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Simulation of Flow in Multi-Scale Porous Media Using the Lattice Boltzmann Method on Quadtree Grids

Part of: Computer aspects of numerical algorithms Flows in porous media; filtration; seepage Incompressible viscous fluids

Published online by Cambridge University Press:  12 April 2016

Lei Zhang ,
Qinjun Kang ,
Li Chen  and
Jun Yao
Lei Zhang
Affiliation:
School of Petroleum Engineering, China University of Petroleum, Qingdao, Shandong 266580, China Computational Earth Science Group (EES-16), Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Qinjun Kang*
Affiliation:
Computational Earth Science Group (EES-16), Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Li Chen
Affiliation:
Computational Earth Science Group (EES-16), Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA Key Laboratory of Thermo-Fluid Science and Engineering of MOE, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China
Jun Yao*
Affiliation:
School of Petroleum Engineering, China University of Petroleum, Qingdao, Shandong 266580, China
*
*Corresponding author. Email addresses:zhlei84@163.com (L. Zhang), qkang@lanl.gov (Q. Kang), lichenmt@lanl.gov (L. Chen), yaojunhdpu@126.com (J. Yao)
*Corresponding author. Email addresses:zhlei84@163.com (L. Zhang), qkang@lanl.gov (Q. Kang), lichenmt@lanl.gov (L. Chen), yaojunhdpu@126.com (J. Yao)
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Abstract

The unified lattice Boltzmann model is extended to the quadtree grids for simulation of fluid flow through porous media. The unified lattice Boltzmann model is capable of simulating flow in porous media at various scales or in systems where multiple length scales coexist. The quadtree grid is able to provide a high-resolution approximation to complex geometries, with great flexibility to control local grid density. The combination of the unified lattice Boltzmann model and the quadtree grids results in an efficient numerical model for calculating permeability of multi-scale porous media. The model is used for permeability calculation for three systems, including a fractured system used in a previous study, a Voronoi tessellation system, and a computationally-generated pore structure of fractured shale. The results are compared with those obtained using the conventional lattice Boltzmann model or the unified lattice Boltzmann model on rectangular or uniform square grid. It is shown that the proposed model is an accurate and efficient tool for flow simulation in multi-scale porous media. In addition, for the fractured shale, the contribution of flow in matrix and fractures to the overall permeability of the fractured shale is studied systematically.

Keywords

Quadtree gridunified lattice Boltzmann methodpermeabilityfractured porous media

MSC classification

Secondary: 76S05: Flows in porous media; filtration; seepage 76D05: Navier-Stokes equations 65Y10: Algorithms for specific classes of architectures
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 4 , April 2016 , pp. 998 - 1014
Copyright
Copyright © Global-Science Press 2016 

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