Numerical study on permeate flux enhancement by spacers in a crossflow reverse osmosis channel

Abstract

The impact of spacer configurations (i.e. cavity, zigzag and submerged) and mesh length on the alleviation of concentration polarization and the enhancement of permeate flux in the crossflow reverse osmosis membrane channels was investigated. In this study, the wall concentration and permeate flux were directly determined from the numerical solutions of the fully coupled governing equations of momentum and mass transfer in the feed channel. It was demonstrated that the average permeate flux could be significantly enhanced by the spacers, especially those with zigzag configuration. Simulations showed that the zigzag configuration was the most effective one to alleviate concentration polarization and to enhance permeate flux while the submerged configuration is the least. It was further found that an optimum mesh length (corresponding to the maximum permeate flux enhancement) existed for cavity and zigzag configurations and the optimum mesh length decreased with increasing salinity of the feed water. The results suggested that different mesh length should be used in membrane modules for feed waters of different salinities to obtain the maximum permeate flux enhancement.

Introduction

Permeate flux in a reverse osmosis (RO) system is affected by salt concentration buildup near the membrane surface, i.e. concentration polarization, which is an inherent phenomenon in membrane separation systems. The effect of concentration polarization becomes more pronounced for RO membranes of high permeability [1], [2], [3]. Feed spacers in the widely used spiral wound modules alter the flow and mass transfer patterns and, consequently, concentration polarization and permeate flux in the channel. Quantifying the effect of feed spacers on concentration polarization will not only enable a more accurate calculation of permeate flux in the practical RO systems, but also provide technical foundations to optimize spacer design for a better system performance.

The effects of spacers on mass transfer enhancement in the membrane channels have attracted continuous attentions and many interesting studies have been reported in the literature [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15]. Notably, Kang and Chang [16] and Kim et al. [17] found that the spacers could enhance mass transfer in the electrodialysis systems by forming recirculation flows. Schwinge et al. [18], [19] showed numerically the enhanced mass transfer in a membrane channel by different filament configurations with the assumptions of fixed and constant wall concentrations and impermeable walls. Geraldes et al. [20], [21] studied the impact of ladder-type spacers on concentration polarization in a nanofiltration (NF) membrane channel. Subramani et al. [22] studied the impact of spacer configurations on pressure drop, flow and wall concentration and compared numerical results from FEMLAB with those from other models.

However, most of the reported studies about the impact of spacers on the performance of RO processes were conducted with pre-described wall concentration or permeate flux or both. These assumptions are fundamentally inappropriate to the problem under investigation. According to the basic membrane filtration theory that the permeate flux ($v_{\text{w}}$) is proportional to the net driving pressure (Δp − Δπ), the constant permeate flux assumption directly leads to constant wall concentration and vice versa. As implied by Brain [15], a constant permeate flux assumption would lead to significant errors in concentration polarization simulations in RO systems especially when local variations of wall concentration are concerned.

It is one of the most important features that solute transport (concentration polarization) and momentum transfer (permeate velocity) are interrelated or coupled in the membrane feed channel [23]. Neither wall concentration nor permeate flux should be or can be determined for a RO membrane channel before concentration polarization and performance of the channel are known. In fact, both wall concentration and permeate flux are actually the intended results of the studies because they are the primary indicators of concentration polarization and performance of RO systems.

Recently, a fully coupled streamline upwind Petrov/Galerkin (SUPG) finite element model was developed for the study of concentration polarization in a spacer filled RO channel [24], [25], which can simulate flow field and concentration distribution in the channel domain without any prescribed wall concentration or permeate flux on the membrane surface. In this paper, this numerical model was used to study the effects of spacer configurations and mesh length on the alleviation of concentration polarization and the enhancement of permeate flux under various operating conditions. Wall concentration and permeate flux in the RO membrane channels were simulated and discussed for a better understanding of the role of feed spacers on performance improvement of RO processes.