TY - JOUR
T1 - Numerical Simulation of a Multi-Frequency Resistivity Logging-While-Drilling Tool Using a Highly Accurate and Adaptive Higher-Order Finite Element Method
AU - Ma , Zhonghua
AU - Liu , Dejun
AU - Li , Hui
AU - Gao , Xinsheng
JO - Advances in Applied Mathematics and Mechanics
VL - 4
SP - 439
EP - 453
PY - 2012
DA - 2012/04
SN - 4
DO - http://doi.org/10.4208/aamm.10-m11158
UR - https://global-sci.org/intro/article_detail/aamm/129.html
KW - Resistivity logging-while-drilling, higher-order finite element method, adaptive,
exponential convergence, numerical simulation.
AB - <p style="text-align: justify;">A novel, highly efficient and accurate adaptive higher-order finite element
method ($hp$-FEM) is used to simulate a multi-frequency resistivity logging-while-drilling (LWD)
tool response in a borehole environment. Presented in this study are the vector expression
of Maxwell&#39;s equations, three kinds of boundary conditions, stability weak formulation of
Maxwell&#39;s equations, and automatic $hp$-adaptivity strategy. The new $hp$-FEM can select
optimal refinement and calculation strategies based on the practical formation model and
error estimation. Numerical experiments show that the new $hp$-FEM has an exponential
convergence rate in terms of relative error in a user-prescribed quantity of interest
against the degrees of freedom, which provides more accurate results than those obtained
using the adaptive $h$-FEM. The numerical results illustrate the high efficiency and
accuracy of the method at a given LWD tool structure and parameters in different physical
models, which further confirm the accuracy of the results using the Hermes
library (http://hpfem.org/hermes) with a multi-frequency resistivity LWD tool
response in a borehole environment.</p>