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 problems are solved using variational principles for fracture opening and the fracturing fluid pressure, respectively. The fracture criterion is 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 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 11, in which several case analyses using the 3-D simulator have been reported along with parametric evaluation of the influence of reservoir conditions.
Hydraulic fracturing is a technique used primarily by the oil and gas industries as a tool primarily by the oil and gas industries as a tool for enhanced recovery, more specifically for reservoir stimulation, well connection, etc. In recent years, the technique has also been established as one of the most reliable means of measuring in-situ stress at great depths below the earth's surface.
The technique lies in isolating and pressurizing a section of the wellbore with a viscous pressurizing a section of the wellbore with a viscous fluid of known rheological characteristics. At some critical pressure, the surrounding rock media breaks down and a fracture is created. Continued injection of fracturing fluid results in fracture propagation. propagation. In Massive Hydraulic Fractures (MHF), used for stimulating production from a hydrocarbon bearing layer (pay zone), high strength beads (proppant), are pumped along with the fracturing fluid to keep the created fracture propped open. This provides a conductive channel for the flow of hydrocarbon to the producing well.
The effectiveness of hydraulic fracturing in most applications is strongly affected by the geometry of the created fracture. Both the areal extent and shape are important from stimulation point of view. A serious concern in this respect point of view. A serious concern in this respect is the intrusion of a fracture initiated from the pay zone into the non-producing barrier layers. pay zone into the non-producing barrier layers. Design and analysis of hydraulic fracturing is a coupled hydromechanical problem. Basic phenomena that must be considered are:
rock phenomena that must be considered are:
fluid flow through fracture,
rock deformation-fluid flow interaction, and
These phenomena reflect the manifestations of some other factors such as,
fluid leak-off into the formation,
layered rock media with stresses and material properties' contrasts,
injection of fracturing fluid through perforations, and
modification of the reservoir or the pore pressure field in the vicinity of the propagating fracture.