Numerical Modeling of Eccentered LWD Borehole Sensors in Dipping and Fully Anisotropic Earth Formations

Abstract

Logging-while-drilling (LWD) borehole sensors are used to provide real-time resistivity data of adjacent earth formations for hydrocarbon exploration. This allows for a proactive adjustment of the dipping angle and azimuth direction of the drill and, hence, geosteering capabilities. The analysis of borehole eccentricity effects on LWD sensor response in full 3 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\times$</tex></formula> 3 anisotropic earth formations is important for correct data interpretation in deviated or horizontal wells. In this paper, we present a cylindrical-grid finite-difference time-domain model to tackle this problem. The grid is aligned to the sensor axis to avoid staircasing error in the sensor geometry but, in general, misaligned to the (eccentered) borehole/formation interface. A locally conformal discretization is used to compute effective conductivity tensors of partially-filled grid cells at those interfaces, involving an isotropic medium (borehole) and a full 3 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$\times$</tex></formula> 3 anisotropic medium in general (dipped earth formation). The numerical model is used to compute the response of eccentered LWD sensors in layered earth formations with anisotropic dipping beds.