Numerical Simulation of a Multi-Frequency Resistivity Logging-While-Drilling Tool Using a Highly Accurate and Adaptive Higher-Order Finite Element Method
Year: 2012
Author: Zhonghua Ma, Dejun Liu, Hui Li, Xinsheng Gao
Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 4 : pp. 439–453
Abstract
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's equations, three kinds of boundary conditions, stability weak formulation of Maxwell'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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.10-m11158
Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 4 : pp. 439–453
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Resistivity logging-while-drilling higher-order finite element method adaptive exponential convergence numerical simulation.