Abstract
ABSTRACT In the present work, some numerical and computational aspects of COSMO-based activity coefficient models were explored. The residual contribution in such models rely on the so called self-consistency equation. This equation does not have a closed-form solution and is usually solved by the successive substitution method. The performance of a classical Newton-Raphson method was tested in solving the self-consistency equation. The results obtained by the Newton implementation and by successive substitution agreed within the convergence tolerance. The CPU times for solving the model using both methods also were compared. Contradicting the usual experience, it was observed that the Newton method becomes slower than successive substitution when the number of components (or number of COSMO segments) in the mixture increases. An analysis of the number of floating point operations required showed the same, Newton’s method will be faster only for small systems.
Highlights
Accurate prediction of mixture behavior and phase equilibrium properties are of great importance in the design, efficient operation, control and optimization of industrial plants
It was verified whether the Newton and the successive substitution methods lead to the same results, within a given tolerance
A Newton-Raphson method was tested in the solution of the so-called self-consistency equation of the residual contribution of COSMO-based models
Summary
Accurate prediction of mixture behavior and phase equilibrium properties are of great importance in the design, efficient operation, control and optimization of industrial plants. Numerical results and computational costs of the Newton method and of the classical successive substitution are compared for different mixtures. Newton-Raphson As noted in the previous sections, successive substitution is reported as the method of choice for most implementations when solving the selfconsistency equation given by Equation 1.
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