Estimation of Concentrations in Chemical Systems at Equilibrium Using Geometric Programming

Document Type: paper

Authors

1 Department of Management, University of Isfahan

2 Department of Chemical Engineering, University of Isfahan

3 Payam Noor University, Semirom

Abstract

Geometric programming is a mathematical technique, which has been developed for nonlinear optimization problems. This technique is based on the dual program with linear constraints. Determination of species concentrations in chemical equilibrium conditions is one of its applications in chemistry and chemical engineering fields. In this paper, the principles of geometric programming and its computational method are presented. Also, for a chemical equilibrium, as an example, the concentrations of species for the ammonia synthesis reaction are determined. The obtained results are compatible with the experimental data available in the literature. This leads to the application of the geometric programming to estimate the concentrations in the equilibrium conditions for reactions where the experimental data are not available.

Keywords


[1] Zener, C., 1961. A mathematical aid in optimizing engineering designs. Proceedings of the National Academy of Sciences, 47(4), pp.537-539.

[2] Paoluzzi, A. (2003). ”Geometric  Programming  for Computer-Aided Design. ” John Wiley & Sons 

[3] Levary, R.R. (1988).  “ Engineering Design .”  North-Holland Publishing Co

[4] Smith, J.M., Van Ness, H.C., Abbott, M.M. (1996).  " Introduction to chemical engineering  thermodynamics ." McGraw- Hill, New York

[5] White, W.B., Seider, W.D. (1981). “Computation of phase and chemical equilibrium, part 4: Approach to chemical equilibrium.”  AIChE, Vol. 27,  No. 3, pp. 466-471

[6] Akbari, F.Zare  Aliabadi, H., Torabi Angaji, M. (2008). "Thermodynamic modeling of the reactor High temperature shift converter using minimization of Gibbs free energy." Twelfth Iranian Congress on Chemical  Engineering http://www.echemica.com/Printable -TE114.html

[7] Dimian, A. C., Bildea, C. S. (2008). " Chemical  Process Design ." Wiley -VCA, Weinheim

[8] Bonilla -Petriciolet, A., Segovia - Hernández, J.G. (2010). "A Comparative Study of Particle  Swarm Optimization and Its Variants for Phase Stability and Equilibrium Calculations in Multicomponent Reactive and Non-Reactive Systems."Fluid Phase Equilibria, Vol. 289, pp. 110–121.

[9] Schittkowski, K. (1985). " Computational  Mathematical Programming." Springer-Verlag.

[10] Passy, U., Wilde, D.J.(1967). “A Geometric programming algorithm for solving chemical equilibrium problems.” SIAM Review,Vol. 11, pp. 8.

[11] Duffin, R. J., Peterson, E.L., Zener, C. (1967). “Geometric Programming-Theory and Application.” John Wiley & Sons.

[12] Alejandre, J.L., Allueva, A.I. , Gonzalez , J.M. (1967). “ A new algorithm for geometric programming based on the linear structure of its dual problem.” Mathematical and Computer Modeling, Vol. 31,  pp. 61-78.

[13] Wall, T .W, Greening, D., Woolsey, R.E.D. (1986) “Solving complex chemical using a geometric programming based technique.” Operations Research , Vol.  34,  No. 3 , pp. 345- 355.

[14] Parker, S.P. (1983). "Mc Graw Hill Encyclopedia Chemistry." Mc Graw Hill.

[15] Chiang, M. (2005). "Geometric Programming for Communication Systems." Foundations and Trends in Communications and Information Theory , Vol. 2, No. 1, pp. 1- 156.