Summarizing, Pd,corr can be maximized by keeping CLOW,in and solution feed velocities in the proximities of the lower limit investigated here. Conversely,  is maximized by intermediate CLOW,in and vLOW,in as low as possible. For all cases, CHIGH,in must be as high as possible, yet lower than its saturation value to avoid undesired precipitation. Figure 10: Closed loop Case I sensitivity analysis: influence of solution velocity. (A) Pd,corr vs vHIGH,in and vLOW,in; (B)  vs vHIGH,in and vLOW,in; (C) Pd,corr and  vs vLOW,in at vHIGH,in = 2.98 cm/s; (D) Pd,corr and  vs vHIGH,in at vLOW,in = 0.45cm/s. Simulations of a RED unit (10x10 cm2, 10 cell pairs) equipped with commercial membranes (αAEM = 0.65, αCEM = 0.90; RAEM = 1.55 Ω cm2; RCEM = 2.96 Ω cm2), 270 μm woven spacers. T = 25 ˚C; CHIGH,in = 5 M; CLOW,in = 0.1 M. Solvent extraction scheme. Regeneration requirements of 40 kWhth/m3 of extracted solvent. Closed loop - CASE II: Perspective analysis of the RED and MED technology This section concerns the same salt-solvent (i.e. water-NaCl) case reported in the previous section, the only difference regards the use of more efficient membranes characterized by lower electrical resistance and higher perm-selectivity. The same sensitivity analysis of Case I was performed for comparison purposes. As it can be observed in Figure 11 and Figure 12, the dependences of Pd,corr and  on operating parameters (solution inlet concentration and velocity) are very similar despite the different membrane features and are not discussed. More important, Figure 11A and Figure 12A show that the high efficiency membranes, even with the use of NaCl-water solutions, could guarantee the achievement of power density of about 18 W/m2, practically doubling the power obtained in Case I. Under these conditions, the efficiency could be greatly increased since it takes advantage from the increase of Pd,corr and the decrease of : Figure 11B and Figure 12B show values up to about 15.3%.
Finally a qualitative comparison with other heat engines based on exergetic efficiency is provided. This comparison highlights that the SGP technologies could be very promising future converters of low-grade heat (temperature range of 50 to 100°C; e.g. solar and geothermal energy or waste heat) into electric energy, thus justifying large room for future research and development aimed at moving each theoretical case beyond conceptualization. Acknowledgement This work has been performed within the RED-Heat-to-Power project (Conversion of Low Grade Heat to Power through closed loop Reverse Electro-Dialysis) - Horizon 2020 programme, Project Number: 640667: . Francesco Giacalone is acknowledged for his help in data processing. Notation A active area of one cell pair [m2] AΛ, BΛ, CΛ Jones and Dole’ equation parameters Aγ, Bγ, Cγ, Dγ, Eγ Staples correlation parameters a separation ratio [-] C molar concentration [mol/l] Dsalt Salt permeability coefficient [m2/sec] Estack Cell pair voltage [V] F volumetric flow rate [m3/sec] F Faraday’s constant (96490) [C/mol] Jsalt salt flux [mol/m2 sec] j electrical current density [A/m2] m molality [mol/kg] N cell pairs number [-] OCV open circuit voltage [V] P electric power [W] Pd power density [W/m2] Q volumetric flow rate [m3/sec] thermal power [W] R universal gas constant [l atm/(mol K)] Rblank blank resistance [Ω m2] Rcells cell pairs resistance [Ω m2] RAEM AEM resistance [Ω m2] RCEM CEM resistance [Ω m2] RHIGH resistance of concentrate solution [Ω m2] RLOW resistance of dilute solution [Ω m2] Rext external load resistance [Ω m2]
Rstack stack resistance [Ω m2] sf spacer shadow factor [-] T temperature [K] v solution velocity [m/s] z ion valence [-] Greek letters α membrane permselectivity [-]  channel thickness [m] energy production per mol of transported salt [kWh/mol] equivalent conductivity [S m2/mol]  activity coefficient [-] ρ solution density [kg/m3]  efficiency [-] Subscripts c Carnot corr corrected value of power density (by subtracting the blank resistance as its contribution is negligible for large scale stacks) ex exergetic HIGH concentrate solution in RED unit inlet LOW dilute solution m membrane out RED unit outlet th thermal wh waste heat Acronyms AccMix accumulator mixing AccMixHE accumulator mixing heat engine AEM anion exchange membrane CC carbon carrier cycle CEM cation exchange membrane IEM ion exchange membrane KC Kalina cycle MD membrane distillation MED multi effect distillation OCV open circuit voltage [V] OHE osmotic heat engine ORC organic Rankine cycle PEPG piezoelectric power generation with waste PRO pressure retarded osmosis RED reverse electrodialysis REDHE reverse electrodialysis heat engine SE Stirling engine SGP salinity gradient power SRC-fuel steam Rankine cycle directly fuelled by oil, coal or other fuels