Electrolysis duties: schedules, the anolyte reservoir and dosing¶

process/duties.yaml (schema cheme/electrolysis-duties/v1) states how a cell of process/cells.yaml is operated over time against the reservoir its anolyte circulates through. cheme process duty integrates each duty and reports the pH, inventory, product, charge, energy, dosing and bleed over time, the time to the stated pH threshold, and the time spent outside the measured conditions. The code is chemeascode.domains.process.electrolysis_duty (model electrolysis-duty v1) with the anolyte models of chemeascode.domains.chemistry.anolyte; the decision is ADR 0043. It builds on the measured cell performance and the membrane block of ADR 0041.

The file¶

schema: cheme/electrolysis-duties/v1
kind: electrolysis_duties
duties:
  - id: D-150
    title: 150 mA/cm2 on 1 L of 1 M KOH
    cell: BPM-1                      # an id of process/cells.yaml
    cells_in_series: 1               # default: the cell's
    stacks: 1                        # stacks in parallel on the one reservoir
    # stack: STK-1                   # or: run at the arrangement that stack is sized at
    schedule: {kind: constant_current, current_density: {value: 150, unit: mA/cm2}}
    reservoir:
      volume: {value: 1, unit: L}
      composition: {hydroxide: {value: 1, unit: mol/L}}   # also carbonate, bicarbonate, co2
      cation: K+
      model: well-mixed-carbonate    # an anolyte model id; there is no default
      degassing:                     # optional; without it CO2 degassing is off (info)
        kla: {value: 2, unit: 1/h, source: "..."}
        co2_partial_pressure: {value: 0.0004, unit: atm, source: "air"}
      # size: to_horizon             # optional: the volume that reaches the horizon
      # time_margin: {value: 0.1}    # with size: a fraction of the horizon, or {value, unit: h}
    dosing:
      kind: on_threshold             # none | on_threshold | continuous
      trigger_ph: 12.5
      stop_ph: 13.0
      concentration: {value: 5, unit: mol/L}
      rate: {value: 10, unit: mL/h}
      density: {value: 1.22, unit: kg/L, source: "..."}   # optional: the solution's mass
    bleed: {rate: {value: 2, unit: mL/h}}
    makeup_water: {rate: {value: 2, unit: mL/h}}
    threshold: {ph: 12, source: "the stated design criterion"}
    horizon: {value: 2000, unit: h}
    minimum_inventory: {volume: {value: 0.5, unit: L}}   # or cation: {value, unit: mol}
    tolerance: 1.0e-8                # relative, optional
    operating_map: {wde: [0.5, 0.995], volume: [0.1, 10], volume_unit: L, resolution: [16, 10]}

Schedules:

kind	gives	notes
`constant_current`	`current` (A per cell) or `current_density`
`piecewise`	`points: [[t, I], ...]` in `time_unit` and `unit` (A or A/m2, mA/cm2)	`interpolation: step` (held) or `linear`; the first point at 0, the last value holds
`power`	`points: [[t, P], ...]`, P of all the duty's cells (W, kW)	`P = N U(j) j A` solved for j inside the measured range; outside it there is no current
`on_off`	`period`, `duty_fraction`, `current` when on	`start: on` or `off`

N is the cells in series times the stacks, all on the one reservoir. A duty a stack of process/cells.yaml names under equipment.duty runs at the arrangement that stack is sized at, in cheme process duty as in cheme process stack (cheme.duty-arrangement, info): its own cells_in_series and stacks are then not used (electrolyser stacks). A duty no stack's equipment names, such as a comparison duty on a skid's hardware, gets that arrangement by naming the stack (stack: STK-1); it may not state other cells_in_series or stacks (cheme.duty-arrangement, error: the duty is refused), and a duty naming a stack that is not in process/cells.yaml, is of another cell, or whose arrangement is not given (the stack refused; the duty run without the stack sizing) is refused too.

What is computed¶

At each instant the cell's voltage U(j), the Faradaic efficiency of its product FE(j), the water dissociation efficiency WDE(j) and the carbon share C_x(j) of the co-ion current come from MeasuredPerformance.at(j) for a measured cell (interpolated between the measured points, never extrapolated) or from a specified cell's constants (voltage, faradaic_efficiency, membrane.water_dissociation_efficiency, membrane.co_ion_crossover) within its operating_range. Per cell, with the current I:

OH- into the anolyte from the bipolar membrane: WDE I / F;
OH- consumed at the anode (oxygen evolution): I / F;
the co-ion current (1 - WDE) I / F: the cation leaving the anolyte (share 1 - C_x) and carbon entering it as HCO3- (share C_x), or the ions and shares of the membrane block;
the product formed: FE I nu / (n F); the power U I.

These, times N, with the dosing (cation and OH- of the solution, its volume), the make-up water and the bleed (at the reservoir's composition), are the fluxes the anolyte model integrates. The cumulative hydroxide deficit is (1 - WDE) Q / F, the charge Q over all cells.

The integration is the adaptive Dormand-Prince 5(4) method of foundation/ode.py with events:

the stated pH threshold (ends the duty; reported as the time to the specified pH threshold, a design criterion, not a corrosion onset);
the minimum inventory (volume or cation), or an empty reservoir;
dosing on at trigger_ph and off at stop_ph;
the product target of a comparison.

The schedule's breakpoints and the times the current density crosses the measured range split the integration. The transient stops at the first exit from the measured range (current density or temperature): the state after it is not computed. The scheduled operating time outside the range is summed (to the horizon when the transient stopped at an exit). Time with the anolyte outside the model's validity (pH, ionic strength, temperature) is summed too.

The totals are also split by route, so that the cation and the carbon balance of the reservoir close on their own (the LCI's reconciliation needs no closing by difference):

total	what
`initial_cation_mol`, `initial_carbon_mol`, `initial_volume_l`	the reservoir at the start
`dosing_cation_mol`	the cation dosed (one per hydroxide: `dosing_mol`)
`membrane_cation_mol`	the cation leaving the anolyte through the membrane, `(1 - C_x)(1 - WDE) Q / F` at constant performance
`membrane_carbon_mol`	the carbon entering through the membrane (one per HCO3- or CO3-2), `C_x (1 - WDE) Q / F`
`bleed_cation_mol`, `bleed_carbon_mol`	the cation and carbon leaving with the bleed, at the reservoir's composition

initial + dosed - bled - membrane = final for the cation and initial + membrane - bled - degassed = final for the carbon, to rounding (a test holds both to 1e-9 relative). They are integrated as quadratures on the integration's own steps, outside its error control, so every other value is as without them.

A duty is feasible when it runs to its horizon (or reaches a comparison's target) without reaching the threshold or the minimum inventory, entirely inside the measured range and the model's validity, and the integration converged.

The reservoir volume that reaches the horizon¶

reservoir.size: to_horizon asks for the reservoir volume that reaches the duty's horizon (plus time_margin: a fraction of the horizon, or a time in h or d) at the stated pH threshold. Without dosing, bleed, make-up water and degassing, and with the cell on at one operating point (one WDE and co-ion split whenever it is on: constant current, on/off, or steps of a specified cell), the reservoir's state moves along the charge Q passed, and the threshold falls at a fixed charge per volume Q* / V0. The volume is then exact:

V = V0 Q(target) / Q*

with V0 the stated volume, Q(target) the schedule's charge up to the target and Q* the charge at the threshold: from the run when it reaches the threshold, otherwise by following the run's straight path in the charge (the model's speciation) to the threshold. At constant current it is V0 H / t_threshold. The threshold is not the only limit: on the same path the concentrations at V after the charge Q are those at V0 after Q V0 / V, and the inventories are V/V0 n0 - Q dn/dQ. So the volume is raised, exactly, where the duty would otherwise end first or leave the model's claim before the target: to keep a stated minimum_inventory (absolute, in mol or L, so it does not scale with the volume: V >= (m + Q(target) dn/dQ) V0 / n0), and to keep the anolyte inside the anolyte model's validity (pH, ionic strength) up to the target. limited_by names the limit that sets it (the pH threshold, the stated minimum, the model's validity). The run itself is at V0, as without size; the volume is in required_volume of the JSON (volume_l, limited_by, target_h, probe_volume_l, the charges and the basis) and a cheme.duty-size info finding. A run at V0 that ends at the stated minimum inventory gives the volume too; a stated volume already below the minimum at the start ends the duty at 0 h (not feasible) and gives none. cheme process stack --write writes it into reservoir.volume for a duty a stack's equipment names (electrolyser stacks), rounded up to 4 significant figures so that the duty at the written volume reaches the target. With dosing, a bleed, make-up water or degassing the volume does not scale exactly and size: to_horizon is refused (cheme.duty-size, error), as for a schedule at more than one operating point, one leaving the measured range before the target, or a run ended otherwise than by the threshold, the horizon or the stated minimum inventory (an exhausted inventory); the duty itself still runs.

The anolyte model `well-mixed-carbonate` v1¶

An independent, concentration-basis implementation of the anolyte balance of Prats Vergel et al. (Nat. Chem. Eng. 2025), on conserved quantities with instantaneous equilibrium speciation instead of the authors' finite-rate kinetics:

state: moles of the cation and of total inorganic carbon C_T, and the volume;
[H+] from the charge balance [M+] + [H+] = [OH-] + [HCO3-] + 2 [CO3-2] with Kw = 1e-14, pK1 = 6.37, pK2 = 10.32 at 25 °C, solved on log10 [H+] (bracketed Newton);
CO2 degassing k_L a V ([CO2] - 0.034 p_CO2) above saturation only, when k_L a is given.

Its validity: ionic strength 0-1.5 mol/L, pH 2-14.5, 293.15-303.15 K. Its limitations: an ideal solution (concentrations, not activities: at 1 mol/L ionic strength the pH is a concentration-basis pH, not an activity pH), constants at 25 °C, no other ions or solids, supersaturated CO2 stays in solution without degassing.

Because the pH is on concentrations, the time to a threshold scales exactly with the reservoir volume at fixed fluxes. The authors' published script stops on -log10 of the H+ amount, which is the pH only at 1 L (process-library#329 D1: at 10 L it stops at pH 13). Against the

329 reproduction (200 mA/cm2, 5 cm2, 1 M KOH, C_x 0.66, WDE 0.95) this model gives 322.30 h to¶

pH 12 at 1 L and 3223.0 h at 10 L, as the authors' model on a concentration basis (tests/test_electrolysis_duty.py). Apart from that reproduction, the validation condition of

329 V1 (20 mL of 0.1 M KOH, 100 mA/cm2) gives 1.54 h, inside the envelope 1.31-1.87 h around¶

the measured 1.47 h.

The NaCl electrolyte route (cheme process electrolyte, electrolytes.yml) does not compute KOH or carbonate solutions and refuses them; the anolyte model is the only place they are handled.

Comparing duties¶

cheme process duty --compare A,B --co 0.5 (compare_duties) integrates each duty until its cumulative product equals 0.5 kg. A duty reaches the target when it delivers it to within the relative tolerance (--tolerance, default 1e-3 of the target); a duty whose horizon, threshold, inventory or measured range ends it first is reported as not reaching it (cheme.duty-target-not-reached). Per duty: the elapsed time, charge, energy, time outside the measured range, final pH, dosing used and the cumulative hydroxide deficit. The duties are named in --compare, not as positional ids (both is an error); --plot DIR draws the compared transients, each up to the target.

Plots¶

--plot DIR writes per duty:

duty-<id>.svg: aligned time plots, one quantity per panel on one time axis: current, voltage, pH with the stated threshold, product delivered, hydroxide dosed; events dotted, the time after a range exit shaded "not simulated". Lines are simulated.
map-<id>.svg: the operating map, time to the threshold over WDE (constant) and reservoir volume (log), with the duty's schedule and dosing; the measured WDE points of the measurement file as markers labelled "measured", the duty's own point, and the WDE outside the measured points shaded. Axis ranges come from operating_map: in the duty.

Findings¶

rule	level	when
`cheme.duty-schema`	error	the file does not follow the schema, a unit or a value out of range, a dosing trigger not above the threshold, an on/off schedule of more than 100 000 periods over the horizon
`cheme.duty-cell-missing`	error	the cell is not in `process/cells.yaml` or lacks what the duty needs (voltage, FE, a bipolar membrane with WDE and co-ion split from the membrane block or the measurement's titration, area, product), its membrane block is invalid (co-ion shares not in 0..1 or not adding up to 1, WDE outside 0..1), or its measurement has errors
`cheme.duty-model-unknown`	error	no anolyte model of that id
`cheme.duty-model-species`	error	a co-ion or anode reaction the model does not carry, or a model whose state names no `cation` (mol) and `volume` (L)
`cheme.duty-out-of-range`	warning	operation outside the measured range, or the anolyte outside the model's validity (info: a specified cell without a current density range)
`cheme.duty-threshold-reached`	info	the time to the stated threshold
`cheme.duty-horizon-reached`	info	the threshold is not reached within the horizon
`cheme.duty-inventory-low`	warning	the minimum inventory is reached, the reservoir empties, or a conserved inventory (cation, carbon) is exhausted: the transient stops there
`cheme.duty-dosing-saturated`	warning	the threshold is reached while dosing, or dosing never reaches its stop pH
`cheme.duty-dosing-chatter`	warning	threshold dosing switched on and off more than 20 000 times (a band `stop_ph - trigger_ph` too narrow for the dosing rate); the transient stops there
`cheme.duty-not-converged`	error	the integration failed
`cheme.duty-degassing`	info	no CO2 degassing stated
`cheme.duty-compare`	error	compared duties form different products
`cheme.duty-target-not-reached`	warning	a compared duty ends before the target
`cheme.duty-arrangement`	info / error	the duty runs at the arrangement a stack of `process/cells.yaml` is sized at, not its own; error (refused): it names a stack (`stack:`) not in the file, of another cell, whose arrangement is not given, that another stack's equipment runs, or states `cells_in_series` or `stacks` other than the stack's
`cheme.duty-size`	info / error / warning	`reservoir.size: to_horizon`: the volume that reaches the horizon, keeping the stated minimum inventory and the model's validity; error: no exact volume (dosing, bleed, make-up, degassing, more than one operating point, the measured range left, a time margin not a fraction or time); warning: a time margin without `size`

cheme validate reports the schema, cell and model findings without integrating: every error cheme process duty refuses a duty on before it integrates (units, ranges, the cell and its membrane, the anolyte model and its species, a stack: not in process/cells.yaml or of another cell, size: to_horizon with dosing, bleed, make-up or degassing). --json records the model ids and versions (the duty's and the anolyte model's), their assumptions and limitations, the range each duty is checked against (measured_range: current density, temperature, the power of all cells for a power schedule, the measured WDE), and the source revision with the sha256 of every input, the measurement file included.