Reducing speci fi c energy consumption in Reverse Osmosis (RO) water desalination: An analysis from fi rst principles

The previously derived characteristic equation of RO in Li, 2010 [8] is used to describe single- or multi-stage ROs with/without an energy recovery device (ERD). Analysis is made at both the theoretical limit (with analytical solutions provided if possible) and practical conditions (using constrained nonlinear optimization). It is shown that reducing specific energy consumption (SEC) normalized by feed osmotic pressure, or NSEC in ROs can be pursued using one or more of the following three independent methods: (1) increasing a dimensionless group γ = AtotalLpΔπ0/Q f, (2) increasing number of stages, and (3) using an ERD. When γ increases, the feed rate is adversely affected and the NSEC reduces but flattens out eventually. Using more stages not only reduces NSEC but also improves water recovery. However, The NSEC flattens out when the number of stages increases and ROs with more than five stages are not recommended. Close to the thermodynamic limit where γ is sufficiently large, the NSEC of ROs up to five stages approaches 4, 3.60, 3.45, 3.38 and 3.33 respectively. The ERD can significantly reduce the NSEC, theoretically to 1, while the corresponding recovery approaches zero. The NSEC becomes larger when the required water recovery increases. It is found that a combination of all three methods can significantly reduce the NSEC while maintaining a high recovery and a reasonable feed or permeate rate. An NSEC around 2.5–2.8 with an 80% water recovery may be possible using 3–5 RO stages and an ERD of 90% efficiency operated at a γ about 3–5 (or Q f = 0.2–0.3 AtotalLpΔπ0). © 2011 Elsevier B.V. All rights reserved.

The previously developed characteristic equation of RO module [8] is used to describe single- or multi-stage ROs with/without energy recovery. Analysis is made both at the theoretical limit (with analytical solutions provided if possible) and at practical conditions (using constrained nonlinear optimization). Reducing NSEC (or SECm/Δπ0) in ROs can be pursued through one or more of the following three independent methods: (1) increasing γ = AtotalLpΔπ0/Qf, (2) increasing number of stages, and (3) using an ERD. The NSEC flattens out when γ becomes sufficiently large. A very large γ is not recommended because it will affect the feed rate, and therefore, the permeate rate. For ROs without ERD, the theoretical Nomenclature α Δπ0/ΔP, dimensionless β ALpΔπ0/Q p, dimensionless Δ difference across the membrane osmotic pressure difference at the entrance of the membrane Δπ0 module, bar ERD efficiency, dimensionless ηerd pump efficiency, dimensionless ηpump γ ALpΔπ0/Q f, dimensionless π osmotic pressure, bar A membrane area, m2 Lp hydraulic permeability, m ⋅ sec− 1 ⋅ bar− 1 N P Q SECm Y b f p number of stages, dimensionless pressure, bar flow rate, m3 ⋅ sec− 1 specific energy consumption times the pump efficiency, J⋅m− 3 Q p/Q f, dimensionless brine feed permeate