CFD Simulation of Dense Gas Extraction through Polymeric Membranes

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1 World Academy of Scence, Engneerng and Technology CF Smulaton of ense Gas Extracton through Polymerc Membranes Azam Marjan*, Saeed Shrazan Abstract In ths study s presented a general methodology to predct the performance of a contnuous near-crtcal flud extracton process to remove compounds from aqueous solutons usng hollow fber membrane contactors. A comprehensve mathematcal model was developed to study Porocrtcal extracton process. The system studed n ths work s a membrane based extractor of ethanol and acetone from aqueous solutons usng near-crtcal CO. Predctons of extracton percentages obtaned by smulatons have been compared to the expermental values reported by Bothun et al. [5]. Smulatons of extracton percentage of ethanol and acetone show an average dfference of 9.3% and 6.5% wth the expermental data, respectvely. More accurate predctons of the extracton of acetone could be explaned by a better estmaton of the transport propertes n the aqueous phase that controls the extracton of ths solute. Keywords Solvent extracton, Membrane, Mass transfer, ense gas, Modelng I. INTROUCTION HEN a compound s subjected to temperatures and Wpressures hgher than the crtcal values, t s defned as a supercrtcal flud (SCF). Under these condtons the SCF shows very nterestng transport and surface propertes as well as a hgh solublzng capacty due to the transton between gas and lqud phases and ts hgh densty. The most popular compound used as SCF s carbon doxde (CO ) because t s nexpensve, non-toxc and nert. Moreover, CO has a relatvely low crtcal pont (7.38MPa, K), whch nvolves many nterestng applcatons as alternatve solvent, reacton medum or adjuvant to reduce the vscosty of the medum. In spte of the progress reached n materals technology and membrane processes, few operatons couplng SCF and membrane technologes have been proposed n the lterature [1-4]. PoroCrt process or Porocrtcal extracton s a commercal SFE whch uses a hollow fber membrane contactor (HFMC) [3]. In ths process a macroporous membrane allows contact between two phases. An aqueous lqud soluton s crculated on one sde and on the other sde the extracton solvent s a near-crtcal or SCF. When the membrane used s hydrophobc, the aqueous soluton does not penetrate nto the membrane pores. A menscus s formed at the mouth of the pores stablzng a dense gas lqud nterface. The chemcal potental gradent that generates a mass transfer through the membrane s a concentraton gradent between the two phases. In ths process the membrane does not play a determnant role as a selectve barrer, and the selectvty s determned manly by the vapor lqud equlbrum between both phases. Fg. 1 shows schematcally the prncple of ths process. In a typcal confguraton, hollow fber macroporous polypropylene membranes wth a mean pore dameter of 0. μm are used [4]. Ths process has several advantages compared to conventonal contactor devces used n solvent and SCF extracton, lke conventonal contactng columns whch dsperse one flud phase n another. Hgh throughput capacty wthout column floodng or emulson formaton, ndependence from solvent and feed densty dfferences, and desgn modularty can be mentoned among ts most mportant advantages. The reduced complexty of the process and ts comparatve low cost allow a wder ndustral use of CO as a non-toxc and envronmentally bengn extracton solvent. Furthermore, the most nterestng characterstc of ths process s the use of an HFMC. Ths module geometry s usually 100 tmes more effcent on a volumetrc bass (m /m 3 ) than a conventonal contactor [4-8]. II. MOEL EVELOPMENTS The mass transfer model was valdated by comparng results of extracton percentages of ethanol and acetone from aqueous solutons obtaned from smulatons wth expermental data reported by Bothun et al. [5]. In the experments, an HFMC has been used wth near-crtcal and SC CO as extracton solvent. Fg. shows a dagram of the expermental devce. The system conssts of a sngle hollow fber housed n stanless steel tubng. The lqud feed (aqueous soluton) crculates nsde the fber and the extracton flud (near-crtcal and SC CO ) crculates n countercurrent flow outsde the fber. The solute s recovered by expanson through a valve from the extractng stream. The raffnate s collected for analyss. The raffnate recever also works as an equalzng vessel connected wth the extracton gas current n order to mantan the same pressure nsde and outsde the fber and therefore ensure the stablzaton of the nterface wthn the membrane porosty. In ths way, an equalty condton for pressures and temperatures has been consdered n calculatons. Operatng condtons, structural parameters of the membrane, and confguraton characterstcs consdered n smulatons are reported n Table1. epartment of Chemstry, Arak Branch, Islamc Azad Unversty-Arak-Iran (a-marjan@au-arak.ac.r) 1043

2 World Academy of Scence, Engneerng and Technology TABLE I OPERATIONAL CONITIONS CONSIERE IN THE SIMULATIONS OF POROCRITICAL EXTRACTION [5] Fg. 1. Prncple of mass transfer n porocrtcal extracton [8]. Operatng condtons used n the experments Pressure (MPa) 6.9 Temperature (K) 98 Lqud feed concentraton (%w/w) 10 Solutes (aqueous solutons) Ethanol & acetone Lqud feed (aqueous soluton), F (ml mn 1 ) Molar flow rato, S/F 3 Structural parameters of the hollow fber membrane contactor Materal (characterstc) Polypropylene (hydrophobc) Number of fbers, n 1 Fber length, L (m) Porosty, ε (%) 75 Mean pore dameter, (μm) 0.4 Fber I, (mm) 0.6 Fber O, (mm) 1.0 Shell I, (mm) 1.5 Shell O, (mm) 3.18 Fg. 3. Model doman Fg.. Expermental devce used n experments [5, 8]. The contnuty equatons for three subdomans of contactor were obtaned and solved to predct the concentratons of lqud phase along the contactor. The model s developed for a hollow fber, as shown n Fg. 3, through whch the lqud flows wth a fully developed lamnar parabolc velocty profle. The fber s surrounded by a lamnar gas flow n an opposte drecton. Therefore, the membrane contactor conssts of three sectons: tube sde, membrane, and shell sde. The steady state two-dmensonal materal balances are carred out for all three sectons. The gas mxture s fed to the shell sde (at z = L), whle the lqud phase s passed through the tube sde (at z = 0). The used assumptons were: (1) steady state and sothermal condtons; () fully developed parabolc lqud velocty profle n the hollow fber; (3) the Henry s law s applcable for gas-lqud nterface; (4) The aqueous feed phase and the dense extracton gas are consdered mmscble; (5) The transton lmt between lamnar and turbulent regmes on the shell sde was consdered between 100 and 4000 for Reynolds number. We now apply the contnuty equatons for three subdomans of contactor. III. SHELL SIE The contnuty equaton for each speces n a reactve system can be expressed as [6]: C t = ( C V ) ( J ) R (1) 1044

3 World Academy of Scence, Engneerng and Technology where C, J, R V and t are the concentraton, dffusve, flux, reacton rate of speces, velocty and tme, respectvely. Ether Fck s law of dffuson or Maxwell Stefan theory can be used for the determnaton of dffusve fluxes of speces. The contnuty equaton for steady state for solute n the shell sde of contactor for cylndrcal coordnate s obtaned usng Fck s law of dffuson for the estmaton of the dffusve flux: V shell z shell C shell 1 C shell C shell = r r r C shell We use Happel s model [7] to characterze the out fbers velocty profle. The lamnar parabolc velocty profle n the outsde fbers s: r Vz shell= u 1 r3 (3) ( r/ r3) ( r / r3) ln( r / r) 4 3 ( r / r ) 4( r / r ) 4ln( r / r ) where u, r3, r represent the average velocty, radus of free surface (Fg. 3) and fber outer radus, respectvely. Boundary condtons for shell sde are gven as: at z = L, C -shell = C -nlet = 0 (4) C at r = r 3, shell = 0 (nsulaton) (5) r at r = r, C -shell = C -membrane (6) IV. MEMBRANE The steady-state contnuty equaton for the transport of solute nsde the membrane, whch s consdered to be due to dffuson alone, may be wrtten as: membrane C membrane 1 C membrane r r r = 0 C membrane Boundary condtons are gven as: () (7) at r = r, C -membrane = C -shell (8) at r = r 1, C -membrane = C -tube m (9) where m s the partton coeffcent of solute n the SCF. V. TUBE SIE The steady-state contnuty equaton for the transport of solute n the tube sde may be wrtten as: V tube z tube C tube 1 C tube C tube = r r r C tube (10) The velocty dstrbuton n the tube s assumed to follow Newtonan lamnar flow [6]: r V Z tube = u 1 (11) r1 where u s average velocty n the tube sde. Boundary condtons: at z = 0, C -tube = C -nlet (1) at r = r 1, C -tube = C -membrane /m (13) C tube at r = 0, = 0 (symmetry) (14) r The dmensonless model equatons related to tube, membrane and shell sde wth the approprate boundary condtons were solved usng COMSOL software, whch uses fnte element method (FEM) for numercal solutons of dfferental equatons. The fnte element analyss s combned wth adaptve meshng and error control usng a verty of numercal solvers such as ASPK. Ths solver s an mplct tme-steppng scheme, whch s well suted for solvng stff and non-stff non-lnear boundary value problems. VI. RESULTS AN ISCUSSION A. Valdaton of the mass transfer model The extracton percentage of solute can be calculated from the equaton below: ( ν C) nlet ( ν C) Outlet % removal = ( ν C) nlet (15) C outlet = Cnlet where ν and C are the volumetrc flow rate and concentraton, respectvely. C outlet s calculated by ntegratng the local concentraton at outlet of tube sde (z=l): C outlet = Z = L C ( r) da Z = L da (16) The change n volumetrc flow rate s assumed to be neglgble and thus extracton percentage can be approxmated by eq. (15). Calculatons of the extracton percentage (defned by Eq. (15)) usng the smulaton developed n ths study were 1045

4 World Academy of Scence, Engneerng and Technology compared wth the expermental data reported by Bothun et al. [5]. Fgures 4 and 5 show the calculated and expermental extracton percentage as a functon of the lqud feed flow (F). Comparng the extracton percentage estmated for ethanol and acetone, better accuracy s found n the predctons for acetone separaton. Ths could be accounted for consderng two aspects: better predcton of transport propertes (vscosty, dffuson coeffcent) n the hydrodynamc characterzaton, and correct estmaton of the vapor lqud equlbrum n the ternary acetone CO water system. For both systems studed greater accuracy of the model was obtaned at lower values of the lqud feed flow (F ), and for dense gas extracton flow (S), snce the S/F rato remans constant (S/F = 3) for most of the expermental measurements [8]. Extracton percentage (% ) Smulaton 50 Expermental Lqud feed flow (ml/mn) Extracton percentage (% ) Smulaton Expermental Lqud feed flow (ml/mn) Fg. 4. Extracton percentage values of ethanol from aqueous solutons (10%w/w) obtaned from experments (Bothun et al., 003) and smulaton (ths work). Molar flow rato s S/F = 3, P = 6.9MPa, T = 98K. The predctng capacty of the model s mproved consderng a lamnar crculaton regme n the shell sde. From fgures 4 and 5 we can observe the most mportant dscrepancy between expermental and calculated extracton percentages when the lqud flow ncreases. Ths dscrepancy should be attrbuted to the fact that the flud s probably not n lamnar regme, but n transton. Ths decrease n the predctve capacty of the model explaned by changes n the hydrodynamc condtons n the shell sde can explan the evoluton of the extracton percentage of ethanol as a functon of the flow seen n fgure 4. On the other hand, smulatons carred out modfyng the mass transfer mechansm n the membrane porosty are presented n fgures 4 and 5. Smulatons of extracton percentage of ethanol and acetone show an average dfference of 9.3% and 6.5% wth the expermental data, respectvely. B. Hydrophobcty/hydrophlcty of the membrane The effect of the membrane hydrophobcty on the mass transfer of the Porocrtcal process was studed usng the smulaton model developed n ths work. Fg. 5. Extracton percentage values of acetone from aqueous solutons (10%w/w) obtaned from experments (Bothun et al., 003) and smulaton (ths work). Molar flow rato s S/F = 3, P = 6.9MPa, T = 98K. A hydrophobc membrane allows stablzng the gas lqud nterface at the pore entrance and the aqueous soluton cannot wet the porosty. In ths case, membrane porosty s flled wth extracton gas. For a hydrophlc membrane, the porosty s flled wth the aqueous phase and the mass transfer n the pores would be descrbed by molecular dffuson of ethanol or acetone n lqud medum. Fgs. 6 presents calculated extracton percentages of ethanol. These values were obtaned by smulaton consderng a completely hydrophobc or hydrophlc membrane when the aqueous soluton s crculated n the lumen sde. Results obtaned by smulaton show that the hydrophobcty of the membrane ncreases extracton percentage of solute. Extracton percentage (% ) hydrophlc hydrophobc Lqud feed flow (ml/mn) Fg. 6. Estmaton of the extracton percentages of ethanol from an aqueous soluton (10%w/w) as a functon of the lqud feed (F) for a hydrophobc and a hydrophlc membrane when the molar flow rato s S/F = 4, P = 6.9MPa, T = 98K. VII. CONCLUSIONS A mathematcal model was developed to study the Porocrtcal extracton n hollow fber membrane contactors. 1046

5 World Academy of Scence, Engneerng and Technology The model predcts the steady state lqud feed concentraton n the contactor by solvng the conservaton equatons. The model was developed for non-wettng condtons, takng nto consderaton axal and radal dffuson n the tube, membrane and shell sdes of the contactor. The model was then valdated usng expermental data reported by Bothun et al. [5] for extracton of ethanol and acetone from aqueous solutons. The smulatons results ndcated that the extracton percentage of lqud feed ncreased wth decreasng lqud velocty n the tube sde. REFERENCES [1] M. Sms, Porocrtcal flud extracton from lquds usng nearcrtcal fluds. Membrane Technology 97 (1998), [] G. Afrane, E.H. Chmowtz, Expermental nvestgaton of a new supercrtcal flud-norganc membrane separaton process. Journal of Membrane Scence 116 (1996), [3] M. Sms, E. McGovern, J.R. Robnson, Porocrtcal flud extracton applcaton: contnuous plot extracton of natural products from lquds wth near crtcal fluds. Proceedng of the Ffth Meetng on Supercrtcal Fluds, Materals and Natural Processng, Nce, France, March (1998). [4] M. Budch, G. Brunner, Supercrtcal flud extracton of ethanol from aqueous solutons. Journal of Supercrtcal Fluds 5 (003), [5] G. Bothun, B. Knutson, H. Strobel, S. Nokes, E. Brgnole, S. az, Compressed solvents for the extracton of fermentaton products wthn a hollow fber membrane contactor. Journal of Supercrtcal Fluds 5 (003), [6] R.B. Brd, W.E. Stewart, E.N. Lghtfoot, Transport Phenomena, JohnWley & Sons, [7] J. Happel, Vscous flow relatve to arrays of cylnders, AIChE J. 5 (1959) [8] Estay, H.; Bocquet, S.; Romeroa, J.; Sanchez, J.; Ros, G. M.; Valenzuela, F. Modelng and smulaton of mass transfer n near-crtcal extracton usng a hollow fber membrane contactor. Chem. Eng. Sc. 007, 6,