Forward modeling and inversion method and its application of array induction logging based on radial layered medium model (Ⅰ): Response of oil-based mud invasion in sandstone reservoirs and forward modeling

When oil-based mud invades into a formation, the resistivity distribution and response characteristics of the invaded zone are complex and cannot be represented by a simple radial two-layer step model. Considering the actual structure and dimensions of the array induction logging tool, this study derives the expressions for the induced electromotive force and effective tool constant of the three-coil measurement structure with a built-in copper tube. The outer diameter of the copper tube is adjusted depending on the derived expression of the effective tool constant and the effective tool constant of the actual tool is simulated to approximate the radial detection characteristics of the actual tool. Subsequently, a forward model for the radial layered medium model of array induction logging is constructed. Based on the analysis of invasion response characteristics under oil-based mud conditions in the fractured tight sandstone formation of the Cretaceous Bashijiqike Formation in the Dabei and Keshen areas of the Kuqa Depression in the Tarim Basin, the radial step invasion model is selected for forward modeling of the complex invasion response characteristics of array induction logging in oil-based mud. The study shows that the radial three-layer step model can reasonably represent the complex response characteristics of formation invaded by oil-based mud, laying a foundation for the subsequent inversion application of array induction logging data.