Abstract
Empirical correlations for mass transfer coefficient and friction factor are often used in process models for reverse osmosis (RO) membrane systems. These usually involve four dimensionless groups, namely Reynolds number (Re), Sherwood number (Sh), friction factor (f), and Schmidt number (Sc), with the associated coefficients and exponents being obtained by fitting to experimental data. However, the range of geometric and operating conditions covered by the experiments is often limited. In this study, new dimensionless correlations for concentration polarization (CP) modulus and friction factor are presented, which are obtained by dimensional analysis and using simulation data from computational fluid dynamics (CFD). Two-dimensional CFD simulations are performed on three configurations of spacer-filled channels with 76 combinations of operating and geometric conditions for each configuration, covering a broad range of conditions encountered in RO membrane systems. Results obtained with the new correlations are compared with those from existing correlations in the literature. There is good consistency in the predicted CP with mean discrepancies less than 6%, but larger discrepancies for pressure gradient are found among the various friction factor correlations. Furthermore, the new correlations are implemented in a process model with six spiral wound modules in series and the predicted recovery, pressure drop, and specific energy consumption are compared with a reference case obtained by ROSA (Reverse Osmosis System Analysis, The Dow Chemical Company). Differences in predicted recovery and pressure drop are up to 5% and 83%, respectively, highlighting the need for careful selection of correlations when using predictive models in process design. Compared to existing mass transfer correlations, a distinct advantage of our correlations for CP modulus is that they can be directly used to estimate the impact of permeate flux on CP at a membrane surface without having to resort to the film theory.
Highlights
This finding justifies the inclusion of Ret in the Concentration polarization (CP) modulus correlation in Equation (16); if Ret was neglected, the effects of transmembrane velocity caused by different feed concentrations and pressures on CP moduli would not be captured
CP moduli and water fluxes obtained with the correlation by Schock and Miquel are more sensitive to changes in flow velocity in that the CP modulus declines more rapidly with increasing flow velocity, leading to a more pronounced increase in water flux
Correlations for CP and friction factor are implemented in a process model, and nine simulations are performed as listed in Table 6, under three operating conditions that lead to a water recovery of approximately 50%
Summary
In order to predict membrane performance and pumping energy requirements, it is essential to gain a quantitative understanding of the mass and momentum transfer processes in a membrane module This has motivated numerous experimental and computational studies on the effects of spacers on CP and pressure drop [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]
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