The past cooperative research program between the Cornell Fracture Group and Schlumberger Cambridge Research and Schlumberger Dowell consists of three main parts. The first is the implementation of a three dimensional boundary element program, BES, on available multi-processor computers. This includes the IBM SP2 and the SG Power Challenge in the Cornell Theory Center. The second part of the program involves extending the capabilities for arbitrary, non-planar, three dimensional fracture nucleation and propagation in FRANC3D. The key issues are: 1) propagation, interaction, and/or coalescence of multiple fractures, 2) fracture in and across material interfaces, 3) splitting/branching/intersecting cracks, 4) general improvements to existing code for extracting stress intensity factors and determining the direction and extension of mixed-mode fractures, and 5) the automation of many or all of these features. The third part of the research program involves coupling the two programs mentioned above with fluid flow in order to simulate hydraulic fracture from an arbitrarily oriented, cased and perforated wellbore within a layered rock mass.
Hydraulic fracture is the process of fluid induced fracture in layers of the earth's crust for stimulating oil and gas production from depleted or low permeability formations. A well is drilled into the earth's crust, a portion of the well is pressurized, and a fracture is produced.
Often the well is cased with a steel casing cemented to the rock. The pressurized fluid that causes cracking must be allowed to pass from the cased wellbore to the rock. This is done by perforating the casing and cement. The process of perforating the casing causes damage to the rock as well as the cement bond between the steel and the rock. Fluid may be able to enter the interface between these materials and fracture initiation may not occur from the perforations as desired.
Finally, the wells may not always be vertical and the fractures may not always be simple planar features. Multiple deviated wells are commonly drilled from ocean drilling platforms, and horizontal wells are increasing. Fractures from these various wells, in addition to vertical wells, need to be modeled.
A very simple model of an uncased vertical borehole, with four perforations is shown below. The fractures extend away from the wellbore due to a prescribed fluid flow rate at the crack mouth, eventually merging and leading to the classical bi-wing shape shown in the final frame.
Recent research (see: Desroches & Carter, 1996) into the behavior of the fluid at the crack front has led to a new formulation for the fluid flow. The new formulation captures the pressure singularity at the crack front as well as the fluid lag (fluid does not reach the actual crack front for a propagating hydraulic fracture). The new formulation has thus far been compared with a rigorous two dimensional model for a radial crack that explicitly models the fluid lag behind the crack tip. A comparison of the width and pressure profiles along a radial line is shown below and further study and modeling is on-going.
Comparison of pressure along a radial direction from the center to the crack front for the 3D model with the pressure from a 2D model.
Comparison of fracture width along a radial direction from the center to the crack front for the 3D model with the pressure from a 2D model.
Color contours of pressure in the 3D model.
Color contours of pressure in the 3D model showing the deformed shape.
This figure shows a deviated wellbore and a crack that turns as it grows and tries to align itself with the applied stress field.
This figure shows a multiply perforated (horizontal) wellbore with cracks growing from each perforation; they are almost ready to merge together.
This figure shows a vertical wellbore and two cracks initiated along the wellbore wall. (Further details can be found in the recent NARMS'96 publication.)