ARTICLE pubs.acs.org/IECR
Sensitivity Analyses for a Membrane Reactor with Cooling Tubes Based on a Simplified Asymmetric Unit H. Inchaurregui Mendez,† F. Tiscare~no Lechuga,*,† and A. Ramírez Serrano‡ †
Departamento de Ingeniería Química, Instituto Tecnologico de Celaya, Avenida Tecnologico S/N, Col. Fovissste, C.P. 38010, Celaya, Guanajuato, Mexico ‡ Facultad de Química, Universidad Autonoma del Estado de Mexico, Paseo Colon esquina Paseo Tollocan S/N, Cipres, 50120 Toluca, Estado de Mexico, Mexico ABSTRACT: A simplified asymmetric unit is proposed as a guide to optimize the internal arrangement of a membrane reactor with cooling tubes. This configuration is similar to a shell and tube heat exchanger, but some of the tubes are membranes. The internal layout has a lot of possible combinations, and its optimization could be considered as an art. A 3D model was developed by adapting a transient 2D model and was solved with Comsol Multiphysics 3.5a, a finite element software. Employing deforming mesh module of Comsol, the internal dimensions and meshing of the simplified unit were dynamically readjusted to allow the sensitivity analysis of one geometric design variable. Interpretation of the results provides good initial estimates on how many membrane and cooling tubes must be assayed so the number of configurations that need to be evaluated is reduced.
’ INTRODUCTION A membrane within a reactor can, in principle, selectively remove one of the products and thus shift the equilibrium toward higher conversions for reversible reactions. Initially it was believed that ceramic membranes with low selectivities based on Knudsen diffusion would suffice to remove hydrogen from other hydrocarbons in dehydrogenation reactions;1,2 however, it was demonstrated that the conversion increased observed in the laboratories with these ceramic membranes were due to dilution of the reacting mixture instead of the selective removal of hydrogen.3 Membranes with higher permselectivities (palladium membranes) were also employed to study dehydrogenation reactions and the concept was proven for dehydrogenation reactions under isothermal conditions.4-6 Membrane reactor applications which involve removal of hydrogen are associated with endothermic reactions for with adiabatic operation is economically unfeasible.7 For an endothermic reaction, a temperature decrease also reduces the equilibrium constant for these reversible reactions and leads to operating conditions where the membrane does not represent a real contributor factor. These arguments lead to the consideration of a heated membrane reactor. Cordova8 studied a modified Costner-Badger process with a heated membrane reactor and conducted an economical analysis that showed that this application was still economically unfeasible. Membrane reactors also have been considered as a promising alternative to increase the yield of partial oxidation reactions.9-14 For these highly exothermic reactions the selectivity can be improved by the selective addition of reactants without sacrificing the conversion. Oxygen is dosed by the membrane not only diminishing the formation of undesirable byproduct but also contributing to a safer operation. At laboratory scale, several research groups have reported successful results in which a membrane reactor outperforms conventional reactors.15,16 However, no evidence has been found regarding an industrial r 2010 American Chemical Society
application of membrane reactors to carry gas phase reactions at high temperatures. Adiabatic operation of membrane reactors for partial oxidation reactions involves highly exothermic reactions, and the temperature will axially increase. This leads to the consideration of membrane reactors with cooling tubes which not only would help maintain the temperature profiles with favorable selectivity but also further improve the safety of the equipment. Ramirez et al.17 justified and developed a 3D model for a membrane reactor with cooling tubes. The reactor involved some membrane tubes and some cooling tubes arranged in a configuration similar to a tube-and-shell heat exchanger. The catalyst is packed in the shell side. Inclusion of the heat exchanger tubes led to flatter temperature profiles which resulted in better performance; however, configurations considered in that work were not formally optimized due not only to the large number of operating conditions but also to the numerous combinations of design variables and possible arrangements. Membrane reactors have been extensively studied for the last three decades as an alternative to overcome equilibrium limited reactions or to improve the yield by dosing one of the reactants.13,18-20 Even though both alternatives have been proven in the laboratory under near isothermal conditions, this technology is still waiting as a candidate for industrial implementation. One factor that could promote their application for partial oxidation reactions would be including cooling tubes and achieving an internal membrane reactor configuration that maintains operating
Special Issue: IMCCRE 2010 Received: March 26, 2010 Accepted: June 28, 2010 Revised: June 25, 2010 Published: July 20, 2010 2683
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in molar flow rates, pressure, and average temperature. For the reacting chamber, ! DNi De D2 Ni D2 Ni ¼ þ 2 -FB rpi ð1Þ Dz us Dx2 Dy ! X FB ð-ΔHr Þrp DT ke D2 T D2 T r ¼ þ Dz us Fcp Dx2 Dy2 us Fcp
Figure 1. Two of the possible configurations for reactor membrane with heat exchanger tubes: (a) square pattern and (b) hexagonal pattern.
conditions for which the inclusion of membranes in fact presents advantages.17 In this work, a simplified asymmetric unit is employed to suggest proper ratios between membrane, cooling tubes, and packed-bed volume for a membrane reactor with cooling tubes. The idea is to have a tool to conduct sensitivity analyses to help in prioritizing some of the design variables and operating conditions. For instance, radii of the membrane tubes and the cooling tubes would be varied freely during an analysis to evaluate the reactor performance; it is clear that these tubes would be available only for a few fixed diameters, especially the membrane tubes; however, information regarding the proper membrane and cooling tube areas for a given catalyst load would suggest the relative number of tubes that should be accommodated. This guide should narrow down the number of possible configurations that need to be further considered.
’ THEORY Asymmetric Units for the Membrane Reactor. Figure 1 depicts two configurations for a membrane reactor with cooling tubes. The configuration is similar to a tube-and-shell heat exchanger with the difference that in addition to the cooling tubes (labeled with T) there are some membrane tubes (labeled with M). The shell side is assumed to be packed with catalyst. Membrane and cooling tubes are arranged with square and hexagonal patterns. The true asymmetric unit for this square configuration is 1/8 of complete cross section, while for this hexagonal configuration it is 1/12. Solutions for these true asymmetric units are particular so any slight modification of the internal tube arrangement will require a reprogramming and a recalculation of everything.17 The idea of the simplified asymmetric unit proposed in this work is that, for a given reactor with a large number of membranes and cooling tubes, a simplified asymmetric unit can satisfactorily describe the behavior of the center region. In this section, the neighboring tubes follow the same arrangement in all directions and the corresponding profiles are not significantly affected by the irregular tube arrangements near the reactor wall. If the section located outside the dotted circle in Figure 1 is to be considered, then the particular true asymmetric unit must be solved. Approximated results from the simplified asymmetric unit are intended for preliminary sensitivity analyses. Model Description. The mathematical model involves molar and energy balances based on fluxes and temperatures considering effective transport coefficients.11,17,21,22 Within the packedbed section, plug flow is assumed; however, the local linear velocity is recalculated at each axial position based on the changes
ð2Þ
where Ni = usCi is the molar flux for component i, subscript r refers to each of the independent reactions, and rp is the catalytic reaction rate. Equation 1 must be repeated for each one of the stoichiometrically independent chemical species. Inside the membrane tube no reaction occurs and the corresponding mass balance is ! DGi Dm D2 Gi D2 Gi ¼ þ 2 ð3Þ Dz um Dx2 Dy where Gi is the molar flux of oxygen inside of membrane. Heat transfer across the membrane was neglected for purposes of this model but could be easily included. Inside the cooling tubes a flat cross sectional temperature profile was assumed; therefore, its energy balance involves an ordinary differential equation that considers heat transfer across its perimeter: Z ai dTci hci ðTci -TÞ ¼ dai ð4Þ dz F ci cpi 0 where ai is the perimeter of the heat exchanger tube of the simplified asymmetric unit. Equation 3 implies tridimensional profiles within the membrane tube while eq 4 considers that the temperature in the cooling tubes changes only in the axial direction. The model can be easily adapted so the lumen of the tubes, membrane or cooling, present either radial profiles or flat profiles. Radial profiles are mentioned only because of the basic geometry of a tube; however, the mass and energy balances are given in Cartesian coordinates because these coordinates are actually employed to solve the model with the finite element software. Oxidation of ethylene was selected as case of study because it is an important partial oxidation reaction that has been studied with membrane reactors.15,23 The system of independent reactions considered is k1
2C2 H4 þ O2 sf 2C2 H4 O k2 2 1 2 C2 H4 þ O2 sf CO2 þ H2 O 3 3 3 Rate constants, transport parameters, physical properties, and justification for the several assumptions can be found elsewhere.17 In particular for the square simplified asymmetric unit, dimensions for the base case and initial conditions for each section were (i) reacting chamber, 171 mol/min of ethylene and 19 mol/min of inert at 220 °C and 10 bar; packed cross sectional area of 0.65 cm2; (ii) membrane tube, 84 mol/min of oxygen at 220 °C and 1.5 bar; radius of 0.4762 mm; and (iii) cooling tubes, 6,000 cm3/min of oil at 220 °C and 1.013 bar; radius of 6.35 mm. The model is solved with Comsol Multiphysics 3.5a24 and the assumptions involved allow the implementation of 3D model by adapting a 2D-transient model.17 2684
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Figure 2. Boundary conditions of the simplified asymmetric unit.
Boundary Conditions for the Simplified Asymmetric Unit. Figure 2 details the boundaries associated with a square asymmetric unit. The only difference between triangular, square, or hexagonal patters is related to the two internal angles of the corresponding right triangle asymmetric units. The unit includes only the three sections inside the right triangle. Since this model is intended as a tool to narrow down the possible tube arrangements, the wall thicknesses of the membrane and cooling tubes have been neglected. Boundaries I-VII involve symmetry conditions. Boundary VIII allows permeation of oxygen but energy transfer is neglected since the membrane is assumed to be made of a poor heat conductor. If proper parameters would be available, the model can be changed to consider both conduction through the membrane wall and the sensible heat transferred by the permeating species. Boundary IX involves only heat transfer because the cooling tube is impermeable. However, since a flat profile was chosen for the lumen of the cooling tube and the external temperature next to this wall changes with position, calculation of the heat transfer must include integration over the perimeter. Deformed Mesh with Parameterized Geometry. Optimization or sensitivity analysis while employing software based on finite element can fall in two categories: (1) manipulation of operating conditions such as inlet flow rates, compositions or temperatures; and (2) manipulation of design variables such as internal dimensions or even the modification of the layout. Changing the values of operating conditions is relatively simple; however, changing internal dimensions requires additional capabilities from the software because it needs to readjust the dimensions and remesh the different domains. Consequently, an explanation follows on how some these adjustment were accomplished with Comsol Multiphysics. The radius of the cooling tube was chosen as the first variable to be manipulated, and for comparison purposes it was decided to keep constant the area of the packed-bed cross section. As a consequence the radius of the membrane tube was also kept constant. Figure 3 presents two simplified asymmetric units while the radius of the cooling tube is swept. Figure 3a shows the base case while Figure 3b shows the adjusted unit. The dotted lines within the adjusted unit correspond to the boundaries of the base case. Gray areas correspond to tubes and the white area corresponds to the packed-bed region. Since the packed-bed area was held constant, areas 1 and 2 depicted in Figure 3b are equal. The total size of the asymmetric unit increases if the cooling tube increases; however, the study could also maintain constant the size of the asymmetric unit while adjusting something else, that is, packed-bed area. The radius of the membrane tubes will be
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Figure 3. Readjustment of the internal dimensions of the simplified asymmetric unit while sweeping the cooling tube radius: (a) base case; (b) with displacement of its dimensions.
Figure 4. Temperature profiles for the true asymmetric unit at the exit of a membrane reactor with cooling tubes. Time simulation = 197 s; degrees of freedom = 34 571.
maintained constant since they are available only for very limited dimensions. Although meshing is not shown in these figures, adjusting the dimensions of the asymmetric unit requires each domain to be remeshed. Parameterized geometry and moving mesh are two tools available with Multiphysics 3.5a that allowed sweeping one of the design variables, in our case, the diameter of the cooling tubes.25 For showing purposes four tube diameters were considered: 6.35, 9.525, 12.7, and 15.875 mm corresponding to 3/8, 1/2, 3/4, and 1 in. Any given number of displacements can be applied with the tool Deformed Mesh with Parameterized Geometry by properly defining a list within the following menu of Comsol 3.5a: Model Navigator/Mode Application/Parameterized Geometry/Physics/ Point Settings/Data Entry Menu.
’ RESULTS Figure 4 presents the cross-section temperature profiles at the exit of the reactor for the true asymmetric unit associated to Figure 1a. These profiles refer only to the packed-bed region that would be analogous to the shell side of a tube and shell heat exchanger. Diameters for the membrane and cooling tubes correspond to the base case, 4.762 and 6.35 mm, respectively. 2685
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Figure 7. Axial average temperature profiles for the simplified asymmetric unit and for regions R1-R8 given in Figure 4. Figure 5. Ethylene oxide concentration profiles for the true asymmetric unit at the exit of a membrane reactor with cooling tubes. Simulation time = 197 s; degrees of freedom = 34 571.
Figure 8. Axial average temperature profiles for simplified asymmetric units with displacement of cooling tubes radius.
Figure 6. Temperature profiles for the simplified asymmetric unit at the exit of a membrane reactor with cooling tubes. Simulation time = 6 s; degrees of freedom = 806.
Its internal lay out has not been optimized. It is only included for comparison purposes and to justify the simplified asymmetric unit. Inspection of Figure 4 around the central region reveals that profiles around the membrane tubes or around the cooling tubes are locally similar. Closer to the outer diameter of the reactor, the tube arrangement is not uniform and each tube is no longer surrounded with similar profiles. This outer region is labeled R7 and R8. It can be observed that around the only membrane tube that is completely inside region R8, the temperature increased close to 300 °C because not enough cooling was provided, while, around the three cooling tubes completely inside region R8, the temperature dropped significantly because not enough oxygen was available. Figure 5 shows the product concentration profiles at the reactor. Visual inspection reveals that profiles around each membrane or cooling tube follow nearly the same pattern for all the tubes inside radius R6. Although not presented, consistent
observations can be observed from equivalent figures corresponding to both reactants. Results from Figures 4 and 5 suggest that a good approximation could be achieved by using a smaller asymmetric unit that would acceptably represent the center region of a reactor providing the existence of a large number of membrane and cooling tubes. Unit cells noted in Figure 1 and the corresponding asymmetric units were labeled as simplified to emphasize their implications. Figure 6 shows the cross sectional temperature profile for the simplified asymmetric unit with the base case dimensions. Upper and lower limits of the color scale of Figure 5 are the same to those of Figure 4 so the profiles can be directly compared. It can be seen that by applying mirror imaging of simplified asymmetric unit, the central region (R1 up to the segment labeled R6) could be acceptably constructed. Although it is not its main justification, employing a simplified asymmetric unit significantly reduces the computing time and memory requirements. Comsol Multiphysics has its own meshing protocols; therefore, it was not possible to extend the exact meshing form the simplified asymmetric unit to the true asymmetric unit. As an effort to have a fair comparison, true and simplified asymmetric units were solved with 34 571 and 806 degrees of freedom, respectively. Computing time was reduced from 197 to 6 s using a Xeon 2.83 GHz 8 GB RAM workstation. 2686
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Figure 9. Cross section temperature profiles at the exit of three simplified asymmetric units with different cooling tube radii.
Figure 10. Oxygen concentration profiles at the exit of three simplified asymmetric units with different cooling tube radii.
Figures 4 and 6 refer to bidimensional temperature profiles at the exit of the reactor. Figure 7 presents the axial profiles for the average temperatures of the packed-bed cross-section area. Represented by continuous curves, average temperatures were calculated from the center of the reactor up to the outer radius of a given labeled region. For example, average temperature R6 also considers regions R1 through R5. Inspection of these curves reveals that average profiles from R1 to R6 overlap, there is a small deviation for average profile R7 while the deviations for average profile R8 are significant. The figure also includes the axial profile for the average temperature of the simplified asymmetric unit which is given with data points so the overlapping can be noticed. It can be concluded that the average profile of the simplified asymmetric unit exhibits excellent agreement with the average profiles for the center region up to R6. Displacement of the Cooling Tube Radius. While keeping constant the membrane tube radius, the packed-bed area, and the variables associated with three feeds, increasing the cooling tube radius will decrease the average temperature profile and influence the selectivity and yield. Figure 8 presents the variation of the average temperature with the axial position and the cooling tube radius. The base case is distinguished by a thicker curve. Near the entrance of the reactor the variations with the cooling tubes radii are relatively small but they become more important for the second half of the reactor. It should be noted that operating conditions associated with the feeds to the membrane and cooling tubes, and to the reacting chambers, have not been optimized. For instance, it is possible to directly feed some oxygen to a packed-bed section while, in the present stage of this model, it was
assumed that oxygen only enters through the membranes. Inspection of the profiles suggests increasing the inlet temperature to the packed-bed region; however, we are planning to explore this and other optimization issues in the future. Figures 9-11 present profiles for temperature and concentrations of oxygen and ethylene oxide at the exit of membrane reactors with cooling tubes radii of 6.3, 12.7, and 15.875 mm. The limits in the color scale are the same within each figure so a direct comparison can be done. These figures also include the average temperature or concentration for each cooling radius. Each unit includes the dimensions of the base case with solid black ink; however, the color profiles presented correspond to the displaced cooling tube radius. For each simplified asymmetric unit, Figure 9 shows that the hot spots are closer to the membrane tube where the second reactant enters while the lower temperatures are around the cooling tubes. Increasing the radius of the cooling tube increases the heat removed from the reacting chamber. Decreasing the temperature reduces the reaction rates and the heat released by these exothermic reactions. Oxygen profiles included in Figure 10 show that mass transfer across the selected membrane is relatively slow at the exit of the reactor. Oxygen concentrations quickly drop around the membrane leaving packed-bed areas that simply do not get oxygen. It is evident that at the exit conditions, the rate of reaction is fast compared to the rate at which oxygen is supplied by the membrane. The internal layout must be optimized according to the specific properties and dimensions of the available membranes. Inspection of the temperature profiles as a first impression seemed to indicate that cold regions may be due to excessive heat 2687
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Figure 11. Ethylene oxide concentration profiles at the exit of three simplified asymmetric units with different cooling tube radii.
removed by the cooling tubes; however, the evidence shown in Figure 9 indicates that lack of oxygen in these areas is the main cause. Since a larger cooling tube diameter involves smaller average temperatures and reaction rates, the average oxygen concentration increased with increasing cooling tube radius. Ethylene profiles were not included because this reactant is fed in excess. Figure 11 includes concentration profiles for the main product. Most of this product was produced in the areas near the membrane; however, through the cross section the product concentrations are greater than 0.55 mol/m3. It should be noticed that some product flowing through the colder sections was produced in the hotter sections and then transferred to the colder sections. The simplified asymmetric unit with the smallest cooling tube achieves the highest conversion but also the lowest yield. Yields are proportional to ethylene oxide concentrations. Larger cooling tubes resulted in lower average temperature and, for these cooling tube radii, achieved higher yields, 0.681 mol/m3 compared to 0.670 or 0.659 mol/m3. These results support the justification of including cooling tubes to keep favorable temperature profiles within the membrane reactor. Activation energy for the main reaction is smaller than that of the secondary reaction; therefore, increasing the temperature will increase conversion but decrease selectivity, a trade-off that makes the optimization process more challenging but also more interesting. A limited number of results regarding the sensitivity analysis of the cooling tubes radius were presented for a configuration that is yet to be optimized. Optimization of the proposed configuration with membrane and cooling tubes is extremely complex. However, the results presented give evidence that the deforming mesh module of Comsol can be a valuable tool to analyze and optimize a membrane reactor with cooling tubes that involves a 3D model. Properties and dimensions of suitable membranes correspond to only very few options, therefore if more oxygen is to be provided then a configuration must be assessed that includes more membrane tubes per packed-bed area per cooling tube.
’ CONCLUSIONS A simplified asymmetric unit was proposed which can represent acceptably the performance of a membrane reactor with cooling tubes if the number of membrane and cooling tubes is relatively large and the arrangement pattern is uniform. This unit can be employed in parametric sensitivity analysis to assess the relative importance of the internal dimensions that are suitable to be modified. Deforming mesh module of Comsol Multiphysics is a
valuable tool that allows conducting sensitivity analyses by sweeping one of these parameters at a time. This software solves the models with finite element techniques and remeshing is necessary during each parametric sweep. Even though the optimization of a membrane reactor with cooling tubes was not yet directly attempted due to its complexity, results presented provide some guide regarding on which operating or design variables the efforts should concentrate in the early assessments. A large number of tubes could be unpractical; however, for a configuration with smaller numbers of membrane and cooling tubes, analysis of a simplified asymmetric unit would provide useful information regarding the relative number of membrane and cooling tubes that must be tried, thus reducing the number of configurations that need to be evaluated. The optimal configuration will directly depend on the particular kinetics for a given reaction system and on the transport parameters associated with the membrane and cooling tubes. Rigorous optimization would require considering a large number of operating and design variables. The proposed simplified asymmetric unit could be employed not only to preoptimize those variables but also to provide an expedite comparison with other regular arrangement patterns. For example, if more membrane area is needed per cooling tube, the hexagonal configuration presented in Figure 1b could be explored. Near future optimization studies can involve objective functions associated only with the performance reactor, that is, yield, but eventually we would like to consider process costs and evaluate the economical feasibility of a membrane reactor with cooling tubes.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ NOMENCLATURE a = perimeter (cm) ci = molar concentration of species i (mol/cm3) Cp = heat capacity (cal/(mol K)) De = effective diffusivity in the shell (cm2/s) De = effective diffusivity in the shell (cm2/s) Dm = effective diffusivity in the membrane (cm2/s) Fi = molar flow (mol/s) Gi = molar flux of species i in the membrane (mol/s cm2) hc = film of heat transfer coefficients (cal/cm2 s K) Hi = enthalpy of the species i (cal/mol) 2688
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Industrial & Engineering Chemistry Research k = reaction rate constant (cm3/g s) ke = effective conductivity (cal/cm s K) Ni = molar flux molar of the species i (mol/s cm2) n = unit normal vector Pi = partial pressure of the species i (bar) Pm = permeability of the species i (cm3/s cm2 s bar) PT = total pressure (atm) Q = Heat flux (cal/cm2 s) Rg = Gas constant S = Cross-sectional area at planes (cm2) T = Absolute temperature (K) um = Superficial velocity in the membrane (cm/s) us = Superficial velocity (cm/s) x, y, z = Cartesian coordinates (cm) rt = Cooling tube radius (mm) Subscripts
m = membrane t = cooling tube B = bed catalytic j = number of tube i = species i r = reaction number ref = reference Greek Symbols
G = density (kg/cm3) r = Nabla operator
’ REFERENCES (1) Al-Sahali, M.; Ettouney, H. M.; Albusairi, B.; Lababidi, H.; AlHulaila, H. Non-isothermal Non-adiabatic Dehydrogenation of Cyclohexane in Catalytic Membrane Reactors. Sep. Sci. Technol. 2007, 42, 2081–2097. (2) Armor, J. N. Applications of Catalytic Inorganic Membrane Reactors to Refinery Products. J. Membr. Sci. 1998, 147, 217–233. (3) Tiscare~no, F.; Hill, C.; Anderson, M. Effect of Dilution in the Experimental Dehydrogenation of Cyclohexane in Hybrid Membrane Reactors. J. Membr. Sci. 1996, 118, 85–92. (4) Gobina, E.; Hou, K.; Hughes, R. Ethane Dehydrogenation in a Catalytic Membrane Reactor Coupled with Reactive Sweep Gas. Chem. Eng. Sci. 1995, 50 (14), 2311–2319. (5) Fernandes, F.; Soares, A., Jr. Methane Steam Reforming Modeling in a Palladium Membrane Reactor. Fuel. 2006, 8, 569–573. (6) Lee, D.; Hacarlioglu, O. P. The Effect of Pressure in Membrane Reactors: Trade-off in Permeability and Equilibrium Conversion in the Catalytic Reforming of CH4 with CO2 at High Pressure. Top. Catal. 2004, 29, 1–2. (7) Saucedo, J. A.; Tiscare~no, F.; Cordova, A. Thermochemical Effect on the Economical Feasibility of Membrane Reactors for Dehydrogenation Process. Proc. Eng. Membr. 2002, 1, 150–156. (8) Cordova Quir oz, A. V. Estudio de la Viabilidad para Reactores con Membranas y Calentamiento en la Deshidrogenacion de Etilbenceno (Feasibility Study of the Membrane Reactor and Heating in the Dehydrogenation of Ethylbenzene). Ph.D. Thesis, Instituto Tecnologico de Celaya, Mexico, 2003. (9) Dalmon, J.; Cruz-Lopez, A.; Farrusseng, D.; Guilhaume, N.; Iojoiu, E.; Jalibert, J.; Miachon, C.; Mirodatos, C.; Pantazidis, P.; RebeilleauDassonneville, M.; Schuurman, Y.; Van Veen, A. Oxidation in Catalytic Membrane Reactors. Appl. Catal. A: General 2007, 325, 198–204. (10) Al-Juaied, M. A.; Lafarga, D.; Varma, A. Ethylene Epoxidation in a Catalytic Packed-Bed Membrane Reactor: Experiments and Model. Chem. Eng. Sci. 2001, 56, 395–402. (11) Baker, R. W. Membrane Technology and Applications; Wiley: New York, 2004.
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(12) Hsieh, H. P. Inorganic Membranes for Separation and Reaction; Membrane Science and Technology Series, Vol. 3; Elsevier Science: New York, 1996. (13) Mcleary, E. E.; Jansen, J. C.; Kapteijn, F. Zeolite Based Films, Membranes and Membrane Reactors: Progress and Prospects. Microporous Mesoporous Mater. 2006, 90, 198–220. (14) Sanchez, M. J. G.; Tsotsis, T. T. Catalytic Membranes and Membrane Reactors; Wiley: New York, 2002. (15) Pe~ na, M. A.; Carr, D. M.; Yeung, K. L. Ethylene Epoxidation in a Catalytic Packed-Bed Membrane Reactor. Chem. Eng. Sci. 1998, 53, 3821–3834. (16) Lafarga, D.; Al-Juaied, M. A.; Bondy, C. M.; Varma, A. Ethylene Epoxidation on Ag-Cs-Al2O3 Catalyst: Experimental Results and Strategy for Kinetic Parameter Determination. Ind. Eng. Chem. Res. 2000, 39, 2148–2156. (17) Ramírez Serrano, A.; Tiscare~ no-Lechuga, F.; Ochoa-Tapia, J. A. Three-Dimensional Model of a Membrane Reactor Configuration with Cooling Tubes. Ind. Eng. Chem. Res. 2009, 48, 1134–1139. (18) Christof, H.; Sascha, T.; Kuno, S.; Andreas, S. Theoretical Analysis of Reactant Dosing Concepts to Perform Parallel-Series Reactions. Chem. Eng. Sci. 2003, 58, 4483–4492. (19) Ji-wei, Yu J.; Neretnieks, I. Modelling of Transport and Reaction Processes in a Porous Medium in an Electrical Field. Chem. Eng. Sci. 1996, 51 (19), 4355–4368. (20) Sousa, J. M.; Mendes, A. Modeling a Catalytic Membrane Reactor with Plug Flow Pattern and a Hypothetical Equilibrium GasPhase reaction with Δn 6¼ 0. Catal. Today. 2005, 104, 336–343. (21) Tiscare~ no-Lechuga, F. ABC para Comprender Reactores Químicos con Multireaccion (ABCs of Understanding Chemical Reactors with Multireactions); Reverte: Mexico City, 2008. (22) Marek, L. M.; Piret, J.; Bowen, B. Two-Dimensional Analysis of Fluid Flow in Hollow-Fibre Modules. Chem. Eng. Sci. 1995, 50 (21), 3369–3384. (23) Westerterp, K.; Ptasinski, K. Safe Design of Cooled Tubular Reactors for Exothermic, Multiple Reactions; Parallel Reactions-I. Chem. Eng. Sci. 1984, 39 (2), 235–244. (24) Comsol Multiphysics: Chemical Engineering Module, and Optimization and Sensibility Analysis Module, version 3.5a; Comsol Group: Burlington, MA, 2009. (25) Comsol Multiphysics: Modeling Guide, Deformed Meshes Module, version 3.5a; Comsol Group: Burlington, MA, 2009.
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