UBC Theses and Dissertations
Computational algorithms for multicomponent phase equilibria and distillation Ohanomah, Matthew Ochukoh
This work has two major objectives: (1) To develop reliable, stable, easily-programmable and fast computational algorithms that would apply to process operation and design. (2) To determine the best algorithms for specific operations through comparative studies. The study covers the following areas: (1) Isothermal phase equilibria in up to four phases — one vapour, two liquid and one solid — with emphasis on vapour-liquid, liquid-liquid, liquid-solid and vapour-liquid-liquid systems. (2) Sensitivity analysis in vapour-liquid equilibria. (3) Saturation-point calculation methods. (4) Adiabatic vapour-liquid equilibria. (5) Conventional equilibrium-stage distillation-unit calculations. The study deals with multicomponent systems and, except where constrained by lack of information, all nonidealities are rigorously accounted for. The phase-equilibria studies embody both mass-balance and free-energy-minimization methods and some of the algorithms are, like the sensitivity-analysis study, based on geometric programming. Vector projection methods, for accelerating multivariate successive-substitution iteration, and a quadratic form of Wegstein's projection method have been developed and successfully applied. The saturation-points study includes three interpolation methods — regula falsi and quadratic interpolations and a dynamic form of Lagrange interpolation — a quasi-Newton formulation and the generally applied Newton and Richmond methods. The results favour the interpolation methods. For adiabatic-flash and distillation-unit calculations, algorithms employing two-dimensional Newton-Raphson, BP-partitioning and SR-partitioning methods have been developed. Methods for reducing equilibrium-ratio calculation to once per iteration per stage in the first two classes and for reducing enthalpy evaluation In the third class, have also been developed. For every problem-type, relevant algorithms have been applied to a wide class of systems and compared. However, the lack of data excluded any applications on solid-liquid-liquid-vapour equilibria and on wide-boiling distillation.
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