Multilayer Rectangular Model

This model simulates the transient flow in any number of independent layers commingled at the wellbore as shown below.

Each layer is considered to have a rectangular geometry with an identical initial pressure (pi) to other layers, as well as its own skin factor, reservoir properties, and outer boundary conditions. This well may be at any location within each layer 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. No crossflow between the layers can occur except at the wellbore. The dual porosity flow within each layer can be modeled either as pseudo-steady state or transient interporosity flow.

References

1. "The Application of the Laplace Transformation to Flow Problems in Reservoirs", A.F. van Everdingen and W. Hurst, Trans. AIME (1949) vol. 186, 305 - 324.

2. "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.

3. "Transient Pressure Behaviour of Commingled Reservoirs", F.J. Kuchuk and D.J. Wilkinson, SPEFE (1991).