Compact Dual-Variable Correlation of Permeability Variation in Naturally Fractured Porous Formations by Stress and Thermal Deformation

Abstract Some deformation mode variations may occur during permeability variation of naturally fractured porous rock formations by variation of stress and thermal conditions at some critical effective stress and temperature values determined by slope discontinuities caused by transition between different deformation processes. A compact dual-variable equation is developed for accurate correlation of permeability dependence on stress and thermal conditions. The dependance of permeability on effective stress is expressed by the modified power-law equation with temperature dependent parameters represented by Arrhenius type equations. The application of this permeability equation, and the correlation method and quality are demonstrated by analyzing experimental data. It is shown that the correlations of the permeability data versus effective stress at various temperatures separately over the portions of the data separated at the critical stress and temperature conditions improved significantly compared to the correlation of the full set of data because the deformation modes are different in these four separate regions. The experimental data analysis and correlation method presented in this paper can be utilized to investigate and continue testing of the core samples until enough required quality data can be generated for best correlation results. The data analyzed and correlated in this paper is useful for demonstrating the effect of the mode variations at the critical stress and temperature. However, the amount and quality of these data were not sufficient for developing the best representative correlations over all four portions of the data separated at the critical stress and temperature conditions. The data analysis and evaluation method presented here can help in future studies for generating sufficient data for accomplishing the best correlation results over all portions of the data separated at the critical stress and temperature conditions. This paper demonstrates the superior performance of the new compact dual-variable stress and temperature correlations. It is proven that the dual-porosity nature of the naturally fractured porous formations is the key factor and the theoretically based stress and temperature dual-variable correlation of the experimental permeability data of naturally fractured porous formations is the best approach for proper and compact description of the combined effect of stress and thermal deformations on permeability. The present approach considering the deformation mode changes at critical stress and temperature is shown to generate much better-quality results than the previous approaches correlating the experimental data by disregarding the effect of deformation mode changes.