recovery target. As with boiler oxygen concentration, an artificial cost was added to the LCOE calculation when recovery was less than 90% based on the formula below:

= +(rθ) (5-7)

Where LCOEθ is the LCOE at the given CO2 recovery rate, r is the interest rate and θ is the difference between given recovery CO2 recovery rate with 90% CO2 recovery rate.

The point where the recovery target could not be satisfied also is indicated in the figure.

The introduction of these artificial costs allowed the generation of continuous LCOE 108

contours over the entire pressure range and increases LCOE sufficiently that the minimum LCOE will correspond only to those conditions that meet CO2 recovery and purity targets at the given oxygen concentration. The latter cost might be considered a tax on carbon emissions while the former the cost of providing auxiliary oxygen to the boiler.

A broad minimum in LCOE appears for all boiler oxygen concentrations for feed pressures in the 2.5-4 bar range and permeate pressure in the 0.25-0.5+ pressure range.

As boiler feed oxygen concentration increases, this minimum value increases from less than 70 to ~71.5. It is interesting to note that the process proposed by Merkel et al. [4] lies near the minimum region in Figure 5-7 for 18% boiler oxygen concentration

The existence of a minimum in LCOE as feed pressure is varied, for a fixed permeate pressure, is expected from a consideration of operating and capital costs. For the lowest feed pressures, carbon capture targets may not be met as seen in the figure.

Once the minimum pressure to satisfy operating requirements is reached, the required membrane area will be the largest and the energy requirement for compression the smallest. As pressure continues to increase, area requirements (capital costs) will decrease while energy requirements (operating costs) will increase. This trade off leads to the emergence of a minimum in LCOE as one moves from left to right along the feed pressure axis for a fixed value on the permeate pressure axis.

The existence of a minimum in LCOE as permeate pressure is varied, for a fixed feed pressure, is less obvious. For low permeate pressures (high vacuum), the permeate from the enriching stage will be more highly enriched in CO2 and able to meet the recovery and purity targets with less CO2 recirculating from the stripping stage through the boiler to the enriching stage. As permeate pressure increases (lower vacuum), the 109

enrichment possible in the enriching stage decreases and more CO2 must be recirculated to satisfy capture targets. Consequently, as permeate pressure increases, energy costs required to produce the vacuum decrease but energy costs associated with recirculating

CO2 through the boiler (in particular recompression before the enriching stage) increase.

The trade-off between these costs leads to a minimum in LCOE.

Figure 5-7: LCOE dependence on feed and permeate pressure for boiler oxygen feed concentrations = 17, 18, and 19% and for αCO2/N2) = 75. CO2 recovery is fixed at 90%.

Base electric price is assumed to be $ 53.96 /MWh.

The broad nature of the minimum and its relatively small variation with boiler feed oxygen is unexpected. Such an observation suggests the membrane process is robust in its ability to meet capture targets and higher boiler feed oxygen concentrations can be achieved without large increases in LCOE.

Figure 5-8 (a) - (c) illustrates the variation of LCOE with operating pressures for a CO2/N2 selectivity of 100 for a range of O2 boiler concentrations. As seen in Figure 5-7

(a)-(c), a broad minimum in LCOE is found. The minimum is slightly higher than that for 110

a selectivity of 75. The differences are remarkably small given the assumptions required to perform this analysis. Additionally, the optimal feed and permeate pressure ranges shift to higher pressures: from 2.5-4 to 3-5 bar for the feed pressure and from 0.25-0.5+ to 0.3-0.5+. Such shifts are expected to compensate partially for the lower permeance of the higher selectivity membrane and the higher pressure ratio required to utilize the higher selectivity effectively.

Results for a CO2/N2 selectivity of 45 are presented in Figure 5-8 (d)-(f). The iso-

LCOE contours are influenced more by an inability to meet capture and boiler oxygen targets than for the higher selectivity materials; such an observation suggests than lower values of selectivity may require additional stages. The minimum values of LCOE are slightly smaller than for a selectivity of 75 as one might expect from the results in Figure

5-4. Moreover, the optimal ranges of pressure are similar to those for a selectivity of 75 but slight narrower, especially for the optimal feed pressure. These results indicate the reduction in membrane area costs (capital) afforded by use of a lower selectivity material are largely offset by an increase in CO2 recirculation costs (operating) to raise the CO2 concentration in the feed to the enriching stage – this increase is need to recover CO2 at the rate and purity needed to meet capture targets.

111

5.6 Influence of Feed Pressure, Permeate Pressure, and CO2/N2 Selectivity on LCOE for Fixed Boiler O2 Mole Faction

Figure 5-9 (a)-(i) shows LCOE for varying feed and permeate pressure with various combinations of enriching and stripping stage CO2/N2 selectivities; the selectivity takes on values of 100, 75 and 45. The results correspond to exactly 90% CO2 recovery and a boiler O2 concentration of 18%. The boiler O2 concentration is fixed at 18% because it is assumed this is the lowest value that will allow operation without significant 112

loss of boiler efficiency. In all cases, a broad minimum in LCOE is observed consistent with the results presented in the previous section.

As shown in Figure 5.9(a)-(c), for a fixed CO2/N2 selectivity of 100 in the enriching stage, reducing the stripping stage selectivity from 100 to 75 and 45 reduces

LCOE; the minimum values for the two are identical. The optimal operating pressure range also shifts to lower values with the reduction in selectivity, especially for the permeate pressure. These results are consistent with the expectation of a tradeoff in capital and operating costs as membrane selectivity and permeability are varied along the

Robeson upper bound.

113

Figure 5-9: LCOE variation with feed and permeate pressure for various combinations of enriching and stripping stage selectivity and a fixed boiler oxygen concentration of 18% and 90% CO2 recovery. Base electric price without CCS system is assumed at $53.96

/MWh.

114

Figure 5-9(a), 5-9(d) and 5-9(g) illustrate the changes in LCOE that occur with fixing the stripping stage selectivity at 100 and reducing the enriching stage selectivity from 100 to 45. While the optimal operating pressure range shifts in a manner similar to that observed for varying the stripping stage selectivity, the minimum LCOE does not change significantly and remains at ~72 $/Kwh.

Examination of the remaining stage selectivity combinations in Figure 5-9 indicates the lowest LCOE is found with use of lower selectivity materials in both the enriching and stripping stages. The lowest LCOE ($70/MWh) can be achieved for feed pressure around

3 bar with permeate pressure range from 0.3 to 0.45 bar with any combination of the 45 and 75 selectivity materials. This insensitivity indicates the production of different membranes and modules for the enriching and stripping stages is not warranted.

5.7 Conclusions

[9] Prior work by Scholes et al indicated that CO2 recirculation from the air feed sweep module could have substantial impact capture cost due to the trade-off relationship between enriching and stripping module area. While this system elevated the CO2 feed partial pressure in the boiler with inevitable boiler O2 reduction, the tradeoff relation between CO2/N2 selectivity and CO2 permeability as highlighted in Robeson plot was not addressed comprehensively. In this chapter, membrane transport properties and operating pressure of membrane stages are optimized to reduce LCOE by considering the trade-off relationship between CO2/N2 selectivity and CO2 permeability and how it changes with boiler O2 concentration.

115

For the fixed cryogenic process parameters considered here, CO2 liquid purity is less sensitive to the variation of enriching and stripping module area in comparison to the

CO2 recovery rate. Maximizing stripping stage area and minimizing enriching stage area gives the lowest LCOE. However, it also results in the lowest boiler O2 concentration.

For a fixed O2 boiler concentration, LCOE increases significantly as the selectivity increases and is attributed to the concomitant drop in CO2 permeability and increase in required membrane area (capital cost).

The optimization space of membrane CO2/N2 selectivity and operating pressures was scanned globally to determine the process design parameters that minimize LCOE.

Results are presented for a range of fixed boiler O2 feed concentrations as boiler O2 concentration increases, LCOE increases as the enriching stage must be operated at higher pressure ratios to meet capture targets.

A broad LCOE minimum is found in the virtually all cases. The minimum of 69-

70 $/Kwh meets the DOE target of less than a 35% increase in electricity cost with carbon capture. This observation recommends focusing not on improving membrane transport properties as much as identifying a material that can used to produce membranes and modules at the lowest cost.

Small reductions in LCOE are achievable by using lower selectivity materials.

These materials possess higher permeances which reduce capital costs by reducing the required membrane area. The capital savings are offset in part by an increasing in operating costs required to achieve capture targets but the net effect is a slight decrease in

LCOE.

116

The results indicate the optimal operating pressures are slightly higher than proposed originally by Merkel et al [4]. This is especially important for the permeate vacuum pressure as pressures of 0.2 bar push the limits of current vacuum technology.

Operating at pressures closer to 0.5 bar is desirable and appear feasible based on this work.

Simulations with different materials in the enriching and stripping stages indicate that LCOE can be minimized with the same material in both stages. Values of selectivity from 45 to 75 lead to nearly identical results. This suggests a manufacturer will not have to produce different products for the enriching and stripping stages thereby reducing manufacturing complexity and cost.

It is important to note that the results presented here assume fixed downstream cryogenic process parameters. According to Scholes et al [9], the cryogenic unit account for only ~10% of overall capture cost. Consequently, one would expect the LCOE values reported here to vary by no more than the same amount if robust optimization of cryogenic operations is performed.

117

Chapter 6

6. Dynamic Simulations of Membrane Separation for

Post-Combustion Applications

6.1 Introduction

Understanding the transient behavior of membrane gas separation processes for post combustion CO2 capture is crucial because these processes must accommodate plant start-up, shut down, and variation of flue gas flow rate and composition due to electricity demand fluctuations and changes in coal feed characteristics[85]. Flue gas fluctuations will impact the CO2 feed partial pressure for a carbon capture process. Ideally, the process would be able to respond and ensure capture targets are met continuously. These fluctuations are expected to impact plant efficiency and carbon capture economics.[86].

The focus of this chapter is to conduct a dynamic simulation for a multi-stage membrane process for post-combustion capture. The work is based on the field test conducted by MTR to capture 1 ton per day of CO2 with their membrane based pilot plant at the National Carbon Capture Center (NCCC) [12]. The unit is designed to meet the separation target of CO2 recovery from 80 to 90% with CO2 purity from 50% to 65%.

This study was to evaluate long-term performance using a slip stream and did not include the boiler feed air swept stripping stage with recycle through the boiler.

Flue gas flow rate and temperature changes can affect capture performance. As temperature increases, it is anticipated that for the materials under consideration CO2

118

permeance will increase and CO2/N2 selectivity decrease and the capture process performance will change accordingly. As flow rate increases, it is anticipated that stage cuts will decrease (since membrane area is fixed) and capture performance will change accordingly.

The dynamic membrane model will be used to study the transient response of the capture process. The multistage membrane dynamics studies reported in this chapter could be used in developing viable control strategies to maintain separation and economic targets.

6.2 Multi-Component Membrane Dynamic Simulations for Isothermal Operation and Constant Permeance

Similar to the approached adopted in Chapter 3, a stage in series approximation is used to transform the governing differential mass balances into a set of coupled non- linear differential equations. The lumen-side mass balances are solved by dividing each fiber into N perfectly mixed stages as shown in Figure 6-1. The volume permeation rate

3 for component i leaving j stage, mi,j in (m /s) is given by Equation (6-1):

, = , (,, − ,, ) (6-1) 3 2 Where Qi,i is the membrane permeance (m /s.m .Pa) of component i, PR is the retentate pressure (Pa), PP is the permeate pressure (Pa), xi,j is the retentate mole fraction, yi,j is the permeate mole fraction and ΔAm is the active area per stage given by:

= (6-2)

Where L is the active (or permeating length) of the hollow fibers in the module, Nf is the number of fibers, and Ro is the hollow fiber outer radius (m). 119

Figure 6-1: Counter-current module configurations divided into N stages

The retentate and permeate volume flow rates of component i leaving stage j

3 (m /s) are given by R i,j and Pi,j, respectively. Species mole fractions, component flow rates and total rates are related as follows:

, =, (6-3)

, =, (6-4)

The total retentate and permeate volume flow rates (m3/s) leaving stage j are the sum of component flow rates:

, =,+, (,, −, ) (6-5)

, =, − (, −,) (6-6)

Molar compositions and flows obtained from the cross flow configuration are used as initial guess as described in Chapter 3. The solution procedure for counter-current The iterative procedure is stopped when the difference between old and new values is less than some prescribed tolerance

120

The transient hollow fiber mass balance model is solved based on the following assumptions:

1) Gas mixtures behave ideally

2) Isothermal operations. All fibers possess uniform thermo-physical properties.

3) Lumen pressure drop is calculated using the Hagen-Poiseuille equation for

compressible flows

4) Gas permeability is independent of gas pressure, i.e., dual mode effects are

negligible

5) Negligible axial diffusion

6) All fibers possess identical physical and transport properties

7) Concentration polarization is negligible

8) Time delays and overshoots are negligible

9) Feed is introduced to the module shell-side

The rate of change of permeate and retentate mole fractions in stage j are given by

Equation (6-8) and (6-9) respectively;

, = , , , , , , (6-8)

, = , , , , , , (6-9)

3 Where VP and VR is the tank volume (m ) in the permeate and retentate side respectively and can be calculated as:

= (6-10)

= (6-11) 121

Where OD is the fiber outer diameter (μm), ID is the fiber inner diameter (μm), Lf is the

2 fiber length (m), Nf is the total number of fiber and Ashell (m ) is the area on the shell side.

2 Ashell (m ) is defined as the difference between module area (Amodule) and fiber area (Afiber) can be calculated as follows;

= − (6-12)

= (6-13)

= (6-14) and ID module is the module inner diameter (m).

Initially a direct iterative substitution algorithm is used to solve for the steady state as described previously in Chapter 3. The obtained steady state is used as the initial condition for the transient simulations. The transient mass balance equations are solved explicitly by using a 4th order Runge-Kutta integration method based on the disturbances introduced into the system.

6.3 Linearization of Non-Linear Multicomponent Membrane Permeator Models.

Transfer functions are often used to describe transient behavior. Derivation of a transfer function necessitates linearization of the non-linear membrane permeator model.

For sufficiently small disturbances, the linearized model will be able to predict transient behavior as a function of membrane properties and operating conditions.

The time constant () measures how quickly the process responds to a disturbance and is defined as the value of time at which the response reaches 63.2% of its

122

final steady value [87]. In order to non-dimensionalize the non-linear transient membrane permeator model; a set of dimensionless variable are defined below:

= (6-15)

= (6-16)

, , = (6-17) ,

, = , , (6-18)

∗ = or ∗ = (6-19)

, = (6-20)

, = (6-21)

, = (6-22) ,

3 Where Rf is the volume feed flow rate (m /s) and Qref, j is the reference gas permeance for stage -j. For CO2 capture, the reference gas is taken to be N2. Using the variables defined by Equation (6-15) to (6-22); the transient mass balances, Equation (6-8) and (6-9), can be rewritten as:

, = ,, − ,, + , − , (6-23) ∗

, = ,, + ,, − , − , (6-24) ∗

Equations (6-15) and (6-16) can be rewritten as:

, = (6-25) ,,,

123

, = (6-26) ,,,

Hence, the transient response for each component depends on:

i) Component permeance and selectivity;

ii) Operating feed to permeate pressure ratio

6.4 Dynamic Simulations of CO2 Capture from Flue Gas

Dynamic simulations are performed of the CO2 capture system used in the recent

[12] MTR field test to capture 1 ton per day of CO2 at their membrane based pilot plant.

Table 6.1 describes the reported base feed flue gas conditions in the test:

Table 6.1: Base Flue Gas Feed in MTR field test [12]

Variable Value Flue gas flow rate (KSCFD)(S1) 148 Feed gas pressure (bar) 1.01 Flue gas composition (mol %)

CO2 12.4

N2 80.6

O2 7.0

The unit is designed to achieve 70-80% CO2 recovery and 50-65% CO2 permeate purity.

As noted previously, the system does not include recycle of the air used to sweep the stripping stage through the boiler; the sweep is mixed with the flue gas feed instead. This allows long term performance testing of the modules used in the process with real flue gas without modification of the boiler air feed system. To meet the eventual target of

124

95%+ CO2 purity in the multi-stage membrane-cryogenic hybrid process proposed by

[4] Merkel et al, , the CO2 permeate stream in S4 must be at least 55%.

Since the system is designed to capture CO2 at lower capacity, the incoming feed flue gas rate and the required membrane area is much smaller than for the commercial power plant in the previous chapter. To see the impact of CO2/N2 selectivity on transient response; three selectivity values are considered; 50,75 and 100. The CO2 permeance for each selectivity is calculated based on the Robeson plot [3] as described in Chapter 5.

Hence, the required module area to meet the above mentioned separation targets varied with selectivity.

6.5 Dynamic Process Descriptions

Enriched CO2 permeate Flue gas feed Vin S1 (S4)

B1 B2 B3 B6 B4

Lean CO2-vent (S5) S2

Air feed

Figure 6-2: Modified Process Diagram for Installed 1 Ton per day CO2 Capture

MTR Membrane separation system at NCCC [12].

125

Figure 6-2 shows the modified process diagram of the multi-stage membrane system. In this process, the incoming dry flue gas feed is assumed comprised of a multicomponent mixture of CO2, N2, and O2 at atmospheric pressure and is sent to compressor (B2) to produce feed pressures ranging from 1.48 to 2.37 bar prior to the membrane separation unit (B4). A vacuum pump (B6) maintains a pressure of 0.1185 bar on the permeate side of the membrane in (S4) to enhance the CO2 permeation driving force. The retentate stream (S2) is sent to a stripping module (B5). Unlike the full MTR process, the permeate stream (S3) from the air feed sweep module (B5) is mixed directly with the flue gas feed to the enriching stage instead of passing through the boiler. This leads to a lower CO2 concentration in the feed than would be achieved in the full proposed process but allows long term testing without the complexity of recycling through the boiler. The retentate stream from the stripping module (S5) on the other hand is venting out to atmosphere. The process is designed so the flow rate of CO2 in the enriching stage permeate (S4) is 70-80% of the flow in the flue gas feed and the concentration in this stream is 50-65%.

6.6 Feed and Permeate Pressure Changes Resulting from a Step Change in Flue Gas

Flow Rate

Changes in feed flue gas flow rate will result in process performance changes that are can be calculated using the dynamic simulation. In this work, it is assumed that both the compressor and vacuum pumps operate at fixed horse power as desired to avoid the cost of variable speed units. Additionally, it is assumed that membrane modules do not allow for area turn up or down to avoid the cost of such design features. Consequently, 126

process performance changes will include changes in feed and permeate pressure as well as changes in the flow and composition of process streams.

Both compressor (Pcomp) and vacuum (Pvac) power requirements can be calculated as follows[20]:

() / = − 1 (6-27) ()

Where is the flow rate through the equipment (mol/s); Tin is the operating temperature

(K); is the equipment efficiency, γ is the adiabatic expansion factor, Pout is the out-coming pressure, Pin is the incoming pressure to the equipment. Since both compressor and vacuum pump horse power are constant; the compressor outlet pressure

(Pout, new) (bar) and vacuum pump inlet pressure (Pin, new) (bar) may change and can be calculated from the variable permeate (S4) and feed flow rate (Vin) by rearranging

Equation (6-27) to yield:

, = ln ∗ 1.01325 (6-28) ()

. , = (6-29) ()

Where z= (6-30)

The outlet and inlet pressure obtained in Equation (6-28) and (6-29) are respectively used as the feed pressure and permeate pressure in Equation (6-7) –(6-9) that determine the new steady state value. The iterative procedure is stopped when the difference between

127

old and new compression power value is less than the prescribed tolerance. The values also are used in the transient simulation using the transient flow rate values.

The changes in outlet pressure of compressor (B2) for two CO2/N2 selectivity values due to a 10% step increase in flue gas flow rate are shown in Figure 6-3(a) –(b).

Because of the increase in flow rate, the outlet pressure must decrease to keep compressor horsepower constant. As feed pressure increases and CO2/N2 decreases, the new steady state is reached faster. While the response in faster with lower selectivity at the same feed pressure, the final steady state values are nearly identical as the recycle flow is similar for both cases and the compressor outlet pressure depends only on feed flow rate and composition through the adiabatic expansion factor.

Figure 6-3(c)-(d) illustrate the feed pressure response to a 10% step decrease in flue gas flow rate. Since the incoming flue gas flow rate decreases, the outlet pressure must increase keep compressor horsepower constant. Similar to Figure 6.3(a)-(b), the response is faster as feed pressure increases or selectivity decreases. As observed for a feed flow increase, the response is controlled primarily by changes in the flow rate and composition of the recycle stream.

128

(b) CO2/N2=50 (a) CO2/N2=100 2.4 2.4 2.2 2.2 2 2 1.8 1.8

1.6 1.6 Feed Pressure Feed Pressure (bar) Feed Pressure Feed Pressure (bar) 1.4 1.4 1.2 1.2 0 5 10 15 20 0 5 10 15 20 Time (s) Time (s) Feed Pressure=1.481 Feed Pressure=1.635 Feed Pressure=1.481 Feed Pressure=1.635 Feed Pressure=2.07 Feed Pressure=2.37 Feed Pressure=2.07 Feed Pressure=2.37

(d) CO2/N2=50 (c) CO2/N2=100 2.6 2.6 2.4 2.4 2.2 2.2 2 2 1.8 1.8 1.6 1.6 Feed Pressure Feed Pressure (bar) Feed Pressure Feed Pressure (bar) 1.4 1.4 1.2 1.2 0 5 10 15 20 0 5 10 15 20 Time(s) Time(s)

Feed Pressure=1.481 Feed Pressure=1.635 Feed Pressure=1.481 Feed Pressure=1.635 Feed Pressure=2.07 Feed Pressure=2.37 Feed Pressure=2.07 Feed Pressure=2.37

Figure 6-3: Outlet compressor (B2) pressure changes for a 10% increase, (a) and (b), and 10%

decrease, (c) and (d) in flue gas flow rate. Values of selectivity and feed pressure (bar) are indicated

in each sub-figure.

129

The corresponding changes in the vacuum pump (B6) inlet pressure associated with a 10% increase in flue gas flow rate are shown in Figure 6-4(a) –(b). Inlet pressure increases in order to keep horsepower constant. This increase occurs because as feed flow rate increases the absolute permeate flow rate increases despite the small decrease in feed pressure. The response is slightly faster for lower feed pressures and significantly faster for the lower selectivity membrane. For a given feed pressure, the final steady state pressure is higher for the lower selectivity membrane as this membrane has higher permeability and permeance values because of the Robeson tradeoff between permeability and selectivity. This leads to higher absolute permeation rates and flows of all components.

Figure 6-4(c)-(d) illustrates the permeate pressure response to a 10% step decrease in flue gas flow rate. The permeate increases and the increase is slightly greater than that for a 10% step decrease in flow. This increase is due primarily to the increase in feed pressure that results from a decrease in feed flow rate.

130

(a) CO2/N2=100 (b) CO2/N2=50 0.125 0.135 0.124 0.133 0.131 0.123 0.129 0.122 0.127 0.121 0.125 0.123 0.12 0.121 Permeate Pressure (bar)

Permeate Pressure (bar) 0.119 0.119 0.118 0.117 0 5 10 15 20 0 5 10 15 20 Time(s) Time(s) Feed Pressure=1.481 Feed Pressure=1.635 Feed Pressure=1.4813 Feed Pressure=1.635 Feed Pressure=2.07 Feed Pressure=2.37 Feed Pressure=2.07 Feed Pressure=2.37

(c) CO /N =100 2 2 (d) CO /N =50 0.127 2 2 0.15 0.126 0.125 0.145 0.124 0.14 0.123 0.135 0.122 0.13 0.121 0.125 0.12 0.12 0.119 0.115 Permeate Pressure Permeate Pressure (bar) 0.118 Permeate Pressure (bar) 0.11 0 5 10 15 20 0 5 10 15 20 Time (s) Time (s) feed Pressure=1.481 Feed Pressure=1.635 feed Pressure=1.481 Feed Pressure=1.635 Feed Pressure=2.07 Feed Pressure=2.37 Feed Pressure=2.07 Feed Pressure=2.37

131

6.7 Composition and Flow Changes Resulting from a Step Change in Flue Gas Flow Rate

Figure 6-5(a)-(c) shows the transient response of CO2 mole fraction in the enriching stage permeate (S4) from a 10% increase in flue gas flow rate while Figure 6-

6(a) –(c) shows the changes for a 10% decrease. Pressure ratio is calculated using the new feed pressure in S1 and permeate pressure in S4 as described in this previous section.

The arrows indicate the time at which the response reaches 63.2% of its final steady value which corresponds to the apparent time constant ()

As seen in Figure 6-5, the membrane separation system shows a rapid response as the incoming flow rate changes due to the small time constant value. Clearly increasing feed flow rate increases CO2 composition as the stage cut decreases. Likewise, Figure 6-

6 indicates that a decrease in composition occurs as the flow rate decreases and stage cut increases.

132

(a) CO2/N2=100 0.64

0.62 Pressure Ratio=12.046 0.6 Pressure Ratio=13.317 0.58

0.56 Pressure Ratio=16.613 0.54 Permeate Mole Fraction 2 0.52 Pressure Ratio=18.357 CO 0.5 0 5 10 15 20 Time(s) (b) CO /N =75 0.61 2 2

0.59 Pressure Ratio=12.141 0.57 0.55 Pressure Ratio=13.193 0.53 Pressure Ratio=16.201 0.51 Pressure Ratio=16.499 0.49 Permeate Mole Fraction 2 0.47

CO 0.45 0 5 10 15 20 Time(s) (c) CO /N =50 0.56 2 2 0.54 Pressure Ratio=11.839 0.52 Pressure Ratio=12.038 0.5 0.48 Pressure Ratio=15.086 0.46 Pressure Ratop=16.7696

Permeate Mole Fraction 0.44 2 0.42 CO 0.4 0 5 10 15 20 Time(s)

Figure 6-5:CO2 Permeate mole fraction transients for various selectivities and pressure ratios in response to a 10% feed flow rate increase. The arrow indicates apparent time constant ()

133

(a) CO2/N2=100 0.63 0.61 0.59 0.57 0.55 Pressure Ratio=12.848 0.53 Pressure Ratio=14.263 0.51 Pressure Ratio=18.37 0.49 Permeate Mole Fraction Pressure Ratio=19.995 2 0.47

CO 0.45 0 5 10 15 20 Time (s) (b) CO /N =75 0.6 2 2

0.55 Pressure Ratio=12.961 Pressure Ratio=14.546 0.5 Pressure Ratio=18.497

0.45 Pressure Ratio=19.834 Permeate Mole Fraction 2

CO 0.4 0 5 10 15 20 Time (s)

(c) CO2/N2=50 0.535 0.515 0.495 Pressuure Ratio=12.878 0.475 Pressure Ratio=13.889 0.455 Pressure Ratio=15.168 0.435 0.415 Pressure Ratio=17.147 Permeate Mole Fraction

2 0.395

CO 0.375 0 5 10 15 20 Time (s)

Figure 6-6:CO2 Permeate mole fraction transients for various selectivities and pressure ratios in response to a 10% feed flow rate decrease. The arrow indicates apparent time constant ()

134

Figure 6-7 the CO2 recovery transient response for a 10% increase in feed flue gas flow rate. As expected, the recovery is higher for lower selectivity due to the higher

CO2 permeances and the purity is lower due to the higher recovery. The observed response is quicker for higher pressure ratios consistent with the approximate first order time constants derived earlier.

An increase in flow rate reduces the amount of CO2 removed in the enriching stage which require greater removal of CO2 in the stripping stage. This leads to an increase in the CO2 concentration in recycle stream S3 and a concomitant increase in the

CO2 feed concentration in S1. Conversely, as the feed pressure increases, more CO2 is removed in the enriching stage and the amount of CO2 sent to the stripping stage decreases. This leads to a reduction in the CO2 concentration in the recycle stream S3 and a reduction in theCO2 feed concentration in S1.

Figure 6-8 represents the CO2 recovery when the flow rate is reduced by 10%.

Since reducing feed flow rate results in higher stage cuts, CO2 permeate concentration in

S4 decreases while the CO2 concentration in the retentate of the enriching module (B4) increases. As discussed for a feed flow increase, CO2 permeate concentration also decreases as pressure ratio increases due to a lower incoming CO2 feed partial pressure in the feed flue gas stream.

135

(a) CO /N =100 1 2 2 0.98 0.96 Pressure Ratio=12.046 0.94 Pressure Ratio=13.316 Recovery 2 0.92 Pressure Ratio=16.613 CO 0.9 Pressure Ratio=18.357 0.88 0 5 10 15 20 Time(s) (b) CO /N =75 1 2 2 0.99 0.98 Pressure Ratio=12.141 0.97 0.96 Pressure Ratio=13.193 Recovery 0.95 Pressure Ratio=16.210 2 0.94 CO 0.93 Pressure Ratio=16.499 0.92 0.91 0 5 10 15 20

Recovery 0.975 2 Pressure Ratio=15.086 0.97 CO 0.965 Pressure Ratio=16.769 0.96 0.955 0 5 10 15 20 Time(s)

Figure 6-7:CO2 recovery transients for various selectivities and pressure ratios in response to a 10% feed flow rate increase. The arrow indicates apparent time constant (τ)

136

(a) CO /N =100 0.99 2 2 0.98 0.97 0.96 Pressure Ratio=12.848 0.95 Pressure Ratio=14.263

Recovery 0.94 Pressure Ratio=18.370 2

CO 0.93 Pressure Ratio =19.995 0.92 0.91 0 5 10 15 20 Time (s)

(b) CO2/N2=75 0.995 0.99 0.985 Pressure Ratio=12.961 0.98 0.975 Pressure Ratio=14.546 Recovery

2 0.97 0.965 CO Pressure Ratio=18.497 0.96 0.955 Pressure Ratio=19.834 0.95 0.945 0.94 0 5 10 15 20 Time (s)

(c) CO2/N2=50 1 0.995 Pressure Ratio=12.878 0.99 Pressure Ratio=13.889 0.985 Recovery Pressure Ratio=15.168 2 0.98 CO Pressure Ratio=17.147 0.975 0.97 0 5 10 15 20 Time (s)

Figure 6-8:CO2 recovery transients for various selectivities and pressure ratios in response to a 10% feed flow rate decrease. The arrow indicates apparent time constant ()

137

The transient response of O2 concentration in S3 for a 10% increase and decrease in feed flow rate is depicted in Figure 6.9 and Figure 6-10, respectively. The O2/N2 selectivity used is based on the calculation from the CO2/N2 Robeson plot as described in

Chapter 5. The time constant is indicated by the arrows in the graph. The O2 concentration in stream S3 depends on the CO2/N2 selectivity and operating pressure ratio

Because the flow rate considered in this chapter is much lower than that for commercial power plant, the O2 concentration in stream S3 is insensitive to feed flue gas fluctuations due to the smaller changes of O2 permeate mole fraction in the recycle stream.

Because O2 has the lower permeation rate in comparison to CO2, it takes longer time to reach the new steady as the indicated by the time constants. Similar to CO2 transient response in the enriching module (B4), using higher pressure ratio shows quicker response. As the pressure ratio increases, the permeate flow rate in S4 increases and the flow to the stripping stage decreases. This leads to an increase in O2 loss from the feed air sweep and a reduction in the O2 concentration of the recycle stream S3

138

(a) O2/N2=9.22( CO2/N2=100) 0.2

0.195

0.19 Pressure Ratio=12.0446

0.185 Pressure Ratio=13.316

0.18 Pressure Ratio=16.612

Permeate Mole Fraction 0.175 Pressure Ratio=18.356 2 O 0.17 0 5 10 15 20 Time(s) (b) O /N =7.79( CO /N =75) 0.2 2 2 2 2

0.19 Pressure Ratio=12.141

0.18 Pressure Ratio=13.193

0.17 Pressure Ratio=16.21

Pressure Ratio=16.499

Permeate Mole Fraction 0.16 2 O 0.15 0 5 10 15 20 Time(s) (c) O /N =6.15( CO /N =50) 0.2 2 2 2 2

0.19 Pressure Ratio=11.839 0.18 Pressure Ratio=12.039 0.17 Pressure Ratio=15.086 0.16

Permeate Mole Fraction Pressue Ratio=16.769 2 0.15 O

0.14 0 5 10 15 20 Time(s) Figure 6-9: Inlet vacuum pump (B6) pressure changes for a 10% increase, (a) and (b), and 10% decrease, (c) and (d) in flue gas flow rate. Values of selectivity and feed pressure are indicated in each sub-figure. The arrow indicates apparent time constant (τ) 139

(a) O2/N2=9.22 ( CO2/N2=100) 0.198 0.196 0.194 0.192 Pressure Ratio=12.848 0.19 Pressure Ratio=14.262 0.188 0.186 Pressure Ratio=18.371 0.184 0.182 Pressure Ratio=19.995 Permeate Mole Fraction

2 0.18 O 0.178 0 5 10 15 20 Time (s)

(b) O /N =7.79 ( CO /N =75) 0.19 2 2 2 2 0.185 0.18 Pressure Ratio=12.961 0.175 Pressure Ratio=14.546 0.17 Pressure Ratio=18.497 Pressure Ratio=19.834

Permeate Mole Fraction 0.165 2

O 0.16 0 5 10 15 20 Time (s)

(c) O2/N2=6.15 ( CO2/N2=50) 0.175 0.17 0.165 Pressure Ratio=12.878 0.16 0.155 0.15 Pressure Ratio=13.889 0.145 0.14 Pressure Ratio=15.168 0.135

Permeate Mole Fraction 0.13

2 Pressure Ratio=17.147

O 0.125 0 5 10 15 20 25 30 Time (s)

Figure 6-10: O2 concentration transients for various selectivities and pressure ratios in response to a 10% feed flow rate decrease. The arrow indicates apparent time constant (τ)

140

Figure 6-11 compares the time constant evaluated from the transient simulations of the enriching stage (i.e. the time value where the response reaches 63.2% of its final steady value indicated by the arrow in the figures) with the value calculated from

Equation 6-25. The calculated time constants are in good agreement with the simulation.

The time constant is smaller for higher feed to permeate pressure ratios and lower selectivity. Thus, the transient response for the membrane system depends on the membrane permeation properties and operating pressures.

Figure 6-12 compares the time constants evaluated from the O2 transients in the sweep module with the value calculated from Equation 6-25. The simulation shows a good agreement with the calculated value Similar to the results for the enriching stage, the time constant depends on O2/N2 selectivity and operating pressure ratio. Because of the lower O2 permeation value, the time constant value is significantly higher especially for high CO2/N2 selectivity.

141

2 Cal Value(CO2/N2=100) Cal Value (CO2/N2=75) Cal Value (CO2/N2=50) Sim CO2/N2=100(+10% Flow) 1.8 Sim CO2/N2=75(+10% flow) Sim Co2/N2=50(+10% Flow) Sim CO2/N2=100 Sim CO2/N2=75 (-10% flow) Sim CO2/N2=50 (-10% flow) 1.6 1.4 1.2 1 0.8 Time Constant (s) 0.6 0.4 0.2 0 10.75 12.75 14.75 16.75 18.75 Feed pressure/ Permate pressure

Figure 6- 11: Comparison of time constants for CO2 obtained from the simulations at various CO2/N2

selectivities and pressure ratios to values calculated from Equation (6-25). The solid line represents the

values from Equation (6-25) while the symbols represents the value evaluated from the simulations

142

20 O2/N2=9.2151 O2/N2=7.791 O2/N2=6.1509 Sim O2/N2=9.151(+10% flow) 18 Sim O2/N2=7.791(+10% flow) Sim O2/N2=6.1509( +10% flow) Sim O2/N2=9.2151 (-10% flow) Sim O2/N2=7.791 (-10% flow) 16 Sim O2/N2=6.1509 (-10% flow) 14 12 10 8

Time Constant (s) 6 4 2 0 10.75 11.75 12.75 13.75 14.75 15.75 16.75 17.75 Feed pressure/ Permeate pressure

Figure 6- 12: Comparison of time constants for O2 obtained from the simulations at various CO2/N2 selectivities and pressure ratios to values calculated from Equation (6-25). The solid line represents the values from Equation (6-25) while the symbols represents the value evaluated from the simulations.

143

6.8 Conclusions

In this chapter, a dynamic hollow fiber membrane module permeator model is developed. The model is further lineralized in order to determine the time constant value.

The dynamic behavior of multistage membrane separation system for post-combustion applications was evaluated by incorporating the input changes of feed flue gas flow rate.

The dynamic response of the membrane separation system depends on the component permeation properties and operating feed to permeate pressure ratio. Since membrane area as well as compressor and vacuum pump power are fixed, step changes of input flue gas flow rate results in changes in operating feed and permeate pressures. This in turn can affect CO2 capture and purity.

144

Chapter 7

7. Conclusions and Future Work

In this dissertation, the economic viability of post-combustion CO2 capture using a combined cryogenic-membrane process is examined. The study explicitly accounts for the tradeoff between CO2/N2 selectivity and CO2 permeability that exists for potential membrane materials by assuming membrane permeability can be computed from selectivity using the expression for the Robeson upper bound. For the multistage membrane-cryogenic air feed sweep configuration, optimal operating pressures and membrane selectivity are sought to minimize the Levelized Cost of Electricity (LCOE)

Dynamic simulations for multistage membrane separations also are performed to determine the effect of CO2/N2 selectivity and operating pressure ratio on transient behavior.

7.1 Conclusions

1. A non-isothermal, multicomponent hollow fiber membrane module model is

proposed and solved using a stages in series approximation to discretize the

differential mass balances and direct substitution to solve the resulting non-linear

algebraic equations. The model is validated by demonstrating good agreement

with previously reported experimental and theoretical results.

145

2. For a single stage membrane hybrid system, low CO2/N2 selectivity membranes

offer the advantage of greater CO2 recovery due to higher CO2 permeance.

However, CO2 permeate purity is significantly lower.

3. Increasing CO2 feed partial pressure in the flue gas stream from 13% to 20% is

essential to make single stage membrane hybrid favorable.

4. Although higher CO2 purity may be obtained for materials possessing high

CO2/N2 selectivity, the required membrane area is greater and may not be

preferred economically.

5. The optimum CO2/N2 selectivity appears to be in the moderate range of 40-75 for

a single stage membrane hybrid system.

6. Additional enriching stages in the multistage membrane-cryogenic process enable

use of lower CO2/N2 selectivity membranes to achieve the 90% CO2 recovery and

95% purity targets. The higher CO2 permeance and lower CO2/N2 selectivity of

PDMS significantly reduces the total module membrane area requirement at the

expense of larger plant parasitic load due to the larger flow rates required to

remove CO2 in the stripping stage and recycle it to the enriching stage.

7. Regardless of membrane CO2/N2 selectivity, membrane compression is the

largest contributor to LCOE due to the low CO2 partial pressure in flue gas.

Increasing CO2 feed partial pressure in an affordable method is essential to

minimize LCOE. Using lower compression equipment cost for CO2 permeation

force generation will also reduce OPEX contribution towards LCOE.

8. Higher CO2/N2 selectivity membranes reduce the operating cost (OPEX)

contribution to LCOE because of lower compression energy requirements while 146

lower CO2/N2 selectivity reduces the capital cost (CAPEX) contribution due to

the lower module area requirement.

9. For the air feed sweep systems, decreasing LCOE comes at the expense of lower

boiler feed air O2 concentration. The CO2/N2 selectivity has a significant impact

on the required CO2 removal in the stripping stage and the accompanying O2 loss.

Reducing the required stripping reduces the O2 loss and requires the use of higher

membrane selectivity.

10. The required module area can be reduced by increasing the feed pressure.

Simultaneously reducing the vacuum (i.e., increasing the permeate pressure) can

reduce the increase in energy requirements associated with higher feed pressures

without compromising separation targets.

11. The optimal operating pressure range is broader for high CO2/N2 selectivity

membranes. Higher feed pressures are desired to reduce oxygen loss in the

stripping stage and reduce area requirements.

12. The use of lower selectivity membranes can greatly reduce the required module

area. However, the minimum LCOE is associated with greater oxygen loss in the

stripping stage than for higher selectivity membranes.

13. Using moderate CO2/N2 selectivity membranes in the enriching stage may meet

higher boiler O2 concentration target within the affordable LCOE range. At the

fixed cryogenic parameters considered here, optimal membrane properties are

likely CO2/N2 selectivity of 65 with CO2 permeability of 1180 GPU as it produces

higher CO2 permeate purity at lower module area requirement.

147

14. It is important to note that LCOE calculated here is based on a fixed compression/

vacuum installation cost of $500/kW. LCOE may change significantly depending

on vendor quotes.

15. In this dissertation, the CO2 permeability is calculated from CO2/N2 selectivity

assuming negligible mixed gas and plasticization effects. These effects may

reduce CO2/N2 selectivity and alter CO2 permeability thus affecting the minimum

LCOE.

16. The hollow fiber membrane permeator model is extended to allow transient

simulations. The model was linearized to determine an approximate first-order

time constant. The results obtained here may be useful in developing control

strategies in future work.

17. Membrane separation system shows a rapid response to incoming flue gas flow

rate changes due to the small time constant value. High pressure ratio and low

CO2/N2 selectivity give the fastest response.

18. For fixed membrane area and compressor and vacuum energy consumption (i.e.,

power), step changes in incoming flue gas flow rate lead to changes in feed and

vacuum pressure. The changes depend on membrane selectivity and feed pressure

are accompanied by changes in CO2 recovery and purity as well as O2

concentration in the recycle stream.

7.2 Future work

1. The multistage membrane cryogenic systems considered in this dissertation are

based on the fixed downstream cryogenic process parameters from the MTR

148

[4] design . For these parameters, in order to meet the CO2 purity target of +95%,

the incoming CO2 concentration from the membrane systems must exceed 55%.

Since the dominant cost contribution comes from the membrane compression

system, optimization of the downstream cryogenic component may lead to

additional incremental cost savings by reducing liquefaction costs and reducing

the minimum CO2 concentration required.

2. Increasing CO2 mole fraction in flue gas stream is essential to make membranes

viable for post-combustion CO2 capture. Combining membrane with oxygen

enriched air combustion technology may potentially reduce the overall energy

requirement by allowing lower O2 concentrations in the recycle from the stripping

stage.

3. Changes in feed gas flow rate typically do not occur in a step-wise manner. A

detailed dynamic simulation of the hybrid membrane cryogenic process that

incorporates actual flow rate changes is desired to examine the changes in CO2

recovery and purity and O2 concentration in the recycle stream that occur.

4. Additionally, a dynamic simulation that incorporates thermal changes is desired.

The transient simulation reported here can be used for this purpose as it includes

the temperature dependence of transport properties but will require an additional

energy balance to account for the thermal inertia of each stage.

5. The membrane permeator model developed in this study can be used in techno-

economic analysis for other commercial gas separation applications.

149

References

1. Solomon, S., et al., Irreversible climate change due to carbon dioxide emissions.

Proceedings of the national academy of sciences, 2009. 106(6): p. 1704-1709.

2. Michael Matuszewski , J.P.C., Scott Chen, Research and Development Goals for

CO2 Capture Technology. 2012: NETL Report DOE/NETL-2009/1366.

3. Robeson, L.M., The upper bound revisited. Journal of Membrane Science, 2008.

320(1–2): p. 390-400.

4. Merkel, T.C., et al., Power plant post-combustion carbon dioxide capture: An

opportunity for membranes. Journal of Membrane Science, 2010. 359(1–2): p.

126-139.

5. Ho, M.T., G.W. Allinson, and D.E. Wiley, Reducing the Cost of CO2 Capture

from Flue Gases Using Membrane Technology. Industrial & Engineering

Chemistry Research, 2008. 47(5): p. 1562-1568.

6. Ramasubramanian, K., H. Verweij, and W.S. Winston Ho, Membrane processes

for carbon capture from coal-fired power plant flue gas: A modeling and cost

study. Journal of Membrane Science, 2012. 421–422: p. 299-310.

7. Belaissaoui, B., et al., Hybrid membrane cryogenic process for post-combustion

CO2 capture. Journal of Membrane Science, 2012. 415–416: p. 424-434.

8. Murad Chowdhury, M.H., et al., A New Numerical Approach for a Detailed

Multicomponent Gas Separation Membrane Model and AspenPlus Simulation.

Chemical Engineering & Technology, 2005. 28(7): p. 773-782.

150

9. Scholes, C.A., et al., Cost competitive membrane—cryogenic post-combustion

carbon capture. International Journal of Greenhouse Gas Control, 2013. 17: p.

341-348.

10. Franz, J., et al., Investigating the influence of sweep gas on CO2/N2 membranes

for post-combustion capture. International Journal of Greenhouse Gas Control,

2013. 13: p. 180-190.

11. Bocciardo, D., Optimisation and integration of membrane processes in coal-fired

power plants with carbon capture and storage. 2015.

12. White, L.S., et al., Extended flue gas trials with a membrane-based pilot plant at

a one-ton-per-day carbon capture rate. Journal of Membrane Science, 2015. 496:

p. 48-57.

13. EIA, U.S. Energy-Related Carbon Dioxide Emissions,2014. November 2015, U.S.

Energy Information Adminstration.

14. EPA, U.S. Future Climate Change. 2014 [cited 2015 June,19]; Available from:

http://www3.epa.gov/climatechange/science/future.html.

15. EIA. US Electricity generation by source 2014. 2015 [cited 2015 June, 19];

Available from: http://www.eia.gov/tools/faqs/faq.cfm?id=427&t=3.

16. Katzer, J., The Future of Coal-Options for a Carbon Constrained World 2007

MIT Interdiscipilinary Study

17. Herzog, H.J., Peer reviewed: what future for carbon capture and sequestration?

Environmental science & technology, 2001. 35(7): p. 148A-153A.

18. Bullis, K., Grasping for Ways to Capture Carbon Dioxide on the Cheap, in MIT

Technology Review 2013. 151

19. Metz, B., et al., Carbon dioxide capture and storage. 2005.

20. Zhai, H. and E.S. Rubin, Techno-Economic Assessment of Polymer Membrane

Systems for Postcombustion Carbon Capture at Coal-Fired Power Plants.

Environmental Science & Technology, 2013. 47(6): p. 3006-3014.

21. Zhai, H., E.S. Rubin, and P.L. Versteeg, Water use at pulverized coal power

plants with postcombustion carbon capture and storage. Environmental science &

technology, 2011. 45(6): p. 2479-2485.

22. Thitakamol, B., A. Veawab, and A. Aroonwilas, Environmental impacts of

absorption-based CO 2 capture unit for post-combustion treatment of flue gas

from coal-fired power plant. International Journal of Greenhouse Gas Control,

2007. 1(3): p. 318-342.

23. Rubin, E.S., et al., A proposed methodology for CO2 capture and storage cost

estimates. International Journal of Greenhouse Gas Control, 2013. 17: p. 488-503.

24. Mat, N.C., Y. Lou, and G.G. Lipscomb, Hollow fiber membrane modules. Current

Opinion in Chemical Engineering, 2014. 4: p. 18-24.

25. Stern, S.A. and S.C. Wang, Countercurrent and cocurrent gas separation in a

permeation stage. Comparison of computation methods. Journal of Membrane

Science. 4: p. 141-148.

26. Shindo, Y., et al., Calculation Methods for Multicomponent Gas Separation by

Permeation. Separation Science and Technology, 1985. 20(5-6): p. 445-459.

27. Pettersen, T. and K.M. Lien, Design studies of membrane permeator processes for

gas separation. Gas Separation & Purification, 1995. 9(3): p. 151-169.

152

28. Chen, H., G. Jiang, and R. Xu, An approximate solution for countercurrent gas

permeation separating multicomponent mixtures. Journal of Membrane Science,

1994. 95(1): p. 11-19.

29. Pan, C.Y., Gas separation by high-flux, asymmetric hollow-fiber membrane.

AIChE Journal, 1986. 32(12): p. 2020-2027.

30. Kovvali, A.S., S. Vemury, and W. Admassu, Modeling of Multicomponent

Countercurrent Gas Permeators. Industrial & Engineering Chemistry Research,

1994. 33(4): p. 896-903.

31. Khalilpour, R., et al., Analysis of hollow fibre membrane systems for

multicomponent gas separation. Chemical Engineering Research and Design,

2013. 91(2): p. 332-347.

32. Kaldis, S.P., G.C. Kapantaidakis, and G.P. Sakellaropoulos, Simulation of

multicomponent gas separation in a hollow fiber membrane by orthogonal

collocation — hydrogen recovery from refinery gases. Journal of Membrane

Science, 2000. 173(1): p. 61-71.

33. Makaruk, A. and M. Harasek, Numerical algorithm for modelling multicomponent

multipermeator systems. Journal of Membrane Science, 2009. 344(1–2): p. 258-

265.

34. Davis, R.A., Solution Method for Countercurrent Plug Flow Models of

Multicomponent Gas Separation by Permeation. Separation Science and

Technology, 2005. 40(15): p. 3017-3031.

153

35. Coker, D.T., B.D. Freeman, and G.K. Fleming, Modeling multicomponent gas

separation using hollow-fiber membrane contactors. AIChE Journal, 1998. 44(6):

p. 1289-1302.

36. Coker, D.T., et al., Nonisothermal model for gas separation hollow-fiber

membranes. AIChE Journal, 1999. 45(7): p. 1451-1468.

37. Scholz, M., et al., Modeling Gas Permeation by Linking Nonideal Effects.

Industrial & Engineering Chemistry Research, 2013. 52(3): p. 1079-1088.

38. Bouton, G.R. and W.L. Luyben, Optimum economic design and control of a gas

permeation membrane coupled with the hydrodealkylation (HDA) process.

Industrial & Engineering Chemistry Research, 2008. 47(4): p. 1221-1237.

39. Katoh, T., et al., Dynamic simulation of multicomponent gas separation by

hollow-fiber membrane module: Nonideal mixing flows in permeate and residue

sides using the tanks-in-series model. Separation and Purification Technology,

2011. 76(3): p. 362-372.

40. KAO, Y.-K. and Z. YAN, Dynamic modeling and simulation of simple membrane

permeators. Chemical engineering communications, 1987. 59(1-6): p. 343-370.

41. Murthy Konda, N., G. Rangaiah, and D.K. Lim, Optimal process design and

effective plantwide control of industrial processes by a simulation-based heuristic

approach. Industrial & engineering chemistry research, 2006. 45(17): p. 5955-

5970.

42. Binns, M., et al., Strategies for the simulation of multi-component hollow fibre

multi-stage membrane gas separation systems. Journal of Membrane Science,

2016. 497: p. 458-471. 154

43. Sanders, D.F., et al., Energy-efficient polymeric gas separation membranes for a

sustainable future: A review. Polymer, 2013. 54(18): p. 4729-4761.

44. Wijmans, J.G. and R.W. Baker, The solution-diffusion model: a review. Journal of

Membrane Science, 1995. 107(1–2): p. 1-21.

45. Baker, R.W., Membrane Transport Theory, in Membrane Technology and

Applications. 2004, John Wiley & Sons, Ltd. p. 15-87.

46. Lin, H., Integrated membrane material and process development for gas

separation. Current Opinion in Chemical Engineering, 2014. 4: p. 54-61.

47. Baker, R.W., Future Directions of Membrane Gas Separation Technology.

Industrial & Engineering Chemistry Research, 2002. 41(6): p. 1393-1411.

48. Van Der Sluijs, J.P., C.A. Hendriks, and K. Blok, Feasibility of polymer

membranes for carbon dioxide recovery from flue gases. Energy Conversion and

Management, 1992. 33(5–8): p. 429-436.

49. Favre, E., Carbon dioxide recovery from post-combustion processes: Can gas

permeation membranes compete with absorption? Journal of Membrane Science,

2007. 294(1–2): p. 50-59.

50. Belaissaoui, B., D. Willson, and E. Favre, Membrane gas separations and post-

combustion carbon dioxide capture: Parametric sensitivity and process

integration strategies. Chemical Engineering Journal, 2012. 211–212: p. 122-132.

51. Brunetti, A., et al., Engineering evaluation of CO2 separation by membrane gas

separation systems. Journal of Membrane Science, 2014. 454: p. 305-315.

155

52. Zhao, L., et al., A parametric study of CO2/N2 gas separation membrane

processes for post-combustion capture. Journal of Membrane Science, 2008.

325(1): p. 284-294.

53. Hussain, A. and M.-B. Hägg, A feasibility study of CO2 capture from flue gas by

a facilitated transport membrane. Journal of Membrane Science, 2010. 359(1–2):

p. 140-148.

54. Zhao, L., et al., Cascaded Membrane Processes for Post-Combustion CO2

Capture. Chemical Engineering & Technology, 2012. 35(3): p. 489-496.

55. Bocciardo, D., M.-C. Ferrari, and S. Brandani, Modelling and Multi-stage Design

of Membrane Processes Applied to Carbon Capture in Coal-fired Power Plants.

Energy Procedia, 2013. 37: p. 932-940.

56. Swisher, J.A. and A.S. Bhown, Analysis and optimal design of membrane-based

CO2 capture processes for coal and natural gas-derived flue gas. Energy

Procedia, 2014. 63: p. 225-234.

57. Shao, P., et al., Simulation of membrane-based CO2 capture in a coal-fired power

plant. Journal of Membrane Science, 2013. 427: p. 451-459.

58. Zhao, L., et al., Multi-stage gas separation membrane processes used in post-

combustion capture: Energetic and economic analyses. Journal of Membrane

Science, 2010. 359(1–2): p. 160-172.

59. Burdyny, T. and H. Struchtrup, Hybrid membrane/cryogenic separation of oxygen

from air for use in the oxy-fuel process. Energy, 2010. 35(5): p. 1884-1897.

156

60. Huang, Y., T.C. Merkel, and R.W. Baker, Pressure ratio and its impact on

membrane gas separation processes. Journal of Membrane Science, 2014. 463: p.

33-40.

61. R.Smith, Chemical Process Design and Integration. 2005: John Wiley & Sons,

Hoboken, NJ.

62. Purnomo, I.S.K. and E. Alpay, Membrane column optimisation for the bulk

separation of air. Chemical Engineering Science, 2000. 55(18): p. 3599-3610.

63. Bhide, B.D. and S.A. Stern, A new evaluation of membrane processes for the

oxygen-enrichment of air. I. Identification of optimum operating conditions and

process configuration. Journal of Membrane Science, 1991. 62(1): p. 13-35.

64. Bhide, B.D. and S.A. Stern, A new evaluation of membrane processes for the

oxygen-enrichment of air. II. Effects of economic parameters and membrane

properties. Journal of Membrane Science, 1991. 62(1): p. 37-58.

65. Bhide, B.D. and S.A. Stern, Membrane processes for the removal of acid gases

from natural gas. I. Process configurations and optimization of operating

conditions. Journal of Membrane Science, 1993. 81(3): p. 209-237.

66. Bhide, B.D. and S.A. Stern, Membrane processes for the removal of acid gases

from natural gas. II. Effects of operating conditions, economic parameters, and

membrane properties. Journal of Membrane Science, 1993. 81(3): p. 239-252.

67. Qi, R. and M.A. Henson, Optimization-based design of spiral-wound membrane

systems for CO2/CH4 separations. Separation and Purification Technology, 1998.

13(3): p. 209-225.

157

68. Qi, R. and M.A. Henson, Membrane system design for multicomponent gas

mixtures via mixed-integer nonlinear programming. Computers & Chemical

Engineering, 2000. 24(12): p. 2719-2737.

69. Kookos, I.K., A targeting approach to the synthesis of membrane networks for

gas separations. Journal of Membrane Science, 2002. 208(1–2): p. 193-202.

70. Scholz, M., et al., Structural optimization of membrane-based biogas upgrading

processes. Journal of Membrane Science, 2015. 474: p. 1-10.

71. Ohs, B., J. Lohaus, and M. Wessling, Optimization of membrane based nitrogen

removal from natural gas. Journal of Membrane Science, 2016. 498: p. 291-301.

72. Chowdhury, M.H.M., Simulation, design and optimization of membrane gas

separation, chemical absorption and hybrid processes for CO2 capture. 2011,

University of Waterloo.

73. Marriott, J. and E. Sørensen, The optimal design of membrane systems. Chemical

Engineering Science, 2003. 58(22): p. 4991-5004.

74. Uppaluri, R.V., P. Linke, and A.C. Kokossis, Synthesis and optimization of gas

permeation membrane networks. Industrial & engineering chemistry research,

2004. 43(15): p. 4305-4322.

75. Chang, H. and W.-C. Hou, Optimization of membrane gas separation systems

using genetic algorithm. Chemical Engineering Science, 2006. 61(16): p. 5355-

5368.

76. Corriou, J.-P., C. Fonteix, and E. Favre, Optimization of a pulsed operation of gas

separation by membrane. AIChE Journal, 2008. 54(5): p. 1224-1234.

158

77. Yuan, M., et al., Consideration of a nitrogen-selective membrane for

postcombustion carbon capture through process modeling and optimization.

Journal of Membrane Science, 2014. 465: p. 177-184.

78. Bird, R.B., W.E. Stewart, and E.N. Lightfoot, Transport Phenomena. 2007:

Wiley.

79. Hao, P., Studies of air dehydration by using hollow fiber modules. 2011, The

University of Toledo.

80. Poling, B.E., J.M. Prausnitz, and J.P. O'Connell, The properties of gases and

liquids. 2001: McGraw-Hill.

81. Lide, D.R. and H.V. Kehiaian, CRC Handbook of Thermophysical and

Thermochemical Data. 1994: Taylor & Francis.

82. Ramezan, M., et al., Carbon dioxide capture from existing coal-fired power

plants. National Energy Technology Laboratory, DOE/NETL Report,

2007(401/110907).

83. Plus, A., Aspen Plus user guide. Aspen Technology Limited, Cambridge,

Massachusetts, United States, 2003.

84. Berean, K., et al., The effect of crosslinking temperature on the permeability of

PDMS membranes: Evidence of extraordinary CO2 and CH4 gas permeation.

Separation and Purification Technology, 2014. 122: p. 96-104.

85. Harun, N., et al., Dynamic simulation of MEA absorption process for CO2

capture from power plants. International Journal of Greenhouse Gas Control,

2012. 10: p. 295-309.

159

86. Chalmers, H. and J. Gibbins, Initial evaluation of the impact of post-combustion

capture of carbon dioxide on supercritical pulverised coal power plant part load

performance. Fuel, 2007. 86(14): p. 2109-2123.

87. Seborg, D.E., et al., Process dynamics and control. 2010: John Wiley & Sons.

160

Appendices

A. Net Permeation Directions for Each Gas Component in Membrane Module

According to Component Permeability.

161

B. Example on LCOE Calculations (Membrane with CO2/N2 Selectivity of 75 with CO2 Permeance of 1180 GPU)

*Cost assumptions and calculation used in this dissertation is based on the guideline published by Rubin et al [20] (in the supporting information section)

Membrane-Cryogenic Capital Cost Breakdown Total required Unit cost Total Constituent area(m2) ($/m2) cost($)/($/year) Remarks Installed membrane Include module housing & 1.38E+06 50 6.90E+07 cost frame

Replacement membrane 20% of installed cost 1.38E+06 10 2.76E+06 cost *replacement rate of 0.2/year

Total required area(m2)/ Power Equipment required Installed Cost Total Constituent (kW) ($/m2)/($/kW) cost($)/($/year) Remarks Total membrane *Vacuum, flue gas 1.06E+05 500 5.30E+07 compression compressor, system & CO2 expander, CO2 product

liquefaction compressor power (kW) CO2 chiller compressor Replacement 20% of installed cost 1.38E+06 10 2.76E+06 membrane cost (m2) *replacement rate of 0.2/year

Total heat exchangers 2.14E+04 300 6.42E+06 (m2)

162

Utilities duties Utilities cost ($/GJ) Total cost Utilities (GJ/hr) /($/kg) ($/hr) Remarks *service compressors and -694.17 0.212 147.16 Cooling water vacuum on the enriching stage

Ammonia Refrigeration 335.00 0.0425 14.24 *service cryogenic unit

*service downstream 17.02 2.5 42.55 Process steam cryo-membrane and expander

Process Facilities Capital (PFC) Calculation Breakdown Constituent Capital Cost (M$/MWh) Membrane module installation 6.90E+01 Heat exchanger installation 6.42E+00

Total membrane compression cost & CO2 liquefaction 5.30E+01 Total process facilities capital (PFC) 1.28E+02

163

Total Capital Requirement (TCR) Calculation

Constituent Capital Cost (M$) Assumptions

Process Facilities Capital (PFC) 1.28E+02

General facilites capital 1.28E+01 10% PFC

Eng & home office fees 8.99E+00 7% of PFC

Project contingency cost 1.93E+01 15% PFC Process contingency cost 6.42E+00 5% of PFC

Total Plant Cost (TPC) 1.76E+02 Total PFC & fees

Royalty fees 6.42E-01 0.5%PFC Inventory capital 8.80E-01 0.5%TPC Preproduction (Startup) cost 1 month of fixed O &M 5.42E-01 1 month of variable O & M 3.22E+00 Total capital requirement (TCR) 1.81E+02

Total Maintance Cost (TMC) 4.40E+00 2.5% TPC

Operating and Maintenance (O&M) Cost Breakdown

Constituent Variable O&M (M$/year) Membrane replacement cost 2.76E+00 Electricity consumption** 3.41E+01 Cooling water 1.10E+00 Refrigeration at -25C 1.06E-01 Process steam 100 psi 3.73E-01

CO2 transport and storage 2.20E-01 Variable (O & M) 3.87E+01 **Electricity consumption is calculated as (total electricity consumption*cost of electricity to run the equipment) **Cost of electricity to run the equipment ($/MWh) =43.2

Constituent Fixed O&M (M$/year) Operating Labor 7.89E-01 Maintenance Labor cost 1.76E+00 Total Labor Cost (TLC) 2.55E+00 Administrative & Support Labor 1.32E+00 Maintance material 2.64E+00 Fixed (O & M) 6.51E+00

164

Total Levelized Annual Cost Calculations

Fixed charge Factor 0.1128 Cost Component M$/year Annual Fixed O &M 6.51E+00 Annual Variable O & M 3.87E+01 Total Annual O & M cost 4.52E+01 Annualized capital Cost 2.04E+01 Total Levelized Annual Cost 6.56E+01

LCOE calculation

Total Levelized Capital Capital Fixed Variable Total Annualized Annual Component Required Required O & M O&M O & M Capital Cost LCOE

(M$) (M$/kWnet) (M$/year) (M$/year) (M$/year) (M$/year) (M$/year) ($/MWh) Membrane- Cryo system 1.81E+02 4.08E-01 6.51E+00 3.87E+01 4.52E+01 2.04E+01 6.56E+01 19.84 Base Cost of Electricity ** 1.03E+03 1.87E+03 5.50E+01 7.50E+01 1.30E+02 8.84E+01 2.21E+02 53.96 Total Levelized Cost of Electricity 1.21E+03 1.87E+03 6.15E+01 1.14E+02 1.75E+02 1.09E+02 2.87E+02 73.81 *Base plant cost of electricity component vary with location, utilities cost, electricity cost, plant output and efficiency according to Rubin et al [20]. *Net plant due to the CCS reduced from 550 MWh to 444 MWh

165

C. Simplified Flow Diagram and Stream Table for MTR Air Feed System

(Membrane with CO2/N2 Selectivity of 75 with CO2 Permeance of 1180 GPU

O2 deficient air (S5) B1 B3 Air feed Treated flue gas stream S3 (S1) S2 S4 Lean-CO2 vent B2 Enriched CO2 Coal permeate (S6)

S13 B4 S9

S12 S11

S7 S10 B5 B7 B6 S14

Liq CO2 S8

Stream Number (S) 1 2 Air feed 3 Component (mol) CO2 0.177 0.182 0.060 N2 0.742 0.766 0.790 0.913 O2 0.023 0.027 0.210 0.025 Water 0.058 0.025 0.002 Pressure (bar) 1 2 1 2 Temperature ( C) 27 35 36 35 Flow rate kmol/s 20.459 21.156 17.984 17.0749

166

Stream Number 4 5 6 7 Component (mol) CO2 0.018 0.039 0.660 0.660 N2 0.944 0.769 0.189 0.189 O2 0.039 0.190 0.037 0.037 Water 0.000 0.002 0.114 0.114 Pressure (bar) 2.000 1.000 0.200 9 Temperature(C) 35 35 35 26 Flow rate kmol/s 16.304 18.7548 4.081 4.081

Stream Number 8 9 10 Liq Co2 Component (mol) CO2 0.001 0.742 0.793 0.977 N2 0.000 0.213 0.160 0.011 O2 0.000 0.041 0.045 0.006 Water 1.000 0.004 0.002 0.007 Pressure (bar) 9 9 25 25 Temperature ( C) 28 27 -25 -25 Flow rate kmol/s 0.452 3.629 6.576 1.929

Stream Number 11 12 13 14 Component (mol) CO2 0.717 0.717 0.858 0.193 N2 0.220 0.220 0.087 0.727 O2 0.061 0.061 0.055 0.080 Water 0.002 0.002 0.001 0.000 Pressure (bar) 25 25 9 25 Temperature ( C) -25 10 10 10 Flow rate kmol/s 4.647 4.647 2.947 1.699

167