Current Efficiency in Electro-Oxidation: How to Measure It and Why Vendors Rarely Quote It

A “100% current efficiency” claim can be true and still understate energy by 23%

On a 5,000 mg/L COD batch at 50 mA/cm², current efficiency stays at 100% for the first two hours and then falls to 8% by hour six. A vendor who quotes the first-hour figure implies 20.1 kWh/kg COD. The full run to 500 mg/L averages 77% and costs 26.2 kWh/kg. Both numbers come from the same run.

Current efficiency is the single variable that converts a removal claim into an energy cost. It is also the one most often missing from proposals, because it falls as COD falls and exposes what the last kilograms cost.

What current efficiency measures

Electro-oxidation passes current through wastewater between two electrodes. At the anode the pollutant is oxidized either directly, by electron transfer at the surface, or indirectly, by hydroxyl radicals or active chlorine generated at the anode. The electrode reaction mechanisms page covers both routes in detail.

Current efficiency is the fraction of the anodic charge that goes into the reaction you want. At constant cell voltage, energy per kilogram removed is inversely proportional to it: halve current efficiency and you double kWh/kg.

Cathodic hydrogen is not a current-efficiency loss. Every electron that leaves the anode reduces water at the cathode, so H₂ forms at 100% of the current, about 0.42 Nm³ per kAh, whatever the anode does. The losses are decided at the anode, where each electron ends in one of four places:

In chloride water the unused fraction is not inert. It becomes oxidant and byproduct, which makes current efficiency a compliance question as well as an energy one. See the byproduct chemistry overview.

The formulas, and why the basis matters

Run-averaged current efficiency compares the charge the removal should have taken with the charge actually delivered:

n is electrons per mole of the target (4 for COD on an O₂ basis, 3 for ammonia-N to N₂), F = 96,485 C/mol, M is the molar mass basis (32 g/mol for COD, 14 g/mol for N), I is current in A and t is time in h. For COD this reduces to 3.35 Ah per gram removed.

Kapałka, Fóti and Comninellis define the instantaneous current efficiency (ICE) over each sampling interval of a constant-current run [1]:

COD in g O₂/m³, V in m³, I in A, Δt in s; 8 is grams of O₂ equivalent per mole of electrons. The run-averaged value is what the same authors call the electrochemical oxidation index (EOI) [1]. For mineralization proven by TOC rather than COD:

n is electrons per molecule for full mineralization, m carbon atoms per molecule, ΔTOC in mg C/L, V in L, t in h; 4.32 × 10⁷ = 3,600 s/h × 12,000 mg C/mol.

The arithmetic is simple. The basis is what makes a number usable. State all of these:

• Which reaction is measured: COD, TOC, ammonia, a specific compound.
• Which analytical method, with its chloride limit and the residual-oxidant correction applied.
• Which current, logged rather than spot-read.
• Which volume: batch, recirculating loop or single pass.
• At what charge (Ah/L) in the run, or over the whole run to a stated endpoint.
• What uncertainty applies.

Why current efficiency falls during a batch

The limiting current density for COD removal is proportional to COD itself, j_lim = 4F·k_m·COD, with k_m the cell's mass-transfer coefficient [1]. While the applied current density is below j_lim, the cell is current-limited and current efficiency stays near 1. Once COD falls far enough that j_lim drops below the applied value, removal is limited by transport and the surplus current goes to oxygen evolution and side reactions.

Base case: 100 L batch, 1 m² BDD anode, 500 A (50 mA/cm²), COD₀ = 5,000 mg/L, k_m = 2×10⁻⁵ m/s, 6.0 V. The cell switches to transport control at 2,073 mg/L, after 1.96 h.

Values modelled with the batch model in [1]. Reaching 500 mg/L takes 3.94 h and 19.7 Ah/L, for a run-averaged efficiency of 0.77 and 26.2 kWh/kg COD at 6.0 V. Stopping at 113 mg/L instead pushes the last interval's marginal energy to 251 kWh/kg. Current efficiency does not drop to zero; it decays as j_lim/j. Lowering the current as COD falls recovers most of the loss, which is why the last kilograms are the ones to watch when electro-oxidation is used as a polishing step.

Why vendors rarely quote it

Understanding the incentive helps you ask better questions.

The number is unflattering. A 90% removal figure sounds strong. A 25% current efficiency sounds weak, yet both can describe the same run.

The number depends on the feed. Refractory fractions, chloride, ammonia and conductivity all move it, so a value measured on one water does not transfer to another.

The number depends on the operating point. Low current density keeps efficiency high but needs more anode area; high current density saves area and spends energy. The efficiency in a proposal is a design choice, not a property of the technology.

The number exposes the byproduct story. When efficiency is low, the missing charge is going somewhere: into oxygen on low-chloride feeds, and into chlorine, chlorate and perchlorate on chloride-bearing ones.

None of this makes vendors dishonest. It makes them selective. The buyer closes the gap by asking for the number, its basis and the point in the run where it was measured.

The four layers of current efficiency

A credible proposal states current efficiency at four layers, each with its own evidence standard.

1. Bench: controlled lab test with known COD, logged current, corrected analytics.
2. Pilot: continuous current logging and sampling by charge over weeks of real feed variability.
3. Design: the run-averaged value assumed in the full-scale design, to the guaranteed endpoint, with its basis.
4. Operating: the value achieved in the plant, measured from operating data.

A proposal that shows all four, consistent with each other, can be trusted. One that shows only a bench value from the first hour cannot. Bench and pilot values come from treatability studies run on your own wastewater.

How to measure it on your own pilot

1. Define the target reaction. Write down n and M before anything else.
2. Measure k_m first. Run a ferrocyanide limiting-current test on the pilot cell at design flow [1]. Without k_m the regime switch cannot be predicted.
3. Run at constant current and log current, cell voltage, temperature and flow continuously.
4. Sample by charge, not by clock: every 1–2 Ah/L, with at least four samples after the predicted regime switch.
5. Measure the interferences with every COD sample: residual H₂O₂, free and total chlorine, NH₄⁺-N, NO₃⁻-N and chloride. Residual H₂O₂ exerts COD of 0.47 mg O₂ per mg H₂O₂; subtract it.
6. Do not quench with sulfite or thiosulfate before COD analysis. Both exert COD. Correct for measured residual oxidant, or use TOC.
7. Check chloride against the masking limit of your COD method. Above it, use a method validated for high-chloride samples or base the efficiency on TOC.
8. Compute interval ICE and the run average, then compare them with the predicted curve. A shortfall points to a refractory fraction; an excess points to stripping or chloride mediation.
9. Report the conditions: current density, cell voltage, conductivity, k_m, temperature, volume, anode area and anode type.

Where the measurement breaks

• Efficiency above 100% is never a sign of a better anode. Volatiles were stripped, oxidant residuals biased the COD test, or active chlorine oxidized organics outside the accounting. See the byproduct chemistry overview.
• MMO anodes in chloride water can show high COD-based efficiency while chlorate forms; see how BDD and iridium-oxide anodes compare.
• Mixed oxidation targets. Ammonia to N₂ takes 5,743 Ah per kg N. When ammonia, sulfide or cyanide share the charge, a COD-only efficiency understates the cell's Faradaic performance and overstates the cost of COD.

What it means for your business case

Current efficiency and cell voltage together set energy per kilogram [1]:

At 6.0 V, a run-averaged efficiency of 0.77 gives 26.2 kWh/kg; 0.30 gives 67 kWh/kg. Cell voltage moves the same number one-for-one, which is why a fair comparison needs both, and why power supply and electrical integration belong in the same review.

Cost per m³ adds anode replacement, chemicals, cooling, byproduct polishing and operation to the electricity. A proposal that does not state current efficiency cannot state any of these honestly. For a first screen of your own stream, use the EO feasibility assessment tool.

Five questions to ask every vendor

1. What current efficiency did you measure, and for which reaction?
2. At what charge in the run, in Ah/L, or over the whole run to which endpoint?
3. On what anode, at what current density and conductivity, and on what feed?
4. Which analytical method, which residual oxidants were corrected for, and what is the uncertainty?
5. What run-averaged efficiency does the full-scale design assume, and on what evidence?

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References

1. Kapałka A., Fóti G., Comninellis Ch. (2008). Kinetic modelling of the electrochemical mineralization of organic pollutants for wastewater treatment. Journal of Applied Electrochemistry 38, 7–16. doi:10.1007/s10800-007-9365-6