Load curve ·
Solid = concentrate outlet, dashed = dilute outlet; dotted lines are the chosen limits. Moving left of 100 % trades electricity for salt transfer.
Every layout ·
All saved stage arrangements and routings at this N and φ (filled = peak power, hollow = 90 % retained). Green ring = both limits met. Rearranging the same resources rarely moves the outlet; adding resources does.
Resource map · concentrate outlet (g/L)
Single‑stage reference survey. Outlined cells meet both limits; orange outline = current selection.
Best saved outlet vs dilute supply
Lowest concentrate outlet that still respects the 35.5 g/L pooled dilute limit, across the whole 40‑segment survey (any layout, any load). Vertical line: conservation floor for equal 35.5 / 35.5 outlets.
Four levers, in order
Each slider moves one lever while the others stay where the side panel has them. The marker is the current setting; the shaded bars are what the next step of that lever buys at the concentrate outlet. When the bars flatten, move to the next lever.
Give up power → move more salt
Design . Lower the minimum retained net power; the solver spends the freed current on salt transfer. The outlet gains less than the salt because water moves too.
Add dilute water → until it flattens
Design . Concentrate outlet at each dilute‑supply ratio φ; bars show the gain from the next quarter‑volume of water. Below the conservation floor nothing else matters.
Add membrane → the strongest lever
Design . Outlet across the 12–96 pair ladder at the current φ and rule; bars show the gain from the next rung. Net power is the thin line.
Rearrange the same membrane → last, and small
Design . Best tested layout of the same pairs and water at each stage count (any routing, any allocation). Bars: outlet gain vs the single stage. Pumping losses grow with subdivision; the module study shows net power falling to 37 % at four stages.
Salt transfer rises as power is given up
Median and 5th–95th percentile across 4,353 distinct designs with separate electrode systems; each design is paired with its own peak‑power state.
…but the outlet improves by less
Absolute decrease in concentrate‑outlet salinity for the same designs. The gap between the two panels is water transport.
Water supply shifts the whole curve
48‑pair single stage at two dilute ratios.
Why salt ≠ salinity: the outlet identity
Change from 100 % to 90 % retained power, split into migration, diffusion and water‑volume terms (Eq. 8). The diamond is the net outlet decrease.
Membrane > load > rearrangement · 30 matched cases
Three ways to spend the same budget, each measured as concentrate‑outlet decrease at the 90 % floor. Bars are medians over six dilute ratios; the order holds in all 30 cases.
Why staging ranks last: pumping
The same 200 module pairs and equal inlet flows arranged in 1, 2 or 4 stages (serial dilute, separate electrodes, each at its own peak). Gross power barely moves; pumping does.
Fewest tested pairs meeting both limits · operate at peak power
40‑segment survey; Bound = excluded by conservation, Unmet = no saved design reached the duty.
…allow operation away from peak power
Any saved load down to 50 % retention. Same duty, less hardware.
Fine‑checked boundary at equal flow (57.5 / 35.5)
Concentrate outlet at peak net power vs total pairs; 640 segments. Peak power first meets the duty at 37 pairs (one stage) or 36 (two stages). Treatment‑first selection meets it at 23.
Required avoided‑treatment value · 4,000 paired cost draws
Median break‑even value per m³ of concentrate (Eq. 11) for the best candidate at each pair count under each selection policy.
Selection outcome
Paired saving, draw by draw
Treatment‑first vs peak‑power required value, same draw.
Reading the result
A published SWRO feed basis · Carlsbad‑informed module case
Feed TDS 33,500 mg/L (supplier), 99.6 % of influent salt load to concentrate (permit), assumed 50 % recovery → 66.73 g/L concentrate. Hypothetical 1.0 g/L dilute feed. Single‑stage module: 0.1 m² sheets, 0.2 mm gap, 8×10⁻⁵ m³/s concentrate. Same 57.5 / 35.5 g/L limits as the reference duty. Resource ratios are scenarios, not plant wastewater availability.
Hardware saving recurs · fewest feasible pairs on the 50‑pair ladder
Treatment‑operated vs peak‑power sizing with both limits and positive net power enforced; highest available fine mesh (≥640 segments).
Scarce supply: the binding outlet flips · 850 pairs, φ = 0.25
Peak power already lowers the concentrate but pushes the dilute outlet past its limit. The feasible point is on the lower‑current side of peak — the opposite of the reference regime.
Diminishing returns to dilute water
Buy back the power: +50 pairs above the minimum
Which inputs move power · Morris μ*
Seven‑input Morris screen, single‑stage module at peak power. Mean absolute elementary effect in native units (W).
Which inputs move the outlet · Morris μ*
Same screen, concentrate‑outlet salinity (g/L). The membrane that favours electricity is not the membrane that favours treatment.
Unfitted benchmark · Hulme et al. 2021, 18 conditions
Modeled vs measured peak gross power density (W/m²), 640 segments, no parameter fitting. The error is geometric: the model under‑separates the three active lengths.
Does the operating‑point benefit survive the assumptions?
Salt gain at 90 % power and outlet decrease under every alternative tested (Table 7). Load adjustment beats the best rearrangement in every degradation group.