ILEDBV consistency-testing model: thermodynamic, stoichiometric, carbon and economic constraints on an integrated SWRO-brine valorization architecture

Abstract

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 fourteen 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 fourteen 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. Revision 2 (v2.4.0) changes presentation only. It answers four comments from the fourth reviewer and alters no model, parameter, assumption or result; every number still regenerates from the model code as it stood at v2.3.0. Equations are rebuilt as native Word equation objects and units and chemical formulae are typeset throughout; the abstract is cut to the journal's 250-word limit; two new figures plot values already present in Tables 1, 5 and 8, the figures are renumbered to citation order and numbered captions are added, which the previous version lacked entirely; and Sections 5.5 and 5.6 now state that the brine concentrator is bounded thermodynamically rather than designed hydraulically, specifying the membrane and product-characterization measurements that would settle the remaining questions. Five internal inconsistencies found in checking were corrected, one of them substantive: the Introduction still carried a conclusion from before the economic reversal. One documentation correction belongs with the numbers: fourteen sampled parameters enter the Monte Carlo and are ranked, not thirteen. The deposit now also contains the complete submitted package under revision2/. Version 2.5.1 merges a third-party language edit of the manuscript and makes five final corrections, changing no result. The edit was accepted paragraph by paragraph: an edited paragraph is taken only when it carries the same content words, numbers, currency and unit tokens and sub/superscript runs as the source. 51 edits were accepted and 44 kept from the source, because the rejected ones were not stylistic: "brine" had become "saltwater", the reagent masses of Section 4.1 had become "solids", "$0.061" had lost its dollar sign, "precipitation train" had become "training" and "vapor" was misspelled. Every decision is recorded in the deposited merge report. The five corrections: Section 5.3 describes the laminate membranes as potential components of alternative brine-concentration and crystallization systems and states that membrane separation and complete crystallization are not interchangeable; the electricity-price crossings of Section 4.12 and the Conclusions are labelled modeled thresholds under the stated cost assumptions rather than demonstrated commercial break-even prices, since the electrochemical capital cost and coproduct handling lie outside the boundary; the generative-AI declaration states what the tool did and what was verified and by what; Data availability names the plotting script for Figures 2 and 7 and the release that contains it, that script having been added after v2.3.0; and numeric ranges are set with en dashes. The numerical audit still reports 18 of 18 headline numbers present and 0 contradictions. Version 2.5.0 adds two bounded research directions to the Discussion and changes no result. Editorial guidance received after the Revision 2 package was assembled asked that two directions be stated without altering the modelled results. Section 5.3 gained two paragraphs on crosslinked graphene oxide and MXene laminate membranes as a possible alternative to the crystallization stage, together with the comparison such a membrane would have to pass against the mechanical vapor compression reference at the modelled crystallizer-feed salinity of 124.8 g/L. A new Section 5.5 sets out brine-derived magnesium as a precursor for metallothermic silicon production, the four stages a future study would need, and the reasons no silicon revenue, energy saving or carbon credit is claimed. Both are excluded from the mass, energy, carbon and economic balances; the former Sections 5.5 and 5.6 are renumbered 5.6 and 5.7 and each records that exclusion. Ten references, [27] to [36], were added, each resolved against its Crossref record. Silicon appears in neither the abstract nor the keywords. No equation, table, figure, parameter or number changed: the numerical audit reports 18 of 18 headline numbers present and 0 contradictions, and the model code is unchanged since v2.3.0, which remains the release tag the manuscript cites. Every specific-energy figure is a bounded model estimate rather than a measured or predicted plant value. No experimental data were used.