A constrained differential evolution algorithm for calculation of two-phase equilibria at given volume, temperature and moles. (English) Zbl 07923413
Summary: A variety of strategies including two types of direct solution methods based on Newton’s method and indirect solution methods based on thermodynamic principles have been developed, which can find satisfactory solutions for the phase equilibrium calculation problem at given volume, temperature and moles (NVT-flash). However, these methods are sensitive to the initial values and depend on the objective function’s derivative during calculation. To resolve these deficiencies, a constrained differential evolution algorithm (abbreviated as CDE) for calculating two-phase equilibria at given volume, temperature, and moles is presented in this paper. The total Helmholtz free energy is regarded as the objective function, and the moles vector and volume of a certain phase are taken as the decision variables. This paper deals with the constraints of the NVT-flash problem by using direct search method and exterior point method. The results of the investigations on pure substance, binary and ternary mixtures are in agreement with the published data, which proves the effectiveness in solving the NVT-flash problem and the energy attenuation characteristic of the algorithm. The proposed algorithm represents the first successful attempt to apply the meta-heuristic optimization algorithm to solve the phase equilibrium computation under NVT-flash, and it shows the promising application prospect of meta-heuristic optimization algorithms for solving the phase equilibrium calculation problems.
MSC:
| 90Cxx | Mathematical programming |
| 65Nxx | Numerical methods for partial differential equations, boundary value problems |
| 76Txx | Multiphase and multicomponent flows |
Keywords:
differential evolution algorithm; Helmholtz free energy minimization; NVT-flash; two-phase equilibriumReferences:
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