Ind. Eng. Chem. Res. 1992,31, 2805-2806 Duran, M. A.; Grossmann, I. E. A Mixed integer nonlinear programming approach for process systems synthesis. AZChE J . 1986,32 (4),592-606. Fluodas, C. A.; Aggarwal, A.; Ciric, A. R. Global optimum search for nonconvex NLP and MINLP problems. Comput. Chem. Eng. 1989,13 (lo),1117-1132. Kocis, G. R.; Grossmann, I. E. Relaxation strategy for the structural optimization of process flow sheets. Znd. Eng. Chem. Res. 1987, 26 (9),1869-1880. Kocis, G. R.; Grossman, I. E. Global optimization of nonconvex mixed-integer nonlinear programming (MINLP) problems in process synthesis. Znd. Eng. Chem. Res. 1988, 27, 1407-1421. Salcedo, R. Solving Nonconvex Nonlinear Programming and Mixed-Integer Nonlinear Programming Problems with Adaptive Random Search. Znd. Eng. Chem. Res. 1992, 31 (l),262-273.
2806
Salcedo, R.; Goncalves, M. J.; Fey0 de Azevedo, S. An improved random-search algorithm for nonlinear optimization. Comput. Chem. Eng. 1990,14 (lo),1111-1126. Vanderplaats, G. N. Numerical Optimization Techniques for Engineering Design-with Applications; McGraw-Hill: New York, 1984;pp 17-19. Viswanathan, J.; Grossmann, I. E. A Combined Penalty Function and Outer-Approximation Method for MINLP Optimization. Comput. Chem. Eng. 1990,14 (9),769.
R. L. Salcedo Centro de Engenharia QuEmica Instituto Nacional de Inuestigaqdo Cientifica Rua dos Bragas, 4099 Porto Codex, Portugal
Response to Comments on “An MINLP Process Synthesizer for a Sequential Modular Simulator” Sir: Professor Salcedo is correct in pointing out that there is an inconsistency in the illustrative example given on p 315 of our recent paper (Diwekar, U. M.; Grossmann, I. E.; Rubin, E. S. Ind. Eng. Chem. Res. 1992,31,313-322). The correct MINLP formulation for that example is as follows: minimize y l + 1.5(y2) + 0.5(y3) + x l l + x12 subject to x l l - x12 = 0 x12 - x22 = 0 ~ 1 -3x2
+ ( x l - 2)’
0
~l - x2 yl
+ 4y2 I4
+ y2 + y3 I1
Y l , Y2, Y3 = 0, 1
The typographical errors were an incorrect sign in the third constraint and the exclusion of the eighth and ninth inequalities. It is for this reason that Professor Salcedo found a different solution. The optimum solution of the problem EBgiven above is indeed the one reported in Table I of the original paper: y l = 0, y2 = 1, y 3 = 0, xl = 1.0, x2 = 1.0, x l l = 1.0, x12 = 1.0, x13 = 0.0, F = 3.5 We regret the typographical errors and would like to thank Professor R. L. Salcedo for bringing them to our attention.
x13 I0 2(yl) - x l = 0
Urmila M. Diwekar, Ignacio E. Grossmann* Edward S. Rubin
1-yl -xl I O
Department of Engineering and Public Policy and Department of Chemical Engineering Carnegie Mellon University Pittsburgh, Pennsylvania 15213
3(y3) - x l - x2 I0 x2 - y2 1 0
Comments on “Direct Oxidative Methane Conversion at Elevated Pressure and Moderate Temperatures” Sir: Walsh et al. (1992) reported that with direct oxidation of methane, product selectivity depended on residence time, temperature, and the catalyst. The main reactions are as follows:
- + - + - +
CHI + ‘/202 CH30H CH4 + O2
CHI + Y2O2 CH,
+ 202
(1)
CH20
H20
(2)
CO
2H20
(3)
C02
2Hz0
(1)
The percent conversion of methane and product distribution depend strongly on which of the four reactions is dominating. The percent conversion of oxygen in almost all the experiments reported (with the exception of run 6) oa8a-58a5192J 2631-2ao5$03.00JO
was loo%, which means that oxygen was the limiting reactant. The theoretical conversion of methane therefore lay between 2.0 and 38.7%. Since the conversion of oxygen was 100% at low and high residence times, the interpretation of data on product distribution would pose a problem. Maximum conversion of methane was achieved at a residence time of 0.2 s (runs 5 and 7). A longer residence time will only promote the coupling of radicals or reactions between products. CH3 + CH3 C2HG (5) CHSOH + CO
-
COZ + CH,
(6)
For the same reason, the effect of reaction temperature on product selectivity could not have been fully evaluated, as the conversion of oxygen was 100% at all the reaction temperatures considered. 1992 American Chemical Society
