Abstract
Special core analysis techniques are often based on the assumption of uniform petrophysical properties of core samples. This assumption is obviously erroneous for heterogeneous core samples. This paper presents an integrated approach for characterizing permeability heterogeneity at the core level. The method combines the results of laboratory core flooding with already developed field scale history matching techniques to identify a 3D heterogeneous permeability field at the core scale. We focus on core samples with local heterogeneities. Their 3D porosity maps are preliminary obtained using conventional tomography techniques. Production data are measured when performing a viscous miscible displacement experiment: a high viscosity glycerin displaces a low viscosity brine at a constant flow rate. Concentration maps are collected at successive times during displacement using a medical CT device. A 1D permeability profile can be determined from the variations in the slope of the pressure signal against front location inside core samples. The 3D permeability fields are modelled using a relationship such as log(k(x)) = Aϕ(x) + b(x) where A is a constant and b(x)is a realization of a random function characterized by a mean, a variance and a variogram. We developed an assisted history-matching process, which takes advantage of all the available static and dynamic data to model permeability heterogeneity inside core samples. A first guess is initially generated honoring the measured Δp(t) variations along the flow axis. This first guess is subsequently modified until the mismatch between dynamic data and fluid flow simulated answers is minimized. To do so, we use a gradual deformation based optimization method, which allows us to vary any given distribution from one or a few deformation parameter(s) while preserving the overall spatial variability. The proposed method is fast and non-destructive. The final 3D permeability map honors the measured dynamic data and respects the spatial variability of the collected static data.
