A Tensorial Archie's Law for Water Saturation Evaluation in Anisotropic Model

In oil and gas exploration, formation water (or hydrocarbon) content estimation is essential for reservoir evaluation, development, and production. Archie's law, which associates the formation resistivity and water saturation, has been widely adopted for reservoir assessment. However, the accuracy of the scalar-based Archie's law falls when the formation exhibits strong heterogeneity (e.g., fractured shales), as the electrical anisotropy is neglected in the scalar model. In this letter, we propose a tensorial Archie's law based on the effective resistivity tensor of the formation. We construct numerical experiments of idealized three-phase formation geometries that contain ellipsoidal inclusions. The resistivity tensor is calculated from the simulation results and used in the newly proposed Archie's law to calculate the water saturation of the formation, and the model is validated by comparing the predicted saturation with the calculated value from the known geometries. The results show that the tensorial Archie's law captures the anisotropy of the formation by including all tensor elements of the resistivity, thus improving the predictability.