Robust Spatial Modeling of Thermodynamic Parameters in a Full-Scale Reverse Osmosis Membrane Channel

Full-scale reverse osmosis (RO) units usually consist of a set of pressure vessels holding up to six (1 m long) membrane modules in series. Since process parameters and water composition change substantially along the filtration channel in full-scale RO units, relevant thermodynamic parameters such as the ion activities and the osmotic coefficient change as well. Understanding these changes will lead to more accurate fouling prediction and to improvement in process and equipment designs. In this article, a rigorous thermodynamic model for RO concentrates in a full-scale module is developed and presented, which is capable of accounting for such changes. The change in concentrate composition due to permeation of water and ions is predicted locally in the membrane filtration channel. The local ionic composition is used to calculate the local activity coefficient and osmotic coefficient along the membrane channel through the Pitzer model for each modeled anion and cation. The approach developed was validated against related literature data, showing that Pitzer coefficient predictions were satisfactory. The spatial variation model was verified experimentally. It was found under the modeled conditions of high recovery that individual solute activity coefficients could be diminished up to 65%, in our case for sulfate, from their initial value from the membrane inlet to the outlet, and the water osmotic coefficient increased 3% as concentrate salinity increased from the membrane inlet to the outlet. Modeled at moderate recovery, the sulfate still achieved a statistically significant drop of 34% and an opposing trend of a decrease of 0.5% for the osmotic coefficient. These variations in internal water chemistry along the channel can significantly impact predicted recovery, fouling propensity, and permeate quality. Fouling prediction with our approach was also assessed through a theoretical fouling index to demonstrate the significance of ion activity over concentration-based calculations. Additionally, data from a pilot plant RO filtration channel was used to carry out a sensitivity analysis to show the capability of the developed model.