Mechanical Model for Geomechanical Pumped Storage in Horizontal Fluid-Filled Lenses

Abstract

Pumped subsurface energy storage entails pumping fluid into fluid-filled lenses in subterranean rock formations during times of peak power production, and then later producing the fluid back to the surface to drive a turbine. A new mechanical model is developed for lens behavior during flowback (production), shut-in, and inflation (storage) stages. The model couples elastic deformation of the lens with Darcy-Weisbach fluid flow spanning the laminar to turbulent regimes. It includes an energy-based inlet boundary condition governing fluid flowing rate out of the lens and up to the Earth’s surface. It also introduces pressure-dependent leakoff of fluid to the surrounding rock and the impact of intact rock bridges, which can arise from the lens having multiple petals or lobes, on lens compliance. The model is then used to illustrate the transition from early-time gradual decline in wellhead pressure and flowing rate to eventual pinching of the lens width at the wellbore, leading to rapid decline of pressure and flowing rate. The model demonstrates the feasibility of efficient storage cycles that generate a desired amount of power over a desired time while avoiding pinching. Maximizing efficiency is shown to have at least two contrasting regimes depending on whether the fluid leakoff rate to the host rock is dependent on the fluid pressure. The development of this model is therefore an essential step in deployment of subsurface energy storage by providing a mechanical basis for storage lens design.