Simulation of 3D DC Borehole Resistivity Measurements with a Goal- Oriented hp Finite-Element Method. Part I: Laterolog and LWD

We simulate and study the combined three-dimensional effects on resistivity logging measurements due to dip angle (in deviated wells), different arrangements of three-dimensional electrodes, and anisotropy effects. All results correspond to electrostatic (zero frequency) measurements. Thus, we consider direct current (DC) electrodes. We simulate both laterolog and logging-while-drilling (LWD) measurements. These simulations are performed by considering optimal hp-grids obtained from a 2D selfadaptive goal-oriented hp-finite element (FE) method, and transferring these grids to a 3D hpFE software. Then, we perform 3D simulations (employing 2D optimal grids) using the 3D software. Finally, an analysis of the error is performed by considering a finer (globally prefined) grid. Numerical results illustrate the accuracy of the simulations, and indicate that LWD-type measurements (at zero frequency) are more sensitive to dip angle, different arrangements of electrodes, and anisotropy effects than laterolog-type measurements. While vertical well measurements may be insensitive to different electrode configurations and anisotropy effects, for highly deviated wells, consideration of the exact electrode geometries and anisotropy effects may become crucial for the correct interpretation of the results. Thus, all these 3D effects are considered simultaneously, rather than as a superposition of individual effects.