membranes for gas conditioning hope baumgarner chelsea ryden
Post on 14-Dec-2015
216 Views
Preview:
TRANSCRIPT
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)
top related