Equivalent 1D modeling of logging-while-drilling electromagnetic resistivity measurement in 2D formations

A new equivalent modeling method has been developed for calculating logging-while-drilling (LWD) electromagnetic (EM) resistivity measurements in axisymmetric formations. This method is distinguished by two main features: simplifying the complex tool geometry and decomposing the formation inhomogeneity. The first feature leverages the non-azimuthal nature of resistivity measurements and assumes an infinite extension of the slot in the vertical direction, thereby significantly simplifying the tool’s geometry. Consequently, the original modeling of a 3D tool complexity in 2D formations is reduced from 3D to 2D. The lateral and vertical effects of the 2D formation inhomogeneity on LWD resistivity responses are then decoupled based on the geometrical factor theory and separation of variables method. The 2D formation model is decomposed into 1D planar and cylindrically layered models, respectively. The planar models in association with 1D semi-analytical algorithm can produce equivalent resistivity curves affected by the surrounding beds. These equivalent curves are integrated to form the cylindrical layered models which are solved via 1D semi-analytical algorithm. Numerical results demonstrate that the equivalent 1D modeling method can accurately compute the responses of LWD EM measurements with 3D tool geometry in 2D formations. Compared with the traditional finite-element method, the new method’s computational speed is hundreds of times faster, facilitating data correction and rapid inversion.