Physics-Driven Interface Modeling for Drainage and Imbibition in Fractures

The geometric distribution of immiscible fluid phases in fractures is not readily accessible experimentally, so aperture-scale simulations of drainage and imbibition in realistic fractures can provide valuable insight. We implement a level set method for computing the location within a fracture of the interface between two fluids controlled by capillary forces. The movement of the interface in response to changes in capillary pressure is approximated as quasistatic displacement. Fluid interfaces are thus constant mean curvature surfaces, satisfying the Young-Laplace equation. We apply a progressive quasistatic (PQS) algorithm to determine when spontaneous pore-level events occur during fluid displacement. The algorithm captures reversible and irreversible behavior. We illustrate the approach in two types of rough-walled fractures. One type is a 3D crack between irregular, impermeable surfaces; the other type is a gap between irregular 2D and 3D rain packs. We focus on the disconnected (defending) fluid volumes and (advancing) fluid main pathway as the geometric properties of the fracture are varied, notably aperture and the number of contact points between the upper and lower fracture surfaces. The curvature of the fluid/fluid interface in the plane of the fracture is often ignored by invasion percolation simulation techniques, yet it is known to influence strongly the fluid cluster properties. Our simulations establish the exact position and shape of the interface in realistic fracture geometries, from which fluid volumes, contact areas, and interface curvatures can be obtained. This establishes a new, mechanistic basis for predicting relative permeabilities in fractures and for evaluating transfer functions in dual-porosity flow models.