GLOPEQ
GLOPEQ: A new computational tool for the phase and chemical equilibrium problem. Calculation of phase and chemical equilibrium represents a crucial phase in the modeling of many separation processes. For conditions of constant temperature and pressure, a necessary and sufficient condition for the true equilibrium solution is that (i) the total Gibbs free energy of the system be at its global minimum, or (ii) the minimum of the tangent plane distance function be nonnegative for all phase models used to represent the system. In this work, the goal is to obtain equilibrium solutions corresponding to a global minimum of the Gibbs free energy as efficiently as possible, for cases where the liquid phase or phases can be modeled by the NRTL, UNIQUAC, UNIFAC, Wilson, modified Wilson and ASOG equations. Vapor phases whose behavior can be described as ideal can also be handled. In achieving this goal, there are two distinct problems of relevance: (i) the minimization of the Gibbs free energy, denoted (G), and (ii) the minimization of the tangent plane distance function, or the tangent plane stability criterion, denoted (S). For all these activity coefficient models, GLOPEQ (GLobal OPtimization for the Phase and chemical EQuilibrium problem) can guarantee global solutions for problems (G) and (S), but a combined algorithm employs them in tandem, using (G) to generate candidate equilibrium solutions which can then be verified for thermodynamic stability by solving (S). Two key features of the combined algorithm are that (i) as much information as is possible is obtained from local searches, and (ii) it is preferable to verify a globally stable equilibrium solution using the tangent plane criterion, as this problem contains fewer variables than the minimization of the Gibbs free energy. Results for several examples are presented, and all but one of them are for the case of phase equilibrium, due to the paucity of examples for reacting systems that employ excess Gibbs free energy models.
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References in zbMATH (referenced in 15 articles )
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Sorted by year (- Boukouvala, Fani; Misener, Ruth; Floudas, Christodoulos A.: Global optimization advances in mixed-integer nonlinear programming, MINLP, and constrained derivative-free optimization, CDFO (2016)
- Bosse, T.; Eneya, L.; Griewank, A.: An algorithm for pointwise evaluation of polyconvex envelopes. II: generalization and numerical results (2015)
- Misener, Ruth; Floudas, Christodoulos A.: ANTIGONE: algorithms for coNTinuous/Integer global optimization of nonlinear equations (2014)
- Caboussat, Alexandre: Primal-dual interior-point method for thermodynamic gas-particle partitioning (2011)
- Caboussat, A.; Landry, C.; Rappaz, J.: Optimization problem coupled with differential equations: a numerical algorithm mixing an Interior-point method and event detection (2010)
- Landry, Chantal; Caboussat, Alexandre; Hairer, Ernst: Solving optimization-constrained differential equations with discontinuity points, with application to atmospheric chemistry (2009)
- Gounaris, Chrysanthos E.; Floudas, Christodoulos A.: Tight convex underestimators for $\mathcalC^2$-continuous problems. II: Multivariate functions (2008)
- Gounaris, Chrysanthos E.; Floudas, Christodoulos A.: Tight convex underestimators for $\mathcal C^2$-continuous problems. I: Univariate functions (2008)
- Amundson, N.R.; Caboussat, A.; He, J.W.; Seinfeld, J.H.: Primal-dual interior-point method for an optimization problem related to the modeling of atmospheric organic aerosols (2006)
- Amundson, Neal R.; Caboussat, Alexandre; He, Jiwen; Seinfeld, John H.: An optimization problem related to the modeling of atmospheric organic aerosols (2005)
- Colonna, G.; Dâ€™angola, A.: A hierarchical approach for fast and accurate equilibrium calculation (2004)
- Gau, Chao-Yang; Stadtherr, Mark A.: Parallel branch-and-bound for chemical engineering applications: Load balancing and scheduling issues (2001)
- McKinnon, Ken; Mongeau, Marcel: A generic global optimization algorithm for the chemical and phase equilibrium problem (1998)
- Floudas, Christodoulos A.: Deterministic global optimization in design, control, and computational chemistry (1997)
- McKinnon, K.I.M.; Millar, C.; Mongeau, M.: Global optimization for the chemical and phase equilibrium problem using interval analysis (1996)