Three-Dimensional Characterization of Permeability at the Core Scale

In this article, we introduce an integrated method for characterizing permeability heterogeneity at the core scale. It combines the results of laboratory core flooding with already-developed field scale history matching techniques such as gradual deformation and pilot points. Prior to any experiment, X-ray computed tomography (CT) imaging techniques are used to obtain three-dimensional porosity distribution in cores. The samples are submitted to viscous, miscible displacement of water by water-glycerin mixture. The dynamic data collected during injection are the time variations in inlet-outlet pressure drop and three-dimensional CT-scan concentration maps of invading fluid collected at successive times. We develop an inversion or matching process which takes advantage of the available data to characterize the spatial distribution of permeability heterogeneities within core samples. Permeability is assumed to be related to porosity. This matching process involves two successive optimizations. First, an initial permeability guess derived from porosity is modified by varying deterministic parameters until the corresponding simulated pressure answer fits the measured pressure drop. Second, an extended optimization process with both deterministic and stochastic parameters is run to match pressure drop and concentration data. This methodology is applied to a synthetic example for which the permeability-porosity relation is known. It yields a three-dimensional permeability model reproducing the reference pressure and concentration maps. The methodology is also applied to experimental data. In this case, it provides three-dimensional permeability models leading to an improved, but perfectible data match. A major difficulty is the unknown relationship between permeability and porosity.