16
Ind. Eng. Chem. Process Des. Dev. 1982, 27, 16-25
Effectiveness Factors for Partially Wetted Catalysts in Trickle-Bed Reactors Wlrat Sakornwimon and Nlcholas D. Sylvester Chemical Englneering Department, The University of Tulsa, Tulsa, Oklahoma 74 104
Cocurrent downflow of gas and liquid over a catalyst bed can result in partial wetting of the catalyst pellets with the flowing liquid, resulting in a nonuniform surface concentration gradient and an unsymmetrical concentration distribution within the pellet. In this paper a finite difference method was used to determine the effectiveness factor for spherical catalyst particles for three different cases: liquid and vapor phase reaction with complete internal wetting and vapor phase reaction with incomplete internal wetting. An approximate explicit expression was developed for each case. The deviations of the explicit expressions from the corresponding numerical results and the effects of various parameters (Le., mass transfer resistances, Thiele moduli, and wetted fraction) on trickle bed reactor performance were studied for each case.
Introduction and Literature Review Partial catalyst wetting is a common phenomena found in trickle bed reactors where gas and liquid flow cocurrently downward (e.g., Sedricks and Kenny, 1973; Satterfield and Ozel, 1973; Saterfield, 1975; Colombo et al., 1976; Herskowitz et al., 1979). The contacting effectiveness is improved as liquid superficial velocity is increased. Bondi (1971) noted that the contacting effectiveness was still improving with liquid flow rate at velocities as high as 3 kg/m2 s. The performance of a trickle bed reactor may be divided into three different cases. First, if the limiting rewtant is present only in the liquid phase (e.g., hydrodesulfurization of a heavy petroleum fraction), the reaction occurs only on the “active” or wetted part of the catalyst. In this case, the observed reaction rate increases with an increase in the fraction of the catalyst external surface wetted by the flowing liquid, and also the liquid flow rate (Mears, 1974; Colombo et al., 1976). In the second case, if the limiting reactant is present in the gas phase (i.e., it is volatile at reaction conditions or it is in the gas phase itself) and the reaction is endothermic or the heat evolved by the exothermic reaction is not sufficient to evaporate the internal liquid, the catalyst pores will be completely filled with liquid due to capillarity. Since both the liquid and gas covered parts of the catalyst surface contribute to the reaction and the gas-solid mass transfer resistance is less than that of gas-liquid-solid (or liquid-solid if the reactant is also present in the liquid phase), the gas covered surface is more efficient. Thus the observed reaction rate decreases with increasing liquid wetted fraction (Satterfield and Ozel, 1973; Herskowitz et al., 1979). Finally, for exothermic and intraparticle diffusion limited reactions, if the heat of reaction and/or the reactant concentration is high, the heat evolved by the reaction on the gas covered part may be sufficient to evaporate some of the internal liquid. When this happens, the observed reaction rate is dramatically increased due to the increase in effective diffusivity (Sedricks and Kenny, 1973; Hanika et al., 1976, 1977). Case 1. Liquid Phase Reaction and Complete Internal Wetting. Dudukovic (1977) has summarized the previous expressions for the interpretation of the effect of incomplete catalyst wetting on trickel bed reactor performance for the nonvolatile reactant case. Most of the expressions assumed that the liquid space time is the basic parameter for the reactor performance (Ross, 1965; Henry and Gilbert, 1973; Sylvester and Pitayagulsarn, 1974). All 0196-4305/82/1121-0016$01.25/0
the expressions except that of Sylvester and Pitayagulsarn (1974) assumed plug flow of liquid, no external mass transfer resistances, isothermal conditions, first-order irreversible reaction, and nonvolatile liquid reactant. Sylvester and Pitayagulsarn (1974) took axial dispersion and external mass transfer into consideration. Mears (1974) assumed that the reaction rate is proportional to the fraction of the external catalyst area contacted by flowing liquid; i.e. VTB = VF (1) By using Aris’ (1957) definition for the modulus of irregular particles, Dudukovic (1977) proposed the relation F tanh (Fi$/F) (2) VTB = 4 In a subsequent paper, Dudukovic and Mills (1978) solved the governing equations for slab geometry. The expression for the effectiveness factor was in the form of an infinite series and the results were presented in graphical form. The results were also compared with expressions (1)and (2). It was found that Mears’ expression showed large deviations from the true values at low and intermediate Thiele moduli and became a good approximation only at high moduli. The agreement of results at high moduli was attributed to the fact that at large moduli the reaction occurs only in a narrow zone (shell) close to the exterior surface; thus, the utilization of the pellet is directly proportional to the size of this zone which in turn is directly related to the fraction of external area wetted. Recently, Mills and Dudukovic (1979) determined the trickle bed reactor effectiveness factor for the case of negligible external mass transfer resistance by applying a residual least-square method to the dual series equations obtained from the governing differential equations and boundary conditions. The method involved the solving of an infinite set of linear equations and it was found that acceptable results were obtained at a matrix size of 140 X 140 for a Thiele modulus [R(k/D.,,)’/2]of 50. Case 2. Vapor Phase Reaction and Complete Internal Wetting. Satterfield and Ozel(1973) studied the hydrogenation of benzene at 76 O C (which is 4 O below its boiling point) in a bed of 2% Pt on alumina spherical pellets 0.635 cm in diameter. They found that even with a good initial liquid distribution, the liquid in the trickle bed reactor tended to flow downward in rivulets, resulting in partial wetting of the catalyst surface. However, the 0 1981 American
Chemical Society
cw,xk!
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 1, 1982
internal wetting was complete due to capillarity. The vapor phase reaction was found to be catalyzed directly by the solid catalyst. Furthermore, the steady state rate of reaction and the ratio of vapor phase to liquid phase reaction decreased with increasing liquid flow rate. Their results show that the fraction of catalyst surface covered with the liquid increased with increasing liquid flow rate and the vapor covered fraction was more efficient. Herskowitz et al. (1979) employed the hydrogenation of a-methylstyrene at 40.6 "C and 1atm as a model reaction to study the effect of partial wetting on trickle bed reactor performance. Using two catalysts of different activities, they found that the plot of observed reaction rate vs. liquid flow rate showed a minimum at intermediate liquid flow rate for the more active catalyst and a steady increase for the less active catalyst. This indicates that as the liquid flow rate increases, there are two competing factors which affect the trickle bed reactor performance. Since the external mass transfer resistances decrease with increasing liquid flow rate, the observed reaction rate tends to increase. In addition, since liquid wetted fraction increases with increasing liquid flow rate and the gas covered portion of the catalyst is more efficient, this tends to decrease the observed reaction rate. Thus, for the more active catalyst a t liquid flow rates below the observed reaction rate minimum, the effect of partial wetting was more significant. On the other hand, for the less active catalyst and the more active catalyst at liquid flow rates above the observed reaction rate minimum, the observed reaction rate increases with increasing liquid flow rate because the effect of external mass transfer is more significant. Ramachandran and Smith (1979) used a standard finite difference method to solve the governing differential equation and boundary conditions for an infinitively long, rectangular catalyst slab. They developed an explicit expression for the effectiveness factor which was found to differ by no more than 13% from the numberical results for particular values of Thiele modulus, wetted fraction, and Sherwood numbers for external mass transfer. Case 3. Vapor Phase Reaction and Incomplete Internal Wetting. Sedricks and Kenny (1973) employed the selective hydrogenation of crotonaldehyde to nbutyraldehyde to investigate the behavior of a trickel bed reactor in which the catalyst was incompletely wetted. The reaction was conducted near ambient conditions over a palladium catalyst deposited on a porous alumina. The reactants and products were present in both the gas and liquid phases due to the moderate vapor pressure of the organic compounds. The liquid phase catalyst effectiveness factor was found to be about 0.1. It was found that direct vaporsolid reaction dominated the overall reaction rate, even when the extent of wetting was large, due to a large vapor phase effective diffusivity and a higher internal temperature. Hanika et al. (1976) used the hydrogenation of cyclohexene to cyclohexane on a palladium catalyst to study the effects of hydrogen flow rate, feed temperature, and concentration on reactor temperature profiles. It was found that under certain conditions the heat liberated by the reaction caused evaporation of the liquid in the reactor which produced a stepwise increase in the observed reaction rate. In a subsequent paper, Hanika et al. (1977) studied the hydrogenation of 1,5-cyclooctadiene dissolved in cyclooctane and found similar results. In this paper a finite difference method is used to obtain the trickle-bed reactor effectiveness factor for spherical catalyst particles for all three cases discussed above. In addition, approximate explicit expressions are obtained
17
w y /
Y
Figure 1. Catalyst system configuration and coordination.
for each case and the effects of mass transfer, Thiele moduli, and wetted fraction on reactor performance are studied. Mathematical Models The porous catalyst is represented by a spherical particle of radius R. The nonwetted region on the outer surface has a circular shape. The angle made by the lines between the center of the sphere and two opposite points on the nonwetted region is BD. Figure 1shows the system under consideration. For this wetting configuration, the fraction of the outer surface which is wetted, F,is related to the angle BD by the expression
]
F = l - [ 1 - COS ( 8 ~ / 2 )
(3)
The reaction is assumed to be isothermal, first order, and irreversible in limiting reactant A. Case 1. Liquid Phase Reaction and Complete Internal Wetting. The internal pores are assumed to be filled with liquid due to capillary forces. Furthermore, it is obvious from Figure 1that the concentration distribution in the pellet is independent of angle ,f3 and is symmetric on the axis z. At steady state, the conservation equation for A in terms of its intraparticle concentration, CAL,in the liquid filled pores is
There are two sets of possible boundary conditions set 1: CAL= C, at p = R , 8D/2 I6 I a (5) CAL = 0 at p = R, 0 I8 I fID/2
(6)
-~CAL - -0
(8)
set 2:
dP
at p = R,O I 8 ItlD/2
The first set of boundary conditions assumes a constant concentration on the wetted region and that the concentration on the nonwetted part is zero. These assumptions are equivalent to the statement that diffusion on both regions is negligible compared to the rates of the external mass transfer and chemical reaction. The second set of boundary conditions was obtained from the equality of the external mass transfer to the catalyst surface and the diffusion rate on the wetted part and by assuming that there is no mass transfer across the outer surface of the nonwetted region. This represents a
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 1, 1982
18
more rigorous set of conditions. At the center, it is obvious the concentration is not a function of angle 0; thus, we have for r = 1 and OD/2 I6 IT
~'CAL 2 ~ C A L CAL - kdp2 P dp DA~
-+---
a9
(9)
Moreover, from the symmetry of the system, we have, at the center and 0 = ~ / 2 ~C -A L -0 dP Applying L'Hospital's rule we have
A
for r = 1 and 0 I O IOD/2 For boundary conditions set 1, the effectiveness factor based on the surface concentration, VTB, is defined as VTB
= 3JZn.Jn.JRcAL p2 sin 0 dp d0 dP/47rR3C,
Since CALis independent of Substituting eq 10 into eq 9 we have ~'CAL ~CAL 3=dp2 DAL Furthermore, at any radius and 6 = 0 or 6 = K, we have aCAL/a6= 0, and, from L'Hospital's rule
Substituting eq 12 into eq 4, we obtain
at 0 = 0; or 0 =
A
Introducing the dimensionless terms r = p/R and 4L =
or in dimensionless terms
For B.C.'s set 2, we have the effectiveness factor based on the bulk liquid concentration, vmL. In dimensionless terms, the expression is the same as eq 21; however, it must be remembered that the definitions of dimensionless concentrations are different. Case 2. Vapor Phase Reaction and Complete Internal Wetting. The limiting reactant will be present in the vapor phase when the limiting reactant is in the gas phase itself or when it is volatile at the reaction conditions. For this case the governing differential equations remain unchanged. However, there is only one set of boundary conditions and following the procedure described for case 1 the dimensionless forms of the boundary conditions are obtained.
Jqm 5R d m =
for r = 1, OD/2 I0 5
Sext
RKgs -(I DAL
P A , = CAL/D, for B.C.'s set 1
or we can transform the differential eq 4, 11, and 13 and boundary eq 5-8 to obtain ar2
2 r
~*AL
ar
+ -1r2
PA,
ao2
+ -cot -- 0
~*AL
r2
d0
- 94L2*AL (14)
A
= 1 for r = 1 and OD/2 5 0 IA
P A , = 0 for r = 1, 0 I0 I6 D / 2
B.C.'s set 2
aPAL =-
ar
(23)
FgLs.
KgLS
B.C.'s set 1 *A,
PAL)
where Kpsis the gas-solid mass transfer coefficient for the nonwetted catalyst surface. When the limiting reactant is present in both the vapor and liquid phases, equilibrium between the phases is assumed. When the limiting reactant is present only in the gas phase, KLsin eq 22 is replaced by the composite coefficient, If KgL represents the overall coefficient for gas to liquid mass transfer, the composite coefficient can be determined from 1
for r = 0, 0 = ~ / 2
for 6 = 0 or 0 =
-
T
for r = 1, 0 I O C OD/2
P A , = CAL/CL for B.C.'s set 2
-PAL +--
0,we have
(17) (18)
- 1 KgL
+- 1
KLS
I t should be noted that Kmis greater than KU and Kp is always greater than K Ls. Thus the gas covered pare is more efficient than the tiquid covered part. Case 3. Vapor Phase Reaction and Incomplete Internal Wetting. In this case the portion of the catalyst between and is assumed to be dry because of evaporation of the incoming liquid by the heat of the reaction. It is known that in the fixed-bed catalytic reactors the major seat of thermal resistance is usually external to the catalyst surface (Carberry, 1976). Thus it is assumed
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 1, 1982 10
that the catalyst is isothermal. In addition to eq 14, 15, and 16, which are applicable to regions OD/2 < 0 < T , r = 0 and 0 = r / 2 , and 0 < r I 1 and 0 = A, respectively, we also have
and eINl.T+P
w
+l g @IN11
Figure 2. Finite difference grid.
O 1.0) the effect of the gas-phase diffusivity overcomes that of H and curves lB, 2B, and 3B are all greater curve C. Figure 10 shows the effect of wetted fraction on gmL for various values of H. For the conditions chosen the gas phase portion is more effective than the liquid and gTBL decreases as F increases. The effectiveness factors for all H values converge to the same value as F approaches unity. Figure 11 illustrates the effect of the liquid-solid Sherwood number on mL for various values of H and the ratio ShLs/Sh,,. Since Db is at least two orders of magnitude greater than DA and since Kgs is an order of ShLsis always greater than magnitude larger than kLs, Sh,. Figure 11shows that gmL increases with increasing ShLs and decreasing ShLs/Sh,, due to the increased rate of external mass transfer. Application of the Results At this time, there are not sufficient data available which can be used to evaluate the models developed for cases 1 and 3. The experimental work of Herskowitz et al. (1979) contains sufficient data to illustrate the application of the model developed for case 2. Equation 53 can be applied to trickle-bed reactor design if the values of 7, 4, effective diffusivity, and particularly F and the mass transfer coefficients are known. The values of g, 4, and effective diffusivity must be determined experimentally when the external wetting is complete (Satterfield, 1970). Herskowitz et al. (1979) presented a method for obtaining F and the liquid-solid mass transfer coefficient from their experimental data. Assuming a cubic catalyst particle, they obtained an implicit relationship between gTBL and the mass transfer coefficients, Thiele modulus and F similar to eq 53. Since the gas-solid mass transfer resistance was found to be negligible, they presented the relationship wLand F and the liquid-solid mass transfer coefficient for two different 4 in graphical form. These two sets of curves were used to graphically determine F and KLS from the experimental data. However, explicit relationships for determining F and K L S can be obtained using eq 53. If the resistance to mass transfer on the gas covered surface is negligible, eq 53 becomes
Since F and ShLs are the same for a given catalyst diameter and at a particular liquid flow rate, they can be determined from the experimental data for two different catalyst activities (i.e., the same R but different 4Land gL). For two data points eq 61 can be solved for F and ShLs as shown in eq 62 and 63
F=
( h 2 7 2- 4i271)(72 - V T B L , ~ ) ( ~~~T B L , ~ ) 4 2 2 1 2 2 ( ~ 1- V T B L , ~ )- d i 2 ~ i 2 (~V 2TBL,~)
ShLs =
4i27i(g~~ - ~0i(1 , i - F)) (71 - V T B L , ~ )
(62) (63)
where ~ T B L , ~ ,T B L are , ~ the effectiveness factors for two different catalyst activities, gl, q2 are the effectiveness factors for the two catalyst activities for completely wetted conditions, and 41,42are the corresponding Thiele moduli. Herskowitz et al. (1979) determined the rate of hydrogenation of a-methylstyrene over a short bed of palladium/aluminum oxide catalyst at 40.6 "C and 1 atm. Reaction rates were measured over a wide range of liquid flow rate for two catalyst activities (corresponding to 0.75% and
INTERPRETED WITH PRESENT MOD
F SATTERFIELO (1975)
3
0 510-2
10-1
uL,
cmh
Figure 12. Wetted fraction vs. superficial liquid velocity.
1631 162
4
1
1
16'
a
//
1
I
I I
I
I
IO
UL, cm/s
Figure 13. Liquid-solid mass transfer coefficient vs. superficial liquid velocity.
2.5% Pd on A1,0,). From their liquid full reactor experiments, the effectiveness factors were found to be 0.169 and 0.0610 for Thiele moduli to 5.58 and 16.1, respectively. Since it was found that the reaction rate did not vary with gas flow rate, the gas-solid mass transfer resistance was negligible and eq 61-63 are applicable to their results. Experimental values of the gmL at specific liquid rates were obtained from their observed reaction rate data. Values of the gTBL, g, and 4 were substituted into eq 62 and 63 to determine the corresponding F and the S h u values. The F values obtained are plotted in Figure 12 as a function of liquid rate. The shaded area is the range of F values suggested by Satterfield (1975). The figure shows that F increases with liquid rate from 0.68 at UL = 2.0 cm/s to practically complete wetting at UL = 2.0 cm/s. From the ShLsvalues obtained, the liquid-solid mass transfer coefficients,Km, were calculated from the relation 3DA,ShLS (64) KLS =
R
These values are plotted in Figure 13 vs. liquid rate. Reasonably good agreement can be seen between the results and the correlations developed by Goto and Smith (1975) and Dharwadkar and Sylvester (1977). Closure Liquid superficial velocity may have different effects on a trickle-bed reactor performance depending upon the phenomena occuring in the reactor. It is well known that mass transfer coefficients and the catalyst external wetted surface increase with liquid flow rate. Furthermore, the observed reaction rate increases with increasing mass transfer rate but it may increase or decrease as catalyst wetted surface increases. If the limiting reactant is non-
Ind. Eng. Chem. Process Des. Dev. 1982, 27, 25-29
volatile the observed reaction rate increases with both mass transfer and wetted fraction; thus, for this case the rate always increases with liquid superficial velocity. For the case where the limiting reactant is also present in the gas phase, the gas-covered surface is more efficient than wetted surface due to a higher rate of mass transfer and the observed reaction rate decreases as wetted fraction increases. Because of the competing effects between wetted fraction and mass transfer resistance, the observed reaction rate may increase or decrease as liquid flow rate increases. Finally, if catalyst internal wetting is incomplete, the gas-phase Thiele modulus and Henry's law constant may play important roles in trickle-bed reactor behavior. The analysis presented demonstrates that trickle-bed reactor effectiveness factors larger than unity are possible for this case if the limiting reactant is highly volatile (H> 1.0) even for isothermal catalyst and especially for I $ ~ or order 1 or less. Nomenclature C, = concentration of reactant A in the liquid-filled pores within the spherical catalyst, mol/cm3 C h = concentration of reactant A in the vapor filled pores within the spherical catalyst, mol/cm3 CL = concentration of reactant A in bulk liquid, mol cm3 C, = concentration of reactant A in bulk gas, mol/cm C, = concentration of reactant A at the catalyst surface, mol/cm3 \ k ~= dimensionless concentration defined as CAL/C~or
5
bAL/ C L @A, = dimensionless concentration
defined as C /C, D, = effective diffusivity of A within the liquid hled pores of catalyst, cmz/s = effective diffusivity of A within the vapor filled pores D$f catalyst, cm2/s F = fraction of the external particle surface covered by liquid Fi = fraction of the internal particle volume filled with liquid K = gas-liquid mass transfer coefficient, cm/s K"" = gas-solid mass transfer coefficient, cm/s f u = gas-liquid-solid mass transfer coefficient, cm/s d m = liquid-solid mass transfer coefficient, cm/s
25
It = reaction rate constant, cm3 liq/cm3 cat. s R = catalyst radius, cm
mass transfer, number for gas-solid mass transfer RK,/ p=
coordinate in spherical system
4L = liquid phase Thiele modulus
& = vapor phase Thiele modulus p,O OD
= spherical coordinates
= angle shown in Figure 1
Literature Cited Aris, R. Chem. Eng. Sci. 1957, 6 , 262. Bondi, A. Chem. Technol. Mar 1973, 185. Carberry. J. J. "Chemical and Catalytic Reaction Engineering"; McGraw-HIII: New York, 1976. Colombo, A. J.; Baldi, G.; Sicardi, S. S. Chem. Eng. Scl. 1976, 37, i i n i - i i n."". ri Dharwadkar, A.; Sylvester, N. D. AIChE J . 1977, 23, 376. Dudukovic, M. P. AIChE J . 1977, 23, 940-944. Dudukovic, M. P.; Mllls, P. L. ACS Symp. Ser. 1978, 65, 387-399. Germaln, A. H.; LeFebvre, A. G.; L'Homme, G. A. Adv. Chem. Ser. 1974, No. 133. 164. Hanika, J.; Sporka, K.; Ruzicka. V.; Hrstka, J. Chem. Eng. J . 1978, 72, 193- 197. Hanika, J.; Sporka, K.; Ruzicka, V.; Pistek, R. Chem. Eng. Sci. 1977, 32, 525-528. Henry, H. C.; Gilbert, J. 8. Ind. Eng. Chem. Process Des. Dev. 1973, 72. 328. Herkowitz, M.; Carbonell, R. G.; Smith, J. M. AIChE J. 1979, 25, 272-283. Mears, D. E. Adv. Chem. Ser. 1974, No. 733, 218-227. Mills, P. L.; Dudukovic, M. P. Ind. Eng. Chem. Fundam. 1979, 18, 139-149. Ramachandran, P. A.; Smith, J. M. AIChE J . 1979, 25, 538-542. Ross, L. D. Chem. Eng. Prog. 1985, 67(10), 77. Satterfieid, C. N. "Mass Transfer in Heterogeneous Catalyst"; M.I.T. Press, CambrMge Mass., 1970. Satterfield, C. N. AIChE J. 1975, 21, 209-226. Satterfield, C. N.; Ozel, F. AIChE J. 1973, 19, 1259. Sedrick, W.; Kenny, C. N. Chem. Eng. Sci. 1973. 28, 559. Sylvester, N. D.; Pltayagulsarn, P. Can. J. Chem. fng. 1974, 52, 539. Sylvester, N. D.; Pltayagulsarn, P. Ind. Eng. Chem. Process Des. Dev. 1975, 14, 421-426.
. .". .
Received for review October 1, 1979 Revised manuscript received October 20, 1980 Accepted September 25, 1981
Kinetics of the K,CO,-Catalyzed Steam Gasification of Carbon and Coal Guillermo L. Gurman and Eduardo E. Wolf' Chemical EnQh39finQ Depafiment, University of Notre Dame, Notre Dame, Indiana 46556
A study of the atmospheric pressure kinetic of the K,C03-catalyzed steam gasification of activated carbon and Illinois No. 6 coal char is presented. The data were obtained using an electrobalance and experimental conditions which excluded mass and heat transport limitations. A model which assumes that the reaction rate is proportional to the catalyst-solid contact area was used to analyze the data. The porosity was related to solid surface area by using the grain model to describe pore structure. The model fits well the data in the complete range of operating conditions used. Activation energies of 58 and 62 kcal/mol obtained for coal and activated carbon, respectively, are independent of conversion and suggest a unique reaction path.
Introduction The use of catalysts in coal gasification was recognized long ago as an effective way of increasing reaction rates and methane yield and decreasing reactor energy demand (Johnson, 1976). Aside from activity considerations, cat0196-4305/82/1121-0025$01.25/0
alyst recovery is a fundamental constraint in catalyst selection. Haynes et al. (1974) reported the effect of over 40 substances in the gasification of coal at 20 atm and 850 OC. These authors reported that K2C03,KC1, and LiC03 were the most active catalysts, producing mainly H2, CO, 0 1981 American
Chemical Society
