An effective calculation procedure for two-phase equilibria in multireaction systems

In this work, we present a method for the calculation of two-phase equilibria in multireaction systems. The procedure uses a transformed composition variable in the orthogonal derivatives of the Gibbs function and the tangent plane equation to form a system of non-linear equations. We solve this system with a Newton–Raphson method and our initialization procedure uses results from the reactive stability analysis and the reactive equal area rule. With this initialization strategy, convergence occurs with only a few iterations in the numerical method. Several examples with multiple chemical reactions demonstrate the performance of our approach. © 2008 Elsevier B.V. All rights reserved.

[1]  R. B. Newell,et al.  Dynamic simulation of bioreactor systems using orthogonal collocation on finite elements , 1999 .

[2]  A. Bonilla-Petriciolet,et al.  Performance of Stochastic Global Optimization Methods in the Calculation of Phase Stability Analyses for Nonreactive and Reactive Mixtures , 2006 .

[3]  William R. Smith,et al.  General optimality criteria for multiphase multireaction chemical equilibrium , 1993 .

[4]  Sanford Gordon,et al.  CALCULATION OF COMPLEX CHEMICAL EQUILIBRIA , 1968 .

[5]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[6]  A non-ideal multiphase chemical equilibrium algorithm , 1998 .

[7]  Alan E. Mather,et al.  Phase equilibria and chemical reaction , 1986 .

[8]  Nicolas Kalogerakis,et al.  A method for the simultaneous phase equilibria and stability calculations for multiphase reacting and non-reacting systems , 1991 .

[9]  M. Doherty,et al.  Vapor-liquid phase equilibrium in systems with multiple chemical reactions , 1995 .

[10]  C. Floudas,et al.  GLOPEQ: A new computational tool for the phase and chemical equilibrium problem , 1997 .

[11]  P. Cummings,et al.  Fluid phase equilibria , 2005 .

[12]  G. M. Platt,et al.  Phase rule calculations and the thermodynamics of reactive systems under chemical equilibrium , 1999 .

[13]  P. T. Eubank,et al.  Equal area rule and algorithm for determining phase compositions , 1995 .

[14]  Michael F. Doherty,et al.  Theory of phase equilibria in multireaction systems , 1995 .

[15]  Aage Fredenslund,et al.  Calculation of simultaneous chemical and phase equilibria in nonideal systems , 1989 .

[16]  Kenneth R. Hall,et al.  An algebraic method that includes Gibbs minimization for performing phase equilibrium calculations for any number of components or phases , 2003 .

[17]  An algebraic formulation for an equal area rule to determine phase compositions in simple reactive systems , 2006 .

[18]  M. Doherty,et al.  Thermodynamic behavior of reactive azeotropes , 1997 .

[19]  William R. Smith,et al.  The Computation of Chemical Equilibria in Complex Systems , 1980 .

[20]  M. Doherty,et al.  Prediction of heterogeneous reactive azeotropes in esterification systems , 2000 .

[21]  W. Seider,et al.  Multiphase equilibria of reactive systems , 1996 .

[22]  B. M. Fulk MATH , 1992 .

[23]  Rajamani Krishna,et al.  Modelling reactive distillation , 2000 .

[24]  G. P. Rangaiah,et al.  Phase and chemical equilibrium calculations by direct search optimization , 1999 .

[25]  M. Stadtherr,et al.  Reliable computation of reactive azeotropes , 2000 .

[26]  Transformed molar Gibbs free energy of mixing in multireaction systems , 2000 .

[27]  Rafiqul Gani,et al.  Reactive separation systems I. Computation of physical and chemical equilibrium , 1997 .

[28]  S. Wasylkiewicz,et al.  Global phase stability analysis for heterogeneous reactive mixtures and calculation of reactive liquid–liquid and vapor–liquid–liquid equilibria , 2000 .

[29]  I. Grossmann,et al.  Computation of phase and chemical equilibria , 1981 .

[30]  Sandro Ridella,et al.  Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithmCorrigenda for this article is available here , 1987, TOMS.

[31]  K. I. M. McKinnon,et al.  A Generic Global Optimization Algorithm for the Chemical and Phase Equilibrium Problem , 1998, J. Glob. Optim..

[32]  J. Seader,et al.  Homotopy continuation method in multi-phase multi-reaction equilibrium systems , 1999 .

[33]  William R. Smith,et al.  On the geometry of chemical reaction and phase equilibria , 1996 .