Effect of the feed and draw solution temperatures on PRO performance:Theoretical and experimental study

• A model for water flux through a PRO membrane is developed. • A validated model for temperature distribution over the membrane is also provided. • The effect of the solution temperatures on the membrane properties was highlighted. • It is shown how raising the feed solution temperature enhances the performance of PRO.

In the current work, models reproducing the water and the salt fluxes in PRO for a flat sheet membrane were developed. After being verified using experimental data, the models showed a good capability to predict the behavior of the process. The effect of operating conditions on PRO performance was investigated. The effect of the draw solution concentrations, the flow rates and the operating temperatures were well predicted by the models. In particular, the impact of the bulk temperature on PRO performance was studied. It has been experimentally noted that the effect of the feed water temperature is more important than the draw water temperature: the water permeability and the salt permeability showed a higher dependency on the feed water temperature, moreover, the structure parameter s is significantly reduced at high feed water temperature compared to the draw water temperature. The effect of the temperature on the salt diffusion was also investigated. It was shown that an increase of the temperature is accompanied by an increase of the salt diffusion. The high water flux resulting from the increase of feed water temperature induced a drastic draw solution diffusion which generated a severe ICP. Further work will be realized to investigate the effect of the operating conditions on the salt diffusion and its consequences in terms of power density. List of symbols A B CD,m CF,m CD,b CF,b Cicp Cp ΔCm dp d dh DD DF Jw Js ha.l hD hF hs.l k K water permeability coefficient. (m·s−1·Pa−1) salt permeability coefficient. (m·s−1) salt concentration of the membrane surface at the draw solution side. (g·l−1) salt concentration on the support layer surface at the side of the feed. (g·l−1) salt concentration of the draw solution bulk. (g·l−1) salt concentration on the feed solution bulk. (g·l−1) salt concentration on the membrane surface at the boundary active layer-support layer. (g·l−1) heat capacity. (J·kg−1·K−1) concentration difference on the membrane surface. (g·l−1) diameter of the pores of the support layer. (m) diameter of the pipe. (m) hydraulic diameter of the flow channel. (m) diffusion coefficient of the draw solution. (m2·s−1) diffusion coefficient of the feed solution. (m2·s−1) water flux that crosses the membrane. (m·s −1) salt flux that crosses the membrane. (g/m2·s) thermal conductivity of the active layer. (W·m−2 K−1) thermal conductivity of the draw boundary layer. (W·m−2 K−1) thermal conductivity of the feed boundary layer. (W·m−2 K−1) thermal conductivity of the support layer. (W·m−2 K−1) mass transfer coefficient. (m·s−1) solute resistivity. (s·m−1) kb L Pw ΔP Δπ R Nu Nux Pr Prx Re Rex Q S S Sc Sh TR TD,b TF,b TD,m TF,m Ticp U V Η πD,m πF,m πD,b πF,b πicp ts τ ε β δD δF ρs ρw μw λs λf λa.l Boltzman constant. (–) length of the channel. (m) the hydrated perimeter. (m) transmembrane Pressure. (Pa) difference of osmotic pressure between the draw solution and the feed solution. (Pa) gas constant. (J·mol−1 K−1) Nusselt number. (–) local Nusselt number. (–) Prandtl number. (–) local Prandtl number. (–) Reynolds number. (–) local Reynolds number. (–) heat flux. (W·m−2) structure parameter of the support layer. (m) surface of the membrane. (m2) Schmidt number. (–) Sherwood number. (–) the normalized temperature. (–) temperature of the draw solution bulk. (°C) temperature of the feed solution bulk. (°C) temperature of the active layer. (°C) temperature of the support layer. (°C) temperature of the limit surface between the active layer and the support layer. (°C) velocity of the fluid in the support layer. (m s −1) velocity of the fluid in the channel. (m s −1) dynamic viscosity of the solution. (Pa·s) osmotic pressure at the surface of the active layer. (Pa) osmotic pressure at the surface of the support layer. (Pa) osmotic pressure of the draw solution bulk. (Pa) osmotic pressure of the feed solution bulk. (Pa) osmotic pressure at the limit surface between the active layer and the support layer. (Pa) length of the support layer. (m) tortuosity of the membrane. (–) porosity of the membrane. (–) van't Hoff coefficient. (–) thickness of the boundary layer at the draw solution side. (m) thickness of the boundary layer at the feed solution side. (m) density of the draw solution. (kg/m3) density of the feed solution. (kg/m3) water kinematic viscosity. (m2/s) thermal conductivity of the solid constituting the support layer.(W·m−1 K−1) thermal conductivity of the liquid phase. (W·m−1 K−1) the thermal conductivity of the active layer. (W·m−1 K−1) Acknowledgments This work was co-funded by the Seventh Framework Program, under grant 288145 (H2OCean), within the ocean of tomorrow joint call 2011.