Revealing the Hydrogen Production Efficiency Part 2! Photovoltaic Electrolysis Hydrogen Production Efficiency: Calculation of Electrical Energy Transfer Efficiency and Proton Exchange Membrane Efficiency

In the previous article "Calculation Method for Hydrogen Production Efficiency of Photovoltaic Electrolysis Device," we have already learned about one of the three factors influencing the efficiency of hydrogen production in photovoltaic electrolysis—photovoltaic cell efficiency η_m. In this article, we will continue to discuss the remaining two key factors, the transfer efficiency η_t between the photovoltaic cell and the electrolysis cell, and the proton exchange membrane efficiency η_e. They directly impact the feasibility and efficiency of hydrogen production in the photovoltaic electrolysis cell.

Transfer Efficiency η_t

Transfer efficiency η_t is relatively simple to calculate. It only requires obtaining the maximum output energy of the photovoltaic cell and the maximum energy input to the electrolysis cell. The calculation method for transfer efficiency η_t is as follows:

p_e is the energy input to the electrolysis cell, measured in J;

p_m is the maximum energy output of the photovoltaic cell, measured in J.

Proton Exchange Membrane Efficiency η_e

Another important factor—proton exchange membrane efficiency η_e—has a more complex calculation process involving multiple parameters that need to be discussed separately.

The calculation method for proton exchange membrane efficiency η_e is as follows^[1]:

is the hydrogen outlet flow rate, measured in L/min;

(Lower Heating Value) is the amount of heat released per unit mass of fuel under complete combustion conditions, i.e., the heat released per gram of H₂ in complete combustion. It is usually around 120-142 MJ/kg, and the specific value may vary due to the purity of hydrogen or other factors;

P_e is the power of the electrolysis cell, measured in W (Note: The calculation of electrolysis cell power P_e involves many parameters and will be discussed separately in later articles, not covered in this article).

Q_e is the heat required for the electrolysis cell to decompose water. According to the nature of the chemical reaction, the reaction of decomposing water in the electrolysis cell needs to absorb a certain amount of heat to overcome intermolecular forces and decompose water molecules into their components. This heat absorbed by the reaction is called the thermodynamic heat of the reaction, usually measured in J;

is the heat required for preheating the water supplied to the electrolysis cell. Since the working temperature of the electrolysis cell is often higher than room temperature, and water needs to be continuously supplied during the electrolysis process, preheating of the water is required before the supply to reach the working temperature of the electrolysis cell, measured in J.

Here are the specific calculation methods for each parameter:

1. Hydrogen outlet flow rate :

I_e is the current of the electrolysis cell, measured in A, which is the product of current density and electrode area:

i_e is the current density, and A_e is the effective electrode area of the electrolysis cell.

F is Faraday's constant, with a value of 96485 C/mol.

2. Heat demand of the electrolysis cell Q_e:

I_e is the current of the electrolysis cell, measured in A, which is the product of current density and electrode area:

i_e is the current density, measured in A/cm², and A_e is the effective electrode area of the electrolysis cell, measured in cm²;

F is Faraday's constant, with a value of 96485 C/mol;

T is the temperature, measured in K;

ΔS is the molar entropy change of the water decomposition reaction, approximately 326.61 J/(mol∙K);

V_con, V_act, V_ohm are the concentration overpotential, activation overpotential, and ohmic overpotential, respectively. The specific calculation process is complex and involves multiple variables, and will be explained in detail in subsequent articles, so stay tuned!

3. Heat required for preheating water supplied to the electrolysis cell :

Since the working temperature of the electrolysis cell is often higher than room temperature, and water needs to be continuously supplied during the electrolysis process, preheating of the water is required before the supply to reach the working temperature of the electrolysis cell.

The calculation method is as follows:

is the inlet water rate, generally measured in L/min;

φ is the efficiency of the heat accumulator, indicating the ability to release and store energy. The efficiency of heat accumulators of different types and manufactured by different manufacturers may vary. Specific values need to be consulted in the relevant product documentation or with relevant technical personnel;

I_e is the current of the electrolysis cell, measured in A, which is the product of current density and electrode area:

i_e is the current density, and A_e is the effective electrode area of the electrolysis cell;

F is Faraday's constant, with a value of 96485 C/mol;

is the molar heat capacity of reactants/products, expressing the heat absorbed or released per unit mole of substance under unit mole quantity. It is usually measured in J/(mol∙K).

The information provided above is sourced from literature, and the editor has only compiled it. If there are any errors, please kindly point them out in a timely manner!

References

[1] Zhang H, Su S, Lin G, et al. Efficiency calculation and configuration design of a PEM electrolyzer system for hydrogen production[J]. International journal of electrochemical science, 2012, 7(4): 4143-4157.