CFD analysis of tracer response technique under cake-enhanced osmotic pressure

A cake-layer mass transfer model applicable for RO, that incorporates the cake-enhanced osmotic pressure (CEOP) effect of a particulate fouling layer, is presented. This model includes the effect of a variable dissolved solute concentration on the specific cake resistance and porosity of the cake layer. The model is based on one-dimensional diffusion of the dissolved solute through the cake layer, and uses the solute concentration at the cake surface and the cake mass per unit area to calculate the solute concentration at the membrane surface and the trans-membrane osmotic pressure. The cake-layer mass transfer model is incorporated into a commercial Computational Fluid Dynamics (CFD) software package. Simulations are validated against experimental data, and the model predictions are within ±7% for permeate fluxes and within ±14% for measured concentration polarisation. The model is used to interpret and assess tracer response test results for estimating concentration polarisation and fouling resistance. Model predictions confirm the assumption for the tracer experiment that the average concentration polarisation along the membrane wall does not change significantly after a step change in the feed concentration of the tracer solute. However, it was found that the tracer experiment over-estimates the concentration polarisation index and under-estimates the fouling resistance, particularly under fouled conditions. The sources of error are discussed and a multiple tracer response test is proposed to minimise estimation error.