Electrochemical measurements: Faradaic efficiency, water dissociation and measured performance¶

experiments/electrochemistry/<id>.yaml (schema cheme/electrochemical-measurements/v1) holds a measured series of one electrochemical cell: a bench cell run at several current densities, each with replicates. cheme experiments electrochem FILE processes it, cheme validate reports its findings, and a cell of process/cells.yaml with performance: measured takes its voltage and efficiencies from it (electrochemical cells). The code is chemeascode.domains.experiments.electrochemistry (model electrochemical-measurements v1); the decision is ADR 0041, and ADR 0042 records why no WaterTAP or IDAES model is used.

The module is generic: any electrolyser whose products are measured in the gas (or given as Faradaic efficiencies) and, for a membrane cell, whose anolyte is titrated.

The file¶

schema: cheme/electrochemical-measurements/v1
kind: electrochemical_measurements
id: rbpm-1m-koh
title: Reverse-bias BPM cell, 1 M KOH
provenance: given                       # the data set as a whole
origin: measured
source: "citation and DOI of the data"
licence: "CC BY 4.0"
cell:
  active_area: {value: 5, unit: cm2}
  temperature: {value: 25, unit: °C}
  electrolyte: {name: 1 M KOH, concentration: {value: 1, unit: mol/L}}
  membrane: {kind: bipolar, bias: reverse, name: "..."}
voltage_basis: cell                     # cell | cell_ir_corrected | electrode_vs_reference
products:
  - {id: CO, electrons: 2, electrode: cathode, reaction: CO2R, thermoneutral_voltage: {value: 1.4664, unit: V}}
  - {id: H2, electrons: 2, electrode: cathode, reaction: WS, thermoneutral_voltage: {value: 1.4812, unit: V}}
gas:
  flow_unit: sccm                       # sccm | slpm | mol/s
  standard_conditions:                  # required for sccm and slpm; never assumed
    temperature: {value: 273.15, unit: K}
    pressure: {value: 101.325, unit: kPa}
  flow_position: outlet                 # outlet | inlet
  flow_correction: {factor: 1.0, source: "..."}
  inlet: {component: CO2, flow: 20}     # for the carbon balance
titration:
  method: warder-double-endpoint
  titrant_concentration: {value: 0.1, unit: mol/L}
  anolyte_volume: {value: 90, unit: mL}
  aliquot_volume: {value: 1, unit: mL}
points:
  - id: P100
    current_density: {value: 100, unit: mA/cm2}   # or current: {value: 0.5, unit: A}
    duration: {value: 3600, unit: s}
    replicates:
      - id: R1
        voltage: {value: 3.30}                     # or series: [[t s, U], ...] and window: [t0, t1]
        outlet_flow: 20.45                         # in gas.flow_unit
        fractions: {CO: {value: 12.78, unit: mol%}, H2: {value: 3.407, unit: mol%}, CO2: {value: 83.82, unit: mol%}}
        titration: {V0: 10.000, V1: 9.855, V2: 9.928}   # mL
        source: "file name in the data set"
validity:                               # optional; what is left out is derived from the points
  current_density: [500, 2000]          # A/m2
  temperature: [293.15, 303.15]         # K
  electrolyte: 1 M KOH
  duration: 3600                        # s, the longest run
  source: "..."

A replicate gives each product either as gas data (fractions with the outlet_flow) or as a faradaic_efficiency directly, and the membrane either as a titration or as a water_dissociation_efficiency directly. Units: current A, mA, kA; current density A/m2, kA/m2, mA/cm2, A/cm2; area cm2, m2; duration s, min, h; voltage V, mV; fractions ppm, mol%, %, a plain fraction; concentrations mol/L (M), mmol/L, mol/m3; volumes mL, L; pressure Pa, kPa, bar, atm (absolute); temperature K, °C.

What is calculated¶

Per replicate, with the current I, the current density j and the point's duration t:

Quantity	Relation
molar outlet flow	`Ndot = c_corr V p_std / (R T_std)` (sccm, slpm; R = 8.314462618 J/(mol K)); mol/s as given
product flow	`Ndot_i = x_i Ndot`
Faradaic efficiency	`FE_i = n_i F Ndot_i / I`, F = 96485.33212 C/mol
partial current density	`j_i = FE_i j`
charge balance, per electrode	`sum FE_i + unassigned = 1` over the products of one electrode (the full current passes the cathode and the anode, so each balances apart)
co-ions from the titration	`n_K = (V0 - V2) c V_anolyte / V_aliquot`, `n_C = (V2 - V1) c V_anolyte / V_aliquot`
water dissociation efficiency	`WDE = 1 - F (n_K + n_C) / (I t)`; carbon share of the co-ion current `n_C / (n_K + n_C)`
power	`P = U I` (terminal voltage only)
heat at an isothermal boundary	`Q = I (U - sum_i FE_i U_tn,i)` over the products of the electrode that gives `U_tn`, when each of them gives it (a product's `U_tn` is that of its overall reaction, which holds the other half-reaction: only one electrode's products give it)
carbon balance (with `gas.inlet`)	carbon fed = in products + unreacted (when its outlet fraction is measured) + into the anolyte (`n_C / t`)

V0 is the titrant to the second end point of the fresh anolyte, V1 and V2 to the first and second end point after the run (Warder double end point; the equations are those of the source paper's Methods, and count one charge per crossing ion, carbon as HCO3-). Per point, every quantity has its mean, sample standard deviation and count; a point with one replicate has no standard deviation.

The Faradaic efficiency and the water dissociation efficiency are different quantities. The first is the share of the current that forms each product at the electrodes; the second is the share of the current the bipolar membrane carries by dissociating water instead of by co-ions. Neither corrects the other, and they are never combined.

Measured performance: interpolated, never extrapolated¶

MeasuredPerformance(report).at(j) returns a PerformancePoint: the voltage, the Faradaic efficiency per product, the water dissociation efficiency and the carbon share, each with its standard deviation, interpolated linearly in the current density between the two bracketing point means (bracket), with in_range and extrapolated. Outside the validity range, or beyond the measured points when a declared range is wider, it returns no value, the bounds and the reason. This is the interface the cell model (performance: measured) uses, and the one dynamic duties and stack sizing will call.

Checks¶

Every finding names the file, the line, a rule id cheme.electrochem-* and a hint.

Rule	Level	When
`schema`	error	the file does not follow the schema or cannot be read as UTF-8; a duplicate id; a product not declared; two points at one current density; `thermoneutral_voltage` on products of both electrodes
`unit`	error	a unit the quantity does not take
`input-missing`	error	a standard flow without standard conditions; fractions without the outlet flow; a titration without the method block or the duration; a voltage series with no sample in its window
`fe-sum-high`	error	the Faradaic efficiencies of a point at one electrode add up to more than `max(1 + 3 sd, 1.05)` (one replicate: 1.05); the replicates' spread says nothing of a calibration bias, so close replicates never tighten the limit below 1.05
`fe-sum-low`	warning	they add up to less than 0.9: an unmeasured product (liquids) or a flow error
`single-replicate`	info	a point with one replicate
`crossover-assumed`	warning	a membrane cell without a measured water dissociation efficiency
`voltage-basis`	info	electrode potentials against a reference: no polarisation curve, power or heat, and no cell voltage
`titration`	warning	volumes not in the order `V1 <= V2 <= V0`
`carbon-balance`	warning	carbon in and out differ by more than 5 % of the carbon fed
`flow-correction`	info	no meter correction stated: factor 1
`flow-position`	warning	the flow was measured at the inlet and is taken as the outlet flow
`heat`	info	a product without a thermoneutral voltage: no heat
`validity`	info / warning	the range is derived from the points / a declared range extends beyond them

The command¶

cheme experiments electrochem FILE [--json] [--plot DIR] prints each point (voltage, FE per product with the partial current density, the FE sum per electrode, the water dissociation efficiency, power and heat, each as mean +- sd (n)), the limitations and the findings. It reads the file only; inside a plant repository the paths are from its root, elsewhere from the file's folder. --json records the model id and version, the core version, the assumptions and limitations, the per-point and per-replicate results, the findings and the sha256 of the file. --plot writes SVG figures (light and dark) for the inputs that support them: polarisation.svg (a terminal voltage; electrode-potential.svg, labelled so, for electrode_vs_reference), faradaic-efficiency.svg (per product and the sum), partial-current-density.svg and water-dissociation-efficiency.svg, each with +- 1 sd bars. Exit 1 on an error finding, 2 when the file does not exist.

Limitations¶

No polarisation model: between points the means and standard deviations are interpolated linearly; nothing outside the measured range is computed.
The standard deviation is over the replicates; the uncertainty of the instruments (flow meter, gas chromatograph, titration) is not propagated.
The heat counts only the products' reaction enthalpies. pH gradients, the neutralisation of crossed-over ions and heats of dilution are not included.
One temperature and one electrolyte per file: the lookup has no temperature or concentration dimension.