A three dimensional simulator based on a coupled hydromechanical analysis is described in the paper. The mathematical formulation is based on analyses of three dimensional rock deformation and two dimensional fluid flow through the fracture. Both the rock deformation and fluid flow problems are solved using variational principles for fracture opening and the fracturing fluid pressure, respectively. The fracture criterion is based on a stress intensity factor approach.
The fracturing fluid is allowed to leak off into a formation at a rate determined by the excess pressure. Linear elastic fracture mechanics concepts are utilized to characterize the critical conditions for fracture propagation as the fluid is injected.
The fracture is assumed to open in a vertical plane and to be perpendicular to the minimum horizontal in-situ compressive stress. The rock mass is modeled as an isotropic homogeneous medium, but variations in permeability and in-situ stress are accounted for. The fracture is created by injection of an incompressible, non-Newtonian fluid with power-law characteristics.
The actual numerical procedure including the details of modeling some important phenomenon such as in-situ stress contrast, fluid loss, etc. has been described.
This paper forms the technical background for a companion paper, part II, in which several case analyses using the 3-D simulator have been reported along with parametric evaluation of the influence of reservoir conditions.