Influence of External Factors on the Selectivity of Catalysts in a Heterogeneous Process
Abstract Generated abstract
This paper systematizes how external operating conditions affect selectivity in heterogeneous catalytic reactions, considering temperature, reactant concentration, contact time, dilution, and diffusion limitations. Using kinetic expressions for parallel and consecutive reaction schemes, the authors relate selectivity to activation energies, reaction orders, partial pressures, and mass transfer conditions, then compare these relations with data for synthesis of organic compounds from carbon monoxide and water vapor over cobalt and iron catalysts. The analysis indicates that selectivity in this system increases with temperature, contact time, carbon monoxide mole fraction within an optimum range, and linear gas velocity until diffusion limitations are reduced, supporting the conclusion that process conditions can substantially alter catalytic selectivity and must be included in evaluating heterogeneous reactions.
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INFLUENCE OF EXTERNAL FACTORS ON THE SELECTIVITY OF CATALYSTS IN A HETEROGENEOUS PROCESS
S. I. Smolyaninov, V. M. Mironov, A. V. Kravtsov
(Presented by the organic section of the KhTF seminar)
The selectivity of a heterogeneous catalytic process is determined not only by the nature of the catalyst, but also by the conditions under which the reaction proceeds, which in general form may be denoted as follows:
\[ \xi = \varphi(T;\ C_i;\ \tau;\ v), \]
where \(\xi\) is selectivity;
\(T\) is the process temperature;
\(C_i\) are the concentrations of the reactants;
\(\tau\) is the reaction time;
\(v\) is the linear velocity of the reaction mixture.
In the literature, questions concerning the dependence of the selectivity of heterogeneous catalysis on external conditions have not yet been systematized, although the influence of individual factors has been established. The need to systematize and study this question is at present highly urgent [1].
In the present work we have attempted to generalize the theoretical material on the selectivity of heterogeneous reactions and to illustrate the obtained dependences with the results of a study of the process of synthesis of organic compounds from carbon monoxide and water vapor at atmospheric pressure over cobalt and iron catalysts.
Differential selectivity is determined by the ratio of the rates of the reactions being compared. Its mathematical expression depends on the mechanism of the process. In the simplest case, for parallel reactions of the type
\[ mA \xrightarrow{k_1} B \]
\[ nA \xrightarrow{k_2} C, \]
the selectivity is determined by the expression
\[ \xi_{\mathrm{par}} = \frac{W_1}{W_2} = \frac{k_1}{k_2}\cdot [A]^{m-n}, \]
where \(k_1\) and \(k_2\) are the rate constants of the reactions being compared;
\(m\) and \(n\) are the kinetic orders of these reactions.
For consecutive reactions
\[ A \xrightarrow{k_1} B \xrightarrow{k_2} C. \]
according to the work of G. K. Boreskov and co-workers [2], the selectivity with respect to the intermediate product is:
\[ \xi_{\text{int}} = 1 - \frac{W_2}{W_1} = 1 - \frac{k_2}{k_1}\cdot \frac{[B]^n}{[A]^m}, \]
and with respect to the final product:
\[ \xi'_{\text{int}} = \frac{W_2}{W_1} = \frac{k_2}{k_1}\cdot \frac{[B]^n}{[A]^m}, \]
or
\[ \xi'_{\text{int}} = 1 - \xi_{\text{int}}. \]
In the first and third cases the value of the selectivity varies from zero to infinity, while in the second case it varies from unity to minus infinity. However, for a qualitative assessment of the selectivity of a process as a function of the conditions under which it is carried out, the difference in the expressions for selectivity is not important. It can also be readily shown that the general character of the dependencies found does not change in a number of cases for reactions proceeding by a more complex mechanism.
In processing the experimental material, the selectivity of synthesis from carbon monoxide and water vapor was determined by the ratio of the degree of conversion of carbon monoxide to hydrocarbons according to the hypothetical equation
\[ 3\mathrm{CO} + \mathrm{H_2O} = (-\mathrm{CH_2}-) + 2\mathrm{CO_2} \tag{1} \]
to the degree of conversion of carbon monoxide in the conversion reaction according to the equation:
\[ \mathrm{CO} + \mathrm{H_2O} = \mathrm{H_2} + \mathrm{CO_2}, \tag{2} \]
that is,
\[ \xi = \frac{Y_1}{Y_2}. \]
\(Y_1\) and \(Y_2\) are the degrees of conversion of CO according to equations (1) and (2), respectively.
In the present case the so-called integral selectivity was obtained, determined by the total amount of reacting substances. Under isothermal conditions, for a reactor length \(l\),
\[ \frac{Y_1}{Y_2} = \int_0^l \frac{W_1}{W_2}\, dl. \]
We have shown [3] that, at low degrees of conversion of carbon monoxide, the temperature gradient along the catalyst bed is insignificant; therefore the system may be considered isothermal.
We assign the methanation reaction to the principal reaction according to equation (1), while the decomposition of carbon monoxide according to the scheme:
\[ 2\mathrm{CO} = \mathrm{C} + 2\mathrm{CO_2} \tag{3} \]
was not taken into account, since it is known [4] that under optimum synthesis conditions its fraction is small.
Let us consider the influence of several factors on the selectivity of a heterogeneous catalytic process.
The effect of temperature is determined by the difference in the temperature coefficients of the rates of the reactions under study. For parallel first-order reactions this question has been sufficiently analyzed
by S. Yu. Elovich [5]. In the general case, for parallel reactions of any order it can be shown that
\[ \xi_{\mathrm{par}}=\frac{Z_1}{Z_2}\cdot e^{\frac{\Delta E}{RT}}\cdot |A|^{m-n}, \]
where
\[ Z_1 \text{ and } Z_2 \text{ are constants, and} \]
\[ \Delta E=E_2-E_1; \]
\(E_2\) and \(E_1\) are the activation energies of the reactions being compared. For consecutive reactions,
\[ \xi_{\mathrm{seq}}=1-\frac{Z_2}{Z_1}\cdot e^{-\frac{\Delta E}{RT}}\frac{|B|^n}{|A|^m} \]
and
\[ \xi'_{\mathrm{seq}}=\frac{Z_2}{Z_1}\cdot e^{-\frac{\Delta E}{RT}}\cdot \frac{|B|^n}{|A|^m}. \]
Thus, the change in selectivity with a change in temperature will be determined by the sign of the quantity \(\Delta E\).
Fig. 1 shows the dependence of the selectivity of the synthesis process from carbon oxide and water vapor on temperature. Calculations of the apparent activation energy of the reactions under study, carried out by us according to equations (1) and (2), transformed to the Arrhenius equation [6], showed that \(\Delta E<0\), i.e., \(E_2<E_1\). Hence it may be assumed that the synthesis reaction proceeds either in parallel with the conversion reaction or precedes it (see [7]).
Fig. 1. Dependence of the selectivity of the synthesis process from carbon oxide and water vapor on temperature. 1, 2, 3 — cobalt catalyst, layer length respectively 200, 100, 26 cm; 4 — iron catalyst, layer length 100 cm.
The influence of contact time on the selectivity of parallel first-order reactions is not manifested. For analogous reactions of higher orders, S. L. Kiperman [8] gives the following dependence:
\[ \xi_{\mathrm{par}}=\frac{k_1}{k_2}\cdot \tau^{\frac{m-n}{(1-m)(1-n)}}, \]
where
\[ \tau \]
is the contact time of the reactants,
\(m\) and \(n\) are the orders of the main and side reactions, respectively. The direction of the change in selectivity of the process in this case will be entirely determined by the ratio of the quantities \(m\) and \(n\).
For consecutive reactions, as is known from the course of chemical kinetics, the selectivity of the process with respect to the intermediate product, regardless of the reaction orders, is characterized by the presence of a maximum.
In our case (Fig. 2), an increase in the contact time leads to an increase in the selectivity of the process. This indicates a possible parallel scheme for the course of the process, and in that case the order of the synthesis reaction should be higher than the order of the conversion reaction.
The effect of the ratio of the initial substances on the selectivity of the process is ultimately characterized by the ratio of the concentrations of the reactants. Thus, for the simplest parallel reactions of the type considered above, and also for a system of the form
\[ mA + B \xrightarrow{k_1} C \]
\[ nA + B \xrightarrow{k_2} E \]
(which is similar to the process we studied for synthesis from carbon monoxide and steam), the selectivity is determined by the expression
\[ \xi_{\text{par}}=\frac{k_1}{k_2}\cdot N_A^{m-n}, \]
where
\[ N_A \]
is the mole fraction of component \(A\) in the mixture.
For consecutive reactions
\[ \xi_{\text{seq}}=1-\frac{k_1}{k_2}\cdot \frac{N_B^n}{N_A^m} \]
or
\[ \xi'_{\text{seq}}=\frac{k_1}{k_2}\cdot \frac{N_B^n}{N_A^m}. \]
Fig. 2. Dependence of the selectivity of the process of synthesis from carbon monoxide and steam on contact time (solid line) and on the mole fraction of CO in the mixture (dashed line).
1—cobalt catalyst, 2—iron catalyst.
The experimental data presented in Fig. 2 show an increase in selectivity with an increase in the mole fraction of carbon monoxide in the mixture. The sharp decrease in selectivity at \(N_{\mathrm{CO}}>0.750\) may be due to departure from the optimum conditions and, as a result, conversion of a large fraction of the carbon monoxide according to equation (3). As was already shown [9], in this case “coking” of the catalyst is observed.
The effect of dilution of the feedstock with inert additives on the selectivity of heterogeneous processes should be characterized analogously to the effect of the concentration of the reacting substances. For ideal gases, in the case of parallel reactions the selectivity will be equal to:
\[ \xi_{\text{par}}=\frac{k'_1}{k'_2}\cdot p^{m-n}. \]
Here the selectivity is also determined by the difference in the orders of the reactions being compared and by the partial pressures of the reactants. Similar conclusions can also be drawn for consecutive reactions.
The dependences obtained are illustrated in Fig. 3 by experimental data.
It is quite possible that the change in selectivity with an increase in the degree of dilution may occur as a result of a change in the diffusion conditions of the reactants.
The influence of diffusional complications on the change in the selectivity of the process must, in all probability, be considerable. It should be noted that all the preceding conclusions concerning the influence of various factors on the selectivity of complex reactions are based on the assumption that the total rate of interaction of the reactants is determined only by the rate of the chemical reaction, i.e., that the process proceeds in the kinetic region for both reactions being compared. If even one of the reactions proceeds in the diffusion region, the relationships indicated above change.
Let us assume that both reactions—regardless of whether they are parallel or consecutive—proceed in the diffusion region. Then the dependence of the selectivity of the process on temperature will be very weak, since in this case \(\Delta E = E_2 - E_1 \simeq 0\), and the quantity
\[ \exp\left(\frac{\Delta E}{RT}\right) \simeq 1. \]
Then the selectivity will be determined only by the values of the surface concentrations of the reactants, which depend only very weakly on temperature.
Returning to Fig. 1, we may note that the increase in selectivity of the process of synthesis from carbon monoxide and steam with increasing temperature proceeds more intensely in the case of high linear velocities of the synthesis gas (catalyst bed length 1 and 2 meters) than in the case of a low linear velocity (catalyst bed length 0.26 meter), when diffusional complications are possible.
Fig. 3. Dependence of the selectivity of the synthesis process from carbon monoxide and steam on the CO content in the initial gas (solid line) and on the fictitious linear velocity of the synthesis gas (dashed line).
1 — cobalt catalyst; 2 — iron catalyst.
Upon transition to the diffusion region, the concentration of a substance on the catalyst surface, and consequently also the rate of the process, will depend on a number of factors not taken into account in the formulas given above. In the case of internal diffusion, the surface concentrations of the reactants will be determined mainly by the physical properties of the catalyst and of the reaction mixture (diffusion coefficient of the components, pore size of the catalyst, etc.). The dependence of the selectivity of the process on the indicated parameters has been analyzed in the works of G. K. Boreskov [10] and E. Wheeler [11].
For the region of external diffusion, the surface concentrations will depend on the conditions of mass transfer between the external surface
the catalyst and the reaction volume. In this case, the dependence of the process selectivity on reversibility will be determined to a great extent by the conditions of convective diffusion in the reaction apparatus.
For consecutive reactions it has been shown [2] that the selectivity changes with variation in the conditions of external diffusion only within the range lying between the kinetic and external-diffusion regions; moreover, for intermediate products it increases with improvement of diffusional mass transfer.
For parallel reactions this question was analyzed in [12]. In Fig. 3 we present the dependence of the selectivity of the process of synthesis from carbon monoxide and water vapor according to reaction (1) on the linear velocity of the feed mixture. It may be noted that the selectivity of the process under study rises sharply in the region of fictitious linear velocities of synthesis gas from 2 to 7 m/sec, and then remains at the same level. It is clear that in this case selectivity is affected by the removal of diffusional limitations due to an increase in the flow velocity of the reactants.
Thus, on the basis of the foregoing it is confirmed that the selectivity of a heterogeneous catalytic process depends substantially on the conditions under which it is carried out, and therefore these must be taken into account in the study of such reactions.
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