Membranes for Gas Conditioning

Hope Baumgarner

Chelsea Ryden

How is natural gas currently processed?

Current Natural Gas Processing

Well & Condensate

RemovalAmine Unit

Sulfur Recovery

Dehydration

Nitrogen Rejection

Natural Gas Liquid Recovery

Natural Gas Liquid

Fractionation

Sale Gas

Amine Unit: CO2 and H2S Removal

Sour GasTreated GasWash WaterCO2Lean Amine

Inlet Separator

Cooler

Filter

Water Wash Drum

Lean Amine Pump

Cross Exchanger

Stripper

Amine Solution Tank

ReboilerPressurized Hot Water

Water

Condenser

CO2 & H2S Removed

Rich Amine Pump Amine Pump

Water Wash Pump

To Atmosphere

Rich Amine

Flash Drum

Contactor

Current Natural Gas Processing

Well & Condensate

RemovalAmine Unit

Sulfur Recovery

Dehydration

Nitrogen Rejection

Natural Gas Liquid Recovery

Natural Gas Liquid

Fractionation

Sale Gas

Claus Unit: Sulfur Recovery

Furnace

Catalytic Section

Liquid Sulfur

Tail Gas

1000-1400°C

Overall Reaction:

2H2S+O2 S2 + 2H2O

Thermal Reaction:

2H2S +3O2 2SO2 + 2H2O

Catalytic Reaction: Al2O3

2H2S+SO2 3S + 2H2O

Current Natural Gas Processing

Well & Condensate

RemovalAmine Unit

Sulfur Recovery

Dehydration

Nitrogen Rejection

Natural Gas Liquid Recovery

Natural Gas Liquid

Fractionation

Sale Gas

Glycol Dehydration Unit

Rich Glycol

Wet Gas

Lean Glycol

Wet Gas

Glycol Contactor

Filter

Reboiler

Flash Gas

Water Vapor

Current Natural Gas Processing

Well & Condensate

RemovalAmine Unit

Sulfur Recovery

Dehydration

Nitrogen Rejection

Natural Gas Liquid Recovery

Natural Gas Liquid

Fractionation

Sale Gas

Nitrogen Rejection

Nitrogen Vent

Feed Gas

CondenserLow Pressure Column

High Pressure Column

Reboiler

Current Natural Gas Processing

Well & Condensate

RemovalAmine Unit

Sulfur Recovery

Dehydration

Nitrogen Rejection

Natural Gas Liquid Recovery

Natural Gas Liquid

Fractionation

Sale Gas

Natural Gas Liquid Recovery

Natural Gas Feed

Refrigerant

Turbo Expander

Sale Gas

DemethanizerCold Reflux Compressor

Cold Separator

NGL

Current Natural Gas Processing

Well & Condensate

RemovalAmine Unit

Sulfur Recovery

Dehydration

Nitrogen Rejection

Natural Gas Liquid Recovery

Natural Gas Liquid

Fractionation

Sale Gas

Natural Gas Liquid Fractionation

Deethanizer Depropanizer Debutanizer

Recycle Vapor Propane Product Butane Product

Reboiler Reboiler Reboiler

Condenser Condenser CondenserReflux Drum Reflux

Drum

Reflux Drum

Overview of Problem

Overall Goal•Explore the use of membrane networks in the separation of CO2, H2S, N2, & heavier hydrocarbons from natural gas

Specific Goal Addressed in This presentation• Separation of CO29 % CO2

89 % CH4

0.001% H2S0.98 % C2H6

0.57 % C3H8

0.35 % C4H10

0.1 % N2

1.9 % CO2

97 % CH4

0.0001% H2S0.68 % C2H6

0.25 % C3H8

0.09% C4H10

0.08 % N294% CO2

1.19 % CH4

0.03% H2S2.14% C2H6

1.18% C3H8

0.86% C4H10

0.60% N2

Overview of Problem

Membranes • Separates based on diffusion and solubility

Membrane Network• Simple case

Overview of Problem

Current Technology: Amine Absorption

Sour GasTreated GasWash WaterCO2Lean Amine

Inlet Separator

Cooler

Filter

Water Wash Drum

Lean Amine Pump

Cross Exchanger

Stripper

Amine Solution Tank

ReboilerPressurized Hot Water

Water

Condenser

CO2 & H2S Removed

Rich Amine Pump Amine Pump

Water Wash Pump

To Atmosphere

Rich Amine

Flash Drum

Contactor

Overview of Problem

• Existing cost comparison for membrane unit vs. amine unit

How do membranes work?

Membrane Theory

•Ideal membraneoHigh permeance =oHigh separation factor (selectivity) =

A, B = componentsyi = mole fraction in permeate

xi = mole fraction in retentate

Membrane Theory

•Fick’s Law describes mass transport

Ni= molar flux species i

Di= diffusivity component i

lm= membrane thickness

Membrane Theory

•Assume thermodynamic equilibrium at interface•Fick’s Law can be related to partial pressure by Henry’s Law

•Assume Hi independent of

total pressure and sametemperature at both interfaces

Membrane Theory

•Combining equations

•Neglecting external mass transfer resistances

•Substituting

Membrane Theory

•Where permeability depends on the solubility and the diffusivity

•High flux with thin membrane and high pressure on the feed side

permeance

Membrane Designs

Common Membrane Modules

Spiral wound•<20% of membranes formed•High permeances and flux•More resistant to plasticization•High production cost: $10-100/m2

•Allow wide range of membrane materials

Common Membrane Modules

•Most common•More membrane area per volume•Low production cost: $2-5/m2

•Low reliability due to fouling•Careful and expensive treatment

Hollow Fiber

Common Membrane Modules

Spiral-Wound Hollow-Fiber

Packing Density, m2/m3

200-800 500-9,000

Resistance to fouling Moderate Poor

Ease of cleaning Fair Poor

Relative cost Low Low

Main applications D, RO, GP, UF, MF D, RO, GP, UF

D=Dialysis, RO=Reverse Osmosis, GP=Gas Permeation, PV=Pervaporation, UF=Ultrafiltration, MF=Microfiltration

Membrane Material

Permeated Component

Preferred Polymer Material

Polymer used Selectivities over CH4 (%)

CO2 Glassy Cellulose AcetatePolyimidePerfluoropolymer

10-20

H2S Rubbery Amide block co-polymer

20-30

N2 GlassyRubbery

PerfluoropolymerSilicone rubber

2-30.3

H2O Rubbery/Glassy several >200

C3+ Rubbery Silicone rubber 5-20

Table 1. Typical selectivities for high pressure natural gas (Baker & Lokhandwala)

Membrane Material

Glassy Polymer

Temperature below glass transition point

Polymer chains fixed, rigid & tough

Separate gases based on size

Membrane Material

Rubbery Polymer

Temperature above glass transition point

Motion of polymer chain material becomes elastic & rubbery

Separate gases based on sorption

Membrane Material

Cellulose Acetate High CO2 / CH4 selectivity

Lower H2S / CH4 selectivity

Non-reactive to most organic solvents

Polyimide Rigid, bulky, non-planar structure

Inhibited local motion of polymer chains

High Permeability to water vapor

Membrane Advantages and Disadvantages

Membrane Advantages

•Lower capital costoSkid mounted

Cost and time are minimalLower installationcost

•Treat high concentration gasoMembrane plant treating 5 mil scfd w/ 20% CO2 would be less than half the size of plant treating 20 mil scfd w/ 5% CO2

Membrane Advantages

•Operational simplicityoUnattended for long periods (Single Stage)oStart up, operation, and shutdown can be automated from a control room with minimal staffing (Multistage)

•Space efficiencyoSkid constructionoOffshore environments

Membrane Advantages

•Design efficiencyoIntegrate operations

Dehydration, CO2 & H2S removal, etc.

•Power generationoReduce electric power/fuel consumption

•EcofriendlyoPermeate gases used as fuel or reinjected into well

Membrane Disadvantages

•PlasticizationoMembrane materials absorb 30-50 cm3 of CO2/cm3 polymer

Absorbed CO2 swells and dilates the polymer•Increases mobility of polymer chains•Decreases selectivity

•Physical agingoGlassy polymers are in nonequilibrium state

Over time, polymer chains relax, resulting in lower permeability

Membrane Disadvantages

•High compressor costoMembranes only 10-25% of total costoSignificant reductions in membrane cost might not markedly change total plant costo Compressor cost is 2-3 times the skid cost

Membrane Network

Membrane Network

•2 Membrane Network

•3 Membrane Network

•How do we find the membrane network?•Superstructure

•Membranes, compressors, mixers, splitters, streams

Superstructure

•Superstructure allows for all possible network configurations

For example:

Superstructure

SuperstructureResulting membrane network:

How do we build this superstructure?

Mathematical Model

•Mathematical programming model•Assumptions: Countercurrent flow in hollow fiber module•Uniform properties in each segment•Steady-state•No pressure drop across permeate or retentate side•Constant permeabilities independent of concentration•No diffusion in axial direction•Deformation not considered

Hollow Fiber Mathematical Model•Flux through membrane

• Shell side component balance

•Tube side component balance

Hollow Fiber Mathematical ModelMixer/Splitter Balances

•Feed balance

Hollow Fiber Mathematical ModelMixer/Splitter Balances

•Splitter balance

1

2

Hollow Fiber Mathematical ModelMixer/Splitter Balances

•CO2 composition

•rcomp=0.02

Hollow Fiber Mathematical ModelMixer/Splitter Balances

•Mixer Balance

1

2

Hollow Fiber Mathematical Model

•Permeate power

1

2

• Non-linear equations in model

• Non-linear equations discretized to give linear program

Hollow Fiber Mathematical Model

Objective Function

Annual Process Cost: minimized

• Fcc: Capital Charge

• Fmr: Membrane Replacement

• Fmt: Membrane Maintenance

• Fut: Utility Cost

• Fpl: Cost of Product loss

Objective Function

Fixed Capital Investment:

• fmh: Membrane Housing ($200/m2)

• fcp: Capital Cost of Gas Powered Compressor ($1000/kW)

• Wcp: Compressor Power (kW)

• ηcp: Compressor efficiency (70%)

Objective Function

• fcc: Capital Charge (27%/yr)

• fwk: Working Capital (10% Ffc)

Capital Charge:

Objective Function

Membrane Replacement:

• fmr: Membrane Replacement ($90/m2)

• tm: Membrane Life (3 yr)

Objective Function

Membrane Maintenance:

• fmt: Membrane Maintenance (5% Ffc)

Objective Function

Utility Cost:

• fsg: Utility and Sale Gas Price ($35/Km3)

• fhv: Sales Gas Gross Heating Value (43 MJ/ m3)

• twk: Working Time (350 days/yr)

Objective Function

Product Loss:

• mp : total flow rate of methane in permeate

How is this implemented?

ProgramSet and Parameter

DeclarationVariable Declaration

ProgramEquations

Program

Results

Results

2 Membrane Network at 79 lb-mol/hr

Objective function: $163,000% CH4 lost: 11.20

0.42 kW

3 Membrane Network at 79 lb-mol/hr

Objective function: $130,000%CH4 lost: 7.77

4 Membrane Network at 79 lb-mol/hr

Objective function: $130,000%CH4 lost: 7.77

Results: Comparison

Objective

Function ($)

Area (m2) Wcp (KW) % CH4 Lost

2-Membrane

Network

163,000 160 0.42 11.2

3-Membrane

Network

130,000 435 80 7.77

4-Membrane

Network

130,000 435 80 7.77

Comparison between membrane models at 79 lb-mol/hr

3 Membrane Network at 127 lb-mol/hr

Objective function: $230,000%CH4 lost: 9.44

3 Membrane Network at 238 lb-mol/hr

Objective function: $539,000%CH4 lost: 10.90

Membrane Network Verification

Membrane Network Verification

Compressor Model Work (kW) Pro-II Work (kW)

C1 82.1 82.9

C2 39.1 39.5

C3 8.3 8.4

C4 93.6 94.7

C5 44.5 44.2

Work comparison for 238 lb-mol/hr

Results

Total Annualized Cost vs. flow rate for an amine unit and 3 membrane network at 19% CO2 in the feed

Results: Cost Analysis

Flow rate (MMscfd) FCI ($) Operating

Cost ($/yr)

TAC ($/yr)

15 yr.

Membrane 90 30.6 M 13 M 15 M

180 61 M 26 M 30 M

270 92 M 39 M 45 M

365 123 M 52 M 60 M

455 153 M 65 M 75 M

550 184 M 77 M 90 M

Amine 90 3 M 21 M 21 M

180 5.4 M 30 M 30 M

270 7.8 M 37 M 38 M

365 9.7 M 43 M 44 M

455 12 M 49 M 50 M

550 14 M 54 M 55 M

Comparison between 3 membrane network and amine unit at 19 %CO2

Results

Adjusted existing cost for membrane network

Results

Results

Total Annualized Cost vs. flow rate for an amine unit and 3 membrane network at 9% CO2 in the feed

0 100 200 300 400 500 600 700$0

$10,000,000

$20,000,000

$30,000,000

$40,000,000

$50,000,000

$60,000,000

$70,000,000

Membrane NetworkAmine Unit

Flow rate( MMscfd)

Tota

l Ann

ulai

zed

Cost

($/y

r) 1

5 ye

ar p

erio

d

Results: Cost Analysis

Comparison between 3 membrane network and amine unit at 9 %CO2

Flow rate

(MMscfd)

FCI ($) Operating Cost

($/yr)

TAC ($/yr) 15 yr.

Membrane 90 18M 9M 10M

180 36M 18M 20M

270 55M 27M 31M

360 73M 36M 41M

455 91M 45M 51M

550 109M 54M 61M

Amine 90 5M 12M 12M

180 6M 17M 18M

270 7M 22M 22M

360 8M 26M 26M

455 10M 29M 30M

550 11M 33M 33M

Recommendations

•Membrane networks have an overall lower total annualized cost and utility cost compared to an amine unit at flow rates less than 200 MMscfd•Cost evaluation for membranes to replace other gas conditioning units•CO2 concentrations other than 20% need to be investigated in more detail

Questions?

References

•Baker, Richard. “Future Directions of Membrane Gas Separation Technology.” Industrial & Engineering Chemistry Research. 2002. Sarkey’s Senior Lab. 7 Feb. 2009. <http://pubs.acs.org> •Baker, Richard and Kaaeid Lokhandwala. “Natural Gas Processing with Membranes: An Overview.” Industrial & Engineering Chemistry Research. 2008. Sarkey’s Senior Lab. 4 Feb. 2009 <http://pubs.acs.org>.

•Kookos, I.K. “A targeting approach to the synthesis of membrane network for gas separations” Membrane Science, 208, 193-202, 2002.

• Mohammadi, T., Moghadam, Tavakol, and et al. “Acid Gas Permeation Behavior Through Poly(Ester Urethane Urea) Membrane.”Industrial & Engineering Chemistry Research. 2008. Sarkey’s Senior Lab. 4 Feb. 2009 <http://pubs.acs.org>.

•Natural Gas Supply Association. 2004. Sarkey’s Senior Lab. 7 Feb. 2009 <http://www.naturalgas.org/index.asp>.

•Perry, R.H.; Green, D.W. (1997). Perry’s Chemical Engineers’ Handbook (7th Edition). McGraw-Hill.

• Seader, J. D., and Henley, E. J. "Separation Process Principles.” New York: John Wiley & Sons, Inc., 1998.

APPENDIX

Membrane Simulation Results

• CO2 flow rate: 0.2

• CH4 flow rate: 0.8

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

XCO2 Tube sideXCH4 Tube SideXCO2 Shell SideXCH4 Shell Side

Membrane Area (m2)

Mol

e Co

mpo

sition

s

Figure 1. Molar compositions with varying membrane area.

2 Membrane Network at 79 lb-mol/hr @ 19%CO2

0.42 kW

3 Membrane Network at 79 lb-mol/hr @ 19%CO2

Programming Output

Programming Output

Programming Output

Programming Output

3 Membrane Network at 127 lb-mol/hr @ 19%CO2

3 Membrane Network at 238 lb-mol/hr @ 19%CO2

3 Membrane Network at 79 lb-mol/hr @ 9% CO2

Hollow Fiber Mathematical ModelDiscrete Equations

•Lower bound component flow rate tube side

• : discrete variable• : binary variable• : total flow rate 1

2

3

41

0.25

0

0.75

0.50

segmentsbinary variables

Hollow Fiber Mathematical ModelDiscrete Equations

•Upper bound component flow rate tube side

• : discrete variable• : binary variable• : total flow rate 1

2

3

41

0.25

0

0.75

0.50

segmentsbinary variables

Amine Unit Simulation

1

2

3

4

5

6

CN-1

V-1

HX-1

2

3

4

5

6

7

8

9

10

11

1

12RG-1

CL-1

SL-2

SC-1

SL-1

MX-1 HXAMX-2

PU-1

HX-2

3

1

2

4

5

6

9

10

7

8

WAT

W1

XWAT

20

19

10B

XMEA

11 11C

3C

3B

Equipment & Utility Cost at 79 lb-mol/hr

Columns Type No. of trays

Operating pressure Cost

1 Absorber Valve trays 6 250 psia $15,3342 Stripper Valve trays 12 16 psia $32,736

Exchangers MOC Duty (MMBtu/hr) Area (ft2)  

1 Rich amine / Lean amine Stainless Steel 16.45 241.73955 $4,772 2 Lean amine / water Stainless Steel 10.96 37.191652 $2,651 3 Lean amine / water Stainless Steel 6.098 28.193677 $2,439

Pump MOC Power (HP)

 

   Pump lean amine solution Stainless Steel 130   $1,803

Valve MOC Diameter (m)

Type

 Rich amine expansion valve Stainless Steel 0.2 Flanged $8,484

MDEA initial amt cost       $552

Total   $68,771

Cooling waterFlow(1000 kg/hr) Price ($ /m3) Cost ($ / yr)

17.53959549 0.29 $42,726

Natural gas as heating utility for reboilerReboiler (MMBtu/hr) Price ( $ / MMBTU)  

2.73 5 $114,516

ElectricityDuty (kW) Price ($ / kWh)  

4.42 0.062 $2,301.94

MDEA RecycleFlow (lb/hr) Price ($/lb)  

0.11917 1.54 $1,541.58Total $161,086

Equipment & Utility Cost at 127 lb-mol/hr

Columns Type No. of trays

Operating pressure Cost

1 Absorber Valve trays 6 250 psia $15,4242 Stripper Valve trays 12 16 psia $37,434

Exchangers MOCDuty

(MMBtu/hr) Area (ft2)  1 Rich amine / Lean amine Stainless Steel 16.45 711.08872 $9,544 2 Lean amine / water Stainless Steel 10.96 94.337643 $3,075 3 Lean amine / water Stainless Steel 6.098 185.37014 $4,242

Pump MOC Power (HP)

 

   Pump lean amine solution Stainless Steel 130   $1,909

Valve MOC Diameter (m)

Type

 Rich amine expansion valve Stainless Steel 0.2 Flanged $8,484

MDEA initial amt cost     $701

Total   $80,813

Cooling waterFlow(1000 kg/hr) Price ($ /m3) Cost ($ / yr)

44.80690133 0.29 $109,150

Natural gas as heating utility for reboilerReboiler (MMBtu/hr) Price ( $ / MMBTU)  

6.96 5 $292,374

ElectricityDuty (kW) Price ($ / kWh)  

11.2611 0.062 $5,864.78

MDEA RecycleFlow (lb/hr) Price ($/lb)  

0.11917 1.54 $1,541.58Total $408,930

Equipment & Utility Cost at 238 lb-mol/hr

Columns Type No. of traysOperating pressure Cost

1 Absorber Valve trays 6 250 psia $27,9322 Stripper Valve trays 12 16 psia $53,235

Exchangers MOC Duty (MMBtu/hr) Area (ft2)  

1Rich amine / Lean amine Stainless Steel 16.45 804.06735 $15,907

2Lean amine /

water Stainless Steel 10.96 113.88082 $4,242

3Lean amine /

water Stainless Steel 6.098 86.315086 $3,712

Pump MOC Power (HP) 

 

 Pump lean

amine solution Stainless Steel 130

 

$2,651

Valve MOC Diameter (m)Type

 Rich amine expansion valve Stainless Steel 0.2 Flanged $8,484

MDEA initial amt cost     $871 Total   $117,033

Cooling waterFlow(1000 kg/hr) Price ($ /m3) Cost ($ / yr)

53.48166714 0.29 $130,281

Natural gas as heating utility for reboilerReboiler (MMBtu/hr) Price ( $ / MMBTU)  

8.311611536 5 $349,088

ElectricityDuty (kW) Price ($ / kWh)  

13.62 0.062 $7,093.30

MDEA RecycleFlow (lb/hr) Price ($/lb)  

0.23834 1.54 $3,083.17Total $489,545

Membrane Theory

•For binary gas mixture

•If PF>>PP

Membrane Theory

•Rearranging to get the Ideal Separation Factor

•Achieve large separation with large diffusivity or solubility ratio

Independent Verification

Comparison of GAMS and Excel Membrane Concentration Profile

0 50 100 150 200 2500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

CO2CH4

Number of Segments

Flow

rate

(mol

/s)

0 50 100 150 200 2500.72

0.74

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0.92

CO2CH4

Number of Segmentsflo

w ra

te (m

ol/s

)

Figure 4. Excel simulation tube side 0.9 CH4 & 0.1 CO2

Figure 5. simulation tube side 0.9 CH4 & 0.1 CO2

Comparison of GAMS and Excel Membrane Concentration Profile

Figure 6. Excel simulation shell side 0.9 CH4 & 0.1 CO2

Figure 7. GAMS simulation shell side 0.9 CH4 & 0.1 CO2

0 50 100 150 200 2500

0.02

0.04

0.06

0.08

0.1

0.12

0.14

CO2CH4

Number of Segments

Flow

rate

(mol

/s)

0 50 100 150 200 2500

0.02

0.04

0.06

0.08

0.1

0.12

0.14

CO2CH4

Number of Segments

flow

rate

(mol

/s)

Comparison of GAMS and Excel Membrane Concentration Profile

Figure 8. Excel simulation tube side 0.8 CH4 & 0.2 CO2

Figure 9. GAMS simulation tube side 0.8 CH4 & 0.2 CO2

0 50 100 150 200 2500.62

0.64

0.66

0.68

0.7

0.72

0.74

0.76

0.78

0.8

0.82

CO2CH4

Number of Segments

flow

rate

(mol

/s)

0 50 100 150 200 2500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

CO2CH4

Number of SegmentsFl

ow r

ate

(mol

/s)

Comparison of GAMS and Excel Membrane Concentration Profile

Figure 10. Excel simulation shell side 0.8 CH4 & 0.2 CO2

Figure 11. GAMS simulation shell side 0.8 CH4 & 0.2 CO2

0 50 100 150 200 2500

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

CO2CH4

Number of Segments

flow

rate

(mol

/s)

0 50 100 150 200 2500

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

CO2CH4

Number of Segments

Flow

rate

(mol

/s)

Comparison of GAMS and Excel Membrane Concentration Profile

Figure 12. Excel simulation tube side 0.7 CH4 & 0.3 CO2

Figure 13. GAMS simulation tube side 0.7 CH4 & 0.3 CO2

0 50 100 150 200 2500.54

0.56

0.58

0.6

0.62

0.64

0.66

0.68

0.7

0.72

CO2CH4

Number of Segments

flow

rate

(mol

/s)

0 50 100 150 200 2500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

CO2CH4

Number of SegmentsFl

ow ra

te (m

ol/s

)

Comparison of GAMS and Excel Membrane Concentration Profile

Figure 14. Excel simulation shell side 0.7 CH4 & 0.3 CO2

Figure 15. GAMS simulation shell side 0.7 CH4 & 0.3 CO2

0 50 100 150 200 2500

0.05

0.1

0.15

0.2

0.25

0.3

CO2CH4

Number of Segments

flow

rate

(mol

/s)

0 50 100 150 200 2500

0.05

0.1

0.15

0.2

0.25

0.3

CO2CH4

Number of Segments

Flow

rate

(mol

/s)

Comparison of GAMS and Excel Membrane Concentration Profile

Figure 16. Excel simulation tube side 0.6 CH4 & 0.4 CO2

Figure 17. GAMS simulation tube side 0.6 CH4 & 0.4 CO2

0 50 100 150 200 2500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

CO2CH4

Number of Segments

flow

rate

(mol

/s)

0 50 100 150 200 2500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

CO2CH4

Number of Segments

Flow

rate

(mol

/s)

Comparison of GAMS and Excel Membrane Concentration Profile

Figure 18. Excel simulation shell side 0.6 CH4 & 0.4 CO2

Figure 19. GAMS simulation shell side 0.6 CH4 & 0.4 CO2

0 50 100 150 200 2500

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

CO2CH4

Number of Segments

flow

rate

(mol

/s)

0 50 100 150 200 2500

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

CO2CH4

Number of Segments

Flow

rate

(mol

/s)

Comparison of GAMS and Excel Membrane Concentration Profile

Figure 20. Excel simulation tube side 0.5 CH4 & 0.5 CO2

Figure 21. GAMS simulation tube side 0.5 CH4 & 0.5 CO2

0 20 40 60 80 100 120 1400

0.1

0.2

0.3

0.4

0.5

0.6

CO2CH4

Segments

Flow

rate

(mol

/s)

0 20 40 60 80 100 1200

0.1

0.2

0.3

0.4

0.5

0.6

CO2CH4

Number of Segments

flow

rate

(mol

/s)

Comparison of GAMS and Excel Membrane Concentration Profile

Figure 22. Excel simulation shell side 0.5 CH4 & 0.5 CO2

Figure 23. GAMS simulation shell side 0.5 CH4 & 0.5 CO2

0 20 40 60 80 100 1200

0.1

0.2

0.3

0.4

0.5

0.6

CO2CH4

Number of Segments

flow

rate

(mol

/s)

0 20 40 60 80 100 1200

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

CO2CH4

Number of Segments

Flow

rate

(mol

/s)