Abstract
In Forward Osmosis the diffusion of the solute is counter to that of the solvent i.e. there is so-called āreverse salt diffusionā. 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 ābreakthroughā 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.
Highlights
Energy production from the controlled mixing of seawater and fresh water has the advantage that it can be operated continuously unlike processes based on solar and wind energy
This is counter to the experimentally observed reverse salt flux that is characteristic of forward osmosis (FO)
From the above theoretical analysis there is no reason to believe that it would be of any benefit to explore practically various degrees of deviation from ideal semi-permeability
Summary
Energy production from the controlled mixing of seawater and fresh water has the advantage that it can be operated continuously unlike processes based on solar and wind energy. The first pilot plant seeking to develop osmotic energy was opened by the Norwegian energy company Statkraft in 2009 but the pilot plant was closed in 2014 due to the low power density (power per unit of membrane area) exhibited by the prototypes and the questionable economic feasibility of the process [5]. Today it is generally accepted that if PRO is to be commercially viable it will be necessary to use resources with a higher salinity than seawater, for example brine from a reverse osmosis desalination plant [6, 7], but the power output will still be modest. There was the prediction that with these appropriate membranes there would be co-current flow of both solvent and solute against a concentration gradient
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