Przegląd modeli numerycznych zjawisk fizycznych występujących w procesach ekstrakcji jonowymiennej metali

W artykule przedstawiono przegląd modeli numerycznych, stosowanych do modelowania zjawisk fizycznych zachodzących w procesach ekstrakcji jonowymiennej metali. Skrótowo omówiony został sam proces oraz najistotniejsze zjawiska. Omówiono metody badawcze, pozwalające na wyznaczenie parametrów modeli numerycznych. Zaprezentowano prace, opisujące modele numeryczne przepływów laminarnych i turbulentnych, powstawania dyspersji dwóch niemieszających się cieczy oraz ich grawitacyjnej separacji, polimeryzacji oraz zachowania powierzchni swobodnej.

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The first step of multiscale model design is choosing numerical models for all significant phenomena. It this paper, the review of existing numerical models for phenomena present in ion-exchange solvent extraction is done. Modelling of this process is focused mainly on calculating of a composition of phases leaving a reactor. Phenomena influencing on a final result are: a flow of two, immiscible fluids, a dispersion of one of them, a gravitational separation and an ion exchange on phase’s boundaries itself. Each of them should be described with a suitable numerical model. A macroscopic flow is usually described with Computational Fluid Dynamic (CFD). An addition of microscopic effects, like bubbles topology and surface tensions allows modelling of dispersion and separation, as well as improves a reliability of a fluid flow model. In a spatial scale comparable with a size of dispersed bubbles, diffusion and an ion exchange are present. Some additional models for phenomena like a surface eddy and a polymerization should be also considered. Due to a lack of a comprehensive description of modelling of an ion-exchange solvent extraction in the literature, models for all phenomena were reviewed separately. Modelling of a two-fluid flow could treat both phases separately or as a single phase with an additional description of its phase composition and a relative movement of phases. The eddy over the mixing zone could be computed basing on CFD techniques, but due to instabilities on the free surface, very short time steps are enforced. Empirical models, based on experimental data are less accurate, but much more stable. There are no models of polymerization in the solvent extraction context in the literature. Available models were developed for processes, where a polymerization is awaited and they are not applicable in described case. Modelling of diffusion and an ion exchange in the microscale are believed to be very important, but an exact description of a dispersion topology is a necessary condition. In fact, it is not practically possible to calculate such a topology with a presently available computing power. The review, presented in this paper will be used to develop the multiscale model for an ion-exchange solvent extraction. It will be based on Agile Multiscale Modelling (AM3), developed by Authors.