Numerical modeling and experimental validation of two-phase flow in porous media.

Transitioning to low-emission energy systems involves subsurface activities such as carbon capture and storage (CCS), geological hydrogen storage, and the sealing and abandoning old hydrocarbon wells. Whether tracking the natural transportation of fluid in the subsurface or injecting CO₂ or H₂, these phenomena are primarily determined by multiphase fluid flow, the deformation of the rock matrix, and chemical fluid-rock interactions. Developing a comprehensive understanding of these processes is essential for reliable assessment of the potential of future storage sites. Here we present newly developed numerical models and validate them with the results of laboratory experiments in transparent microfluidics cells.

Over the last decade, the computational power of Graphics Processing Units (GPUs) showed remarkable growth in absolute terms, per unit cost, and per unit power.  At the same time, novel parallel algorithms and efficient and concise high-level packages (e.g., ParallStencil.jl) significantly reduced the difficulty of code development. Therefore, we build a new, robust numerical model to simulate two-phase flow in porous media. The governing equations are derived from the conservation of mass and momentum, which, in the simplest case, results in a coupled system of an elliptic (fluid pressure) and nonlinear advection (saturation) equation, known as the Buckley-Leverett equation. The system of equations is solved with the pseudo-transient method, using staggered grid finite element discretization with a first-order advection scheme (upwind). The model is written in Julia language using GPU-ready algorithms, well suited to exploit the parallel computational efficiency of modern GPU platforms. This will allow detailed simulations of sophisticated subsurface processes. In our presentation, we will briefly discuss the numerical strategies used to apply the pseudo-transient method, traditionally used for elliptic equations, to coupled elliptic-advective systems. We will demonstrate that the numerical method is able to resolve shock fronts with reasonable accuracy.

The numerical results are compared with laboratory experiments in transparent microfluidics cells. The experiments conducted utilizing the microfluidics cell were developed to reproduce the pore-scale behavior of subsurface reservoirs. The experimental setup modeled the injection and displacement of a gas phase (representing H₂ with N₂) inside a medium similar to inert sandstone. Different injection rates were studied to assess the influence on gas distribution and preservation during injecting and backflow mechanisms. Capillary forces, pore-scale interactions, and gas bubble dynamics were analyzed comprehensively by visualization of gas flow pathways. Results from the experiments provide a benchmark for validating the numerical models, mainly in obtaining the impact of injection rate on gas emplacement, efficiency of displacement, and retention of residual gas in porous media.