condition \(-1 \le x_3 \le +1\). The solution of this one-dimensional problem is no longer difficult. We record the maximum value of \(J\) obtained and the corresponding coordinate values. Then, in succession, we additionally fix \(x_2=I\), \(x_3=+I\), \(x_3=-I\), find and record the maximum value of \(J\). From these four maximum values of \(J\), we select the greatest—the solution of the problem on the face \(x_1=+I\).

b) We fix \(x_1=-I\) and again repeat all the operations described in item “a.”

Then we successively examine the faces \(x_2=+I\), \(x_2=-I\), \(x_3=+I\), \(x_3=-I\). At the end, for each face we select, from among the solutions, the one that corresponds to the greatest value of \((x)\).

Conclusion. On the basis of the algorithm described, the authors solved extremal problems for finding the optimal conditions for conducting the hydrocracking process in obtaining pure benzene, naphthalene, and mesitylene / 1 /. The algorithm is simple from a computational standpoint, is accessible to any process engineer, and can be implemented on a digital computer at little cost.

Literature

1. Ruban A.I., Elbert E.I. Calculation of extremal values of hydrocracking parameters in obtaining pure benzene, naphthalene, and mesitylene. Research report. Tomsk–Novokuznetsk, 1971.

STUDY OF THE SORPTION CAPACITY OF MAGNESIUM OXIDE WITH ADDITIVES

V.V. Nakhalov, N.F. Stas, G.G. Savel’ev, T.S. Gordina

Studies on the sorption of carbon dioxide and water vapor were carried out on 13 samples of magnesium oxide obtained under different conditions, and on 11 samples with “homophase” additives.

Magnesium oxide without additives was obtained by thermovacuum decomposition of basic magnesium carbonates directly in the cell of a gravimetric apparatus. The basic carbonates were precipitated from solutions of magnesium nitrate or magnesium chloride of various concentrations by solutions of ammonium, potassium, or sodium bicarbonates. All syntheses were carried out at room temperature. The principal data on the methods ...

synthesis are given in Table I.

Table I

Conditions for obtaining basic magnesium carbonates without additives (temperature—20°C)

The analyses performed showed that the composition of the samples corresponds to the formula $(4 \div 7)\mathrm{MgCO_3}\cdot\mathrm{Mg(OH)_2}\cdot(4 \div 9)\mathrm{H_2O}$.

The first series of experiments was carried out with sample No. 11 in order to determine the optimal temperature for decomposition of the basic carbonate at which the most active magnesium oxide absorbents are obtained. For this purpose, after 30-minute evacuation the weighed portions were decomposed for one hour at various temperatures in the range 280–430°C; after cooling, carbon dioxide was sorbed for 120 minutes. With increasing temperature, the degree of decomposition increases from 11.4% at 280°C to 98.2% at 430°C, while the sorption curve passes through a maximum corresponding to decomposition of the basic carbonate by 70.5%.

The results obtained indicate that a temperature of 360°C with evacuation to $10^{-3}$ mm Hg is opti-

low for obtaining the most active samples of magnesium oxide.

In the second series of experiments, dry carbon dioxide gas was sorbed on all samples of magnesium oxide obtained by decomposition of basic carbonates at \(360^\circ\mathrm{C}\). Samples Nos. 2 and 5–7 sorbed 40–70 mg/g, while the remaining ones had a capacity in the range of 130–190 mg/g over two hours at \(20^\circ\mathrm{C}\).

The results obtained show that both the capacity of the samples and the rate of the process depend strongly on the conditions of their preparation. When magnesium nitrate is used as the starting substance, the activity of the samples is low and does not exceed 70 mg/g, with the exception of sample No. 3, where potassium bicarbonate was used as the precipitant and was added to the solution in crystalline form, as a result of which the capacity increased twofold. When magnesium chloride is used, the activity of the samples increases. The most active was sample No. 13, which had a capacity of 194 mg/g over two hours of sorption.

The rate of the sorption processes on magnesium oxide is rather high: within one hour, up to 90% is absorbed of the amount of \(\mathrm{CO}_2\) that is absorbed over two hours.

Thus, despite the high regeneration temperature, magnesium oxide can be regarded as a promising absorber of carbon dioxide. Therefore, further studies were undertaken, primarily on the effect of various “homophase” additives.

By the method of coprecipitation of hydroxides, samples were synthesized with “homophase” additives of the oxides of beryllium, copper, zinc, nickel, iron, chromium, and aluminum. The sample with an additive of lithium oxide was prepared by impregnating freshly precipitated wet magnesium hydroxide with lithium hydroxide, followed by thorough mixing during evaporation and drying. The silver additive was introduced by impregnating freshly precipitated wet magnesium hydroxide with a solution of silver nitrate, and the vanadium additive by impregnating it with a solution of ammonium vanadate. The syntheses were carried out at room temperature using 2 N salt solutions and a 20% ammonia solution as the precipitant. For comparison, magnesium hydroxide without additives (sample No. 15) was prepared from magnesium nitrate under the same conditions.

Dehydration of the samples was carried out, as in all previous

in the experiments, directly in the cell of the weighing apparatus before carrying out the sorption process. On each sample, dry carbon dioxide gas, then moist carbon dioxide gas \((P/P_s = 1)\), and water vapor (nitrogen carrier) were sorbed successively. The final sorption results after 2 hours are given in Table 2.

Table 2

Effect of “homophase” additives on the sorption capacity of magnesium oxide

It is evident from the table that the capacity of magnesium oxide for dry CO₂ and the rate of its absorption are increased only by the addition of nickel oxide (among those studied), whereas the number of additives that increase activity toward moist CO₂ is considerably larger \((\mathrm{CuO}, \mathrm{BeO}, \mathrm{Cr_2O_3}, \mathrm{Ag_2O}, \mathrm{Li_2O})\).

The maximum values of the capacity of sorbents based on MgO attained on the samples studied are (at \(\tau = 2\) hours): for dry carbon dioxide gas, 214 mg/g (sample no. 21), and for moist gas, 510 mg/g (sample no. 19). The high capacity values indicate that absorbents based on magnesium oxide are promising and that the indicated samples may be recommended for further testing.