Averaging of Relative Permeability in Heterogeneous Reservoirs

Abstract

been increasingly used to capture the effects of small scale heterogeneities, in coarse grid reservoir simulation. This mode of use suggests a close relationship to the concept of effective properties, e.g. effective relative permeabilities. The two concepts are reviewed in some detail in the paper, and the relationship between them is explored. It is shown that fundamental differences exist. Effective properties can be defined only on a much larger spatial scale than that of the heterogeneities themselves. Effective properties become universally valid in the sense that they appear as parameters in the ensuing partial differential equations for the large scale variables. Dynamic pseudos are constructed from one single (approximate) solution of the governing equations. No scale restrictions apply to this “parent” solution. If properly constructed, dynamic pseudos allow exact reproduction, in a subsequent coarse grid simulation, of the parent solution. Dynamic pseudos generally become dependent on the particular parent solution chosen, and on the numerical grid (and numerical method) with which they are later to be employed.