Research ArticleCFD Simulation for Separation of Carbon Dioxide-MethaneMixture by Pressure Swing Adsorption
K Rambabu L Muruganandam and S Velu
School of Mechanical and Building Sciences VIT University Vellore Tamil Nadu 632014 India
Correspondence should be addressed to K Rambabu rambabukvitacin
Received 13 January 2014 Revised 28 May 2014 Accepted 29 May 2014 Published 19 June 2014
Academic Editor Donald L Feke
Copyright copy 2014 K Rambabu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
A developing technology for gas separations is pressure swing adsorption which has been proven to be more economical andenergy efficient compared to other separation methods like cryogenic distillation and membrane separation A pressure swingadsorption (PSA) column with carbon dioxide-methane as feed mixture and 6-FDA based polyimides as the adsorbent wasmodeled and simulated in this work Ansys Fluent 121 along with supplementary user defined functions was used to developa 2D transient Eulerian laminar viscous flow model for the PSA column The model was validated by comparing the simulatedresults with established analytical models for PSA The developed numerical model was used to determine the carbon dioxideconcentration in the column as a function of time based on different operating conditions Effect of various operating parameterslike pressure temperature and flow rate on the separation efficiency has been studied and reported Optimization studies werecarried out to obtain suitable operating conditions for the feed gases separation Simulation studies were carried out to determinethe separation length required for complete separation of the feed mixture corresponding to different inlet feed concentrationswhich were entering the column at a given flow rate
1 Introduction
Traditionally industrial gas separation is done by chemicaland physical absorption membrane separation and lowtemperature distillation [1] Owing to high energy consump-tion and associated problems like cost and process degra-dation newer avenues are being explored With differentkinds of adsorbents available each offering a wide rangeof equilibrium properties adsorption is being seen as aviable option for gas separation especially for binary gasmixtures [2] Separation processes utilizing adsorption arelow cost and energy efficient alternatives in comparison withother separation processes particularly at low to moderatethroughput [3]
Adsorption is mainly performed by periodic variationsof pressure and temperature of the system Temperatureswing adsorption (TSA) is widely used for removal of traceamounts of pollutants such as volatile organic compoundsfrom gaseous streams [4] However TSA needs preciseprocess controls huge columns and longer operating time
compared to pressure swing adsorption (PSA) and henceTSA is preferred for systems having strong adsorbing naturewith respect to the adsorbent [5]
Pressure swing adsorption is based on Skarstrom cycle[6] in which feed mixture is sent in at high pressuresSeparation takes place due to selective adsorption of oneor more feed components by the adsorbent and the rateof adsorption is regulated by the operating pressure of theprocess The adsorbed component (adsorbate) is recoveredlater by reducing the pressure of the column Adsorptioninvolves contacting a free fluid phase (gas or liquid) with arigid particulate phase which has the property of selectivelytaking up and storing one or more solute species originallycontained in the fluid [7] The strength of the surfaceinteraction between the adsorbent and adsorbate depends onthe nature of the solid adsorbent the fluid adsorbate and thesystemrsquos thermodynamic properties especially density andpressure
Consequently different adsorbents adsorb feed com-ponents with different affinities which are regulated by
Hindawi Publishing CorporationInternational Journal of Chemical EngineeringVolume 2014 Article ID 402756 7 pageshttpdxdoiorg1011552014402756
2 International Journal of Chemical Engineering
the thermodynamics of the system This gives raise to thewide range of processes in PSA processes with respect to theadsorbent used
Two separations of particular commercial interest thathave been mostly reported in the literature are the car-bon dioxide-methane (CO
2-CH4) separation and oxygen-
air separation Separation of oxygen from air by PSA usingzeolite 5A as adsorbent has been studied experimentally[8 9] Modelling of the oxygen separation from air by PSAusing 13X zeolite as adsorbent has been carried out byequilibrium model with a linear isotherm for oxygen and apolynomial isotherm for nitrogen [10] Experimental studieson the separation of the carbon dioxide-methane systemusing membrane technology have been reported in scientificliterature [11] Simulation study on the effect of gas solubilityin the adsorbent with respect to feed mixture separation isalso made for CO
2-CH4system using PSA [12] However the
effect of operating parameters on the separation efficiency ofthe system has not been explored so far
Removal of carbon dioxide from natural gas is extremelyimportant in order to meet the transportation pipelinespecifications as well as produce natural gas from associatedgas dug out from oil wells [11 13] The most commonadsorbents used in PSA separation processes for carbondioxide-methane systemare inorganic adsorbents like zeoliteactivated charcoal and polymer adsorbents like polysulfoneand polyacetate The 6-FDA based polyimides have beenreported to be a promising adsorbent material for gasseparation [14] The hexafluoroisopropylidene linkage in thepolyimides enhances the permselectivity of the 6-FDA basedpolyimides for the binary systems [15] Polyimides also showexcellent mechanical strength as well as temperature andchemical resistance [16]
In this study the separation process of CO2-CH4system
was modeled based on dynamic pressure-swing adsorptionprocess with FDA based polyimides particles as adsorbentCFD package Ansys Fluent 121 along with supplementaryuser defined functions was used to develop a 2D transientEulerian laminar viscous flow model for the adsorptioncolumnThe objective of the investigation was to simulate thedeveloped numericalmodel to study the individual feed com-ponentrsquos concentration distribution and separation efficiencywith respect to time and column operating parameters
2 Process Modelling
21 Model Setup and Analysis A typical model of the PSAadsorption column is shown in Figure 1 The model wasdeveloped and simulated using Ansys Fluent 121 The detailsof the adsorption columnmodel were taken as used in earlierrelated work [12] and are shown in Table 1 The fluid wastaken to be incompressible Newtonian and in a laminarflow regime Carbon dioxide-methane system at standardconditions was chosen as the feed mixture in a 50-50volume concentration The porous medium approach wasused in the simulation of the fluid flow in the packed bedsince the adsorbent inside the packed bed can be treatedas porous medium The porous medium is assumed to
Outlet
WallAxis
Inlet
Figure 1 Schematic of the PSA column model with feed inlet andoutlet
Table 1 Parameters used in separation of binary gas mixtures
Molar feed composition CO2-CH4 (50-50 by volume)Adsorbent Polyimide (6FDA-ODA)Particle radius 120583m 100Bed length m 035Bed diameter m 006Bed voidage 05Operating temperature K 300Operating pressure atm 20Glass transition temperature sim450K
be isotropic The approach uses an additional mass sourceterm to the standard fluid flow equations to account forthe flow resistance due to the porous medium The mixingand transport of binary species are modeled by solvingconservation equations describing convection and diffusionfor each component species The following assumptions havebeen made in the modelling approach
(i) The process is assumed to be isothermal(ii) Ideal gas law is applicable(iii) Plug flow is assumed that is there is no axial or radial
dispersion(iv) The mass transfer rate is given by linear driving force
(LDF) model
User defined functions were introduced to incorporatesource terms in order to include the effects of solubility anddiffusivity The effect of temperature on permeability wasincorporated in the source term by (1) using the data given inTable 2 [17] PISO scheme was used as the pressure velocitycoupling algorithm The governing equation for fluid flow
International Journal of Chemical Engineering 3
Table 2 Activation energies for permeation for 6-FDA basedmembranes at 35∘C and 20 atm
in isotropic porous media is given by (2) Incorporating thesource term 119878
0 in (2) would enable to define concentration
points of adsorbed gas Thus the mass and momentumconservation equations for the discussed model are givenby (3) and (4) respectively Inertial and viscous resistanceencountered by the fluid are incorporated in themodel by thelast two terms Permeability (120572) is calculated using Darcyrsquoslaw (see equation (5)) due to the presence of porous mediaThe linear driving force model describing the mass transferphenomena for PSA is given by (6) and (7) The governingequations were discretized by second-order upwind scheme
22 Model Validation The adsorption of small molecules inglassy polymers is described best by the dual mode (DM)sorption model [18 19] The dual sorption mechanism isgiven as a combination of Henryrsquos law of solubility andLangmuir adsorption [18] Henryrsquos law accounts for thedissolution of the penetrant molecule in the continuouspolymer chain matrix and its sorption in microvoids isdescribed by Langmuir model According to DM sorptionmodel the gas concentration in the polymer is given by thefollowing equation as a function of operating pressure
Table 3 DM sorption model parameters for carbon dioxide sorbedin polyimide
119896119863(cm3 of CO2cm
3 of adsorbent bar) 156
1198621015840
119867(cm3 of CO2cm
3 of adsorbent) 546
119887 (barminus1) 0544
20
40
60
80
100
120
140
0 10 20 30 40 50Pressure (bar)
DM modelHenrys model
Langmuir modelNumerical model
Con
cent
ratio
n (c
m3
of g
asc
m3
of ad
sorb
ent)
Figure 2 Comparison of DMmodel and numerical model
where 119862 is the concentration of the gas adsorbed in unitvolume of the polymer 119862
119863is the gas concentration by
dissolution 119862119867is the gas concentration by hole filling 119901 is
the applied pressure 119896119863is dissolution constant1198621015840
119867is the hole
saturation constant and 119887 is the affinity constantDM model assumes that both modes occur simultane-
ously and are always in equilibrium [18 20] The diffusioncoefficient is independent of concentrationThe values of theparameters for the DM sorption model for carbon dioxidesorbed in polyimide are specified in Table 3 [21]
Validation of the numerical model was conducted bystudying the steady state adsorbed CO
2concentration as
a function of operating pressure and comparing with theCO2concentration obtained using analytical DM model As
shown in Figure 2 the behaviour of the numerical model isin accordance with the analytical DM sorption model Thevariation in the amount of CO
2adsorbed per unit volume
of adsorbent between the DM model and numerical modelreported an average error of 87 (in magnitude) calculatedover the operating pressure for the adsorption column Theerror between the DM model and the proposed numeri-cal model could be due to the truncation discretizationand round-off phenomena in the simulation The deviationbetween numerical model and the DMmodel was very muchless in comparison to the deviation between Langmuir modeland theDMmodel (average error of 425) and the deviationbetween Henry model and the DM model (average error of349)
Figure 3 Concentration of methane as a function of time
07
075
08
085
09
095
1
0025 0075 0125 0175 0225 0275 0325 0375Column position from inlet (m)
minus0025
Sepa
ratio
n ra
tio (C
CO
2C
CH
4)
1 atm5 atm
10 atm20 atm
Figure 4 Pressure effects on separation ratio (flow velocity =015msec and temperature = 200K)
23 Simulation Carbon dioxide-methane mixture at a vol-ume composition of 50-50 was given as the inlet feedstream At the end of the cycle the mole fraction of carbondioxide was reduced to 005 from 05 due to the adsorptionof carbon dioxide in the column The result of the unsteadystate simulation is presented in Figure 3 It is evident fromFigure 3 that the concentration of methane at a given spatialposition increasedwith time of adsorption It was also evidentthat the rate of adsorption at a given point in the columndecreased with the time of adsorption This was due to thedecreasing concentration gradient between the feed streamand the adsorbent material
0976
098
0984
0988
0992
0996
1
0025 0075 0125 0175 0225 0275 0325 0375Column position from inlet (m)
minus0025
200K300K400K
Sepa
ratio
n ra
tio (C
CO
2C
CH
4)
Figure 5 Temperature effects on separation ratio (flow velocity =015msec and pressure = 15 atm)
231 Effect of Pressure Simulation results showed thatdecreasing the operating pressure leads to better separationAs shown in Figure 4 the separation ratio (ratio of concen-tration of CO
2to concentration of CH
4) decreased along the
length of the column as pressure was reduced from 15 atm to1 atm
232 Effect of Temperature For most gases solubilityincreases with increase in temperature till the glass transitiontemperature is reached Simulations were carried out at200K 300K and 400K keeping the pressure constant Itwas observed that separation increases with increase intemperature The temperature effect on the adsorption isshown in Figure 5
233 Effect of Flowrate Flowrate of the feed stream is animportant factor affecting the separation process The modelwas simulated for three different flow ratesmdash01ms 001msand 0001msThe highest degree of separation was obtainedat 0001ms as evident from Figure 6
24 Optimization The optimum operating conditions forcarrying out the pressure swing adsorption for the separationof carbon dioxide-methane mixture at a volume compositionof 50-50 entering the column at a velocity of 0001mswas obtained by simulating the model at different operatingpressures and temperatures Pressure was reduced from20 atm to 1 atm and the temperature dependence study wasperformed for 200K 300K and 400K For every run theseparation ratio was calculated and plotted to find the opti-mum conditions for operating the PSA column The resultsare presented in Figure 7 The optimization study revealedthat a separation length of about 0125m guaranteed 100
International Journal of Chemical Engineering 5
04
05
06
07
08
09
1
0 005 01 015 02 025 03 035 04Column position from inlet (m)
Sepa
ratio
n ra
tio (C
CO
2C
CH
4)
01ms001ms0001ms
Figure 6 Effect of feed velocity on the separation ratio (pressure =5 atm and temperature = 200K)
0
01
02
03
04
05
06
07
08
09
1
0 005 01 015 02 025 03 035 04Column position from inlet (m)
minus01minus005
1 atm and 200K2 atm and 300K10 atm and 400K1 atm and 300K
5 atm and 300K1 atm and 400K10 atm and 200K
Sepa
ratio
n ra
tio (C
CO
2C
CH
4)
Figure 7 Optimization studies on separation ratio on operationconditions (feed velocity = 0001ms)
separation for the specified feed inlet conditions Optimumoperating conditions were found to be 1 atm and 400K
Further as a comparative study simulations were carriedout to determine the separation length required for completeseparation of the feed corresponding to different initialconcentrations of the feed mixture The results obtained arepresented in Table 4
As a future scope of study for the pressure swing adsorp-tion using 6-FDA-ODA particles bed a more improved
User defined functioninclude ldquoudfhrdquoDEFINE SOURCE(second c t dS eqn)
real sourcesource = minus000004461296 lowast C P(c t) lowast exp(1C T(c t))dS[eqn] = minus000004461296 lowast exp(1C T(c t))return source
include ldquoudfhrdquoDEFINE SOURCE(third c t dS eqn)
real sourcesource = minus0000108218 lowast C P(c t) lowast exp(1C T(c t))dS[eqn] = minus0000108218 lowast exp(1C T(c t))return source
Algorithm 1 User defined function
model (3-dimensional) incorporating most of the real timecorrelations radial variation studies and temperature depen-dence studies for the adsorption process are to be carried out
3 Conclusions
A CFD model based on pressure swing adsorption wasdeveloped for binary gas mixture separation namely CO
2-
CH4 using 6-FDAbased polyimides as adsorbentThemodel
was validated against the analytical dual mode sorptionmodel for adsorption of gases (CO
2) on glassy polymers
The model was used to determine the carbon dioxide con-centration in the column as a function of time based ondifferent operating conditions Analysis clearly indicated thatproviding an optimal residence time by lowering the velocityof the flow produces the maximum separation efficiency Fora fixed column length of 0035m an optimal residence timeof 50 seconds corresponding to a flow velocity of 0001msyielded a separation efficiency of around 97 Lowering theoperating pressure leads to better separation as permeabilityof gases is inversely proportional to the operating pressureIncreasing the temperature of the adsorption bed producedbetter separation of the gases As an outcome of optimizationstudies a reference table specifying the separation lengthrequired for complete separation of the feedmixture enteringthe adsorption column at different initial concentrations(with a flow velocity of 0001ms) was also presented
Appendix
Algorithm 1 User defined function
Nomenclature
119875 Total bed pressure (kPa)120582119900 Permeability (Barrer)
119864119901 Activation energy (kJmol)
6 International Journal of Chemical Engineering
Table4Dependences
tudies
ofseparatio
nleng
thon
initialconcentrationof
feed
Positionof
thec
olum
n(m
)
Con
centratio
nof
CO2(kmolm3)a
long
thec
olum
nleng
thford
ifferentinitia
lcon
centratio
nsof
feed
mixture
95CO
2in
feed
85CO
2in
feed
75CO
2in
feed
65CO
2in
feed
55CO
2in
feed
45CO
2in
feed
35CO
2in
feed
25CO
2in
feed
15CO
2in
feed
5CO
2in
feed
0306
00
00
00
00
00
0253
00
00
00
00
00
0201
00
00
00
00
00
0157
000
0481
00
00
00
00
00105
00800
440053567
002707
0005331
00
00
00
0052
0419499
0345991
0277279
0212829
0152186
009501
004
090001032
00
0017
149493
115133
088624
0675398
0503622
036095
024045
0137306
0047937
000
695
International Journal of Chemical Engineering 7
119877 Universal gas constant (Jgmol K)120588 Density (kgm3)120574 Volume (m3) Velocity (msec)Φ Any given property997888rarr
119861119891 Body forces per unit volume (Nm3)
119879 Gas-phase temperature in the bed (K)120591 Fluid stress (Nm2)120583 Absolute viscosity (kgm sec)120572 Gas permeability (Barrer)119889119901 Particle diameter (m)
120576 Bulk void fraction119902119894 Solid-phase concentration of 119894th
component (gmolkg)119902lowast
119894 Equilibrium solid-phase concentration of
119894th component (gmolkg)119896119894 LDF model mass transfer coefficient of 119894th
component (1sec)119863119901119894 Diffusivity of 119894th component (m2sec)
119905 Time (sec)119887 Affinity constant (barminus1)119862 Gas-phase concentration of a given
component (cm3 of adsorbatecm3 ofadsorbent)
119862119863 Gas concentration by dissolution (cm3 ofadsorbatecm3 of adsorbent)
119862119867 Gas concentration by hole filling (cm3 ofadsorbatecm3 of adsorbent)
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R E Treybal Mass-Transfer Operations vol 3 McGraw-HillNew York NY USA 1980
[2] C M Yon and J D ShermanAdsorption Gas Separation Kirk-Othmer Encyclopedia of Chemical Technology 2004
[3] D Aaron and C Tsouris ldquoSeparation of CO2from flue gas a
reviewrdquo Separation Science and Technology vol 40 no 1ndash3 pp321ndash348 2005
[4] F I Khan and A K Ghoshal ldquoRemoval of Volatile OrganicCompounds from polluted airrdquo Journal of Loss Prevention in theProcess Industries vol 13 no 6 pp 527ndash545 2000
[5] M A Kalbassi R J Allam and T C Golden ldquoTemperatureswing adsorptionrdquo US Patent no 5846295 US Patent andTrademark Office Washington DC USA 1998
[6] C W Skarstrom ldquoMethod and apparatus for fractionatingrdquoUS Patent no 2944627 US Patent and Trademark OfficeWashington DC USA 1970
[7] A Kapoor and R T Yang ldquoKinetic separation of methanemdashcarbon dioxide mixture by adsorption on molecular sievecarbonrdquo Chemical Engineering Science vol 44 no 8 pp 1723ndash1733 1989
[8] A M Mendes C A Costa and A E Rodrigues ldquoOxygenseparation from air by PSA modelling and experimental
results part Irdquo Separation and Purification Technology vol 24no 1-2 pp 173ndash188 2001
[9] S Farooq D M Ruthven and H A Boniface ldquoNumerical sim-ulation of a pressure swing adsorption oxygen unitrdquo ChemicalEngineering Science vol 44 no 12 pp 2809ndash2816 1989
[10] J C Kayser and K S Knaebel ldquoPressure swing adsorptiondevelopment of an equilibrium theory for binary gas mixtureswith nonlinear isothermsrdquo Chemical Engineering Science vol44 no 1 pp 1ndash8 1989
[11] S Sridhar B Smitha and T M Aminabhavi ldquoSeparation ofcarbon dioxide from natural gas mixtures through polymericmembranesmdasha reviewrdquo Separation amp Purification Reviews vol36 no 2 pp 113ndash174 2007
[12] H S Pierre Simulation of dynamic pressure-swing gas sorptionin polymers [PhD Dissertation] 2005
[13] S Li J G Martinek J L Falconer R D Noble and T QGardner ldquoHigh-pressure CO
2CH4separation using SAPO-34
membranesrdquo Industrial amp Engineering Chemistry Research vol44 no 9 pp 3220ndash3228 2005
[14] H Hachisuka T Ohara and K Ikeda ldquoNew type asymmetricmembranes having almost defect free hyper-thin skin layer andsponge-like porous matrixrdquo Journal of Membrane Science vol116 no 2 pp 265ndash272 1996
[15] M R Coleman and W J Koros ldquoIsometric polyimides basedon fluorinated dianhydrides and diamines for gas separationapplicationsrdquo Journal of Membrane Science vol 50 no 3 pp285ndash297 1990
[16] M K Ghosh and K L Mittal Polyimides Fundamentals andApplications vol 36 CRC Press New York NY USA 1996
[17] T H Kim W J Koros and G R Husk ldquoTemperature effectson gas permselection properties in hexafluoro aromatic poly-imidesrdquo Journal of Membrane Science vol 46 no 1 pp 43ndash561989
[18] B Xing and J J Pignatello ldquoDual-mode sorption of low-polaritycompounds in glassy poly (vinyl chloride) and soil organicmatterrdquo Environmental Science amp Technology vol 31 no 3 pp792ndash799 1997
[19] RM Barrer ldquoDiffusivities in glassy polymers for the dualmodesorption modelrdquo Journal of Membrane Science vol 18 pp 25ndash35 1984
[20] E Glueckauf ldquoThe influence of ionic hydration on activitycoefficients in concentrated electrolyte solutionsrdquo Transactionsof the Faraday Society vol 51 pp 1235ndash1244 1955
[21] T Hirose Y Mi S A Stern and A K S Clair ldquoThe solubilityof carbon dioxide and methane in polyimides at elevatedpressuresrdquo Journal of Polymer Science B Polymer Physics vol29 no 3 pp 341ndash347 1991
the thermodynamics of the system This gives raise to thewide range of processes in PSA processes with respect to theadsorbent used
Two separations of particular commercial interest thathave been mostly reported in the literature are the car-bon dioxide-methane (CO
2-CH4) separation and oxygen-
air separation Separation of oxygen from air by PSA usingzeolite 5A as adsorbent has been studied experimentally[8 9] Modelling of the oxygen separation from air by PSAusing 13X zeolite as adsorbent has been carried out byequilibrium model with a linear isotherm for oxygen and apolynomial isotherm for nitrogen [10] Experimental studieson the separation of the carbon dioxide-methane systemusing membrane technology have been reported in scientificliterature [11] Simulation study on the effect of gas solubilityin the adsorbent with respect to feed mixture separation isalso made for CO
2-CH4system using PSA [12] However the
effect of operating parameters on the separation efficiency ofthe system has not been explored so far
Removal of carbon dioxide from natural gas is extremelyimportant in order to meet the transportation pipelinespecifications as well as produce natural gas from associatedgas dug out from oil wells [11 13] The most commonadsorbents used in PSA separation processes for carbondioxide-methane systemare inorganic adsorbents like zeoliteactivated charcoal and polymer adsorbents like polysulfoneand polyacetate The 6-FDA based polyimides have beenreported to be a promising adsorbent material for gasseparation [14] The hexafluoroisopropylidene linkage in thepolyimides enhances the permselectivity of the 6-FDA basedpolyimides for the binary systems [15] Polyimides also showexcellent mechanical strength as well as temperature andchemical resistance [16]
In this study the separation process of CO2-CH4system
was modeled based on dynamic pressure-swing adsorptionprocess with FDA based polyimides particles as adsorbentCFD package Ansys Fluent 121 along with supplementaryuser defined functions was used to develop a 2D transientEulerian laminar viscous flow model for the adsorptioncolumnThe objective of the investigation was to simulate thedeveloped numericalmodel to study the individual feed com-ponentrsquos concentration distribution and separation efficiencywith respect to time and column operating parameters
2 Process Modelling
21 Model Setup and Analysis A typical model of the PSAadsorption column is shown in Figure 1 The model wasdeveloped and simulated using Ansys Fluent 121 The detailsof the adsorption columnmodel were taken as used in earlierrelated work [12] and are shown in Table 1 The fluid wastaken to be incompressible Newtonian and in a laminarflow regime Carbon dioxide-methane system at standardconditions was chosen as the feed mixture in a 50-50volume concentration The porous medium approach wasused in the simulation of the fluid flow in the packed bedsince the adsorbent inside the packed bed can be treatedas porous medium The porous medium is assumed to
Outlet
WallAxis
Inlet
Figure 1 Schematic of the PSA column model with feed inlet andoutlet
Table 1 Parameters used in separation of binary gas mixtures
Molar feed composition CO2-CH4 (50-50 by volume)Adsorbent Polyimide (6FDA-ODA)Particle radius 120583m 100Bed length m 035Bed diameter m 006Bed voidage 05Operating temperature K 300Operating pressure atm 20Glass transition temperature sim450K
be isotropic The approach uses an additional mass sourceterm to the standard fluid flow equations to account forthe flow resistance due to the porous medium The mixingand transport of binary species are modeled by solvingconservation equations describing convection and diffusionfor each component species The following assumptions havebeen made in the modelling approach
(i) The process is assumed to be isothermal(ii) Ideal gas law is applicable(iii) Plug flow is assumed that is there is no axial or radial
dispersion(iv) The mass transfer rate is given by linear driving force
(LDF) model
User defined functions were introduced to incorporatesource terms in order to include the effects of solubility anddiffusivity The effect of temperature on permeability wasincorporated in the source term by (1) using the data given inTable 2 [17] PISO scheme was used as the pressure velocitycoupling algorithm The governing equation for fluid flow
International Journal of Chemical Engineering 3
Table 2 Activation energies for permeation for 6-FDA basedmembranes at 35∘C and 20 atm
in isotropic porous media is given by (2) Incorporating thesource term 119878
0 in (2) would enable to define concentration
points of adsorbed gas Thus the mass and momentumconservation equations for the discussed model are givenby (3) and (4) respectively Inertial and viscous resistanceencountered by the fluid are incorporated in themodel by thelast two terms Permeability (120572) is calculated using Darcyrsquoslaw (see equation (5)) due to the presence of porous mediaThe linear driving force model describing the mass transferphenomena for PSA is given by (6) and (7) The governingequations were discretized by second-order upwind scheme
22 Model Validation The adsorption of small molecules inglassy polymers is described best by the dual mode (DM)sorption model [18 19] The dual sorption mechanism isgiven as a combination of Henryrsquos law of solubility andLangmuir adsorption [18] Henryrsquos law accounts for thedissolution of the penetrant molecule in the continuouspolymer chain matrix and its sorption in microvoids isdescribed by Langmuir model According to DM sorptionmodel the gas concentration in the polymer is given by thefollowing equation as a function of operating pressure
Table 3 DM sorption model parameters for carbon dioxide sorbedin polyimide
119896119863(cm3 of CO2cm
3 of adsorbent bar) 156
1198621015840
119867(cm3 of CO2cm
3 of adsorbent) 546
119887 (barminus1) 0544
20
40
60
80
100
120
140
0 10 20 30 40 50Pressure (bar)
DM modelHenrys model
Langmuir modelNumerical model
Con
cent
ratio
n (c
m3
of g
asc
m3
of ad
sorb
ent)
Figure 2 Comparison of DMmodel and numerical model
where 119862 is the concentration of the gas adsorbed in unitvolume of the polymer 119862
119863is the gas concentration by
dissolution 119862119867is the gas concentration by hole filling 119901 is
the applied pressure 119896119863is dissolution constant1198621015840
119867is the hole
saturation constant and 119887 is the affinity constantDM model assumes that both modes occur simultane-
ously and are always in equilibrium [18 20] The diffusioncoefficient is independent of concentrationThe values of theparameters for the DM sorption model for carbon dioxidesorbed in polyimide are specified in Table 3 [21]
Validation of the numerical model was conducted bystudying the steady state adsorbed CO
2concentration as
a function of operating pressure and comparing with theCO2concentration obtained using analytical DM model As
shown in Figure 2 the behaviour of the numerical model isin accordance with the analytical DM sorption model Thevariation in the amount of CO
2adsorbed per unit volume
of adsorbent between the DM model and numerical modelreported an average error of 87 (in magnitude) calculatedover the operating pressure for the adsorption column Theerror between the DM model and the proposed numeri-cal model could be due to the truncation discretizationand round-off phenomena in the simulation The deviationbetween numerical model and the DMmodel was very muchless in comparison to the deviation between Langmuir modeland theDMmodel (average error of 425) and the deviationbetween Henry model and the DM model (average error of349)
Figure 3 Concentration of methane as a function of time
07
075
08
085
09
095
1
0025 0075 0125 0175 0225 0275 0325 0375Column position from inlet (m)
minus0025
Sepa
ratio
n ra
tio (C
CO
2C
CH
4)
1 atm5 atm
10 atm20 atm
Figure 4 Pressure effects on separation ratio (flow velocity =015msec and temperature = 200K)
23 Simulation Carbon dioxide-methane mixture at a vol-ume composition of 50-50 was given as the inlet feedstream At the end of the cycle the mole fraction of carbondioxide was reduced to 005 from 05 due to the adsorptionof carbon dioxide in the column The result of the unsteadystate simulation is presented in Figure 3 It is evident fromFigure 3 that the concentration of methane at a given spatialposition increasedwith time of adsorption It was also evidentthat the rate of adsorption at a given point in the columndecreased with the time of adsorption This was due to thedecreasing concentration gradient between the feed streamand the adsorbent material
0976
098
0984
0988
0992
0996
1
0025 0075 0125 0175 0225 0275 0325 0375Column position from inlet (m)
minus0025
200K300K400K
Sepa
ratio
n ra
tio (C
CO
2C
CH
4)
Figure 5 Temperature effects on separation ratio (flow velocity =015msec and pressure = 15 atm)
231 Effect of Pressure Simulation results showed thatdecreasing the operating pressure leads to better separationAs shown in Figure 4 the separation ratio (ratio of concen-tration of CO
2to concentration of CH
4) decreased along the
length of the column as pressure was reduced from 15 atm to1 atm
232 Effect of Temperature For most gases solubilityincreases with increase in temperature till the glass transitiontemperature is reached Simulations were carried out at200K 300K and 400K keeping the pressure constant Itwas observed that separation increases with increase intemperature The temperature effect on the adsorption isshown in Figure 5
233 Effect of Flowrate Flowrate of the feed stream is animportant factor affecting the separation process The modelwas simulated for three different flow ratesmdash01ms 001msand 0001msThe highest degree of separation was obtainedat 0001ms as evident from Figure 6
24 Optimization The optimum operating conditions forcarrying out the pressure swing adsorption for the separationof carbon dioxide-methane mixture at a volume compositionof 50-50 entering the column at a velocity of 0001mswas obtained by simulating the model at different operatingpressures and temperatures Pressure was reduced from20 atm to 1 atm and the temperature dependence study wasperformed for 200K 300K and 400K For every run theseparation ratio was calculated and plotted to find the opti-mum conditions for operating the PSA column The resultsare presented in Figure 7 The optimization study revealedthat a separation length of about 0125m guaranteed 100
International Journal of Chemical Engineering 5
04
05
06
07
08
09
1
0 005 01 015 02 025 03 035 04Column position from inlet (m)
Sepa
ratio
n ra
tio (C
CO
2C
CH
4)
01ms001ms0001ms
Figure 6 Effect of feed velocity on the separation ratio (pressure =5 atm and temperature = 200K)
0
01
02
03
04
05
06
07
08
09
1
0 005 01 015 02 025 03 035 04Column position from inlet (m)
minus01minus005
1 atm and 200K2 atm and 300K10 atm and 400K1 atm and 300K
5 atm and 300K1 atm and 400K10 atm and 200K
Sepa
ratio
n ra
tio (C
CO
2C
CH
4)
Figure 7 Optimization studies on separation ratio on operationconditions (feed velocity = 0001ms)
separation for the specified feed inlet conditions Optimumoperating conditions were found to be 1 atm and 400K
Further as a comparative study simulations were carriedout to determine the separation length required for completeseparation of the feed corresponding to different initialconcentrations of the feed mixture The results obtained arepresented in Table 4
As a future scope of study for the pressure swing adsorp-tion using 6-FDA-ODA particles bed a more improved
User defined functioninclude ldquoudfhrdquoDEFINE SOURCE(second c t dS eqn)
real sourcesource = minus000004461296 lowast C P(c t) lowast exp(1C T(c t))dS[eqn] = minus000004461296 lowast exp(1C T(c t))return source
include ldquoudfhrdquoDEFINE SOURCE(third c t dS eqn)
real sourcesource = minus0000108218 lowast C P(c t) lowast exp(1C T(c t))dS[eqn] = minus0000108218 lowast exp(1C T(c t))return source
Algorithm 1 User defined function
model (3-dimensional) incorporating most of the real timecorrelations radial variation studies and temperature depen-dence studies for the adsorption process are to be carried out
3 Conclusions
A CFD model based on pressure swing adsorption wasdeveloped for binary gas mixture separation namely CO
2-
CH4 using 6-FDAbased polyimides as adsorbentThemodel
was validated against the analytical dual mode sorptionmodel for adsorption of gases (CO
2) on glassy polymers
The model was used to determine the carbon dioxide con-centration in the column as a function of time based ondifferent operating conditions Analysis clearly indicated thatproviding an optimal residence time by lowering the velocityof the flow produces the maximum separation efficiency Fora fixed column length of 0035m an optimal residence timeof 50 seconds corresponding to a flow velocity of 0001msyielded a separation efficiency of around 97 Lowering theoperating pressure leads to better separation as permeabilityof gases is inversely proportional to the operating pressureIncreasing the temperature of the adsorption bed producedbetter separation of the gases As an outcome of optimizationstudies a reference table specifying the separation lengthrequired for complete separation of the feedmixture enteringthe adsorption column at different initial concentrations(with a flow velocity of 0001ms) was also presented
Appendix
Algorithm 1 User defined function
Nomenclature
119875 Total bed pressure (kPa)120582119900 Permeability (Barrer)
119864119901 Activation energy (kJmol)
6 International Journal of Chemical Engineering
Table4Dependences
tudies
ofseparatio
nleng
thon
initialconcentrationof
feed
Positionof
thec
olum
n(m
)
Con
centratio
nof
CO2(kmolm3)a
long
thec
olum
nleng
thford
ifferentinitia
lcon
centratio
nsof
feed
mixture
95CO
2in
feed
85CO
2in
feed
75CO
2in
feed
65CO
2in
feed
55CO
2in
feed
45CO
2in
feed
35CO
2in
feed
25CO
2in
feed
15CO
2in
feed
5CO
2in
feed
0306
00
00
00
00
00
0253
00
00
00
00
00
0201
00
00
00
00
00
0157
000
0481
00
00
00
00
00105
00800
440053567
002707
0005331
00
00
00
0052
0419499
0345991
0277279
0212829
0152186
009501
004
090001032
00
0017
149493
115133
088624
0675398
0503622
036095
024045
0137306
0047937
000
695
International Journal of Chemical Engineering 7
119877 Universal gas constant (Jgmol K)120588 Density (kgm3)120574 Volume (m3) Velocity (msec)Φ Any given property997888rarr
119861119891 Body forces per unit volume (Nm3)
119879 Gas-phase temperature in the bed (K)120591 Fluid stress (Nm2)120583 Absolute viscosity (kgm sec)120572 Gas permeability (Barrer)119889119901 Particle diameter (m)
120576 Bulk void fraction119902119894 Solid-phase concentration of 119894th
component (gmolkg)119902lowast
119894 Equilibrium solid-phase concentration of
119894th component (gmolkg)119896119894 LDF model mass transfer coefficient of 119894th
component (1sec)119863119901119894 Diffusivity of 119894th component (m2sec)
119905 Time (sec)119887 Affinity constant (barminus1)119862 Gas-phase concentration of a given
component (cm3 of adsorbatecm3 ofadsorbent)
119862119863 Gas concentration by dissolution (cm3 ofadsorbatecm3 of adsorbent)
119862119867 Gas concentration by hole filling (cm3 ofadsorbatecm3 of adsorbent)
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R E Treybal Mass-Transfer Operations vol 3 McGraw-HillNew York NY USA 1980
[2] C M Yon and J D ShermanAdsorption Gas Separation Kirk-Othmer Encyclopedia of Chemical Technology 2004
[3] D Aaron and C Tsouris ldquoSeparation of CO2from flue gas a
reviewrdquo Separation Science and Technology vol 40 no 1ndash3 pp321ndash348 2005
[4] F I Khan and A K Ghoshal ldquoRemoval of Volatile OrganicCompounds from polluted airrdquo Journal of Loss Prevention in theProcess Industries vol 13 no 6 pp 527ndash545 2000
[5] M A Kalbassi R J Allam and T C Golden ldquoTemperatureswing adsorptionrdquo US Patent no 5846295 US Patent andTrademark Office Washington DC USA 1998
[6] C W Skarstrom ldquoMethod and apparatus for fractionatingrdquoUS Patent no 2944627 US Patent and Trademark OfficeWashington DC USA 1970
[7] A Kapoor and R T Yang ldquoKinetic separation of methanemdashcarbon dioxide mixture by adsorption on molecular sievecarbonrdquo Chemical Engineering Science vol 44 no 8 pp 1723ndash1733 1989
[8] A M Mendes C A Costa and A E Rodrigues ldquoOxygenseparation from air by PSA modelling and experimental
results part Irdquo Separation and Purification Technology vol 24no 1-2 pp 173ndash188 2001
[9] S Farooq D M Ruthven and H A Boniface ldquoNumerical sim-ulation of a pressure swing adsorption oxygen unitrdquo ChemicalEngineering Science vol 44 no 12 pp 2809ndash2816 1989
[10] J C Kayser and K S Knaebel ldquoPressure swing adsorptiondevelopment of an equilibrium theory for binary gas mixtureswith nonlinear isothermsrdquo Chemical Engineering Science vol44 no 1 pp 1ndash8 1989
[11] S Sridhar B Smitha and T M Aminabhavi ldquoSeparation ofcarbon dioxide from natural gas mixtures through polymericmembranesmdasha reviewrdquo Separation amp Purification Reviews vol36 no 2 pp 113ndash174 2007
[12] H S Pierre Simulation of dynamic pressure-swing gas sorptionin polymers [PhD Dissertation] 2005
[13] S Li J G Martinek J L Falconer R D Noble and T QGardner ldquoHigh-pressure CO
2CH4separation using SAPO-34
membranesrdquo Industrial amp Engineering Chemistry Research vol44 no 9 pp 3220ndash3228 2005
[14] H Hachisuka T Ohara and K Ikeda ldquoNew type asymmetricmembranes having almost defect free hyper-thin skin layer andsponge-like porous matrixrdquo Journal of Membrane Science vol116 no 2 pp 265ndash272 1996
[15] M R Coleman and W J Koros ldquoIsometric polyimides basedon fluorinated dianhydrides and diamines for gas separationapplicationsrdquo Journal of Membrane Science vol 50 no 3 pp285ndash297 1990
[16] M K Ghosh and K L Mittal Polyimides Fundamentals andApplications vol 36 CRC Press New York NY USA 1996
[17] T H Kim W J Koros and G R Husk ldquoTemperature effectson gas permselection properties in hexafluoro aromatic poly-imidesrdquo Journal of Membrane Science vol 46 no 1 pp 43ndash561989
[18] B Xing and J J Pignatello ldquoDual-mode sorption of low-polaritycompounds in glassy poly (vinyl chloride) and soil organicmatterrdquo Environmental Science amp Technology vol 31 no 3 pp792ndash799 1997
[19] RM Barrer ldquoDiffusivities in glassy polymers for the dualmodesorption modelrdquo Journal of Membrane Science vol 18 pp 25ndash35 1984
[20] E Glueckauf ldquoThe influence of ionic hydration on activitycoefficients in concentrated electrolyte solutionsrdquo Transactionsof the Faraday Society vol 51 pp 1235ndash1244 1955
[21] T Hirose Y Mi S A Stern and A K S Clair ldquoThe solubilityof carbon dioxide and methane in polyimides at elevatedpressuresrdquo Journal of Polymer Science B Polymer Physics vol29 no 3 pp 341ndash347 1991
in isotropic porous media is given by (2) Incorporating thesource term 119878
0 in (2) would enable to define concentration
points of adsorbed gas Thus the mass and momentumconservation equations for the discussed model are givenby (3) and (4) respectively Inertial and viscous resistanceencountered by the fluid are incorporated in themodel by thelast two terms Permeability (120572) is calculated using Darcyrsquoslaw (see equation (5)) due to the presence of porous mediaThe linear driving force model describing the mass transferphenomena for PSA is given by (6) and (7) The governingequations were discretized by second-order upwind scheme
22 Model Validation The adsorption of small molecules inglassy polymers is described best by the dual mode (DM)sorption model [18 19] The dual sorption mechanism isgiven as a combination of Henryrsquos law of solubility andLangmuir adsorption [18] Henryrsquos law accounts for thedissolution of the penetrant molecule in the continuouspolymer chain matrix and its sorption in microvoids isdescribed by Langmuir model According to DM sorptionmodel the gas concentration in the polymer is given by thefollowing equation as a function of operating pressure
Table 3 DM sorption model parameters for carbon dioxide sorbedin polyimide
119896119863(cm3 of CO2cm
3 of adsorbent bar) 156
1198621015840
119867(cm3 of CO2cm
3 of adsorbent) 546
119887 (barminus1) 0544
20
40
60
80
100
120
140
0 10 20 30 40 50Pressure (bar)
DM modelHenrys model
Langmuir modelNumerical model
Con
cent
ratio
n (c
m3
of g
asc
m3
of ad
sorb
ent)
Figure 2 Comparison of DMmodel and numerical model
where 119862 is the concentration of the gas adsorbed in unitvolume of the polymer 119862
119863is the gas concentration by
dissolution 119862119867is the gas concentration by hole filling 119901 is
the applied pressure 119896119863is dissolution constant1198621015840
119867is the hole
saturation constant and 119887 is the affinity constantDM model assumes that both modes occur simultane-
ously and are always in equilibrium [18 20] The diffusioncoefficient is independent of concentrationThe values of theparameters for the DM sorption model for carbon dioxidesorbed in polyimide are specified in Table 3 [21]
Validation of the numerical model was conducted bystudying the steady state adsorbed CO
2concentration as
a function of operating pressure and comparing with theCO2concentration obtained using analytical DM model As
shown in Figure 2 the behaviour of the numerical model isin accordance with the analytical DM sorption model Thevariation in the amount of CO
2adsorbed per unit volume
of adsorbent between the DM model and numerical modelreported an average error of 87 (in magnitude) calculatedover the operating pressure for the adsorption column Theerror between the DM model and the proposed numeri-cal model could be due to the truncation discretizationand round-off phenomena in the simulation The deviationbetween numerical model and the DMmodel was very muchless in comparison to the deviation between Langmuir modeland theDMmodel (average error of 425) and the deviationbetween Henry model and the DM model (average error of349)
Figure 3 Concentration of methane as a function of time
07
075
08
085
09
095
1
0025 0075 0125 0175 0225 0275 0325 0375Column position from inlet (m)
minus0025
Sepa
ratio
n ra
tio (C
CO
2C
CH
4)
1 atm5 atm
10 atm20 atm
Figure 4 Pressure effects on separation ratio (flow velocity =015msec and temperature = 200K)
23 Simulation Carbon dioxide-methane mixture at a vol-ume composition of 50-50 was given as the inlet feedstream At the end of the cycle the mole fraction of carbondioxide was reduced to 005 from 05 due to the adsorptionof carbon dioxide in the column The result of the unsteadystate simulation is presented in Figure 3 It is evident fromFigure 3 that the concentration of methane at a given spatialposition increasedwith time of adsorption It was also evidentthat the rate of adsorption at a given point in the columndecreased with the time of adsorption This was due to thedecreasing concentration gradient between the feed streamand the adsorbent material
0976
098
0984
0988
0992
0996
1
0025 0075 0125 0175 0225 0275 0325 0375Column position from inlet (m)
minus0025
200K300K400K
Sepa
ratio
n ra
tio (C
CO
2C
CH
4)
Figure 5 Temperature effects on separation ratio (flow velocity =015msec and pressure = 15 atm)
231 Effect of Pressure Simulation results showed thatdecreasing the operating pressure leads to better separationAs shown in Figure 4 the separation ratio (ratio of concen-tration of CO
2to concentration of CH
4) decreased along the
length of the column as pressure was reduced from 15 atm to1 atm
232 Effect of Temperature For most gases solubilityincreases with increase in temperature till the glass transitiontemperature is reached Simulations were carried out at200K 300K and 400K keeping the pressure constant Itwas observed that separation increases with increase intemperature The temperature effect on the adsorption isshown in Figure 5
233 Effect of Flowrate Flowrate of the feed stream is animportant factor affecting the separation process The modelwas simulated for three different flow ratesmdash01ms 001msand 0001msThe highest degree of separation was obtainedat 0001ms as evident from Figure 6
24 Optimization The optimum operating conditions forcarrying out the pressure swing adsorption for the separationof carbon dioxide-methane mixture at a volume compositionof 50-50 entering the column at a velocity of 0001mswas obtained by simulating the model at different operatingpressures and temperatures Pressure was reduced from20 atm to 1 atm and the temperature dependence study wasperformed for 200K 300K and 400K For every run theseparation ratio was calculated and plotted to find the opti-mum conditions for operating the PSA column The resultsare presented in Figure 7 The optimization study revealedthat a separation length of about 0125m guaranteed 100
International Journal of Chemical Engineering 5
04
05
06
07
08
09
1
0 005 01 015 02 025 03 035 04Column position from inlet (m)
Sepa
ratio
n ra
tio (C
CO
2C
CH
4)
01ms001ms0001ms
Figure 6 Effect of feed velocity on the separation ratio (pressure =5 atm and temperature = 200K)
0
01
02
03
04
05
06
07
08
09
1
0 005 01 015 02 025 03 035 04Column position from inlet (m)
minus01minus005
1 atm and 200K2 atm and 300K10 atm and 400K1 atm and 300K
5 atm and 300K1 atm and 400K10 atm and 200K
Sepa
ratio
n ra
tio (C
CO
2C
CH
4)
Figure 7 Optimization studies on separation ratio on operationconditions (feed velocity = 0001ms)
separation for the specified feed inlet conditions Optimumoperating conditions were found to be 1 atm and 400K
Further as a comparative study simulations were carriedout to determine the separation length required for completeseparation of the feed corresponding to different initialconcentrations of the feed mixture The results obtained arepresented in Table 4
As a future scope of study for the pressure swing adsorp-tion using 6-FDA-ODA particles bed a more improved
User defined functioninclude ldquoudfhrdquoDEFINE SOURCE(second c t dS eqn)
real sourcesource = minus000004461296 lowast C P(c t) lowast exp(1C T(c t))dS[eqn] = minus000004461296 lowast exp(1C T(c t))return source
include ldquoudfhrdquoDEFINE SOURCE(third c t dS eqn)
real sourcesource = minus0000108218 lowast C P(c t) lowast exp(1C T(c t))dS[eqn] = minus0000108218 lowast exp(1C T(c t))return source
Algorithm 1 User defined function
model (3-dimensional) incorporating most of the real timecorrelations radial variation studies and temperature depen-dence studies for the adsorption process are to be carried out
3 Conclusions
A CFD model based on pressure swing adsorption wasdeveloped for binary gas mixture separation namely CO
2-
CH4 using 6-FDAbased polyimides as adsorbentThemodel
was validated against the analytical dual mode sorptionmodel for adsorption of gases (CO
2) on glassy polymers
The model was used to determine the carbon dioxide con-centration in the column as a function of time based ondifferent operating conditions Analysis clearly indicated thatproviding an optimal residence time by lowering the velocityof the flow produces the maximum separation efficiency Fora fixed column length of 0035m an optimal residence timeof 50 seconds corresponding to a flow velocity of 0001msyielded a separation efficiency of around 97 Lowering theoperating pressure leads to better separation as permeabilityof gases is inversely proportional to the operating pressureIncreasing the temperature of the adsorption bed producedbetter separation of the gases As an outcome of optimizationstudies a reference table specifying the separation lengthrequired for complete separation of the feedmixture enteringthe adsorption column at different initial concentrations(with a flow velocity of 0001ms) was also presented
Appendix
Algorithm 1 User defined function
Nomenclature
119875 Total bed pressure (kPa)120582119900 Permeability (Barrer)
119864119901 Activation energy (kJmol)
6 International Journal of Chemical Engineering
Table4Dependences
tudies
ofseparatio
nleng
thon
initialconcentrationof
feed
Positionof
thec
olum
n(m
)
Con
centratio
nof
CO2(kmolm3)a
long
thec
olum
nleng
thford
ifferentinitia
lcon
centratio
nsof
feed
mixture
95CO
2in
feed
85CO
2in
feed
75CO
2in
feed
65CO
2in
feed
55CO
2in
feed
45CO
2in
feed
35CO
2in
feed
25CO
2in
feed
15CO
2in
feed
5CO
2in
feed
0306
00
00
00
00
00
0253
00
00
00
00
00
0201
00
00
00
00
00
0157
000
0481
00
00
00
00
00105
00800
440053567
002707
0005331
00
00
00
0052
0419499
0345991
0277279
0212829
0152186
009501
004
090001032
00
0017
149493
115133
088624
0675398
0503622
036095
024045
0137306
0047937
000
695
International Journal of Chemical Engineering 7
119877 Universal gas constant (Jgmol K)120588 Density (kgm3)120574 Volume (m3) Velocity (msec)Φ Any given property997888rarr
119861119891 Body forces per unit volume (Nm3)
119879 Gas-phase temperature in the bed (K)120591 Fluid stress (Nm2)120583 Absolute viscosity (kgm sec)120572 Gas permeability (Barrer)119889119901 Particle diameter (m)
120576 Bulk void fraction119902119894 Solid-phase concentration of 119894th
component (gmolkg)119902lowast
119894 Equilibrium solid-phase concentration of
119894th component (gmolkg)119896119894 LDF model mass transfer coefficient of 119894th
component (1sec)119863119901119894 Diffusivity of 119894th component (m2sec)
119905 Time (sec)119887 Affinity constant (barminus1)119862 Gas-phase concentration of a given
component (cm3 of adsorbatecm3 ofadsorbent)
119862119863 Gas concentration by dissolution (cm3 ofadsorbatecm3 of adsorbent)
119862119867 Gas concentration by hole filling (cm3 ofadsorbatecm3 of adsorbent)
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R E Treybal Mass-Transfer Operations vol 3 McGraw-HillNew York NY USA 1980
[2] C M Yon and J D ShermanAdsorption Gas Separation Kirk-Othmer Encyclopedia of Chemical Technology 2004
[3] D Aaron and C Tsouris ldquoSeparation of CO2from flue gas a
reviewrdquo Separation Science and Technology vol 40 no 1ndash3 pp321ndash348 2005
[4] F I Khan and A K Ghoshal ldquoRemoval of Volatile OrganicCompounds from polluted airrdquo Journal of Loss Prevention in theProcess Industries vol 13 no 6 pp 527ndash545 2000
[5] M A Kalbassi R J Allam and T C Golden ldquoTemperatureswing adsorptionrdquo US Patent no 5846295 US Patent andTrademark Office Washington DC USA 1998
[6] C W Skarstrom ldquoMethod and apparatus for fractionatingrdquoUS Patent no 2944627 US Patent and Trademark OfficeWashington DC USA 1970
[7] A Kapoor and R T Yang ldquoKinetic separation of methanemdashcarbon dioxide mixture by adsorption on molecular sievecarbonrdquo Chemical Engineering Science vol 44 no 8 pp 1723ndash1733 1989
[8] A M Mendes C A Costa and A E Rodrigues ldquoOxygenseparation from air by PSA modelling and experimental
results part Irdquo Separation and Purification Technology vol 24no 1-2 pp 173ndash188 2001
[9] S Farooq D M Ruthven and H A Boniface ldquoNumerical sim-ulation of a pressure swing adsorption oxygen unitrdquo ChemicalEngineering Science vol 44 no 12 pp 2809ndash2816 1989
[10] J C Kayser and K S Knaebel ldquoPressure swing adsorptiondevelopment of an equilibrium theory for binary gas mixtureswith nonlinear isothermsrdquo Chemical Engineering Science vol44 no 1 pp 1ndash8 1989
[11] S Sridhar B Smitha and T M Aminabhavi ldquoSeparation ofcarbon dioxide from natural gas mixtures through polymericmembranesmdasha reviewrdquo Separation amp Purification Reviews vol36 no 2 pp 113ndash174 2007
[12] H S Pierre Simulation of dynamic pressure-swing gas sorptionin polymers [PhD Dissertation] 2005
[13] S Li J G Martinek J L Falconer R D Noble and T QGardner ldquoHigh-pressure CO
2CH4separation using SAPO-34
membranesrdquo Industrial amp Engineering Chemistry Research vol44 no 9 pp 3220ndash3228 2005
[14] H Hachisuka T Ohara and K Ikeda ldquoNew type asymmetricmembranes having almost defect free hyper-thin skin layer andsponge-like porous matrixrdquo Journal of Membrane Science vol116 no 2 pp 265ndash272 1996
[15] M R Coleman and W J Koros ldquoIsometric polyimides basedon fluorinated dianhydrides and diamines for gas separationapplicationsrdquo Journal of Membrane Science vol 50 no 3 pp285ndash297 1990
[16] M K Ghosh and K L Mittal Polyimides Fundamentals andApplications vol 36 CRC Press New York NY USA 1996
[17] T H Kim W J Koros and G R Husk ldquoTemperature effectson gas permselection properties in hexafluoro aromatic poly-imidesrdquo Journal of Membrane Science vol 46 no 1 pp 43ndash561989
[18] B Xing and J J Pignatello ldquoDual-mode sorption of low-polaritycompounds in glassy poly (vinyl chloride) and soil organicmatterrdquo Environmental Science amp Technology vol 31 no 3 pp792ndash799 1997
[19] RM Barrer ldquoDiffusivities in glassy polymers for the dualmodesorption modelrdquo Journal of Membrane Science vol 18 pp 25ndash35 1984
[20] E Glueckauf ldquoThe influence of ionic hydration on activitycoefficients in concentrated electrolyte solutionsrdquo Transactionsof the Faraday Society vol 51 pp 1235ndash1244 1955
[21] T Hirose Y Mi S A Stern and A K S Clair ldquoThe solubilityof carbon dioxide and methane in polyimides at elevatedpressuresrdquo Journal of Polymer Science B Polymer Physics vol29 no 3 pp 341ndash347 1991
Figure 3 Concentration of methane as a function of time
07
075
08
085
09
095
1
0025 0075 0125 0175 0225 0275 0325 0375Column position from inlet (m)
minus0025
Sepa
ratio
n ra
tio (C
CO
2C
CH
4)
1 atm5 atm
10 atm20 atm
Figure 4 Pressure effects on separation ratio (flow velocity =015msec and temperature = 200K)
23 Simulation Carbon dioxide-methane mixture at a vol-ume composition of 50-50 was given as the inlet feedstream At the end of the cycle the mole fraction of carbondioxide was reduced to 005 from 05 due to the adsorptionof carbon dioxide in the column The result of the unsteadystate simulation is presented in Figure 3 It is evident fromFigure 3 that the concentration of methane at a given spatialposition increasedwith time of adsorption It was also evidentthat the rate of adsorption at a given point in the columndecreased with the time of adsorption This was due to thedecreasing concentration gradient between the feed streamand the adsorbent material
0976
098
0984
0988
0992
0996
1
0025 0075 0125 0175 0225 0275 0325 0375Column position from inlet (m)
minus0025
200K300K400K
Sepa
ratio
n ra
tio (C
CO
2C
CH
4)
Figure 5 Temperature effects on separation ratio (flow velocity =015msec and pressure = 15 atm)
231 Effect of Pressure Simulation results showed thatdecreasing the operating pressure leads to better separationAs shown in Figure 4 the separation ratio (ratio of concen-tration of CO
2to concentration of CH
4) decreased along the
length of the column as pressure was reduced from 15 atm to1 atm
232 Effect of Temperature For most gases solubilityincreases with increase in temperature till the glass transitiontemperature is reached Simulations were carried out at200K 300K and 400K keeping the pressure constant Itwas observed that separation increases with increase intemperature The temperature effect on the adsorption isshown in Figure 5
233 Effect of Flowrate Flowrate of the feed stream is animportant factor affecting the separation process The modelwas simulated for three different flow ratesmdash01ms 001msand 0001msThe highest degree of separation was obtainedat 0001ms as evident from Figure 6
24 Optimization The optimum operating conditions forcarrying out the pressure swing adsorption for the separationof carbon dioxide-methane mixture at a volume compositionof 50-50 entering the column at a velocity of 0001mswas obtained by simulating the model at different operatingpressures and temperatures Pressure was reduced from20 atm to 1 atm and the temperature dependence study wasperformed for 200K 300K and 400K For every run theseparation ratio was calculated and plotted to find the opti-mum conditions for operating the PSA column The resultsare presented in Figure 7 The optimization study revealedthat a separation length of about 0125m guaranteed 100
International Journal of Chemical Engineering 5
04
05
06
07
08
09
1
0 005 01 015 02 025 03 035 04Column position from inlet (m)
Sepa
ratio
n ra
tio (C
CO
2C
CH
4)
01ms001ms0001ms
Figure 6 Effect of feed velocity on the separation ratio (pressure =5 atm and temperature = 200K)
0
01
02
03
04
05
06
07
08
09
1
0 005 01 015 02 025 03 035 04Column position from inlet (m)
minus01minus005
1 atm and 200K2 atm and 300K10 atm and 400K1 atm and 300K
5 atm and 300K1 atm and 400K10 atm and 200K
Sepa
ratio
n ra
tio (C
CO
2C
CH
4)
Figure 7 Optimization studies on separation ratio on operationconditions (feed velocity = 0001ms)
separation for the specified feed inlet conditions Optimumoperating conditions were found to be 1 atm and 400K
Further as a comparative study simulations were carriedout to determine the separation length required for completeseparation of the feed corresponding to different initialconcentrations of the feed mixture The results obtained arepresented in Table 4
As a future scope of study for the pressure swing adsorp-tion using 6-FDA-ODA particles bed a more improved
User defined functioninclude ldquoudfhrdquoDEFINE SOURCE(second c t dS eqn)
real sourcesource = minus000004461296 lowast C P(c t) lowast exp(1C T(c t))dS[eqn] = minus000004461296 lowast exp(1C T(c t))return source
include ldquoudfhrdquoDEFINE SOURCE(third c t dS eqn)
real sourcesource = minus0000108218 lowast C P(c t) lowast exp(1C T(c t))dS[eqn] = minus0000108218 lowast exp(1C T(c t))return source
Algorithm 1 User defined function
model (3-dimensional) incorporating most of the real timecorrelations radial variation studies and temperature depen-dence studies for the adsorption process are to be carried out
3 Conclusions
A CFD model based on pressure swing adsorption wasdeveloped for binary gas mixture separation namely CO
2-
CH4 using 6-FDAbased polyimides as adsorbentThemodel
was validated against the analytical dual mode sorptionmodel for adsorption of gases (CO
2) on glassy polymers
The model was used to determine the carbon dioxide con-centration in the column as a function of time based ondifferent operating conditions Analysis clearly indicated thatproviding an optimal residence time by lowering the velocityof the flow produces the maximum separation efficiency Fora fixed column length of 0035m an optimal residence timeof 50 seconds corresponding to a flow velocity of 0001msyielded a separation efficiency of around 97 Lowering theoperating pressure leads to better separation as permeabilityof gases is inversely proportional to the operating pressureIncreasing the temperature of the adsorption bed producedbetter separation of the gases As an outcome of optimizationstudies a reference table specifying the separation lengthrequired for complete separation of the feedmixture enteringthe adsorption column at different initial concentrations(with a flow velocity of 0001ms) was also presented
Appendix
Algorithm 1 User defined function
Nomenclature
119875 Total bed pressure (kPa)120582119900 Permeability (Barrer)
119864119901 Activation energy (kJmol)
6 International Journal of Chemical Engineering
Table4Dependences
tudies
ofseparatio
nleng
thon
initialconcentrationof
feed
Positionof
thec
olum
n(m
)
Con
centratio
nof
CO2(kmolm3)a
long
thec
olum
nleng
thford
ifferentinitia
lcon
centratio
nsof
feed
mixture
95CO
2in
feed
85CO
2in
feed
75CO
2in
feed
65CO
2in
feed
55CO
2in
feed
45CO
2in
feed
35CO
2in
feed
25CO
2in
feed
15CO
2in
feed
5CO
2in
feed
0306
00
00
00
00
00
0253
00
00
00
00
00
0201
00
00
00
00
00
0157
000
0481
00
00
00
00
00105
00800
440053567
002707
0005331
00
00
00
0052
0419499
0345991
0277279
0212829
0152186
009501
004
090001032
00
0017
149493
115133
088624
0675398
0503622
036095
024045
0137306
0047937
000
695
International Journal of Chemical Engineering 7
119877 Universal gas constant (Jgmol K)120588 Density (kgm3)120574 Volume (m3) Velocity (msec)Φ Any given property997888rarr
119861119891 Body forces per unit volume (Nm3)
119879 Gas-phase temperature in the bed (K)120591 Fluid stress (Nm2)120583 Absolute viscosity (kgm sec)120572 Gas permeability (Barrer)119889119901 Particle diameter (m)
120576 Bulk void fraction119902119894 Solid-phase concentration of 119894th
component (gmolkg)119902lowast
119894 Equilibrium solid-phase concentration of
119894th component (gmolkg)119896119894 LDF model mass transfer coefficient of 119894th
component (1sec)119863119901119894 Diffusivity of 119894th component (m2sec)
119905 Time (sec)119887 Affinity constant (barminus1)119862 Gas-phase concentration of a given
component (cm3 of adsorbatecm3 ofadsorbent)
119862119863 Gas concentration by dissolution (cm3 ofadsorbatecm3 of adsorbent)
119862119867 Gas concentration by hole filling (cm3 ofadsorbatecm3 of adsorbent)
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R E Treybal Mass-Transfer Operations vol 3 McGraw-HillNew York NY USA 1980
[2] C M Yon and J D ShermanAdsorption Gas Separation Kirk-Othmer Encyclopedia of Chemical Technology 2004
[3] D Aaron and C Tsouris ldquoSeparation of CO2from flue gas a
reviewrdquo Separation Science and Technology vol 40 no 1ndash3 pp321ndash348 2005
[4] F I Khan and A K Ghoshal ldquoRemoval of Volatile OrganicCompounds from polluted airrdquo Journal of Loss Prevention in theProcess Industries vol 13 no 6 pp 527ndash545 2000
[5] M A Kalbassi R J Allam and T C Golden ldquoTemperatureswing adsorptionrdquo US Patent no 5846295 US Patent andTrademark Office Washington DC USA 1998
[6] C W Skarstrom ldquoMethod and apparatus for fractionatingrdquoUS Patent no 2944627 US Patent and Trademark OfficeWashington DC USA 1970
[7] A Kapoor and R T Yang ldquoKinetic separation of methanemdashcarbon dioxide mixture by adsorption on molecular sievecarbonrdquo Chemical Engineering Science vol 44 no 8 pp 1723ndash1733 1989
[8] A M Mendes C A Costa and A E Rodrigues ldquoOxygenseparation from air by PSA modelling and experimental
results part Irdquo Separation and Purification Technology vol 24no 1-2 pp 173ndash188 2001
[9] S Farooq D M Ruthven and H A Boniface ldquoNumerical sim-ulation of a pressure swing adsorption oxygen unitrdquo ChemicalEngineering Science vol 44 no 12 pp 2809ndash2816 1989
[10] J C Kayser and K S Knaebel ldquoPressure swing adsorptiondevelopment of an equilibrium theory for binary gas mixtureswith nonlinear isothermsrdquo Chemical Engineering Science vol44 no 1 pp 1ndash8 1989
[11] S Sridhar B Smitha and T M Aminabhavi ldquoSeparation ofcarbon dioxide from natural gas mixtures through polymericmembranesmdasha reviewrdquo Separation amp Purification Reviews vol36 no 2 pp 113ndash174 2007
[12] H S Pierre Simulation of dynamic pressure-swing gas sorptionin polymers [PhD Dissertation] 2005
[13] S Li J G Martinek J L Falconer R D Noble and T QGardner ldquoHigh-pressure CO
2CH4separation using SAPO-34
membranesrdquo Industrial amp Engineering Chemistry Research vol44 no 9 pp 3220ndash3228 2005
[14] H Hachisuka T Ohara and K Ikeda ldquoNew type asymmetricmembranes having almost defect free hyper-thin skin layer andsponge-like porous matrixrdquo Journal of Membrane Science vol116 no 2 pp 265ndash272 1996
[15] M R Coleman and W J Koros ldquoIsometric polyimides basedon fluorinated dianhydrides and diamines for gas separationapplicationsrdquo Journal of Membrane Science vol 50 no 3 pp285ndash297 1990
[16] M K Ghosh and K L Mittal Polyimides Fundamentals andApplications vol 36 CRC Press New York NY USA 1996
[17] T H Kim W J Koros and G R Husk ldquoTemperature effectson gas permselection properties in hexafluoro aromatic poly-imidesrdquo Journal of Membrane Science vol 46 no 1 pp 43ndash561989
[18] B Xing and J J Pignatello ldquoDual-mode sorption of low-polaritycompounds in glassy poly (vinyl chloride) and soil organicmatterrdquo Environmental Science amp Technology vol 31 no 3 pp792ndash799 1997
[19] RM Barrer ldquoDiffusivities in glassy polymers for the dualmodesorption modelrdquo Journal of Membrane Science vol 18 pp 25ndash35 1984
[20] E Glueckauf ldquoThe influence of ionic hydration on activitycoefficients in concentrated electrolyte solutionsrdquo Transactionsof the Faraday Society vol 51 pp 1235ndash1244 1955
[21] T Hirose Y Mi S A Stern and A K S Clair ldquoThe solubilityof carbon dioxide and methane in polyimides at elevatedpressuresrdquo Journal of Polymer Science B Polymer Physics vol29 no 3 pp 341ndash347 1991
0 005 01 015 02 025 03 035 04Column position from inlet (m)
Sepa
ratio
n ra
tio (C
CO
2C
CH
4)
01ms001ms0001ms
Figure 6 Effect of feed velocity on the separation ratio (pressure =5 atm and temperature = 200K)
0
01
02
03
04
05
06
07
08
09
1
0 005 01 015 02 025 03 035 04Column position from inlet (m)
minus01minus005
1 atm and 200K2 atm and 300K10 atm and 400K1 atm and 300K
5 atm and 300K1 atm and 400K10 atm and 200K
Sepa
ratio
n ra
tio (C
CO
2C
CH
4)
Figure 7 Optimization studies on separation ratio on operationconditions (feed velocity = 0001ms)
separation for the specified feed inlet conditions Optimumoperating conditions were found to be 1 atm and 400K
Further as a comparative study simulations were carriedout to determine the separation length required for completeseparation of the feed corresponding to different initialconcentrations of the feed mixture The results obtained arepresented in Table 4
As a future scope of study for the pressure swing adsorp-tion using 6-FDA-ODA particles bed a more improved
User defined functioninclude ldquoudfhrdquoDEFINE SOURCE(second c t dS eqn)
real sourcesource = minus000004461296 lowast C P(c t) lowast exp(1C T(c t))dS[eqn] = minus000004461296 lowast exp(1C T(c t))return source
include ldquoudfhrdquoDEFINE SOURCE(third c t dS eqn)
real sourcesource = minus0000108218 lowast C P(c t) lowast exp(1C T(c t))dS[eqn] = minus0000108218 lowast exp(1C T(c t))return source
Algorithm 1 User defined function
model (3-dimensional) incorporating most of the real timecorrelations radial variation studies and temperature depen-dence studies for the adsorption process are to be carried out
3 Conclusions
A CFD model based on pressure swing adsorption wasdeveloped for binary gas mixture separation namely CO
2-
CH4 using 6-FDAbased polyimides as adsorbentThemodel
was validated against the analytical dual mode sorptionmodel for adsorption of gases (CO
2) on glassy polymers
The model was used to determine the carbon dioxide con-centration in the column as a function of time based ondifferent operating conditions Analysis clearly indicated thatproviding an optimal residence time by lowering the velocityof the flow produces the maximum separation efficiency Fora fixed column length of 0035m an optimal residence timeof 50 seconds corresponding to a flow velocity of 0001msyielded a separation efficiency of around 97 Lowering theoperating pressure leads to better separation as permeabilityof gases is inversely proportional to the operating pressureIncreasing the temperature of the adsorption bed producedbetter separation of the gases As an outcome of optimizationstudies a reference table specifying the separation lengthrequired for complete separation of the feedmixture enteringthe adsorption column at different initial concentrations(with a flow velocity of 0001ms) was also presented
Appendix
Algorithm 1 User defined function
Nomenclature
119875 Total bed pressure (kPa)120582119900 Permeability (Barrer)
119864119901 Activation energy (kJmol)
6 International Journal of Chemical Engineering
Table4Dependences
tudies
ofseparatio
nleng
thon
initialconcentrationof
feed
Positionof
thec
olum
n(m
)
Con
centratio
nof
CO2(kmolm3)a
long
thec
olum
nleng
thford
ifferentinitia
lcon
centratio
nsof
feed
mixture
95CO
2in
feed
85CO
2in
feed
75CO
2in
feed
65CO
2in
feed
55CO
2in
feed
45CO
2in
feed
35CO
2in
feed
25CO
2in
feed
15CO
2in
feed
5CO
2in
feed
0306
00
00
00
00
00
0253
00
00
00
00
00
0201
00
00
00
00
00
0157
000
0481
00
00
00
00
00105
00800
440053567
002707
0005331
00
00
00
0052
0419499
0345991
0277279
0212829
0152186
009501
004
090001032
00
0017
149493
115133
088624
0675398
0503622
036095
024045
0137306
0047937
000
695
International Journal of Chemical Engineering 7
119877 Universal gas constant (Jgmol K)120588 Density (kgm3)120574 Volume (m3) Velocity (msec)Φ Any given property997888rarr
119861119891 Body forces per unit volume (Nm3)
119879 Gas-phase temperature in the bed (K)120591 Fluid stress (Nm2)120583 Absolute viscosity (kgm sec)120572 Gas permeability (Barrer)119889119901 Particle diameter (m)
120576 Bulk void fraction119902119894 Solid-phase concentration of 119894th
component (gmolkg)119902lowast
119894 Equilibrium solid-phase concentration of
119894th component (gmolkg)119896119894 LDF model mass transfer coefficient of 119894th
component (1sec)119863119901119894 Diffusivity of 119894th component (m2sec)
119905 Time (sec)119887 Affinity constant (barminus1)119862 Gas-phase concentration of a given
component (cm3 of adsorbatecm3 ofadsorbent)
119862119863 Gas concentration by dissolution (cm3 ofadsorbatecm3 of adsorbent)
119862119867 Gas concentration by hole filling (cm3 ofadsorbatecm3 of adsorbent)
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R E Treybal Mass-Transfer Operations vol 3 McGraw-HillNew York NY USA 1980
[2] C M Yon and J D ShermanAdsorption Gas Separation Kirk-Othmer Encyclopedia of Chemical Technology 2004
[3] D Aaron and C Tsouris ldquoSeparation of CO2from flue gas a
reviewrdquo Separation Science and Technology vol 40 no 1ndash3 pp321ndash348 2005
[4] F I Khan and A K Ghoshal ldquoRemoval of Volatile OrganicCompounds from polluted airrdquo Journal of Loss Prevention in theProcess Industries vol 13 no 6 pp 527ndash545 2000
[5] M A Kalbassi R J Allam and T C Golden ldquoTemperatureswing adsorptionrdquo US Patent no 5846295 US Patent andTrademark Office Washington DC USA 1998
[6] C W Skarstrom ldquoMethod and apparatus for fractionatingrdquoUS Patent no 2944627 US Patent and Trademark OfficeWashington DC USA 1970
[7] A Kapoor and R T Yang ldquoKinetic separation of methanemdashcarbon dioxide mixture by adsorption on molecular sievecarbonrdquo Chemical Engineering Science vol 44 no 8 pp 1723ndash1733 1989
[8] A M Mendes C A Costa and A E Rodrigues ldquoOxygenseparation from air by PSA modelling and experimental
results part Irdquo Separation and Purification Technology vol 24no 1-2 pp 173ndash188 2001
[9] S Farooq D M Ruthven and H A Boniface ldquoNumerical sim-ulation of a pressure swing adsorption oxygen unitrdquo ChemicalEngineering Science vol 44 no 12 pp 2809ndash2816 1989
[10] J C Kayser and K S Knaebel ldquoPressure swing adsorptiondevelopment of an equilibrium theory for binary gas mixtureswith nonlinear isothermsrdquo Chemical Engineering Science vol44 no 1 pp 1ndash8 1989
[11] S Sridhar B Smitha and T M Aminabhavi ldquoSeparation ofcarbon dioxide from natural gas mixtures through polymericmembranesmdasha reviewrdquo Separation amp Purification Reviews vol36 no 2 pp 113ndash174 2007
[12] H S Pierre Simulation of dynamic pressure-swing gas sorptionin polymers [PhD Dissertation] 2005
[13] S Li J G Martinek J L Falconer R D Noble and T QGardner ldquoHigh-pressure CO
2CH4separation using SAPO-34
membranesrdquo Industrial amp Engineering Chemistry Research vol44 no 9 pp 3220ndash3228 2005
[14] H Hachisuka T Ohara and K Ikeda ldquoNew type asymmetricmembranes having almost defect free hyper-thin skin layer andsponge-like porous matrixrdquo Journal of Membrane Science vol116 no 2 pp 265ndash272 1996
[15] M R Coleman and W J Koros ldquoIsometric polyimides basedon fluorinated dianhydrides and diamines for gas separationapplicationsrdquo Journal of Membrane Science vol 50 no 3 pp285ndash297 1990
[16] M K Ghosh and K L Mittal Polyimides Fundamentals andApplications vol 36 CRC Press New York NY USA 1996
[17] T H Kim W J Koros and G R Husk ldquoTemperature effectson gas permselection properties in hexafluoro aromatic poly-imidesrdquo Journal of Membrane Science vol 46 no 1 pp 43ndash561989
[18] B Xing and J J Pignatello ldquoDual-mode sorption of low-polaritycompounds in glassy poly (vinyl chloride) and soil organicmatterrdquo Environmental Science amp Technology vol 31 no 3 pp792ndash799 1997
[19] RM Barrer ldquoDiffusivities in glassy polymers for the dualmodesorption modelrdquo Journal of Membrane Science vol 18 pp 25ndash35 1984
[20] E Glueckauf ldquoThe influence of ionic hydration on activitycoefficients in concentrated electrolyte solutionsrdquo Transactionsof the Faraday Society vol 51 pp 1235ndash1244 1955
[21] T Hirose Y Mi S A Stern and A K S Clair ldquoThe solubilityof carbon dioxide and methane in polyimides at elevatedpressuresrdquo Journal of Polymer Science B Polymer Physics vol29 no 3 pp 341ndash347 1991
119877 Universal gas constant (Jgmol K)120588 Density (kgm3)120574 Volume (m3) Velocity (msec)Φ Any given property997888rarr
119861119891 Body forces per unit volume (Nm3)
119879 Gas-phase temperature in the bed (K)120591 Fluid stress (Nm2)120583 Absolute viscosity (kgm sec)120572 Gas permeability (Barrer)119889119901 Particle diameter (m)
120576 Bulk void fraction119902119894 Solid-phase concentration of 119894th
component (gmolkg)119902lowast
119894 Equilibrium solid-phase concentration of
119894th component (gmolkg)119896119894 LDF model mass transfer coefficient of 119894th
component (1sec)119863119901119894 Diffusivity of 119894th component (m2sec)
119905 Time (sec)119887 Affinity constant (barminus1)119862 Gas-phase concentration of a given
component (cm3 of adsorbatecm3 ofadsorbent)
119862119863 Gas concentration by dissolution (cm3 ofadsorbatecm3 of adsorbent)
119862119867 Gas concentration by hole filling (cm3 ofadsorbatecm3 of adsorbent)
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R E Treybal Mass-Transfer Operations vol 3 McGraw-HillNew York NY USA 1980
[2] C M Yon and J D ShermanAdsorption Gas Separation Kirk-Othmer Encyclopedia of Chemical Technology 2004
[3] D Aaron and C Tsouris ldquoSeparation of CO2from flue gas a
reviewrdquo Separation Science and Technology vol 40 no 1ndash3 pp321ndash348 2005
[4] F I Khan and A K Ghoshal ldquoRemoval of Volatile OrganicCompounds from polluted airrdquo Journal of Loss Prevention in theProcess Industries vol 13 no 6 pp 527ndash545 2000
[5] M A Kalbassi R J Allam and T C Golden ldquoTemperatureswing adsorptionrdquo US Patent no 5846295 US Patent andTrademark Office Washington DC USA 1998
[6] C W Skarstrom ldquoMethod and apparatus for fractionatingrdquoUS Patent no 2944627 US Patent and Trademark OfficeWashington DC USA 1970
[7] A Kapoor and R T Yang ldquoKinetic separation of methanemdashcarbon dioxide mixture by adsorption on molecular sievecarbonrdquo Chemical Engineering Science vol 44 no 8 pp 1723ndash1733 1989
[8] A M Mendes C A Costa and A E Rodrigues ldquoOxygenseparation from air by PSA modelling and experimental
results part Irdquo Separation and Purification Technology vol 24no 1-2 pp 173ndash188 2001
[9] S Farooq D M Ruthven and H A Boniface ldquoNumerical sim-ulation of a pressure swing adsorption oxygen unitrdquo ChemicalEngineering Science vol 44 no 12 pp 2809ndash2816 1989
[10] J C Kayser and K S Knaebel ldquoPressure swing adsorptiondevelopment of an equilibrium theory for binary gas mixtureswith nonlinear isothermsrdquo Chemical Engineering Science vol44 no 1 pp 1ndash8 1989
[11] S Sridhar B Smitha and T M Aminabhavi ldquoSeparation ofcarbon dioxide from natural gas mixtures through polymericmembranesmdasha reviewrdquo Separation amp Purification Reviews vol36 no 2 pp 113ndash174 2007
[12] H S Pierre Simulation of dynamic pressure-swing gas sorptionin polymers [PhD Dissertation] 2005
[13] S Li J G Martinek J L Falconer R D Noble and T QGardner ldquoHigh-pressure CO
2CH4separation using SAPO-34
membranesrdquo Industrial amp Engineering Chemistry Research vol44 no 9 pp 3220ndash3228 2005
[14] H Hachisuka T Ohara and K Ikeda ldquoNew type asymmetricmembranes having almost defect free hyper-thin skin layer andsponge-like porous matrixrdquo Journal of Membrane Science vol116 no 2 pp 265ndash272 1996
[15] M R Coleman and W J Koros ldquoIsometric polyimides basedon fluorinated dianhydrides and diamines for gas separationapplicationsrdquo Journal of Membrane Science vol 50 no 3 pp285ndash297 1990
[16] M K Ghosh and K L Mittal Polyimides Fundamentals andApplications vol 36 CRC Press New York NY USA 1996
[17] T H Kim W J Koros and G R Husk ldquoTemperature effectson gas permselection properties in hexafluoro aromatic poly-imidesrdquo Journal of Membrane Science vol 46 no 1 pp 43ndash561989
[18] B Xing and J J Pignatello ldquoDual-mode sorption of low-polaritycompounds in glassy poly (vinyl chloride) and soil organicmatterrdquo Environmental Science amp Technology vol 31 no 3 pp792ndash799 1997
[19] RM Barrer ldquoDiffusivities in glassy polymers for the dualmodesorption modelrdquo Journal of Membrane Science vol 18 pp 25ndash35 1984
[20] E Glueckauf ldquoThe influence of ionic hydration on activitycoefficients in concentrated electrolyte solutionsrdquo Transactionsof the Faraday Society vol 51 pp 1235ndash1244 1955
[21] T Hirose Y Mi S A Stern and A K S Clair ldquoThe solubilityof carbon dioxide and methane in polyimides at elevatedpressuresrdquo Journal of Polymer Science B Polymer Physics vol29 no 3 pp 341ndash347 1991
119877 Universal gas constant (Jgmol K)120588 Density (kgm3)120574 Volume (m3) Velocity (msec)Φ Any given property997888rarr
119861119891 Body forces per unit volume (Nm3)
119879 Gas-phase temperature in the bed (K)120591 Fluid stress (Nm2)120583 Absolute viscosity (kgm sec)120572 Gas permeability (Barrer)119889119901 Particle diameter (m)
120576 Bulk void fraction119902119894 Solid-phase concentration of 119894th
component (gmolkg)119902lowast
119894 Equilibrium solid-phase concentration of
119894th component (gmolkg)119896119894 LDF model mass transfer coefficient of 119894th
component (1sec)119863119901119894 Diffusivity of 119894th component (m2sec)
119905 Time (sec)119887 Affinity constant (barminus1)119862 Gas-phase concentration of a given
component (cm3 of adsorbatecm3 ofadsorbent)
119862119863 Gas concentration by dissolution (cm3 ofadsorbatecm3 of adsorbent)
119862119867 Gas concentration by hole filling (cm3 ofadsorbatecm3 of adsorbent)
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] R E Treybal Mass-Transfer Operations vol 3 McGraw-HillNew York NY USA 1980
[2] C M Yon and J D ShermanAdsorption Gas Separation Kirk-Othmer Encyclopedia of Chemical Technology 2004
[3] D Aaron and C Tsouris ldquoSeparation of CO2from flue gas a
reviewrdquo Separation Science and Technology vol 40 no 1ndash3 pp321ndash348 2005
[4] F I Khan and A K Ghoshal ldquoRemoval of Volatile OrganicCompounds from polluted airrdquo Journal of Loss Prevention in theProcess Industries vol 13 no 6 pp 527ndash545 2000
[5] M A Kalbassi R J Allam and T C Golden ldquoTemperatureswing adsorptionrdquo US Patent no 5846295 US Patent andTrademark Office Washington DC USA 1998
[6] C W Skarstrom ldquoMethod and apparatus for fractionatingrdquoUS Patent no 2944627 US Patent and Trademark OfficeWashington DC USA 1970
[7] A Kapoor and R T Yang ldquoKinetic separation of methanemdashcarbon dioxide mixture by adsorption on molecular sievecarbonrdquo Chemical Engineering Science vol 44 no 8 pp 1723ndash1733 1989
[8] A M Mendes C A Costa and A E Rodrigues ldquoOxygenseparation from air by PSA modelling and experimental
results part Irdquo Separation and Purification Technology vol 24no 1-2 pp 173ndash188 2001
[9] S Farooq D M Ruthven and H A Boniface ldquoNumerical sim-ulation of a pressure swing adsorption oxygen unitrdquo ChemicalEngineering Science vol 44 no 12 pp 2809ndash2816 1989
[10] J C Kayser and K S Knaebel ldquoPressure swing adsorptiondevelopment of an equilibrium theory for binary gas mixtureswith nonlinear isothermsrdquo Chemical Engineering Science vol44 no 1 pp 1ndash8 1989
[11] S Sridhar B Smitha and T M Aminabhavi ldquoSeparation ofcarbon dioxide from natural gas mixtures through polymericmembranesmdasha reviewrdquo Separation amp Purification Reviews vol36 no 2 pp 113ndash174 2007
[12] H S Pierre Simulation of dynamic pressure-swing gas sorptionin polymers [PhD Dissertation] 2005
[13] S Li J G Martinek J L Falconer R D Noble and T QGardner ldquoHigh-pressure CO
2CH4separation using SAPO-34
membranesrdquo Industrial amp Engineering Chemistry Research vol44 no 9 pp 3220ndash3228 2005
[14] H Hachisuka T Ohara and K Ikeda ldquoNew type asymmetricmembranes having almost defect free hyper-thin skin layer andsponge-like porous matrixrdquo Journal of Membrane Science vol116 no 2 pp 265ndash272 1996
[15] M R Coleman and W J Koros ldquoIsometric polyimides basedon fluorinated dianhydrides and diamines for gas separationapplicationsrdquo Journal of Membrane Science vol 50 no 3 pp285ndash297 1990
[16] M K Ghosh and K L Mittal Polyimides Fundamentals andApplications vol 36 CRC Press New York NY USA 1996
[17] T H Kim W J Koros and G R Husk ldquoTemperature effectson gas permselection properties in hexafluoro aromatic poly-imidesrdquo Journal of Membrane Science vol 46 no 1 pp 43ndash561989
[18] B Xing and J J Pignatello ldquoDual-mode sorption of low-polaritycompounds in glassy poly (vinyl chloride) and soil organicmatterrdquo Environmental Science amp Technology vol 31 no 3 pp792ndash799 1997
[19] RM Barrer ldquoDiffusivities in glassy polymers for the dualmodesorption modelrdquo Journal of Membrane Science vol 18 pp 25ndash35 1984
[20] E Glueckauf ldquoThe influence of ionic hydration on activitycoefficients in concentrated electrolyte solutionsrdquo Transactionsof the Faraday Society vol 51 pp 1235ndash1244 1955
[21] T Hirose Y Mi S A Stern and A K S Clair ldquoThe solubilityof carbon dioxide and methane in polyimides at elevatedpressuresrdquo Journal of Polymer Science B Polymer Physics vol29 no 3 pp 341ndash347 1991
