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Abstract

All sandstone fabrics contain a characteristic complex of microstructures of a scale that is large with respect to the size of sample plugs conventionally used to measure permeability. A fundamental element of this microstructure consists of circuits composed of oversized pores and throats representing the sites of loose or flawed packing, and largely controlling permeability at the permeability-plug scale. Very small changes in the location of a permeability plug with respect to these circuits can result in significant variation in measured permeability. In the terminology of geostatistics, this is a classic problem of insufficient sample support, producing artificially heightened variance over small spatial scales as a result of a sampling volume that is too small. The varying pattern of the spatial variability of the microstructure dictates that permeability plugs must vary in size to contain enough of the microstructure to ensure adequate sample support. This is impossible in practice, but a combination of physical data and image analysis can yield permeability values representing rock volumes of the requisite size. A minimum sample size can be determined by measuring the scales of structural complexity using Fourier transforms of the image of the porous microstructure taken from thin sections. An adequate sample size is that which ensures local homogeneity (a measure of the scales of spatial variability within an image) and local stationarity (a measure of the variance between a set of mutually adjacent samples). A set of mutually adjacent samples that attains local stationarity defines a bed, wherein all samples at a scale of local homogeneity have either the same permeability or vary systematically The physical significance of the structure can be determined by relating Fourier data to the relationship between pore type and throat size determined from petro-graphic image analysis. Methods of modeling permeability at the required scale can be based on the Darcy's law of empiricism or can be based on local volume-averaging theory and large-scale volume-averaging theory wherein the permeability tensor arises naturally from first principles. The methodology discussed in this chapter represents a logical procedure for scaling up local observations and, in principle, can be operated validly over any scale range.

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