A Goal-oriented Adaptive Discontinuous Galerkin Method for 3D Electromagnetic Induction Logging-While-Drilling in Fractured Media

Summary Electromagnetic induction logging-while-drilling tools measure real-time electromagnetic data to characterize the electrical properties of formations, thereby supporting geosteering decisions. The multiscale structures formed by heterogeneous fractures within complex reservoirs lead to electromagnetic field discontinuities, which in turn limit the accuracy of reservoir evaluation. To elucidate the mechanisms by which multiscale fracture conductivity and spatial distribution influence the attenuation of the electromagnetic field, a discontinuous Galerkin method based on vector basis functions is developed, using the open-source finite element library deal.II, for modelling complex fracture clusters. To reduce the number of elements associated with the explicit volumetric discretization of fractures and truncate the computational domain, the impedance transition boundary condition that treats the fractures as element interfaces and the perfectly matched layer approach are employed. A goal-oriented adaptive mesh refinement strategy based on element-wise residuals and interelement field jumps is adopted to flexibly refine the mesh near the transmitter–receiver system and fractures, since the complex distribution of field discontinuities induced by fracture clusters renders empirical mesh refinement inadequate. The numerical results validate the accuracy and performance of the algorithm. For a layered fracture model, the numerical accuracy is assessed by comparison with the semi-analytical solutions from the open-source software empymod. In interlaced fracture models with different in-plane dimensions, the flexibility and adaptability in modelling fractures are demonstrated by the mesh distributions after adaptive refinement. For fracture cluster models, an advantage in computational efficiency over the finite element method for complex fracture networks is demonstrated as fracture complexity increases. These results demonstrate the applicability to electromagnetic induction logging-while-drilling modelling of fractures in conductive-to-moderately resistive sedimentary formations, with improved computational efficiency and modelling flexibility.