MNRC — struvite precipitation and NH₃ stripping

N and P recovery, struvite mass and purity from N/P-rich streams — not power.

Each relation is transcribed from the implementation. Where the code cites no source, the source line says so.

1. $$\mathrm{pH} = \min\!\left(11,\ \mathrm{pH}_0 + 3\left(1 - e^{-x}\right)\right), \qquad x = \frac{j A t / F}{\mathrm{Alk}/50\,000 \cdot V}$$

   Source: Empirical buffer-saturation curve with a soft ceiling at pH 11; mnrc.ts cites no source for it.

   An empirical curve, not a carbonate speciation model.

   Symbol	Meaning	Unit
   $\mathrm{pH}_0$	influent pH	pH
   $x$	H⁺ consumed per mole of alkalinity	1
   $j$	anode current density from predict.ts	A/m²
   $A$	anode area, fixed at 0.003	m²
   $t$	run duration (default 24 h)	s
   $\mathrm{Alk}$	alkalinity (default 500); 50 000 mg CaCO₃ per equivalent	mg CaCO₃/L
   $V$	recovery chamber volume (default 100 mL)	L

   Worked example

   These inputs, passed to the predictor, return the output below. A test re-runs the example on every change, so this number is the one the code produces.

   input	value	unit
   temperatureC	25	°C
   ph	7	pH
   electrodeSpacingCm	2	cm
   hrtHours	24	h
   codMgL	1,000	mg/L

   Output · mnrc.catholytePh = 7.995 pH, within ±0.1 %

   By hand · j = 0.15 A/m² from predict.ts at 25 °C, pH 7, 1000 mg/L COD, no anode named (see the MFC worked example). I = 0.15 × 0.003 = 4.5×10⁻⁴ A; charge over 24 h = 38.88 C = 4.030×10⁻⁴ mol H⁺. Alkalinity = 500/50 000 × 0.1 = 1.0×10⁻³ mol, so x = 0.403. pH = 7 + 3 × (1 − e^−0.403) = 7.995.

   Reproduce · Pinned by libs/shared/electrochemistry/src/predictors/worked-examples.test.ts. Run it from the repository root:

   pnpm exec jest -c libs/shared/electrochemistry/jest.config.js worked-examples.test.ts -t "mnrc.catholytePh"

2. $$SI = \log_{10}\mathrm{IAP} + pK_{sp}, \qquad \mathrm{IAP} = [\mathrm{Mg}]\,(1 - f_{NH_3})[\mathrm{NH_4}]\,10^{\mathrm{pH}-12.35}[\mathrm{PO_4}], \quad pK_{sp} = 13.27$$

   Source: K_sp from Münch & Barr 2001, Water Res. 35:151.

   Activity coefficients are ignored (dilute-solution assumption).

   Symbol	Meaning	Unit
   $SI$	struvite saturation index; nucleation above 0.5	1
   $[\mathrm{Mg}], [\mathrm{NH_4}], [\mathrm{PO_4}]$	total influent concentrations (activities taken as 1)	mol/L
   $10^{\mathrm{pH}-12.35}$	free PO₄³⁻ fraction	1
   $pK_{sp}$	−log₁₀ of the struvite solubility product at 25 °C	1

3. $$f_{NH_3} = \frac{1}{1 + 10^{\,pK_a - \mathrm{pH}}}, \qquad pK_a = 9.25$$

   Source: Henderson-Hasselbalch speciation with pK_a = 9.25; mnrc.ts cites no source for it.

   Symbol	Meaning	Unit
   $f_{NH_3}$	free-ammonia share of total ammoniacal nitrogen	1
   $pK_a$	NH₄⁺/NH₃ acid constant at 25 °C	1

4. $$n_{s} = \min\left(n_N, n_P, n_{Mg}\right)\cdot \min\left(0.95,\ 0.4 + 0.55\,(SI - 0.5)\right) \quad (SI > 0.5)$$

   Source: Linear precipitation-efficiency ramp above the nucleation threshold; mnrc.ts cites no source for it.

   A heuristic ramp from 40 % at SI = 0.5 to a 95 % cap.

   Symbol	Meaning	Unit
   $n_s$	struvite precipitated	mol
   $n_N, n_P, n_{Mg}$	moles of each reactant in the chamber	mol

• Anode current from the shared Butler-Volmer biofilm kinetics in predict.ts (Geobacter on acetate), with the same Arrhenius, substrate, pH and ohmic corrections as the MFC predictor.
• Cathode pH rise is an empirical function of charge passed per unit alkalinity.
• Nucleation above SI = 0.5.
• Default urine matrix: 200 mg/L NH₄-N, 30 mg/L PO₄-P, 25 mg/L Mg — unsourced defaults.

• Purity penalty from deviation of Mg:NH₄:PO₄ from 1:1:1.

• Crystal habit / dewaterability (needs CFD + supersaturation-gradient modelling).
• Calcium carbonate scaling — only a binary purity penalty.
• Continuous-flow operation — assumes batch over the stated duration.
• Temperature dependence of Henry's constant — 25 °C value used.

• Münch & Barr 2001, Water Res 35:151
• Kuntke et al. 2012, Water Res 46:2627

libs/shared/electrochemistry/src/predictors/mnrc.ts

heuristic_fixed_fraction — A fixed ±25 % placeholder band. It is NOT a calibrated interval; when served through /api/ml/predict it is replaced by the benchmark band below, or withheld. How served intervals are built

• Benchmark out-of-fold residual quantiles: bes-benchmark-v1 · gkf5 · generated 2026-09-09
• Split-conformal calibration: split-conformal · generated 2026-05-21
• Hierarchical-priors v2 trust snapshot: populated · generated 2026-05-16

Each row is a stratum with n ≥ 30 residuals at nominal level 90%. Coverage is the cross-validated share of held-out points inside the band.

No benchmark cell reaches the minimum n for these systems — intervals are withheld.

The state the lab badge shows for each served parameter and system, from the v2 priors fit.

No v2 prior row for these systems.

pnpm verify:science runs these rules over the committed priors and validation artifacts in pre-commit. Known violations are baselined per rule and slug; a new one blocks the commit. Baseline from hierarchical-priors-v2.json@2026-10-26T00:10:47.721880+00:00.