Minimization of Energy in Reverse Osmosis Water Desalination Using Constrained Nonlinear Optimization

This work focuses on the minimization of energy in reverse osmosis water desalination. First, a set of dimensionless parameters were derived to characterize the reverse osmosis desalination process. On the basis of the assumptions of constant pump efficiency and no pressure change in the retentate, the minimization of energy cost per volume of produced permeate or specific energy consumption (SEC) for three different reverse osmosis modules (single-stage, two-stage, and single-stage with an energy recovery device (ERD)) were then formulated and solved as constrained nonlinear optimization problems. Without ERD, the optimal solution to SEC normalized by the feed salinity was solely dependent on a dimensionless parameter gamma that is comprised of the membrane area, hydraulic permeability, feed rate, and salinity. In the thermodynamic limit where gamma approaches infinity, the minimal SEC approaches 4 and 3.596 times the feed salinity and the fractional recovery approaches 0.5 and 0.574 for single-stage and two-stage reverse osmosis modules, respectively. However, the water yield approaches zero in both cases. With an ERD, the SEC can be further reduced to the feed salinity while the fractional recovery approaches zero. It is also shown that the SEC flattens out quickly as gamma increases, and a cutoff of gamma (around 0.5-1.5 for one-stage and 1-3 for two-stage membrane modules) can be used to achieve a reasonable water yield as well as a low SEC slightly above the theoretical global minimum.