Petrophysical inversion of borehole array-induction logs: Part I — Numerical examples

Abstract

We have developed a new methodology for the quantitative petrophysical evaluation of borehole array-induction measurements. The methodology is based on the time evolution of the spatial distributions of fluid saturation and salt concentration attributed to mud-filtrate invasion. We use a rigorous formulation to account for the physics of fluid displacement in porous media resulting from water-base mud filtrate invading hydrocarbon-bearing rock formations. Borehole array-induction measurements are simulated in a coupled mode with the physics of fluid flow. We use inversion to estimate parametric 1D distributions of permeability and porosity that honor the measured array-induction logs. As a byproduct, the inversion yields 2D (axial-symmetric) spatial distributions of aqueous phase saturation, salt concentration, and electrical resistivity. We conduct numerical inversion experiments using noisy synthetic wireline logs. The inversion requires a priori knowledge of several mud, petrophys-ical, and fluid parameters. We perform a systematic study of the accuracy and reliability of the estimated values of porosity and permeability when knowledge of such parameters is uncertain. For the numerical cases considered in this paper, inversion results indicate that borehole electromagnetic-induction logs with multiple radial lengths of investigation (array-induction logs) enable the accurate and reliable estimation of layer-by-layer absolute permeability and porosity. The accuracy of the estimated values of porosity and permeability is higher than 95% in the presence of 5% measurement noise and 10% uncertainty in rock-fluid and mud parameters. However, for cases of deep invasion beyond the radial length of investigation of array-induction logging tools, the estimation of permeability becomes unreliable. We emphasize the importance of a sensitivity study prior to inversion to rule out potential biases in estimating permeability resulting from uncertain knowledge about rock-fluid and mud properties.