Mathematical Modeling of CO 2 /CH 4 Separation by Hollow Fiber Membrane Module Using Finite Difference Method

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1 Journl of Memrne nd Seprtion Technology, 2012, 1, Mthemticl Modeling of CO 2 /CH 4 Seprtion y Hollow Fier Memrne Module Using Finite Difference Method Ahmd Ari Shmsdi 1, Ali Krgri 2,*, Foroogh Frshdpour 2 nd Seed Lki 2 1 Petroleum University of Technology, Koot Adullh, Ahwz, Irn 2 Memrne Processes Reserch Lortory (MPRL), Deprtment of Petrochemicl Engineering, Amirkir University of Technology (Tehrn Polytechnic), Mhshhr Cmpus, Mhshhr, Irn Astrct: Removl of CO 2 in lndfill gs recovery processes nd frctured wells s well s its ppliction in enhnced oil recovery nd its environmentl spects re of interest. Also seprtion of CO 2 from CH 4 in Ethylene Oxide plnt is n environmentl policy of Mrun Petrochemicl Compny. In the present work, shell-fed hollow fier module ws modeled mthemticlly for CO 2 seprtion from CH 4. Finite difference method ws used for solving the equtions. Comprison etween co-current nd counter-current flow ptterns showed tht for ll conditions, counter current pttern hd etter efficiency for CO 2/CH 4 seprtion. Influence of operting prmeters such s feed pressure, permete pressure, feed flow rte, fier length nd CO 2 concentrtion of feed on seprtion efficiency of CO 2/CH 4 mixture ws investigted. Also the effect of feed nd permete pressures on required memrne re showed tht the memrne re increses y incresing permete pressure nd decreses y incresing feed pressure. The modeling offers vlule dt out fesiility study nd economicl evlution of gs seprtion unit opertion s helpful unit in the industry. Keywords: Hollow fier, modeling, CO 2 /CH 4, operting prmeter, memrne re. 1. INTRODUCTION The focus of much of the new wreness hs turned towrds exmining greenhouse gs emissions nd their impct on glol climte [1]. Cron dioxide which is emitted from fossil fuels, nturl nd refinery off-gses nd mny other sources is representing out 80% of greenhouse gses [2-5]. From the glol environmentl perspective, it is importnt to seprte CO 2 from gs mixtures to vert the thret of glol wrming; therey ttining the cron emission reduction trgets set out y the Kyoto Agreement [2] therefore, recovery of cron dioxide from lrge emission sources is formidle technologicl nd scientific chllenge which hs received considerle ttention for severl yers [1]. Currently, commercilly ville CO 2 seprtion technologies, including pressure swing dsorption, mine sorption, nd cryogenic seprtion re highly energy intensive [6, 7], ut memrne technologies re ecoming more frequently used for seprtion of wide vrying gs mixtures in different industries ecuse of the economic competitiveness of the existing seprtion technologies nd the present chllenges of ggressive environments [8,9]. The ppliction of memrne technology for CO 2 removl from CH 4 for upgrding the nturl gs, lndfill gs nd enhnced oil recovery emerged in the 1980s fter severl mjor *Address corresponding to this uthor t the Memrne Processes Reserch Lortory (MPRL), Deprtment of Petrochemicl Engineering, Amirkir University of Technology (Tehrn Polytechnic), Mhshhr Cmpus, Mhshhr, Irn; Tel/Fx: ; E-mil: li_krgri@yhoo.com E-ISSN: /12 rekthroughs [10-12]. One of the principl revolutions ws the preprtion of high flux symmetric Loe- Sourirjn memrnes with selective lyer thicknesses of less thn 0.1 m [13]. In the lst 40 yers, the symmetric single-lyer hollow fier memrne is lwys fvorle configurtion in the memrne sed gs seprtion systems owing to their lrge surfce re over unit volume, self mechnicl support, good flexiility nd esy scle [14]. Hollow-fier memrnes re the most dvntgeous form of memrnes used in the gs seprtion processes. They cn e produced y ny method employed for the mnufcture of chemicl fiers [15]. Hollow fiers re the chepest on per squre meter sis with the highest memrne re to module volume rtio. They do not require ny support, whether the feed flows inside or outside of the fier tues [16]. A hollow fier module contins lrge numer of memrne fiers housed in shell; its rrngement is similr to countercurrent shell nd tue het exchngers. Feed cn e introduced on either the fier or shell side, ut commonly, pressurized feed gs is fed to the shell side nd the components permete t different rtes to the fier ore. Permete is usully withdrwn in cocurrent or counter-current mnner, with the ltter eing generlly more effective [17]. In co-current mnner, the driving force nd mss trnsfer rte re reduced due to concentrtion reduction of penetrted constituent ut in counter-current mode, except of inlet nd outlet sections, mss trnsfer rte remins constnt [18]. In order to improve the performnce of memrne gs seprtion process, optimiztion (operting nd 2012 Lifescience Glol

2 20 Journl of Memrne nd Seprtion Technology, 2012 Vol. 1, No. 1 Shmsdi et l. design) nd nlysis of the process should e ccomplished. Modeling nd simultion re tools to chieve these ojectives [19]. An pproprite modeling, offers importnt informtion out design, optimiztion, nd the economics of memrne units. The issue of mthemticl modeling of memrne gs seprtors ws first ddressed y Weller& Steiner [20]. In recent yers, simultion of memrne gs seprtion hs ttrcted incresing more ttention nd mny reserchers hve studied modeling of hollow fier memrne for gs seprtion. Boucif et l. [21, 22] derived n lgeric model for inry mixtures, this model ws otined from differentil mss lnce equtions nd these equtions were highly non-liner. They offered numericl solution of oundry vlue prolems encountered in hollow fier inry gs permetors hving co-current or countercurrent permete flow with nd without xil pressure drop inside the fier ore. Chern et l. [23] developed model for simulting the performnce of n isotherml countercurrent hollow-fier gs seprtor for inry mixture. The model equtions were solved numericlly s oundry-vlue prolem. Permete pressure uildup hs een considered explicitly nd concentrtion dependence of the permeilities re tken into ccount y using the dul-mode sorption nd trnsport models. Rutench & Dhm [24] presented n nlyticl solution for inry mixtures in the counter current module. They considered constnt permete pressure long the permete side. Krovvidi et l. [25] derived two models with different ssumptions for inry mixtures in co-current nd counter current module. They ssumed liner (OLM model) or qudrtic (DFM model) reltionship etween the feed composition nd the permete composition long the memrne. The DFM model is implicit model nd more ccurte thn OLM model (explicit model). Kovlli et l. [26] presented liner pproximtion model (LAM) to solve the multi-component countercurrent gs permetor trnsport equtions considering pressure vrition inside the fiers. The models provided very effective nd quick solution to the nonliner coupled differentil equtions using the ssumption of the linerity of feed nd permete side compositions. This ssumption leds to lgeric nlyticl expressions for the prediction of memrne re nd pressure rtios. Coker et l. [27, 28] presented model for multi-component gs mixture in n isotherml nd nonisotherml hollow-fier gs seprtion contctor tht permits rpid solution of the governing differentil mss nd pressure distriution using computtionl scheme tht does not rely on conventionl shooting techniques for numericl integrtion. The model ws developed for countercurrent, co-current nd cross flow ptterns with nd without permetes purging. Kldis et l. [29] presented model for multi-component gs mixture; the equtions were solved y orthogonl colloction to pproximte differentil equtions, nd to solve the resulting system of non-liner lgeric equtions y the Brown method. Zho et l. [30] simulted inry gs seprtion permetor for countercurrent hollow fier memrne modules. A differentil mthemticl model nd n efficient numericl solution procedure sed on orthogonl colloction nd Qusi-Newton method ws developed.peer et l. [31] presented mthemticl model for simultion of gs seprtion in hollow fier memrne modules with ll flow ptterns (cross-flow, counter-current nd co-current). This model cn e used for clcultion of memrne performnce or its required surfce re for specific seprtion. Mdeni et l. [32] modeled counter-current module for inry mixture. They considered s the memrne s unit consisting of mny sections nd derived equtions from mss lnce. Seprtion of CO 2 /CH 4 is the second most investigted gs pir for memrne processes. Most of the industril processes to seprte CO 2 from CH 4 re high-pressure pplictions with totl feed pressures up to 100 rs. Depending on the frction of CO 2 in these feeds, the resulting CO 2 prtil pressures re pproximtely rs [18, 33]. In this pper, seprtion of CO 2 /CH 4 y memrne ws modeled mthemticlly in hollow fier module. Effect of operting prmeters such s feed pressure; permete pressure, feed flow rte, fier length nd CO 2 concentrtion of feed on seprtion efficiency of CO 2 /CH 4 mixtures of Ethylene Oxide plnt of Mrun Petrochemicl Compny ws investigted. This modeling gives vlule informtion out fesile study optimum process nd design condition nd economicl clcultion for this seprtion nd cn e modified for seprtion of other gses from inry gs mixtures. 2. MODELING 2.1. Model Assumptions The following ssumptions were used for simplifiction of the model [31, 32]: 1- Module opertes t stedy stte nd isotherml conditions.

3 Mthemticl Modeling of CO 2/CH 4 Seprtion Journl of Memrne nd Seprtion Technology, 2012 Vol. 1, No Idel gs ehvior is considered. 3- Mss is only trnsferred through selective lyer nd permetion mechnism is solution-diffusion. 4- Pressure drop in feed side is negligile. 5- Gs flow in oth sides is plug flow. 6- Memrne permeility is independent of pressure nd feed composition. 7- No xil mixing occurs due to gses flow. 8- All fiers hve uniform outer nd inner dimeter nd selective lyer thickness is considered constnt. 9- Fiers deformtion under high pressure condition is neglected Model Equtions The permetion of gses through polymeric memrne occurs y comintion of kinetic nd equilirium controlled phenomen [17]. Diffusion of gses from selective lyer cn e descried y Fick s first lw s eqution (1): J i = D i * dc i dl Where D i * is the concentrtion dependent diffusion coefficient of component i in the memrne nd dc i /dl is the concentrtion grdient in the permetion direction inside the memrne. Integrting Eqution (1) under the ssumption of constnt diffusivity nd connecting the concentrtions t the gs/memrne nd memrne/gs interfces y Henry s lw to the ulk gses properties results in Eqution (2) (1) J i = Q i (P F x i P P y i ) (2) Where P F nd P P re feed nd permete pressure side of memrne respectively, nd Q i is the permence. Under the present ssumptions, the permeility does not vry with composition nd operting conditions is therefore constnt. Figure 1 shows schemtic of counter current gs permetion in hollow fier. The mteril lnce for component i in hollowfier module is presented s Eqution (3) ±d[lx i ] = d[vy i ] = Q i da(p F x i P P y i ) (3) For hollow fier: da = N F D LM dz (4) The Hgen-Poiseuille reltion [34] ws used to clculte pressure drop for permete side s Eqution (5) dp P dz = 128μQ N F D i 4 Due to gs idel ehvior: Q = TVR g P P (6) By introducing the dimensionless vriles s: z * = z l E ; L * = L F 0 ; V * = V F 0 ; = P P P F ; i = Q i Q n (7) K 1 = D LM l E N F P F P G n (8) F 0 (5) Figure 1: Schemtic of counter current permetion into hollow fier memrne.

4 22 Journl of Memrne nd Seprtion Technology, 2012 Vol. 1, No. 1 Shmsdi et l. Figure 2:, - Co-current nd countercurrent pttern in hollow fier modules, respectively. K 2 = 128μTR g l E F 0 N F D i 4 P F 2 By introducing of these vriles in to Equtions 3 nd 5, governing equtions for co-current nd countercurrent shell-fed hollow fier module ws otined. Figure 2, present co-current nd countercurrent pttern in hollow fier modules, respectively. Tles 1, 2 present the governing differentil equtions for co-current nd counter-current shell-fed hollow fier module for the present system, respectively. Tle 1: Governing Equtions for Co-Current Shell-Fed Hollow Fier Module for Two Component System [35] dx (1 x)(x y) x[(1 x) (1 y)] = K dz * 1 (1 V * ) dy = K dz * 1 (10) [ (1 y)(x y) y[(1 x) (1 y)] V * (11) dv * dz * = K 1 [ (x y) + (1 x) (1 y)] (12) d dz * = K V * 2 (13) Boundry conditions: t z * = 0 V * = 0, x = x F nd y = (x, ) (14) t z * = 1 = ( 0,V * ) (15) 2.3. Solution Method For oth flow ptterns, the model equtions re represented y set of coupled nonliner oundry (9) vlue prolem differentil equtions. Finite difference method ws used [36]. Shooting method ws employed for co-current pttern ut for counter current flow, the resulting set of equtions for y i cn e represented in mtrix nottion s Eqution (22) Tle 2: Governing Differentil Equtions for Counter- Current Shell-Fed Hollow Fier Module for Two Component System [35] dx (1 x)(x y) x[(1 x) (1 y)] = K dz * 1 (1 V * ) dx = K dz * 1 (16) [ (1 x)(x y) y[(1 x) (1 y)] V * (17) dv * dz * = dl * dz * = K 1 [ (x y) + (1 x) (1 y)] (18) d dz * = K V * 2 (19) Boundry conditions: t z * = 0 V * = 0 nd y = (x, ) (20) t z * = 1 L * = 1, x = x F nd = ( 0,V * ) (21) A i y i = i (22) Where, A i is the mtrix of constnts nd the oundry conditions were ppered s oundry elements in i mtrix. The mtrix expression ws written for ech of the dependent vriles involved in the set of differentil equtions. The solution of the mtrix equtions ws strted with n estimte of ll the dependent vriles t ll the grid points. The successive itertions were proceeded till convergence chieved. Figure 3, show flowchrt of equtions

5 Mthemticl Modeling of CO 2/CH 4 Seprtion Journl of Memrne nd Seprtion Technology, 2012 Vol. 1, No Figure 3:, - Flowchrt of equtions solution for co-current nd counter-current flow pttern, respectively. solution for co-current nd counter-current flow pttern, respectively. 3. RESULTS AND DISCUSSIONS The mthemticl model ws pplied for CO 2 /CH 4 seprtion in shell-fed hollow fier module with cocurrent nd counter-current flow ptterns. The selected mteril for the memrne is polyimide nd the experimentl vlues for the permeilities re tken from Ngel et l. [37]. Operting conditions nd module prmeters hve een presented in Tle 3. The concentrtions of ech component in permete nd retentte strems depend on design nd operting conditions. Feed flow rte, feed temperture, feed nd permete pressure hve een denoted to the operting condition nd memrne re ws considered s the design trget. Feed enters in shell nd permete flows in fiers. In fiers; CO 2 diffuses fster thn CH 4 in order to higher permeility, therefore long the module CO 2 Tle 3: Bsic Operting Conditions nd Modeling Prmeters for the Present Study Prmeter Vlue Unit T 308 K P F 35*10 5 P P P P Q CO *10-13 mol/(p.s.m 2 ) Q CH *10-13 mol/(p.s.m 2 ) F 0 50 mol/s l E 2 m N F 3* D i 125*10-10 m D o 250*10-10 m

6 24 Journl of Memrne nd Seprtion Technology, 2012 Vol. 1, No. 1 Shmsdi et l. Figure 4: - CO 2 concentrtion profile long the module for (50%-50%) mixture t 35 rs nd 308 K. - CH 4 concentrtion profile long the module for (50%-50%) mixture t 35 rs nd 308 K. concentrtion in shell side flls nd CH 4 concentrtion increse grdully. Figures 4, 4 show the concentrtion profile long the module Effect of Feed Pressure Figure 5 represents the influence of feed pressure on CO 2 concentrtion profile in retentte strem with for co-current nd counter- current flow ptterns. CO 2 concentrtion decreses y incresing feed pressure for oth flow ptterns ut CO 2 concentrtion rte for cocurrent is slightly higher thn counter-current. At higher feed pressure; the driving force for mss trnsfer increses nd, therefore, the CO 2 purity of the permete is enhnced. Incresing feed pressure results in more CO 2 pssge through memrne nd therefore less CO 2 in retentte strem. By incresing feed pressure, CH 4 pssge through memrne is lso incresed ut less thn CO 2, Figure 5: - CO 2 concentrtion profile in retentte strem with feed pressure in co-current nd counter- current flow ptterns for (50%-50%) mixture t 308 K. - CH 4 concentrtion profile in retentte strem with feed pressure in co-current nd counter- current flow ptterns for (50%- 50%) mixture t 308 K.

7 Mthemticl Modeling of CO 2/CH 4 Seprtion Journl of Memrne nd Seprtion Technology, 2012 Vol. 1, No Figure 6: - Influence of feed flow rte on CO 2 concentrtions in retentte for co-current nd counter-current flow ptterns for (50%-50%) mixture t 35 rs nd 308 K. - Influence of feed flow rte on CH 4 concentrtions in retentte for co-current nd counter-current flow ptterns for (50%- 50%) mixture t 35 rs nd 308 K. therefore CH 4 concentrtion in retentte will e incresed (Figure 5) Effect of Feed Flow Rte The influence of feed flow rte on CO 2 nd CH 4 permetion for co-current nd counter-current flow ptterns hve een shown in Figures 6 nd 6. By incresing feed flow, the frction of CO 2 removed from the feed decreses, consistent with the shorter contct time of the high-pressure residue gs with the ctive memrne re t higher feed flow rtes, therefore the concentrtion of CO 2 in retentte will e incresed Effect of Permete Pressure Permete pressure is key prmeter for memrne unit design. The CH 4 nd CO 2 concentrtion profile in retentte for co-current nd Figure 7: - CO 2 concentrtion profile in retentte for co-current nd counter-current flow ptterns s function of permete pressure for (50%-50%) mixture t 35 rs nd 308 K. - CH 4 concentrtion profile in retentte for co-current nd counter-current flow ptterns s function of permete pressure for (50%-50%) mixture t 35 rs nd 308 K.

8 26 Journl of Memrne nd Seprtion Technology, 2012 Vol. 1, No. 1 Shmsdi et l. Figure 8: - Influence of CO 2 concentrtion in feed on CO 2 concentrtions in retentte for co-current nd counter-current flow ptterns t 35 rs nd 308 K. - Influence of CO 2 concentrtion in feed on CH 4 concentrtions in retentte for co-current nd counter-current flow ptterns t 35 rs nd 308 K. counter-current flow ptterns s function of permete pressure hve een depicted in Figures 7 nd 7. The results showed the permete pressure hs considerle effect on CO 2 concentrtion in the retentte due to driving force reduction for oth flow ptterns, ut the co-current pttern is more sensitive thn counter-current. By incresing pressure, CO 2 pssge through the memrne will e decresed. Opposite ehvior ws oserved for CH 4 concentrtion profiles in retentte strem for co-current nd countercurrent ptterns Effect of CO 2 Concentrtion in Feed The most importnt prmeter in memrne process design is concentrtion of impurities in feed. Required memrne re nd the numer of modules Figure 9: - Effect of fier s length on CO 2 concentrtion profiles in retentte strem for co current nd counter current flow ptterns for (50%-50%) mixture t 35 rs nd 308 K. - Effect of fier s length on CH 4 concentrtion profiles in retentte strem for co current nd counter current flow ptterns for (50%-50%) mixture t 35 rs nd 308 K.

9 Mthemticl Modeling of CO 2/CH 4 Seprtion Journl of Memrne nd Seprtion Technology, 2012 Vol. 1, No depend on the impurities in feed. In CO 2 /CH 4 seprtion, s feed CO 2 concentrtion increses, the mount of gs tht cn e diffused decreses ecuse more CO 2 must e removed from the feed gs with fixed mount of memrne re. Figures 8, 8 represent the influence of CO 2 concentrtion in feed on CO 2 nd CH 4 concentrtions in retentte for oth cocurrent nd counter-current ptterns, respectively Effect of Fier s Length By incresing fier s length, memrne re rises. This rrngement will prepre higher memrne re nd leds to higher permetion of gses. More permetion of CO 2 mkes higher concentrtion of CO 2 compred with CH 4 in permete strem, therefore y incresing fier s length while the numer of fiers re constnt, CO 2 concentrtion in permete strem will e rised. Figures 9 nd 9 indicte the effect of fier s length on CO 2 nd CH 4 concentrtion profiles in retentte strem for co-current nd counter- current flow ptterns, respectively Effect of Feed nd Permete Pressures on Memrne Are Memrne re is considered s the most importnt design vrile for economicl evlution. Incresing memrne re cn rise cpitl cost; therefore optimum condition should e determined. Pressure chnging of feed nd permete chnge the memrne re for specil permete purity. Figure 10 indictes the influence of permete nd feed pressures on memrne re for 98% purity of methne in permete strem in counter current flow pttern. Results show the required memrne re is rised y incresing permete pressure nd declined y incresing feed pressure. Also it is ovious tht required memrne re increses shrply for low pressure feeds nd high pressure permetes. 4. CONCLUSION A shell-fed co-current nd counter-current hollow fier module ws modeled mthemticlly for CO 2 seprtion from CH 4 in Ethylene Oxide plnt of Mrun Petrochemicl Compny s n environmentl policy. This model is vlid to predict specifictions of retentte nd permete strems t vrious conditions. Comprison of co-current nd counter-current flow ptterns showed such s the other unit opertions, the counter current pttern hd etter efficiency for CO 2 /CH 4 seprtion for ll conditions. It ws found tht feed flow rte, feed pressure nd module fier length hd direct effect nd permete pressure hd dverse effect on CH 4 purity in the retentte for oth flow ptterns. Also required memrne re incresed y incresing permetes pressure nd decresed y incresing feed pressure. Becuse of hving no dt out fixed properties of used memrne nd chnging memrne ehvior with temperture, study of these prmeters on seprtion fctor were impossile. Appliction of memrne with much informtion out memrne properties nd performnce is suggested. Modeling of CO 2 seprtion from ternry nd multi-component gs mixture nd comprison of finite difference method with other solving methods such s orthogonl colloction re future directions of this work. 5. NOMENCLATURES A = memrne re, [m 2 ] A i = see eqution 22, [-] i = see eqution 22, [-] C i = concentrtion of component i, [mol/m 3 ] D i * D i = diffusion coefficient for component i, [m 2 /s] = inner dimeter of fier, [m] Figure 10: Influence of permete nd feed pressures on memrne re for 98% purity of methne in permete strem in counter current flow pttern t 308 K. D LM = log men dimeter of fier, [m] D o = outer dimeter of fier, [m]

10 28 Journl of Memrne nd Seprtion Technology, 2012 Vol. 1, No. 1 Shmsdi et l. F 0 J i = feed flow rte, [mol/s] = diffusion of component i, [mol/ (m 2.s)] K 1 = constnt see eqution 8, [-] K 2 = constnt see eqution 9, [-] L * = dimensionless form of retentte flow rte, [-] L l E = retente flow rte, [mol/s] = effective length of fier in module, [m] N F = numer of fiers, [-] P F = feed pressure, [P] P n G = Permeility of component n, [mol/ (m.p.s)] P P = permete pressure, [P] Q Q i = Volumetric flow rte in permete side, [m 3 /s] = Permence of component i, [mol/ (m 2.P.s)] R g = Universl gs constnt, [P.m 3 / (mol.k)] T = Temperture, [K] V * = dimensionless form of permete flow rte, [-] V = permete flow rte, [mol/s] x = mole frction of fst gs in shell side, [-] x F = mole frction in feed,[-] y = mole frction of fst gs in tue side, [-] z * z = dimensionless form of diffusion direction,[-] = diffusion direction,[m] Greek Letters i = selectivity for component i, [-] = permete pressure to feed pressure rtio, [-] = gs mixture viscosity, [P/s] = see eqution 15, 21, [-] REFERENCE [1] Ympolskii Y, Freemn BD. Memrne gs seprtion. John Wiley &Sons, New York [2] Sohri MR, Mrjni A, Mord, S, Dvllo M, Shirzin, S. Mthemticl modeling nd numericl simultion of CO 2 trnsport through hollow-fier memrnes. Appl Mth Modeling 2011; 35: [3] Al-Mrzouqi MH, El-Ns MH, Mrzouk SAM, et l. Modeling of CO 2 sorption in memrne contctors. Sep Purif Tech 2008; 59: [4] Khoo HH, Tn RBH. Life cycle investigtion of CO 2 recovery nd sequestrtion. Environ Sci Tech 2006; 40: [5] Ji P, Co Y, Zho H, et l. Preprtion of hollow fier poly (N, N-dimethylminoethyl methcrylte) poly (ethylene glycol methyl ether methyl crylte)/polysulfones composite memrnes for CO 2/N 2 seprtion. J Memrne Sci 2009; 342: [6] Bsu S, Cno-Oden A, Vnkelecom IFJ. Asymmetric memrne sed on Mtrimid nd polysulphone lends for enhnced permence nd stility in inry gs (CO 2/CH 4) mixture seprtions. Sep Purif Tech 2010; 75: [7] Bsu S, Khn A, Cno-Oden A, Liu C, Vnkelecom IFJ. Memrne sed technologies for iogs seprtions. Chem Soci Rev 2010; 39: [8] Tkht Rvnchi M, Kghzchi T, Krgri A. Appliction of memrne seprtion processes in petrochemicl industry: review. Deslintion 2009; 235(1-3): [9] Vu DQ, Koros WJ, Miller SJ. Mixed mtrix memrnes using cron moleculr sieves I. Preprtion nd experimentl results. J Memrne Sci 2003; 211: [10] Sneepur H, Edi Amooghin A, Moghdssi AR, et l. CO 2/CH 4 Seprtion vi Polymeric Blend Memrne. Irnin J Polym Sci Tech 2010; 23(1): [11] Edi Amooghin A, Sneepur H, Moghdssi AR, et l. Modifiction of ABS Memrne y PEG for Cpturing Cron Dioxide from CO 2/N 2 Strems. Sep Sci Tech 2010; 45(10): [12] Studt-Bickel C, Koros WJ. Improvement of CO 2/CH 4 seprtion chrcteristics of polyimides y chemicl crosslinking. J Memrne Sci 1999; 155: [13] Xio Y, Low BT, Hosseini SS, Chung TS, Pul DR. The strtegies of moleculr rchitecture nd modifiction of polyimide-sed memrnes for CO 2 removl from nturl gs A review. Prog Polym Sci 2009; 34: [14] Li Y, Chung TS, Xio Y. Superior gs seprtion performnce of dul-lyer hollow fier memrnes with n ultrthin dense-selective lyer. J Memrne Sci 2008; 325: [15] Soni V, Aildskov J, Jonsson G, Gni R. A generl model for memrne-sed seprtion processes. Comput Chem Eng 2009; 33: [16] Antonson CR, Grdner RJ, King CF, Ko DY. Anlysis of gs seprtion y permetion in hollow fiers. Ind Eng Chem Process Design nd Development 1977; 16(4): [17] Tessendorf S, Gni R, Michelsen ML. Modeling, simultion nd optimiztion of memrne-sed gs seprtion systems. Chem Eng Sci 1999; 54:

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