Chemical Engineering Science 56 (2001) 395}402            Ethylene epoxidation in a catalytic packed-bed membrane         ...
396                            M. A. Al-Juaied et al. / Chemical Engineering Science 56 (2001) 395}402stainless-steel memb...
M. A. Al-Juaied et al. / Chemical Engineering Science 56 (2001) 395}402                         397                       ...
398                             M. A. Al-Juaied et al. / Chemical Engineering Science 56 (2001) 395}402a new step in the a...
M. A. Al-Juaied et al. / Chemical Engineering Science 56 (2001) 395}402                              399of the catalyst, a...
400                                 M. A. Al-Juaied et al. / Chemical Engineering Science 56 (2001) 395}402Fig. 4. Compari...
M. A. Al-Juaied et al. / Chemical Engineering Science 56 (2001) 395}402                        401concentrations in the fe...
402                                    M. A. Al-Juaied et al. / Chemical Engineering Science 56 (2001) 395}402n        num...
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  1. 1. Chemical Engineering Science 56 (2001) 395}402 Ethylene epoxidation in a catalytic packed-bed membrane reactor: experiments and model M. A. Al-Juaied, D. Lafarga, A. Varma* Department of Chemical Engineering, University of Notre Dame, Notre Dame, IN 46556, USAAbstract A mathematical model was developed for the ethylene epoxidation reaction over a cesium-doped silver catalyst in a packed-bedmembrane reactor (PBMR) and compared with the experimental results. The dusty gas model, based on the Maxwell}Stefanequations, was used to describe transport through the porous stainless-steel membrane. Two reactor con"gurations were investigatedwhere either oxygen (PBMR-O) or ethylene (PBMR-E) permeated through the membrane, with the co-reactant fed to the catalyst bed.The model results were in good agreement with the experimental data. Simulations showed that the imposed pressure gradientresulted in predominantly convective #ow through the membrane, which inhibited backdi!usion of components from the catalyst bed.The variables studied included reaction temperature and inlet reactant concentrations. The model results, as also demonstratedexperimentally, con"rmed that the PBMR-E is the best con"guration, followed by the conventional "xed-bed reactor (FBR) and thePBMR-O, respectively. 2001 Elsevier Science Ltd. All rights reserved.Keywords: Ethylene epoxidation; Ethylene oxide; Membrane reactor; Dusty gas model; Reactor model; Inorganic membranes1. Introduction reactions where by the use of membrane reactors, increase in yield of desired products has been demon- Recent developments in the synthesis of inorganic strated (Lafarga, SantamarmH a & Menendez, 1994; Hmembranes make them attractive for many applications Coronas, Menendez & SantamarmH a 1994; Tonkovich, Hincluding catalytic reactions in aggressive environments Jimenez, Zilka & Roberts, 1996a and Tonkovich, Zilka, H(cf. Bhave, 1991; Hsieh, 1996). Comprehensive reviews of Jimenez, Roberts Cox, 1996b; Pena, Carr, Yeung Hinorganic membrane reactors are available in the litera- Varma, 1998; Lafarga Varma, 2000).ture (cf. Zaman Chakma, 1994; Saracco Spechia, The epoxidation of ethylene to obtain ethylene oxide is1998; Saracco, Neomagus, Versteeg van Swaaij, 1999). an industrially important reaction, as the product isTwo di!erent concepts are used in the inert membrane a valuable intermediate in the chemical industry (cf. Be-reactor applications. In one, the membrane is used to rty, 1983; Van Santen Kuipers, 1987). The reactionpreferentially separate reaction product(s) from an equi- scheme is generally considered to be parallel, with twolibrium-limited reaction, resulting in conversions exceed- competing reactions involved: epoxidation and completeing thermodynamic values. The membrane can also be combustion. Depending on the conditions, a third reac-used to preferentially remove the reaction component(s) tion involving the oxidation of ethylene oxide can alsothat could react further to form undesired product(s), as occur, but its rate is typically much smaller than those ofin the case of consecutive reaction networks. In the other reactions (1) and (2):concept, the membrane is used for segregation and con-trolled addition of one or more reactants through themembrane. An example of this application is the con-trolled addition of reactants for partial oxidation * Corresponding author. Tel.: #1-219-631-6491; fax:#1-219-631-8366. The approach described in this work involves a cata- E-mail address: avarma@nd.edu (A. Varma). lytic packed-bed membrane reactor with an inert porous0009-2509/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved.PII: S 0 0 0 9 - 2 5 0 9 ( 0 0 ) 0 0 2 3 5 - 9
  2. 2. 396 M. A. Al-Juaied et al. / Chemical Engineering Science 56 (2001) 395}402stainless-steel membrane. In order to describe transport The di!usion process in gas phase includes two di!er-through the membrane, several earlier models (cf. ent asymptotic regimes, molecular and Knudsen di!u-Itoh, Shindo, Haraya, Botata, Hakuta Yoshitome, sion, depending on whether collisions between molecules1985; Mohan Govind, 1988; Tsotsis, Champagnie, or molecule}wall, respectively, control the process. EachVasileiadis, Ziaka Minet, 1993) used simplifying de- regime corresponds to a distinct di!usion coe$cient andscriptions such as non-interacting Knudsen #ow. Recent to evaluate the overall value in the transition region, theworks have shown the necessity of using more rigorous Bosanquet formula can be used (Aris, 1975):models, particularly, in the presence of pressure gradient 1 1 1through the membrane (Saracco, Veldsink, Versteeg # , (1) Van Swaaij, 1995; Neomagus, van Swaaij Versteeg, DC DC DC G GK GI1998). where Mechanisms that may contribute to the total transportthrough a porous membrane include Knudsen, mole- 1 L DC DC x , DC DM ,cular, and surface di!usion, as well as viscous #ow. GK 1!x GH H GH GH G HJH$G (2)A proper description of this transport is important for 2r 8R ¹ the design of membrane reactors and for the interpreta- DC N E ,tion of experimental data. The transport process through GI 3 M Gporous media has been investigated extensively and stud- and the other quantities are dened in the Notation.ies have shown that the dusty gas model (DGM) is The simplest model to describe di!usional transport ofa good model to use (Veldsink, Versteeg Van Swaaij, components is the Fick Model (FM):1994 and Veldsink, van Damme, Versteerg VanSwaaij, 1995). The Fick model is simpler than the DGM, DC d(x P) N ! G G , i1,2, n. (3)hence it is frequently used, but DGM is the preferred G R ¹ dr Emodel for description of transport through membranes. We have recently investigated ethylene epoxidation in When a pressure gradient contributes to the totala catalytic packed-bed membrane reactor (PBMR) ex- transport, the Darcy equation can be utilized and resultsperimentally, and demonstrated that signicant improve- in the so-called extended Fick model (EFM):ment in ethylene oxide selectivity and yield can be 1 d(x P) rx P dPachieved over the conventional xed-bed reactor (FBR) N ! DC G # N G , i1,2, n. (4) G R ¹ G dr 8 dr (Pena et al., 1998; Lafarga Varma, 2000). In the present Estudy, we rst report structural characterization of the The above Ficks-law-based models calculate indi-membrane and its permeation characteristics. Then, by vidual component #ows independently of the others. Theusing these independently determined parameters, a reac- di!usion process can be expressed more rigorously ac-tor model based on the DGM #ux relations is used to cording to the Stefan}Maxwell equations, which resultssimulate experimental results for the PBMR. An approx- in the DGM:imate model that decreases computational e!ort signi- L (x N !x N ) Ncantly is also suggested and is compared with the DGM G H H G ! G PDC PDCmodel. The reactor model includes kinetic rate expres- HJH$G GH GIsions determined in a previous study (Lafarga, Al-Juaied, 1 dx x rP dPBondy Varma, 2000). A comparison between the FBR G# G N #1 , i1,2, n. R ¹ dr PR ¹ 8 DC drand PBMR performances is also made for di!erent tem- E E GI (5)peratures and inlet reactant concentrations. The DGM is fundamentally more correct than the EFM because the convective motion is directly incorpor-2. Model development ated into the model and drag e!ects caused by the motion of other components are taken into account,2.1. Gas transport through a porous membrane which are neglected in the EFM (Veldsink et al., 1995). However, the DGM equations are more di$cult to solve As stated above, various mechanisms can govern the numerically. A comprehensive review on the historicaltransport of a gas mixture through porous membranes. background and derivation of the model equations canFor a given mixture, the relative importance of these be found elsewhere (cf. Mason Malinauskas, 1983).mechanisms depends on the permeation conditions (i.e.pressure, temperature, mole fractions) and characteristics 2.2. Membrane reactor modelof the membrane (e.g. pore size and volume, structure,adsorption capacity). In many cases, the transport must A schematic diagram of the membrane reactor set-upbe described by a combination of mechanisms. is shown in Fig. 1. The catalyst is located in the shell (i.e.
  3. 3. M. A. Al-Juaied et al. / Chemical Engineering Science 56 (2001) 395}402 397 expressions (Lafarga et al., 2000): 1.33;10 exp(!60.7/R ¹)P P r E # - , (9) (1#6.50P ) # 1.80;10 exp(!73.2/R ¹)P P r E # - . (10) (1#4.33P ) # The in#uence of internal and external mass transfer resistances for the catalyst was found to be negligible using the Weisz}Prater criterion (Froment Bischo!, 1990), where for the experimental conditions the observ- able was typically of the order of 10. At each reactor axial position, z, the radial permeation #uxes of species i, N , must be determined by solving the G DGM relations. In the present case, for six species (ethy- lene, oxygen, nitrogen, ethylene oxide, carbon dioxide and water) we have six unknown mole fractions (x ), six G unknown #uxes (N ), and the total tube pressure (P ). G R Since there is no reaction in the membrane and the system operates in steady state, the membrane mass Fig. 1. Schematic diagram of the reactor setup. balance equations for all species can be written as !N 0, i1,2,6, r (r(r , z0. (11) G R Qannulus) side. The reactor feed consists of two parts;catalyst bed feed and the membrane tube feed. Reac- The DGM expressions, (see Eq. (5)) provide six addi-tant(s) fed to the tube permeate through the membrane, tional equations. Finally, the sum of mole fractions,react with co-reactants over the catalyst, and exit to- which must be unity, provides the last relationgether. L x 1, r (r(r , z0. (12)2.2.1. Basic model equations G R Q G The steady-state mass balance equations for species i,considering isothermal plug-#ow conditions on both the In order to solve this set of equations, 13 boundarytube and shell sides, with negligible internal and external conditions are required. These correspond to species mole fractions at the tube and shell sides (i.e. rr andmass transfer resistances, are given by R r , respectively), and the total pressure at the shell side of QdF the membrane, P . These equations can be solved numer- RG !2 r N , 0(r(r , z0, i1,2, n, Q dz R G PR R ically using the relaxation technique (cf. Press, Flannery, (6) Teukolsky Vetterling, 1986), where the radial deriva- tives in Eqs. (5) and (11) are replaced with nite di!erencedF approximations for a total of M mesh points on the QG 2 r N # (r !r) (1! )R , interval r (r(r . dz Q G PQ U Q A @ G R Q Relaxation rewards a good initial guess with rapid r (r(r , z0, i1,2, n, (7) convergence. For this, initial guesses of all variables are Q U calculated using the linearized form of the DGMwhere F and F are the axial molar #ow rates of species (Krishna, 1987), where average values for the mole frac- RG QG tions and the total pressure are used, and the gradientsi on the tube and shell sides, respectively, z is the axialdirection, and R is the net reaction rate of species i given are estimated by assuming linear pressure and composi- G tion proles along the length of the di!usion path. Theby equations are solved iteratively until all residuals are smaller than a specied value, typically 10.R r, (8) G GH H The reactor balance ODEs (6) and (7) are integrated by H the Runge}Kutta method for the rst step in the z direc-where ((0 for reactants and 0 for products) is the tion, with the initial conditions at the reactor inlet, the GHstoichiometric coe$cient for species i in reaction j with determined #uxes from solution of the DGM equationsrate r , following the previously determined kinetic rate and a guessed value of P , the tube side pressure. Next, H R
  4. 4. 398 M. A. Al-Juaied et al. / Chemical Engineering Science 56 (2001) 395}402a new step in the axial direction is taken with new values 3.2. Experimental setupfor the initial conditions calculated from the previousstep. To satisfy the mass balance at the reactor exit, the The membrane reactor setup (see Fig. 1) has beenguessed P value is changed (within the experimental described in detail elsewhere (Pena et al., 1998; Lafarga Rrange). The calculation procedure also includes changes Varma, 2000). The PBMR uses a membrane for thein the number of steps in the z direction, and repeats the distribution of ethylene or oxygen from the tube side tocalculations until the overall reactor mass balance is the shell side. The membrane was a 45 mm long 316 ¸satised to a prescribed accuracy (error (0.1%). porous stainless-steel tube (Mott Metallurgical Corp; 0.20 m grade; 10 mm OD) welded to a non-porous2.2.2. Approximate model for membrane transport 316 ¸-SS tube. The membrane was inserted in a 19 mm An approximate model for membrane transport was OD quartz tube (17 mm ID). The catalyst was packedalso formulated. In this model, #ow in the membrane uniformly in the annular space formed between the mem-tube is assumed to be equally divided along the tube brane and the quartz tube. There were two modes oflength. Thus, di!usive transport in the membrane is ne- operation; either ethylene #owed over the catalyst bedglected and #ow is assumed to be purely convective. The and oxygen was distributed across the membranepressure on the shell side, P as shown in the experiments, (PBMR-O) or oxygen #owed over the catalyst bed and Qis 1.08}1.10 bar and on the tube side, P is constant with ethylene was distributed from the tube side (PBMR-E). R the value depending on the #ow condition (Pena et al.,1998). Thus, viscous transport across the membrane is 3.3. Determination of the structural parametersapproximately constant. The DGM calculations showedthat #ow through the membrane is primarily convective In order to calculate species #uxes through the mem-and the di!usive transport typically contributes less than brane, N , the structural parameters should be estimated10% of the total #ow. G independently. These parameters were determined from Using this approximation, the tube side equation (6) is single gas permeation experiments for various gases. Thedropped, and in Eq. (7) N is calculated as F /¸ where same experimental setup described above in the absence G RG¸ is the reactor length. The use of DGM accounts for the of catalyst bed was used to perform the permeationcoupling of convective #ow with the individual partial experiments of di!erent pure gases through the mem-pressure gradient, and permits to assess the magnitude of brane. In the case of pure gas permeation, the DGMbackdi!usion. However, in the present case, the approx- Eq. (5) reduces toimate model also performs rather well, as discussed laterin Section 4.6. 2 r (P !P ) 8 N N R Q G 3 t R ¹M E G3. Experimental r (P !P ) (P #P ) #N R Q R Q . (13) 8 tR ¹ 2 E3.1. Catalyst preparation and characterization A plot of the permeability, N /(P !P ), versus the G R Q average membrane pressure, (P #P )/2, gives a straight The catalyst preparation was based on the procedure R Qdeveloped by Bhasin, Ellgen and Hendrix (1990). The line with slope and y-intercept equal to !Al O pellets (Norton SA 5102, cylindrical, 3 mm r NOD) were pretreated by acid leaching with hydrochloric 8 tR ¹acid and calcined at 11003C for 24 h. The dried pellets Ewere used as support for impregnation with a solution andcontaining silver oxide, cesium hydroxide, lactic acid andhydrogen peroxide. A calcination treatment with N 2r 8 N ,(5003C for 5 h) was then performed to decompose the 3 t R ¹M E Glactic acid. Finally, to stabilize the activity, the catalystwas treated alternatively under oxygen and hydrogen respectively. From these values, the apparent pore radius,#ows (3 h each, 100 sccm) in two oxidation}reduction r , and the value of the porosity to tortuosity ratio, / Ncycles at 3503C. (both based on the assumption that the pores are uni- The nal catalyst contained 13.54 wt.% Ag and 0.005 form-sized and cylindrical), can be calculated directly.wt.% Cs (based on dried weight of the support andreduced catalyst). The support was densely covered with 3.4. Reaction experiments0.3}0.5 m silver crystallites. The silver surface area was925 cm Ag g-cat, while the BET surface area was All experiments were performed with the same batch of0.97 m g-cat. catalyst. The experimental reaction procedure, activation
  5. 5. M. A. Al-Juaied et al. / Chemical Engineering Science 56 (2001) 395}402 399of the catalyst, and the experimental results are described elsewhere (Pena et al., 1998; Lafarga Varma, 2000).During the course of the experiments, the catalyst activ-ity was checked regularly by performing an experiment atstandard conditions. The data were obtained at di!erent inlet reactant con-centrations and catalyst temperatures. The total #ow ratein all the experiments was 200 sccm. The temperaturewas varied in the range 210}2703C for each feed composi-tion. In the xrst set of experiments, oxygen concentrationwas varied over 3, 6, 9 and 12%, while maintainingethylene concentration xed at 6%. In the second set,ethylene concentration was varied over 3, 6, 9 and 12%,while maintaining oxygen concentration xed at 6%.These concentrations are based on the overall composi- Fig. 2. Permeation measurements of helium, nitrogen and oxygention and not of the separated feed. The diluent in all the through the membrane plotted according to Eq. (13).experiments was nitrogen and the molar ratio betweenthe nitrogen introduced with ethylene (N ) and oxygen #(N ) was held xed at N /N 1.5. - # - For all the di!erent feed compositions and temper-atures, the performance of PBMR (with ethylene or oxy-gen permeating through the membrane) was comparedwith the conventional FBR. The latter was achieved byco-feeding ethylene and oxygen (mixed feed) from theshell side in the same reactor setup, with the membraneinlet plugged, thus, behaving as a solid non-porous tube.4. Results and discussion In this section, we describe results of the PBMR model as compared with the experiments (Pena et al., 1998), andalso present results for the FBR under the same reaction Fig. 3. Flux prole as a function of distance along the reactor for PBMR-O at 3% oxygen and 12% ethylene in feed.conditions. As noted above, the PBMR was operated intwo modes by distributing either the oxygen (PBMR-O)or ethylene (PBMR-E) from the tube side with an appliedpressure gradient to the shell side containing the catalyst. membrane tube to the shell side, and negative in the opposite direction. As shown, there is no product transfer4.1. Pure gas permeation results from the shell to the tube side, due to high pressure drop across the membrane and the relatively small driving Fig. 2 shows results of the permeation experiments force as compared to the feed components. Near thewith pure oxygen, nitrogen, and helium presented graphi- reactor inlet, ethylene di!uses from the shell to the tubecally according to Eq. (13). The average r and / values side in the uphill direction of #ow. Later, as the concen- Nwere calculated from the slope and y-intercept to be 93.7 tration of ethylene increases in the tube, it reverses itsand 0.167 nm, respectively. These, together with Eq. (13), direction because of the convective #ow, in spite of thelead to the dashed lines shown in the gure, where a good opposing ethylene partial pressure gradient. It is clearagreement with the experimental data may be observed. that since oxygen is consumed by reaction on the shellThese average values are used in the subsequent calcu- side, its #ux change is larger than for nitrogen. Similarlations. results are also found for the PBMR-E, but in this case the nitrogen permeation #ux is higher since N N . # -4.2. DGM predictions and evaluation of backdiwusion 4.3. Comparison of PBMR-O experiments with model Fig. 3 shows the #ux proles in PBMR-O (12% ethy- predictionslene and 3% oxygen in the feed) along the reactor length.The arrows indicate the directions of mass transfer, Fig. 4 presents a quantitative comparison between thewhere the #ux is positive when the transport is from the experiments and the PBMR-O model predictions for
  6. 6. 400 M. A. Al-Juaied et al. / Chemical Engineering Science 56 (2001) 395}402Fig. 4. Comparison of PBMR-O experimental (lled symbols) andcalculated (open symbols) results. Selectivity to ethylene oxide vs. Fig. 5. Comparison of PBMR-E experimental (lled symbols) andethylene conversion for various feed oxygen levels at 6% ethylene. calculated (open symbols) results. Selectivity to ethylene oxide vs. ethylene conversion for various feed oxygen levels at 6% ethylene.selectivity to ethylene oxide as a function of ethyleneconversion, for di!erent levels of oxygen in the feed. Thestructural parameters of the membrane determined inSection 4.1 were used in the simulations. No other adjust-able parameters were used. Both the experiments and thecalculations show that ethylene oxide selectivity increaseswith oxygen concentration in the feed and decreases withincrease of temperature. As for the FBR (Lafarga et al.,2000), the model predicts the experimental results satisfac-torily, but the deviations increase for lower P /P ratios. - #The reason for this is that the kinetic expressions (9) and(10) are not as accurate for low oxygen concentrations,and this problem becomes more acute for the PBMR-O asthe O level is relatively low over the entire catalyst bed. Similar conclusions can also be drawn for the casewhere ethylene concentration is varied in the feed, whilemaintaining the oxygen concentration xed. In this case,the selectivity increases as ethylene concentration de-creases. In general, as noted earlier, high oxygen to ethy-lene ratio increases the selectivity to ethylene oxide.4.4. Comparison of PBMR-E experiments with modelpredictions Fig. 5 shows a comparison between the model predic-tions and the experimental results for various levels ofoxygen. Both, the experiments and the calculations, ex-hibit the same features as the PBMR-O (Section 4.3) Fig. 6. Comparison of experimental (lled symbols) and calculatedregarding the variations of reactant concentrations and (open symbols) results for the di!erent reactor congurations. Selectiv-temperature. However, the model match is better for the ity to ethylene oxide at 12% ethylene conversion vs. (a) oxygen concen-PBMR-E as compared to the PBMR-O, because now the tration in feed at 6% ethylene, and (b) ethylene concentration in feed at 6% oxygen.e!ect of low oxygen to ethylene ratio is less pronounced.4.5. Comparison of diwerent reactor conxgurations results for the two PBMR congurations as well as the To summarize the results, in Fig. 6 a comparison is FBR. The selectivity to ethylene oxide is shown as apresented between the model and the experimental function of oxygen (Fig. 6a) and ethylene (Fig. 6b)
  7. 7. M. A. Al-Juaied et al. / Chemical Engineering Science 56 (2001) 395}402 401concentrations in the feed at 12% ethylene conversion. In case (typically less than 10%). Both models require noall cases, for both the experiments and model, selectivity adjustable parameters. However, the DGM is more gen-to ethylene oxide increases when oxygen concentration erally applicable because it includes both the viscous andincreases or ethylene concentration decreases. The gure di!usion transport mechanisms. It was important in thealso shows the important conclusion that, for all reaction present study to assess the backdi!usion e!ect, whichconditions, the relative performance is in the order cannot be done using the approximate model.PBMR-EFBRPBMR-O.4.6. PBMR simulations using approximate model for 5. Concluding remarksmembrane transport This study provides a mathematical model that The approximate model for membrane transport de- describes the performance of a packed bed membranescribed in Section 2.2.2 was compared with the DGM. reactor (PBMR) for the ethylene epoxidation reactionFigs. 7a and b show results of the DGM and approxim- network. The model uses intrinsic reaction kinetics, plug-ate models for PBMR-O and PBMR-E at 12% oxygen #ow behavior over the packed bed catalyst and the dustyand 6% ethylene feed, respectively. gas model (DGM) for membrane transport. A good Clearly, the DGM compares well with the experi- agreement between the model and experimental resultsmental results. Further, predictions using the approxim- was obtained. The model deviations were noticeable inate model are relatively close to those obtained from the a few cases for the PBMR-O, particularly at low oxy-DGM model. Similar results were also found at other gen/ethylene ratios where the oxygen conversion is high,feed reactant concentrations. The good agreement be- because the kinetic expressions utilized (Lafarga et al.,tween the two models is due to the fact that the di!usive 2000) are not as accurate for low oxygen concentrations.transport contribution is relatively small in the present The model results showed that the use of a membrane for feed distribution leads to improvements in selectivity and yield to ethylene oxide as compared to a FBR. In the PBMR-E conguration, the local partial pressure of ethylene is reduced relative to a FBR, due to segregation of ethylene across the membrane, and, as a result, the selectivity to ethylene oxide is larger. On the other hand, the selectivity in a PBMR-O is lower because the local oxygen concentration is lower than in a FBR. The model faithfully reproduced all experimental ob- servations. Specically, as observed in the experiments, the model demonstrated increased selectivity to ethylene oxide as oxygen concentration increased or the temper- ature decreased. It showed that the reactor performance is in the order PBMR-EFBRPBMR-O. An ap- proximate reactor model was also developed, where #ow through the membrane was assumed to be uniform over its entire length. Predictions of this model were relatively close to those obtained using the DGM, because convec- tive #ow dominates over di!usion for the membrane utilized. In general, the developed reactor model can be used successfully for predicting and optimizing operating conditions for ethylene epoxidation in packed-bed mem- brane reactors. It can also be adapted for use with other reaction systems. Notation D Knudsen di!usion coe$cient of component GI i, m sFig. 7. Comparison of DGM (open circles) and approximate (open D binary di!usion coe$cient of species i in j, m striangles) model results for 6% ethylene and 12% oxygen feed. Selectiv- GHity to ethylene oxide vs. ethylene conversion for (a) PBMR-O, and (b) ¸ reactor length, mPBMR-E. M molecular weight of component i, Kg mol G
  8. 8. 402 M. A. Al-Juaied et al. / Chemical Engineering Science 56 (2001) 395}402n number of components Itoh, N., Shindo, Y., Haraya, K., Botata, K., Hakuta, T., Yoshitome, H.N #ux of component i, mol m s (1985). Simulation of a reaction accompanied by separation. Inter- G national Chemical Engineering, 25, 138}142.P total pressure, Pa Krishna, R. (1987). A simplied procedure for the solution of the dustyP partial pressure of component i, bar G gas model equations for steady state transport in non-reactingr radial coordinate, m systems. Chemical Engineering Journal, 35, 75}81.r rate of reaction j, mol kg s Lafarga, D., Al-Juaied, M. A., Bondy, C. M., Varma, A. (2000). H Ethylene epoxidation on Ag-Cs/ -Al O catalyst: Experimentalr pore radius, m N results and strategy for kinetic parameter determination. IndustrialR universal gas constant (8.314 J mol K) E and Engineering Chemistry Research, 39, 2148}2156.t membrane thickness, m Lafarga, D., SantamarmH a, J., Menendez, M. (1994). Methane oxidative H¹ temperature, K coupling using porous ceramic membrane reactors-I. Reactor devel-x mole fraction of species i opment. Chemical Engineering Science, 49, 2005}2014. G Lafarga, D., Varma, A. (2000). Ethylene epoxidation in a catalyticz axial coordinate, m packed-bed membrane reactor: E!ects of reactor conguration and 1,2-dichloroethane addition. Chemical Engineering Science, 55,Greek letters 749}758. porosity Mason, E. A., Malinauskas, A. P. (1983). Gas transport in porous viscosity, Pa s media: The Dusty Gas model; Chemical Engineering Monographs, 17. density, kg m Amsterdam: Elsevier. tortuosity Mohan, K., Govind, R. (1988). Analysis of equilibrium shift in isothermal reactors with a permselective wall. A.I.Ch.E Journal, 34, Weisz}Prater parameter 1493}1503. Neomagus, H. W. J. P., van Swaaij, W. P. M., Versteeg, G. F. 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