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Direct Calculation of Permeability by High-Accurate Finite Difference and Numerical Integration Methods

Part of: Flows in porous media; filtration; seepage

Published online by Cambridge University Press:  21 July 2016

Yi Wang  and
Shuyu Sun
Yi Wang*
Affiliation:
National Engineering Laboratory for Pipeline Safety/MOE Key Laboratory of Petroleum Engineering/Beijing Key Laboratory of Urban Oil and Gas Distribution Technology, China University of Petroleum-Beijing, Beijing 102249, China
Shuyu Sun*
Affiliation:
Computational Transport Phenomena Laboratory, Division of Physical Science and Engineering, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia
*
*Corresponding author. Email addresses:yiwang1031@gmail.com (Y. Wang), shuyu.sun@kaust.edu.sa (S. Sun)
*Corresponding author. Email addresses:yiwang1031@gmail.com (Y. Wang), shuyu.sun@kaust.edu.sa (S. Sun)
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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.

Keywords

Finite difference methodnumerical integration methodhigh accuracyfull tensor permeabilitystokes

MSC classification

Secondary: 76S05: Flows in porous media; filtration; seepage
Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 2 , August 2016 , pp. 405 - 440
Copyright
Copyright © Global-Science Press 2016 

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