A Comprehensive Model f o r Catalytic Membrane Reactor

Transcription

1 INTERNATIONAL JOURNAL OF CHEMICAL REACTOR ENGINEERING V o l u m e Article A5 A Comprehensive Model f o r Catalytic Membrane Reactor Shashi Kumar Sukrit Shankar Pushan R. Shah Surendra Kumar Indian Institute of T e c h n o l o g y Roorkee, Roorkee, U.A., India, sashifch@iitr.ernet.in Jaypee Institute of InformationTechnology Noida (Deemed University) U.P., India, helvectica883@yahoo.com Indian Institute of T e c h n o l o g y Roorkee, Roorkee, U.A., India, pushan shah@yahoo.com Indian Institute of T e c h n o l o g y Roorkee, Roorkee, U.A., India, skumar@iitr.ernet.in ISSN Download Date /3/3 3:06 PM

2 A Comprehensive Model for Catalytic Membrane Reactor Shashi Kumar, Sukrit Shankar, Pushan R. Shah, and Surendra Kumar Abstract Catalytic membrane reactors are multifunctional reactors, which provide improved performance over conventional reactors. These are used mainly for conducting hydrogenation/ dehydrogenation reactions, and synthesis of oxyorganic compounds by using inorganic membranes. In this paper, comprehensive model has been developed for a tubular membrane reactor, which is applicable to Pd or Pd alloys membrane, porous inorganic membranes. The model accounts for the reaction on either side, tube or shell, isothermal and adiabatic conditions, reactive and non reactive sweep gas, multicomponent diffusion through gas films on both sides of membrane, and pressure variations. Equations governing the diffusion of gaseous components through stagnant gas film, and membranes have been identified and described. The model has been validated with the experimental results available in literature. By using the developed model catalytic dehydrogenation of ethylbenzene to produce styrene in a tubular membrane reactor have been simulated. Four catalysts available for this reaction have been evaluated for their performance. It is our view that the model may be used to develop general purpose software for the analysis and design of tubular catalytic membrane reactors through numerical simulation. KEYWORDS: catalytic membrane reactor, dehydrogenation reaction, reactor modeling, permeation, porous inorganic membrane Download Date /3/3 3:06 PM

3 Kumar et al.: Model for Catalytic Membrane Reactor. INTRODUCTION In the last two decades, the demand for higher conversion, and better yield and selectivities of the desired reaction products with energy saving considerations has led to new, ingenious configuration and design of chemical reactors. In this regard, multifunctional reactors where reactions combined with separation, have received much attention in both academic and industrial research. Membrane reactors are such type of multifunctional reactors and these are currently being applied to many chemical reactions worldwide. The most widely used perspective of membrane reactor is the removal of a product to change the existing thermodynamic limits on the yield of desired product and thereby to drive the equilibrium limited reactions towards completion. Besides, other potential advantages of membrane reactors are: fewer side reactions, expanded allowable range of temperature and pressure for a reaction (Armor, 989), increased residence time for a given volume of the reactor (Armor, 995) and more efficient purification. The applications of membrane reactor are mainly focused on the reaction systems containing hydrogen (e.g. dehydrogenation /hydrogenation reactions) or oxygen (e.g. Synthesis of oxyorganic compounds) using inorganic membranes. Membrane as defined by Coronas and Santamaria (999) is a semi permeable barrier, which is selective only to certain molecules and imposes resistance on the permeation flux for the rest. The most important characteristics of the membrane are, thus, permeability and selectivity. Both are dependent on the membrane layer configuration and its porous structure (pore size, porosity, and tortuosity), temperature, molecular weight and in addition on different transport mechanisms. Inorganic membranes may be either porous materials or non porous impervious films. Dense impervious films include Pd-Pd alloy membrane which are semipermeable to hydrogen, and solid oxide electrolyte dense membranes such as modified zirconias and perovskites which are highly selective for oxygen at high temperatures. Since Pd-Pd alloy membranes offer high permeability only for specific gases mainly hydrogen, these have been in use for dehydrogenation and hydrogenation reactions. However, on commercial scale their applications are limited due to their high cost and low permeability due to high wall thickness of µm (Hermann et al., 997), difficulty in fabrication, sensitivity to poisoning by sulfur species, and embrittlement upon aging (Julbe et al., 00). In order to overcome these drawbacks and to search suitable and cheaper membranes having sufficient thermal, mechanical and chemical stability, various valuable efforts have been made. Inorganic porous membranes are found to have promising future for industrial applications in catalytic reactor and thereby currently are in great use. Coronas and Santamaria (999) and Dixon (003) reviewed and illustrated more precisely the applications of porous inorganic membranes in catalytic reactions. The porous inorganic membranes can be divided into three types depending upon the pore sizes, namely macroporous (d p >50 nm), mesoporous (50>d p > nm ) and microporous (d p < nm), (Dixon, 003). Macroporous membranes provide no separation and are used as support layers of small pore size to form composite membranes. These are also applied some times where a well controlled reactive interface is required. α -alumina membranes are of macroporous type. Mesoporous membranes have generally pore sizes in the range of 4-5 nm. The examples of mesoporous membranes are Vycor glass, and composite membrane of γ alumina supported on macroporous α -alumina support. Mesoporous membranes have low selectivity but high permeability. Microporous membranes being of very small pore sizes, provide high potential for molecular sieving effects with very high separation factors. Carbon molecular sieves, porous silica and zeolite membranes are few examples of microporous membranes (Dixon, 003). These membranes are stable at high temperature and resist chemical attack. Currently the supported thin film of microporous materials on alumina or on porous stainless steel is most active area of membrane applications (Coronas and Santamaria, 999). Commercial ceramic membranes are available comparatively at low cost. These membranes have an asymmetric structure consisting of two layers namely support layer and separation layer. The support layer is composed of generally α alumina and has large pores with a low-pressure drop. The separation layer is prepared from different materials such as γ alumina, zirconia, silica etc. and controls the permeation flux. Ceramic membrane exhibits high permeability but relatively low selectivity and, therefore, low separation factor since available pore size ( 4 nm) is sufficient for molecular sieving. The separation of gaseous components through ceramic membrane is governed by Knudsen diffusion. The effective Knudsen permeability is inversely proportional to the square root of molecular weight of separating gas component. This implies that in dehydrogenation reactions, the hydrogen gas as product, being low in molecular weight, may be permeated easily through the membrane as compared to the other gases of high molecular weight. This fact leads to the conclusion that one of the methods to improve the separation factor of product and to reduce the permeability of reactant through membrane is to choose a reactant, which has a high molecular weight such as ethyl benzene (Yang et al., 995). In this regard for instance, the H /N separation factor lies in the range of.8 3. Download Date /3/3 3:06 PM

4 International Journal of Chemical Reactor Engineering Vol. 4 [006], Article A5 (Yang et al., 995) whereas the H /EB separation factor is 7.3 (Wu and Liu, 99), which is comparatively very much high. A large number of modelling studies on membrane reactors have been carried out using various chemical reactions specially dehydrogenation and hydrogenation reactions. These models are specific under certain limited conditions of the system studied. Wu and Liu (99) developed pseudohomogeneous model for isothermal operation using ceramic membrane with reaction in tube. Gobina et al. (995b) developed the model for isothermal condition considering radial concentration gradient, reaction in tube and microporous membrane system. Abdalla and Elnashaie (995) gave pseudohomogeneous model for fluidized bed reactor with or without Pd membrane. Hermann et al. (997) presented the model with reaction in tube, which takes into account the mass transport mechanism prevailing in the various layers of membrane. The model by Koukou et al. (997) takes into account the various heat exchanges occuring inside the reactor. Elnashaie et al. (00) developed pseudohomogeneous model with reaction in tube using Pd membranes. Gobina et al. (995a), Elnashaie et al. (000), and Moustafa and Elnashaie (000) considered reactive sweep gas and Pd membrane to develop pseudohomogeneous model. Assabumrungrat et al. (00) developed model for non isothermal condition with reaction in shell using Pd membranes. In view of the above, a comprehensive model has been developed in the present work, which takes into account isothermal / non-isothermal conditions, reactive / non-reactive sweep gas, multicomponent diffusion in the stagnant gas films on both sides of the membrane, effective multicomponents diffusion through membrane, permeation through various types of porous and Pd composite membranes, multicomponent mass transport through catalyst particles, pressure drop variations in reaction and permeate sides. This model has been reduced to pseudohomogeneous model and based upon this a case study for the production of styrene has been numerically simulated. Four catalysts, viz. Catalyst I, Catalyst A, Catalyst B, and Catalyst C have been studied in terms of yield and selectivity of styrene using ceramic membrane. The best catalyst thus found, has been considered for further studies. The model has been solved at various temperature conditions, purge gas to feed conditions. Optimum value of temperature and purge to feed ratio have been estimated. The yield and selectivity results are compared with Pd membranes.. DEVELOPMENT OF THE COMPREHENSIVE MODEL The catalytic membrane reactor is a cylindrical reactor equipped with a membrane. This membrane is inert with respect to chemical reaction and tubular in shape. The tubular membrane divides the reactor in two zones, viz. zone and zone, as shown in figure. Zone is reaction zone, which is packed with catalyst particles. The reaction feed is introduced into this zone. The zone is permeate zone where the purge gas or sweep gas is introduced counter currently or cocurrently with respect to the feed to carry away the permeated gasses from the permeate zone. Either of the zones may be the reaction zone. Obviously, other zone will be the permeate zone. The purge gas may be reactive or nonreactive. If purge gas is reactive and the corresponding reaction is catalytic, the permeate zone is also packed with appropriate catalyst. As far as the permeation through membrane is concerned, the permeation of gaseous component through membrane takes place from higher partial pressure side to lower partial pressure side for that component. Thus, permeation may be from either side of the membrane depending upon the partial pressures. Keeping above facts in view the comprehensive model equations are developed for catalytic tubular membrane reactor as shown in fig.. The model supports different process options such as the use of inert sweep gas or the reactive sweep on permeate side, isothermal or non-isothermal operation, porous membrane or Pd alloy composite membrane with porous support. The permeance of species through porous membrane and permeance of hydrogen through Pd-Pd alloy membrane have been discussed in detail in the section 3.. Assumptions The model equations are developed on the basis of following assumptions. (i) The reaction and permeate sides of the reactor are operated under steady state conditions. (ii) In both sides the behaviour of bulk gas is assumed to be ideal. (iii) The plug flow of bulk gas is assumed. Axial diffusion of mass and heat and radial concentration gradients on both sides are considered to be negligible. (iv) The stagnant gas films on both sides of membrane are considered, while radial temperature gradients across the membrane are neglected. Download Date /3/3 3:06 PM

5 Kumar et al.: Model for Catalytic Membrane Reactor 3 membrane Shell side ( Permeate zone) Purge gas Purge gas + permeated gas Reaction feed R R R3 products Purge gas L Purge gas + permeated gas Tube side filled with catalyst (Reaction zone). Mass balance equations Figure Schematic diagram of membrane reactor This section comprises of the mass balance equations for transport through tube, for transport through shell, for transport in catalyst particles, and for transport though membrane. In the tube and shell side mass balance equations + sign with r j is used for the component which is produced by the reaction j, and - sign with r j is used for the component which is consumed by the reaction j... Mass balance equations for tube side The reaction feed is introduced into the tube which is packed with catalyst particles. Let n be the total number of reactions occurring in tube which includes main reactions and all side reactions as well. Let n be the total number of components present in gaseous mixture flowing through packed tube. This includes all gaseous reactants, products and inerts (if any). Set of the component mass balance equations has been developed by taking mass balances around control volume in the tube as follows. + sign with J i indicates the permeation of component i from tube to shell and - sign indicates the permeation of component i from shell to tube through membrane. These equations can be written for all n components accordingly as follows. In terms of molar flux it is given below. dn dz ti ρ n B j= η j J i ( ± s r ) ± = 0 ij j R i = to n () This equation can be written for molar flow rate of i th component as follows: n dfti πr ρb η j ( ± sij rj ) ± π R Ji = 0 i = to n () dz j= For plug flow, the variation of fractional conversion of i th reactant in j th reaction is given by dxtij π R ρb η j rj sij = (3) dz F tio If n 3 represents the number of reactions where component i is the reactant, then over all conversion of i th component will be n = 3 j= x (4) tij Download Date /3/3 3:06 PM

6 4 International Journal of Chemical Reactor Engineering Vol. 4 [006], Article A5 The value of n 3 may be different for different components. Mole fraction y ti of i th component is computed by the following equation. Fti Nti yti = = (5) n n F N ti i= i=.. Mass balance equation for shell side ti The sweep gas may be reactive or inert. If it is reactive, reactions will also occur in the permeate side, i.e. in the shell. Let n 4 be the number of reactions occurring in shell and n 5 be the total number of components. The component material balances give the following equations. 4 m dn ( ) βρ n si R Ji B η j ( ± sijrj ) ± β = 0 ; i = to n 5 (6) dz R R ( ) j = 3 Where, m = for co-current flow of sweep gas in shell and reactants in tube, m = for counter current flow of sweep gas in shell and reactants in tube, and β =, if sweep gas is reactive and reactions occur in shell side. β = 0, if sweep gas is inert and no reaction occurs in shell. β = 0, if component i is not permeated through membrane β =, if component i is permeated through membrane + sign with β indicates the permeation of component i from the shell to tube and - sign indicates the permeation of component i from the tube to shell. In porous membranes, the permeation of component may occur in either direction depending upon the partial pressure of the component in shell and tube. In terms of molar flow rate, equation (6) can be written as follows: n df βρ Bπ R3 R η j. ± sijrj ± β π RJ i = 0 dz j = 4 m si ( ) ( ) ( ) i = to n 5 ; (7) If membrane is very thin in comparison to the tube diameter, then R can be taken equal to R. If reactions occur in shell side, then we can use equation (3) for the variation of fractional conversion of i th reactant in j th reaction in the shell with small modifications as under. dx sij dz ( ) π R R ρ η. r s β 3 B j j ij = (8) F sio Here, F sio is molar flow rate of reactant i in the feed in shell. It will include the molar flow rate of reactant i with sweep gas and molar flow rate of reactant i permeated through membrane from tube side. If n 6 represents the number of reactions where component i is the reactant, then over all conversion of reactant i will be 6 = n sij j= x (9) The mole fraction of i th component in the shell side gaseous mixture is given by the following equation. Fsi Nsi ysi = = (0) n5 n5 F N si i= i= si Download Date /3/3 3:06 PM

7 Kumar et al.: Model for Catalytic Membrane Reactor 5 In above mass balance equations for tube side and shell side, the effectiveness factor is used. The value of this factor is generally available in the literature for a particular catalyst and reaction. If it is not available then it may estimated as follows. The effectiveness factor is a measure of how far the reactant diffuses into the catalyst particle before reacting. It is defined as the ratio of the actual reaction rate to the rate of reaction that would result if entire interior surface were exposed to the external particle surface conditions, i.e. rate of reaction at bulk conditions of concentration and temperature (Fogler, 00). Thus the effectiveness factor η j, for j th reaction is computed by the following equation. 3 η = p j r r r r. 3 0 j dr p ( rj ) b Here (r j ) b is the reaction rate at bulk conditions of concentration and temperature. For tube side reaction r p is used for the tube side catalyst; likewise for the shell side reaction (if any) r p is used for the shell side catalyst. In order to estimate bulk concentration of reactant component i in gas contained within the pores, following equation may be used. r is the radial coordinate representing the radius of a spherical catalyst particle. dc s i ijrjρb + = () dr r dr D d Ci ( ) The boundary conditions are: At r = 0, C i is finite, i.e. dc i /dr = 0. At r = r p ; C i = C is. i e ()..3 Mass balance equations for diffusion through membrane The membrane is surrounded by stagnant thin gas film on the tube side as well as on the shell side. The temperature and pressure are considered to be constant within the gas film. The multicomponent diffusion through membrane in radial direction involves the diffusion through gas film and through porous membrane. The diffusion of component i in multicomponent ideal gas mixture (having n 7 components) at low density through stagnant gas film is described by Stefan-Maxwell s equation (Bird et al., 00) as follows. n7 dyi = ( yj i j y j Ji ) (3) dr C D j= T ij For tube side gas film the above equation is n7 R Tt ( yj i j y j Ji ) (4) dyi = dr P D tt j= ( ij ) t and for the shell side gas film, it assumes the following form. n7 dyi R Ts = ( yj i j y jji ) (5) dr P D st j= ( ij ) s In equations (4) and (5), (D ij ) t and (D ij ) s are binary diffusion coefficients of the pair i-j in multicomponent mixture at temperature and pressure conditions of tube and shell sides respectively. These diffusivities are independent of concentration. r is radial coordinate which represents the thickness of the gas film. Thickness of gas film may be computed by various methods as suggested by Bird et al. (00). The multicomponent diffusion through the porous membrane is described by dusty gas model, which takes into account the Knudson diffusion and viscous flow of gas through the membrane. By using dusty gas model (Hermann et al., 997; and Seader and Henley, 998), one obtains. Download Date /3/3 3:06 PM

8 6 International Journal of Chemical Reactor Engineering Vol. 4 [006], Article A5 ( yj i j y j Ji ) yi / ( D ) ( ) ( ) n7 dyi R T J i Bo dp = + dr P j= ε τ D ij ik P µ e d Dik dr t e (6) where ε d p B o = τ 3 (7) and dci Ji = ( Dik ) e dr (8) (D ik ) e is evaluated by using equation (40) described later. P and T are pressure and temperature respectively at the side from where the component is getting permeated through membrane. r is radial coordinate which represents the thickness of membrane..3 Energy balance equations The temperature gradient dt/dz in tube and shell side under isothermal conditions is zero. Under adiabatic conditions, the energy balance differential equation is derived by assuming that the membrane offers no resistance to heat transfer, and external heat transfer resistances between bulk gas and catalyst particle are negligible due to high conductivity of catalyst particle (Elnashaie et al., 00; Hermann et al., 997; and Moustafa and Elnashaie, 000). Therefore, T t and T s are assumed to be identical and equal to T. The energy balance gives the equation for overall temperature gradient as follows. n n4 dt FT C p = πr ρ B ± H j η j. rj + βπ R3 R ρ B ± H j η j. rj ( ) ( ) ( ) (9) dz j= j= + sign with H j is used for endothermic reaction and - sign with H j is used for exothermic reaction. F T is total flowrate of gases which includes the flowrate in shell as well as in tube. C P is average heat capacity of this gaseous mixture..4 Momentum balance equation The Ergun equation is used to calculate the pressure drop across solid bed packed with catalyst particle in the tube side (Bird et al., 00) as follows. dp dz ( rp ) ( ) v 5 ρ tt µ t vtz b 5 g tz εb 50 x 0.75 x εb rp εb ε = (0) Where v tz is superficial velocity of gas in tube in z direction. The ideal behaviour of gases gives T = n t vtz N ti = G o /ρ g () i= if a is total particle surface area/ volume of bed, then 3( ε) r p = () a Modified Hagen Poiseuille law (Bird et al., 00) is used to compute pressure drop in shell side. If there is no packing, this law yields, Download Date /3/3 3:06 PM

9 Kumar et al.: Model for Catalytic Membrane Reactor 7 R 8µ svsz ln dpst R3 = (3) dz R ln R3 + R + ( R3 R ) R 3 For ideal gas behaviour, v sz reads 5 T = n s vsz N si (4) i= The partial pressure of i th component in tube and shell can be expressed by the following equations. Nti x PtT Pti = (5) n N P si = i= si n5 i= ti N x P N si st 3. PERMEATION RATE OF GASES THROUGH MEMBRANE As discussed in the introduction, inorganic membranes include dense membranes and porous membranes. Dense membranes are exclusively permselective to either H or O and so are largely and successfully used in reactions consuming or generating H or O. In these membranes transport process involves the desolution of the gas in the membrane material. H permselective dense membranes include Pd and Pd alloy membranes. The synthesis and permeation rate of hydrogen through Pd-Pd alloy membranes have been discussed by Collins and Way (993), and Shu et al. (99). The transport mechanism in porous membranes include viscous flow Knudsen diffusion, surface diffusion, capillary condensation and molecular sieving. These membranes have higher value of permeability and lower value of selectivity. A notable exception are zeolite membranes with a promising future for applications to catalytic reactors (Coronas and Santamaria, 999). Zeolite membranes are a type of microporous membranes. The gas transport through mesoporous membrane is governed mainly by Knudsen diffusion. In case of microporous membrane, the permeation of gases is governed by adsorption and diffusion of molecules for which Stefan-Maxwell flux equations supplemented by configurational Monte Carlo Simulation of adsorption equilibria may be used. Non equilibrium dynamic simulations are also being used to understand phenomena at the molecular level (Dixon, 003). There are a number of research papers addressing progresses on microporous membranes regarding their synthesis and permeability characteristics. A few studies on microporous membranes are reviewed and summarized by Coronas and Santamaria (999), Julbe et al. (00) and Zaman and Chakma (994). Caro et al. (000) focused their studies on zeolite and Sol-get based microporous membranes. Coronas et al. (997) discussed the characterization and permeance properties of ZSM-5 tubular membranes and revealed that the permeance bahaviour may be the result of permeation through non zeolite pores in parallel to zeolite pores. They prepared the membrane by in-situ synthesis. Meizner and Dyer (993) studied the transport properties of microporous inorganic membranes and discussed theoretical basis for describing gas transport through both monolithic and multilayer porous systems. Bhandarkar et al. (99) and Shelekhin et al. (99) studied gas permeability properties of various gases in microporous silica membranes mathematically as well as theoretically in terms of selectivity factors by considering diffusion as well as adsorption. Jeong et al. (003 a & b) reported the synthesis of a FAU type zeolite membrane on a porous α-al O 3 support tube using a hydrothermal process. They studied the permeation and separation properties of this membrane for mixture of benzene and saturated C 4 -C 7 hydrocarbons. The transport mechanism of gases through molecular sieve carbon membrane has been studied by Sznejer and Sheintuch (004), Itoh and Haraya (000), and Sznejer et al. (004). The aforementioned literature portrays a brief review regarding the permeation of gases through microporous membranes. A delineate analysis and formulation of the permeation rate of hydrogen through Pd-Pd alloy membranes and permeation rate of gases through porous ceramic membranes in hydrogenation / dehydrogenation membrane reactor is carried out in the following subsections. Since, we intend to confine our (6) Download Date /3/3 3:06 PM

10 8 International Journal of Chemical Reactor Engineering Vol. 4 [006], Article A5 studies to the systems where only porous ceramic and Pd-Pd alloy membranes are applied, a detailed mathematical formulation of permeance through microporous membranes is kept out of the scope of this paper. 3. Permeation rate of gases through Pd and Pd alloy composite membranes Pd and its alloys have very high permeabilities for hydrogen as compared to other gases. Commercially available Pd/Pd alloys membranes are either thick films or thick walled tubes. However, the high cost of Pd metal leads the prospects for the improvement of the preparation techniques of membranes with very thin Pd or Pd-alloy films to make the processes economically more feasible. In this regard the composite Pd microporous ceramic membranes are prepared by plating a thin film of Pd or its alloys on the selective layer of commercially available ceramic membrane tubes. H gas permeates through the ceramic support as well as through Pd alloy film. (Collins and Way, 993) has mentioned that the H fluxes for a 4 nm Membralox membrane at transmembrane pressure difference from 00 to 000 kpa are 3-44 times higher than the fluxes measured for the composite Pd ceramic membrane. This leads to the conclusion that mass transfer resistance of the ceramic support is minimal. Therefore, hydrogen permeabilities through composite membranes are essentially considered to be the permeabilities of the Pd film. Hence for Pd membranes as well as for Pd alloys composite microporous ceramic membranes the permeation rate Q i for all components except H is zero. This gives J i = 0; i represents all gaseous components except H. The diffusion of gas in Pd-Pd alloy film does not depend on the actual structure of the membrane film. The diffusion occurs when the gas is dissolved in the film to form more or less homogeneous solution. This type of diffusion can be considered to follow Fick s Law (Geankoplis, 00). The membrane film is treated as a uniform homogeneous like material. In many cases, the experimental data for diffusion of gases in membranes are not given as diffusivities and solubilities but as permeabilities. The permeability coefficient p mi is generally defined as mole of gas i diffusing per second per m cross sectional area through a membrane m thick under a pressure difference of atm pressure. Thus, using Fick s law, the permeation flux of hydrogen though Pd-Pd alloy composite membrane in terms of permeability coefficient can be written as follows (Collins and Way, 993; Moustafa and Elnashaie, 000; and Uemiya el al., 99). pmh n n J = H PtH P SH δ (7) Here hydrogen permeability coefficient p mh is in mole. m/m sec (atm) n. Consequently the permeation rate of hydrogen at any radial distance r in the membrane is given by dqh = π r J H (8) dz Thus the permeation rate of H through the membrane to the permeate side is dqh = π R J H (9) dz and by equation (7), it is dqh p mh n n = π R PtH P SH dz δ (30) A number of Pd membrane tubes embedded into catalyst bed are also in use (Abdalla and Elnashaie, 995). The cross sectional area of all membrane tubes is assumed to be equal to that of the single tube passing through the center. The sweep gas flow rate is equally divided through the membrane tubes. In this case, equation (7) for H permeation rate is expressed as dqh π n 8R n n = p mh PtH P SH dz δ (3) Where n 8 represents the number of membrane tubes. For single tube n 8 =. Download Date /3/3 3:06 PM

11 Kumar et al.: Model for Catalytic Membrane Reactor 9 The value of n in above equation (3) is influenced by the solubility of H in metal, rates of surface processes and bulk diffusion. All these factors depend on temperature. Therefore, n and permeability coefficient vary with temperature. The dependence of permeability coefficient on temperature (Collins and Way, 993) is as follows: p mh = p mh,0 exp [-E/RT] ; T is in K (3) When H atoms form an ideal solution in Pd or Pd - alloy metal, Sievert s half power pressure law is followed (Abdalla and Elnashaie, 994; Collins and Way, 993; Shu et al.,99). In this case n is equal to 0.5. Hence equation (7) and (30) are reduced to as given below. pmh J = H PtH P SH (33) δ dqh p mh = π R PtH P SH (34) dz δ H permeation flux and rate, for instance, through a composite membrane consisting of a 6 µm thick Pd Ag alloy on 0. cm Vycor glass support are expressed by equations (33) and (34) respectively, where permeability coefficient p is determined as a function of temperature according to following equation (Gobina et al., 995b). mh pmh = x mole m m atm T exp,. / sec ; T is in K For non-ideal solution n may be different from 0.5. The values of n and p mh at specific temperature for composite Pd alloy ceramic membranes with different configurations are given in the Table (Collins and Way, 993; and Dittmeyer et al., 999). Table The values of n and hydrogen permeabilities at specific temperatures for composite Palladium Ceramic membranes Membrane Description T(K) n 0-µm palladium film on ceramic membrane with 0 nm pore layer 7-µm palladium film on ceramic membrane with 00 nm pore layer p mh (mol.m/(m.s.pa n )) 83.43x x x x µm palladium film on ceramic membrane with 00-nm pore layer x x x From Table, the H permeation data for composite Pd ceramic membrane with 7 µm, and.4 µm Pd film are combined for all temperatures mentioned in the table, and the calculated parameters of equations (30) and (3) are as follows: (i) (ii) For 7 µm Pd film p = 5.9 x 0-8 mol.m/m.s Pa mh,0 E = 4450 J/mol n = For.4 µm Pd film p =.6 x 0-8 mol.m/m.s Pa mh,0 Download Date /3/3 3:06 PM

12 0 International Journal of Chemical Reactor Engineering Vol. 4 [006], Article A5 E = 8880 J/mol n = Moreover, the permeability of H depends on the equilibrium solubility of H and its diffusivity in Palladium. Therefore, in equations (33) and (34), the term at any radial distance r, may be defined in terms δ of diffusion and concentration of H in pure Pd as follows (Abdalla and Elnashaie, 994; Elnashaie et al., 000; Elnashaie el al., 00; and Hermann et al., 997 ). pmh D H Co = (35) δ R r Po ln R Where D H is Fick s diffusion coefficient of hydrogen dissolved in Pd and C o is the solubility or standard concentration of dissolved H in Pd. Both are determined as a function of temperature according to following equations DH =.3 x 0 exp, m / s T ; T is in K C o = 3.03 x 0 5 T.0358, mole/m 3 P o is standard pressure at permeate side in atm. Thus, the molar flux of H through membrane is, DHCo J = H PtH P SH (36) R r P ln R o Consequently, the permeation rate of H from equation (8) reads dqh π D HCo = PtH P SH (37) dz R P ln R o p mh Table gives the configuration of few membranes where equations (36) and (37) are applicable. Table Configuration of Membranes Configuration of membrane 0 µm thick Pd layer on mm thick porous support with pore size of 0. µm and porosity of x 0-4 mm thick Pd layer on porous ceramic support tube with a diameter of 6.87 cm Metal membrane developed by Bend Research Inc. (996), are composed of base metal support layer carrying an intermediate layer of silica or alumina above which there is a coating of metal layer of Pd alloy. Porous ceramic membrane tube with a 5 x 0-4 mm thick Pd film deposited on the surface. Reference Hermann et al., 997 Elnashaie et al., 00 Elnashaie et al., 000 Abdalla and Elnashaie, 995 Table 3 provides the summary of hydrogen fluxes based on feed pressure of pure hydrogen equal to Pa and a permeate pressure of 035 Pa for different membranes (Collins and Way, 993). Composite Pd micorporous membranes have the highest hydrogen fluxes with the exception of the ceramic membrane which has highest H fluxes due to Knudsen diffusivity. Download Date /3/3 3:06 PM

13 Kumar et al.: Model for Catalytic Membrane Reactor Table 3 Hydrogen Fluxes for Inorganic Membranes Membrane Description T (K) Hydrogen flux (mol/m.s) Composite palladium ceramic membrane (.4-µm palladium film) Composite Palladium porous glass membrane µm palladium film Composite metal membrane (5-µm palladium film on 30 - µm vanadium with - µm intermetallic diffusion barrier between palladium and vanadium) Composite metal membrane (--µm palladium film on 0.5 mm thick niobium tube) Metal oxide membrane (SiO deposited in pores of 4-nm Vycor glass membrane) Ceramic membrane (asymmetric membrane with 4 nm pore top layer) Permeation rate of gases through porous ceramic membranes The diffusion of gases through porous membrane depends on actual structure of the membrane and inter connected voids, i.e. pores in the membrane. The gas diffuses in the void volume and takes a tortuous path which is greater than the membrane thickness δ by a factor τ called tortuosity. Diffusion does not occur in the inert solid of the membrane. If the pore diameter of the membrane is large compared to the molecular diameters of the gaseous components and pressure difference exists across the membrane, bulk or convective flow through the pores occurs. Such a flow is not perm selective and therefore, no separation between gaseous components occurs. However, if partial pressure differences for various components exist across the membrane keeping total pressure same on both sides of the membrane, perm selective diffusion of the components through the pores by Fickian type diffusion will take place, resulting in the effective separation. If the pores are of the order of molecular size of few components in the gaseous mixture, the diffusion of molecules of these components and the molecules of size greater than the pore will be restricted, resulting in an enhanced separation. This situation is highly desirable. Another special situation exists for gas diffusion where the mean free path of the molecules is greater than the pore diameter and / or the total pressure is low. This type of diffusion is called Knudsen diffusion and generally occurs in porous membranes. It is dependent on molecular weight. The collisions occur primarily between gas molecules and the pore wall rather than between gas molecules. Thus, the permeation flux of gaseous component i through membrane can be written as (Geankoplis, 00; and Seader and Henley, 998 ). ( Di ) ( Pti Psi ) e Ji = (38) RTδ ) e i Where ( D is the effective diffusivity of component i. In the absence of a bulk flow effect, the effective diffusivity can be written as ( D ) i e ε = + τ Di Dik (39) In ceramic porous membrane, Knudsen diffusion controls the permeation flux of the various gaseous components through membrane. Hence effective diffusivity by equation (39) is modified as Download Date /3/3 3:06 PM

14 International Journal of Chemical Reactor Engineering Vol. 4 [006], Article A5 D ε i e ik ik e τ D D (40) ( ) = = ( ) If the kinetic theory of gases is applied to a straight cylindrical pore, the Knudsen diffusivity is given by the following equation (Seader and Henley, 998) D ik / / d p 8RT T = = d p 3 πm i M i (4) Hence, permeation flux of gaseous component i through porous ceramic membrane by equations (38), (40), and (4), can be written as ε Dik Ji = ( Pti Psi ) (4) τ RT δ In terms of permeability, J i can be expressed as pmi Ji = ( Pti P si ) (43) δ By equation (4), thus the permeability of component i is ε Dik pmi = (44) τ RT The permeation rate of component i at any radial distance r in the membrane is dqi = π r Ji (45) dz and permeation rate of component i through membrane to permeate side (eg from tube to shell side) of reactor will be as given below. dqi = π R Ji (46) dz 4. CASE STUDY In the case study the dehydrogenation of ethylbenzene (EB) has been studied in a commercial ceramic membrane reactor. The catalytic dehydrogenation of ethyl benzene to produce styrene, is an example of commercially important dehydrogenation reactions. This reaction is reversible and endothermic in nature. It is therefore, limited by thermodynamic equilibrium. This reaction has been widely studied in various types of membrane reactors. Wu et al. (990) studied experimentally the dehydrogenation of ethyl benzene in an alumina membrane with 4 nm pore size using industrial catalyst and achieved 5 % high conversion of ethyl benzene as compared to the conversion in packed bed. Wu and Liu (99) carried out simulation studies on a hybrid system, i.e. a conventional packed bed reactor followed by porous ceramic membrane reactor. They observed an increase in ST yield by more than 5 % over the thermodynamic limit. Becker et al. (993) also investigated the conversion of ethyl benzene to ST in alumina membrane reactor and observed again 0 to 5% higher conversion in membrane reactor. Abdalla and Elnashaie (994) have studied two fluidized bed configurations with and without selective metallic membranes by comparing it with equivalent industrial fixed bed unit. A considerable increase in the ST production has been achieved over that of the industrial fixed bed unit. Quicker et al. (000) also observed an increase in ST yield by 4% in a Pd composite membrane, compared to conventional packed bed reactor. Moustafa and Elnashaie (000) and Elnashaie et al. (000) studied simultaneous production of ST and cyclohexane in an integrated membrane reactor using Pd membranes and found considerable increase in selectivity and ST yield over the industrial value. Download Date /3/3 3:06 PM

15 Kumar et al.: Model for Catalytic Membrane Reactor 3 Besides, simulation results on the use of Pd composite membranes have been reported in several studies (Abdalla and Elnashaie, 994; Gobina et al., 995b; She et al, 00). In this case study, the mixture of EB and steam is fed into the reaction zone to perform the reaction. In the permeation zone, steam as sweep gas or purge gas is introduced to carry away the permeated gases from the reactor. The developed comprehensive model in section, is reduced to a pseudo homogeneous one dimensional mathematical model considering one main dehydrogenation reaction and five other side reactions under isothermal conditions. In first step, the model equations are solved for an industrial catalyst. It is known that the kinetic properties of the catalyst and the balance between the amount of gases produced and amount of gases permeated play a key role for the utilization of membrane effect besides membrane permeability (Dittmeyer et al., 999). Therefore, three catalysts available in literature, have also been employed in the reactor and their performances along with industrial catalyst in terms of yields of products are compared. The best catalyst, thus found, is considered for further simulation studies. The operating conditions that will lead to maximum ST yield are evaluated. Commercial ceramic membrane results are compared with Pd-alloy composite membrane. 4. Kinetic model The dehydrogenation of ethylbenzene (EB) to styrene (ST) can be represented by one main reaction (i.e. ethylbenzene to styrene) along with five side reactions (Clough and Ramirez, 976; Elnashaie et al., 000; Sheppard and Maier, 986; and Wu and Liu, 99). These six reactions are reversible. However, all side reactions are much slower in comparison to the main reaction (Sheppard and Maier, 986) and are far from equilibrium at finite time where the main reaction may get completed. In view of this fact, all side reactions are considered irreversible and their reverse rates are excluded from the kinetic model. The reactions along with respective rate expressions are as follows: () C 6 H 5 C H 5 C 6 H 5 C H 3 +H PST PH r = k PEB = k PEB PEB, eq KEB 0 F PST, eq PH, eq KEB = exp =, atm RT PEB, eq F 0 = a + bt + ct J/mole (47) where a = 75.6 (J/mol), b = -6.7 (J/mol.K) and c = -.9 x 0-3 (J/mol K ) () C 6 H 5 C H 5 + H C 6 H 5 C H 5 + CH 4 ( ) r k P P (48) = EB H (3) C 6 H 5 C H 5 C 6 H 6 +C H 4 r 3 = k 3 P EB (49) (4) /C H 4 +H O CO + H 0.5 ( ) r k P P (50) 4 = 4 H O C H 4 (5) CH 4 + H O CO + 3H ( ) r k P P (5) 5 = 5 H O C H 4 (6) CO + H O CO + H 3 ( )( ) r k P T P P (5) 6 = 6 T / H O CO Four catalysts are considered for the present study. The rate constant for jth reaction is represented by k j = 000 exp ( A j E j /RT) (53) Download Date /3/3 3:06 PM

16 4 International Journal of Chemical Reactor Engineering Vol. 4 [006], Article A5 Here A j is the dimensionless pre-exponential factor and E j is activation energy in J/mole. The kinetic parameters for all six reactions corresponding to each catalyst are given in Table 4 (Elnashaie et al., 00). The compositions of four catalysts are as follows (Elnashaie et al., 00; Wu and Liu, 99). Industrial Catalyst (Catalyst I): 6 % Fe O 3-36% K CO 3 -% Cr O 3 Catalyst A: 80% Fe O 3-0% K O Catalyst B: 75% Fe O 3-0% K O-5% CeO Catalyst C: 70% Fe O 3-0 % K O - 5% CeO - 5% Cr O 3 Table 4 Values of Kinetic Parameters for Four Catalysts Reaction Kinetic Catalyst I Catalyst A Catalyst B Catalyst C Number Parameters A E A E A E A E A E A E Pseudohomogeneous model The comprehensive mathematical model is reduced to pseudohomogeneous model by setting following conditions. (i) Commercial tubular ceramic membrane is considered. Therefore permeation flux J i in balance equations has been considered according to section 3.. (ii) The reactions are considered to occur in tube. Therefore, catalyst is packed in tube, i.e. inside the commercial ceramic membrane tube. There are six reactions as mentioned in section 4.. The components are ethylbenzene (EB), styrene (ST), hydrogen (H ), steam (H O), toluene (TOL), benzene (BEN), methane (CH 4 ), ethylene (C H 4 ), carbon monooxide (CO), and carbon dioxide (CO ). Thus, in tube side, for mass balance n = 6, and n =0. (iii) Purge gas is non reactive. Thus no reaction is considered to occur in the shell side. Therefore, β = 0, n 4 = 0 in shell side balances. (iv) Steam is used as purge gas, which is also a reactant in tube. Since commercial membrane is selective for all components. Therefore, the permeation is from tube to shell. Thus n 5 = n 7 = 0, viz. (EB), (ST), (H ), (H O), (TOL),(BEN), (CH 4 ), (C H 4 ), (CO), (CO ). β = with - sign and P tt > P st in shell side mass balance. J i with + sign in tube side mass balance equations. (v) The purge gas in shell and tube are assumed to flow in cocurrent mode since this represents optimum conditions for the use of porous membranes (Gobina et al., 995b). Therefore m = in shell side balance equations. (vi) The catalyst pellet equations are discarded because concentration gradients in catalyst pellets are neglected due to small pellet size (Gobina et al., 995b). (vii) Isothermal condition is considered. Therefore dt/dz = 0. (viii) All the effectiveness factors with reaction rates are taken to be equal to unity. Download Date /3/3 3:06 PM

17 Kumar et al.: Model for Catalytic Membrane Reactor 5 (ix) Since the effect of pressure drop on the performance of reactor is negligible (Wu and Liu, 99), isobaric conditions are assumed to prevail in tube side as well as in shell side. Therefore P tt and P st are constant. (x) Radial species gradients through membrane are neglected. (xi) Since ethylbenzene and steam are two reactants in feed, equation (3) can be written for ethylbenzene and steam as follows. dx tebj dz and π R ρ B = = j = F tebo r j 0 ;,, 3 (54) dxthoj π R ρb r j = = 0 ; j = 4, 5, 6 dz F th OO According to equation (4), for the overall conversion of EB and H O are 3 5 x and x respectively (56) tebj j= j= 4 th Oj (55) The performance of porous membrane reactor has been compared in terms of yields and selectivities of product and byproducts, and conversion of ethyl benzene. The mechanism of reaction (3) clearly shows that the reactions () and (3) are two parallel reactions. Therefore, benzene is also a primary product. Reaction () shows the consumption of ethyl benzene to form toluene. Thus, it is decided to estimate the yield and selectivities of only three products, viz styrene, benzene and toluene. Percent selectivity and percent yield of product, percent conversion of ethyl benzene can be expressed by the following formulae [PI = styrene, benzene, toluene] PI (Pr oduced) % yield of PI = x00 Ethylbenzene (Feed) % selectivity of PI = PI (Pr oduced) x00 PI (produced) PI where PI (produced) = PI (retented) + PI (permeated) % conversion of EB = EB (Feed) EB (outlet) EB (Feed) x 00 where, PI (produced) = PI (retented) + PI (permeated) and EB (outlet) = EB at outlet of permeate side + EB at outlet of retented side. 5. MODEL VALIDATION In order to validate the model, experimental results obtained by Yang et al. (995) on the dehydrogenation of EB to ST in a laboratory tubular porous alumina membrane reactor, were considered. The permeation properties of the membrane were: permeation area = 0.8 x.7 x 0-3 m ; H /N separation factor =.8-3.; H flux = 7 x 0-7 mol/m sec - Pa -. On this basis the flux through membrane for other gaseous species can be calculated by using equations (4) and (4). The catalyst used was similar to industrial catalyst and it was packed in tubes. Its properties are: specific area = 3-4m /g; packed density =.-.4 x 0 3 kg/m 3 ; particle size = 0-30 mesh. The other operating conditions were: catalyst loading = 0 ml; bed height = 37 mm; LHSV =.0 hr - ; H /EB (volume ratio) =.3-.6; reaction temperature = 893 K. Download Date /3/3 3:06 PM

18 6 International Journal of Chemical Reactor Engineering Vol. 4 [006], Article A5 The percent increase in EB conversion was investigated as a function of purge gas flow rate, and reaction temperature. Here, the percent increase in EB conversion is defined as Percent increase in EBConversion = ( Conversion membrane Conversionfixed bed ) Conversion fixedbed x00 The pseudohomogeneous model is solved for the operating conditions of this laboratory reactor to verify the model predictions. Table 5 provides the comparison of the model predictions with the experimental data. It is clear from the table that all model predictions are in good agreement with the experimental data. Thus model simulates the laboratory reactor very well. Table 5 Percent increase in ethyl benzene conversion Percent increase in ethyl benzene conversion Purge gas flow rate in ml/min Operating temperature at purge gas flow rate = 00 ml/min K 893 K Experimental Calculated % error RESULTS AND DISCUSSION OF SIMULATION The standard operating conditions and physical parameters for the membrane reactor selected in this study for simulation are listed in table 6. The model equations constitute initial value problem. The computer program in MATLAB using its ordinary differential equation solver, ode 45 is used to solve these model equations. An exhaustive numerical simulation have been carried out to obtain the following results. Table 6 Operating conditions and physical parameters of reactor Parameters Value Length 0.0 m Density of Industrial Catalyst 46 kg/m 3 Density of Catalyst A 454 kg/m 3 Density of Catalyst B 490 kg/m 3 Density of Catalyst C 4939 kg/m 3 Radius of Industrial Catalyst x 0-3 m Pore radius of Industrial catalyst 40 x 0-9 m Pore radius of catalyst A 0.7 x 0-9 m Pore radius of catalyst B 5.5 x 0-9 m Pore radius of catalyst C.3 x 0-9 m Temperature 93 K Total pressure in reaction side. bar Total pressure separation side.0 bar Steam to Ethylbenzene Ratio (Dilution Ratio) 6.0 mol/mol Membrane Pore diameter 40 x 0-0 m Membrane Thickness 5 x 0-6 m Membrane Porosity 0.5 Membrane Tortuosity.95 Download Date /3/3 3:06 PM

19 Kumar et al.: Model for Catalytic Membrane Reactor 7 6. Comparative performance of four catalysts For valid comparison amongst four catalysts, namely catalyst I, catalyst A, catalyst B, and catalyst C, mathematical model is solved for all four catalysts for similar design and operating conditions as mentioned in table 6. Table 7 shows the values of yields and selectivities of styrene (ST), benzene (BEN), and Toluene (TOL) and conversion of ethyl benzene (EB) for all four catalysts in porous ceramic membrane reactor. Table 7 Comparative Performance Studies of Different Catalysts in Membrane Reactor S.No. Catalyst I A B C Parameter Yield of ST (%) Yield of BEN(%) Yield of TOL (%) Conversion of EB (%) Selectivity of ST (%) Selectivity of BEN(%) Selectivity of TOL(%) Following conclusions may be drawn. The conversion of EB is highest with catalyst B and lowest with catalyst A. This implies that catalyst B is most active and catalyst A is least active catalyst. The highest conversion of EB with catalyst B is at the expense of large production of undesired product benzene. This gives the highest benzene yield with catalyst B, which is 4.67 % higher than catalyst I and % higher than catalyst C. Additionally, the yield and selectivity of styrene is lowest with catalyst B. These results prove unsuitability of catalyst B for production of desired product styrene. Amongst catalyst I, catalyst A and catalyst C, the yield of styrene with catalyst C is 4.87 % higher than catalyst A and 7.65 % higher than catalyst I. Although, the yield of benzene is higher with catalyst C than catalyst I and lower than with catalyst A, selectivity of styrene is higher in case of catalyst C as compared to catalyst I and catalyst A. The above facts leads to the conclusion that the catalyst C is the best catalyst for the production of styrene in porous membrane reactor. Among catalyst I, A, and B, catalyst I is best. Although the activity of catalyst A is poor, it gives better quality of products than catalyst B. For further studies, the effect of various parameters on the performance of ceramic membrane reactors have been studied by using catalyst C. The results are discussed in the following sections. 6. Effect of operating temperature Operating temperature has significant effect on the membrane reactor performance. The suitable operating temperature range is 850 to 950 K. Table 8 clearly shows that yields of ST, BEN, TOL increase with temperature due to endothermic nature of reactions. Percent increase in yield of ST, BEN, TOL decreases with increase in temperature. At 950 K yield of ST is only 3 % higher than at 95 K. At 950 K the increase in BEN and TOL yields is 46.3% and.4% respectively. Selectivity of ST decreases with temperature and percent decrease in selectivity of ST is high at temperature 950 K. Thus, it can be concluded that the operating temperature must lie between 900 K to 950 K to obtain significant yield of ST. Therefore, a temperature of 95 K has been chosen for further studies. Download Date /3/3 3:06 PM