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Chemical equilibrium systems as numerical test problems

Published: 01 June 1990 Publication History

Abstract

A system of nonlinear equations has been used as a test case by at least two authors. This system is purported to describe the equilibrium of the products of hydrocarbon combustion. The given system does not describe the stated physical problem, a fact which invalidates it as a test of solution methods for chemical equilibrium systems. In this note, the problem is correctly stated and then solved by the method of element variables.

References

[1]
BENSON, S.W. Chemical Calculations. Wiley, New York, 1971.
[2]
BREMMERMANN, H. J. Calculation of the equilibrium points for models of ecological and chemical systems. In Proceedings of the Conference on the Application of Undergraduate Mathematics in the Engineering, Life, Managerial and Social Sciences, P. J. Knopp and G. H. Meyer, Eds. Georgia Institute of Technology, Atlanta, 1973, 198-217.
[3]
BUTLER, J.N. Calculating molar solubilities from equilibrium constants. J. Chem. Edu. 38 (1961), 460-463.
[4]
DAMKOHLER, G., AND EDSE, R. The composition of associating combustion gases and the calculation of simultaneous equilibria. Z. Elektrochem 49 (1943), 178-186.
[5]
HIEBERT, K. L. An evaluation of mathematical software that solves systems of nonlinear equations. ACM Trans. Math. Softw. 8 (1983), 5-20.
[6]
KANDINER, n. J., AND BRINKLEY, S.a. Calculation of complex equilibrium relations. Ind. Eng. Chem. 42 (1950), 850-855.
[7]
KONOPASEK, M., AND JAYARAMAN, S. The TK!Solver Book. Osborne/McGraw-Hill, New York, 1984.
[8]
MEINTJES, K., AND MORGAN, A.P. A methodology for solving chemical equilibrium systems. Appl. Math. Comput. 22 {1987), 333-361.
[9]
MEINTJES, K., AND MORGAN, A.P. Element variables and the solution of complex chemical equilibrium problems. G.M. Res. Rep. GMR-5827, 1987 and Combust. Sci. Tech. 68 (1989), 35-48.
[10]
MORGAN, A.P. Solving Polynomial Systems Using Continuation for Scientific and Engineering Problems. Prentice-Hall, Englewood Cliffs, N.J., 1987.
[11]
SHACHAM, M. Numerical solution of constrained non-linear equations. Int. J. Numer. Meth. Eng. 23 (1986), 1455-1481.
[12]
SCULLY, D.B. Calculation of the equilibrium compositions for multiconstituent systems. Chem. Eng. Sci. 17 (1962), 977-985.
[13]
SMITH, W. R., AND MISSEN, R. W. Chemical Reaction Equilibrium Analysis: Theory and Algorithms. Wiley-Interscience, New York, 1982.
[14]
VAN ZEGGEREN, F., AND STOREY, S.H. The Computation of Chemical Equilibria. Cambridge University Press, London, 1970.

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Published In

cover image ACM Transactions on Mathematical Software
ACM Transactions on Mathematical Software  Volume 16, Issue 2
June 1990
70 pages
ISSN:0098-3500
EISSN:1557-7295
DOI:10.1145/78928
Issue’s Table of Contents

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 June 1990
Published in TOMS Volume 16, Issue 2

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