On the application of the Spiegler-Kedem model to forward osmosis

In Forward Osmosis the diffusion of the solute is counter to that of the solvent i.e. there is so-called “reverse salt diffusion”. Furthermore, the ratio of the two fluxes is generally taken to be a constant because of the assumption of ideal semi-permeability. However with the Spiegler-Kedem (S-K) model there is an allowance for a minor deviation from ideal semi-permeability and the ratio of the solute flux and solvent flux is no longer constant. The theoretical variation of the solute flux with increasing draw solution concentration is illustrated for various degrees of deviation from ideal semi-permeability. A novel variant of the S-K model is also introduced and predictions compared with those obtained using the standard form. With the acceptance that the form of “breakthrough” involving co-current flow is impossible, a limitation is imposed upon the S-K model but even with this limitation the theoretically predicted variation of solvent flux with increasing draw concentration is for certain sets of parameters of an unexpected form for minor deviation from ideal semi-permeability. That intriguing counter-intuitive outcomes can result from application of the S-K model indicates a need to rethink its formulation of the equations and the expressions for the coefficients. This will have implications for forward osmosis and possibly reverse osmosis modelling.