Modelling of a Slurry Reaction. Hydrogenation of Glucose on Raney Nickel' P. H. Brahme and L. K. Doralswamy' National Chemical Laboratory, Pwna, lndh
Investigations were undertaken on the hydrogenation of glucose on Raney nickel in a stirred reactor. It was found that there is a definite transition from diffusionto chemical control around 100OC;hence kinetic modelling of the reaction was undertaken at temperatures less than 100°C after ensuring that mass transfer effects had been eliminated. Discrimination between rival models was accomplished by using two methods, viz. (1) by intrinsic parameters, and (2) from the dependence of one of the intrinsic parameters on the initial glucose concentration. The second of these provides a powerful tool for slurry reactors. From both tests it was concluded that a single mathematical model can be selected which represents the data satisfactorily. This model implies that the desorption of sorbitol with reaction between molecularly adsorbed hydrogen and glucose in the liquid phase could be the controlling step.
Introduction The catalytic hydrogenation of glucose to sorbitol is a problem of twofold interest: it is an excellent example of a slurry reactor which provides ready means of testing theory pertaining to such reactor systems, and the reaction itself is of great industrial significance since sorbitol is a versatile chemical. In slurry reactors three regimes of control are possible: mass transfer from gas to liquid, mass transfer from liquid to catalyst particles, and chemical reaction on the catalyst surface. However, no complete study has been made so far wherein the entire spectrum of controlling regimes has been investigated for a system of industrial importance which can form the basis for reactor scale-up and design. Sorbitol is a versatile chemical which is used commercially in a variety of physical and chemical processes. Its major use is in the synthesis of vitamin C. It is widely used as a softener and as a humectant. Its esters and derivatives are used in protective coatings, plasticizers, emulsifiers, detergents, etc. Sorbitol is produced by the hydrogenation of glucose in the presence of a catalyst according to the reaction H-C=O
I
CHZOH
I
H-C-OH
H-C-OH
H-C-OH
~-6-0~
I
CH,OH
I
I
CH,OH
Innumerable patents and papers are available on this reaction. The usual data reported are conversions obtainable under different process conditions and with different catalysts, and little is available on the kinetics of the reaction. Some significant conclusions using Raney nickel are outlined below. Schoenemann (1957) studied the continuous hydrogenation of glucose and found that the rate was proportional to the catalyst concentration. Hofmann and Bill (1959) investigated the relative roles of reaction and diffusion using a NCL Communication No. 1693. 130
Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 1, 1976
magnetic lift autoclave and found the hydrogenation to be first order with reference to glucose as well as catalyst concentrations and dependent on agitation and hydrogen pressure. The activation energy in the diffusion regime was calculated to be 3 kcal/mol and that in the kinetic regime 19.5 kcal/mol. Schnyder (1962) studied the influence of process variables on the reaction rate and determined the rate-controlling steps involved in experiments conducted in an oscillating type reactor. The hydrogenation was found to be first order with respect to hydrogen pressure and zero order with respect to glucose concentration. The reaction rate was proportional, but not directly, to catalyst concentration and was greatly dependent on agitation. The activation energy for the reaction in the temperature range 8012OOC was 4.5 kcal/mol, and the overall controlling factor for this reaction was concluded to be one of diffusion. Bizhanov et al. (1967) studied the hydrogenation of glucose over skeletal Ni-Pd and Ni-Ru catalysts. The calculated apparent activation energy in the region 80-120°C was 12-1 4 kcal/mol. gstergaard (1968) and Satterfield (1970) have surveyed the various approaches adopted to study the theoretical aspects of reactors for such three-phase contact systems. Practically all the studies reported on such reactors postulate a simple power law equation for the kinetic regime, and quite often first-order behavior is assumed. In the present investigation a detailed analysis of the controlling regimes in the hydrogenation of glucose on Raney nickel in a slurry reactor is attempted, and a rate (Hougen-Watson) model is proposed for the kinetic regime. While the methods of discrimination developed in recent years for vapor phase catalytic reactions can also be used for chemical reaction in a slurry system, discrimination procedures have been formulated which may be regarded as being peculiar to slurry reactors. Experimental Section Chemically pure glucose monohydrate and electrolytic hydrogen in standard high-pressure cylinders were used. Raney nickel catalyst was prepared from a 50:50 nickel aluminum alloy powder by the conventional method described by Mozingo (1941). For all the experiments the catalyst from the same batch was used in order to exclude fluctuations of activity. The catalyst was tested periodically during the course of the investigation to see if the same rate data could be reproduced under a given set of conditions. The results have agreed to within f 2 % .
An agitated 2-1. stainless steel autoclave (Parr Instrument Co.) was used for the present investigation. This autoclave was heated electrically and the temperature of the reaction mixture was controlled by a powerstat. Two stainless steel propellers were fitted to the agitated shaft, and a drive equipped with changeable pulleys powered by $$ h p motor provided variable agitation. The equipment was fitted with conventional safety devices and instruments for measuring temperature and pressure. A sampling tube extending almost to the bottom of the reactor permitted withdrawal of samples a t frequent and specified intervals. This was fitted with a fine wire mesh for preventing the solids from being withdrawn. Hydrogen was supplied from a high-pressure cylinder through the dip-tube. Hydrogenation runs were started by charging the autoclave with 500 ml of 25% glucose solution and an appropriate quantity of the catalyst. One gram of magnesium powder was added so as to maintain the pH as constant as possible. (Inertness of this powder to the reaction was established by conducting a blank run with magnesium.) Air was then flushed out of the autoclave with low-pressure hydrogen, after which the inlet valve was closed and heating commenced. During these operations the stirrer was kept running to prevent settling of the catalyst. When the required temperature was reached, hydrogen was fed rapidly to the predetermined pressure which was maintained throughout the hydrogenation. During a reaction about six samples were withdrawn for analysis of sugar by Bertrand’s method (1920). This analysis was frequently supplemented by the periodate method (Kolthoff and Belcher, 1957) to confirm the absence of any degradation product. In order to obtain the rates of reaction precisely an equation of the form
Cc: = a
+ bt + Ct2
,
I
I
/
I
0 028/
E
:0O 0O220 I
c
J
0012
$ ““ 1 cn 0 008
O
OO
10
20
30
40
50
ABSOLUTE P R E S S U R E , o l m
Figure 1. Solubility of hydrogen in 25% aqueous glucose solution.
spective temperatures: 27OC, 6.86 X 10-4; ioooc, 5.14 x 10-4.
65OC, 5.89 X
Controlling Regimes in Glucose Hydrogenation Satterfield (1970) and Smith (1970) have developed the following (now generally accepted) model for stirred slurry reactors based on the concept of three first-order resistances in series, i.e., those associated with (1)mass transfer from the gas-liquid interface to the bulk liquid phase, (2) mass transfer from the bulk liquid to the external surface of the catalyst particles, and (3) surface reaction on the catalyst particles
(1)
was fitted to the data for each set of conditions. Differentiation of this equation gave directly the rate of reaction. The values of the initial reaction rate ro were also obtained from the above equation by calculating the rate at the initial glucose concentration [i.e., a t t = 01.
Solubility of Hydrogen in Glucose Solution Data on the solubility of hydrogen in glucose solution and a knowledge of the Henry’s law constant for the system are necessary in the kinetic modelling of the reaction described subsequently in the paper. These were determined in an apparatus similar to that used by Wiebe et al. (1932) for the measurement of the solubility of hydrogen in water a t high pressures. The autoclave itself was used as the equilibrium cell and the solubilities of hydrogen in 25% glucose solution were determined a t three temperatures, 27, 65, and 100°C, and in the pressure range 8-55 atm. The solubility data were correlated by the following empirical equation
+
S = 1.17 X lo-’ - 2.71 X 10-3T 1.23 X 10-2P + 3.17 X lOW5PT+ 6.57 X 10-?P2T - 4.93 X 1 0 - 7 ~ ~+ 21.57 x 10-52-2 + 6.63 x 1 0 - 5 ~ 2 (2) where S is the solubility in molfl., T is the absolute temperature in K, and P is the total pressure in atm. In addition to the correlation presented above, the Henry’s law constant a , defined as a = S/P, molh. atm
o 012
(3)
was determined from plots of the solubility as a function of pressure. Such plots a t the three different temperatures studied are shown in Figure 1. I t will be seen that cx is independent of pressure and has the following values a t the re-
In the absence of an a priori knowledge of the reaction order, it would not be possible to use this equation for estimating the magnitudes of the three coefficients, although the equation is still conceptually useful. Even assuming first-order kinetics it is only possible to determine the mass L the gas-liquid interface (from transfer coefficient ~ G for the intercept of a plot of l / r vs. l / m ) , but not the coeffis mass transfer from the bulk liquid to the catacient k ~ for lyst surface and the surface reaction rate constant k s separately as they are combined together in the slope. Thus, in order to establish the regimes of control in the hydrogenation of glucose, more general considerations will have to be invoked. In the analysis described in this section, pseudo-steady state has been assumed; i.e., initial reaction rates (corresponding to the initial glucose concentrations) have been used. When gas-liquid mass transfer controls the reaction rate, the most important factor is the speed of the stirrer. In the present investigation the gas-liquid mass transfer resistance was of negligible importance at stirrer speeds higher than about 575 rpm (corresponding to a tip speed of 11000 cm/min), as shown by the results in Figure 2. There is no direct way of ensuring the absence of the liquid-solid mass transfer effect, but an approximate indication of the effect can be had by assuming first-order kinetics, plotting l / r vs. l/m (in accordance with eq 4) and determining the slope of the resulting straight line. Then, from a knowledge of pp, d,, and C, (obtained from the solubility data), the combined effect of the surface reaction and liquid-solid mass transfer can be obtained by estimating a composite constant, k’ = l / ( l / k s l / k L s ) . This value can be compared with the liquid-solid mass transfer coefficient k L S estimated by the correlation of Brian and Hales (1969).
+
Ind. Eng. Chem., Process Des. Dev., Vol. 15,No. 1, 1976
131
Based on the observations presented above, kinetic control can safely be assumed at 575 rpm or above and at temperatures below 100OC. A complete modelling of the reaction in the kinetic regime was therefore attempted under these conditions.
P
A Plausible Rate Model Initial Choice of Models. The parameters of all proba-
1
I 0 00
120
240
STIRRER 2SPEED, R P M
~
Figure 2. Initial rate as a function of stirrer speed at various catalyst loadings.
1
236
248
2 60
2 72
j
284
296
X IO3 ('k-')
Figure 3. Controlling regimes in glucose hydrogenation.
The following values were obtained a t 98°C and a stirrer speed of 575 rpm: k' = 90 cm/min; kLS = 420 cm/min. This provides a rough indication that liquid-solid mass transfer does not affect the reaction. The most conclusive criterion for discerning the controlling regime is perhaps the magnitude of the activation energy. An Arrhenius plot of ro is shown in Figure 3 at a catalyst loading of 10 g/l. It can be clearly seen that there is a shift in the controlling mechanism from chemical control in the lower temperature region to mass transfer control in the higher temperature region. Activation energies in the two temperature regions are estimated as E(77-100°C) = 10.5 kcal/mol E(100-145.5°C) = 1.4 kcal/mol This analysis does not distinguish between gas-liquid and liquid-solid mass transfer but ensures that both the resistances are insignificant. Since pore diffusion effects were eliminated the value of 10.5 kcal represents the activation energy for the intrinsic reaction. Recent studies by Furusawa and Smith (1974) have shown that pore diffusional effects in slurry reactors can be serious for particle sizes greater than about 200 p but negligible for smaller sizes. In the present case, the average particle size was of the order of 10 p. The Thiele modulus calculated for this size (with an estimated effective diffusivity cm2/sec) was found to be approximately value of 5 X 0.96. Hence the effect of pore diffusion was assumed to be negligible. It may be noted that Ruether and Puri (19731, working on the hydrogenations of allyl alcohol and fumaric acid over Raney nickel, also report absence of pore diffusion in particles of 16 p size. 132
Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 1, 1976
ble models were first estimated by linearizing them. The acceptable rival models selected by preliminary screening of all these models (Brahme, 1972) were then subjected to further discrimination among them to arrive a t the final model. The initial selection of acceptable models from all the possible candidates was based on several now well known statistical criteria.L These have been summarized by Kittrell (1970), and in a recent paper Choudhary and Doraiswamy (1975) have demonstrated their application to a specific reaction. As a result of this preliminary screening, five models were found to merit consideration (Table I). These models were then subjected to nonlinear least-squares analysis by an iterative procedure involving a combination of the methods proposed by Law and Bailey (1963), Rubin (1963), and Levenberg (1944) which ensured fast rates of convergence from the initial estimates (obtained from the linear least-squares analysis) by putting restrictions on the changes in the parameters. The data were processed in a Honeywell-400 computer and the values of the various constants along with their limits of confidence are included in Table I. Of the various methods of model discrimination described in the literature, the intrinsic parameter method, described concisely by Kittrell (1970), provides the best basis for selection over a wide range of conversions, as against the initial rate method in which discrimination is restricted to the low conversion region, and hence has been employed as the principal discriminatory criterion in the present work (although other methods have also been used). In addition, a new method, which is of particular value in slurry reactors, has been used which is based on the initial glucose concentration in the liquid phase. Discrimination through Intrinsic Parameters. When any Langmuir-Hinshelwood model is written in terms of fractional conversion instead of partial pressures or concentrations the adsorption term resolves itself into two distinct groups, one (Cl) which does not include the conversion and the other (Cz) which is a multiplier for the conversion. This method of model discrimination does not require an a priori knowledge of the rate and adsorption constants and as such is a powerful tool for distinguishing between rival models exclusively from raw rate data. The application of this method of discrimination to one of the five probable models listed in Table I-to model 3-is described below. The rate equation for model 3 is
Written in terms of fractional conversion instead of concentrations, and with CH expressed as a function of pressure, this equation reduces to
This can be recast as r=
P[1- x] czx
c1-
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m 1
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3
Ind. Eng. Chem., Process Des. Dev.. Vol. 15, No. 1 , 1976
133
Table 11. The Intrinsic Parameter C, as a Function of Pressurea Pressure, atm l4
4.4
9.5
14.6
21.4
-__
Values of C, for model 3
1.63 1.63 1.02 0.34 -1.02
2.79 2.65 2.58 2.38 2.18
4.08 4.08 4.01 3.88 3.60
5.30 5.37 5.37 5.30 4.97
Values of C, for model 4
0.313 0.287 0.209 0.078 -0.182
0.469 0.469 0.443 0.41’7 0.391
0.626 0.626 0.626 0.600 0.574
0.730 0.756 0.756 0.756 0.730
Values of C, for model 8
0.155 0.135 0.098 0.033 0.094
0.220 0.216 0.208 0.200 0.180
0.278 0.273 0.278 0.273 0.253
0.318 0.331 0.335 0.335 0.318
0.35 0.31 0.31 0.37 0.43
0.37 0.34 0.32 0.35 0.37
0.40 0.37 0.34 0.32 0.38
0.36 0.33 0.33 0.32 0.35
Values of C, for model 10
Values of C , for model 11
-1.63 -2.79 -4.08 -1.63 -2.65 -4.08 -1.02 -2.58 -4.01 -0.34 -2.38 -3.88 +1.02 -2.18 -3.60 a Temperature: 98°C; catalyst loading: 29.4 g/l.
t
I3l
i 2
10 jt:
/
CATALYST LOADING
=
TEMPERATURE
=sa
29.4 o / l i t -C
MODEL: DESORPTION OF SORBITOL CONTROLLING, WITH REACTION B E T W E E N MOLECULARLY AQSORBED HYDROGEN A N D GLUCOSE IN LIQUID PHASE
4O
4
B
12
16
20
24
28
P,olm
Figure 4. Model discrimination by intrinsic parameter method.
-5.30 -5.37 -5.37 -5.30 -4.97
sure and conversion contrary to the requirements of the corresponding equations for C2 and therefore these models are also unacceptable. In the case of model 10 the parameter C2 is constant and is independent of pressure and conversion indicating the adequacy of the model. The rate equation for this model in terms of C1 and Cz is
where (8)
(9) The values of C1 and C2 can be evaluated as follows. For zero conversion (i.e., in terms of the initial rate), eq 7 becomes P ro = (10)
r=
P[1-
XI
c1+ C2P
where C1 and C2 are defined in Table 111. In terms of initial reaction rate, eq 12 reduces to
ro =
P
c1+ C2P
or
c1
Hence C1 can be estimated. The term C2 can then be estimated by combining eq 7 and 10 to give
P cz=--rox
P[l-x] rx
(11)
From eq 9 it is clear that the intrinsic parameter CZ is constant and independent of pressure and conversion, and this fact can be exploited in discriminating between rival models. For this purpose the experimental conversion-time data taken at four pressure levels (4.4, 9.5, 14.6, and 21.4 atm) and a t 98OC with a catalyst concentration of 29.4 g/l. were used. From eq 11 the values of CZ corresponding to several conversion points a t each pressure level were calculated, and the results are presented in Table 11. It is clear that the parameter C2 is not independent of pressure and conversion contrary to the requirement of eq 9. Therefore this model is not acceptable. In a similar manner the method was applied to the remaining four models, i.e., 4, 8, 10, and 11,and the resulting equations for C1 and C2 are presented in Table 111. The same experimental data used in the analysis of model 3 were used for testing these models also for their adequacy, and the results are included in Table 11. Clearly the parameter Cz for models 4, 8, and 11 is not independent of pres134
Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 1, 1976
The adequacy of the model may be further confirmed from Figure 4 which shows a linear relationship between P/ro and P in accordance with eq 14. The value (0.40) of CZ obtained from the slope of this line also agrees well with the average value of Cz from Table I1 for this model. Discrimination from t h e Effect of Initial Glucose Concentration. This test is based on the behavior of the intrinsic parameter C2 with respect to the initial glucose concentration CGO.From the defining equations for C2 for the five models presented in Table I11 it will be seen that C2 is either a well defined function of CGO(all other terms in the equations being constant) or independent of it. In order to test the models from the equations for Cz, data were obtained a t four initial glucose concentrations (including that at which the bulk of the work was done as reported earlier), and the rate was determined a t various values of CG, including ro corresponding to CGO.From the values of ro and r , C2 for models 3, 4, 8, and 11 were calculated from the corresponding equations listed in Table 111. For model 10, a knowledge of C1 is also required (see table), and this was obtained from the intercepts of the plots similar to the one shown in Figure 4. The computed values of CZ for model 3 are presented in
Table 111. Equations for Intrinsic Parameters C , and
__--
Model no.
Equation for C,
c, =
3
c,
_-___ Equation for C, -_--
1 + @ K H + CGOKG
c
=-- 1
1 + @KH + CGOKG
c
8
c, =
=-
((YCGOKGKHk ) I ”
c
=-
1 + (@KH)’” + CGOKG
___--
P -P(1-x) c2 = -
aKHk
QCGOKGKH~ 4
~
Equation for calculating C, from experimental data rLJ
( K G - Ks)CGO’” (CYKGKHk)’”
c,
rx
;
=2/);(
-
(
P(l y J- x l )
!
2
X
c, := (KG - K S )CG02/3
KG K H k ) ’
(aCGOKGKH , ) ‘ I 3
c,
=-
X
1
CGO
(C, is obtained from the intercept of the graph P / r , vs. PFigure 4 )
c,
=
P ( 1 - x ) -P rx r,x ~
Table IV. Effect of Initial Glucose Concentration CGO on the Intrinsic Parameter C, for Models 3 and 11
__
CGO, mol/l. Values o f C, for model 3 Values o f C, for model 11
0.99
0.80
1.31
0.69
-1.31
-0.69
0.70
-4.58 4.58
0.60 -0.58 0.58
Table IV. It will be seen that Cz varies with CGOand therefore does not satisfy the equation listed in Table 111. This model was therefore rejected. Model 11 was also rejected on similar grounds (nonconstancy of C 2 ) . For the other three models the equations listed in Table I11 require that the following linear plots should result: model 4, C p vs. C ~ o l /model ~; 8, C2 vs. C G ~ ~model / ~ ; 10, CZ vs. 1/CGO. Figure 5 shows that model 10 alone passes the test. Further, for this model the line should pass through the origin and have a slope of Ilk, where k is the rate constant for desorption of sorbitol. The values of k as obtained from nonlinear least-squares analysis (as given later in Figure 7 ) and that obtained from Figure 5 are as follows: k from present test, Figure 5 = 3.1, l/hr; k from Figure 7 = 3.4, l/hr. The agreement is satisfactory. A summary in respect of discrimination between the five rival models from the dependence of CZ on CGOis presented in Table V. As in the case of the previous discriminatory test, the present test also points to model 10 as the most probable one. Parameters of Model 10 as Functions of Temperature and Catalyst Concentration. Since only model 10 has been found acceptable by the tests described in the previous sections, the values of the model parameters were determined by nonlinear least-squares analysis of the data a t various temperatures (
