Transcript Membranes for Gas Conditioning

Membranes for Gas Conditioning
Hope Baumgarner
Chelsea Ryden
How is natural gas
currently processed?
Current Natural Gas Processing
Sulfur Recovery
Well &
Condensate
Removal
Amine Unit
Dehydration
Natural Gas
Liquid
Fractionation
Natural Gas
Liquid Recovery
Nitrogen
Rejection
Sale Gas
Amine Unit: CO2 and H2S Removal
Sour Gas
Treated Gas
Wash Water
CO2
Lean Amine
Rich Amine
To Atmosphere
Water Wash Drum
CO2 & H2S Removed
Water Wash Pump
Condenser
Lean Amine Pump
Stripper
Water
Contactor
Filter
Cooler
Cross Exchanger
Inlet Separator
Amine Solution Tank
Pressurized Hot Water
Reboiler
Rich Amine Pump
Flash Drum
Amine Pump
Current Natural Gas Processing
Sulfur Recovery
Well &
Condensate
Removal
Amine Unit
Dehydration
Natural Gas
Liquid
Fractionation
Natural Gas
Liquid Recovery
Nitrogen
Rejection
Sale Gas
Claus Unit: Sulfur Recovery
Catalytic Section
Furnace
Tail Gas
1000-1400°C
Liquid Sulfur
Overall Reaction:
2H2S+O2
S2 + 2H2O
Thermal Reaction:
2H2S +3O2
2SO2 + 2H2O
Catalytic Reaction:
Al2O3
2H2S+SO2
3S + 2H2O
Current Natural Gas Processing
Sulfur Recovery
Well &
Condensate
Removal
Amine Unit
Dehydration
Natural Gas
Liquid
Fractionation
Natural Gas
Liquid Recovery
Nitrogen
Rejection
Sale Gas
Glycol Dehydration Unit
Water
Vapor
Flash Gas
Wet Gas
Lean Glycol
Reboiler
Glycol
Contactor
Rich Glycol
Wet Gas
Filter
Current Natural Gas Processing
Sulfur Recovery
Well &
Condensate
Removal
Amine Unit
Dehydration
Natural Gas
Liquid
Fractionation
Natural Gas
Liquid Recovery
Nitrogen
Rejection
Sale Gas
Nitrogen Rejection
Condenser
Low Pressure
Column
Reboiler
High Pressure
Column
Feed Gas
Nitrogen Vent
Current Natural Gas Processing
Sulfur Recovery
Well &
Condensate
Removal
Amine Unit
Dehydration
Natural Gas
Liquid
Fractionation
Natural Gas
Liquid Recovery
Nitrogen
Rejection
Sale Gas
Natural Gas Liquid Recovery
Turbo
Expander
Natural Gas
Feed
Cold Reflux
Compressor
Sale Gas
Demethanizer
Refrigerant
Cold Separator
NGL
Current Natural Gas Processing
Sulfur Recovery
Well &
Condensate
Removal
Amine Unit
Dehydration
Natural Gas
Liquid
Fractionation
Natural Gas
Liquid Recovery
Nitrogen
Rejection
Sale Gas
Natural Gas Liquid Fractionation
Propane Product
Recycle Vapor
Condenser
Reflux
Drum
Reflux
Drum
Reboiler
Deethanizer
Condenser
Condenser
Reflux
Drum
Butane Product
Reboiler
Depropanizer
Reboiler
Debutanizer
Overview of Problem
•Explore the use of membrane networks in the
separation of CO2, H2S, N2, & heavier hydrocarbons
from natural gas
• Separation of CO2
9 % CO2
89 % CH4
0.001% H2S
0.98 % C2H6
0.57 % C3H8
0.35 % C4H10
0.1 % N2
94% CO2
1.19 % CH4
0.03% H2S
2.14% C2H6
1.18% C3H8
0.86% C4H10
0.60% N2
1.9 % CO2
97 % CH4
0.0001% H2S
0.68 % C2H6
0.25 % C3H8
0.09% C4H10
0.08 % N2
Overview of Problem
Membranes
Separates based on diffusion and solubility
Membrane Network
Simple case
Overview of Problem
Current Technology: Amine Absorption
Sour Gas
Treated Gas
Wash Water
CO2
Lean Amine
Rich Amine
To Atmosphere
Water Wash Drum
CO2 & H2S Removed
Water Wash Pump
Condenser
Lean Amine Pump
Stripper
Water
Contactor
Filter
Cooler
Cross Exchanger
Inlet Separator
Amine Solution Tank
Pressurized Hot Water
Reboiler
Rich Amine Pump
Flash Drum
Amine Pump
Overview of Problem
How do membranes
work?
Membrane Theory
•Ideal membrane
oHigh permeance =
oHigh separation factor (selectivity) =
A, B = components
yi = 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 same
temperature at both interfaces
Membrane Theory
•Combining equations
•Neglecting external mass transfer resistances
•Substituting
Membrane Theory
•Where permeability depends on the solubility
and the diffusivity
permeance
•High flux with thin membrane and high
pressure on the feed side
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
Hollow Fiber
•Most common
•More membrane area
per volume
•Low production cost:
$2-5/m2
•Low reliability due to
fouling
•Careful and expensive
treatment
Common Membrane Modules
Spiral-Wound
Hollow-Fiber
200-800
500-9,000
Moderate
Poor
Ease of cleaning
Fair
Poor
Relative cost
Low
Low
Packing Density,
m2/m3
Resistance to fouling
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 Polymer used
Material
Selectivities over
CH4 (%)
CO2
Glassy
Cellulose Acetate
Polyimide
Perfluoropolymer
10-20
H2S
Rubbery
Amide block copolymer
20-30
N2
Glassy
Rubbery
Perfluoropolymer
Silicone rubber
2-3
0.3
H2O
Rubbery/Glassy
several
>200
C3 +
Rubbery
Silicone rubber
5-20
Table 1. Typical selectivities for high pressure natural gas (Baker & Lokhandwala)
Membrane Material
Temperature below glass
transition point
Glassy Polymer
Polymer chains fixed,
rigid & tough
Separate gases based on
size
Membrane Material
Temperature above glass
transition point
Rubbery Polymer
Motion of polymer chain
material becomes elastic
& rubbery
Separate gases based on
sorption
Membrane Material
Non-reactive to most
organic solvents
Cellulose Acetate
High CO2 / CH4 selectivity
Lower H2S / CH4 selectivity
High Permeability to water
vapor
Polyimide
Rigid, bulky, non-planar
structure
Inhibited local motion of
polymer chains
Membrane Advantages
and Disadvantages
Membrane Advantages
•Lower capital cost
oSkid mounted
Cost and time are
minimal
Lower installation
cost
•Treat high concentration gas
oMembrane 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 simplicity
oUnattended for long periods (Single Stage)
oStart up, operation, and shutdown can be automated
from a control room with minimal staffing
(Multistage)
•Space efficiency
oSkid construction
oOffshore environments
Membrane Advantages
•Design efficiency
oIntegrate operations
Dehydration, CO2 & H2S removal, etc.
•Power generation
oReduce electric power/fuel consumption
•Ecofriendly
oPermeate gases used as fuel or reinjected into well
Membrane Disadvantages
•Plasticization
oMembrane materials absorb 30-50 cm3 of CO2/cm3
polymer
Absorbed CO2 swells and dilates the polymer
•Increases mobility of polymer chains
•Decreases selectivity
•Physical aging
oGlassy polymers are in nonequilibrium state
Over time, polymer chains relax, resulting in
lower permeability
Membrane Disadvantages
•High compressor cost
oMembranes only 10-25% of total cost
oSignificant reductions in membrane cost might not
markedly change total plant cost
o Compressor cost is 2-3 times the skid cost
Membrane Network
Membrane Network
•Membranes, compressors, mixers,
splitters, streams
•2 Membrane
Network
•How
do we find
the membrane
network?
•3 Membrane
•Superstructure
Network
Superstructure
•Superstructure allows for all possible network
configurations
Superstructure
For example:
Superstructure
Resulting 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 Model
Mixer/Splitter Balances
•Feed balance
Hollow Fiber Mathematical Model
Mixer/Splitter Balances
•Splitter balance
1
2
Hollow Fiber Mathematical Model
Mixer/Splitter Balances
•CO2 composition
•rcomp=0.02
Hollow Fiber Mathematical Model
Mixer/Splitter Balances
•Mixer Balance
1
2
Hollow Fiber Mathematical Model
•Permeate power
1
2
Hollow Fiber Mathematical Model
• Non-linear equations in model
• Non-linear equations discretized to give linear
program
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
Capital Charge:
• fcc: Capital Charge (27%/yr)
• fwk: Working Capital (10% Ffc)
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?
Program
Set and Parameter
Declaration
Variable Declaration
Program
Equations
Program
Results
Results
2 Membrane Network at 79 lb-mol/hr
0.42 kW
Objective function: $163,000
% CH4 lost: 11.20
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: $130,000
%CH4 lost: 7.77
Results: Comparison
Area (m2)
Wcp (KW)
% CH4 Lost
163,000
160
0.42
11.2
130,000
435
80
7.77
130,000
435
80
7.77
Objective
Function ($)
2-Membrane
Network
3-Membrane
Network
4-Membrane
Network
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: $539,000
%CH4 lost: 10.90
Membrane Network Verification
Membrane Network Verification
Compressor
Model Work (kW)
Pro-II Work (kW)
C1
82.1
82.9
C2
39.1
39.5
C3
8.3
8.4
C4
93.6
94.7
C5
44.5
44.2
Work comparison for 238 lb-mol/hr
Results
Total Annualized Cost vs. flow rate for an amine unit
and 3 membrane network at 19% CO2 in the feed
Results: Cost Analysis
Flow rate (MMscfd)
Membrane
Amine
FCI ($)
Operating
TAC ($/yr)
Cost ($/yr)
15 yr.
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
90
3M
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 Annulaized Cost ($/yr) 15 year period
$70,000,000
$60,000,000
$50,000,000
$40,000,000
Membrane Network
$30,000,000
Amine Unit
$20,000,000
$10,000,000
$0
0
100
200
300
400
500
600
700
Flow rate( MMscfd)
Total Annualized Cost vs. flow rate for an amine unit
and 3 membrane network at 9% CO2 in the feed
Results: Cost Analysis
Flow rate
FCI ($)
(MMscfd)
Membrane
Amine
Operating Cost
TAC ($/yr) 15 yr.
($/yr)
90
18M
9M
10M
180
36M
18M
20M
270
55M
27M
31M
360
73M
36M
41M
455
91M
45M
51M
550
109M
54M
61M
90
5M
12M
180
6M
17M
18M
270
7M
22M
22M
360
8M
26M
26M
455
10M
29M
30M
550
11M
33M
33M
12M
Comparison between 3 membrane network and amine unit at 9 %CO2
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
0.9
0.8
Mole Compositions
0.7
0.6
0.5
XCO2 Tube side
0.4
XCH4 Tube Side
0.3
XCO2 Shell Side
XCH4 Shell Side
0.2
0.1
0
0
0.5
1
1.5
Membrane Area
2
2.5
3
(m2)
Figure 1. Molar compositions with varying membrane area.
• CO2 flow rate: 0.2
• CH4 flow rate: 0.8
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 Model
Discrete Equations
•Lower bound component flow rate tube side
1
0.75
•
•
•
: discrete variable
: binary variable
: total flow rate
0.50
4
3
2
0.25
0
binary variables
1
segments
Hollow Fiber Mathematical Model
Discrete Equations
•Upper bound component flow rate tube side
1
0.75
•
•
•
: discrete variable
: binary variable
0
: total flow rate
0.50
4
3
2
0.25
binary variables
1
segments
Amine Unit Simulation
3
3B
HX-2
PU-1
1
2
1
3C
3
2
2
CL-1
7
4
8
5
3
6
11
11C
7
4
MX-1
8
SC-1
5
HXA
MX-2
10
9
W1
10
6
1
10B
20
WAT
11
9
5
CN-1
HX-1
XWAT
12
RG-1
SL-2
4
19
XMEA
SL-1
V-1
6
Equipment & Utility Cost at 79 lb-mol/hr
Type
Valve trays
Valve trays
No. of trays
6
12
Operating
pressure
250 psia
16 psia
MOC
Duty (MMBtu/hr)
Area (ft2)
Rich amine / Lean amine
Lean amine / water
Lean amine / water
Stainless Steel
Stainless Steel
Stainless Steel
16.45
10.96
6.098
241.73955
37.191652
28.193677
Pump
Pump lean amine solution
MOC
Stainless Steel
Power (HP)
130
Columns
1
2
Absorber
Stripper
Exchangers
1
2
3
Cost
$15,334
$32,736
$4,772
$2,651
$2,439
$1,803
Type
Valve
Rich amine expansion valve
MDEA initial amt cost
MOC
Stainless Steel
Diameter (m)
0.2
Flanged
$68,771
Total
Flow(1000 kg/hr)
17.53959549
Reboiler (MMBtu/hr)
Natural gas as heating utility for reboiler
2.73
Duty (kW)
Electricity
4.42
Flow (lb/hr)
MDEA Recycle
0.11917
Total
Cooling water
$8,484
$552
Price ($ /m3)
0.29
Price ( $ / MMBTU)
5
Price ($ / kWh)
0.062
Price ($/lb)
1.54
Cost ($ / yr)
$42,726
$114,516
$2,301.94
$1,541.58
$161,086
Equipment & Utility Cost at 127 lb-mol/hr
Type
Valve trays
Valve trays
No. of trays
6
12
Operating
pressure
250 psia
16 psia
Exchangers
Rich amine / Lean amine
Lean amine / water
Lean amine / water
MOC
Stainless Steel
Stainless Steel
Stainless Steel
Duty
(MMBtu/hr)
16.45
10.96
6.098
Area (ft2)
711.08872
94.337643
185.37014
Pump
Pump lean amine solution
MOC
Stainless Steel
Power (HP)
130
Columns
1
2
1
2
3
Absorber
Stripper
Cost
$15,424
$37,434
$9,544
$3,075
$4,242
$1,909
Type
Valve
Rich amine expansion valve
MDEA initial amt cost
MOC
Stainless Steel
Diameter (m)
0.2
Flanged
$80,813
Total
Flow(1000 kg/hr)
44.80690133
Reboiler (MMBtu/hr)
Natural gas as heating utility for reboiler
6.96
Duty (kW)
Electricity
11.2611
Flow (lb/hr)
MDEA Recycle
0.11917
Total
Cooling water
$8,484
$701
Price ($ /m3)
0.29
Price ( $ / MMBTU)
5
Price ($ / kWh)
0.062
Price ($/lb)
1.54
Cost ($ / yr)
$109,150
$292,374
$5,864.78
$1,541.58
$408,930
Equipment & Utility Cost at 238 lb-mol/hr
Type
Valve trays
Valve trays
No. of trays
6
12
Operating
pressure
250 psia
16 psia
MOC
Duty (MMBtu/hr)
Area (ft2)
Stainless Steel
16.45
804.06735
$15,907
Stainless Steel
10.96
113.88082
$4,242
Stainless Steel
6.098
86.315086
$3,712
MOC
Power (HP)
Stainless Steel
130
Columns
1
2
Absorber
Stripper
Exchangers
Rich amine /
Lean amine
Lean amine /
water
Lean amine /
water
1
2
3
Pump
Pump lean
amine solution
Cost
$27,932
$53,235
$2,651
Type
Valve
Rich amine expansion valve
MDEA initial amt cost
MOC
Stainless Steel
Diameter (m)
0.2
Flanged
$117,033
Total
Flow(1000 kg/hr)
Cooling water
53.48166714
Reboiler (MMBtu/hr)
Natural gas as heating utility for reboiler
8.311611536
Duty (kW)
Electricity
13.62
Flow (lb/hr)
MDEA Recycle
0.23834
Total
$8,484
$871
Price ($ /m3)
0.29
Price ( $ / MMBTU)
5
Price ($ / kWh)
0.062
Price ($/lb)
1.54
Cost ($ / yr)
$130,281
$349,088
$7,093.30
$3,083.17
$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
1
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.5
CO2
0.4
CH4
flow rate (mol/s)
Flow rate (mol/s)
Comparison of GAMS and Excel Membrane
Concentration Profile
0.6
0.5
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
CO2
CH4
0
0
50
100
150
200
250
Number of Segments
Figure 4. Excel simulation tube side 0.9
CH4 & 0.1 CO2
0
50
100
150
200
250
Number of Segments
Figure 5. simulation tube side 0.9 CH4 &
0.1 CO2
1.400000000E-01
0.14
1.200000000E-01
0.12
1.000000000E-01
0.1
8.000000000E-02
CO2
6.000000000E-02
CH4
Flow rate (mol/s)
flow rate (mol/s)
Comparison of GAMS and Excel Membrane
Concentration Profile
0.08
4.000000000E-02
0.04
2.000000000E-02
0.02
0.000000000E+00
0
50 100 150 200 250
Number of Segments
Figure 6. Excel simulation shell side 0.9
CH4 & 0.1 CO2
CO2
0.06
CH4
0
0
50
100
150
200
250
Number of Segments
Figure 7. GAMS simulation shell side 0.9
CH4 & 0.1 CO2
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
CO2
0.4
CH4
0.3
Flow rate (mol/s)
flow rate (mol/s)
Comparison of GAMS and Excel Membrane
Concentration Profile
0.5
CO2
0.4
CH4
0.3
0.2
0.2
0.1
0.1
0
0
0
50
100
150
200
250
Number of Segments
Figure 8. Excel simulation tube side 0.8
CH4 & 0.2 CO2
0
50
100
150
200
250
Number of Segments
Figure 9. GAMS simulation tube side 0.8
CH4 & 0.2 CO2
2.000000000E-01
0.2
1.800000000E-01
0.18
1.600000000E-01
0.16
1.400000000E-01
0.14
1.200000000E-01
1.000000000E-01
CO2
8.000000000E-02
CH4
Flow rate (mol/s)
flow rate (mol/s)
Comparison of GAMS and Excel Membrane
Concentration Profile
0.12
0.1
6.000000000E-02
0.06
4.000000000E-02
0.04
2.000000000E-02
0.02
0.000000000E+00
CO2
0.08
CH4
0
0
50
100 150 200 250
Number of Segments
Figure 10. Excel simulation shell side 0.8
CH4 & 0.2 CO2
0
50
100
150
200
250
Number of Segments
Figure 11. GAMS simulation shell side 0.8
CH4 & 0.2 CO2
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.4
CO2
0.3
CH4
Flow rate (mol/s)
flow rate (mol/s)
Comparison of GAMS and Excel Membrane
Concentration Profile
0.5
0.4
0.3
0.2
0.2
0.1
0.1
0
CO2
CH4
0
0
50
100
150
200
250
Number of Segments
Figure 12. Excel simulation tube side 0.7
CH4 & 0.3 CO2
0
50
100
150
200
250
Number of Segments
Figure 13. GAMS simulation tube side 0.7
CH4 & 0.3 CO2
3.000000000E-01
0.3
2.500000000E-01
0.25
2.000000000E-01
0.2
1.500000000E-01
CO2
CH4
1.000000000E-01
5.000000000E-02
Flow rate (mol/s)
flow rate (mol/s)
Comparison of GAMS and Excel Membrane
Concentration Profile
0.15
CO2
CH4
0.1
0.05
0.000000000E+00
0
0
50
100 150 200 250
Number of Segments
Figure 14. Excel simulation shell side 0.7
CH4 & 0.3 CO2
0
50
100
150
200
250
Number of Segments
Figure 15. GAMS simulation shell side 0.7
CH4 & 0.3 CO2
0.7
0.7
0.6
0.6
0.5
0.5
0.4
CO2
0.3
CH4
Flow rate (mol/s)
flow rate (mol/s)
Comparison of GAMS and Excel Membrane
Concentration Profile
0.4
CH4
0.2
0.2
0.1
0.1
0
CO2
0.3
0
0
50
100
150
200
250
Number of Segments
Figure 16. Excel simulation tube side 0.6
CH4 & 0.4 CO2
0
50
100
150
200
250
Number of Segments
Figure 17. GAMS simulation tube side 0.6
CH4 & 0.4 CO2
Comparison of GAMS and Excel Membrane
Concentration Profile
4.000000000E-01
0.45
3.500000000E-01
0.4
0.35
2.500000000E-01
2.000000000E-01
CO2
1.500000000E-01
CH4
1.000000000E-01
Flow rate (mol/s)
flow rate (mol/s)
3.000000000E-01
0.3
0.25
CO2
0.2
CH4
0.15
0.1
5.000000000E-02
0.05
0.000000000E+00
0
0
50
100 150 200 250
Number of Segments
Figure 18. Excel simulation shell side 0.6
CH4 & 0.4 CO2
0
50
100
150
200
250
Number of Segments
Figure 19. GAMS simulation shell side 0.6
CH4 & 0.4 CO2
0.6
0.6
0.5
0.5
0.4
0.4
0.3
CO2
CH4
0.2
0.1
Flow rate (mol/s)
flow rate (mol/s)
Comparison of GAMS and Excel Membrane
Concentration Profile
0.3
CO2
CH4
0.2
0.1
0
0
0
50
100
150
Number of Segments
Figure 20. Excel simulation tube side 0.5
CH4 & 0.5 CO2
0
50
100
150
Segments
Figure 21. GAMS simulation tube side 0.5
CH4 & 0.5 CO2
Comparison of GAMS and Excel Membrane
Concentration Profile
6.000000000E-01
0.45
0.4
5.000000000E-01
4.000000000E-01
3.000000000E-01
CO2
CH4
2.000000000E-01
Flow rate (mol/s)
flow rate (mol/s)
0.35
0.3
0.25
0.2
CO2
0.15
CH4
0.1
1.000000000E-01
0.05
0.000000000E+00
0
0
50
100
150
Number of Segments
Figure 22. Excel simulation shell side 0.5
CH4 & 0.5 CO2
0
20
40
60
80
100
120
Number of Segments
Figure 23. GAMS simulation shell side 0.5
CH4 & 0.5 CO2