On the optimization of RO (Reverse Osmosis) system arrangements and their operating conditions H. Kotb, E.H. Amer * , K.A. Ibrahim 1 Mechanical Power Engineering Department, Faculty of Engineering, Menofia University, Shebin El-Kom, Egypt article info Article history: Received 17 January 2015 Received in revised form 20 December 2015 Accepted 27 February 2016 Keywords: Reverse osmosis Multi-stage Operating conditions Optimum configuration Minimum cost Design charts abstract A simple approach has been implemented to identify the optimum RO (Reverse Osmosis) system structure and the operating parameters leading to the minimum total cost. Various two-stage and three- stage arrangements of practical functionality have been optimized. All possible operating points and its corresponding cost have been obtained and a linear search is used to find the minimum cost. The minimum overall costs per unit permeate for the single, two and three-stage arrangements are 1.41,1.00 and 0.91 $/m 3 respectively at product rates of 5.5,11.5 and 17 m 3 /h. For two-stage systems, parallel arrangement is recommended for production up to 3 m 3 /h. Series arrangement with feed and retentate bypass is recommended for demands between 3 and 9 m 3 /h. For higher permeate rates, series arrangement is recommended. Using three-stage configuration, parallel arrangement is recommended for production less than 6 m 3 / h. Series arrangement with feed bypass is recommended for production up to 15 m 3 /h while series arrangement would be preferred above 15 m 3 /h. Design charts have been developed as a convenient tool for selecting system configuration, operating parameters, membrane area and system cost. The use of design charts provides estimations of the system requirements and cost with about 5% accuracy without resorting to difficult computations. © 2016 Elsevier Ltd. All rights reserved. 1. Introduction Seawater desalination by RO (Reverse Osmosis) has been the main source of drinking water supply in many regions in the world. RO membranes used in water desalination are capable of producing good water quality by removing salts and contaminants from seawater with lower cost compared to other desalination processes [1]. Designing a cost effective RO network depends mainly on the determination of optimal operational and structural schemes. RO system performance is affected by several factors, such as feed pressure, feed salinity, and water flux. The optimization of RO network problem has been addressed by many research studies to look for optimal sizes and configuration of process units, and their optimal operation. Attempts have been made to obtain optimal designs of RO units by reducing the cost of the units. Lu et al. [2] have investigated various multistage RO systems under different feed concentrations and product specifications. An optimization method using the process synthesis approach has been developed to design RO sys- tems. The optimum design problem has been formulated as a mixed-integer nonlinear programming problem which minimizes the total annual cost. Skiborowski et al. [3] have investigated the combination of a reverse osmosis network and a forward-feed multi-effect distillation in a hybrid plant as a structural optimiza- tion problem. A generalized superstructure for the hybrid desali- nation plant is constructed and conceptual design considerations have been used to reduce its complexity. A mathematical model for the whole plant and an economical objective function has been developed resulting in a highly nonlinear and non-convex model. Guria et al. [4] have carried out multi-objective optimization using genetic algorithm for the desalination of brackish and seawater using spiral wound or tubular modules. The optimization problem has considered several objective functions. It has been reported that the membrane area is the most important decision variable in designing a spiral wound module for desalination of brackish water * Corresponding author. Tel.: þ2 048 222 15 49x1204; fax: þ2 048 223 56 95. E-mail addresses: emad.amer@sh-eng.menofia.edu.eg, amer_h_emad@yahoo. com (E.H. Amer). 1 Visiting Professor; Arab Academy for Science, Technology and Maritime Transport. Contents lists available at ScienceDirect Energy journal homepage: www.elsevier.com/locate/energy http://dx.doi.org/10.1016/j.energy.2016.02.162 0360-5442/© 2016 Elsevier Ltd. All rights reserved. Energy 103 (2016) 127e150