Ind. Eng. Chem. Fundam., Vol. 17, No. 3, 1978 199
Bi,
= Biot number for external mass transfer, kgLID C = reactant concentration, mol/cm3 d = mfc#q2/rlBi,A D = intrapellet diffusivity, cm2/s Da = Damkohler number, k/kg?i f = external area as a fraction of total area k = homogeneously defined rate constant, s-l k' = rate constant based on active area, cm/s k = external mass transfer coefficient, cm/s K2 = constants, defined by eq 16 and 21 1 = distance from center of slab, cm L = half-thickness of slab, cm m = k A/k p = - 771/2 q = (1 + r2)1/2 r l = kdk2 r2 = k3/kl s = internal active area per unit volume, cm-l t = constant, defined by eq 21 u = CIC,
21,
x = 11L Y = yield
Greek Letters
6 = Thiele modulus, L(k/D)1/2 y = diffusivity ratio, DA/DB 7 = catalytic effectiveness factor
Subscripts 0 = bulk fluid conditions A = pertaining to species A B = pertaining to species B L i t e r a t u r e Cited Carberry, J. J., "Chemical and Catalytic Reaction Engineering."McGraw-Hill, New York, N.Y., 1976. Goldstein, W., Carberry. J. J., J. Catal., 28, 33 (1973). Kramer, S.J., J. Catal., 5, 190 (1966).
Received for review July 29,1977 Accepted April 17, 1978
lntraparticle Mass Transfer Effects and Selectivity in the Palladium-CatalyzedHydrogenation of Methyl Linoleate Kellchl Tsuto,' Peter Harriott, and Kenneth B. BIschoff** School of Chemical Engineering, Cornell University, lthaca, New York 74853
The hydrogenationof methyl linoleate to methyl oleate and methyl stearate was studied in a 6-in. stirred batch reactor using several particle size fractions of a 1% Pd/carbon catalyst. The hydrogenations of both methyl linoleate and methyl oleate were first order with respect to hydrogen, but some of the linoleate appeared to react directly to stearate, perhaps because of nonequilibrium adsorption of reactants. The intraparticle mass transfer of the liquid reactants had effects on the product distribution (selectivity), and the effective diffusivity of the liquid reactants in the catalyst particle was estimated to be about that of hydrogen. The selectivity was more sensitive to hydrogen concentration than to the catalyst particle diameter.
Introduction
In a previous study by Cordova and Harriott (1975), the hydrogenation of methyl linoleate to methyl oleate and methyl stearate was studied in a 6-in. stirred semibatch reactor using 1%Pdlcarbon powder catalysts. Some features of the kinetics of the two reactions were determined, but the selectivity was different for different particle sizes and different operating conditions and there were not enough data to develop a correlation. It was suggested that the diffusion of linoleate and oleate in the catalyst pores would have to be considered as well as the diffusion of hydrogen. In work by van der Plank et al. (1974), intraparticle mass transfer effects were also found in the hydrogenation of fatty oils using Ni/SiO2 catalysts with particle sizes ranging from 1.8 to 3.8 wm. To fit the data, they had to use very low values of the diffusivity for the liquid reactants, 10-3 to times the diffusivity for hydrogen, but the calculations were inaccurate because of very steep concentration gradients near the particle surface. Industrial Research Laboratories, Kao Soap Company, Ltd., Wakayama, Japan. Address correspondence to this author at the Department of Chemical Engineering, University of Delaware, Newark, Del. 19711.
0019-7874/78/1017-0199$01.00/0
As shown by several workers, the equations for absorption of hydrogen, transfer of hydrogen to the external particle surface, and pore diffusion plus first-order reaction can be combined to give an overall rate equation -1=
1
1 kcac(H2)i
~k(H2)i
or
For runs made at constant hydrogen pressure, a plot of l / r o vs. l / m should be linear as pointed out by Davis et al. (1932), reported by Sherwood (1937). The intercept is the gas absorption resistance, and the slope is the catalyst resistance RCR,which includes an external resistance Rc and an internal resistance RR. The gradients for linoleate and oleate are ignored a t this stage because both are strongly adsorbed, and the hydrogen consumption rate is found to be nearly constant in each stage of the reaction. The external and internal resistances can be separated using data for different particle sizes. The external area varies inversely with d,, and k, varies with about d,-0.75 for 10 to 0 1978 American Chemical Society
200
Ind. Eng. Chem. Fundam., Vol. 17, No. 3, 1978
Table I. Reaction Rates at 80 "Cand 6 L of Hz/min
run no.
pm
catalyst loading, m , g of cat./ L of oil
101 102 103 112 104 105 106 107 108 109 110
unfractionated unfractionated unfractionated unfractionated 12 50 70 25 12 50 12 70
0.448 0.995 0.240 5.509 0.452 0.452 0.453 0.453 0.717 0.716 0.722 0.714
particle size,
111
t
> -10
hydrogen pressure, psia 85.0 85.0
85.0 85.0
85.0 85.0 85.0 85.0 44.7 44.7 44.7 44.7
0.0262 0.0343 0.0162 0.0432 0.0315 0.0195 0.0145 0.0273 0.0238 0.0160 0.0310 0.0132
8.00 8.00 8.00 8.00 4.86 13.69 21.73 7.08 11.50 26.13 11.50 35.52
oleate reaction overall catalyst resistance, reaction RCR, rate, r2, min g g-mol/ of cat./ min L g-mol 0.0104 0.0194 0.00431 0.0333 0.0122 0.00862 0.00510 0.0116 0.0122 0.00694 0.0208 0.00342
33.5 33.5 33.5 33.5 25.30 42.95 79.34 29.54 40.00 84.54 40.00 190.15
min. 2.50
The reaction rate constant can be obtained by a trial-anderror procedure. (1) Assume a value of 4 for the smallest size and calculate 4 for the other sizes. (2) Get values of from eq 5. (3) Plot ~ R Cvs. R qdp1.75,and if the plot is linear, get l/k(Hz)i from the intercept.
o.lop cn
linoleate reaction overall catalyst initial" resistance, reaction RCR, rl, min g g-mol/ of cat./ g-mol min L
1
I
I
I
50
100
I50
Time, min
Figure 1. Hydrogenation of methyl linoleate.
100-pm particles (Harriott, 1962). The catalyst resistance is
RCR= ad,'.75
1 + ___ +(Hdi
(3)
Rearranging eq 3 gives
+
1
~ R C= R 77adP1.75 (4) k(H2)i The effectiveness factor is a function of the diffusion modulus 4, which is proportional to d,. (5) (6)
Experimental Procedure Batch hydrogenations were carried out in the 6-in. stirred tank used by Cordova and Harriott (1975). The 1%Pd/carbon catalyst (P.V. = 1.3 cm3/g; S.A. = 343 m2/g) was separated by sieves into fractions with average sizes of 12,25,50, and 70 pm. Some runs were made with unfractionated catalyst, which had an average size of 27 pm. The reaction rates were determined by chromatographic analysis of liquid samples. The range of experimental variables studied and the reaction results are given in Table I. A typical reaction curve with the smallest particle size is given in Figure 1. The linoleate concentration decreased at a constant rate with time after the second sample was taken or after about 10 min. The lower beginning rate may be caused by the time needed to purge nitrogen from the system; this effect was not observed in previous tests where the gas flow rate was three times higher. After the beginning period, the linoleate concentration decreased linearly with time, and only a small amount of stearate was formed until the linoleate almost disappeared (first step). The rate of stearate formation (second step) then increased severalfold, which indicates that linoleate is adsorbed much more strongly than oleate. The first step is apparently zero order with respect to linoleate except very near the end of linoleate hydrogenation. The oleate reaction is probably also zero order, though most runs were carried to only moderate oleate conversion. Although the amount of stearate formed was low in the initial stages of the reaction, there were significant changes in selectivity with reaction conditions. These effects will be treated in detail after the mass transfer resistances for hydrogen have been discussed. Separation of Resistances The hydrogen reaction rates for the first step were calculated from the slope of the essentially straight lines of linoleate concentration vs. time. The reciprocals of these rates were plotted against the reciprocal of catalyst loading in Figure 2. The rates of reaction of methyl oleate to methyl stearate
Ind. Eng. Chem. Fundam., Vol. 17, No. 3, 1978
d P * V
Key
un-fractionated
Q
100 /
201
0
12
A
25 50
v
70
0 A
12 50
V
70
Linoleate 0
a5 psla
a
Oleate
45 PSI0
,
100
50
Pressure, psia
Figure 4. Effect of pressure on hydrogenation of methyl linoleate and methyl oleate.
6-
200
!
I
assumed q for 12-pn Poriiclns
Key same as in Figure 2
A
0.95
0 9.90 0 0.85
I
I I
I I
,I
01
0
100
200
300
400
500
600
77475
Figure 5. Determination of intrinsic catalyst resistance for linoleate hydrogenation.
I
I
I
I
1
1
0
I
2
3
4
5
.&, gr-' Figure 3. Determination of bubble and catalyst resistance for oleate hydrogenation. were measured after all the methyl linoleate had reacted. The reciprocal rates are plotted in Figure 3. The reciprocd plot for unfractionated catalyst deviates from a straight line at the lowest catalyst loading, but this does not affect the determination of gas absorption resistance. The increase in reaction resistance at the lowest catalyst loading may be caused by catalyst poison, which is more important a t lower catalyst loadings. Agglomeration of catalyst particles might also cause the plots to curve upward; however, in this study, visual observation of the catalyst particles in the oil indicated uniform particle distribution and no evidence of agglomeration. For a given pressure, the intercepts of the reciprocal plots for the first step and the second step are the same, which is expected, since the gas absorption resistance should be almost
the same for hydrogen in methyl linoleate and in methyl oleate. Figure 4 shows the effect of pressure on the hydrogenation rates. The ordinate, the reciprocal of RCR, is the expected reaction rate per gram of catalyst for a solution saturated with hydrogen. Both reactions are first order with respect to hydrogen, which does not completely agree with previous work, where one half order was reported for oleate hydrogenation a t 121 "C (Cordova and Harriott, 1975). According to the method mentioned earlier, intrinsic reaction resistances l/k (H2)iwere separated from the catalyst resistance RCRusing the data for methyl linoleate hydrogenation at high pressure. The method is illustrated in Figure 5 , and a good fit was obtained for 12,25, and 50-pm particles assuming an effectiveness factor of 0.9 for the smallest particles. The data for the larger particles did not fit very well and were not used in determining the intrinsic catalyst resistance. From the intercept of Figure 5 and the hydrogen solubility [estimated from data of Wisniak and Albright (1961)], 0.0125 mol/L, values of k and D e were calculated, giving D e = 3.6 X 10-5 cm2 s. This is a reasonable value, though not very accurate, since a change in 7 from 0.9 to 0.95 would increase De by 70%. The values of 17 and k were not much affected by using an exponent of 1.65 or 2.0 instead of 1.75 in Figure 5 . The external resistances for other sizes were calculated from RCRby subtracting l/qk(Hz)i and values are given in Table 11. The external resistances vary from 9 to 46%of the overall catalyst resistance, which means that the hydrogen concen-
202
Ind. Eng. Chem. Fundam., Vol. 17, No. 3, 1978
Table 11. Catalyst Resistances for Step 1
RCR, d,,
pm 12 25 21 50
RC,
mind mol
calcd
4.86 7.08 8.00 13.70 21.7
0.90" 0.70 0.61 0.44 0.34
9,
70 0 Assumed
4 1-32" 2.15 2.97 5.50 1.70
ming/ mol
%ext. resist.
0.42 1.37 2.03 4.61 9.94
9 19 25 34
2
e
0.10
0
c
46
0
c
s
.-
v)
0
0,151
l -
e
010-
0 0 c
O.I0
0
calculated curves
0
i
5 0
0.05
0.5
0
1.0
Linoleate conversion X,
Figure 7. Determination of kdeaO for case I1 with run 105.
c
C
P 0.15-
Key
A
m 0 0
*
X
Run No.
103 101
102 112
HES, initial
rn
0240 0448 0995 5509
000571 000423 000252 000058
0
c
e0
J
0
05 0.5
10
010-
c
Linoleate conversion X L
0
-calculated curves
c
Figure 6. Product distribution for run 105 and predictions based on case I.
E
0
r 0.05
tration at the surface was 91 to 54% of the value in the bulk solution, which in turn was less than the solubility because of the gas absorption resistance. As a check on the separation of resistances, the estimate of D e was used to calculate values of 4 and 9 for the second stage of the reaction, which had an intrinsic rate constant that of the first stage. The predicted values of 7 ranged from 0.98 for 12-hm particles to 0.76 for the 50-pm fraction. The measured catalyst resistances indicated a somewhat greater effect of pore diffusion, with 9 falling to 0.64 for the 50-pm particles, but this degree of agreement seems satisfactory.
Product Distribution The amount of stearate formed in the first stage of the reaction was small, but varied with reaction conditions. Some of the results are shown in Figures 6-8, where x s is the amount of stearate formed divided by the initial concentration of linoleate, and X L is the total conversion of linoleate. The slope of these curves is the reaction rate ratio
u
0
I .o
05
Linoleate
conversion
X,
Figure 8. Effect of catalyst loading on product distribution at 85 psia. -=rz k2KoO
(8) r l klK& If eq 8 applied with 0 and L equal to the bulk concentrations, the stearate conversion curves would be the same for different particle sizes and hydrogen concentrations, which is not the case. The selectivity, defined as the ratio of rates a t equal concentrations, would also be constant during a run if eq 8 applies, and calculations indicated an increase in selectivity with conversion for most runs.
0
(7) If methyl linoleate and methyl oleate were competitively adsorbed and were at equilibrium coverage on the surface, and if the two reactions had similar kinetics, the ratio of reaction rates would depend on the ratio of the rate constants, the adsorption constants, and the solution concentrations.
sel. = 2 x r2 L An increase in selectivity with conversion would be expected if the internal gradients for 0 and L are significant. T o evaluate this effect, the equations for pore diffusion and reaction were solved numerically. The effective diffusivities for linoleate, oleate, and stearate were assumed to be equal.
D~~
(%+
= r1 r dr D,, (E+ 2 dO = -rl r2 dr2 r d r
--)
+
Ind. Eng. Chem. Fundam., Vol. 17, No. 3, 1978
Des(%
+-2ds) r dr
(T+--
De(Hp)
r
=-r
203
2
d(H2)) = r l + r 2 dr
(13)
(19)
at r = R, L = L,, 0 = Os,S = S,, (H2) = (Hz),, and at r = 0, dL/dr = dO/dr = dS/dr = d(H2)/dr = 0. For case I, the kinetic expressions were based on Langmuir adsorption isotherms, with equilibrium coverage assumed for linoleate and oleate. The reactions were taken to be first order to hydrogen and proportional to the fraction of surface covered by linoleate or oleate.
Since KLL
+ KoO >> 1 with
The rate constants k l and k2 were obtained from initial rate data by the extrapolation method shown in Figure 5. The values (based on a unit volume of catalyst) are k l = 179.5s-l and k 2 = 28.9 s-1, and are of the same order of magnitude as those collected by Marangozis et al. (1977), when adjusted for the different kinetics assumed, catalysts, feeds, and other experimental conditions. Equations 10-13 were solved for the gradients within the catalyst at a given time. The iteration method of Marquardt (1963) was used to satisfy the two-point boundary conditions. The hydrogen concentrations at the surface were calculated from the known gas-liquid interfacial value, the bubble and particle mass transfer resistances, and the hydrogen reaction rate, obtained from the gradient at the surface from the previous iteration
previous iteration
r2 = kdo(H2) (22) Then, these relations can be combined using the pseudo-stationary-state (PSS) approximation for the chemisorbed species-see, e.g., Aris (1969). For the linoleate, this gives 0
N
ItadsLLos - kdesLeL - kleL(H2)
(23)
or
kdesL
where K L = kadsL/kdeq,. Combining this with eq 20 gives
(17)
The magnitudes of (H2)i - (Hz), ranged from about 50% to 99% of (H2)i. The stearate conversion was then determined from
AS _
AL
AXS AXL
- (dS/dr)R
and then (18)
(dLldr)R Increments of 0.01 were used for XL, and the procedure was repeated with new boundary values for L, 0, and S until all the linoleate was consumed. The stearate formation curves calculated for case I for different values of KL/Ko do not have the same shape as the experimental curves, as shown in Figure 6. The amount of stearate formed is greater than predicted at low values of XL, and less at high values. Decreasing the assumed value of KJKo shifted the curves upward but did not change their shape. Other calculations for De(Hz)lDeL = 100 or 400 gave no better fit to the data, suggesting that a more complex model is needed. For case 11, a reaction mechanism with nonequilibrium adsorption is proposed to account for the increased formation of stearate at low conversions. This concept was discussed by Wei (1966) and illustrated for deuterium-neopentane exchange by Dwyer et al. (1968).
r2
e,
kzflo(H2)
= 1 - eL
(28)
- e,,
(29) The nonequilibrium model, case 11, has 2 more adjustable parameters than case I, but preliminary calculations showed that the effect of kdeso might be more important than kdesL. The amount of linoleate on the surface will be somewhat less than the value for adsorption-desorption equilibrium, but the effect on r1 will be small if 80-9096 of the surface is covered with linoleate. Therefore, it can be additionally assumed that kl(H2)
