Fig. 2: Thermodynamic and corrected work requirements for water treatment and resource extraction.
a Thermodynamic minimum and adsorption/desorption swing and Nernstian corrected work requirement (Supplementary Notes 1–4, assuming typical parameter values shown therein) for water treatment, also indicating increase in work required as thermodynamic efficiency ηT decreases. Water treatment spans numerous applications with varying initial concentrations (which are similar in magnitude to final concentrations), shown here for the elimination of PFAS, lead, copper, nitrates, and salt from brines (Supplementary Table 1)42,53,54,55, but energy requirements are always much lower than water splitting. (These curves use the molecular weight of sodium chloride to report molar quantities in mass units; see Supplementary Fig. 1 for the negligible effect of molecular weight on these curves) b, c Flow-corrected thermodynamic work requirements for water treatment at the household (b) and municipal (c) scales, and increases in those requirements with decreasing Faradaic efficiency, ηF, compared to water splitting. Note that the work requirement is normalized by the volume of the dilute product stream Ldilute in (a–c), which is the valuable stream of interest in treatment applications. d Thermodynamic, swing-corrected, and swing-and-flow-corrected work requirements in resource extraction applications, and corresponding increases due to Faradaic losses, also compared to water splitting. Resource extraction applications involve the enrichment of species across a wide range of concentrations spanning multiple unit operations (shown here for the extraction of rare earth elements (REEs) from brines and municipal waste, platinum group metals (PGMs) from mine tailings, lithium (Li) from brines and battery waste, and recovery of nitrogen/phosphorus from urine (nutrient recovery); see Supplementary Table 1)36,56,57,58,59,60,61,62. Note that the work requirement is normalized by the volume of the concentrated product stream Lconcentrate in (d), which is the valuable stream of interest in resource extraction applications.
