Ind. Eng. Chem. Res. 1991,30, 689-691 Shinji, 0.;Misono, M.; Yoneda, Y.The Dehydrogenation of Cyclohexane by the Use of a Porous-glaee Reactor. Bull. Chem. SOC. Jpn. 1982,56,2760-2764. Sun, Y. M.; Khang, S. J. Catalytic Membrane for Simultaneous Chemical Reaction and Separation Applied to a Dehydrogenation Reaction. Znd. Eng. Chem. Res. 1988,27,1136-1142. Suzuki, Y.;Kimura, S. Separation and Concentration of Hydrogen Isotopea by Palladium-Alloy Membrane (I). Nippon Genshiryoku Gakkai Shi 1984,26,802-810. Uemiya, S.; Kude, Y.;Sugino, K.; Sato, N.; Matauda, T.; Kikuchi, E. A Palladium/Porous-Glass Composite Membrane for Hydrogen Separation. Chem. Lett. 1988,1687-1690. Uemiya, S.;Matauda, T.; Kikuchi, E. Aromatization of Propane Assisted by Palladium Membrane Reactor. Chem. Lett. 1990a, 1335-1338. Uemiya, S.;Sato, N.; Ando, H.; Kude, Y.; Matauda, T.; Kikuchi, E. Separation of Hydrogen through Palladium Thin Film Supportad
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on a Porous Glass Tube. J . Membr. Sci. 1990b,in press. Uemiya, 5.;Sato, N.;Ando, H.; Matsuda, T.; Kikuchi, E. Steam Reforming of Methane in a Hydrogen-permeable Membrane Reactor. Appl. Catal. 1991,67,223-230. Wood,B. J. Dehydrogenationof Cyclohexane on a Hydrogen-Porous Membrane. J. Catal. 1968,11,30-34.
Shigeyuki Uemiya,* Noboru Sato Hiroehi Ando, Eiichi Eikuchi* Department of Applied Chemistry School of Science and Engineering, Waseda University 3-4-1Okubo, Shinjuku-ku, Tokyo 169,Japan Received for review June 25, 1990 Revised manuscript received December 4,1990 Accepted December 17, 1990
Mass Transport in Finite Baths: Effect of Surface Barriers Mass transfer of diffusants to the surface of solid polymeric material from some external medium can occur through a diffusional boundary layer. Equations exist that permit the description of such mass-transfer phenomena, but such equations are valid only for infinite bath systems, i.e., systems in which the concentration of diffusant in the external medium is constant. A new technique ia given that permits the mathematical description of mass transfer through a diffusional boundary layer for finite bath systems, i.e., systems in which the concentration of diffusant in the external medium changes during the sorption process. Diffusion-controlled mass transfer of diffusanta to (or from) the surface of porous solids of various geometrical shapes is strongly influenced by the thickness of diffusional boundary layer barriers at the solid surface (Levich, 1962). Newman was the first to describe in mathematical terms the effect of the diffusional boundary layer on rates of sorption by the slab, cylinder, and sphere (Newman, 1931). Newman’s equations are, however, only applicable to infinite bath sorption systems, i.e., systems in which the concentration of diffusant in the external medium is constant during the sorption process. No equation exists that describes the effect of the diffusional boundary layer on mass transport in finite bath systems, Le., systems in which the concentration of diffusant in the external medium is not constant during the sorption process. Since many real sorption systems are finite bath systems in which a significant boundary layer exists, it is useful to be able to model such systems mathematically. The purpose of the present work is to provide a new technique that can be effective in describing sorption rates of diffusanta from finite bath systems in which a diffusional barrier exists at the solid surface. The technique will be illustrated only for the case of diffusant uptake by a morphologically stable, homogeneous, endless cylinder. However, it should be understood that the technique also is applicable to the case of the plane sheet (slab) and the sphere.
where the P i s are the roots of the transcendental equation: OnJl(On) - LJo(Bn) = 0 (3) in which Joand J1are zero- and first-order Bessel functions. Equation 2 reveals that the rate of sorption is strongly influenced by the numerical value of the dimensionleas parameter, L. As L decreases, the rate of sorption decreases. Equations similar to eq 2 also are given by Crank for the case of the plane sheet and the sphere (Crank, 1975). Finite Bath Systems When no diffusional boundary layer exists at the solid surface, i.e., when the dimensionless parameter, L, is equal to infinity, Wilson’s equation (Wilson, 1948)can be used to describe the relationship between fractional sorption of diffusant, M t / M m dimensionless , time, Dt/a2,and the dimensionless bath exhaustion parameter, a. In functional form:
M , / M , = Ff= f(Dt/a2,.)
(4)
Wilson’s equation for diffusant uptake by a cylinder from f i i t e baths in which no boundary layer exists at the solid surface is given by
Infinite Bath Systems The infinite bath, surface barrier equations of Newman are notationally encumbered and have been rewritten in a more straightforward manner by Crank (Crank, 1976). The functional relationship between fractional sorption of diffusant, Mt/M,, dimensionless time, D t / a 2 ,and dimensionless boundary layer, L, is given by M t / M - = Fi = f(Dt/UZ,L) (1) For the case of diffusant sorption by a cylinder surrounded by a diffusional boundary layer, Crank’s computational solution is given by
-Mt =
M,
F,= 1 -
-
c nil
4a(1 + a) exp(-qn2(Dt/a2)) 4 + 4a + d q , 2
(5)
where the qn’s are the positive, nonzero roota of W n J o ( q n ) + 2Jl(Qn) = 0 (6) in which Jo and Jl again are zero- and first-order Bessel functions. Equation 5 reveals that the rate of sorption is strongly influenced by the value of the dimensionless bath exhaustion parameter, a. As a increases, the rate of sorption decreases. Finite bath equations for the case of (8
1991 American Chemical Society
590 Ind. Eng. Chem. Res., Vol. 30, No. 3, 1991
Table 1. Dimensionless Time for Various Values of Fractional Sorption (a = 0.010101, L = SO) FI Fi [Dtla'Io [Dtla211 [Dt/a212 0.10 0.001110 1.2605 X 2.3143 X 1.2616 X lod 0.15 0.001762 2.0669 X lod 5.6938 X lo-' 2.0710 X 3.0236 X 10" 3.0127 X lod 1.1130 X lo4 0.20 0.002494 1.9242 X 10" 4.1509 X 4.1264 X 10" 0.25 0.003322 5.4956 X 10" 5.4463 X 3.0880 X 10" 0.30 0.004267 7.1159 X 4.7233 X lo4 0.35 0.005356 7.0238 X 10" 7.0003 x 10" 9.0904 X 10" 8.9269 X 0.40 0.006 623 1.1533 X lo-' 1.1253 X lo-' 1.0169 X 0.45 0.008115 1.4615 X lo4 1.4144 X 10" 1.4609 X 10" 0.50 0.009901 2.0919 X 10" 1.8573 X lo-' 1.7788 X lo-' 0.55 0.012075 2.3843 X lo-' 2.2538 X lo-' 3.0084 X 0.60 0.014778 3.1091 X lo-' 4.3824 X 0.65 0.018233 2.8899 X lo-' 4.1514 X lo4 3.7149 X lo-' 6.5358 X 0.70 0.022801 5.7485 X lo4 5.0765 X lo-' 1.0131 X lo-' 0.75 0.029 126 1.6714 X lo-' 8.4283 X 10" 0.80 0.038462 7.1502 X lo-' 1.3586 X 0.85 0.053628 1.0881 X 3.0642 X lo-' 0.90 0.082569 1.9207 X 6.8475 X lo-' 2.6201 X 0.95 0.159664 4.9323 X 2.4584 x 10-3 7.8256 X
the plane sheet and the sphere also are available (Wilson, 1948; Crank, 1975). New Technique As previously stated, no analytical solution in equation form exists for the functional relationship given by M , / M - = f(Dt/a2,aL) (7) It can be shown, however, that for linear, transitional kinetic systems, i.e., for systems (characterized by linear sorption isotherms and constant, concentration-independent diffusion coefficients) that change from infinite bath to finite bath systems during the course of diffusant sorption, the relationship between Fi and Ff at the point of transition is given by (McGregor and Etters, 1979)
Equation 8 permits Fi to be calculated for all values of Ff between zero and unity for given values of a. All values of M t / M , for both infinite and finite systems are, therefore, equated to each other through corresponding transitional ualues. Through the use of such continuously transitional, fractional sorption values it is possible to estimate the effect of the dimensionless boundary layer, L, on the rate of diffusant sorption in finite bath systems having a given dimensionless bath exhaustion, a. Computational Example The following example will serve to illustrate the computational sequence employed in the new technique. It is desired to compute the value of dimensionless time associated with various fractional sorption values, M t / M, = Ff,obtained under finite bath, boundary layer conditions; these values of dimensionless time are designated [Dt/a2Io.In the present example, [Dt/a2Ioassociated with each finite bath fractional sorption value, Ff,is determined for a system having an a value of 0.010 101, corresponding to a fractional equilibrium bath exhaustion E, = 0.99, and an L value of 50,corresponding to a small but significant boundary layer. Dimensionless time is iteratively computed for each value of Ff by the use of eq 5, using an a value of 0.010 101. These values are designated [Dt/a2I1.By the use of eq 8, values of Fi are determined for each value of FP For each value of Fi,dimensionless time is iteratively determined by the use of eq 2, using an L value of 50. These values of dimensionless time are designated [Dt/a2I2.Finally, dimensionless time is iteratively determined for each value of Fi by the use of eq 2, using an L value of infinity. These
[Dtla21s 2.4203 X 10-3' 6.1001 x 10-7 1.2225 X 10" 2.1697 X 10" 3.5810 X 10" 5.6445 X 10" 8.6451 X lo4 1.2972 X loa 1.9323 X 10" 2.8765 X 4.3131 X 10" 6.5747 X 1.0301 X lo-' 1.6851 X lo-' 2.9495 X IO-' 5.7697 X lo-' 1.3842 x 10-3 5.3517 X lo"
values are designated [Dt/a2I3.Dimensionless time for the finite bath system having an a of 0.010 101 and an L of 50 is given by [Dt/a210 = [Dt/a211 + [[Dt/a212 - [Dt/a2131
(9)
The results of the computations are given in Table I. Formal iterative solutions such as those of Table I can be expanded to include many different values of a and L. An ultimate result of such computations may be the development of a useful analytical approximation, i.e., an empirical, modeling function by which the fractional sorption, Ff,may be calculated directly from a knowledge of D t / a 2 , a,and L. Nomenclature a = radius of cylinder or sphere, or half-thickness of slab, m C, = initial concentration of diffusant in external medium C , = equilibrium concentration of diffusant in external medium Lj = diffusion coefficient of diffusant in solid, m2/s D = diffusion coefficient of diffusant in the external phase, m2/s E, = fractional equilibrium exhaustion of external medium, given by E, = (C, - C,)/C, Ff = fractional equilibrium diffusant uptake in finite systems Fi = fractional saturation diffusant uptake in infinite systems Jo = zero-order Bessel function J1 = first-order Bessel function K = linear distribution coefficient of diffusant between solid phase and external phase L = dimensionless parameter given by L = (Ba)/(DKG) M,= concentration of diffusant in solid at time t M, = concentration of diffusant in solid at equilibrium qn = positive, nonzero root of transcendentalequation (eq 6) t = time of sorption, s Creek Letters a = dimensionless finite bath exhaustion given by (1- E , ) / E , p,, = roots of transcendental equation (eq 3) 6 = thickness of diffusional boundary layer, m Subscripts f = finite bath systems i = infinite bath systems n = root number t = time, s a = infinite time, s (equilibrium)
Literature Cited Crank, J. Diffusion in a Cylinder. In The Mathematics of Diffusion, 2nd ed.; Clarendon Press: Oxford, 1975; pp 69-88.
Znd. Eng. Chem. Res. 1991,30,591-594 Levich, V. G.Convective Diffusion in Liquids. In Physicochemical Hydrodynamics; Prentice-Ha& Englewood Cliffs, NJ, 1962;pp 39-138. McGregor, R.; Etters, J. N. Transitional Kinetics in Disperse Dyeing. Text. Chem. Color. 1979,11, 202159-206163. Newman, A. B. The Drying of Porous Solids: Diffusion and Surface Emission Equations. Trans. Am. Znst. Chem. Eng. 1931, 27, 203-220. Wilson, A. H. A Diffusion Problem in Which the Amount of Dif-
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fusing Substance is Finite. Philos. Mag. 1948, 39, 48-58.
Jamee N.Etters Textile Sciences, Dawson Hall, The University of Georgia Athens, Georgia 30602 Received for review July 30, 1990 Revised manuscript received January 7, 1991 Accepted January 17,1991
Development of a Composite Palladium Membrane for Selective Hydrogen Separatioq at High Temperature A method is described for development of a composite palladium membrane for selective hydrogen separation a t high temperature. Electroless plating is used to form a thin palladium film on a silver porous substrate. The composite formed showed excellent mechanical strength and very large selectivity for hydrogen. The studies performed so far suggest that electroless plating can be utilized in making a metal composite membrane that can be used at high temperatures. Composite properties seem fairly constant at high temperatures. The permeability of the composite membrane is comparable to theoretical permeabilities for pure palladium. Introduction Recently there has been increased interest in applying inorganic membranes for in situ separation of product species-particularly hydrogen-to achieve equilibrium shift. From thermodynamic considerations, in a chemical reaction, if one of the reaction products that slows down the reaction rate can be continuously removed, the equilibrium state of the reaction can be shifted in the direct of forward reaction, thereby increasing the conversion. Experimentalisb have shown that it is possible to remove products selectively through pores of thermally stable Vycor glass (Shinji et al., 1982). Itoh (1987) obtained enhanced conversion of cyclohexane to benzene from equilibrium conversion of 14% at 473 K and 1-atm pressure to 100% by removing hydrogen selectively through a thin (25 pm) palladium membrane from the reaction mixture. Recently, Zhao et al. (1990) have presented similar experimental results for dehydrogenation of 1butene to butadiene using a palladium membrane reactor. However, the productivity of these membrane reactors is severely limited by the poor permeability of the membrane. Commercially available membranes are either thick films or thick-walled tubes. Since the permeability is inversely proportional to the film thickness, a thick membrane acts as a poor separator. However, the thermal stability and mechanical strength of a film is directly proportional to its thickness. Hence, we need to provide the necessary mechanical strength to the thin film. Thus a major challenge lies in developing a permselective thin solid film, without compromising the integrity as well as the desired properties of the film. Availability of such a membrane for high-temperature application will open a new area of research in membrane reactor technology and gas separation. Metals like palladium can be used as membranes at high temperatures owing to their selectivity toward certain gases like hydrogen. However, to obtain high flux we need thin membranes. These thin membranes cannot withstand high pressure differentials,hence we need to provide mechanical strength to these membranes. This can be achieved if a thin film of metal can be supported by a thermally stable porous substrate. The composite thus formed will act as a membrane with high selectivity and high flux. Electroless plating can be used to plate a thin film of metal on any porous substrate. It involves reduction of 0888-5885/91/2630-0591$02.50/0
Table I. TyDical Platina Bath ComDosition component concentration palladium chloride 0.375g/L ammonium hydroxide 30.0 mL/L ammonium chloride 4.5 g/L sodium hypophosphite monohydrate 10.0g/L
a metal salt by a reducing agent like hypophosphite preferentiallyon a catalytic surface. Once plated the metal on the surface acts as a catalyst for further reaction. The metal forms a thin uniform film on the surface. Although relatively expensive, electroless plating is superior to electrolytic plating because of the following reasons (Lowenheim, 1978): 1. Nonconducting (ceramics, Vycor glass, polymeric) surfaces can also be coated by use of electroless plating. 2. The deposits are thin, more dense, and uniform. 3. Complicated apparatus like power supply and electrical contacts are not needed. 4. The throwing power of electrolss plating is nearly perfect. 5. There is no formation of projections or buildup on the edges in electroless plating. The objective of this paper is to describe the methods and procedures used to achieve the goal of forming a composite membrane using electroless plating and to describe the characterization of the composite formed. Experimental Section The experiments were divided into two parts: plating of metal on a porous substrate and characterizing the composite formed. Plating. Porous silver disks (Poretics Corporation, Livermore, CA; 47-mm diameter, 0.2-pm pores, 0.5-mm thickness) were used as porous substrate. These disks were cleaned in acidified boiling water for 10 min to remove organics and dirt. One surface was activated with a sensitizing solution consisting of tin chloride and palladium chloride. This activated disk was then plated with palladium by electroless plating. The plating bath consisted of a palladium-amine complex and sodium hypophosphite as reducing agent. The pH of the bath was maintained at 10.2 by using an amine buffer (Athaval and Totiani, 1989). Table I shows typical plating bath composition and
k~1991 American Chemical Society
