Interference Tests Analysis in Fractured Formations With a Time-Fractional Equation

摘要

Fluid flow analytical models traditionally used in well test analysis not always yield adequate results for reservoir characterization. Contrastingly, fractal formulations have proved to be a more suitable tool. Among the various formulations, the Metzler-Glockle-Nonnemacher (MGN) equation includes a fractional time derivative. In this paper, that equation was applied to analyze interference tests in actual field cases. The MGN equation was applied and automatically matched to the observed pressures. Both usual reservoir properties -porosity and permeability- and also fractal exponents were varied in the matching procedure. Automatic matches of the involved variables resulted in pressure increments that compare fairly well with observed data from the field tests. The responses show a high anisotropy in the rock properties. The MGN equation implemented in this paper comprises fractal behavior in spatial variables as well as in the time term. Thus, well tests recorded in highly heterogeneous media, not amenable to standard techniques, can be analyzed with such analytical fractal approach.