Automatic estimation of permeability from array induction measurements: applications to field data

This paper describes the successful application of a new petrophysical inversion algorithm to estimate permeability from borehole array induction measurements. We consider measurements acquired in a North Louisiana low-permeability, tight-gas sand formation subject to water-base mud-filtrate invasion. The inversion methodology incorporates the physics of two-phase immiscible displacement and salt mixing between the invading water-base mud-filtrate and connate water. Moreover, the invasion model honors the physics of mudcake growth as well as the petrophysical properties that govern the process of two-phase three-component flow, namely, relative permeability, capillary pressure, fluid density, and viscosity. The outcome of the inversion is the absolute permeability for each flow sub-unit within a gas-bearing production zone. Rock formations under consideration consist of low-permeability amalgamated sands. Array induction measurements exhibit significant vertical fluctuations within an individual production unit. In view of this, the estimation procedure is designed to consider the effect of the number of layers and of their thickness when describing a production unit. We show how the progressive addition of flow sub-units produces a better match of the array induction measurements within the limits of vertical resolution. Accurate reconstructions of layer-by-layer permeability are primarily constrained by the availability of a-priori information about time of invasion, rate of mud-filtrate invasion, overbalance pressure, capillary pressure, and relative permeability. Sensitivity analyses show that the estimated values of permeability properly reproduce the measured array induction logs even in the presence of small changes of relative permeability, capillary pressure, porosity, and Archie?s parameters. Moreover, the estimated values of permeability agree well with those of rock-core measurements acquired from other wells in the same gas-bearing formation.