An Efficient Method for Approximating Directional Electromagnetic LWD Responses in Complex 2D Formation Models

Electromagnetic logging while drilling (EM LWD) provides unique capabilities for both look-around and look-ahead detection, making it a foundational technology for identifying formation interfaces in complex horizontal and ultra-deep well applications. Over recent decades, its detection depth has advanced from a few meters to a remarkable range of several tens of meters. Nevertheless, directional EM LWD remains the primary geosteering method in horizontal wells, largely due to its sensitivity to formation boundaries and relatively low operational cost. In early directional EM LWD applications, where the maximum detection range was generally below 5 meters, one-dimensional (1D) formation models were widely adopted for forward simulation and inversion. However, current-generation tools can achieve detection ranges approaching ten meters, meaning that formation influences now extend across a significantly larger volume. Continuing to use conventional 1D models under such conditions may introduce substantial errors. While transitioning to two-dimensional (2D) models preserves accuracy, the increased model dimensionality substantially reduces computational speed, hindering real-time inversion.

In this paper, we propose an approximate method for simulating directional EM LWD responses in 2D models, designed to address this inherent trade-off between computational efficiency and accuracy. The core concept involves reducing complex 2D geological models into a series of 1D representations, which are then solved using a pseudo-analytical algorithm. First, the computational domain is divided into sliding windows of varying widths, defined with reference to the tool’s depth of investigation. Within each window, curved formation interfaces are approximated by straight lines to construct a 1D model, from which the tool response is computed. The series of 1D responses is then synthesized to obtain an approximate response for the original 2D model. To ensure both efficiency and reliability, an automated workflow integrating progressive model reduction with real-time quality control is implemented. The process begins with a coarse 1D approximation (typically 3–5 models). A divergence metric quantifies its representativeness; if below a preset threshold, the result is accepted. Otherwise, an iterative refinement phase is activated, dynamically increasing the number of 1D models only where necessary until the synthesized response stabilizes. The algorithm was validated on representative fault and fold models. Numerical results demonstrate that the proposed method successfully avoids the oversimplification inherent in conventional 1D modeling while achieving a computational speedup of more than 10 times compared to conventional full 2D numerical simulations.

We are indebted to the financial support from the National Natural Science Foundation of China (42304140).