Joint Radial Inversion of Resistivity and Sonic Logs to Estimate In-Situ Petrophysical and Elastic Properties of Formations

Abstract

Abstract Presence of near-wellbore damage, resulting from drilling and mud-filtrate invasion, can substantially affect sonic and resistivity borehole logging measurements. Therefore, unbiased log interpretation must account for presence of invasion in order to procure accurate estimates of formation properties. Our objective is to estimate the formation's dry bulk and shear moduli, porosity, and water saturation from the joint inversion of borehole array-induction resistivity and sonic measurements. We assume a radial one-dimensional (1D) model in the inversion, with the formation model described by a radial variation of water and hydrocarbon saturations representative of mud-filtrate invasion. The inversion is guided by the data misfit of both array-induction apparent resistivities and sonic-log flexural and Stoneley wave velocity-frequency dispersion curves. Radial distributions of fluids are converted to distributions of resistivity, density, and bulk modulus, which are input to the simulations of apparent resistivity and sonic logs. We make use of fluid-substitution models to relate bulk density, dry bulk modulus, and dry shear modulus to porosity and fluid saturation. Apparent resistivities are simulated based on a commercially available array-induction logging tool. Sonic measurements are analyzed in the frequency domain via flexural and Stoneley wave mode dispersions, which are calculated directly in the frequency domain. Synthetic cases consider water-base mud filtrate invading a hydrocarbon-bearing sand and oil-base mud filtrate invading a water-bearing sand. Porosities and elastic properties consistent with a soft formation are considered in the models. Sensitivity analysis indicates that sonic flexural and Stoneley mode dispersions naturally complement apparent resistivity measurements in the presence of mud-filtrate invasion. Inversions of synthetic cases produce reliable estimates of dry-rock bulk and shear moduli, porosity, and initial water saturation. Furthermore, these cases show that combining resistivity and sonic measurements reduces ambiguity in the inversion.