Consistency Testing of an Integrated SWRO-Brine Valorization Architecture: Alkalinity as the Binding Constraint

This version reverses the conclusions of the previous one. Peer review identified two errors in the earlier analysis; correcting them removes both the claimed energy advantage over conventional SWRO and the favorable levelized cost. The brine concentrator as originally specified is thermodynamically inadmissible. The reversible minimum work of separation for the modeled brine is 0.94 kWh per cubic meter of brine processed; the assumed range of 0.5-1.0 kWh/m3 spans 0.53 to 1.06 times that minimum. A bounded estimate from the minimum and a 25-55% second-law efficiency is 1.7-3.8 kWh/m3, raising the modeled total specific energy consumption to a median 13.1 kWh/m3. Magnesium recovery is limited by alkalinity, not by magnesium. Two equivalents of base are required per mole of Mg(OH)2 however the base is supplied. Costed explicitly, soda ash and lime come to $1.70 per cubic meter of permeate against a realizable mineral credit of $1.25, and carry 10.0 kg CO2/m3 of embodied carbon against 5.2 kg from grid electricity. Assessments restricted to electricity account for about a third of the total. The calcium balance does not close. Lime dosing returns 5.3 times more calcium than the preceding carbonate step removes, and total dissolved solids rise across precipitation from 121.7 to 124.8 g/L, so selective precipitation slightly increases the crystallizer duty rather than reducing it. Monte Carlo propagation over thirteen parameters (300,000 samples, seed 20260919) gives a net levelized cost of $2.20/m3 (90% interval $1.38-$3.01) against $0.76/m3 for conventional SWRO. 271 of the 300,000 samples (0.09%) did undercut the comparator, the best reaching $0.35/m3; none was carbon negative. The architecture is therefore not categorically more expensive, but competitive only in a small corner of the sampled space. Alkalinity, not thermodynamics, is what reverses the conclusion. An ablation isolates the two corrections: after the thermodynamic fix alone the architecture still costs $0.64/m3, under the comparator; costing the reagents explicitly is worth $1.55/m3, 6.8 times as much. Rank correlation over the thirteen sampled parameters agrees, and the admissibility map gives the specification a future version would have to meet: at present reagent prices the recovered minerals must be worth 2.1 times their modeled value. One supply route unbinds the constraint. Generating the base electrochemically on site with captured CO2 as the carbonate source closes the calcium balance exactly (closure ratio 5.33 to 0.00), makes reagent carbon net negative at -0.94 kg CO2/m3, and replaces the reagent bill with 27.1 kWh/m3 of electrochemical demand. Because that substitutes an energy price for a commodity price it has a crossing the purchased-alkali route does not: route D reaches the conventional comparator below $0.033/kWh, whereas route A stays $0.34/m3 above it even at zero electricity cost. The result is conditional on low-carbon supply and excludes the uncosted electrochemical capital and coproduct handling. Alkalinity and calcium as one design problem (v2.3.0). A linear program chooses among lime, purchased NaOH and on-site electrochemical base, soda ash and dosed CO2, and a gypsum step that removes calcium, with the calcium balance imposed as a constraint. Closing the balance costs $0.44 per cubic meter of permeate at the base case with the gypsum step and $0.73 without it. Above $0.069/kWh no on-site base can close the loop against the comparator, because the reversible limit of water dissociation (45.1 mol OH- per kWh) binds. The work identifies and quantifies the conditions required to close the system; it does not report a working valorization process. Correction in v2.3.0: the dosed CO2 of route D had been credited twice. On solar-dominated supply route D emits +1.07 kg CO2/m3 (previously reported as +0.13) against +9.68 for purchased alkali, and +21.2 on the grid mix (previously +20.3). Route D therefore still requires low-carbon power; its reagent-carbon term alone is net negative. Every specific-energy figure is a bounded model estimate rather than a measured or predicted plant value. No experimental data were used.