Effect of the local clay distribution on the effective electrical conductivity of clay rocks

Abstract

The "local porosity theory" proposed by Hilfer was revisited to develop a "local clay theory" (LCT) that establishes a quantitative relationship between the effective electrical conductivity and clay distribution in clay rocks. This theory is primarily based on a "local simplicity" assumption; under this assumption, the complexity of spatial clay distribution can be captured by two local functions, namely, the local clay distribution and the local percolation probability, which are calculated from a partitioning of a mineral map. The local clay distribution provides information about spatial clay fluctuations, and the local percolation probability describes the spatial fluctuations in the clay connectivity. This LCT was applied to (a) a mineral map made from a Callovo-Oxfordian mudstone sample and (b) (macroscopic) electrical conductivity measurements performed on the same sample. The direct and inverse modeling shows two results. First, the textural and classical model assuming that the electrical anisotropy of clay rock is mainly controlled by the anisotropy of the sole clay matrix provides inconsistent inverted values. Another textural effect, the anisotropy induced by elongated and oriented nonclayey grains, should be considered. Second, the effective conductivity values depend primarily on the choice of the inclusion-based models used in the LCT. The impact of local fluctuations of clay content and connectivity on the calculated effective conductivity is lower.