Using the Reverse Reaction to Design a Catalytic Reactor. The Example of the Low-Temperature Para-Orthohydrogen Shift Alan M. Claude, Harold L. Hutchinson, Lee F. Brown,. and Paul L. Barrick Department of Chemical Engineering, University of Colorado, Boulder, Colorado 80309
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It is sometimes desirable to design a reactor from experiments on the reverse reaction direction. An example is given; systems were needed involving the reaction parahydrogen orthohydrogen, carried out at cryogenic temperatures over an oxide catalyst, but it was safer and more convenient to measure the reverse reaction. The Langmuir-Hinshelwood rate equation correlated the data very well in the reverse direction, but it proved valueless for extrapolation to the forward direction. A rate expression of the form r = CT In { [ ( x / x e ) @[(l ] - xe)/( 1 x ) ] ) proved adequate for the purpose. It is speculated that the reason the logarithmic expression worked so well was that it could be derived from so many different assumptions concerning system characteristics, giving it flexibility in application.
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Introduction There can arise circumstances wherein it may be desirable to use a reverse reaction to determine quantitative rate information about the forward reaction. In synthesis reactions, as in methanol synthesis for example, it might be simpler to carry out experimental measurements of the decomposition reaction rather than measurements of the synthesis itself. If sufficient information can be obtained from the measurements of the decomposition, much labor might be saved. Another situation in which it might be desirable to use a reverse reaction to determine quantitative behavior of the forward reaction would exist when side reactions interfere with accurate or simple determination of the forward rates. An example of this might be the reaction of carbon monoxide with methanol. Both acetaldehyde and methyl formate may be produced from this reaction, and information about either one of the reactions might be obtained with less difficulty if the reverse reaction were studied. A third possibility for the desirability of measuring a reverse reaction rather than the forward reaction might occur if the forward reaction had some safety considerations which were not present when measuring the reverse reaction. In this last case, money and time might be saved by not having to take the precautions which would be necessary for measuring the forward reaction. An example of the last type of situation arose in a program of study in our laboratories, and this paper presents what was necessary to implement the reverse reaction approach successfully for the system we were investigating. The principal element in using a reverse reaction to predict forward reaction behavior is to have a reaction rate expression that is valid for both directions and whose parameters are identical for the two directions. There appear to be no previous studies reported in the literature in which, for a heterogeneous reaction, a rate expression valid for one direction was examined for its validity in the other direction using the same catalyst and the same operating conditions. A study of this type would seem to be the essential precondition for successful application of the reverse-reaction-application concept, and the present paper does this. The Low-Temperature Para-Orthohydrogen Shift The original program involved an investigation and development of catalysts, principally of the ferric oxide type, for promoting the conversion of parahydrogen to orthohydrogen (they differ in nuclear spin) at cryogenic temperatures. At the time of the study, it was proposed to use this reaction as a heat sink on space vehicles using liquid hydrogen as a fuel (the heat
of reaction is +333 cal/g-mol at 76 K). Experimental evidence indicates that when using oxide catalysts at low temperatures, the reaction is unimolecular and the surface reaction is the rate-limiting step (Hutchinson et al., 1967; Kauffman, 1970). In the laboratory, especially a t the higher cryogenic temperatures ranging from about the triple point of nitrogen to the boiling point of oxygen (63-90 K), it is much easier to carry parahydrogen than the out the reaction orthohydrogen desired parahydrogen orthohydrogen reaction. Hydrogen obtained in a cylinder contains 75% orthohydrogen and 25% parahydrogen, the equilibrium amount at room temperature and higher. At lower temperatures, the equilibrium shifts toward parahydrogen. At the temperature of boiling nitrogen (75.7 K in Boulder, Colo.) the equilibrium percentage is 51.3% parahydrogen; at boiling hydrogen temperature (20 K), an equilibrium mixture contains 99.8% parahydrogen. Because of this, cylinder hydrogen, with only simple purification steps, may be used as a reactant source for the reverse parahydrogen. For the forward reaction orthohydrogen reaction, however, a source of parahydrogen must be prepared. This means passing hydrogen over a catalyst immersed in liquid hydrogen, for it is only at this low temperature that the 25% parahydrogen mixture will be converted to a parahydrogen-rich source for the forward reaction. The safety precautions attendant on the use of liquid hydrogen made it very desirable to carry out as much of the program as possible using the reverse reaction. As a result, an effort was made to see if a complete design orof a catalytic reactor for the reaction parahydrogen thohydrogen could be made using information gained from studying the reverse reaction, orthohydrogen parahydrogen. In order to accomplish this, it was necessary to have a reaction-rate expression which was valid for both directions of the reaction, and for which the parameters in the expression could be determined by carrying out the reaction in one direction only. An additional desirable characteristic of the rate expression would be an insensitivity to system characteristics; e.g., if the expression were valid whether the catalyst possessed a uniform or a nonuniform surface, this would extend the versatility of the expression. While this characteristic would seem a drawback to the kineticist, who uses a rate expression to limit the number of possible reaction paths and system characteristics, it is a distinct advantage to the reactor designer because it frees him from the necessity of knowing the mechanism in order to proceed with reliable design equations.
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Ind. Eng. Chern., Process Des. Dev., Vol. 16, No. 3, 1977
263
L A N G M U I R - HINSHELWOOD PREDICTION BASED ON
-K;;;
-!
a 'Ob
q E 60
B C PA R OSEREDRDIECLON TAI T OINO N
~
k In
FOR
OR
0
iHO
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a 50 2 0
u
+ z
z
w
5 4 0 -LANGMUl R - H I NSHELWOOD CORRELATION FOR ORTHO-PARA k- I O IO0 2 00
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Rate Expressions Considered Early experiments on the catalytic promotion of the reverse reaction indicated that a first-order reversible rate expression of the form
(1)
was adequate to describe the behavior of this reaction. Previous studies in our laboratory (Hutchinson et al., 1967; Kauffman, 1970) confirmed this for catalysts of lesser activity, but showed that more active catalysts may demand a more complex rate expression to describe the reaction behavior satisfactorily. Since this program was being carried out using one of the most active catalysts known a t the time, it was apparent that a first-order rate expression would most probably not be useful for our purposes. The next expression considered was that resulting from a Langmuir-Hinshelwood approach
It was reported in an earlier publication (Hutchinson et al., 1967) that this rate expression could be predicted to apply to the catalytically promoted low-temperature ortho-parahydrogen shift irrespective of which reaction step or combination of steps were assumed to be rate-limiting. Even though experimental evidence did indicate that the rate-limiting step was the surface reaction rather than the adsorption or desorption steps, as mentioned above, nevertheless this characteristic of the rate expression did give it a desirable flexibility of application. It was also reported in this paper that for this expression to be valid for both directions with identical values of the rate constants, a uniform surface apparently must be assumed. This latter characteristic was seen as a drawback, limiting the possibility of the expression's applicability for the purposes of this study. It was also shown in the paper that this expression correlated the data from either direction quite well. Figure 1 illustrates the good quality of the correlation achieved in one direction by using this expression for some typical reaction conditions. Also shown in Figure 1 is the predicted behavior of the forward reaction using the Langmuir-Hinshelwood Ind. Eng. Chern., Process Des. Dev., Vol. 16, No. 3, 1977
100
PARA 200
300
SPACE VELOCITY ( r n i n - ' )
Figure 1. Langmuir-Hinshelwood correlation for ortho-para conversion and prediction of para-ortho conversion from ortho-para correlation: 0 ,experimental data for para-ortho conversion; 0 , experimental data for ortho-para conversion; pressure, 4.15 atm; temperature, 76 K.
r = kCt(x - x , )
FOR ORTHO
10
300
SPACE VELOCITY (rnrn-')
264
40t
LOGARITHMIC
LL
LL
Figure 2. Logarithmic correlation for ortho-para conversion and
prediction of para-ortho conversion from ortho-para correlation: 0, experimental data for para-ortho conversion; 0 , experimental data for ortho-para conversion; pressure, 4.15 atm; temperature,76 K.
expression and the L-H constants obtained from the reverse reaction data. The prediction fails utterly to match the actual behavior of the forward reaction. Therefore the LangmuirHinshelwood expression was useless for the purpose of using the reverse reaction to predict the behavior of the forward reaction, even though it correlated the data of the reverse reaction very well. The third rate expression considered was
(3) Various derivations of this expression have been presented by one of the authors (Claude, 1975). It was shown that this expression could apply to many different circumstances if it were assumed that the reaction was unimolecular and that the surface reaction was the rate-limiting step, as discussed earlier. Given these preconditions, it was shown that this rate expression could be derived assuming adsorption of the Langmuir, the Temkin, or the Freundlich types. It could also be derived assuming either linear or nonlinear dependences of the reaction rates upon surface concentrations, combined with any of the listed adsorption types. Since the Temkin and the Freundlich adsorption isotherms and the nonlinear dependence of the rate on surface concentration are all usually ascribed to varying types of surface nonuniformity, this expression appears to be valid for differing types of nonuniform surfaces, in addition to uniform surfaces. From the point of view of flexibility of assumptions, therefore, this too seemed to be a reasonable expression, though from a different aspect than the Langmuir-Hinshelwood expression. The assumptions and approximations used in the derivation should make the rate expression most accurate in the region near equilibrium. It is obviously not applicable as x approaches either 1 or 0, because it has r approaching + a and - O D , respectively, at these values of x. A crude estimate of the point of failure of the expression (Claude, 1975) indicates that it should be reasonably good when X 1- x e 0.6 I- I1.5 and 0.6 5 -I1.5 Xe
1-x
(4)
For reactor design, of course, it is not necessary for both ends of the reactor to be in the proper range for the logarith-
Table I. Comparison of the Logarithmic and the Langmuir-Hinshelwood Models When Correlations for One Reaction Direction Are Used to Predict Data for the Other Reaction Direction Sum of squared deviations No. of data
Pressure, atm 2.04 2.04 4.15 8.30 15.3
points deleted" 0
4 0 4 0 4 0 4 0
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Correlation for para direction only LangmuirLogarithmic Hinshelwood ortho
1.54
0.950
0.512
0.639
0.223
0.0842
0.432
0.168
0.303
0.272
0.586
0.188
4 34.0
0
X IO4
Predicted para based on ortho
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Logarithmic 9.41 2.85 14.7 2.63 1.69 0.125 O.l5
