Pressure Transients in a Fractal-Cluster Model of Porous Media

The reservoir is described as a "supercritical cluster"; that is, an aggregate of conductive elements that comprises a "backbone" of connected pores or fractures that span the zone of interest, and also a collection of "sub-critical clusters" or "dangling ends" joined to the backbone to a limited extent. The scheme resembles the usual fracture and matrix-blocks setting but both backbone and sub-clusters are of the same material and share similar petrophysical properties. Whereas the backbone is a homogeneous porous medium, the sub-critical clusters behave as fractal porous media. The backbone-cluster type of flow has been observed in laboratory experiments. The sub-critical clusters were approximated as linear fractal media characterized by static and dynamic fractal exponents and also by porosity and permeability of the compound medium. One of the ends of the linear clusters is closed and the other is joined to the backbone, where the mainstream occurs. A new solution was developed for that problem. The Laplace transform in time and space was used in the mathematical scheme. The theory developed was applied to field cases of interference between wells in aquifers. The matches of computed and observed dynamic pressures show fair fits.