Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-23T19:51:48.342Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Part of: Flows in porous media; filtration; seepage Computer aspects of numerical algorithms 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)
Get access

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Chen, S. Y. and Doolen, G. D., Lattice Boltzmann methode for fluid flows. Annu. Rev. Fluid. Mech., 30 (1998), 329–364.CrossRefGoogle Scholar
[2]Martys, N. S. and Chen, H., Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann method. Phys. Rev. E, 53 (1996), 743.CrossRefGoogle ScholarPubMed
[3]Chen, L., Kang, Q., He, Y.-L., and Tao, W.-Q., Pore-scale simulation of coupled multiple physicochemical thermal processes in micro reactor using lattice Boltzmann method Int. J. Hydrogen Energy 37 (2012), 13943–13957.CrossRefGoogle Scholar
[4]Chen, L., He, Y.-L., Kang, Q., and Tao, W.-Q., Coupled numerical approach combining finite volume and lattice Boltzmann methods for multi-scale multi-physicochemical processes. J. Comput. Phys., 255 (2013), 83–105.CrossRefGoogle Scholar
[5]Biferale, L., Perlekar, P., Sbragaglia, M., and Toschi, F., Convection in multiphase fluid flows using lattice Boltzmann methods. Phys. Rev. Lett., 108 (2012), 104502.CrossRefGoogle ScholarPubMed
[6]Joshi, A. S. and Sun, Y., Multiphase lattice Boltzmann method for particle suspensions. Phys. Rev. E, 79 (2009), 066703.CrossRefGoogle ScholarPubMed
[7]Kang, Q., Zhang, D., Chen, S., and He, X., Lattice Boltzmann simulation of chemical dissolution in porous media. Phys. Rev. E, 65 (2002), 036318.CrossRefGoogle ScholarPubMed
[8]Kang, Q. J., Zhang, D. X. and Chen, S. Y., Simulation of dissolution and precipitation in porous media. J. Geophys. Res. Solid Earth, 108 (2003), 2505.CrossRefGoogle Scholar
[9]Chen, L., Kang, Q., Robinson, B. A., He, Y.-L., and Tao, W.-Q., Pore-scale modeling of multiphase reactive transport with phase transitions and dissolution-precipitation processes in closed systems. Phys. Rev. E, 87 (2013), 043306.CrossRefGoogle ScholarPubMed
[10]Chen, L., Luan, H.-B., He, Y.-L., and Tao, W.-Q., Pore-scale flow and mass transport in gas diffusion layer of proton exchange membrane fuel cell with interdigitated flow fields. Int. J. Therm. Sci., 51 (2012), 132–144.CrossRefGoogle Scholar
[11]Kang, Q. J., Lichtner, P. C. and Zhang, D. X., Lattice Boltzmann pore-scale model for multicomponent reactive transport in porous media. J. Geophys. Res. Solid Earth, 111 (2006), B05203.CrossRefGoogle Scholar
[12]Balasubramanian, K., Hayot, F. and Saam, W. F., Darcy's law from lattice-gas hydrodynamics. Phys. Rev. A, 36 (1987), 2248–2253.CrossRefGoogle ScholarPubMed
[13]Spaid, M. A. and Phelan, F. R. Jr, Lattice Boltzmann methods for modeling microscale flow in fibrous porous media. Phys. Fluids, 9 (1997), 2468–2474.CrossRefGoogle Scholar
[14]Freed, D. M., Lattice-Boltzmann method for macroscopic porous media modeling. Int. J. Mod. Phys. C, 9(1998), 1491–1503.CrossRefGoogle Scholar
[15]Guo, Z. and Zhao, T. S., Lattice Boltzmann model for incompressible flows through porous media. Phys. Rev. E, 66 (2002), 036304.CrossRefGoogle ScholarPubMed
[16]Kang, Q., Zhang, D. and Chen, S., Unified lattice Boltzmann method for flow in multiscale porous media. Phys. Rev. E, 66 (2002), 056307.CrossRefGoogle ScholarPubMed
[17]He, X., Luo, L.-S. and Dembo, M., Some progress in lattice Boltzmann method. Part I. nonuni- form mesh grids. J. Comput. Phys., 129 (1996), 357–363.CrossRefGoogle Scholar
[18]Filippova, O. and Hänel, D., Grid refinement for lattice-BGK models. J. Comput. Phys., 147 (1998), 219–228.CrossRefGoogle Scholar
[19]Yu, D., Mei, R. and Shyy, W.A multi-block lattice Boltzmann method for viscous fluid flows. Int. J. Numer. Methods Fluids, 39 (2002), 99–120.CrossRefGoogle Scholar
[20]Nannelli, F. and Succi, S., The lattice Boltzmann equation on irregular lattices. J. Stat. Phys., 68 (1992), 401–407.CrossRefGoogle Scholar
[21]Cao, N., Chen, S., Jin, S., and Martínez, D., Physical symmetry and lattice symmetry in the lattice Boltzmann method. Phys. Rev. E, 55 (1997), R21-R24.CrossRefGoogle Scholar
[22]Ubertini, S. and Succi, S., Recent advances of lattice Boltzmann techniques on unstructured grids. Prog. Comput. Fluid. Dy., 5 (2005), 85–96.CrossRefGoogle Scholar
[23]Rossi, N., Ubertini, S., Bella, G., and Succi, S., Unstructured lattice Boltzmann method in three dimensions. Int. J. Numer. Methods Fluids, 49 (2005), 619–633.CrossRefGoogle Scholar
[24]Li, Y., LeBoeuf, E. J. and Basu, P. K., Least-squares finite-element scheme for the lattice Boltzmann method on an unstructured mesh. Phys. Rev. E, 72 (2005), 046711.CrossRefGoogle Scholar
[25]Luan, H.-B., Xu, H., Chen, L., Sun, D.-L., He, Y.-L., and Tao, W.-Q., Evaluation of the coupling scheme of FVM and LBM for fluid flows around complex geometries. Int. J. Heat Mass Transfer, 54 (2011), 1975–1985.CrossRefGoogle Scholar
[26]Chen, Y., Kang, Q. J., Cai, Q. D., and Zhang, D. X., Lattice Boltzmann method on quadtree grids. Phys. Rev. E, 83 (2011), 10.CrossRefGoogle ScholarPubMed
[27]Chen, Y. and Cai, Q. D., The lattice Boltzmann method based on quadtree mesh. Mod. Phys. Lett. B, 23 (2009), 289–292.CrossRefGoogle Scholar
[28]Klinger, A. and Dyer, C. R., Experiments on picture representation using regular decomposition. Computer Graphics and Image Processing, 5 (1976), 68–105.CrossRefGoogle Scholar
[29]Samet, H., The quadtree and related hierarchical data structures. ACM Comput. Surv., 16 (1984), 187–260.CrossRefGoogle Scholar
[30]Crouse, B., Rank, E., Krafczyk, M., and Tolke, J., A LB-based approach for adaptive flow simulations. Int. J. Mod. Phys. B 17 (2003), 109–112.CrossRefGoogle Scholar
[31]Dupont, T. F. and Liu, Y., Back and forth error compensation and correction methods for removing errors induced by uneven gradients of the level set function. J. Comput. Phys., 190 (2003), 311–324.CrossRefGoogle Scholar
[32]Dupont, T. F. and Liu, Y., Back and forth error compensation and correction methods for semi-Lagrangian schemes with application to level set interface computations. Math. Comput., (2007), 647–668.Google Scholar
[33]Byung Moon, K., Liu, Y., Llamas, I., and Rossignac, J., Advections with Significantly Reduced Dissipation and Diffusion. IEEE Trans. Vis. Comput. Graph., 13 (2007), 135–144.Google Scholar
[34]Baehmann, P. L., Wittchen, S. L., Shephard, M. S., Grice, K. R., and Yerry, M. A., Robust, geometrically based, automatic two-dimensional mesh generation. Int. J. Numer. Methods Eng., 24 (1987), 1043–1078.CrossRefGoogle Scholar
[35]Popinet, S., Gerris: A tree-based adaptive solver for the incompressible Euler equations in complex geometries. J. Comput. Phys., 190 (2003), 572–600.CrossRefGoogle Scholar
[36]Qian, Y. H., Humières, D. D. and Lallemand, P., Lattice BGK Models for Navier-Stokes Equation. Europhys. Lett., 17 (1992), 479–484.CrossRefGoogle Scholar
[37]Zou, Q. and He, X., On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys. Fluids, 9 (1997), 1591–1598.CrossRefGoogle Scholar
[38]Voronoi, G., Nouvelles applications des paramèteres continus à la théorie des formes quadratiques. J. Reine. Angew. Math., 134 (1908), 198–287.CrossRefGoogle Scholar
[39]Wu, M., Xiao, F., Johnson-Paben, R. M., Retterer, S. T., Yin, X., and Neeves, K. B., Single- and two-phase flow in microfluidic porous media analogs based on Voronoi tessellation. Lab. Chip., 12(2012), 253–261.CrossRefGoogle ScholarPubMed
[40]Vengosh, A., Jackson, R. B., Warner, N., Darrah, T. H., and Kondash, A., A Critical Review of the Risks to Water Resources from Unconventional Shale Gas Development and Hydraulic Fracturing in the United States. Environ. Sci. Technol., 48 (2014), 8334–8348.CrossRefGoogle ScholarPubMed
[41]Best, M. and Katsube, T., Shale permeability and its significance in hydrocarbon exploration. The Leading Edge, 14 (1995), 165–170.CrossRefGoogle Scholar
[42]Carlson, E. S. and Mercer, J. C., Devonian shale gas production: Mechanisms and simple models. J. Petrol. Technol., 43 (1991), 476–482.CrossRefGoogle Scholar