Using Bruggeman's effective medium theory, the hydraulic permeability and dc electrical conductivity of sandstone are both expressed in terms of the ratio of two microscopic lengths, which are the dimensions of a characteristic pore throat and pore chamber, respectively. The theory is consistent with Kozeny‐Carman formulas in the limit of a perfectly microscopically homogeneous pore structure. Based on the effective medium approximation, the transport properties of Fontainebleau sandstone are predicted from a quantitative study of the pore space morphology. A series of epoxy‐impregnated thin sections of Fontainebleau sandstone was prepared from cores with porosity ranging between 5 and 22%. Using an image analyzer, throat and pore size distributions were constructed from the digitized and segmented microsections. For each sample the transport coefficients are calculated from the characteristic lengths, which are estimated directly from the experimental size histograms. The changes of both permeability and conductivity are predicted within a factor of 3 over the whole range of porosity. The variations of transport coefficients with porosity are interpreted from the contrasting evolution of pores and throats during diagenesis. Large pore chambers alternate with narrow passages in Fontainebleau sandstone. With decreasing porosity, some of the large pores remain stable, while the throats gradually shrink and are finally eliminated. The microscopic inhomogeneity of the pore geometry of Fontainebleau sandstone implies that its flow properties deviate from Kozeny‐Carman predictions.

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Using a geostatistical technique called cokriging, the areal distribution of porosity is estimated first in a numerically simulated reservoir model, then in an oil‐bearing channel‐sand of Alberta, Canada. The cokriging method consistently integrates 3-D reflection seismic data with well measurements of the porosity and provides error‐qualified, linear mean square estimates of this parameter. In contrast to traditional seismically assisted porosity mapping techniques that treat the data as spatially independent observations, the geostatistical approach uses spatial autocorrelation and crosscorrelation functions to model the lateral variations of the reservoir properties. In the simulated model, the experimental root‐mean square porosity error with cokriging is 50 percent smaller than the error in predictions relying on a least‐squares regression of porosity on seismically derived transit time in the reservoir interval. In the Alberta reservoir, a cross‐validation study at the wells demonstrates that the cokriging procedure is 20 percent more accurate, in a mean square sense, than a standard regression method, which accounts only for local correlations between porosity and seismically derived impedances. In both cases, cokriging capitalizes on areally dense seismic measurements that are indirectly related to porosity. As a result, when compared to estimates obtained by interpolating the well data, this technique considerably improves the spatial description of porosity in areas of sparse well control.

A geostatistical modelling technique called cokriging is used to describe the lateral variations of porosity, f, in a synthetic and a real reservoir. Using this method, an error-qualified porosity model is estimated for each of the two reservoirs from sparse well porosity measurements and seismically derived velocities. The method capitalizes on the high spatial density of the seismic measurements and on their correlation with f. Compared with conventional reservoir models derived solely from sparse well control, the seismically consistent models are better spatially constrained and, hence, provide more detailed and accurate reconstructions of the porosity variations.

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