DEPENDENCE OF THE SELECTIVITY OF SYNTHESIS FROM CARBON MONOXIDE AND WATER VAPOR ON THE CONDITIONS OF ITS CONDUCT

S. I. Smolyaninov, A. V. Kravtsov, V. M. Mironov

(Presented by the scientific-methodological seminar of the Faculty of Chemical Technology)

Along with activity, the selectivity of a heterogeneous catalytic process is the most important characteristic determining, in the final analysis, the feasibility of its practical application. The selectivity of such a process is determined not only by the nature of the catalyst, but also to a considerable degree by the conditions under which the reaction proceeds, that is:

\[ \xi = \varphi(T; C_i;\tau; v), \]

where
\(\xi\) — selectivity;
\(T\) — temperature;
\(C_i\) — concentrations of the components;
\(\tau\) — contact time;
\(v\) — linear velocity of the reactants.

In the present work we have attempted to generalize the theoretical material on the selectivity of heterogeneous reactions and to apply the dependences obtained to explain the results of studies of the processes of synthesis of organic compounds from carbon monoxide and water vapor on cobalt and iron catalysts.

In processing the experimental material it is assumed that hydrogen in the synthesis process is formed by the reaction of conversion of carbon monoxide with water vapor:

\[ \mathrm{CO} + \mathrm{H_2O} \to \mathrm{CO_2} + \mathrm{H_2}. \]

The methane-formation reaction has been assigned by us to the principal reactions, while the decomposition of carbon monoxide according to the equation:

\[ 2\,\mathrm{CO} \to \mathrm{C} + \mathrm{CO_2} \]

is not taken into account, since it has been shown [1] that under optimal process conditions its share is insignificant.

The differential selectivity of formation of organic compounds from carbon monoxide and water vapor is represented by the ratio of the reaction rate according to the hypothetical equation:

\[ 3\mathrm{CO} + \mathrm{H_2O} \to (-\mathrm{CH_2}-) + 2\mathrm{CO_2} \tag{2} \]

to the rate of hydrogen formation according to reaction (1), with instead of the rate—

of these reactions, we use quantities symbatic with them: the degrees of conversion of carbon monoxide to hydrocarbons and hydrogen, i.e.,

\[ \zeta=\frac{W_{CH_2}}{W_{H_2}}\simeq\frac{Y_{CH_2}}{Y_{H_2}}, \quad \text{where} \tag{3} \]

\(W_{CH_2}\), \(W_{H_2}\) are the rates of the reactions of formation of hydrocarbons and hydrogen;
\(Y_{CH_2}\), \(Y_{H_2}\) are the corresponding degrees of conversion of carbon monoxide.

The mathematical expression for selectivity, with the chosen method of determining it, 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 following expression:

\[ \zeta=\frac{W_1}{W_2}=\frac{k_1}{k_2}\,[A]^{m-n}, \quad \text{where} \]

\(k_1\), \(k_2\) are the rate constants of the reactions being compared;
\(m\), \(n\) are their kinetic orders.

In this case, the selectivity may vary from zero to infinity. For consecutive reactions

\[ A \xrightarrow{k_1} B \xrightarrow{k_2} C, \]

according to G. K. Boreskov [2],

\[ \zeta=1-\frac{W_2}{W_1}=1-\frac{k_2}{k_1}\,[A]^{-m}\cdot[B]^n, \quad \text{where} \]

\(W_1\) is the rate of consumption of substance \(A\);
\(W_2\) is the rate of formation of substance \(C\).

Here the selectivity already varies from 1 to \(-\infty\). However, for a qualitative assessment of the dependence of the selectivity of the process on the conditions under which it is carried out, this difference in the expression for selectivity plays no role. As will be shown later, the principal pattern of the dependences found does not change in a number of cases also for reactions proceeding by a more complex mechanism.

Let us consider the influence of several factors on the selectivity of the heterogeneous catalytic process under study.

The influence of temperature is determined by the difference between the temperature coefficients of the reactions being compared. For parallel reactions of first order this question has been developed quite fully by S. Yu. Elovich [3]. In the case of parallel reactions of any order, it can be shown that

\[ \zeta=\frac{k'_1}{k'_2}\cdot e^{\frac{E_2-E_1}{RT}}\cdot[A]^{m-n}, \quad \text{where} \]

\(E_1\), \(E_2\) are the activation energies of the reactions being compared.

For consecutive reactions

\[ \zeta=1-\frac{k'_2}{k'_1}\cdot e^{-\frac{E_2-E_1}{RT}}\cdot[A]^{-m}\cdot[B]^n. \]

Thus, the change in selectivity for both types of reactions with change in temperature will be determined by the sign of the quantity

\[ \Delta E = E_2 - E_1 \]

At \(\Delta E > 0\), the selectivity of the process should decrease with increasing temperature and, conversely, at \(\Delta E < 0\), it should increase.

Figure 1 shows the dependence of the selectivity of the synthesis process from carbon monoxide and water vapor, expressed by equation (3), on temperature. From this it may be concluded that the temperature coefficient of the reaction rate according to equation (2) is apparently higher than that according to equation (1) and, consequently, the activation energy of the synthesis is higher than the activation energy of the conversion reaction. Calculations of the apparent activation energy of these reactions, which we carried out using a modified Arrhenius equation [4], confirm this conclusion.

The effect of contact time on the selectivity of parallel first-order reactions is not observed. For analogous reactions of higher orders, S. L. Kiperman [5] gives the following dependence:

\[ \zeta = \frac{k_1}{k_2} \cdot \tau^{\frac{m-n}{(1-m)(1-n)}}, \]

where

\[ \begin{aligned} \tau &\text{— contact time;}\\ m &\text{— order of the principal reaction;}\\ n &\text{— order of the side reaction.} \end{aligned} \]

Fig. 1. Dependence of the selectivity of the synthesis process on temperature. 1, 2, 3—cobalt catalyst; 4—iron catalyst; 1, 4—catalyst bed length 200 cm; 2—100 cm; 3—26 cm.

The direction of change in the selectivity of the process with changing contact time in this case will be determined entirely by the ratio of the quantities \(m\) and \(n\). At \(m > n\), selectivity increases with increasing reaction time; at \(m < n\), the dependence is opposite; and at \(m = n\), selectivity does not depend on contact time. (These conclusions are valid when \(m\) and \(n\) are simultaneously greater than or simultaneously less than unity; otherwise the dependences change places.)

For consecutive reactions, as is known from the course of chemical kinetics, regardless of the reaction orders, the selectivity of the process with respect to the intermediate product is characterized by the presence of a maximum when the contact time is varied.

In our case, as is seen from Fig. 2, a decrease in contact time causes a decrease in the selectivity of the process with respect to the principal reaction. If the reactions proceed in parallel, this may mean that the order of the synthesis reaction according to equation (2) is higher than the order of the conversion reaction according to equation (1). If a consecutive mechanism of these reactions is assumed, then the principal amount of hydrogen must be liberated as a result of conversion dehydrogenation of hydrocarbons, as we described in [6].

Effect of the ratio of the initial substances on the selectivity of the process is ultimately characterized by the ratio of the reactant concentrations. Thus, for the simplest parallel reactions of the type:

\[ mA \xrightarrow{k_1} B \]

\[ nA \xrightarrow{k_2} C \]

the selectivity is determined by the expression

\[ \zeta = \frac{k_1}{k_2}\cdot N_A^{m-n}, \]

where \(N_A\) is the mole fraction of component \(A\) in the mixture; that is, the selectivity of the process will not depend on the ratio of the reactants if the reaction orders with respect to the initial substance are the same. Similar dependences are also possible for more complex reactions.

In the case of consecutive reactions, for example,

\[ mA \to nB \to pC \]

\[ \zeta = 1 - \frac{k_2}{k_1}\cdot N_A^{-m}\cdot N_B^{n}. \]

Experimental data for the process studied by us (Fig. 3) show that the selectivity with respect to the principal reaction increases with an increase in the mole fraction of carbon monoxide in the initial mixture. If it is assumed that the two reactions under consideration are parallel, then the indicated dependence is possible when \(m > n\). A further decrease in selectivity with respect to the principal reaction may be due to a sharp increase in the reaction of carbon monoxide decomposition for mixtures containing more than 0.75 mole fraction of the latter. As was shown earlier [7], in this case “coking” of the catalyst is observed.

Fig. 2. Dependence of the selectivity of the synthesis process on the fictitious reaction time. 1—cobalt catalyst; 2—iron catalyst.

Effect of diffusion complications on the change in selectivity of the process must, in all probability, be significant. It should be noted that all the preceding conclusions concerning the effect 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 by the rate of the chemical reaction, i.e., the process proceeds in the kinetic region for both reactions being compared. If, however, at least one of the reactions being compared proceeds in the diffusion region, the dependences 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 process selectivity on temperature will be very weak, since in this case \(\Delta E = E_2 - E_1 \approx 0\), and the quantity

\[ e^{\frac{\Delta E}{RT}} \approx 1. \]

Then the selectivity will be determined only by the magnitudes of the surface concentrations of the reactants, which depend only very weakly on temperature.

Returning to Fig. 1, we may note that the selectivity of the synthesis process increases with temperature more intensively in the case of higher linear velocities (catalyst-bed length 1--2 meters) than in the case of a low linear velocity of synthesis gas (catalyst-bed length 0.26 meter), when diffusion retardation is possible.

Upon transition to the diffusion region, the concentration of the substance on the catalyst surface, and consequently also the process rate, will be determined by a number of factors not taken into account in the above formulas. In the case of internal diffusion, the surface concentrations of the reactants will be determined mainly by the physical properties of the reaction mixture and the catalyst (diffusion coefficients of the components, catalyst pore size, etc.). The dependence of the process selectivity on these parameters has been analyzed in the works of G. K. Boreskov [8] and E. Wheeler [9].

Fig. 3. Dependence of the selectivity of the synthesis process on the molar concentration of the reactants. 1 -- cobalt catalyst; 2 -- iron catalyst.

For external diffusion, the surface concentrations will be determined by the conditions of mass transfer between the external surface of the catalyst and the reaction volume. In this case, the dependence of the process selectivity will in many respects be determined by the conditions of the hydrodynamic regime in the contact apparatus.

For consecutive reactions it has been shown [12] that the selectivity changes with a change in diffusion conditions only within the transition region, and it increases for intermediate products; for parallel reactions of the type:

\[ A_{\mathrm{vol}} \begin{cases} \nearrow\ mA_{\mathrm{s}} \to B_{\mathrm{s}} \to B_{\mathrm{vol}},\\ \searrow\ nA_{\mathrm{s}} \to C_{\mathrm{s}} \to C_{\mathrm{vol}}, \end{cases} \]

where the subscript "vol" refers to the concentration of the substance in the volume, and the subscript "s" to the concentration on the contact surface, the selectivity is equal to

\[ = \frac{k_1}{k_2}\left[A_{\mathrm{s}}\right]^{m-n}, \]

that is, the selectivity will be determined by the surface concentration of component \(A\) to the power \((m-n)\). When \((m-n)>0\), the selectivity increases with the removal of diffusion complications; when \((m-n)<0\), it decreases; and in the case where \((m-n)=0\) (in the particular case when \(m\) and \(n\) are both equal to 1; see, for example, works [2, 10, 11]), the selectivity will not depend on the diffusion conditions of the reaction components.

Fig. 4. Dependence of the selectivity of the synthesis process on the fictitious linear velocity of the synthesis gas.
1 — cobalt catalyst; 2 — iron catalyst.

Fig. 5. Dependence of the selectivity of the synthesis process on the carbon monoxide content in the feed gas.
1 — cobalt catalyst; 2 — iron catalyst.

In Figure 4 we present the dependence of the selectivity of the process with respect to reaction (2) on the linear velocity of the reactants. It may be noted that the selectivity of the process under consideration increases sharply in the region of fictitious linear velocity from 2 to 7 m/s and then remains at the same level. It is clear that in this case the selectivity is affected by the removal of diffusional complications owing to an increase in the flow rate.

The effect of dilution of the feed with inert additives is determined by a change in the concentrations of the reacting substances. For ideal gases, in the case of parallel reactions, the selectivity will be equal to:

\[ \zeta = \frac{k_1}{k_2} \cdot P_A^{m-n}. \]

Analogously to the effect of the ratio of the initial substances, the selectivity in this case will depend on the difference in the orders of the reactions being compared and on the partial pressures of the reactants.

Similar conclusions can also be drawn for consecutive reactions. The dependences obtained are illustrated in Figure 5 by experimental data.

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 they must be taken into account in the study of such reactions.

Conclusions

1. A qualitative assessment has been made of the dependence of the selectivity of some complex heterogeneous catalytic reactions on the conditions under which they are carried out.

2. It has been shown that the derived dependences are confirmed by experimental data on synthesis from carbon monoxide and water vapor on two catalysts.

LITERATURE

1. Köbel H., Hammer H. Z. für Elektrochem. Ber. Bunsenges. Phys. Chem. 64, 224, 1960.

2. Boreskov G. K., Dzisko V. A., and Borisova M. S. ZhFKh, vol. XXVIII, issue 6, 1055—1066, 1954.

3. Elovich S. Yu. Problems of Kinetics and Catalysis, VI. Heterogeneous Catalysis, pp. 375—404. Publishing House of the Academy of Sciences of the USSR, 1949.

4. Orochko D. I. Theoretical Foundations of Conducting Syntheses of Liquid Fuels, Gostoptekhizdat, Moscow, 1951.

5. Kiperman S. L. Introduction to the Kinetics of Heterogeneous Catalytic Reactions, Nauka Publishing House, Moscow, 1964.

6. Smolyaninov S. I., Kravtsov A. V., and Mironov V. M. Izv. TPI (in press).

7. Kelbel G., Forverk E. Chemistry and Chemical Technology, No. 11, 1957, 122.

8. Boreskov G. K. Heterogeneous Catalysis in the Chemical Industry, p. 3, Goskhimizdat, Moscow, 1955.

9. Uider E. Catalysis. Questions of Theory and Research Methods, pp. 479—563, Izd., Moscow, 1955.

10. Frank-Kamenetskii D. A. Diffusion and Heat Transfer in Chemical Kinetics, Publishing House of the Academy of Sciences of the USSR, Moscow, 1947.

11. Roiter V. A., Gaukhman S. S. Catalysis. Proceedings of the All-Union Conference on Catalysis, 161—163, Publishing House of the Academy of Sciences of the Ukrainian SSR, Kiev, 1950.

Noted Misprints