Volume 4, Issue 4
Numerical Simulation of a Multi-Frequency Resistivity Logging-While-Drilling Tool Using a Highly Accurate and Adaptive Higher-Order Finite Element Method

Zhonghua Ma, Dejun Liu, Hui Li & Xinsheng Gao

Adv. Appl. Math. Mech., 4 (2012), pp. 439-453.

Published online: 2012-04

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  • 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.

  • Keywords

Resistivity logging-while-drilling, higher-order finite element method, adaptive, exponential convergence, numerical simulation.

  • AMS Subject Headings

35Q61, 35Q86, 74S05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-4-439, author = {}, title = {Numerical Simulation of a Multi-Frequency Resistivity Logging-While-Drilling Tool Using a Highly Accurate and Adaptive Higher-Order Finite Element Method}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2012}, volume = {4}, number = {4}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m11158}, url = {http://global-sci.org/intro/article_detail/aamm/129.html} }
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 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 -

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.

Zhonghua Ma, Dejun Liu, Hui Li & Xinsheng Gao. (1970). Numerical Simulation of a Multi-Frequency Resistivity Logging-While-Drilling Tool Using a Highly Accurate and Adaptive Higher-Order Finite Element Method. Advances in Applied Mathematics and Mechanics. 4 (4). 439-453. doi:10.4208/aamm.10-m11158
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