Conductivity of carbonate formations with microfracture systems

This paper studies the influence of microfracture orientation, shape and conductivity on the effective electrical properties of carbonate formations. The conductivity model of these formations can be presented as a conductive porous matrix in which the oblate spheroids representing microfractures are embedded. The spheroid aspect ratio varies in the range of 10− 2–10− 4 that corresponds to crack shapes in carbonates. To simulate the effective conductivity of formations with different aligned fracture systems we have used the approach of non-interacting fractures (dilute inclusion concentration). Based on the comparison of the modeling results for the non-interactive approach and effective medium methods we have demonstrated that the first-order equations can be applied for calculating the conductivity tensor for the fracture porosity up to 0.03. If the fracture conductivity is higher than the matrix one (fractures saturated with water of the same or higher conductivity), the first-order expression is introduced for the effective conductivity tensor. In the case when the inclusion conductivity is lower than the matrix one (fractures filled with oil, gas, or sealed by solid phase), the first-order approximation should be applied to the resistivity tensor to provide the similar calculation accuracy in the required fracture-porosity range.We present the results of the effective conductivity simulation for formations with arbitrary oriented fractures, one system of aligned fractures, one system of fractures with normal distribution of orientations along one direction, and three systems of fractures (conductive and resistive) with non-orthogonal orientations.The modeling results demonstrate the feasibility of assessing the fracture parameters (conductivity, orientation, aspect ratio, and concentration) in carbonate formations using borehole measurements of the conductivity tensor.