Multiphase flow simulation in deformable porous media using DEM

Abstract

Multiphase flow in deformable porous media underpins a wide array of energy and environmental applications, including enhanced oil and gas recovery, geological carbon and hydrogen storage, and groundwater remediation. The efficiency, safety, and predictability of these operations hinge on the coupled interactions between immiscible fluids and the evolving solid skeleton at the pore scale, which govern the onset of flow instabilities, fracture propagation, and overall displacement efficiency. However, traditional models often neglect key aspects such as matrix deformation, gas compressibility, and the influence of confining stress, limiting their ability to predict or control complex flow patterns in realistic geological settings.

This thesis develops and applies a fully coupled hydro-mechanical discrete element method (HM-DEM) framework to systematically investigate multiphase flow in deformable granular media. The model integrates an implicit, large-timestep pressure solver with explicit grain mechanics, enabling efficient and robust simulation of both stable (high-viscosity) and unstable (low-viscosity) displacement regimes, as well as the direct incorporation of fluid compressibility and dynamically evolving pore structure. Validation against benchmark Hele–Shaw and granular displacement experiments demonstrates the model’s ability to faithfully reproduce a rich diversity of flow regimes—including infiltration-dominated (viscous fingering, capillary fingering, and stable displacement) and fracture-dominated patterns—across a wide range of operational and boundary conditions.

For the first time, the framework systematically extracts and analyzes grain-scale quantities—including viscous and capillary pressures, interfacial energies, contact forces, and flow resistances—to provide unprecedented mechanistic insight into the micro-scale fluid–fluid and fluid–grain interactions that underpin pattern formation and transition. This mechanistic approach enables a fundamental understanding of how and why various flow morphologies arise as a function of capillary number, confining stress, compressibility, and other critical parameters.

Using this HM-DEM framework, two central research thrusts were pursued. First, the role of confining stress and boundary conditions in stable displacement was elucidated, revealing how mechanical resistance governs transitions between infiltration- and fracture-dominated regimes. A novel regime classification metric, combining flow-front sphericity and area ratio, was introduced, along with a dimensionless phase diagram that generalizes findings across practical scenarios. Second, the impact of gas compressibility on unstable drainage was investigated, leading to the introduction of a dimensionless compressibility number that, together with the capillary number, predicts pattern transitions and breakthrough energetics in compressible injection operations. In both thrusts, energy-based metrics were formulated to directly link observed flow morphologies to operational efficiency and energy dissipation, providing practical guidance for optimizing field-scale injection strategies.

This thesis’ mechanistic grain-scale analysis provides critical new insights into the control of flow instabilities and the trade-offs between displacement efficiency and formation integrity. The research demonstrates that confining stress and gas compressibility, alongside capillary number, are key dimensionless parameters for predicting and tuning flow regimes in deformable, multiphase systems. The extensible HM-DEM platform, validated with experimental data, bridges the gap between laboratory and field scales, enabling the formulation of operational metrics directly relevant to subsurface energy storage, waste disposal, and resource extraction.

Future work will enhance the model by incorporating cemented and cohesive granular media, extending regime maps to imbibition and wettability-controlled flows, and systematically exploring the effects of confining stress and gas compressibility in both stable and unstable displacement regimes. Collectively, this thesis establishes a robust computational foundation for the predictive design and management of multiphase flow in complex, deformable porous environments.