A two-coefficient water transport equation for pressure-retarded osmosis

Abstract In Pressure-Retarded Osmosis (PRO), the osmotic pressure gradient exceeds the hydraulic pressure gradient. Hence water permeation flux should be uphill with regard to the latter gradient. While this usually occurred in PRO tests with the Permasep B-10 polyamide fiber, it frequently did not occur with the Fiber Research Laboratory (FRL) composite fiber, i.e., flux was negative. Results with both of these asymmetric fibers could be correlated by using an equation for the water flux, J1, containing two permeation coefficients, AΠ and Ap: J1 = AΠΠsh — ApΔP, where IIsh was the high osmotic pressure used on the skin side of the fiber (that on the porous substructure side being zero), and ΔP was the hydraulic pressure difference across the fiber wall, the high hydraulic pressure also being on the skin side. The consequence of the above equation is that positive flux in PRO does not occur unless Πsh/ΔP exceeds the “threshold” ratio, Ap/AΠ. This value was 2.4 and 1.4 for the FRL and Permasep fibers, respectively, and accounted for both the usually negative fluxes of the former and the usually positive fluxes of the latter. The two-coefficient equation can be understood physically as an extension to PRO of the patchwork model frequently applied to the membrane skin to explain Reverse Osmosis results. The extension requires consideration of the porous substructure and the semipermeable patches of the membrane skin as two resistances in series impeding osmotic pressure-driven transport through the semipermeable region. The extended model enabled correlation of attempted PRO tests with skin and porous substructure properties in both the FRL and Permasep fibers. It was also possible to state requirements of a fiber for which the threshold ratio of Πsh/ΔP would be minimized. Thus the two-coefficient equation appears to be a useful method for categorizing membranes in PRO operation.