Fracture with Boundaries Model

This model simulates the pressure response in a vertical well intercepted by an infinite-conductivity vertical fracture within a rectangular-shaped reservoir with homogeneous or dual porosity characteristics (see figure below). This well may be at any location within the reservoir and the model supports infinite, no-flow, and constant pressure boundaries. Thus, classical configurations like a well near a sealing fault, or a constant pressure boundary near intersecting faults can be easily modeled. 

At very early times, the cylindrical source solution is used, which is followed by Green’s function solutions. The Green’s function solution, as developed by Thompson et al. (1991) with slight modifications, is used to simulate an infinite-conductivity vertical fracture. No-flow boundaries are modeled using the method of images. The result is superposed in time based on the rate history provided. Note that the dual porosity model provided is based on pseudo-steady state interporosity flow.

References

1. "Efficient Algorithms for Computing the Bounded Reservoir Horizontal Well Pressure Responses", L.G. Thompson, J.L. Manrique and T.A. Jelmert, Paper SPE 21827 presented at 1991 Rocky Mountain Regional Meeting and Low-Permeability Reservoirs Symposium, Denver, CO, April 15 - 1

2. "Pressure Analysis for Fractured Wells", A.C. Gringarten, H.J. Ramey, Jr., and R. Raghavan, Paper SPE 4051 presented at the 1972 AFM, San Antonio, TX, October 8 - 11.