(Digital Presentation) Modeling Water Transport in Proton Exchange Membrane Electrolyzers through First Principles
Authors: Motupally Shikhar , Mishra Lubhani , Subramanian Venkat R. 
Published: February 2024

The efforts to decarbonize transportation and heavy industries, like agricultural chemicals, steel, etc., have increased over the past decade [1-2]. A practical solution to these efforts is using renewable energy (wind, solar, hydro) to produce hydrogen to replace fossil fuels in these energy-intensive applications [1]. The production of hydrogen via water electrolysis has been receiving tremendous attention over the past few years [1-3]. There are mainly three technologies that are employed for water electrolysis – alkaline, polymer electrolyte membrane (PEM), and solid oxide [3]. Intermittent renewable energy provides an advantage to PEM electrolysis due to the robustness of the technology capable of multiple start-stops and variation in applied power [4].
PEM electrolyzer technology is improving and becoming market-ready in several countries [3]. The current focus on PEM electrolyzers ranges from improving lifetimes and electrical efficiency, reducing cost by the development of advanced materials/designs, and simplifying the balance of plant/systems designs [1]. The mathematical modeling of PEM electrolyzers is thus an active area of research for substantially reducing development costs and timelines and improving electrolyzer designs [3-4]. However, there are certain phenomena with PEM electrolysis where the current models are semi-empirical and simple first principles-based mechanistic quantifications are lacking.
Figure 1 shows a simplified schematic of the physical and chemical phenomena during the operation of a PEM electrolyzer. The anode and cathode are divided by a membrane that is capable of exchanging cations across. The membrane is coated with catalyst layers on both sides to facilitate the reactions. Typical membranes used in electrolyzers belong to the Nafion® family and are perfluorosulfonic acid-based materials [3-7]. Porous transport layers are used to facilitate the interaction between gas and liquid phases in the cell. Water is fed to the anode side of the electrolyzer and is oxidized to produce oxygen gas. Typically, no water is fed to the cathode, since the anode is maintained at a high pressure (~3-70 bar), liquid water condenses and exits the electrolyzer with the hydrogen. The hydrogen gas is fed through a dryer before it is deemed suitable for use. The oxygen gas is also dried and used where needed.
In this work, we present a first principles-based water transport model to quantify the movement of water across the electrolyzer cell and predict the quality of the hydrogen gas produced as a function of varying operating conditions and cell designs [4,8,9]. To model the movement of water on the cathode side, three sets of equations are obtained – I. material balances for hydrogen and water in the flow channel (z-direction), II. water movement across the membrane in the x-direction, and III. expressions for variable membrane properties to serve as inputs for I and II [4,5,6,8]. For water movement across the membrane, we consider the contributions from diffusion, electro-osmotic drag, and pressure-driven flow. The condensation of water at the cathode is also modeled to understand the respective transport contributions from the vapor and liquid phases. The coupled equation sets are solved using a Runge-Kutta ODE routine with appropriate boundary conditions. The results of the modeling case studies will be compared with the experimental data available for water transport [9].

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Figure 1