SIMPLEX DESIGN OF EXPERIMENTS IN THE STUDY OF THE HYDROCARBON PYROLYSIS PROCESS

M. D. MEDVEDEV

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

In studying the process of hydrocarbon pyrolysis using the simplex method of design, the formulation of the problem reduces to the following: by varying three variables ($\alpha$—temperature at the reactor outlet, $\beta$—feed rate of the raw material, and $\gamma$—degree of dilution with steam), we find the response function ($\eta$—ethylene yield) [1]

\[ \eta = f(\alpha; \beta; \gamma). \]

As an example, we present a study of the pyrolysis process for the 180–350°C fraction of Samotlor oil. The fraction was obtained by vacuum distillation of oil on an ARN-2 unit and has the following physicochemical characteristics:

yield — 32.8 wt.%;
molecular weight — 198;
density — 0.8541;
content of paraffinic hydrocarbons — 47.8 wt.%;
content of naphthenic hydrocarbons — 21.8 wt.%;
content of aromatic hydrocarbons — 30.4 wt.%.

Initial levels and intervals of variation of the process parameters were selected on the basis of the results of studies described in the literature [2, 3, 4]. It should be noted that correctly selected initial levels and variation intervals reduce by a factor of 1.5–2 the number of experiments required for finding the parameters of the “ethylene” regime.

For the fraction under study, the selected initial levels and variation intervals are presented in Table 1.

Table 1

Basic levels and intervals of variation of parameters in the study of the 180–350°C fraction

In accordance with the matrix of the initial simplex [1], we plan the first series of experiments. This series is shown in Table 2, experiments 1, 2, 3, 4. The numerical value is taken as the quality index of the process.

ethylene yield in percent of the feedstock. From Table 2 we see that the worst result (ethylene yield 14.9 wt.%) was obtained in the first experiment. This point is replaced by a new one, which is its “mirror reflection” with respect to the opposite face of the simplex. The fifth point, together with the remaining ones (2, 3, 4), again forms a regular simplex, whose centroid is directed toward improvement of the process quality. Stepwise ascent continues until an increase in the process quality is observed.

Table 2

Matrix of simplex design of experiments for the 180–350° C fraction of Samotlor crude oil

The maximum ethylene yield was obtained in the seventh experiment after the third reflection and is equal to 25.5 wt.%.

The following parameters correspond to the found “ethylene” regime:

temperature at the reactor outlet, °C — 765;
feedstock supply, ml/min — 2.2;
dilution with steam, wt.% — 51.

Thus, by moving along the response surface, an “almost stationary” region was found. This assumption is confirmed by experiments 8, 9, 10, and 11, which were carried out after reaching the extremal point.

From experiments 12, 13, 14, and 15, the arithmetic mean value of the ethylene yields was found to be \(\overline{y_0} = 22.8\) wt.%. The standard deviation is \(\sigma(y)=0.3\); thus, the value of the response function at the center of the simplex is as follows:

\[ \overline{y_0}=22.8 \pm 0.3. \]

Its expected value, determined as the arithmetic mean over the points of the last simplex, is \(\overline{y_c}=24.0\) wt.%. The difference

$\bar y_c - \bar y_0 = 24.0 - 22.8 = 1.2$ is a measure of the nonlinearity of the response function. The calculated Student criterion is $t = 14.0$, while the value found from tables [5] is $t_\alpha = 3.182$.

$$ t > t_\alpha . $$

The inequality necessary to prove the nonlinearity of the response surface is satisfied.

Conclusions

1. The method of simplex design of experiments has been applied in studying the process of hydrocarbon pyrolysis.

2. It has been shown that application of this method greatly reduces the number of experiments in the search for the optimal parameters of the “ethylene” regime.

3. The pyrolysis process of the 180–350°C fraction of Samotlor crude oil has been studied.

4. The ethylene regime found for this fraction corresponds to the following parameters:

temperature at the reactor outlet — 765°C;
feed rate — 2.2 ml/min;
dilution with steam — 51 wt.%.

1. Under the specified process conditions, the ethylene yield is 25.5 wt.% based on the initial feedstock, which indicates that the 180–350°C fraction is a fairly good feedstock for pyrolysis for the purpose of obtaining monoolefins.

References

1. V. G. Gorskii, V. Z. Brodskii. Zavodskaya laboratoriya. 7–12, 831, 1965.

2. P. I. Luk’yanov, A. G. Basistov. Pyrolysis of Petroleum Feedstock. Moscow, Gostoptekhizdat, 1962.

3. Review of Foreign Literature, series “Petrochemistry Abroad,” issue 5. Moscow, TsNIITÉneftekhim, p. 3, 1971.

4. N. L. Barabanov. Thematic Reviews, series “Petrochemistry Abroad,” Moscow, TsNIITÉneftekhim, p. 26, 1971.

5. L. Z. Rumshinskii. Mathematical Processing of Experimental Results. Moscow, “Nauka,” 1971.