Feasibility of Manufacturing Hydrogen and Styrene through the Use of

Knudsen diffusion. The model is suitable for preliminarily evaluating the separation and feasibility of porous ceramic membranes in chemical processes...
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Ind. Eng. Chem. Res. 1999, 38, 4491-4495

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RESEARCH NOTES Feasibility of Manufacturing Hydrogen and Styrene through the Use of Porous Ceramic Membranes Jeffrey Chi-Sheng Wu† Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 10617

The gas separation of multiple-component mixtures was studied in a porous ceramic membrane through mathematical simulation at high temperature. The separation mechanism is based on Knudsen diffusion. The model is suitable for preliminarily evaluating the separation and feasibility of porous ceramic membranes in chemical processes. Hydrogen and styrene plants using membrane separators are evaluated. Four recycle streams as well as five compressors are required to obtain high-purity hydrogen by a commercial alumina membrane, while only one stage is needed if the hydrogen permselectivity could be enhanced. An intermediate membrane separator is proposed to insert between two dehydrogenation reactors in a typical styrene plant. Simulation results indicate that the production of styrene can be substantially increased because of the removal of most of the hydrogen through a membrane separator. In addition, no extra heating load is necessary for processing more fresh ethylbenzene in the second reactor. For an existing styrene plant, the capital investment of the membrane separator would be less compared with that of a catalytic membrane reactor. 1. Introduction The use of ceramic membranes is one of the most promising aspects of current separation technology, especially at high temperature and chemically harsh conditions. A ceramic membrane is usually synthesized from metal oxide, such as alumina, silica, and zirconia.1 The unique properties of ceramics make them suitable for many applications in chemical plants compared to those of their organic polymer counterparts. Ceramic membranes not only have excellent thermal and mechanical properties but also are resistant to organic solvent and microbiological attack. One of the important applications is gas separation at high temperature.2 The gas permeation of a porous membrane depends on the pore size, porosity, tortuosity, and thickness.3 The gas separation mechanism can be classified into four categories, depending on the physical properties of the gas and membranes. (a) Knudsen diffusion: The separation of the gas mixture is in inverse proportion to molecular weight in this regime. (b) Surface diffusion: Molecule diffusion is induced by surface adsorption and migration. The driving force is the surface concentration gradient.4 (c) Molecular sieving: The gas molecule is screened when its size is larger than the pore diameter. (d) Capillary condensation: The condensable gas is liquefied in the pores as a result of vapor pressure reduction. It flows through the membrane as a result of the pressure gradient. The simulations of in situ separation by the membrane have been studied in many chemical processes, † Tel.: +886-2-23631994. Fax: +886-2-23623040. E-mail: [email protected].

such as hydrogen production5 and catalytic membrane reactor for dehydrogenation.6-8 The operation conditions of the membrane reactor can be considerably different from those of the traditional process. Generally, catalyst kinetics and/or membrane permselectivities are required to be adjusted to obtain an optimum condition. A new plant can be thoroughly designed to benefit from such a concept. However, it would be extremely difficult to adopt membrane reactors in an existing dehydrogenation plant. Extensive renovation of the old process may be required, such as the catalyst, reactor, piping, and controllers, as a result of the changes of temperatures, pressures, flow rates, and stream compositions. This study proposes a feasible way to improve the efficiency of an existing dehydrogenation plant by taking advantage of the ceramic membrane without significant investment. For a hydrogen production plant, which uses steam reforming/water-gas shift, can also benefit by the membrane in a reduction of the separation cost. A mathematical model is established for multiplecomponent gas separation using porous ceramic membranes. Unlike many mathematical modeling using initial conditions, the differential equations are solved by boundary values. This model is able to evaluate the performance and seek the optimum operation conditions of a given system. 2. Theory The gas permeation of porous ceramic membranes is governed by Knudsen diffusion and viscous flow. Viscous flow can be negligible for pore size 40-200 Å at high temperature.9,10 Knudsen diffusion is dominant when the mean free path of gas molecule is 10 times larger

10.1021/ie990235n CCC: $18.00 © 1999 American Chemical Society Published on Web 09/28/1999

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influenced by the packing density of the catalyst particles. That is estimated by the Ergen equation (eq 5).11 The pressure drop along the shell side is derived from the momentum balance of the annulus. The system thus has (2n + 2) equations (i.e., n × eq 3 + n × eq 4 + eq 5 + eq 6) and (2n + 2) variables. A unique solution can be found once the boundary conditions are set.

( )

dPt 150µvz (1 - )2 1.75Fvz2 1 -  ) + dz Dp Dp2 3 3 Figure 1. Mass balance in a tubular membrane. Table 1. Characteristics of a Tubular Alumina Membrane1 tube diameter shell diameter pore diameter (membrane) membrane thickness tortuosity (membrane) porosity (membrane)

-

0.634 cm 1.574 cm 40 Å 5 µm 2.95 0.5

than the pore diameter. The collision frequency of gas with the pore wall is much higher than that of the molecules. The smallest pore diameter of a commercial alumina membrane is ∼50 Å. Therefore, the separation mechanism falls in the regime of Knudsen diffusion. Knudsen diffusivity (Dk) is an inverse proportion to the square root of the molecular weight according to eq 1. The diffusivity increases with the square root of the temperature. Gas permeance (Ki) depends on not only its diffusivity but also the pore radius, porosity and tortuosity of the membrane as shown in eq 2.

Dk ) Ki )

x8RT πM

2r 3

2rp 3τRTd

x

T 8000R πMi

(1) (2)

3. Mathematical Model The mathematical model is based on the following assumptions: (1) Ideal gas (i.e., high temperature and low pressure); (2) isothermal conditions; (3) steady state; (4) Lucas mixing rule; (5) independent Knudsen diffusion of individual gas (i.e., no interaction); (6) plug flow (i.e,. radial concentration gradient negligible). A set of differential equations is established with the mass balance of the tube and shell sides as shown in Figure 1. Equations 3 and 4 represent the component i of the tube and shell, respectively. Individual gas permeance (Ki) is calculated from the Knudsen equations (eqs 1 and 2). There are 2n equations when the system contains n components.

dNi 2Ki (P - Pi′) ) 0 + dz R1 i

(3)

2R1Ki dNi′ (Pi - Pi′) ) 0 dz (R22 - R12)

(4)

The simulation requires the length, diameter, thickness, porosity, pore size, and tortuosity of the membrane to define a membrane system. These parameters determine the gas permeances of a given membrane based on eq 2. The pressure drop along the tube side can be

dPs ) dz

8µvz′ ln

()

() R1 R2

R1 ln (R 2 + R12) + (R22 - R12) R2 2

(5)

(6)

In a real membrane separator, the flow rates, pressures, and concentrations of the feed, purge, permeate, and reject are either specified or measured, depending on the operation. These values are assigned to the boundary values and can be given or calculated in the mathematical model. Each variable contains two values of the inlet and outlet, respectively. Therefore, there will be (4n + 4) boundary values. To find a unique solution, (2n + 2) boundary values are necessary to be specified. These values are assigned in any combination, depending on how the separation is operated. For example, the concentrations and pressures of the outlet (permeate and reject) can be calculated if the pressures and components of the inlet (feed and purge) are designated. Then, the separation results are obtained by simulating the membrane separator with a given feed condition. The model can also calculate the requirement of the feed conditions to achieve a specific permeate condition if boundary values of the permeate are assigned. The geometry of the membrane, such as inside and outside diameters, length, and packing density of catalyst particle, can be assigned according to the membrane separator. The physical data of gases, including the molecular weight, critical pressure, critical temperature, molar volume, compressibility factors, and dipole moment, are required to estimate the viscosity of the mixture. The properties of the mixture are calculated according to the Lucas mixing rule.12 The differential equations were translated to FORTRAN and solved by the computer. Newtonic iteration and deferred correction technique were used to solve the boundary value problem. Maximum relative numerical errors were controlled under 0.5%. 4. Results and Discussion The model was applied to two industrial cases to evaluate the performance of membrane separation. A tubular alumina membrane was used for simulation since it was widely available commercially. The characteristics of the membrane and module are listed in Table 1.1 Hydrogen Plant. A hydrogen plant used coal gasification to generate hydrogen via the water-gas shift reactions.13 Major reactions are listed in eqs 7 and 8. Carbon dioxide is the major byproduct. In a typical plant, the temperature of gases at the exit of the reactor is near 650 °C, the pressure is slightly higher than atmosphere and the flow rate is 113.3 m3/h at STP. The stream contains 64% hydrogen, 32% carbon dioxide, and

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Figure 2. Hydrogen separation by a ceramic membrane: isothermal operation at 650 °C, 50% of theoretical Knudsen separation, and stage cut ≈ 0.5

other minor components such as carbon monoxide, methane, and ethane.

C + H2O f H2 + CO

(7)

CO + H2O f H2 + CO2

(8)

The traditional separation of those gases is by a cryogenic process, pressure swing adsorption, or solution adsorption, which must cool the gases to or below ambient temperature to remove carbon dioxide and others. If the purified hydrogen is the feed of the next processes which require high temperature such as hydrogenation or hydrodesulfurization, then hydrogen must be reheated. A huge amount of energy can be saved if the separation is carried out at high temperature directly, using a ceramic membrane separator.

The model was applied to estimate the membrane performance. The flow rate, temperature, and components of the feed were used as mentioned above. The feed was compressed to 5 bar to provide the driving force for membrane separation. The pressure drop across the membrane was assumed to be 4 bar so that the permeate pressure would be 1 bar. The separation efficiency was assumed to be only 50% of the Knudsen theorem for conservative evaluation. The purity of hydrogen must meet the requirement of the next process, which was at least 90%. Figure 2 depicts the simulation results. The detailed concentrations and flow rates of each stage are listed in the figure. Four recycle streams as well as five membranes and compressors are necessary to achieve hydrogen purity higher than 90% with the outlet (permeate) flow at 56.5 m3/h. The recovery of

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Figure 5. Ethylbenzene dehydrogenation with a intermediate membrane separator: temperature ) 600 °C, pressure ) 1 atm, permeate pressure ) 0.16 atm, and unit, mol/min. Figure 3. Hydrogen separation by H2-permselective membranes: isothermal operation at 650 °C, set separation factor, H2/ CO2 ) 35 (ideal Knudsen H2/CO2 ) 4), and stage cut ≈ 0.5

Figure 4. Traditional ethylbenzene dehydrogenation with packedbed reactor: temperature ) 600 °C, pressure ) 1 atm, and unit, mol/min.

hydrogen is near 70%. The reject stream contains 33.6% hydrogen with the flow at 56.5 m3/h. The total membrane area required is 1.96 m2. Such a process could not be feasible since large recycles and five compressors would consume lots of power. The hydrogen selectivity was reported as higher than that of the Knudsen theorem for a modified alumina membrane and could be as high as 7.5 times of the Knudsen value. However, the permeance was reduced to 5% of the original membrane after surface modification.14 The simulation was applied to such a membrane. Figure 3 shows the simulation results. Only one membrane separator is needed and can reach 95% purity of hydrogen with the same permeate flow. The recovery of hydrogen increases to 75% compared with that in the previous case. The membrane area increases to 4.8 m2 due to smaller permeance. No cycle and only one compressor are required. Therefore, the high-permselective membrane can significantly improve the performance of separation. Styrene Plant. Styrene is produced through the dehydrogenation of ethylbenzene. The main reaction is shown in eq 9. The conversion, which ranged from 40 to 60%, is limited by thermodynamics and side reactions. Thus, the reaction temperature was limited between 550 and 650 °C at pressures of 0.7-3 atm in industry.15 Five to fifteen times of steam to ethylbenzene is co-fed in the reactor to reduce coking. A heat exchanger or direct steam injection is used to supply the thermal energy in the intermediate stage to increase yield since this reaction is endothermic.16

C6H5C2H5 f C6H5C2H3 + H2

(9)

If it is necessary to supply heat between reactors, it would be convenient to retrofit a membrane separator which can selectively remove one of the products (i.e., hydrogen). Thus, only the remaining reactant is heated before entering the second reactor. Furthermore, the conversion can be enhanced according to Le Chaˆtelier’s principle since part of the products is removed. Figures 4 and 5 are two simplified ethylbenzene dehydrogenation processes. Figure 4 is the traditional styrene plant in which a heat exchanger is placed between reactors. Figure 5 shows a ceramic membrane separator which is inserted ahead of the heat exchanger.

The model simulated the retrofitted process and compared the performance with the traditional one. The detailed simulation results are shown in the figures. The membrane separator splits the stream from the first reactor into two equal molar flows. Most of the hydrogen and a small amount of ethylbenzene and styrene are removed and carried by the permeate stream. This stream does not enter the second reactor and is directly sent to the distillation unit. The reject stream contains much less hydrogen so that more ethylbenzene converts to styrene in the second reactor. If the second reactor is the same size as the first one, then extra fresh ethylbenzene can be fed into the second reactor to produce more styrene. The conversions of the two processes are the same, 57%, because the simulation assumes dehydrogenation reacting equilibrium.17,18 However, the retrofitted process has a higher styrene yield with the cost of a membrane separator. No extra heating load is required for processing more fresh ethylbenzene in the second reactor since most of the hydrogen and part of the styrene are removed. If a membrane separator is considered in the initial plant design, the size of the second reactor could be reduced by half. The capital investment would be less compared with the same capacity of the old one. 5. Summary A mathematical model of a porous ceramic membrane is established to evaluate the performance of multiplecomponent gases separation at high temperature. The separation mechanism is governed by Knudsen diffusion. A set of differential equations were solved numerically with boundary values. This model is expandable and suitable for preliminarily evaluating the separation and feasibility. The simulation of a hydrogen plant indicates that the permselectivity of the membrane is crucial. The operation cost can be significantly reduced if hydrogen permselectivity could be increased. Currently, a commercial alumina membrane may not have enough incentive to be used. For an existing styrene plant, the investment of an intermediate membrane separator could be worthwhile since it would not alter the current process, while more styrene could be produced under the same capacity of the original plant. Acknowledgment The author is grateful for the financial support by the National Science Council, Republic of China, under the project number NSC-84-2215-002-040. Nomenclature d ) membrane thickness (m) Dk ) Knudsenl diffusivity (cm2/s) Dp ) diameter of catalyst (m)

Ind. Eng. Chem. Res., Vol. 38, No. 11, 1999 4495 Ki ) effective Knudsen permeance, i ) H2, CH4, etc. (mol/ m2‚s‚Pa) L ) total reactor length (m) M, Mi ) molecular weight, i ) H2, CH4, etc. (g/mol) Ni ) molar flux in the axial direction of the tube side, i ) H2, CH4, etc. (mol/m2‚s) Ni′ ) molar flux in the axial direction of shell side, i ) H2, CH4, etc. (mol/m2‚s) Pi ) partial pressure in the tube side, i ) H2, CH4, etc. (Pa) Pi′ ) partial pressure in the shell side, i ) H2, CH4, etc. (Pa) Ps ) total pressure of the shell side (Pa) Pt ) total pressure of the tube side (Pa) R ) gas constant (8.313 Pa‚m3/mol‚K) r ) pore diameter of the membrane (m) R1 ) inside radius of the membrane, i.e., tube side (m) R2 ) inside radius of the membrane module, i.e., shell side (m) T ) temperature (K) vz ) mixture linear velocity in the tube side (m/s) vz′ ) mixture linear velocity in the shell side (m/s) z ) reactor length (m) Greek Symbols µ ) viscosity of the mixture, (N‚s/m2 or 10 cP)  ) porosity of the packed catalyst in the reactor p ) porosity of the membrane F ) density of the mixture (kg/m3) τ ) tortuosity of membrane

Literature Cited (1) Hsieh, H. P. Inorganic Membranes for Separation and Reaction; Elsevier: Amsterdam, 1996; pp 95-118. (2) Ilias, S.; Govind, R. Development of High-Temperature Membranes for Membrane Reactor: An Overview. In AIChE Symposium 268; AIChE: New York, 1989; Vol. 85, p 18. (3) Lin, Y. S.; Burggraaf, A. J. Experimental Studies on Pore Size Change of Porous Ceramic Membranes After Modification, J. Membr. Sci. 1993, 79 (1), 65. (4) Ruthven, D. M. Principles of Adsorption and Adsorption Processes; John Wiley & Sons: New York, 1984; p 137. (5) Uemiya, S.; Sato, N.; Ando, H.; Kikuchi, E. The WaterGas Shift Reaction Assisted by a Palladium Membrane Reactor, Ind. Eng. Chem. Res. 1991, 30, 585.

(6) Itoh, N.; Shindo, Y.; Haraya, K.; Obata, K.; Hakuta, T.; Yoshitome, H. Simulation of a Reaction Accompanied by Separation, Int. Chem. Eng. 1985, 25 (1), 138. (7) Itoh, N.; Govind, R. Combined Oxidation and Dehydrogenation in a Palladium Membrane Reactor, Ind. Eng. Chem. Res. 1989, 28, 1554. (8) Shindo, Y.; Itoh, N.; Haraya, K. High Performance Reactor Using A Membrane, In AIChE Symposium Series 272; Fouda, A. E., Ed.; American Institute of Chemical Engineers: New York, 1989; Vol. 85, p 80. (9) Wu, J. C. S.; Flowers, D. F.; Liu, P. K. High-Temperature Separation of Binary Gas Mixture Using Microporous Ceramic Membranes. J. Membr. Sci. 1993, 77 (1), 85. (10) Shindo, Y.; Itoh, N.; Haraya, K. A Theoretical Analysis of Multicomponent Gas Separation by Means of a Membrane with Perfect Mixing. Sep. Sci. Technol. 1989, 24 (7&8), 599. (11) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Tranport Phenomena; John Wiley & Sons: New York, 1960; pp 51 and 200. (12) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1987; pp 397-420. (13) Weissermel, K.; Arpe, H.-J. Industrial Organic Chemistry; Translated by A. Mullen; Verlag Chemie: New York, 1978; pp 1518. (14) Wu, J. C. S.; Sabol, H.; Smith, G. W.; Flowers, D. L.; Liu, P. K. T. Characterization of Hydrogen-permselective Microporous Ceramic Membranes. J. Membr. Sci. 1994, 96 (3), 275. (15) Kearby, K. K. Catalytic Dehydrogenation, In Catalysis vol. III Hydrogenation and Dehydrogenation; Emmett, P. H., Ed.; Reinhold Publishing Co.: New York, 1955; Chapter 10. (16) Voge, H. H. Dehydrogenation Processes of Industrial Importance. In Encyclopedia of Chemical Processing And Design; McKetta, J. J., Cunningham, W. A., Eds.; Marcel Dekker: New York, 1982; Vol. 14, pp 282-290. (17) Sheppard, C. M.; Maier, E. D. Ethylbenzene Dehydrogenation Reactor Model. Ind. Eng. Chem. Process Des. Dev. 1986, 25, 207. (18) Wu, J. C. S.; Liu, P. K. T. Mathematical Analysis on Catalytic Dehydrogenation of Ethylbenzene Using Ceramic Membrane. Ind. Eng. Chem. Res. 1992, 31, 322.

Received for review March 30, 1999 Revised manuscript received August 17, 1999 Accepted August 25, 1999 IE990235N