A volumetric approach for the resistivity response of freshwater shaly sandstones

Abstract

The dc electrical response of freshwater-saturated shaly sandstone is analyzed on the basis of effective volume conductivity concepts for a concentrated mixture of “solid grains” in a continuous electrolyte. The bulk conductivity of this model is physically controlled by (1) the effective porosity and the average electrical tortuosity of its free-pore electrolyte, and (2) the amount and concentration of bound water that coats charged solid surfaces (mainly of clays), and a corresponding averaged electrical surface tortuosity. The latter is combined in an equivalent volume conductivity that is mainly due to the electrical double layers of charges developed at the clay-electrolyte interfaces. Analytical expressions, based on effective medium and general mixture theories, are developed to describe both the whole rock conductivity and the specific conductivities of its constituent elements. The derived equations for the bulk conductivity of the system describe, with sufficient precision, experimental core data over a large range of water conductivity. The equations are also written in a modified Archie-Winsauer form, wherein their coefficients are shown to be strongly dependent on the electrolyte and matrix conductivity, the effective medium porosity, and the cementation exponent. The scheme is shown to describe satisfactorily laboratory data for clay gels, shales, and shaly sandstones saturated with saline to fresh water. The scheme can also be used for interpreting resistivity logs of wells in freshwater aquifers. To accomplish this, we use the simultaneous measurements of formation resistivity at two different values of salinity: the freshwater virgin zone obtained from a deep induction log or laterolog and the mud filtrate–invaded zone inferred from a short normal or microfocused log. It must be assumed that either the effective porosity or the cementation exponent, and the native water and mud filtrate resistivities are known from other sources. The new method is being applied to the interpretation of logging data from wells drilled in the Recôncavo-Tucano Basin, Bahia, northeast Brazil.