Multi-objective optimization of reverse osmosis networks by lexicographic optimization and augmented epsilon constraint method

This study proposes a multi-objective optimization (MOO) of reverse osmosis (RO) networks for seawater desalination. The membrane transport model takes into consideration of the longitudinal variation of the velocity, the pressure, and the concentration in the membrane modules. The RO network with three type energy recovery device options (pressure exchanger (PX), Hydraulic Turbocharger, and turbine) is introduced. Lexicographic optimization (for calculation of a more effective payoff table) and augmented ε-constraint method (to avoid inefficient Pareto solutions) are proposed to solve the MOO problem. A fuzzy decision maker is introduced to derive the most efficient solution among Pareto-optimal solutions. Firstly, different energy recovery option studies show that using PX is seen to be the most profitable option. Exergy analysis is used to evaluate the contribution of the equipments in energy degradation. Secondly, the proposed multi-objective framework simultaneously optimizes the total annualized cost (TAC) and energy consumption. With the increases of weighting for the main objective function: TAC, the most efficient solution moves to lower TAC direction. Finally, system recovery rate is added as the third objective function. It is reasonable to stay at the appropriate system recovery rather than to increase up to its limit and generating high energetic losses. © 2013 Elsevier B.V. All rights reserved.

Fig. 12. RO multi-objective optimal Pareto-curve for unit product cost, specific energy consumption, and recovery rate. Blue balls (dark colored) denote two-stage RO system and an inter-stage booster pump with PX; yellow balls (light colored) denote two-stage RO system and an inter-stage booster pump with turbocharger. Min TAC (upc = 0.541 $/m3, Ew = 3.219 kW h/m3, recovery = 58.08%), Min Ew (upc = 0.615 $/m3, Ew = 2.779 kW h/m3, recovery = 34.27%), Min Rt (upc =0.569 $/m3, Ew = 3.599 kW h/m3, recovery = 61.45%). The most preferred Pareto solution: a, equal weightings; b, a large higher weighting for the TAC. value that is fairly near to its ideal value of 568462.66 $ per year. Its relatively high membership of 0.9977 confirms that the cost value is a high efficient value. The goodness of the energy consumption and recovery rate are also efficient. When a large higher weighting factor is assigned to the main objective function TAC, the ideal value (membership value is 1.0000) of 568462.66 $ per year for the TAC is selected. There is a trade-off between energy consumption and system recovery rate. When the system recovery rate decreases form 58.08% to 56.24%, the energy consumption decreases 8.36 kW h/m3, while the TAC is almost the same (568645.48 − 568462.66 = 182.82 $ per year). It seems therefore reasonable to stay at the appropriate system recovery rate rather than to increase the recovery rate up to its limit and generating high energetic losses. Note that the multi-objective optimal design in an RO system involves many influence factors, such as feed seawater salinity, energy cost, permeate quality, environmental impact. The influences of such factors on the multi-objective optimal design in an RO system were done by Vince et al. [19], Guria et al. [20], and Karim Hamza et al. [21].