Physical Chemistry

A. M. BRODSKII, R. A. KALINENKO,
Corresponding Member of the Academy of Sciences of the USSR K. P. LAVROVSKII, and L. V. SHEVELKOVA

ON THE MECHANISM OF FORMATION OF SECONDARY PRODUCTS IN THE HIGH-TEMPERATURE CRACKING OF ETHANE

The present work is devoted to an investigation of the mechanism of formation of the principal secondary products in the high-temperature cracking of ethane to ethylene. The formation of CH₄, C₂H₂, C₃H₈, C₃H₆, C₄H₁₀, C₄H₈, and C₄H₆ was studied. The mechanism of the formation of ethylene from ethane at 770–890° was studied by us earlier (¹), using a specially developed method for studying the kinetics of high-temperature reactions (²). It was found that, under the conditions studied, the formation of C₂H₄ proceeded mainly by a molecular route. Indications were also obtained that the hydrocarbons C₃ and C₄ were formed with the participation of radicals. To clarify the regularities of the formation of secondary products, we carried out a study of the cracking of ethane with additions of ethylene labeled with carbon C¹⁴, in a turbulent reactor (²) at temperatures of 800–880° and a pressure of \(90 \pm 3\) mm Hg. Corundum was used as the heat carrier in all experiments, and in experiment No. 18, powdered quartz. The procedure for carrying out the experiments, the chromatographic analysis, and the determination of the radioactivity of the products obtained was analogous to that described in detail in (¹). All experiments were carried out on a mixture of composition 99.5% C₂H₆ + 0.45% C₂H₄. The activity of the initial C₂H₄ was \(1.33 \cdot 10^6\) imp/cm³·min, and that of the initial mixture \(6 \cdot 10^3\) imp/cm³·min.

The most complete data were obtained in experiments at 880°, where it was possible to determine the concentrations and specific activities of the secondary products. This made it possible to elucidate the mechanism in greatest detail precisely at this temperature. Tables 1 and 2 give the compositions of the products obtained and their specific and absolute activities. The yield of the secondary products of cracking and their specific activity do not depend on the heat-carrier material; this is shown by the data of experiment No. 18, in which quartz was used as the heat carrier. From the data of Table 2 it is seen that the specific activities

Table 1*

Compositions of the products of cracking of C₂H₆ (vol. %)

* The accuracy of the analytical determination of the concentrations of C₂H₆, C₂H₄, H₂, and CH₄ was \(\pm 1\)–2% (relative), and for C₂H₂, C₃H₈, C₃H₆, C₄H₁₀, C₄H₈, and C₄H₆ present in small amounts, \(\pm 10\)% (relative).

** The quantity \(kt = C_0/\alpha C + 1\), where \(k\) is the total rate constant for decomposition of C₂H₆, \(t\) is the reduced reaction time, \(C_0\) is the initial concentration and \(C\) the current concentration of C₂H₆, and \(\alpha\) is the coefficient of increase in the number of moles during cracking; it characterizes the depth of reaction.

Table 2

Specific activities \((a)\) (imp/min per 1 mm gas pressure in the counter) and concentrations of active products \((A)\) (in imp/min per 1 cm\(^3\) of gas obtained)*

* The specific activity of C\(_2\)H\(_6\) was 4–5 imp/mm·min at 880°, 2–3 imp/mm·min at 840°, and 1–2 imp/mm·min at 800°. The accuracy of determining the specific activities of all products was ±3%. In those experiments in which it was not possible to measure the specific activities of C\(_2\)H\(_2\), C\(_3\)H\(_8\), C\(_3\)H\(_6\), C\(_4\)H\(_{10}\), C\(_4\)H\(_8\), and C\(_4\)H\(_6\), which were present in small amounts, the determination of the total activities of these products was carried out as follows: inactive gases were added to the reaction mixture; the mixture was separated chromatographically and the total activity of the individual hydrocarbons was determined. In order to calculate the fraction of radioactive molecules for each hydrocarbon, it is necessary to multiply the corresponding value of \(a\) by the coefficient \(2.5 \cdot 10^{-9}\).

C\(_2\)H\(_2\), C\(_3\)H\(_6\), and C\(_4\)H\(_8\) are close to the specific activity of ethylene, from which it may be concluded that these products are formed with the participation of one molecule of ethylene. The specific activity of divinyl in all experiments is approximately twice the specific activity of C\(_2\)H\(_4\). Evidently C\(_4\)H\(_6\) is formed with the participation of two molecules of C\(_2\)H\(_4\) or of products obtained from ethylene and having the same specific activity (for example, from C\(_2\)H\(_4\) and C\(_2\)H\(_2\)), and not from C\(_4\)H\(_6\). The specific activities of methane, ethane, propane, and butane are comparatively small and, consequently, these products are formed chiefly from low-activity ethane and the products of its transformations. Thus, from consideration of the specific activities of the products it is immediately possible to draw a conclusion about a qualitative difference in the pathways of formation of saturated, unsaturated, and diene hydrocarbons in the cracking of ethane. From the data on the concentrations of active products in the reaction mixture it follows that the main directions of ethylene consumption are the formation of acetylene, methane, propylene, and divinyl. Reverse hydrogenation of ethylene to ethane proceeds only to an insignificant extent: less than 0.01 of the fraction of C\(_2\)H\(_4\) is converted into ethane. It should be noted that the rate constant of the reaction \({}^{*}\)C\(_2\)H\(_4\) + H\(_2\) \(\to\) \(\to\) C\(_2^{*}\)H\(_6\) proves, with good accuracy, to be equal to the product \(Kk\), where \(K\) is the equilibrium constant for the reaction under consideration and \(k\) is the rate constant of ethane dehydrogenation by the molecular path. Consequently, the reaction written above corresponds to the actual path of formation of C\(_2^{*}\)H\(_6\) under the conditions investigated.

Let us now dwell on the specific pathways of formation of the individual products. From the fact that the specific activities and concentrations of C\(_3\)H\(_8\) and C\(_4\)H\(_{10}\) are relatively small, it follows that their formation occurs, in accordance with (1), predominantly through recombination of low-activity radicals CH\(_3\) and C\(_2\)H\(_5\).

According to (2), we have:

\[ [\mathrm{C_3H_8}] = \frac{k_1[\mathrm{CH_3}][\mathrm{C_2H_5}]\,t} {1+k_{\mathrm{C_3H_8}}t}; \tag{1} \]

\[ [\mathrm{C_4H_{10}}] = \frac{k_1[\mathrm{C_2H_5}]^2\,t} {1+k_{\mathrm{C_4H_{10}}}t}. \tag{2} \]

* Molecules containing radioactive carbon C\(^ {14}\) are marked with an asterisk.

where \(k_1\) is the rate constant of the radical recombination reaction, and \(k_{\mathrm{C_3H_8}}\) and \(k_{\mathrm{C_4H_{10}}}\) are the overall rate constants of the decomposition reactions of \(\mathrm{C_3H_8}\) and \(\mathrm{C_4H_{10}}\). The formulas for the formation of labeled products are written analogously. Combining equations (1) and (2), we find that at \(880^\circ\) and for the ratio \((1+k_{\mathrm{C_4H_{10}}}t)\) to \((1+k_{\mathrm{C_3H_8}})\) equal to \(\sim 1.5\), the ratio \([\mathrm{C_2H_5}]:[\mathrm{CH_3}]\) is \(\sim 1.5\). Using the value of \(k_1\) obtained in (1), at \(880^\circ\) we obtain, in agreement with an independent calculation (1), \([\mathrm{C_2H_5}]=2 \div 4 \cdot 10^{14}\) radicals/\(\mathrm{cm^3}\), since, by estimate, \(2 < (1+k_{\mathrm{C_4H_{10}}}t) \leq 4\). Analysis of the data obtained shows that the formation of propylene and butylene proceeds according to the scheme:

\[ \begin{aligned} \mathrm{C_2H_6}+\mathrm{R} &\xrightarrow{k_2} \mathrm{C_2H_5}+\mathrm{RH}, \qquad& \mathrm{C_4H_9} &\xrightarrow{k_5} \mathrm{C_4H_8}+\mathrm{H},\\ \mathrm{C_2H_5} &\xrightarrow{k_3} \mathrm{C_2H_4}+\mathrm{H}, \qquad& \mathrm{C_4H_9} &\xrightarrow{k_6} \mathrm{C_3H_6}+\mathrm{CH_3},\\ \mathrm{C_2H_5}+\mathrm{C_2H_4} &\xrightarrow{k_4} \mathrm{C_4H_9}, \qquad& \mathrm{C_4H_9} &\xrightarrow{k_7} \mathrm{C_2H_4}+\mathrm{C_2H_5}. \end{aligned} \]

Neglecting the consumption of \(\mathrm{C_4H_9}\)* (i.e., using unity in the denominators), we have:

\[ [\mathrm{C_3H_6}]=k_6[\mathrm{C_4H_9}]t= \frac{k_6\cdot k_2\cdot k_4[\mathrm{C_2H_4}][\mathrm{C_2H_6}][\mathrm{R}]t} {(k_5+k_6+k_7)k_3}, \tag{3} \]

\[ [\mathrm{C_4H_8}]=k_5[\mathrm{C_4H_9}]t= \frac{k_5\cdot k_2\cdot k_4[\mathrm{C_2H_4}][\mathrm{C_2H_6}][\mathrm{R}]t} {(k_5+k_6+k_7)k_3}. \tag{4} \]

From the ratio of the specific activities of \(\mathrm{C_3H_6}\) and \(\mathrm{C_3H_8}\), \(\mathrm{C_4H_8}\) and \(\mathrm{C_4H_{10}}\), it follows that, under the conditions studied, there was no appreciable formation of \(\mathrm{C_3H_6}\) from \(\mathrm{C_3H_8}\) or of \(\mathrm{C_4H_8}\) from \(\mathrm{C_4H_{10}}\). At a temperature of \(880^\circ\), propylene and butylene were also not formed by recombination of \(\mathrm{C_2H_3}\) with \(\mathrm{CH_3}\) and \(\mathrm{C_2H_5}\). Otherwise, the concentration \([\mathrm{C_4H_8}]\) would have been greater than \([\mathrm{C_3H_6}]\), since \([\mathrm{C_2H_5}] \gg [\mathrm{CH_3}]\). In reality, however, at \(880^\circ\), \([\mathrm{C_4H_8}] \ll [\mathrm{C_3H_6}]\). This fact can readily be explained if it is assumed that the formation of both \(\mathrm{C_3H_6}\) and \(\mathrm{C_4H_8}\) occurs mainly in the decomposition of \(\mathrm{C_4H_9}\). The preferential formation of \(\mathrm{C_3H_6}\) from \(\mathrm{C_4H_9}\), and not from \(\mathrm{C_3H_7}\), is due, on the one hand, to the fact that \([\mathrm{C_4H_9}] > [\mathrm{C_3H_7}]\), since \([\mathrm{C_2H_5}] \gg [\mathrm{CH_3}]\), and, on the other hand, to the greater ease of breaking the C—C bond as compared with breaking the C—H bond**. Using the experimental data and the values of \([\mathrm{R}]\), \(k_2\), and \(k_3\) obtained in (1), and also assuming \(k_6:(k_5+k_6+k_7)\simeq 2/3\), from equations (3) and (4) one can estimate the value of the rate constant for the reaction of radical “addition” to the olefin, \(k_4\), which at \(880^\circ\) is equal to \(9\cdot 10^{-16}\) \((\mathrm{molecule}^{-1}\cdot \mathrm{cm^3}\cdot \mathrm{sec}^{-1})\), i.e., twice as large as the rate constant of the substitution reaction. The ratio \(k_6/k_5\), determined from equations (3) and (4), is equal to 5 at \(880^\circ\), 3 at \(840^\circ\), and 1 at \(800^\circ\). Since the activation energy \(E_6\) is less than \(E_5\), the ratio \(k_6/k_5\) should not have increased with increasing temperature, but should have decreased. Evidently, at the lower temperatures studied there are other pathways for obtaining \(\mathrm{C_4H_8}\), in particular recombination of \(\mathrm{C_2H_3}\) and \(\mathrm{C_2H_5}\).

The interrelated formation of acetylene and divinyl*** is described

* In the present work, when considering pathways for the formation of secondary products involving free radicals, we, in agreement with the results of (1), assume that at the high temperatures studied the main pathway for the disappearance of the radicals \(\mathrm{C_3H_7}\) and \(\mathrm{C_4H_9}\) is decomposition, and not substitution or recombination reactions. This is confirmed, in particular, by the total activity of \(\mathrm{C_3H_8}\), which is approximately an order of magnitude lower than the activity of \(\mathrm{C_3H_6}\). At \(880^\circ\), the main pathway for the disappearance of \(\mathrm{C_2H_5}\), according to (1), is also decomposition. At the lower temperatures studied, neglecting other pathways for the disappearance of \(\mathrm{C_2H_5}\) leads to an overestimate of \([\mathrm{C_2H_5}]\) by no more than a factor of two.

** In processing the results in (1), the possibility of formation of \(\mathrm{C_3H_6}\) from \(\mathrm{C_4H_9}\) was not taken into account. This led to a somewhat overestimated value of the ratio \([\mathrm{C_2H_5}]/[\mathrm{CH_3}]=4\), compared with the value 1.5 obtained in the present work.

*** A special experiment, in which 0.2% labeled \(\mathrm{C_2H_2}\) was added to the initial mixture, confirmed that \(\mathrm{C_4H_6}\) is formed not from two \(\mathrm{C_2H_2}\) molecules, but from a \(\mathrm{C_2H_2}\) molecule and \(\mathrm{C_2H_4}\). The specific activities of \(\mathrm{C_2H_4}\), \(\mathrm{C_2H_2}\), and \(\mathrm{C_4H_6}\) in this experiment were respectively 2370, 800, and 3140 imp/mm·min.

by the following overall equations:

\[ [\mathrm{C_2H_2}] = \frac{k_8[\mathrm{C_2H_4}]t}{1+k_9[\mathrm{C_2H_4}]t} \tag{5} \]

\[ [\mathrm{C_4H_6}] = k_9[\mathrm{C_2H_2}][\mathrm{C_2H_4}]t . \tag{6} \]

The rate constant for the reaction of formation of \(\mathrm{C_2H_2}\) from \(\mathrm{C_2H_4}\) (\(k_8\)) was found to be \(0.65\ \mathrm{s}^{-1}\) at \(880^\circ\), \(0.17\ \mathrm{s}^{-1}\) at \(840^\circ\), and \(0.04\ \mathrm{s}^{-1}\) at \(800^\circ\). This variation of \(k_8\) with temperature corresponds to an activation energy of \(\sim 95\) kcal. The effective rate constant for the reaction of \(\mathrm{C_2H_2}\) with \(\mathrm{C_2H_4}\) with formation of \(\mathrm{C_4H_6}\) (\(k_9\)), determined from the independent equations (5) and (6) at \(880^\circ\), is equal to \(1.6 \cdot 10^{-16}\ \mathrm{molecule}^{-1}\cdot\mathrm{cm}^3\cdot\mathrm{s}^{-1}\) and changes hardly at all when the temperature is lowered. At \(840\) and \(800^\circ\), the value of \(k_9\) calculated from equation (5) was approximately twice the value of \(k_9\) obtained from equation (6). Possibly, at lower temperatures other reactions begin to play a substantial role in the disappearance of \(\mathrm{C_2H_2}\), for example, the addition of alkyl radicals to \(\mathrm{C_2H_2}\). The detailed mechanism of the very interesting reaction of divinyl synthesis is complex and apparently includes steps involving free radicals. This is indicated by the fact that the concentration \([\mathrm{C_4H_6}]\) in the products is higher than the equilibrium concentration for the process \(\mathrm{C_4H_6} \rightleftarrows \mathrm{C_2H_2}+\mathrm{C_2H_4}\). The established independence of the constant \(k_9\) from the depth of conversion shows that only chemically highly reactive radicals, the concentration of which is stationary, can act as intermediate compounds in the indicated reaction.

The specific activity of \(\mathrm{C_2H_5}\) (\(a_{\mathrm{C_2H_5}}\)) should be equal to half of \(a_{\mathrm{C_4H_{10}}}\). From the ratio of \(a_{\mathrm{C_3H_8}}\) and \(a_{\mathrm{C_4H_{10}}}\), one can determine \(a_{\mathrm{CH_3}}\) and, consequently, the specific activity of \(\mathrm{CH_4}\) formed in substitution reactions involving \(\mathrm{CH_3}\). Thus, in experiment No. 18, where \(a_{\mathrm{C_4H_{10}}}\) was measured especially accurately, \(a_{\mathrm{CH_3}} = 40\ \mathrm{imp/mm\cdot min}\), while \(a_{\mathrm{CH_4}} = 75\ \mathrm{imp/mm\cdot min}\). Thus, about one half of the \(\mathrm{CH_4}\) was not formed through \(\mathrm{CH_3}\). Since the concentration of active \(\mathrm{CH_4}^*\), \(A_{\mathrm{CH_4}}\), is relatively large, it cannot be assumed that \(\mathrm{CH_4}\) is formed to a significant extent by decomposition of high-molecular active products present in small quantities. Evidently there is a reaction of \(\mathrm{CH_4}\) formation involving \(\mathrm{C_2H_4}\), possibly by molecular processes, as is also indicated in work \((^3)\). With increasing temperature, \(a_{\mathrm{CH_4}}\) falls, which indicates a decrease in the fraction of the reaction of formation of \(\mathrm{CH_4}\) through \(\mathrm{C_2H_4}\). The specific activity of coke, measured in the form of \(\mathrm{CO_2}\) (\(a_{\mathrm{CO_2}}\)), at \(880^\circ\) is \(\sim 630\)—\(640\ \mathrm{imp/mm\cdot min}\), i.e., \(1/2\,a_{\mathrm{C_2H_4}}\). Hence it may be concluded that at \(880^\circ\) coke is formed from highly active unsaturated products. At \(840\) and \(800^\circ\), \(a_{\text{coke}}\) is equal, respectively, to \(230\) and \(90\)—\(160\ \mathrm{imp/mm\cdot min}\). At these temperatures, reactions of interaction of unsaturated and condensed hydrocarbons with less active alkyl radicals begin to play a substantial role in coke formation.

Institute of Petrochemical Synthesis
Academy of Sciences of the USSR

Received
27 II 1962

REFERENCES

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