Qué responde: con la corriente de la celda, el área de cada cátodo y el número de cátodos, esta calculadora entrega la densidad de corriente catódica; con el tiempo de deposición, la eficiencia de corriente y la tensión, entrega además cuánto metal se deposita por hora y por día y cuánta energía consume cada tonelada. Es el cálculo que se hace antes de decidir si conviene subir la corriente o si el problema está en otra parte de la casa de tanques.
This calculator converts your cell current and cathode area into current density, applies Faraday's law to give theoretical production, corrects it by current efficiency, and turns cell voltage into specific energy consumption per tonne of metal. It is a mass-balance tool for sizing a cell house or interpreting a bench cell — not a deposit-quality prediction, which depends on electrolyte flow, temperature and additives as well as on current density.
Results
The results appear here and update as you type. Each result is followed by the conditions under which it holds.
How to use it
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Fix the cathode area correctly
Count only the wetted cathode area that the current actually travels through. Including anodes, or counting both faces of a plate that is immersed on one side only, is the most common source of a wrong current density.
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Divide current by area
Current density is total cell current divided by total cathode area. It is the number that governs deposit morphology, cell voltage and the acceptable impurity level in the electrolyte.
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Apply Faraday's law
The theoretical mass follows from current, time and the electrochemical equivalent mass of the metal. No assumptions are needed here — it is stoichiometry.
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Correct for current efficiency
Multiply by measured current efficiency. Determine it by weighing the actual deposit against the theoretical mass for the charge passed — that single measurement is the most useful diagnostic you can run on an electrowinning cell.
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Convert voltage into energy
Specific energy is proportional to cell voltage and inversely proportional to current efficiency. Every part of the cell voltage above the decomposition potential is waste heat that has to be removed from the cell house.
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Sanity-check against the operating band
Compare the current density with the range normally run for your metal and electrolyte. If it is far outside it, expect a deposit problem before an energy problem.
Formulas used
Total cathode area A = plate area × number of cathodes
Current density CD = I / A [A/m²]
Theoretical mass m = (I × t × M_eq) / F [g]
F = 96 485 C/mol ; M_eq in g per mole of electrons
Actual mass = theoretical × current efficiency
Specific energy W = V / (M_eq × CE) × 26 801 [kWh per tonne]
factor 26 801 = 3 600 000 × 1000 / (96 485 × 1000) grouped for g and tonne
Cell power = I × V [W]Assumptions & applicability
- ★ Electrochemical parameters are given as engineering estimates only. Current density, current efficiency and cell voltage are all system-specific — they depend on electrolyte composition, temperature, circulation, additives and electrode spacing — and no single-point value should be treated as a specification.
- Faraday's law is applied to a single-electron-transfer half reaction at 100% faradaic selectivity before the efficiency correction. Side reactions competing for the same current are lumped into the current efficiency you enter.
- Current efficiency is taken as a measured input, not predicted. Iron cycling between anode and cathode, short circuits and dendritic growth all reduce it and none of them can be calculated from the data entered here.
- Cell voltage is taken as measured across the busbars. The split between decomposition potential, overpotential, electrolyte ohmic drop and contact resistance is not modelled.
- Specific energy is per tonne of metal deposited and excludes rectifier losses, cell house ventilation, and any heating or cooling of the electrolyte.
- Deposit quality — smoothness, nodulation, adhesion and purity — is NOT predicted. It depends strongly on the same variables and must be established experimentally.
FAQ
What current density should I run for copper electrowinning?
Most copper tankhouses operate in the range of roughly 250 to 350 A/m², with some running higher. Treat that as a reference band rather than a target: the practical ceiling for a given electrolyte usually shows up first as rough, nodular or dendritic deposit, and the limit depends on electrolyte temperature, circulation rate, acid concentration and additive regime. Establish it in a bench cell with your own solution.
Why is my current efficiency lower than expected?
The usual causes, roughly in order of how often they appear: ferric iron in the electrolyte cycling between the electrodes without depositing metal; electrical short circuits through nodules or misaligned plates; low electrolyte temperature; and leakage current losses. Weighing the deposit and comparing it with the Faraday prediction tells you that you have a loss but not which one — measure the iron concentration first, as it is the most common single cause.
How much energy does electrowinning consume?
Copper electrowinning typically falls in the range of about 1,800 to 2,500 kWh per tonne of cathode, depending mainly on cell voltage and current efficiency. Since specific energy is proportional to voltage and inversely proportional to efficiency, the fastest route to lower energy cost is normally reducing the electrolyte ohmic drop — by shortening the electrode gap or improving conductivity — rather than pushing current density in either direction.
Equipment sized with this calculation
Further reading
Reference entry TL-ELECTROWINNING-CURRENT-DENSITY. The calculator returns a pre-feasibility number. For a quotation we need the feed assay, throughput, medium and temperature — and, where the result hinges on it, test data from your own material.
Send the campaign results — we return the configuration, the calculation and what we would change in the next test round.
Qué calcula
La primera salida es geométrica: el área catódica total, es decir el área de una cara sumergida multiplicada por el número de cátodos. Con ella se obtiene la densidad de corriente. Después entra la ley de Faraday: la masa teórica depositada en un tiempo dado, corregida por la eficiencia de corriente para dar la masa real, la producción diaria y el depósito por cátodo y por ciclo. Al final, la energía específica en kWh por tonelada y la potencia que dibuja la celda.
Datos de entrada
| Dato | Qué representa | Unidad |
|---|---|---|
| Metal a depositar | Determina el equivalente electroquímico M_eq | — |
| Corriente de celda | Corriente total que atraviesa la celda | A |
| Área catódica por placa | Área de una cara sumergida de la placa | m² |
| Número de cátodos | Cátodos en la celda | — |
| Eficiencia de corriente | Fracción de la carga que efectivamente deposita metal | % |
| Tensión de celda | Tensión medida entre barras colectoras | V |
| Tiempo de deposición | Duración del ciclo | h |
Cómo se calcula
El área total de cátodos es A = área de placa × número de cátodos y la densidad de corriente es la corriente dividida por esa área: CD = I / A, en A/m². La masa teórica sigue la ley de Faraday, con F = 96 485 C/mol y M_eq en gramos por mol de electrones:
m = (I × t × M_eq) / F
La masa real es masa real = masa teórica × eficiencia de corriente. La energía específica se obtiene con W = V / (M_eq × CE) × 26 801, en kWh por tonelada, donde el factor 26 801 agrupa la conversión de segundos a horas y de gramos a toneladas. La potencia de la celda es simplemente I × V, en W.
Cómo leer el resultado
La densidad de corriente no es un objetivo en sí: es el resultado de haber elegido corriente y área. Súbala sólo mientras el depósito siga siendo liso y adherente; el primer signo de límite es la rugosidad, luego la nodulación y después la dendrita que provoca cortocircuito. La brecha entre producción teórica y real es la eficiencia de corriente que se ingresó, de modo que sirve como control: si la producción pesada en planta se aleja de la real calculada, hay una pérdida no contabilizada. En energía, recuerde que la cifra es por tonelada depositada y no incluye pérdidas de rectificador, ventilación de la nave ni calefacción o enfriamiento del electrolito.
Errores frecuentes
- Usar el área de las dos caras de la placa cuando sólo una está sumergida y enfrentada al ánodo: la densidad de corriente sale a la mitad.
- Suponer una eficiencia de corriente en lugar de medirla. El hierro férrico, los cortocircuitos y la temperatura baja son pérdidas que no se pueden calcular con estos datos.
- Esperar que la calculadora prediga la calidad del depósito. No lo hace: la lisura, la nodulación, la adherencia y la pureza dependen de las mismas variables y deben establecerse experimentalmente.
- Comparar consumos específicos medidos en la celda con consumos de la casa de tanques completa, que incluyen rectificador y servicios.
Para pasar de una estimación a una cifra de diseño hacen falta la concentración de hierro, el régimen de aditivos, la temperatura y el caudal de circulación. Con esos datos se puede fijar la densidad de corriente que el depósito admite, que es la que finalmente manda sobre la producción.