Numerical Modeling of the Induction Logging Signalin Anisotropic Oil and Gas Reservoirswith a Layered Structure

The aim of this work is to analyze the effect of the anisotropic nature of the electric conductivity in an oil-bearing formation on the induction logging signal. The numerical modeling of the logging signal from a device consisting of an alternating current excitation coil and two receiving coils moved along the wellbore is carried out. The electromotive force induced in the receiving coils is investigated. The electric conductivity of the oil-bearing formation is characterized by either a diagonal tensor with dominant $$ \sigma _{xx} $$ , $$ \sigma _{yy} $$ components or a dense tensor obtained by rotation to a specified zenith angle. Numerical modeling is performed with the vector finite element method on an adaptive unstructured tetrahedral grid taking into account the geometry of the logging device, vertical well, and layered host medium. The tensor electric conductivity is plugged into the variational formulation. Dependences of the apparent electric conductivity of the depth are obtained based on the electromotive force induced in the receiving coils.