A model for the observed secondary-maximum in backwash-effluent-TDS-data obtained during backwash of spiral-wound RO membranes

Abstract

Observation of a “secondary maximum” in the effluent Total Dissolved Solids (TDS) concentration data, during back-washing of micro-scale spiral-wound Reverse Osmosis (RO) membranes, has been reported (Varma and Chatterjee, 2023). This observation is of interest because a “wash-out” process for any system, may be expected to produce effluent water, which shows an exponential decline in the contaminant, from its initial peak concentration, to that of the water used for washing. Hence the observation of a “secondary maximum” in the back-wash effluent TDS data is interesting and has been examined experimentally in (Varma and Chatterjee, 2023). In this work, we present a mathematical model, which can explain the above observations. This model shows that high TDS water is trapped in the RO membrane element, when the RO system is shut-off. A complete wash-out of this high TDS water, which is held close to the membrane surface requires RO permeate osmotic backwash of a “critical” volume. This “critical” RO permeate volume, can be estimated from the method used in this study. The model is based on coupled-unsteady-state material balances for the salt held in different pseudo-compartments within the RO membrane module.