Reverse osmosis at elevated temperatures: influence of temperature on degree of concentration polarization and transmembrane flux

A model describing the influence of temperature on longitudinal distribution of the degree of concentration polarization (CP) and transmembrane flux in reverse osmosis systems was developed. The model is based on the following assumptions: (1) membrane morphology is temperature independent; (2) transport characteristics of membranes are invariant with their coordinate; (3) specific water permeability of membranes is based on exponential dependence of viscosity vs. temperature; (4) temperature dependence of membrane rejection is assumed to be linear. The proposed model gives quantitative correlations between the longitudinal mass flow and the CP degree at different operating temperatures. The model enables analyzing the influence of temperature, mass flow, bulk concentration, axial velocity, channel geometry, physical properties and membrane rejection on longitudinal distribution of the degree of CP. This model can be hybridized with sub-models describing driving force, gel resistance, etc., and segmented into a more advanced algorithm for modeling longitudinal variation of characteristics. The model does not contain digital integration and can be easily incorporated into optimization algorithms.