Effect of Stress Shock and Pressurization/Depressurization Hysteresis on Petrophysical Properties of Naturally-Fractured Reservoir Formations

Abstract

Abstract This paper presents a theoretically rigorous formulation and correlation of the effect of poroelasticity on stress-dependent petrophysical properties of naturally-fractured reservoirs, including porosity, permeability, relative permeability, and capillary pressure, by consideration of the stress shock effect across a critical effective stress and the pressurization/depressurization hysteresis. This model accounts for the deformation, transformation, deterioration, and collapse of the pore structure during pressurization and depressurization processes and their effects on the properties of naturally-fractured reservoir formations. A stress shock is shown to occur in naturally-fractured reservoir formations at a critical stress during transition between open and closed natural fractures in loading and unloading applications. The effect of the stress shock and pressurization/depressurization hysteresis on petrophysical properties of reservoir formations is formulated by means of a modified power-law equation derived from a phenomenological model referred to as a rate equation. The modified power-law equation is shown to alleviate the shortcomings of the ordinary power-law equation applied in many studies. The comprehensive model developed in this study is validated by means of various experimental data gathered by testing of samples from sandstone, carbonate, and shale reservoirs. The phenomenological parameters of the rock samples are determined for best match of experimental data. The scenarios examined in this study indicate that pressurization/depressurization hysteresis has a significant effect on the stress-dependent porosity and permeability of reservoirs. The model developed in this paper can describe the stress-dependent porosity and permeability of the fractured rock formations much more accurately than the commonly used empirical correlations. The accurate methodology presented for proper correlation of stress-dependent properties of reservoir formation rocks honors the slope discontinuity at a yield or critical effective stress. The stress-dependency of rock properties are described by the modified power-law expressions separately over the low stress region below the critical stress and the high stress region above the critical stress. The proposed data correlation methodology is proven to be highly effective in the analyses and correlations of the experimental data of various types of reservoir rock formations as indicated by the correlations achieved with significantly high coefficients of regressions very close to the unity.