REPRESENTATION OF GRID BLOCK PERMEABILITY IN COARSE SCALE MODELS OF RANDOMLY HETEROGENEOUS POROUS-MEDIA

The two basic approaches for the assignment of coarse scale grid block permeabilities from highly detailed permeability descriptions are sampling, where the permeability of the coarse scale grid block is simply specified as the fine scale permeability evaluated at the grid block center (no averaging is performed), and scaleup or homogenization, where the coarse scale permeability is determined through some procedure which appropriately averages the fine scale data. The intent of this paper is to quantitatively compare these two approaches, through extensive numerical calculations, for the modeling of single phase flow through two-dimensional realizations of randomly heterogeneous porous media, with heterogeneity quantified through the correlation length (l) and the variance of the log of permeability (sigma(phi)2). Several different flow scenarios and two scaleup techniques (local and global) are considered over a range of l and sigma(phi). It is seen that for flows driven by smoothly varying boundary conditions, a sampling procedure is more accurate than global scaleup when the length scale of a typical grid block is less than l, independent of sigma(phi). For flows driven by source terms, by contrast, more resolution is required for a sampling approach to be preferable to global scaleup, particularly at high variances. Local scaleup is shown to be preferable to either sampling or global scaleup in essentially all cases, though its use for more general permeability fields requires additional numerical calculations.