Improved Determination of Stress-Dependent Permeability for Anisotropic Formations

Abstract

Abstract Qualitative determination of formation permeability is often obtained through laboratory flow tests on core plugs. However, the experimental determination of the permeability for anisotropic plugs (particularly the horizontal permeability) is difficult and less than perfect; generally relying on a highly simplified Darcy flow analysis. Numerical analyses could greatly improve the resolution, reduce the testing costs, and allow parametric investigations using sophisticated 3-D formulations. This paper reports such an analysis that interprets the analytical Darcy flow-pressure measurements, using numerical results to provide a "geometric factor". A numerical iterative procedure correlates the core plug measured flow and pressures at the inlet and outlet boundaries for different boundary sources to derive the core plug anisotropic permeabilities. Since stress changes generally influence permeability, a conceptual model is developed - again via an iterative numerical method - that accounts for the effects of the solid deformations. From this, numerical schemes have been developed using "equivalent geometric factors" with embedded mechanisms for modifying core plug permeability based on the changes in the solid strains that simulate the coupled flow-deformation behavior of selected reservoir rocks.This is the first detailed 3-D numerical analysis iterative scheme that practically allows realistic determination of permeabilities in anisotropic core plugs. Introduction Permeability is one of the most important properties of reservoir rocks. The complications of this "geometric" property may be reflected by the permeability tensor which may provide a mathematical explanation of anisotropy or preferred flow pathways. Heterogeneous porous media may possess a spatial variable characteristic as a result of point-to-point variation in permeability. In contrast, the directional permeability changes may be primarily attributed to the formation anisotropy.1,2 If permeability is dependent on position within a geological formation, the formation is heterogeneous. Heterogeneities may result from faulting and fracturing induced during subsequent tectonism. These heterogeneities may be present at various length scales, from grain scale of the order of microns to fault zones covering many kilometers; typically inducing a degree of anisotropy that may further control the hydraulic and transport performance of porous and fractured media. The primary cause of anisotropy on a small scale is the orientation of clay minerals in sedimentary rocks or the alignment of microcracks in indurated materials. Laboratory core samples of clays and shales show horizontal to vertical permeability anisotropy ratios in the range 3:1 to 10:1.3 At a larger scale, field observations indicate a relationship between layered heterogeneity and anisotropy which may lead to regional anisotropy values on the order of 100:1 or even greater.4,5 Snow6 showed that fractured rocks behave anisotropically because of the directional variations in fracture aperture and spacing.