Two-phase fluid-flow modeling in a dilatant crack-like pathway

Abstract

Two-phase fluid flow in tight rocks containing cracks is not fully understood. Published experimental studies performed on water-saturated tight rocks often associate gas flow with instabilities. A common observation is that gas begins to flow once it has reached a given breakthrough pressure. Pronounced sample dilation associated with the gas breakthrough is frequently observed experimentally, which is difficult to explain using standard two-phase flow models developed for porous and fractured rocks. Previously it was suggested that such two-phase fluid-flow mechanism is possible via network of connected dilatant crack-like pathways, which opened and closed depending on the magnitude of gas pressure, stress, and water pressure. In order to better understand the hydro-mechanical coupling between two-phase flow and deformation of dilatant crack-like pathway, a new theoretical model is proposed in this paper. We model two-phase fluid flow in a representative volume element (RVE) containing a deformable crack. The initial geometry of the crack is approximated by an elliptical cavity of high aspect ratio (major to minor axes of ellipse). The final spindle-like cross-section of the crack is calculated analytically by two-way coupling of the capillary pressure with the deformation of fracture aperture. It depends on pressure in the wetting fluid phase occupying crack tips; pressure in the non-wetting fluid phase occupying central part of the crack, and far-field rock stresses. This approximation can accurately predict the fluid flux through tortuous and rough-walled network of microfractures if the appropriate hydraulic aperture of elliptical crack is considered. Using the model, we analyzed conditions controlling formation of dilatant crack-like pathways, which were found to depend on a dimensionless parameter. The deformation of fracture aperture and tensile fracturing are shown to be controlled by generalized effective stress similar to Bishop's effective stress, experimentally introduced for partially saturated soils and rocks. The conceptual model provides an insight into the stress and pressure effects on two-phase permeabilities and the capillary pressure of tight rocks containing cracks.