Abstract:
We developed a numerical manifold method (NMM) model for analysis of coupled hydro-mechanical processes in porous rock containing discrete fractures. Using a non-conforming mesh approach, fractures are conveniently discretized by dividing NMM mesh covers along fracture traces resulting in a discontinuous model, which can consider discrete fracture deformation (e.g. opening and slip) and fracture fluid flow within a permeable and deformable porous rock matrix. We revised Shi`s original scheme (Shi, 1988) by adding a fracture constitutive model with fracture normal and shear stiffness for mechanically open states. For fluid flow in fractures, we developed a new model to consider along-fracture and normal-to-fracture fluid flow without introducing additional degrees of freedom. We further implemented the new model into NMM with a two-cover-mesh system and with a tree-cutting algorithm to generate the non-conforming mesh. We verified the code for hydro-mechanical coupling in deformable porous media containing single and two sets of fractures and we demonstrated the capability on a problem involving coupled hydro-mechanical behavior of a complex fracture network with multiple fracture intersections. The ultimate goal is to develop an efficient and practical model for analyzing large-scale hydraulic fracturing and fracture network stimulations in energy production.
Introduction
Coupled hydro-mechanical (HM) processes, i.e., the interaction between hydraulic and mechanical fields, are significant in geological engineering, such as oil and gas extraction, geothermal energy and nuclear waste disposal, especially when the geological media consists of fractured rock (Rutqvist and Stephansson, 2003). Fractured rock may contain arbitrarily oriented and complexly intersected, thin (millimeters to microns) fractures. In such a geological system, two types of hydro-mechanical couplings prevails, i.e., direct and indirect couplings. Direct coupling occurs directly between mechanical and hydraulic fields in forms of pore-volume interaction. Specifically, the fluid pressure changes instantaneously affect deformation and the volume change instantaneously induces changes in fluid pressure. This pore-volume interaction can be described by Biot`s equations (Biot, 1941). Indirect coupling refers to indirect interaction between mechanical and hydraulic fields through changes in their material properties. Specifically, effective stress, affected by fluid pressure, would change the stiffness of fractures, and the deformation of fractures change their hydraulic conductivities. This interaction, involving changing fracture mechanical and hydraulic properties is usually represented by constitutive functions based on laboratory data or in situ experiments (Rutqvist et al., 1998, 2000).
