In this work, we propose a methodology to solve a nonlinear mathematical model for the optimal design of reverse osmosis (RO) networks, which ameliorates the shortcomings of the computational performance and sometimes convergence failures of commercial software to solve the rigorous mixed integer nonlinear programming (MINLP) models. Our strategy consists of the use of a genetic algorithm to obtain initial values for a full nonlinear MINLP model. In addition, because the genetic algorithm based on the rigorous model equations is insurmountably slow, we use metamodels to reduce the mathematical complexity and considerably speed up the run. We explore the effects of the feed flow, seawater concentration, number of reverse osmosis stages, and the maximum number of membrane modules in each pressure vessel on the total annualized cost of the plant.

In a recent study [ParraA. Parra, A. Ind. Eng. Chem. Res.20195830603071, the design of reverse osmosis (RO) systems for desalination of water at different concentrations was studied and optimal solutions were obtained. Equipped now with a powerful tool to solve the problem, we explore its use to determine if RO coupled with a pressure-retarded osmosis (PRO) unit can improve its economics. We present different configurations and different scenarios of RO integrated with PRO. Possible changes in electricity cost and water and salt permeability effects were also studied. We studied different scenarios of seawater desalination aided by recycled fresh water from users, as well as the limited use of low-salinity water from wells, and we present four configurations of RO-PRO aside from the pure RO case. For the cases we studied, the cost parameters we used, and the scale of the production that we chose, we conclude that PRO does not help RO, that is, the stand-alone RO always shows a lower cost per unit permeate.