437
Ind. Eng. Chem. Prod. Res. Dev. 1986, 25, 437-443
Kinetics of Hydrodesulfurization on a CoMo/y-Al,O, Catalyst. 2. Kinetics of the Hydrogenolysis of Benzothiophene Ignace A. Van Parljs, Luclen H. Hosten, and Gilbert F. Froment" Laboratorium voor Petrochemische Techniek, Rijksuniversiteit Gent, B-9000 Gent, Belgium
The kinetics of the hydrogenolysis of benzothiophene on a commercial CoMoly-Al,O, catalyst were studied in a tubular reactor. A sequential design of the experimental program was used for both the model discrimination and precise parameter estimation. Model selection was effectively achieved among 16 rival sets of rate equations of the Hougen-Watson type for both the hydrogenolysis of benzothiophene into ethylbenzene and the hydrogenation of benzothiophene into dihydrobenzothiophene with subsequent hydrogenolysis into ethylbenzene. The procedure was carried out at 513, 533, 553, and 573 K. The concerted surface reaction between benzothiophene or dihydrobenzothiiphene and two competitively adsorbed hydrogen atoms was found to be the ratedetermining step, a conclusion close to that arrived at in the study of thiophene hydrogenolysis.
1. Introduction Hydrodesulfurization on Co-Mo catalysts has received considerable attention in the literature. In nearly all kinetic studies, model sulfur compounds, such as thiophene or benzothiophene, were chosen to describe the kinetics of the process (Vrinat and de Mourgues, 1983). I t is now commonly accepted that the hydrogenolysis is proceeding through a parallel reaction scheme, involving both the cleavage of the carbon-sulfur bond and the hydrogenation of the carbon-carbon double bond as primary reactions. The modeling of these reactions is lagging far behind, however. For benzothiophene, e.g., the only rate equation reported is that of Morooka and Hamrin (1979) also derived by Kilanowski and Gates (1980): Within their experimental range of process variables (pt = 1 bar), no intermediate reaction products (styrene or dihydrobenzothiophene) were detected in the effluent. Consequently, only the overall rate of disappearance of benzothiophene could be modeled. Furthermore, the range of the hydrogen partial pressure was too small to determine the influence of the H2 adsorption on the reaction rate. The present paper aims a t a rigorous kinetic study of both the hydrogenolysis and the hydrogenation of benzothiophene over a broad range of the operating variables. To reduce the experimental effort, this kinetic study is entirely based upon a sequential design of the experimental program for both the model discrimination and precise parameter estimation.
2. Sequential Discrimination Procedure In the last two decades, a variety of sequential experimental design methods for model discrimination have been proposed (Hunter and Reiner, 1965; Roth, 1965; Hunter and Hill, 1966; Box and Hill, 1967; Hsiang and Reilly, 1971; Hosten and Froment, 1976; Buzzi-Ferraris et al., 1983, 1984), applied, reviewed, and amended (Kittrell, 1970; Froment and Mezaki, 1970; Reilly, 1970; Podolski and Kim, 1974; Pritchard and Bacon, 1974; Groment, 1975; Dumez et al., 1977; Hosten, 1978; Mandler et al., 1983). The sequential experimental design procedure for optimal discrimination is based upon a design criterion that selects optimal settings of the variables for the next experiment, making use of the information collected from 0196-4321/86/1225-0437$01.50/0
all previous runs. After the designed experiment has been completed, the competing models are confronted with all the data obtained up to that stage to test their adequacy. The observed value for the ith response in the kth experiment, Yki, the value calculated by the model r, and the experimental error are related by k = 1 , 2,..., n ; i = 1 , 2,..., u ; r = 1 , 2,..., m It is assumed that the experimental errors are normally distributed with zero mean and with a covariance matrix which is identical for all experiments. Also, errors associated with different experiments are statistically independent. The parameters are then estimated by means of the generalized least-squares criterion, which consists of minimizing the objective function
with respect to the parameters 8'. This leads to the estimates b, for the parameters 8, in model r and to corresponding calculated model values gki(r) = fF)(uk,br), which are the closest possible estimates for Yki under model r. The design criterion selects those experimental settings that maximize the divergence between the rival models. For multiresponse models, the divergence is defined as I = 1 s=l+l
i=l
where Y)$'(uk) is the predicted value under model 1 for the ith response a t the experimental settings uk. The weighting factors wi depend upon the precision with which the responses are measured. The maximum of the divergence is obtained by a grid search over the operability region. The model adequacy criterion is based on the property that the variable v
S(bc)=
n
u Uii
i=lj=1
k=l
(Yki
- gki('))(Ykj - gkj"))
(4)
is distributed like x2 with nu - p c degrees of freedom, provided model c is adequate. For all competing inadequate models, S(b,)is biased due to significant lack of fit. For nonlinear models, this property is only approximately 0 1986 American Chemical Society
Ind. Eng. Chem. Prod. Res. Dev., Vol. 25, No. 3, 1986
438
true. A model r is discarded when the bias has become so pronounced that the minimum objective function eq 4 pertaining to model r exceeds the tabulated value x:(nu - p , ) at the 0.95 probability level. The discrimination is continued with the remaining models.
3. Sequential Estimation Procedure After a kinetic model has been selected, its parameters frequently need to be determined more precisely. The selection of the experimental conditions that yield parameter estimates with the highest possible precision, i.e., with the lowest degree of statistical uncertainty, is based upon the variance-covariance matrix of the parameter estimates v
V(b) = [
k = l , 2 ,..., n
(5)
l = l , 2,..., p
b is the vector of parameter estimates that minimizes the objective function eq 4. The sequential experimental design is commonly based on the joint confidence region of the parameter estimates, represented by v
u
6 = (b - 8)TCCdJJITJJ(b - 8)
(7)
1=1/=1
The minimum volume design, as proposed by Box and Lucas (1959) for single-response models and by Draper and Hunter (1966) for multiresponse models and applied to the oxidation of o-xylene by McLean et al. (1980), consists of selecting the experimental conditions that minimize the volume of the joint confidence region. The minimization of this volume requires the maximization of the determinant of
5 ?uLJJ,TJJ
I=lJ=l
The spherical shape design discussed by Hosten (1974) for single-response models and by Hosten and Emig (1975) for multiresponse models, having the form of a set of coupled differential equations, aims at increasing the sphericity of the joint confidence region. This condition leads to the maximization of the smallest eigenvalue of L
110 WIFi i kg hlkmdl
60
160
Figure 1. Experimental operability region and selected experimental settings at 533 K: (P) preliminary experiments; (D)experiments designed by the sequential discrimination procedure; (E) experiments designed by the sequential estimation procedure.
u
C djJiTJj]-l ;=y=1
with
i = 1 , 2 ,..., u
10
U
CuLJJITJJ 1'1]=1
In the design of the (n + 1)th experiment, the matrices J,, 1 = 1, 2, ..., u, consist of n + 1 rows, the last of which is related to the next experiment. Again, a grid search is carried out. The last row of the matrices J, is calculated for the settings corresponding to the current grid point, and the ( n + 1)th experiment is performed for those settings that maximize the determinant or the smallest eigenvalue, depending upon the criterion used. In this work, the procedure was started with the determinant criterion. After stabilization of the determinant value, the procedure was switched to the eigenvalue criterion.
4. Experimental Study All experiments were performed in an integral reactor. To avoid diffusional limitations the catalyst (Pro Catalyse HR306) was crushed to a size between 150 and 300 km. Details of the experimental equipment and pretreatment procedure were reported in part 1. In the present case, the gas chromatographic product analysis was carried out by means of one GC equipped with a FID and a FPD detector and a capillary column OV-101 of 50-m length and 0.25" internal diameter. n-Decane, the internal standard, was fed in a well-defined quantity (0.5097 wt 740) to the solution of 0.96 wt 7% of benzothiophene in n-heptane. The reaction products detected in measurable quantities were H2S,benzothiophene, ethylbenzene, and dihydrobenzothiophene. The primary reaction product of the direct cleavage of the carbon-sulfur bond of benzothiophene, viz. styrene, could not be detected. For the kinetic analysis, benzothiophene, dihydrobenzothiophene, and ethylbenzene were chosen to be the independent reaction components. The independent variables of the tridimensional operability region were the total pressure, pt, the molar hydrogen to hydrocarbon ratio, y,and the space time, W /F B o . The feasible experimental combinations are shown in Figure 1. The sequential experimental program was carried out at 4 temperature levels, T = 513, 533, 553, and 573 K. The selected experimental settings at 533 K are represented in Figure 1. Table I shows the selected and actual experimental conditions for all experiments a t 533 K along with the results in sequential order. 5. Kinetic Analysis
A. Reaction Network. The triangular reaction scheme shown in Figure 2 is proposed for the hydrogenolysis of benzothiophene (B) into ethylbenzene (E) and H,S (S). The hydrogenolysis and the hydrogenation take place on different kinds of active sites, u and 7. Styrene is an intermediate between benzothiophene and ethylbenzene, but since it is not detected it is probably rapidly hydrogenated into ethylbenzene. Therefore, styrene is assimilated to ethylbenzene. B. Data Treatment. Since the experiments were conducted in an integral reactor, the integral method of kinetic analysis was adopted (Froment and Bischoff, 1979). The calculated conversions,x,were obtained by integration of the continuity equations of the reaction components in a tubular reactor with plug flow dF/dW = R
(8)
where F is the vector of molar flow rates, defined as FB
Ind. Eng. Chem. Prod. Res. Dev., Vol. 25, No. 3, 1986
Table I. Exuerimental Results at 533 K settings (selected) n nR Pt wIFB0 30 9 120 1" 149 150 2" 90 10 9 30 4 28 3" 123 160 10 2 4 4" 5b 77 10 6 100 30 9 40 6* 141 60 25 2 9 7b 30 4 60 8' 130 160 30 2 9 9' 30 4 24 10' 122 5 4 160 11c 40 20 9 40 12' 111 5 4 160 13d 40 14d 141 30 9 40 Preliminary experiments.
actual settings Pt 29.9 10 29.8 2 10.1 29.9 1.9 30 2 30.1 4.8 20 4.9 30
Discrimination experiments.
T 533.5 532.9 533.2 535.2 533.2 533.2 533.5 533.5 533.0 533.4 533.2 533.2 533.1 533.2
439
obsd convn WIFBo
119 149.8 28.2 158.5 100.9 40.3 59.5 60.6 160 24.2 157.6 39.5 160 40.2
Y
XB
XD
XE
9.09 8.58 4 4.47 6.28 9 8.96 4.02 9.18 4.0 4.04 8.77 4.1 9.03
0.9051 0.7842 0.5028 0.3437 0.6708 0.6507 0.1417 0.739 0.3108 0.4256 0.6651 0.5548 0.6480 0.6504
0.0475 0.0483 0.1278 0.0622 0.0761 0.0916 0.0505 0.0767 0.0605 0.1471 0.0636 0.0778 0.0641 0.0744
0.8425 0.7265 0.3897 0.3249 0.5778 0.5617 0.1083 0.6427 0.2503 0.2785 0.5764 0.4519 0.5456 0.5524
Experiments for precise parameter estimation.
Nonplanned experiments.
'+H2S
(E)
(S)
0.
Figure 2. Reaction scheme for the hydrogenolysis of benzothiophene.
50. 100. WIFA [ kg hlkmol)
150
1.
= F B " ( 1 - xB) for benzothiophene and Fi= FB0xi for the reaction products. The net production rates, Rx, derived from Figure 2 , are defined by
RB = -rB,o - r B , ~
WlFB ( kg hikmoi )
RH =
Figure 3. Comparison between the calculated and experimental conversions xB and xE vs. F B o for various temperature levels (pt = 30 bar, y = 9).
-3rB,m - r B , ~- 2rD,o
rB,,, = f,(P,e), rD,,, = g,(P,O), and rB,* = f h e ) are formal notations for the rate equations of the three reactions represented in Figure 2. The parameter estimation criterion 2 and the sequential design methods require the error covariance matrix 2. A reliable estimate S for 2 was obtained by performing ne replicate experiments, yielding the following numerical value:
2.367 X 1.535 X 1.432 X lo-*
1.535 X 1.409 X -4.200 X
lo4
1.432 X -4.200 X lo4 6.171 X lo4
1
(IO)
The weighting factors wk in eq 3 were taken to be inversely proportional to the variances Skk. C. Model Discrimination. From the results of the model discrimination for the kinetic modeling of the hydrogenolysis of thiophene, it was assumed that the surface reaction on both active sites CI and T is rate-determining.
The reaction mechanisms differ by the adsorption mode of hydrogen only: competitively (model group a) or noncompetitively (model group b) and molecularly or atomically. For the case of atomically adsorbed hydrogen, three rate-determining steps can be considered: the addition of the first atom, the addition of the second atom, and the simultaneous addition of two hydrogen atoms, corresponding to a concerted mechanism. These assumptions can be made for both the hydrogenolysis and the hydrogenation function. Consequently, 16 rival models were derived. The models are represented by m(a)n(a),where m and n represent the model group for respectively the hydrogenolysis and hydrogenation. For the adsorption of atomic hydrogen, the bracketed value a is added, with a = 1, 2, or 3, depending upon whether the addition of the first or the second hydrogen atom or the concerted mechanism with the simultaneous addition of two hydrogen atoms is rate-determining. As an illustration, the reaction mechanism and the corresponding rate equations for the final selected kinetic model a3a3 are given below.
440
Ind. Eng. Chem. Prod. Res. Dev., Vol. 25, No. 3, 1986
a. For the hydrogenation of benzothiophene (B) into dihydrobenzothiophene (D) on the T sites H2 + 27 =S2H.7
D*T+ D
+
T
b. For the hydrogenolysis of benzothiophene into styrene (Y) on the u sites H2 + 2u + 2H.u
B
S-u
+ u + B*u
+ H2 Y - u ?==! Y
H2S +
a
+u
c. For the hydrogenolysis of dihydrobenzothiophene into ethylbenzene (E) on the u sites H2 + 2 u 2H-a D
+ 0 + D-u
The preliminary experiments at 533 K are shown as Pl-P4 in Figure 1. The discrimination procedure is given in Table 11, which contains the calculated x: value together with the corresponding tabulated value X: for the given number of degrees of freedom and confidence level for all competing models. The boldfaced values correspond to discarded models. In order to avoid the rejection of a plausible model by an "outlier" at an early stage, the model adequacy test was applied to all the models throughout the sequential discrimination. The procedure was stopped
Ind. Eng. Chem. Prod. Res. Dev., Vol. 25, No. 3, 1986 441 Table 111. Estimation Procedure at 533 K for the Kinetic Model of Equations 14-16” expt D3
kB,,
0.041 93 (4.3) 0.041 17 (4.9) 0.041 2 (5.4) 0.043 46 (6.0) 0.040 11 (4.3) 0.041 23 (5.2)
El E2 E3 E4 E5
KBJ 1.94 (2.0) 1.987 (2.3) 2.005 (3.4) 1.961 (3.6) 2.028 (3.4) 2.023 (3.0)
KE,7 262 (1.7) 254.5 (2) 261.2 (2.7) 274.8 (2.4) 249.3 (2.2) 290.5 (2.3)
Kn,a 0.4174 (2.3) 0.4288 (2.6) 0.3911 (3.5) 0.3459 (3.5) 0.4017 (3.1) 0.3528 (3.2)
kD,,
0.1192 (3.1) 0.1251 (3.7) 0.1251 (4.1) 0.1264 (4.3) 0.1157 (3.8) 0.1042 (3.8)
Calculated n values are given in parentheses below parameter values. n probability level). 0,
KS,, 407.4 (2.6) 411.5 (3.5) 384.2 (4.7) 334.2 (4.3) 195.6 (3.3) 207.8 (4.0)
kB,,
0.2353 (7.6) 0.2331 (8.5) 0.2358 (9.4) 0.2231 (8.7) 0.188 (9) 0.2035 (10)
> 1.96 indicates a significant parameter estimate (at the 0.95
the adsorption constants of dihydrobenzothiophene on both the Q and the T sites, KD,, and KD,,, were not statistically different from the corresponding constants KB,oand KB,?for benzothiophene. Finally, the reaction rate rB,,for the hydrogenation of benzothiophene into dihydrobenzothiophene was not significantly influenced by the term in the denominator KH,?pH,so that this term was deleted. The subsequent sequential estimation procedure was carried out on the following reduced eq 14-16 corresponding to model a3a3:
-2.. Ink
-4. I
1.6
KB,s 18.69 (5.6) 18.73 (8.0) 18.16 (11) 19.27 (12) 19.09 (10) 19.09 (11)
103/T iK-’l
Figure 4. Arrhenius plot of rate coefficients kB,., kD,,, and kB,i,
when the difference between the predicted responses of the remaining models became smaller than the experimental error. To simplify the parameter estimation and the corresponding discrimination procedure, the adsorption coefficients KB,,, KD,,, KE,,, and Ky,,, on one hand, and KB,?,KD,?,KE,,, and KY,,, on the other hand, were set equal to one another. The number of parameters was thus reduced to eight for each model. From Table I1 it can be seen that the model discrimination was straightforward. After only three designed experiments, or seven experiments in total, fourteen models could be discarded due to significant lack of fit. Models ala1 and a3a3 remained as the only possible candidates. The selected experimental conditions, D,, D2,and D,, are shown in Figure 1. Notice that they are all located on the boundaries of the operability region, a typical feature of sequential design. The sequential discrimination procedure a t the other temperature levels was less conclusive. After four designed experiments, ten models remained in competition a t 513 K, five at 553 K, and nine at 573 K. Further discrimination between these models was effected by means of an analysis of residuals and an inspection of the binary correlation coefficients between the parameter estimates. The only model that remained in competition for all temperature levels was model a3a3. In this model the concerted surface reaction between the adsorbed reactant and two competitively adsorbed hydrogen atoms is the rate-controlling step in both the hydrogenation and the hydrogenolysis. The reaction mechanism and corresponding rate equations are given by eq 11-13. Scrutiny of the terms of the denominator of the model a3a3, eq 11-13, at the end of the discrimination procedure allowed some simplification of the equations. The terms Ky,:pE/PH in eq 11and Ky,:pE/PH in eq 12 and 13, which relate to the undetected styrene, were 2-3 orders of magnitude smaller than the accompanying terms, so that they could be neglected with respect to the latter terms. Also,
a. For the hydrogenation of benzothiophene into dihydrobenzothiophene on the T sites kB,r*KB,,(PBPH - PD/K1) rB,r
=
[1 + K B , r ( P B + PD) + KE,rPE13
(14)
b. For the hydrogenolysis of benzothiophene into styrene on the u sites
~B,~KB,~KH,,PBPH rB,o
=
Ps
3
c. For the hydrogenolysis of dihydrobenzothiophene into ethylbenzene on the u sites kD,AB,&H,oPDPH
D. Precise Parameter Estimation. The course of the design procedure is given in Table 111, which contains the parameter estimates along with the calculated n values, which should be compared with the tabulated n value of the Gaussian distribution at the selected probability level, e.g., n = 1.96 at the 0.95 level. Since the Jacobian Ji eq 6 depends upon the parameter estimates, only one experiment a t a time was designed. Table I1 shows that the parameter estimation at 533 K was straightforward. After the last discrimination experiment D3, all parameters except KE,, were significantly estimated a t the 95% probability level. One single experiment, E l , (Figure 1)designed according to the determinant criterion
442 Ind Eng. Chem. Prod. Res. Dev., Vol. 25, No. 3, 1986
sufficed to reach a significant estimate for KE,T.To further improve the parameters the design was extended with runs E2-E4 (Figure l),all based upon the determinant criterion. At this point, the parameter estimates and their n. values were stabilized. Also, the value of the determinant stabilized over the whole experimental region. For these reasons, E5 was designed by the eigenvalue criterion. No further significant improvement was observed, however. During the design stage for precise parameter estimation, the determinant steadily rose from 1.27 X lo* after the preliminary and discrimination experiments to 1.81 X 10" after E5, thereby achieving a 40-fold reduction of the volume of the approximate joint confidence region. A similar evolution was observed at 513 K, but a t 553 and 573 K the improvement was less spectacular: whereas all parameters related to the u sites could be significantly estimated from the point of view of statistical testing, this was not the case for the parameters related to the T sites. A couple of observations concerning the values of the adsorption parameters should be mentioned. The adsorption of ethylbenzene on the T sites is very strong and much more pronounced than that of butene and butane in the thiophene reaction (part 1). The adsorption of benzothiophene and of dihydrobenzothiophene is rather strong on the u sites, but very weak on the T sites. The difference between the adsorption coefficients of these components on respectively the u and the 7 sites is considered to be an a posteriori support for the distinction between u and T sites. The agreement between the model predictions and the experimental conversions is shown in Figure 3. Figure 4 shows an Arrhenius plot for the rate coefficients hR kIl,o,and kB,r. The corresponding activation energies are 73.6, 130.9, and 100.6 kJ/mol. #,
6. Comparison of the Intrinsic Rates of Thiophene and Benzothiophene Hydrogenolysis Figure 5 compares conversion vs. space time curves for thiophene and benzothiophene hydrogenolysis at 5 and 30 bar for a ratio of hydrogenjhydrocarbon of 4 and a mole fraction of the sulfur compound of 0.05. Benzothiophene is clearly more reactive than thiophene, in agreement with Kilanowski and Gates (1980) and Morooka and Hamrin (1979). This conclusion is not necessarily valid for largesize catalysts when diffusional limitations become of importance.
0
5
10
WiFi : kq hikmd J 1
v
P,=30 bar
0
1 benzothiophene 2 thiopherie
:
5
10
WIF; ( kg hi kmol)
Figure 5. Comparison of thiophene and benzothiophene hydrogenolysis conversions.
showed that the chemisorption of thiophene can proceed via the sulfur atom (Sedlacek and Zdrazil, 1977) or via the carbon-carbon double bond (Kwart et al., 1980), and this also results in a different interaction of the adsorbed molecule with the adsorbed hydrogen. The subsequent sequential estimation procedure yielded accurate estimates for all the parameters after no more than four additional experiments. The selected kinetic model, eq 11-13, is quite different from the rate equation reported by Morooka and Hamrin (1979) or Kilanowski and Gates (1980).
Acknowledgment I.A.V.P. is grateful to IWONL-IRSIA for a Research Fellowship from 1981 to 1984, and L. H. Hosten to the Belgian Nationaal Fonds Voor Wetenschappelijk Onderzoek for an appointment as "Onderzoeksleider". Notation
7. Conclusion
The experimental kinetic study of a complex reaction, namely the hydrogenolysis of benzothiophene accompanied by hydrogenation, was entirely and uniquely based upon sequential design procedures for discrimination between rival models and precise parameter estimation. The sequential discrimination procedure, supplemented with a statistical analysis of the data, selected a kinetic model out of 16 rival models after a maximum of 10 experiments, 5 of which were designed. The implications behind the selected model, eq 11-13 or eq 14-16, are identical with those already derived in part 1 for one of the two final kinetic models for the hydrogenolysis of thiophene followed by hydrogenation, namely that the surface reaction between adsorbed reactants and competitively atomically adsorbed hydrogen are rate-determining. Unlike the thiophene case, this model was selected in a straightforward way. Kwart et al. (1980) suggested that benzothiophene is adsorbed through the carbon-carbon double bond rather than through the sulfur atom. Quantum chemical calculations
vector of the maximum likelihood parameter estimates vector of molar flow rates molar feed flow rate of benzothiophene, kmol/h Jacobian of the ith response variable, defined in eq 6 reaction rate coefficient, kmol/(kg of catalyst h) thermodynamic equilibrium constants for the hydrogenation of respectively styrene into ethylbenzene and benzothiophene into dihydrobenzothiophene adsorption coefficient for benzothiophene on the u and T sites, bar-' number of rival models number of experiments number of replicated experiments at the same experimental settings number of parameters vector of the partial pressures total pressure, bar net production rate of component X, kmol/(kg of catalyst h)
Ind. Eng. Chem. Prod. Res. Dev., Vol. 25, No. 3, 1986 443
reaction rate of component X on the u and 7 sites estimate for the response error covariance matrix (ij)th element of matrix S absolute temperature, K vector of the settings of the independent variables variance covariance matrix of the parameter estimates number of independent responses conversion, defined as xB = (Fgo - FB)/FBofor benzothiophene and X D = FD/Fgo,X E = FE/Fgo for the reaction products observed value for the ith response variable during the kth experiment arithmetic mean valwof the ne replicated observed values of the ith response catalyst weight, kg weighting factor (in eq 3)
Greek symbols molar hydrogen to hydrocarbon ratio in the feed Y experimental error for the kth experiment vector of the true (unknown) parameters u,, 11' uij element (i, j ) of respectively the error covariance matrix of responses E and the inverse matrix of
7 U
E 7
2 active site for hydrogenolysis covariance matrix of the responses active site for hydrogenation
Superscripts calculated T transpose Subscripts B, D, E, benzothiophene, dihydrobenzothiophene, ethylH, S, benzene, hydrogen, hydrogen sulfide, and styY rene, respectively with respect to the hydrogenolysis or the hydro0, 7 genation function
Registry No. B, 95-15-8; D, 4565-32-6; Hz, 1333-74-0; Co, 7440-48-4; Mo, 7439-98-1.
Literature Cited Box, G, E, P.; Hill, W. J. Technometrics 1987, 9, 57. Box, G. E. P.;Hunter, W. G. Proc.. IBM Sci. Comput. Symp. Stat. 1965, 113. Box, G. E. P.; Lucas, H. L. Biometrika 1959, 4 6 , 77. Buzzi-Ferraris, G.; Forzatti, P. Chem. Eng. Sci. 1983, 3 8 , 225. BuzzCFerraris, G.; Forzatti, P.; Emig, G.; Hofmann, H. Chem. Eng. Sci. 1984, 39.81. Draper, N. R.; Hunter, W. G. Biometrika 1988, 5 3 , 525. Dumez, F. J.; Hosten, L. H.; Froment, G. F. Ind. Eng. Chem. Fundam. 1977, 16, 298. Froment. G. F. AIChE J. 1975, 21, 1041. Froment, G. F.; Bischoff, K. B. Chemical Reactor Analysis and Design; Wiley: New York, 1979. Froment, G. F.; Mezaki, R. Chem. Eng. Sci. 1970, 25, 293. Hosten, L. H. Chem. Eng. Sci. 1974, 29, 2247. Hosten, L. H. "Mathematische Modelbouw in de Chimische Reaktietechniek", Aggregatieproefschrift, Rijksuniveriiteit Gent, 1978. Hosten, L. H.; Emig, G. Chem. Eng. Sci. 1975, 30, 1357. Hosten, L. H.: Froment, G. F. Proceedings of the 4th InfernationallGth European Symposium on Chemical Reaction Engineering, Heidelberg, April 6-9, 1979; Dechema: Frankfurt, 1979. Hsiang, T.; Reilly, P. Can. J. Chem. Eng. 1971, 49, 865. Hunter, W. G.; Hill, W. J. "M.B.R. Technical Report No. 65", Department of Statistics, University of Wisconsin, Madison, WI, 1966. Hunter, W. G.; Reiner, A. M. Technometrics 1985, 7, 307. Kilanowski, D. R.; Gates, B. C. J. Catai. 1980, 62,70. Kittrell, J. R. A&. Chem. Eng. 1970, 8 , 98. Kwart, H.; SchuA, G. C. A.; Gates, B. C. J. Catai. 1980, 61, 128. Mandler, J.; Lavie, R.; Sheintuch, M. Chem. Eng. Sci. 1983, 3 8 , 979. McLean, D. D.;Bacon, D. W.; Downie, J. Can. J. Chem. Eng. 1980, 5 8 , 608. Morooka, S.;Hamrin, Ch. E., Jr. Chem. Eng. Sci. 1979, 3 2 , 125. Podolski, W.; Kim, Y. G. Ind. Eng. Chem. Proc. Des. Dev. 1974, 13, 415. Pritchard, D. J.; Bacon, D. W. Can. J. Chem. Eng. 1974, 52, 13. Reilly, P. M. Can. J. Chem. Eng. 1970, 48, 168. Roth, P. M. Ph.D. Thesis, Princeton University, Princeton, NJ, 1965. Sedlacek, J.; Zdrazil, M. Collect. Czech. Chem. Commun. 1977, 42, 3133. Vrinat, M. L.; de Mourgues, L. Appi. Catai. 1983, 5 , 43.
Received for review July 24, 1985 Revised manuscript received January 28, 1986 Accepted February 12, 1986
