Mathematical Modeling and Simulation of Metal Hydride Hydrogen Storage

Abstract

Abstract. Energy storage is considered one of the most challenging with the rising energy demands. High energy density requires more extended storage than traditional storage. Recently, hydrogen has been considered one of the solutions for the future energy transition in terms of several aspects, such as hydrogen generation, safety, and storage. Metal hydride hydrogen storage has gained much interest as a possible medium for ample storage. This study introduces mathematical modeling and numerical simulation of metal hydride hydrogen storage. The metal hydride is a porous medium that absorbs or releases hydrogen under different heat transfer conditions. The mathematical model should clearly describe the complicated physics in the metal hydride hydrogen storage, such as absorbent, transport in porous media, and extracting the hydrogen from the absorbent material. Therefore, heat and mass transfer to and from the metal hydride is critical in the storage process. Moreover, since the pressure inside the bed is moderate, hydrogen is considered an ideal gas. It is assumed that the solid phase is isotropic and uniformly porous. The Van't Hoff equation expresses the gas pressure equilibrium. The hydrogen invades the alloy bed, and metal grains absorb it, which leads to density variation. This change in hydride density produces both absorption reaction and diffusive movement due to the hydride concentration, where the porosity and diffusion movement coefficient will be constant. Based on that, governing partial differential equations are provided in polar coordinates along with algebraic empirical relationships and initial/boundary conditions. Then, the developed mathematical system was solved numerically using the mixed finite element. The results have been presented and discussed by considering possible heating/cooling scenarios. It was found that hydrogen reaction with the porous hybrid metal, including density variation, depends mainly on the heating and cooling efficiency.