Modeling pH in Reverse Osmosis Desalination Membranes

Noga Fridman-Bishop, Chemical engineering, Technion-ITT, Haifa, ISRAEL
Oded Nir, Chemical Engineering, Rwth-aachen University, Aachen, Germany
Ori Lahav, Civil And Environmental Engineering, Technion-itt, Haifa, Israel
Viacheslav (Slava) Freger, Chemical Engineering, Technion-itt, Haifa, Israel

When a saline feed is desalinated using reverse osmosis (RO), the pH of the permeate stream is often altered realtive to the feed pH. While in some cases this may partly be caused by rejection of weakly acidic or weakly basic species (e.g., carbonates), present in water, the direct effect of  H⁺ and OH^- permeation ions may play a significant role as well. Unfortunately, this phenomenon at operational conditions relevant to RO desalination has been modeled thus far only in an approximate and empirical manner, assuming independent rejection of H⁺ and OH^-. For most real-life RO applications operating within the pH range close to neutral, H⁺ and OH^- permeation may be commensurate, inter dependent, and further complicated by the concurrent permeation of salt, thereby a more sound modeling approach is required.

In order to addres this problem, we rigorously combine the Nernst-Planck equations of ion transport with the chemical equilibrium between H⁺ and OH^-. The exact analytical solution is valid only in cases the flux of either H⁺ or OH^- is dominant. Nevertheless,we propose to approximate the general solution with a formula combining the solutions for the two ions as traces, which is nearly exact everywhere beyond a crossover pH range, about 1 pH unit wide.

Data was obtained using a spiral wound reverse osmosis module operated under different permeate fluxes, NaCl feed concentrations and feed pH values. The mathematical description resulted was in excellent agreement with the experimental results (Figure 1). The very high permeability obtained for hydronium and hydroxide ions confirm that their diffusion and electromigration, rather than convection, are the major contributors to the pH change and convection may indeed be neglected in the model.

The presented approach has the potential to improve the predictability of reverse osmosis transport models including acid-base equilibrium, thereby improving process design and control.