Finite Conductivity Fracture Model

The finite conductivity fracture model simulates a vertical well that is intercepted by a finite-conductivity vertical fracture within a cylindrical shaped reservoir as shown below. The boundaries can be either infinite or no-flow boundaries. Due to the complexity of the solution method, changing wellbore storage, dual porosity, and an observation well are not supported in this model.

At early times, this model uses the concept of Lee and Brockenbrough (1986) of tri-linear flow to represent a finite conductivity fracture (see figure below). Three linear-flow zones that dominate the pressure behavior are:

1. Fracture flow in the x-direction

2. Formation flow in the y-direction

3. Formation flow in the x-direction

Fracture diffusivity has been assumed constant at 1.0X106, as suggested by Cinco-Ley et al. (1978). The tri-linear fracture flow results merge into the solution for infinite-acting radial flow in the middle times. Thus, the tri-linear flow solution is truncated as soon as the flow becomes pseudo-radial. Occasionally, the merging of these two solutions is not smooth, and the derivative exhibits discontinuities (spikes). These are localized aberrations and can be ignored as they do not affect the rest of the results. Ultimately at late times, the model uses the solution for pseudo-steady state for a no-flow outer boundary, or continues to use the solution for infinite-acting radial flow.

References

1. "A New Analytic Solution For Finite Conductivity Vertical Fractures with Real Time and Laplace Space Parameter Estimation", Lee, S.T. and Brockenbrough, J., SPEFE (Feb. 1986) p. 75, SPE 12013.

2. "Transient Pressure Behavior for a Well with a Finite-Conductivity Fracture", H. Cinco-Ley, F. Samaniego-V., and N. Dominguez-A., SPEJ (August 1978) 253 - 264.