Energy Consumption in Spiral-Wound Seawater Reverse Osmosis at the Thermodynamic Limit

Several theorems are presented and proved analytically for normalized specific energy consumption (NSEC) in single- or multistage spiral-wound seawater reverse osmosis (RO) desalination with or without brine energy recovery. It is shown that a spiral-wound RO unit employing an infinite number of RO stages and interstage booster pumps is essentially equivalent to a fully reversible RO process in terms of NSEC if the energy in the brine can be fully recovered. Without energy recovery, the minimum of NSEC decreases monotonically from 4 to 3.1462 and the corresponding optimal recovery increases monotonically from 50% to 68.22% as the number of RO stages increases from 1 to infinity. NSEC decreases monotonically as the number of stages or the energy recovery device (ERD) efficiency increases. An effective way to reduce NSEC in seawater RO is to use an ERD at low recoveries and a multistage design with interstage booster pumps at high recoveries. A combination of the two methods would bring NSEC toward its lowe...