Multiphase flow and transport in underground hydrogen storage

Abstract

The accelerating climate crisis demands rapid deployment of new technologies. Underground hydrogen storage offers a means to store renewable energy in subsurface porous formations. Its successful implementation requires a detailed understanding of hydrogen flow and transport in porous media, which exhibit complex behaviour due to hydrogen’s unique hydrodynamic and molecular properties. In this thesis, we use theoretical modelling to investigate Darcy-scale flow and multiscale transport of hydrogen in porous formations. First, we extend existing long-wave models of gas injection into a water-saturated planar channel to incorporate the effects of gas compressibility. The coupled evolution of the interface height and pressure field is governed by two nonlinear partial differential equations. Focusing on long domains, high gas mobility, and weak compressibility, we use asymptotic analysis to develop reduced-order models that capture the dominant behaviour across a broad range of parameter space, and validate these models against full numerical simulations. Our analysis demonstrates that compressibility can significantly alter plume dynamics, reducing the spreading rate relative to the near-incompressible limit through two distinct mechanisms: flux-driven spreading and pressure-driven spreading. These effects are further quantified across parameter space via the characteristic scales for pressure, pressure rise time, and breakthrough time, as revealed by the asymptotic analysis. Next, we develop an incompressible model for gas injection into curved, axisymmetric porous channels. By expressing the governing equations in coordinates local to the channel geometry, we use a composite approximation to derive an evolution equation for the gas–liquid interface. In the limit of weak curvature and shallow channel slopes, this reduces to a simpler evolution equation that is more amenable to asymptotic analysis. Using these models, we investigate the dynamics of gas plume evolution in parabolic and Gaussian-shaped channels in the high-gas-mobility limit. In a parabolic channel, when buoyancy effects are relatively weak, we show how the increasing channel slope drives a competition between injection and buoyancy, producing distinct spreading rates and interface dynamics across different timescales. In a Gaussian channel, we demonstrate that attenuation of the gas velocity allows buoyancy effects to influence the late-time dynamics. Finally, we investigate the influence of spatial heterogeneity in diffusivity on hydrogen leakage through the caprock, modelled as an oscillatory forced diffusive–reactive transport process. The mean diffusivity is perturbed by a Gaussian random field with a squared–exponential covariance to represent spatial uncertainty. Using a Green’s function approach, we derive integral mappings between the statistical moments of the diffusivity field and those of the concentration field. Analytical evaluation of these integrals provides approximations for the first and second moments, enabling systematic exploration of their dependence on key parameters without the computational cost of Monte Carlo simulations. The analysis shows that uncertainty is maximised when the correlation length matches the diffusion–reaction length scale and the forcing frequency is comparable to the reaction rate.

Date of Award	22 Jun 2026
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Igor Chernyavsky (Main Supervisor), Oliver Jensen (Co Supervisor), Lin Ma (Co Supervisor) & Radha Boya (Co Supervisor)