Volume 20, Issue 2
Direct Calculation of Permeability by High-Accurate Finite Difference and Numerical Integration Methods

Yi Wang & Shuyu Sun

Commun. Comput. Phys., 20 (2016), pp. 405-440.

Published online: 2018-04

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  • Abstract

Velocity of fluid flow in underground porous media is 6∼12 orders of magnitudes lower than that in pipelines. If numerical errors are not carefully controlled in this kind of simulations, high distortion of the final results may occur [1–4]. To fit the high accuracy demands of fluid flow simulations in porous media, traditional finite difference methods and numerical integration methods are discussed and corresponding high-accurate methods are developed. When applied to the direct calculation of full-tensor permeability for underground flow, the high-accurate finite difference method is confirmed to have numerical error as low as 10−5% while the high-accurate numerical integration method has numerical error around 0%. Thus, the approach combining the high-accurate finite difference and numerical integration methods is a reliable way to efficiently determine the characteristics of general full-tensor permeability such as maximum and minimum permeability components, principal direction and anisotropic ratio.

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@Article{CiCP-20-405, author = {}, title = {Direct Calculation of Permeability by High-Accurate Finite Difference and Numerical Integration Methods}, journal = {Communications in Computational Physics}, year = {2018}, volume = {20}, number = {2}, pages = {405--440}, abstract = {

Velocity of fluid flow in underground porous media is 6∼12 orders of magnitudes lower than that in pipelines. If numerical errors are not carefully controlled in this kind of simulations, high distortion of the final results may occur [1–4]. To fit the high accuracy demands of fluid flow simulations in porous media, traditional finite difference methods and numerical integration methods are discussed and corresponding high-accurate methods are developed. When applied to the direct calculation of full-tensor permeability for underground flow, the high-accurate finite difference method is confirmed to have numerical error as low as 10−5% while the high-accurate numerical integration method has numerical error around 0%. Thus, the approach combining the high-accurate finite difference and numerical integration methods is a reliable way to efficiently determine the characteristics of general full-tensor permeability such as maximum and minimum permeability components, principal direction and anisotropic ratio.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.210815.240316a}, url = {http://global-sci.org/intro/article_detail/cicp/11158.html} }
TY - JOUR T1 - Direct Calculation of Permeability by High-Accurate Finite Difference and Numerical Integration Methods JO - Communications in Computational Physics VL - 2 SP - 405 EP - 440 PY - 2018 DA - 2018/04 SN - 20 DO - http://doi.org/10.4208/cicp.210815.240316a UR - https://global-sci.org/intro/article_detail/cicp/11158.html KW - AB -

Velocity of fluid flow in underground porous media is 6∼12 orders of magnitudes lower than that in pipelines. If numerical errors are not carefully controlled in this kind of simulations, high distortion of the final results may occur [1–4]. To fit the high accuracy demands of fluid flow simulations in porous media, traditional finite difference methods and numerical integration methods are discussed and corresponding high-accurate methods are developed. When applied to the direct calculation of full-tensor permeability for underground flow, the high-accurate finite difference method is confirmed to have numerical error as low as 10−5% while the high-accurate numerical integration method has numerical error around 0%. Thus, the approach combining the high-accurate finite difference and numerical integration methods is a reliable way to efficiently determine the characteristics of general full-tensor permeability such as maximum and minimum permeability components, principal direction and anisotropic ratio.

Yi Wang & Shuyu Sun. (2020). Direct Calculation of Permeability by High-Accurate Finite Difference and Numerical Integration Methods. Communications in Computational Physics. 20 (2). 405-440. doi:10.4208/cicp.210815.240316a
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