Fractal Distributions of Reservoir Heterogeneity and their Influence on Fluid Transport

ABSTRACT Theories of fluid flow in heterogeneous porous media show that their transport properties are determined by the structure of spatial correlations in the permeability distribution. When the range of these correlations is comparable to or larger than the fluid flow path, solutions of the convective-dispersion equation with an effective dispersivity augmented to account for the dispersive effects of reservoir heterogeneity do not provide accurate predictions of the transport characteristics of the medium. Measurements of property distributions in sedimentary environments show a fractal character with long range correlations. Evaluation of the influence of fractal distributions of permeability on oil recovery process performance requires simulation on a distributed field of properties with a correlation structure matching that in field measurements. The geometric properties and spatial correlation structure of fractal distributions are discussed and methods for measuring the fractal character of field data and synthesizing fields with a similar correlation structure are reviewed.