Investigating Matrix/Fracture Transfer via a Level Set Method for Drainage and Imbibition

Abstract

Summary Multiphase flow and transport phenomena within fractures are important because fractures often represent primary flow conduits in otherwise low-permeability rock. Flows within the fracture, between the fracture and the adjacent matrix, and through the pore space within the matrix typically happen on different length and time scales. Capturing these scales experimentally is difficult. It is, therefore, useful to have a computational tool that establishes the exact position and shape of fluid/fluid interfaces in realistic fracture geometries. The level set method (LSM) is such a tool. Our progressive quasistatic (PQS) algorithm based on the level set method finds detailed, pore-level fluid configurations satisfying the Young-Laplace equation at a series of prescribed capillary pressures. The fluid volumes, contact areas, and interface curvatures are readily extracted from the configurations. The method automatically handles topological changes of the fluid volumes as capillary pressure varies. It also accommodates arbitrarily complicated shapes of confining solid surfaces. Here, we apply the PQS method to analytically defined fracture faces and aperture distributions, to geometries of fractures obtained from high-resolution images of real rocks, and to idealized fractures connected to a porous matrix. We also explicitly model a fracture filled with proppant, using a cooperative rearrangement algorithm to construct the proppant bed and the surrounding matrix. We focus on interface movement between matrix and fracture, and snap-off of nonwetting phase into the fracture during imbibition in particular. The extent to which nonwetting phase is trapped in fracture/enclosed gaps is very sensitive to the direction of the displacement. Simulated drainage curves in matrix differ systematically from drainage curves in fracture and matrix with transfer between them. In a reservoir simulation, the latter might serve as an upscaled drainage curve input for a fractured medium.