The Permeability Variogram from Pressure Transients of Multiple Wells: Theory and 1-D Application

Summary This paper presents 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 non-local difFusivity equation for the ensemble-average pressure, which incorporates directly the permeability correlation function, is obtained, from the analysis of which the permeability semi-variogram of the reservoir can be constructed in principle. We consider a particular application to 1-D geometries, where a type-curve is also derived for the case of an exponential correlation function. Numerical simulations results support the applicability of the method.