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多孔介质内溶解与沉淀过程的格子Boltzmann方法模拟

张婷 施保昌 柴振华

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多孔介质内溶解与沉淀过程的格子Boltzmann方法模拟

张婷, 施保昌, 柴振华

Lattice Boltzmann simulation of dissolution and precipitation in porous media

Zhang Ting, Shi Bao-Chang, Chai Zhen-Hua
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  • 本文采用格子Boltzmann方法模拟了多孔介质内的溶解和沉淀现象, 并分析了雷诺数、施密特数、达姆科勒数对多孔介质孔隙结构及浓度分布的影响. 结果表明: 对于多孔介质内的溶解(沉淀)过程, 当雷诺数越大时, 孔隙率越大(小), 平均浓度值越小(大); 当达姆科勒数或施密特数较小时, 溶解和沉淀过程均受反应控制, 此时反应在多孔介质的固体表面较为均匀的发生; 当达姆科勒数或施密特数较大时, 溶解和沉淀过程均受扩散控制, 此时反应主要发生在上游及大孔隙区域.
    In this paper, we simulate numerically the dissolution and precipitation in porous media by using the lattice Boltzmann method (LBM). The fluid flow in porous media is simulated by using a multiple-relaxation-time (MRT) LBM, while a D2Q9 lattice BGK model is used for reactive solute transport. Frst, the code of LBM is tested by simulating the diffusion and reaction at a boundary in an open rectangular domain, and comparing the results with the analytic solution. Then, the effects of the Reynolds number (Re), the Schmidt number (Sc) and the Damkohler number (Da) on the variations of the geometry of the porous media and the concentration field are carefully studied. It can be found that for the dissolution (precipitation), as Re is increased, the porosity of the porous media will be increased (decreased), and the average concentration will be decreased (increased). Besides, at low Damkohler numbers or Schmidt numbers, the dissolution and precipitation will be reaction-controlled and are highly uniform. However, as Da or Sc is high, the dissolution and precipitation will be diffution-controlled, and mainly occur in the upstream and large pore space.
    • 基金项目: 国家自然科学基金(批准号:51306133, 11272132)资助的课题
    • Funds: Projected supported by the National Natural Science Foundation of China (Grant Nos. 51306133, 11272132).
    [1]

    Guo Y L, Xu H H, Shen S Q, Wei L 2013 Acta Phys. Sin. 62 144704 (in Chinese) [郭亚丽, 徐鹤函, 沈胜强, 魏兰 2013 物理学报 62 144704]

    [2]

    Mao W, Guo Z L, Wang L 2013 Acta Phys. Sin. 62 084703 (in Chinese) [毛威, 郭照立, 王亮 2013 物理学报 62 084703]

    [3]

    Huang Q G, Pan G, Song B W 2014 Acta Phys. Sin. 63 054701 (in Chinese) [黄桥高, 潘光, 宋保维 2014 物理学报 63 054701]

    [4]

    Wells J T, Janecky D R, Travis B J 1991 Physics D 47 115

    [5]

    Janecky D R, Chen S, Dawson S, Eggert K C, Travis B J 1992 Proceedings of the 7th International Symposium on Water-Rock Interaction Park City, United States, July 13-18, 1992 p1043

    [6]

    Chen S, Doolen G D 1998 Annu. Rev. Fluid Mech. 30 329

    [7]

    Kingdon R D, Schofield V 1992 J. Phys. A 25 907

    [8]

    Dawson S P, Chen S, Doolen G D 1993 J. Chem. Phys. 98 1514

    [9]

    Kelemen P B, Whitehead J A, Aharonov E, Jordahl K A 1995 J. Geophys. Res. 100 475

    [10]

    He X, Li N, Goldstein B 2000 Mol. Simul. 25 145

    [11]

    Kang Q, Zhang D, Chen S, He X 2002 Phys. Rev. E 65 036318

    [12]

    Kang Q, Zhang D, Chen S 2003 J. Geophys. Res. 108 2505

    [13]

    Kang Q, Lichtner P C, Zhang D 2006 J. Geophys. Res. 111 B05203

    [14]

    Chen L, Kang Q, Carey B, Tao W Q 2014 Int. J. Heat Mass Transfer 75 483

    [15]

    Chen L, Kang Q, Viswanathan H S, Tao W Q 2014 Water Resour. Res. 50 9343

    [16]

    Nogues J P, Fitts J P, Celia M A, Peters C A 2013 Water Resour. Res. 49 6006

    [17]

    Tartakovsky A M, Meakin P, Scheibe T D, Eichler West R M 2007 J. Comput. Phys. 222 654

    [18]

    Yoon H, Valocchi A J, Werth C J, Dewers T 2012 Water Resour. Res. 48 W02524

    [19]

    Huber C, Shafei B, Parmigiani A 2014 Geochim. Cosmochim. Acta 124 109

    [20]

    Li X, Huang H, Meakin P 2008 Water Resour. Res. 44 W12407

    [21]

    Luo H, Quintard M, Debenest G, Laouafa F 2012 Comput. Geosci. 16 913

    [22]

    Pan C, Luo L L, Miller C T 2006 Comput. Fluids 35 898

    [23]

    Chai Z H, Shi B C, Lu J H, Guo Z L 2010 Comput. Fluids 39 2069

    [24]

    Zhang T, Shi B C, Guo Z L, Chai Z H, Lu J H 2012 Phys. Rev. E 85 016701

    [25]

    Guo Z L, Zheng C G, Shi B C 2002 Phys. Fluids 11 374

  • [1]

    Guo Y L, Xu H H, Shen S Q, Wei L 2013 Acta Phys. Sin. 62 144704 (in Chinese) [郭亚丽, 徐鹤函, 沈胜强, 魏兰 2013 物理学报 62 144704]

    [2]

    Mao W, Guo Z L, Wang L 2013 Acta Phys. Sin. 62 084703 (in Chinese) [毛威, 郭照立, 王亮 2013 物理学报 62 084703]

    [3]

    Huang Q G, Pan G, Song B W 2014 Acta Phys. Sin. 63 054701 (in Chinese) [黄桥高, 潘光, 宋保维 2014 物理学报 63 054701]

    [4]

    Wells J T, Janecky D R, Travis B J 1991 Physics D 47 115

    [5]

    Janecky D R, Chen S, Dawson S, Eggert K C, Travis B J 1992 Proceedings of the 7th International Symposium on Water-Rock Interaction Park City, United States, July 13-18, 1992 p1043

    [6]

    Chen S, Doolen G D 1998 Annu. Rev. Fluid Mech. 30 329

    [7]

    Kingdon R D, Schofield V 1992 J. Phys. A 25 907

    [8]

    Dawson S P, Chen S, Doolen G D 1993 J. Chem. Phys. 98 1514

    [9]

    Kelemen P B, Whitehead J A, Aharonov E, Jordahl K A 1995 J. Geophys. Res. 100 475

    [10]

    He X, Li N, Goldstein B 2000 Mol. Simul. 25 145

    [11]

    Kang Q, Zhang D, Chen S, He X 2002 Phys. Rev. E 65 036318

    [12]

    Kang Q, Zhang D, Chen S 2003 J. Geophys. Res. 108 2505

    [13]

    Kang Q, Lichtner P C, Zhang D 2006 J. Geophys. Res. 111 B05203

    [14]

    Chen L, Kang Q, Carey B, Tao W Q 2014 Int. J. Heat Mass Transfer 75 483

    [15]

    Chen L, Kang Q, Viswanathan H S, Tao W Q 2014 Water Resour. Res. 50 9343

    [16]

    Nogues J P, Fitts J P, Celia M A, Peters C A 2013 Water Resour. Res. 49 6006

    [17]

    Tartakovsky A M, Meakin P, Scheibe T D, Eichler West R M 2007 J. Comput. Phys. 222 654

    [18]

    Yoon H, Valocchi A J, Werth C J, Dewers T 2012 Water Resour. Res. 48 W02524

    [19]

    Huber C, Shafei B, Parmigiani A 2014 Geochim. Cosmochim. Acta 124 109

    [20]

    Li X, Huang H, Meakin P 2008 Water Resour. Res. 44 W12407

    [21]

    Luo H, Quintard M, Debenest G, Laouafa F 2012 Comput. Geosci. 16 913

    [22]

    Pan C, Luo L L, Miller C T 2006 Comput. Fluids 35 898

    [23]

    Chai Z H, Shi B C, Lu J H, Guo Z L 2010 Comput. Fluids 39 2069

    [24]

    Zhang T, Shi B C, Guo Z L, Chai Z H, Lu J H 2012 Phys. Rev. E 85 016701

    [25]

    Guo Z L, Zheng C G, Shi B C 2002 Phys. Fluids 11 374

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出版历程
  • 收稿日期:  2014-10-26
  • 修回日期:  2015-02-28
  • 刊出日期:  2015-08-05

多孔介质内溶解与沉淀过程的格子Boltzmann方法模拟

  • 1. 理学院, 武汉科技大学, 武汉 430081;
  • 2. 数学与统计学院, 华中科技大学, 武汉 430074
    基金项目: 国家自然科学基金(批准号:51306133, 11272132)资助的课题

摘要: 本文采用格子Boltzmann方法模拟了多孔介质内的溶解和沉淀现象, 并分析了雷诺数、施密特数、达姆科勒数对多孔介质孔隙结构及浓度分布的影响. 结果表明: 对于多孔介质内的溶解(沉淀)过程, 当雷诺数越大时, 孔隙率越大(小), 平均浓度值越小(大); 当达姆科勒数或施密特数较小时, 溶解和沉淀过程均受反应控制, 此时反应在多孔介质的固体表面较为均匀的发生; 当达姆科勒数或施密特数较大时, 溶解和沉淀过程均受扩散控制, 此时反应主要发生在上游及大孔隙区域.

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