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.
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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
2806
Ind. Eng. Chem. Res. 1992,31, 2806-2807
The rates of methane consumption at 550 and 600 " C were, respectively, 4.8 x and 5.12 x mol min-' ~ m - ~The . difference between the two rates is too small to be considered significant, and is not compatible with Arrhenius' law. It should also be noted that the catalytic rate of methane consumption was 4.23 X mol min-' ~ m -which ~ , was slightly lower than the rate of homogeneous reaction (runs 7 and 9). Thus it would be difficult to draw any conclusion about the contribution of homogeneous reactions in experiments where a catalyst was used. We would suggest that the interpretation of the results should take into account complete conversion of oxygen, and the effects of residence time and reaction temperature
on the product distribution should be investigated with excess oxygen at the exit of the reactor. Registry No. CHI, 14-82-8; 02, 1182-44-1.
Literature Cited Walsh, D. E.; Martenak, D.J.; Han, S.; Palermo, R. E. Direct Oxidative Methane Conversion at Elevated Pressure and Moderate Temperatures. Ind. Eng. Chern. Res. 1992, 31, 1259.
0. Olaofe, P. L. Yue* School of Chemical Engineering University o f Bath Bath BA2 7AY, U.K.
Response to Comments on "Direct Oxidative Methane Conversion at Elevated Pressure and Moderate Temperatures" Sir: Based on their comments on our paper (Walsh et al., 1992), it would appear that Olaofe and Yue are restating remarks already presented in the article, and are interpreting more in the data than we, the authors, intended, asserted, or believed was justified. Their general observation that oxygen is the limiting reactant in this study is self-evident; it is also characteristic of most current direct oxidative methane conversion studies in the literature. Likewise, the discussion of the range over which methane conversion can vary and its limiting values which are governed by different stoichiometries has been appreciated by those working in the field. Their discussion that longer residence times can promote further reactions among products appears to be a restatement of our remarks in the article (p 1261, column 1,paragraphs 1and 2). In particular, we noted that oxygen consumption remained complete when residence time was reduced by a factor of 3; consequently, we suspected that since more residence time was available in most runs than was required to achieve complete oxygen consumption, certain thermodynamically feasible secondary reactions might occur. As reported, the similarity of the product distributions (and associated methane conversions) in two runs at substantially different residence times suggested that such reactions "do not proceed extensively" during the available incremental time (
