Dynamics of a compressible gas injected into a confined porous layer

Underground gas storage is a critical technology in global efforts to mitigate climate change. In particular, hydrogen storage offers a promising solution for integrating renewable energy into the power grid. When injected into the subsurface, hydrogen’s low viscosity compared with the resident brine causes a bubble of hydrogen trapped beneath caprock to spread rapidly into an aquifer through release of a thin gas layer above the brine, complicating recovery. In long aquifers, the large viscous pressure drop between source and outlet induces significant pressure variations, potentially leading to substantial density changes in the injected gas. To examine the role of gas compressibility in the spreading dynamics, we use long-wave theory to derive coupled nonlinear evolution equations for the gas pressure and gas/liquid interface height, focusing on the limit of long domains, weak gas compressibility and low gas/liquid viscosity ratio. Simulations are supplemented with a comprehensive asymptotic analysis of parameter regimes. Unlike the near-incompressible limit, in which gas spreading rates are dictated by the source strength and viscosity ratio, and compressive effects are transient, we show how compression of the main gas bubble can generate dynamic pressure changes that are coupled to those in the thin gas layer that spreads over the liquid, with compressive effects having a sustained influence along the layer. This coupling allows compressibility to reduce spreading rates and gas pressures. We characterise this behaviour via a set of low-order models that reveal dominant scalings, highlighting the role of compressibility in mediating the evolution of the gas layer.