In the articles "Calculation Method for Hydrogen Production Efficiency of Photovoltaic Electrolysis Devices" and "Calculation Method for Electrical Transfer Efficiency and Proton Exchange Membrane Efficiency," we have already learned about the three factors influencing the efficiency of hydrogen production in photovoltaic electrolysis: photovoltaic cell efficiency ηm, transfer efficiency between photovoltaic cells and electrolytic cells ηt, and proton exchange membrane efficiency ηe. These factors directly impact the feasibility and efficiency of hydrogen production in photovoltaic electrolysis cells.
Among these, the calculation formula for the proton exchange membrane efficiency ηe involves an important parameter—electrolytic cell power Pe. Due to its complex calculation process, it was not discussed in detail in the previous text, and this issue will be the focus of this edition.
The calculation method for the power of the electrolytic cell Pe is as follows:
Where RI is the equivalent internal resistance of the electrolytic cell, a combination of the internal resistance of the electrolytic cell and the parallel resistance of the electrolyte, measured in Ω;
RL is the leakage resistance, reflecting the degree of leakage of the electrolytic cell, the resistance value of the membrane between the cathode and anode chambers inside the electrolytic cell, measured in Ω;
E is the minimum voltage required for the water decomposition reaction, theoretically 1.23 V; in practical use, it needs to be determined based on actual conditions, measured in V;
Vcon is the concentration overpotential, the overpotential caused by the concentration difference of the electrolyte during electrolysis, measured in V;
Vact is the activation overpotential, indicating the additional energy needed in electrochemical reactions. The activation overpotential of the anode is mainly determined by the rate of hydroxide ion generation, while the activation overpotential of the cathode is mainly determined by the rate of oxygen reduction, measured in V;
Vohm is the ohmic overpotential, the change in electrode surface potential with increasing current density, measured in V;
Ie is the current of the electrolytic cell;
Ve is the voltage of the electrolytic cell, measured in V.
The calculation method for the current of the electrolytic cell Ie is as follows:
Where ie is the current density, measured in A/m²;
Ae is the effective area of the electrolytic cell electrodes, measured in m².
The calculation method for the equivalent internal resistance of the electrolytic cell RI is as follows:
Where Vcon is the concentration overpotential, Vact is the activation overpotential, Vohm is the ohmic overpotential, and Ie is the current of the electrolytic cell.
The calculation method for the voltage of the electrolytic cell Ve is as follows:
The calculation method for the minimum voltage required for the water decomposition reaction E is as follows:
Where T is the operating temperature of the electrolytic cell, T0 is the ambient temperature, pH2, pO2, pH2O are the partial pressures of reactants/products; Vcon is the concentration overpotential, Vact is the activation overpotential, Vohm is the ohmic overpotential.
The calculation method for the concentration overpotential Vcon is as follows:
At low current densities, the concentration overpotential Vcon can be negligible (ie < 10000 Am⁻²).
Where ie is the current density, β1 is a constant related to temperature, obtained by consulting relevant literature or fitting experimental data, iL is the limiting current density, and β2 is a constant obtained by consulting relevant literature or fitting experimental data.
The calculation method for the activation overpotential Vact is as follows:
Where R is the gas constant (8.314 J/mol·K⁻¹), ne is the number of electrons involved in the reaction, F is Faraday's constant (96485 C/mol), i0 is the alternating current density (1.08×10-17e^0.086T), and T is the temperature measured in K.
The calculation method for the ohmic overpotential Vohm is as follows:
Where dm is the thickness of the membrane measured in mm, τm is the conductivity of the membrane, representing the ability of the electrolyte to conduct current over a unit length (usually 1 m), measured in S/m.
The calculation method for the conductivity of the membrane τm is as follows:
Where φm is the membrane humidity calculated as follows:
When the membrane is fully humidified, the water activity of the membrane (a) is 1; T is the temperature measured in K.
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