On the Determination of the Main Kinetic Parameters of Synthesis from Carbon Monoxide and Water Vapor

S. I. Smolyaninov, V. M. Mironov

(Presented by the scientific-methodological seminar of the KhTF)

To determine a set of kinetic parameters (rate constants, reaction orders, and apparent activation energy), it is necessary to represent the experimental data in the form of a kinetic equation.

For the process of synthesis of organic compounds from carbon monoxide and water vapor, the rate of formation of hydrocarbons according to the hypothetical equation

\[ 3\mathrm{CO}+\mathrm{H}_2\mathrm{O}=(-\mathrm{CH}_2-)+2\mathrm{CO}_2 \tag{1} \]

can be described as follows:

\[ r_y=\frac{dC_y}{d\tau}=k^* C_{\mathrm{co}}^{n_1} C_{\mathrm{v}}^{n_2}; \quad \text{where} \tag{2} \]

\(C_y\) — concentration of hydrocarbons;
\(k^*\) — effective rate constant;
\(C_{\mathrm{co}}\) — concentration of carbon monoxide;
\(C_{\mathrm{v}}\) — concentration of water vapor;
\(n_1; n_2\) — the corresponding reaction orders.

According to the conclusions of G. K. Boreskov [1], the kinetic equation of a heterogeneous process proceeding with a change in volume, as is also the case for the process according to (1), must be expressed through the degrees of conversion of the reaction components. Then (2) will take the form

\[ r_y=\frac{dy_y}{d\tau}=k_y^*(1-y_c)^{n_1}(1-y_{\mathrm{v}})^{n_2}, \quad \text{where} \]

\(y_c\) — overall degree of conversion of CO;
\(y_{\mathrm{v}}\) — overall degree of conversion of water vapor;
\(y_y\) — degree of conversion of CO to hydrocarbons.

Introducing the coefficient

\[ a=\frac{1-y_{\mathrm{v}}}{1-y_c}, \]

under the condition that the reaction time \(\tau\) is proportional to the fictitious contact time \(\omega\), we finally obtain

\[ r_y=\frac{dy_y}{d\omega}=k_y^* a^{n_2}(1-y_c)^{n_1+n_2} \tag{3} \]

According to the data of H. Kölbel [2], the value of \(a\) is linear within the limits of the total degree of CO conversion from 0 to 0.7; therefore, the indicated equation is applicable within these limits.

Taking logarithms of (3), we obtain

\[ \lg r_y=\lg k_y^*+n_2\lg a+(n_1+n_2)\lg(1-y_c). \]

At \(k_y^*=\mathrm{const}\), the dependence of \(\lg r_y\) on \(\lg(1-y_c)\) will be linear, with slope \((n_1+n_2)\), which is the overall order of the reaction according to (1). Naturally, at \(y_c=0\), \(y_{\mathrm{v}}=0\) and \(a=1\); therefore, by extrapolating the straight-line dependences of \(\lg r_y\) on \(\lg(1-y_c)\) to their intersection with the ordinate axis, one can obtain values of the effective rate constant of the reaction, \(k_y^*\).

The rate of the hydrocarbon-formation reaction was determined by graphical differentiation of kinetic isotherms reduced to a constant hydrodynamic regime (in the range of Reynolds criterion values 0.3–1.5).

The temperature dependence of the effective rate constant in Arrhenius coordinates is shown in Fig. 1. In the temperature interval studied, this dependence is linear.

Fig. 1. Temperature dependence of the effective rate constant of the process: — pressure atmospheric, fictitious linear velocity \(x\)—0.295 cm/sec, \(o\)—0.590 cm/sec, \(\Delta\)—0.885 cm/sec, ●—1.475 cm/sec; — — pressure medium.

The values of the apparent activation energy, calculated from the slope of the straight lines in the indicated figure, are as follows: for the process at atmospheric pressure, 67 kJ/mol, and for synthesis at medium pressure \((0.98\ \mathrm{MN}/\mathrm{m}^2)\), 73 kJ/mol.

For synthesis at atmospheric pressure, a change in the linear velocity of the synthesis gas, while affecting the value of the rate constant, does not affect the values of the apparent activation energy. For the process at medium pressure, the effective rate constant does not depend on the linear flow velocity (Fig. 1).

From the nature of the dependence of the effective rate constant on the conditions of external diffusion, from the values of the apparent activation energy, and on the basis of the general principles of diffusion kinetics, it may be assumed that the synthesis of organic compounds from carbon monoxide and water vapor according to (1) proceeds in the external transition region when operating at atmospheric pressure, and in the region of internal diffusion when operating at medium pressure.

An analysis of the dependence of the overall reaction order on the fictitious linear velocity and temperature, based on the propositions advanced by S. Ya. Pshezhetskii [3] and G. M. Panchenkov [4], confirms the stated assumption of a significant influence of external and internal diffusion on the process under consideration.

Conclusions

1. A simplified kinetic equation is proposed for the process of formation of organic compounds from carbon monoxide and water vapor, applicable up to values of the total degree of conversion of CO of 0.5–0.7.

1. The apparent activation energy of the process has been determined from the temperature dependence of the effective rate constant.

2. The possibility has been demonstrated that synthesis from CO and water vapor proceeds at atmospheric pressure in the external transition region, and at medium pressure in the region of internal diffusion.

REFERENCES

1. G. K. Boreskov, Catalysis in the Production of Sulfuric Acid. Moscow–Leningrad, 1954, Goskhimizdat, p. 48.
2. H. Kölbel, Fr. Engelhardt, Brennst. Chem., 42, No. 3, 65–72, 1961.
3. S. Ya. Pshezhetskii, ZhFKh, 21, issue 9, 1019–1025, 1947.
4. G. M. Panchenkov, Yu. M. Zhorov. In: Kinetics and Catalysis, 133–139, Publishing House of the USSR Academy of Sciences, Moscow, 1963.