Effective Correlation of Stress and Thermal Effects on Porosity and Permeability of Naturally Fractured Formations by a Modified Power Law

Abstract

Summary Effective theory and methodology are proposed and validated for accurate correlation of stress–dependent petrophysical properties of naturally fractured or induced–fractured reservoir formations by means of a matrix/fracture dual–compressibility treatment. Inspection of various experimental data indicates a sudden change in trends at a certain critical net effective stress in the stress dependence of petrophysical properties of porous rocks as a result of a stress shock caused by the opening or closing of fractures. The variation of petrophysical properties in fractured–rock formations subjected to stress loading/unloading and thermally induced stress occurs mainly by deformation of the fractures below the critical effective stress and the deformation of the matrix above the critical effective stress. The alteration of petrophysical properties and a slope discontinuity might also be experienced when the stress exceeds the onset of other rock–alteration/damaging processes, such as pore collapsing and grain crushing. Proper formulations of the relevant processes and special correlation methods are presented in a manner to capture this nature of the petrophysical experimental data obtained by testing of cores extracted from naturally fractured or induced–fractured reservoir–rock formations. The dependency of porosity and permeability of fractured–rock samples under stress because of thermal, hydraulic, and mechanical effects is represented accurately by a modified–power–law equation derived from a kinetics model as confirmed by effective correlations of various experimental data. It is shown that this new model represents the thermal effect better than the frequently used Arrhenius (1889) equation and Vogel–Tammann–Fulcher (VTF) equation (Vogel 1921; Fulcher 1925; Tammann and Hesse 1926).