Abstract: Scaling Relations for Flow in Heterogeneous Porous Media

Jeffery Yarus

The effects of reservoir heterogeneity on oil recovery processes may be studied through numerical simulation of the flow processes of interest in high resolution numerical models of the reservoir property distributions. These high resolution reservoir models are produced by a geostatistical technique known as conditional simulation, which honors available data at their sample locations and reproduces measures of spatial correlation at unsampled points.

Procedures for scaling up the behavior observed in these detailed probabilistic models of heterogeneity include the definition of effective flow properties, heuristic fractional flow models and streamtube scaling methods. The length dependence observed in miscible displacements for dispersion induced by correlated permeability heterogeneity precludes the definition of an effective dispersion coefficient and requires the use of methods based on the linear scaling of fractional flow models. Effective relative permeabilities (pseudo-functions) can be defined which will reproduce the results of the cross-section simulations from which they were derived, but complications arise in their use in rescaled flow models. The use of a Lagrangian displacement calculation employing streamtubes is d scussed and shown to avoid the problems introduced by the definition of effective relative permeabilities.

AAPG Search and Discovery Article #90986©1994 AAPG Annual Convention, Denver, Colorado, June 12-15, 1994