Electrochemical Engineering, Green Hydrogen & PEM / Alkaline Electrolyzers
PEM Electrolyzer Faradaic H2 Rate & LHV Efficiency Formula
Calculate Multi-Cell PEM / Alkaline Electrolyzer Stack DC Input Power (MW), Faradaic Hydrogen Mass Production Rate (kg H2/hr), Specific Stack Energy Consumption (kWh/kg H2), and Lower Heating Value (33.33 kWh/kg) Efficiency.
Link Faraday’s 2-electron law directly to kWh/kg green-hydrogen stack efficiency!
In a bipolar Proton-Exchange Membrane (PEM) or Alkaline water electrolyzer stack of N_cells wired electrically in series at stack current I (A), the same current passes through every cell—producing H2 mass rate m_H2 (kg/hr) = (N_cells * I * η_F * 3600 * 0.002016) / (2 * 96485), where η_F is Faradaic efficiency (~98%–99.5% after membrane gas crossover), F = 96,485 C/mol, and M_H2 = 0.002016 kg/mol! Dividing Stack DC Power P_kW = (N_cells * I * V_cell) / 1000 by m_H2 cancels N_cells * I completely, proving that Specific Stack Energy Consumption SEC (kWh/kg H2) depends ONLY on Operating Cell Voltage V_cell and η_F, benchmarked against hydrogen’s Lower Heating Value LHV = 33.33 kWh/kg!
Verify on a 3.7 MW Industrial PEM Stack—Series_Cell_Count = 400 cells (B2), Stack_Current = 5,000 A (B3), BeginningOfLife_Cell_Voltage = 1.85 V (B4 -> Stack DC Power = (400 * 5000 * 1.85) / 10^6 = 3.7000 MW in E2), and Faradaic_Efficiency = 0.99 (99.0%, B5): Hydrogen Production Rate reaches 74.47 kg H2/hr (E3), Specific Stack Energy Consumption is 3,700 / 74.4678 = 49.69 kWh/kg H2 (E4), and Stack LHV Efficiency is 33.33 / 49.6859 = 0.6708 (67.08% in E5)!
| PEM Electrolyzer Stack Metric (400 Cells, 5,000 A, V_cell = 1.85 V, η_F = 99%) | Formula | Verified Output |
|---|---|---|
| Stack DC Power Input (MW) | (N_cells * I_Amps * V_cell) / 1,000,000 | 3.7000 MW (4.2000 MW @ 2.10 V) |
| Faradaic H2 Output (kg/hr) | (N * I * η_F * 3600 * 0.002016) / (2 * 96485) | 74.47 kg/hr |
| Specific Stack Energy (kWh/kg) | Stack_Power_kW / H2_Rate_kg_hr | 49.69 kWh/kg (56.40 @ 2.10 V) |
| Stack LHV Efficiency | 33.33 / Specific_Energy_kWh_kg | 0.6708 (0.5910 @ 2.10 V EOL) |
PEM Electrolyzer Stack LHV Efficiency Formula
Validate N_cells >= 1, Current > 0, Cell_Voltage >= 1.23 V (low-temperature reversible Nernst water-splitting potential), and Faradaic_Efficiency in (0.50, 1]!
=LET(nc_s, B2, ia_s, B3, vc_v, B4, ef_f, B5, IF(OR(nc_s < 1, ia_s <= 0, vc_v < 1.23, vc_v > 3.5, ef_f <= 0.5, ef_f > 1), "Invalid Electrolyzer Stack Input", LET(pw_k, (nc_s * ia_s * vc_v) / 1000, mh_2, (nc_s * ia_s * ef_f * 3600 * 0.002016) / (2 * 96485), sc_e, pw_k / mh_2, ROUND(33.33 / sc_e, 4))))End-of-Life Catalyst Degradation Check (Set Cell Voltage = 2.10 V)
Model 60,000-hour membrane/iridium-anode voltage degradation by raising Cell_Voltage B4 from 1.85 V to 2.10 V at the same 5,000 A current: H2 output stays 74.47 kg/hr, while Stack Power E2 climbs to 4.20 MW, Specific Energy E4 rises to 56.40 kWh/kg, and LHV Efficiency E5 drops to 0.5910 (59.10%)!
=IF(ISTEXT(E5), E5, ROUND(((B2 * B3 * B4) / 1000) / ((B2 * B3 * B5 * 3600 * 0.002016) / (2 * 96485)), 2))Try the example
Use the original values or change them to test your understanding.