Effect of the local clay distribution on the effective elastic properties of shales

• Relationship between elastic constants and spatial clay organization of shales.
• Quantitative relationship between elastic properties and microstructure of shales.
• Theoretical framework applied on a Callovo-Oxfordian mudstone sample.

This paper revisits the “Local Porosity Theory” developed by Hilfer to propose a “local clay theory” (LCT) that establishes a quantitative relationship between the effective elastic properties and clay distribution of shales. This approach 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 fraction distribution μ and the local percolation probability λ which are calculated by partitioning a mineral map. The local clay fraction distribution provides information about spatial fluctuations of clay fraction and the local percolation probability describes the spatial fluctuations in the clay connectivity.This LCT was applied to a mineral map made from a Callovo-Oxfordian mudstone sample for which petrophysical data were available. This application demonstrated that the local functions μ and λ can be reasonably approximated by a Gaussian and simple sigmoid function, respectively.LCT was also used in a sensitivity analysis to evaluate the impact of the spatial fluctuations of the clay phase and clay connectivity on the effective elastic properties of shales. This impact has been investigated by comparing the effective properties obtained from LCT with those provided by a percolating inclusion-based model (a non-clay spherical grain embedded in a transverse isotropic clay matrix with neither spatial clay fluctuations nor spatial fluctuations in the clay connectivity). This inclusion-based model was built from a differential effective medium scheme. The results of this sensitivity analysis indicated that spatial clay fluctuations have only a slight impact on the calculated effective properties. However, when the spatial fluctuations of clay connectivity were considered, the quantitative deviations between the effective properties inferred from LCT and those from the percolating inclusion-based model were large exceeding 50% in some cases.