Abstract
This chapter summarizes the results of a new approach for the estimation of the large-scale correlation function of reservoir heterogeneity from the analysis of the pressure transient response of multiple wells. The approach is based on the theory of small fluctuations of the logarithm of the permeability and models the response of the ensemble-average pressure, obtained by averaging the pressure response of multiple well tests. A nonlocal diffusivity equation for the ensemble-average pressure, which incorporates directly the permeability correlation function, is obtained, from the analysis of which the permeability semivariogram of the reservoir can, in principle, be constructed. We consider a particular application to one-dimensional geometries, where a type curve is also derived for the case of an exponential correlation function.
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