A hybrid-dimensional approach for an efficient numerical modeling of the hydro-mechanics of fractures

Abstract

Characterization of subsurface fluid flow requires accounting for hydro-mechanical coupling between fluid-pressure variations and rock deformation. Particularly, flow of a compressible fluid along compliant hydraulic conduits, such as joints, fractures, or faults, is strongly affected by the associated deformation of the surrounding rock. We investigated and compared two alternative numerical modeling approaches that describe the transient fluid-pressure distribution along a single deformable fracture embedded in a rock matrix. First, we analyzed the coupled hydro-mechanical problem within the framework of Biot's poroelastic equations. Second, in a hybrid-dimensional approach, deformation characteristics of the surrounding rock were combined with a one-dimensional approximation of the fluid-flow problem to account for the high aspect ratios of fractures and the associated numerical problems. A dimensional analysis of the governing equations reveals that the occurring physical phenomena strongly depend on the geometry of the hydraulic conduit and on the boundary conditions. For the analyzed geometries, hydro-mechanical coupling effects dominate and convection effects can be neglected. Numerical solutions for coupled hydro-mechanical phenomena were obtained and compared to field data to characterize the fractured rock in the vicinity of an injection borehole. Either approach captures convection, diffusion, and hydro-mechanical effects, yet the hybrid-dimensional approach is advantageous due to its applicability to problems involving high-aspect-ratio features. For such cases, the modeling of pumping tests by means of the hybrid-dimensional approach showed that the observed inverse-pressure responses are the result of the coupling between the fluid flow in the fracture and the rock deformation caused by fluid-pressure variations along the fracture. Storage capacity as a single parameter of a fracture is insufficient to address all aspects of the coupling.