Study of Pressure Retarded Osmosis Process in Hollow Fiber Membrane: Cylindrical Model for Description of Energy Production

Endre Nagy, Ibrar Ibrar, Ali Braytee and Béla Iván
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Endre Nagy: Research Institute of Biomolecular and Chemical Engineering, Faculty of Engineering, University of Pannonia, 8200 Veszprém, Hungary
Ibrar Ibrar: School of Civil and Environmental Engineering, University of Technology Sydney, Ultimo, NSW 2007, Australia
Ali Braytee: School of Computer Science, University of Technology Sydney, Ultimo, NSW 2007, Australia
Béla Iván: Polymer Chemistry Research Group, Institute of Materials and Environmental Chemistry, Research Centre for Natural Sciences, Magyar Tudósok Körútja 2, 1117 Budapest, Hungary

Energies, 2022, vol. 15, issue 10, 1-23

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 2 N 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 Δ R thickness. The predicted results correspond to that of the flat-sheet membrane layer at r o = 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.

Keywords: pressure retarded osmosis; hollow fiber membrane; cylindrical model; water flux; power density; blue energy; mass transport (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2022
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