Cyclic steam stimulation in highly viscous oil bearing formations, such as those of Gold Lake, entails formation parting in many cases. This paper presents a numerical treatment of the phenomena involved in this process, viz. fluid flow in cyclic steam stimulation, formation parting, fracture propagation, and closure. The latter part of the model involves the calculation of stresses and strains in the formation as well as in the surrounding rocks, as a result of pressure and temperature changes, which are used to calculate the fracture length at various times.
Fluid flow in the cyclic steam stimulation process is simulated by a three-phase. heat-fluid flow model, with implicit solution and special procedures to minimize computational time. A coupled well model allows for six different well operation conditions, including fluid storage in the fracture.
Rock stresses and strains were computed using a finite element model, developed for this study, which also gives the displacements and stresses at the fracture tip. Several fracture propagation criteria were. tested, and as a consequence, all the pertinent criteria from the literature were rejected for the case of non-isothermal fractures. Instead, it is postulated that for materials containing a propagating fracture, whose strain and/or surface energy is supplied by loading of the fracture face and/or pore pressure or thermal expansion, the strain energy may not fully balance the imposed loads. A new criterion for fracture propagation and closure is offered that seems to reflect the reported behaviour in the field.
The failure criteria used to determine the critical length of a fracture are all based on energy considerations. Griffith(1) recognized that this length is a function of the displacement work done by surface forces and the energy released by the creation of the fracture surface. Griffith postulated that a crack will start to propagate if the energy released by the body is greater than the creation of the surface energy due to the new surface. If u designates the surface energy, it can be expressed in terms of fracture length and specific surface energy as follows: Equation (1) (Available in full paper)
Equation (2) (Available in full paper)
Figure1 shows u and was functions of fracture length, if the solid is subject to a fixed load boundary condition. The critical length is graphically indicated at the maximum of the potential energy T at Lf.
For a perfectly brittle material, Irwin (2) showed that the specific surface energy is identical to the critical surface energy release rate. Accounting for the fact that a fracture is two-sided, one can write Equation (3) (Available in full paper)
However, Irwin states that most materials do not behave as perfectly brittle, but develop a plastic zone near the fracture tip. This plastic energy is also included in G. In fact, the plastic energy contribution is in general more than two orders of magnitude higher than the specific surface energy that Griffith originally considered. The critical energy release rate is a measurable quantity and has been determined for many industrial materials and rocks (3).