Partial Penetration Model

The partial penetration model simulates the pressure response in a partially penetrated vertical well within a rectangular-shaped reservoir with homogeneous or dual porosity characteristics. 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. 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

"The Use of Source and Green’s Functions in Solving Unsteady-Flow Problems in Reservoirs", A.C. Gringarten and H.J. Ramey, Jr., SPEJ (October 1973) 285 - 296.