Analytical solutions for two-phase subsurface flow to a leaky fault considering vertical flow effects and fault properties

Conductive faults in geologic formations can serve as leakage pathways for fluids such as CO₂ and methane, which would otherwise remain trapped beneath low-permeability layers. To estimate leakage rates and the associated pressure effects on adjacent aquifers, modeling of the flow in the vicinity of leaky faults must be performed. The flow from an aquifer to a leaky fault is controlled by aquifer properties as well as fault properties, including the fault permeability, fault width, and anisotropy in the fault permeability. Depending on aquifer properties and leakage rates, vertical flow equilibrium may not be reached in the aquifer in the vicinity of the leaky fault. Therefore, analytical solutions for leakage through faults that allow for vertical flow need to be developed. To do this, the vertically integrated form of the two-phase flow formulation based on vertical equilibrium is expanded by assuming a linearly structured vertical flow field, and steady state analytical solutions for single-phase and two-phase leakage are derived. In the case of two-phase leakage, anisotropic aquifer permeabilities are shown to produce stronger vertical flow effects than in the case of single-phase leakage. Using numerical simulations, a model representing fault properties that is compatible with the analytical solutions is developed. The combination of the fault model and the analytical solutions captures the effects of leakage through faults with different properties and vertical flow effects. The incorporation of this fault model/analytical solution in larger basin-wide multiscale models can enable subgrid-scale effects due to leakage through faults to be captured with improved efficiency.