Mathematical modelling, asymptotic approximation and numerical simulation of reverse-osmosis desalination processes

Dr Matteo Icardi (University of Nottingham)

Thursday 26th September 14:00-15:00 Maths 311B

Abstract

We present a mathematical model to describe the desalination process which includes the flow and transport of saltwater, the membrane filtration process and the chemical reactions leading to scaling (precipitation and deposition of salts) which causes a reduction of the membrane permeability in time. The main challenge in desalination is due to the high energy required to counterbalance potentially very large osmotic pressure caused by the concentration polarisation effects near the membrane and the degradation of the membrane efficiency in time. The mathematical model shows the non-trivial coupling and non-linear relations and evolution in time of operating pressure, system efficiency (recovery rate). We propose a simplified one-dimensional model based on lubrication theory with a Taylor dispersion model for the concentration and a localised first-order correction to describe polarisation effects. The homogenised model is complemented with fully resolved numerical simulation via the newly developed open-source finite-volume solver “membraneFoam”, based on the OpenFOAM-8 library. Extensions to multiphase mixture and interfacial lubrication models and to poly-dispersed evolving particle size distributions will be discussed.

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