A general, resistance-in-series, salt- and water flux models for forward osmosis and pressure-retarded osmosis for energy generation

•Convective–diffusive model is applied for description of the external mass transport.•Solute mass transfer rate is defined for every single sub-layer.•The overall solute transfer rate and water flux is expressed.•Predicting the interface concentration the power density can be determined.

A general mass transport model of forward osmosis and pressure retarded osmosis has been developed and presented in this paper. Essential of this model is that it takes into account the effect of all mass transport layers of this process, namely the external boundary layers on both sides of the membrane, the dense and the sponge layers of an asymmetric membrane used, applying the diffusive–convective mass transport equation for every sub-layer except of the skin/dense layer of the membrane. A widely applied, “diffusive” transport equation was used for the dense layer, for the salt transport through it. The water flux and the energy density obtained by means of the presented and the literature models have been compared in the paper in order to test the model developed. It was shown, that the general model presented describes the process performance under all operating conditions independently of the values of the mass transport parameters, namely of the external and internal polarization layers, salt- and water permeability coefficients or inlet concentrations of the fluid phases and hydraulic pressure difference.

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