Effectiveness–mass transfer units (ε–MTU) model of an ideal pressure retarded osmosis membrane mass exchanger

• A strong analogy exists between heat exchangers and PRO membrane mass exchangers.
• ε–MTU analytical models are developed for PRO mass exchangers.
• Parallel and counterflow configurations are considered.
• A numerical model is developed and compared with the analytical expressions.

Many membrane-based systems, such as reverse osmosis (RO), forward osmosis (FO) and pressure retarded osmosis (PRO), are being used in desalination, water treatment, and energy production. These systems work on the basis of mass transfer through a semi-permeable membrane which allows for the permeation of water while rejecting salts and other substances. The membrane-based devices are essentially mass exchangers which are analogous to heat exchangers. The driving potentials in these mass exchangers are the concentration and pressure differences, whereas in heat exchangers the driving potential is the temperature difference. Closed form solutions of the permeation rate through an ideal PRO mass exchanger are obtained for parallel and counter flow configurations. The recovery ratio (RR) is obtained as a function of dimensionless parameters such as the number of mass transfer units (MTU), mass flow rate ratio (MR), and osmotic pressure ratio (SR). The resulting mathematical expressions form an effectiveness–MTU model for osmotic mass exchangers. These expressions are analogous to those for heat exchangers and can be used as an initial design for PRO membrane based mass exchange devices.