Reverse osmosis (RO) network design problem is presented in this study for seawater desalination. The RO pressure vessel is multiple spiral wound modules connected in series. We exploit in this study the RO pressure vessel operation by considering stream property variations within the pressure vessel itself. The design problem allows extraction of high-quality permeates from different locations along the pressure vessel length. Superstructure optimization is adopted to model the RO network in order to find: (1) optimal arrangement of the process units, (2) optimal permeate extraction locations, and (3) production of several permeate streams with different qualities. Several case studies are presented to show the applications of the proposed mathematical programming model. In general, lower treatment cost and higher permeate recovery can be achieved by allowing permeate extraction streams from the RO pressure vessels. (c) 2013 American Institute of Chemical Engineers AIChE J 60: 520-532, 2014