1136
Ind. Eng. Chem. Res, 1988,27, 1136-1142
Catalytic Membrane for Simultaneous Chemical Reaction and Separation Applied to a Dehydrogenation Reaction Yi-Ming Sun and Soon-Jai Khang* Department of Chemical and Nuclear Engineering, University of Cincinnati, Cincinnati, Ohio 45221
This research demonstrated the possibility of achieving conversions above the original equilibrium conversion based on the feed conditions by combining the selective separation effect of a membrane and the catalytic function of transition metals. A catalytic membrane reactor, containing a tubular Vycor glass membrane which was impregnated with a platinum catalyst, was studied with the model reaction of cyclohexane dehydrogenation. The equilibrium shift was significant for the operation with high space time. Numerical simulations using a single-cell model showed good agreements with experimental data. The performance of the catalytic membrane reactor was theoretically compared with that of a reactor consisting of a n inert tubular Vycor glass membrane and catalyst pellets in the feed-side chamber. The result showed that the catalytic membrane reactor was superior to the inert membrane reactor for the operation with high space time but was less effective for the operation with low space time. In the past few years, interest in the application of a membrane reactor to many chemical processes has substantially increased. A number of investigations have concentrated on the membrane reactor built with a microporous Vycor glass membrane (average pore diameter of about 40 A, surface area of about 200-250 m2/g, porosity of about 0.28, and density of about 1450-1500 kg/m3). Kameyama et al. (1981) applied this type of reactor to the decomposition of hydrogen sulfide, Shinji et al. (1982) and Ito et al. (1985) to the dehydrogenation of cyclohexane, and Ito et al. (1984) to the decomposition of hydrogen iodide. All of these researchers employed a tubular Vycor glass membrane reactor with a bed of catalyst on the feed side (upstream or reject stream). Experiments and simulations in their studies showed that the chemical equilibrium shift could be favorably achieved because the hydrogen (one of the products) was preferentially removed from the reaction zone. However, the Vycor glass membrane itself has a large surface area (200 m2/g), and for this reason, it is possible to use the membrane also as a catalyst carrier. It would be interesting, therefore, if the membrane was impregnated with catalytic transition metals so that the catalytically impregnated membrane would perform a dual function of chemical reaction and selective separation. There is a need to understand the interaction between reaction and diffusion inside the catalytic membrane and the applicability of the catalytic membrane to actual chemical processes. In this work, a reactor containing a platinum-impregnated Vycor glass membrane was designed and operated in such a way as to have a catalytic reaction in the membrane itself. The platinum-catalyzed dehydrogenation of cyclohexane was used as a model reaction.
each stream is maintained constant. The feed-side (upstream) pressure, Pf, is higher than the permeate-side (downstream) pressure, PV The total molar flow rate and the composition of each input stream was maintained constant during the operation. A single or multiple reaction may take place at the catalytic membrane, and the reaction rate expression of each reaction is denoted by ri = kifi(P),where i, k, and P are, respectively, the reaction number, the reaction rate constant, and the vector expression for the partial pressures of all the.components. I t is assumed that the system is isothermal and the interfacial mass-transfer resistance between the gas phase and the surface of catalytic membrane is negligible compared to the internal mass-transfer resistance in the membrane. It is also assumed that the contents in the feed-side chamber and the permeate-side chamber are well-mixed because the length-to-diameter ratio is relatively small in the present experimental setup. The model is called a single-cell model because no longitudinal variation is considered. The steady-state equations for the system are given as follows. I n the catalytic membrane
1 d
F
[ ] @j
r -
dr
m
+ iCvijkifi(P) =O =l
( j = 1,2,...,n )
The boundary conditions are
Pi = xjPf
at r = rf
Pj = y j P p
at r = rp
I n the feed-side chamber (shell side)
This paper presents both a mathematical model for the catalytic Vycor glass membrane reactor and the experimental results demonstrating the equilibrium-shift effects. A comparison between the catalytic membrane reactor and an inert membrane reactor with catalyst pellets in the feed-side chamber is made by using the model.
=0
QPxjo - Qfxj -
( j = 1,2,...,n )
rf
(3)
I n the permeate-side chamber (tube side):
Model Development: Single-cell Model A. Catalytic Membrane Reactor (CMR). A schematic diagram of the annular catalytic membrane reactor is shown in Figure la. In the operation, the pressure of 0888-588518812627-ll36$01.50/0 0 1988 American Chemical Society
(4)
Ind. Eng. Chem. Res., Vol. 27, No. 7, 1988 1137
B. Inert Membrane Reactor with Catalyst Pellets in the Feed-Side Chamber (IMRCF). For an inert membrane reactor with catalyst on the feed side, as shown in Figure lb, the governing equations based on the differential material balance in the direction of diffusion and the material balance for each component in the feed-side and the permeate-side chambers are derived assuming a well-mixed condition in each chamber. In the membranes
Fwmrate Side
r =o
Direction of Diffusion (in the Membrane)
where
Catalyst Bed
Pj= xjPf
at r = rf
Pj= yjP,
a t r = rp
In the feed-side chamber (shell side)
.. Figure 1. Single-cell model: (a) the catalytic membrane reactor, and (b) the inert membrane reactor with catalyst in the feed side.
( j = l,2,...,n ) (9)
In the permeate-side chamber (tube side)
13
(10)
(A
There is no reaction term in eq 8; thus, the dimensionless pressure gradient is constant throughout the membrane. Equation 8 can be omitted, and eq 9 and 10 can be rewritten in dimensionless forms as m
xj0
- efxj- aj4(xj- yjpr)+ pzvijKifi(~) =o L=l
xio - Ofxj Figure 2. Experimental setup: 1, mass flow meter; 2, regulating valve; 3, metering valve; 4,temperature indicator; 5, syringe pump; 6, heating lamp; 7, membrane (reactor) cell; 8, electric furnace; 9, temperature controller; 10, sampling ports; 11,condenser; 12, bubble flow meter; 13, pressure gauge; 14, adjustable check valve; 15, plug valve; 16, liquid collector.
The dimensionless forms of eq 2, 3, and 4 are written as follows:
$j
$j
= xj = yjP,
at t = 1 at 5 = 0
where + j , C;, and 8, are, respectively, the dimensionless partial pressure of component j , the dimensionless radius, and the dimensionless molar flow rate. (See Nomenclature for other definitions.)
+ a j @ ( x j- yjPr)= 0
( j = 1,2,...,n ) (11) ( j = l,2,...,n ) (12)
Experiments and Numerical Simulations The present study is designed to avoid the so-called "fudge-factor" effect due to adjusting a number of parameters to fit the experimental results. The model parameters consisting of diffusivities and kinetic constants are independently measured and substituted into the model equations; thus, the simulation does not contain any adjustable parameters. A. Measurement of the Effective Diffusivity in the Vycor Glass Membrane. A diagram of the experimental setup is shown in Figure 2. The membrane cell has a double-pipeconfiguration. The membrane is a Vycor glass tube (Corning Vycor brand glass No. 7930, Code 742078, 0.d. 0.0068 m, i.d. 0.0044 m) with one end connected to a lI4-in. ordinary Pyrex glass tube using a Vycor-Pyrex graded seal (Corning Catalog No. 6466-7). The other end of the inner tube is closed by glass fusion alone. The active porous section of the inner tube is about 0.095 m in length. The outer shell is an ordinary Pyrex glass tube of 0.022-m inside diameter and 0.145-m length. One end of the inner tube is suspended in order to prevent breakage due to different thermal expansions of the inner tube and the outer shell. The temperature is measured by three thermocouples located at the outer shell and is controlled within f l O C of the desired value. The gas feed (H2 or N,) is from a gas cylinder and the flow rate is measured by a mass flow
1138 Ind. Eng. Chem. Res., Vol. 27, No. 7, 1988
meter. The liquid feed (cyclohexane or benzene) is injected at a constant flow rate by using a syringe pump. The heating lamps are used to preheat the input stream and prevent condensation in the output streams. The downstream of the permeate-side chamber is opened to the atmosphere;thus, the permeate-sidepressure is maintained at atmospheric pressure. The feed-side pressure is elevated by applying an adjustable check valve to the purge stream of this side. A pressure gauge is used to measure the feed-side pressure. For gases such as hydrogen and nitrogen, pure gas was fed and the volume flow rate of permeated gas was measured by a bubble flow meter. Then the effective diffusivity of component j in the Vycor glass membrane could be determined from Fick's law. The working equation used for calculating the effective diffusivity of gas in the annular shape membrane in this research is as follows:
D, =
Q&TtAr 2LrmAP
1n (rf/rp) 2LAP
Q&Ttest
In (rf/rp) (13) 2LTroom(Pf - P p )
VProomTtest
For components such as benzene and cyclohexane, which are in the liquid state at room temperature, nitrogen was used as a carrier gas together with the liquid feed. The liquid feed was heated and evaporated in the carrier gas stream. The liquid output in each stream was collected in a condenser. The amount of collected liquid component j in the permeate-side output was used to calculate the effective diffusivity in the membrane by the following equation:
The partial pressure difference of component j in eq 14 was obtained from the following relationship: (AP)j = P f X j - PQj
(15)
B. Measurement of Reaction Rate Constant. The following rate expression is used for the cyclohexane dehydrogenation (It0 et al., 1984):
x)
r1 = k( Pl - P z P ~ ~kmol/(m3.s)
(16)
where k and Kp are, respectively, the reaction rate constant and the reaction equilibrium constant. The equilibrium constant is calculated from the Gibbs free-energy data (Reid et al., 1977):
Kp = 2.524 X
loZ6exp(
-2.606
X
lo4
)
kPa3 (17)
The rate constant was independently measured by using a fixed-bed reactor of 0.005-m i.d. and 0.12-m length packed with crushed Vycor glass particles sized between 210 and 500 m and impregnated with chloroplatinic acid solution (0.34 wt % Pt in the Pt-impregnated Vycor glass). Some inert Vycor glass particles were mixed with the catalytically active particles in order to minimize the axial temperature gradient in the bed and to improve the contact efficiency between the reactant gas and the particles. Before reaction, the catalyst was treated with air (about 15 mL/min) overnight at 743 K and then with H2 (about 15 mL/min) for at least 3 h at the same temperature. The pretreatment was to regenerate the catalytic activity of the catalyst which had been deactivated due to coke deposition
in the previous run. Hydrogen was continuously fed into the reactor as the temperature dropped to the reaction temperature. Then, cyclohexane was injected and the reaction started. Hydrogen was kept flowing during the reaction as a carrier gas of cyclohexane to minimize the coke formation in the catalyst (Jothimurugesanet al. 1985). The output stream was sampled and analyzed for the compositions of the organic portion (cyclohexane and benzene) by a Perkin-Elmer Sigma-300 gas chromatograph equipped with a FID detector and a Supelco 0.1% SP-loo0 on 80/100 Carbopack C column. This allowed the calculation of the conversion, based on the molar fraction of cyclohexane consumed. The experiments were carried out at several different input conditions and reaction temperatures, and the data were further analyzed to calculate the rate constant by the use of a plug-flow reactor model. C. Catalytic Membrane Reactor. The experimental setup for a catalytic membrane reactor is the same as that used in the effective diffusivity measurement except that the membrane was impregnated with platinum catalyst. The impregnation was carried out after the Vycor glass membrane was completely secured within the reactor cell. The finished catalytic Vycor glass membrane contained 0.34 wt % platinum catalyst. No input line was installed in the permeate-side chamber; thus, Qpowas effectively kept zero during all the experiments. The pretreatment was identical with that used in the measurement of the reaction rate constant. The operating conditions (input flow rate, temperature, pressure, etc.) were controlled in the same manner as that used for the diffusivity measurement. The output flow rates of gas (mainly H2) and liquid (cyclohexane and benzene) from the feed and permeat streams were measured in the same way as described in section A and were simultaneously monitored to determine the composition of the organic portion. In order to obtain enough steady-state data, each reaction run lasted about 6-8 h. Neither a significant side reaction nor measurable change in the catalytic activity was observed during each period of valid experimentalruns. (There were some experimental runs with significant catalyst deactivation due to other unintended impurities or operating conditions, but they were excluded from the final data analyses and are not discussed in this paper. See Sun (1987) for details.) D. Numerical Simulations. The two governing equations sets in their dimensionless forms, eq 5-7 and 11-12, were solved numerically. Ideally, the boundary value problem given by eq 5-7 could be solved by the shooting method with an initial value problem approach (Gerald and Wheatley, 1984). However, the computation with realistic values showed that this approach produced a stiff system (Ferziger, 1981). The numerical stiffness problem was avoided by the use of unsteady-state simulations. Thus, one additional partial differential term of time variation was added to the right-hand sides of eq 5, 6, and 7, and the new partial differential equations were successfully solved by the explicit fiiite difference method. The steady-state solution was obtained when the dependent variables showed no more change with time increase. This method was proved efficient and stable when proper initial conditions were used. Equations 11 and 12 formed a system of nonlinear equations and were successfully solved by the ZSCNT routine from International Mathematical & Statistical Libraries (IMSL Library Reference Manual, 1984).
Results and Discussion The temperature dependence of the effective diffusivity in the Vycor glass membrane is plotted in Figure 3 for
Ind. Eng. Chem. Res., Vol. 27, No. 7, 1988 1139 Table I. Data from the Experiments with the Catalytic Membrane Reactor run temp, K 7, 8
YbT Ybf YbP
25
1
2
3
4
5
573 10.10 0.5784 0.5109 0.8921
573 22.53 0.7047 0.6111 0.8984
573 30.36 0.7381 0.6195 0.8807
553 10.90 0.3726 0.3199 0.6318
553 23.58 0.5090 0.4238 0.6491
HYDROGEN NITROGEN I BENZENE CYCLOHEXANE
A
4
6 E
'O-
a-
9
15-
X
> c 2
3 k CI
l0-
..
*-4-4-+*-4-+-4-4
7.L. 53-*-*-.-
* . . l j -
I-.
& ' ;"A'&';" TEMPERATURE, K
i &'
Figure 3. Experimental effective diffusivities of various gases in the Vycor glass membrane.
hydrogen, nitrogen, benzene, and cyclohexane. The ratio of the effective diffusivities between hydrogen and nitrogen in the studied temperature range is 3.70, which is very close to the theoretical value of 3.74 predicted by the Knudsen diffusion mechanism in which the diffusivity ratio of two gases is reciprocally proportional to the square roots of their molecular weights. However, the effective diffusivities of benzene and cyclohexane do not follow the prediction by Knudsen diffusion flow. The experimental data for benzene deviate up to 48% from the expected ones predicted by Knudsen diffusion flow at 523 K. The surface diffusion (Barrer and Barrie, 1952; Hwang and Kammermeyer, 1966) and condensation flow (Lee, 1984) for these two components may be appreciable in this temperature range because of their relatively high boiling points. In the experiments, the effective diffusivity for hydrogen in the Pt-impregnated Vycor glass membrane is still the same as that in the unimpregnated one. The effective diffusivities of cyclohexane and benzene in the Pt-impregnated Vycor glass membrane are thus considered the same as those in the unimpregnated one. Some significant catalyst deactivation was occasionally observed during the measurements of reaction rate constants in a fixed-bed reactor with low space time (7 = V J F "), but no measurable deactivation was detected during each period of valid experimental runs in the catalytic membrane reactor. Therefore, the observed initial reaction rate constant data, which was not affected by any appreciable catalyst deactivation, were used to fit an Arrhenius equation for simulations, as shown in Figure 4. The forward rate constant, k, in eq 16 is k = 3.754 x 1011 exp
-1.598
X
lo5 kmol/(m3-s-kPa) (18)
It was suspected that there were some intraparticle mass-transfer effects at the highest temperature (575 K),
IITxltf
K-'
Figure 4. Arrhenius plot of the observed reaction rate constant of cyclohexane dehydrogenation.
' 'O .
.
Experlmenial A
0.8
-
Calculated -.
....-
-. .-.
._
YbP Ybf
0 YbT ('T) Ybq,p (Xe,& ..._.____.._________---.-
as the Thiele modulus for the catalyst particles [aB= ( F , / ~ ) ( R T ~ , / D , ) was ~ / ~ estimated ] to be in the range of 0.9-2.12. However, it was assumed that eq 16 and 18 would at least predict a value of the reaction rate of the correct order of magnitude, and it could be used for the subsequent simulatin works before any further refined results are obtained. The results from the experiments with the catalytic membrane reactor are shown, along with the results of the numerical simulations, in Figures 5-8. The feed composition and total pressures of the feed side and permeate side are kept relatively constant ( x l 0 = 0.49, x 2 0 = 0, x 3 0 = 0.51, Pf = 191 kPa, and P, = 99 kPa). The experimental conditions and obtained results are also listed in Table I. In Figures 5 and 6, the total benzene molar fraction of the organics in total output (YbT = X,) and the individual ones (Ybf and Yb,) in the feed-side output (reject stream) and the permeate-side output are plotted as a function of the space time (7 = V c / F o ) .The total conversion (X,) is
1140 Ind. Eng. Chem. Res., Vol. 27, No. 7, 1988 1 .o
defined as the mole fraction of benzene (product) in the total organics (cyclohexaneand benzene) present in each output:
0.8
Ybf =
0.6
n
> 0.4 Experimental
Calculated -.
&
YbP Ybl Ybi (XT)
0.2 e
0.0
5
10
15
20
-
25
40
35
30
J 45
SPACE T I M E , s
.
25
25
Experimental Calculated
%x w
$ a
4
LL
15-
\
\
'0-
3 0 z
- - - -- - -
20-
\
\
- - --
5-
\
- '\
k
\
-L - -- - L- - -- - -- -
'
