Abstract
A new mathematical model was developed to predict the cylindrical effect of the membrane performance in the pressure retarded osmosis process. The cylindrical membrane transport layers (the draw side boundary and the porous membrane) were divided into very thin sublayers with constant mass transport parameters, among others with a constant radius in every sublayer. The obtained second-order differential mass balance equations were solved analytically, with constant parameters written for every sublayer. The algebraic equation system involving 2N equations was then solved for the determinant solution. It was shown that the membrane properties, water permeability (A), salt permeability (B), structural parameter (S) and the operating conditions (inlet draw side solute concentration and draw side mass transfer coefficient) affect the water flux strongly, and thus the membrane performance, due to the cylindrical effect caused by the variable surface and volume of the sublayers. This effect significantly depends on the lumen radius. The lower radius means a larger change in the internal surface/volume of sublayers with ΔR thickness. The predicted results correspond to that of the flat-sheet membrane layer at ro = 10,000 μm. At the end of this manuscript, the calculated mass transfer rates were compared to those measured. It was stated that the curvature effect in using a capillary membrane must not be left out of consideration when applying hollow fiber membrane modules due to their relatively low lumen radius. The presented model provides more precise prediction of the performance in the case of hollow fiber membranes.