Countercurrent Imbibition in Porous Media with Dense and Parallel Microfractures: Numerical and Analytical Study

Abstract

Summary Countercurrent imbibition is the process in which the wetting fluid spontaneously displaces the nonwetting fluid, while the nonwetting fluid is recovered at the wetting fluid inlet. It is a major mechanism for the recovery of shale oil, shale gas, and tight oil. In shale and tight formations, microfractures are highly developed. Specifically, some typical formations, such as continental shales, consist of dense and parallel microfractures (DPFs). In DPF systems, microfractures are segregated by low-permeability matrix layers, while the very close distance betwen neighboring microfractures results in strong capillary correlation. The underlying assumptions of the classical dual-porosity (DP) model break down. Despite extensive studies on layered media, there is still no suitable model to describe imbibition in the DPF system at the representative elementary volume (REV) scale. In this study, we first numerically simulate countercurrent imbibition in DPF systems with fine grids, adopting typical continental shale parameters. For imbibition parallel to microfractures, two distinct stages are identified: an early stage where fractures are not correlated and a late stage where neighboring fractures are strongly correlated by capillarity. In both stages, cumulative oil production (Q) is proportional to the square root of imbibition time (t1/2), while the prefactors are very different. The late stage is the dominant stage in oil recovery. We note that the matrix permeability rarely contributes to imbibition parallel to microfractures at the late time, indicating that the matrix’s role here is to store fluid rather than to provide flow resistance. In addition, we rationalize the failure of the classical DP model, as it significantly overestimates fracture-matrix fluid exchange near the displacement front. Similarly, for imbibition perpendicular to microfractures, Q is also proportional to t1/2 in the late stage. After elucidating the mechanisms of fracture-fracture capillary interaction, we successfully derive analytical solutions for uni-directional countercurrent imbibition kinetics in DPF systems at the late stage, for imbibition parrallel and perpendicular to microfractures, respectively. We accordingly propose an equivalent REV scale model and examine it with fine-grid simulations. We highlight the importance of adopting anisotropic relative permeability in this DPF system at REV scale for reservoir simulation rather than simply adopting anisotropic absolute permeability. This presents a new challenge for numerical simulations at reservoir scale.