Thermohydraulic Leaky Tank Model for Inventory Analysis of Hydrogen Storage, Loading, and Unloading in Subsurface Salt Caverns

Summary The formulation of hydrogen gas thermodynamics and behavior is incorporated into mass, momentum, and energy conservation equations to determine the conditions of hydrogen reserves in subsurface storage salt caverns coupled with the inflow and outflow through loading/unloading wells. The hydrogen storage salt cavern is treated like a leaky tank having permeable and conductive walls allowing heat transfer and gas leakage through the interlayer formations, and the cracks and fractures created by thermal and stress variation during hydrogen loading/unloading processes. The numerical solution of the set of differential equations forming the dynamic thermohydraulic mathematical model subject to prescribed initial and boundary conditions can be facilitated to determine the temperature, pressure, flow, and accumulation/depletion conditions as functions of time during loading, storage, and unloading. This allows an effective inventory analysis of hydrogen storage in subsurface salt caverns. This paper provides the relevant thermodynamics relationships and the important theoretical background and mathematical formulations required for the development of large-scale simulators, which can be applied for effective designing, optimizing, controlling, management, and inventory analysis of the hydrogen gas storage processes in large subsurface salt caverns, practical view and concept of the salt cavern storage of the hydrogen gas as a leaky tank, description of the hydrogen gas behavior and storage processes in subsurface salt caverns at different levels of sophistication, rigorous mathematical formulations of the theoretical relationships of the governing processes at the subsurface salt cavern storage pressure and temperature conditions, and the demonstration of an application and numerical solution by a simplified salt cavern macroscopic model. The rigorous mathematical formulations of the theoretical relationships of the governing processes at the subsurface salt cavern storage pressure and temperature conditions are developed. The relevant thermodynamics relationships and the comprehensive mass, momentum, and energy balance equations at various levels of complexity are provided. This paper develops the microscopic balance equations of the gas stored inside the salt cavern, macroscopic balance equations for the porous salt rock formation surrounding the salt cavern, salt cavern control volume-averaged macroscopic balance equations, heat transfer and gas leakage between the salt cavern gas and the salt rock formation, and transforming transport equations to simple convenient forms by combining the time and radial distance variables into a single combined variable. The numerical solution of the full set of complex differential equations presented in this paper requires the application of advanced numerical methods for generating numerical solutions for hydrogen gas storage, loading, and unloading by considering the actual shape of the subsurface salt caverns. The formulations developed in this paper are applied for a simplified case involving a cylindrical shape-elongated salt cavern accessed by a single well both for loading and unloading. The application was presented using a practical and accurate equation of state (EOS) for hydrogen. The numerical solution was accomplished using Euler’s method. The numerical results indicate that temperature and pressure decrease by gas expansion during hydrogen gas unloading and vice versa during hydrogen gas loading.