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A predictive mathematical model has been developed to simulate the pertraction of phenolic compounds in the agitated bulk liquid membrane system (ABLM). A bond-graph method, based on pseudo-thermodynamic network analysis, was applied for the detailed description of the three steps pertraction mechanism, i.e., extraction, diffusion, and re-extraction with the neutralization reaction in the stripping solution. The corresponding mathematical model (a set of ordinary differential equations) was solved to predict the time evolution of local fluxes and concentrations of p-nitrophenol (PNP) in the experimental system: PNP aq. soln.|tolunene|NaOH soln. The calculations were carried out mainly with the data accessible in literature (diffusion coefficients, thickness of diffusion layers) or measured in independent experiments (extraction and re-extraction kinetic constants, equilibrium distribution coefficient). The results of numerical calculations were compared with the experimental PNP transport data. It was found that the model and calculation procedures allow the prediction of time dependent-concentration or fluxes profiles of the transported species in the feed, membrane, and stripping solution as a function of operating parameters (volumes, concentrations), as well as pertraction mechanism parameters (distribution coefficients, diffusion coefficients, kinetic constants). |
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