# Evolutionary Design Optimization of an Alkaline Water Electrolysis Cell for Hydrogen Production
## 1 Introduction  
Mitigation of the climate change consequences is the main global challenge in the 21 century. The different IPCC (Intergovernmental Panel on Climate Change) reports stated that the climate change is mainly due to greenhouse gas emissions to the atmosphere produced by human activities. The IPCC recommends in their scenarios the decrease of energy consumption, the increase of renewable production, and sequestration of harmful CO2 produced by the industrial activities including the production of cement and steel. The renewable energies generated from various systems such as wind turbines and photovoltaic panels do not produce greenhouse gases but suffer from time intermittencyand geographic limitations. In order to resolve this challenge, energy produced at off-peak hours must be stored. Batteries can store this energy, but their energy density is low, and they discharge the stored energy over time. Thus, if the energy needs to be stored more than a month, another storage mean must be provided. Hydrogen storage can store (renewable) energy with a high density for a long period and its use (by combustion and by reduction) only produces water. Most hydrogen is currently produced via a process that needs fossil fuels and which produces greenhouse gases. However, although there exist several other processes that can generate hydrogen without generating pollutants, water electrolysis is one of these processes and is very promising. Nevertheless, the high operation cost hampers its development. One way to decrease the cost is to choose the cheapest water electrolysis technology: Alkaline water electrolysis. There are two other technologies: PEM electrolysis and high temperature electrolysis. They both are theoretically more efficient than alkaline water electrolysis but they need noble and expensive material (PEM) or suffer from low life duration (high temperature electrolysis). Although alkaline electrolysis is the cheapest technology among all the electrolysis technology, it is still needed to decrease the hydrogen cost. Like most electrochemical processes, the cost of the hydrogen production is divided into two parts: CAPEX and OPEX. CAPEX represents the capital cost divided by the total hydrogen production. The OPEX is the production process cost. Thus, the higher the cell voltage increase, the higher the OPEX is. The cell voltage is a sum of overvoltage as shown in Equation (1). \[U_{cell}(j)=E_{rev}(P,T)\ +\ R(T,\ Y_{KOH},\varepsilon)\ j\ +\ \eta_{act\ ann}\bigg{(}\frac{j}{1\ -\ \theta}\bigg{)}\ +\ \eta_{act\ cath}\bigg{(}\frac{j}{1\ -\ \theta}\bigg{)}\ +\ R_{memb}\ j \tag{1}\]  
\(E_{rev}\) is the reversible voltage in V, \(\eta_{act}\) is the activation overvoltage in V, \(R\) and \(R_{memb}\) respectively the electrolyte resistance and membrane resistance in \(\Omega\) cm\({}^{2}\) and, \(j\) the current density in A m\({}^{-2}\). The \(E_{rev}\) voltage represents the minimum thermodynamic cell voltage. This value is around 1.23 V at atmospheric pressure at 25 \({}^{\circ}\)C. Increasing temperature and decreasing the pressure decrease this minimum cell voltage. The majority of previous studies have focused on finding a cheap, robust and electroactive electrode material or electrocataly to decrease the activation overpotential, which are the second and third terms in Equation (1). There is also another research trend aiming at increasing efficiency, which is to reduce an ohmic resistance and surface coverage through electrolyzer design by means of simulations or experiments. Previous studies modeled the void fraction and velocity distribution [1; 2; 3; 4; 5] or the cell voltage [6]. There exist only few studies about optimization of this process. [PERSON] et al. [7] showed that there exists an optimum current density for a given design of PEM electrolyzer. [PERSON] et al. [8] demonstrated that there exists an optimum of pressure for a given PEM electrolyzer. The goal of this study is to find the optimal design and the current density for an alkaline electrolysis cell.