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CN 34-1054/N

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Non-Fickian model and experimental study of solute transport in porous media

  • 1.

    School of Resources and Environmental Engineering, Hefei University of Technology , Hefei 230000, China

  • 2.

    Shandong Academy of Water Conservancy , Jinan 250013, China

  • 3.

    School of Biotechnology and Food Engineering,Hefei University of Technology , Hefei 230000, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2017.05.007
  • Received Date: 11 April 2016
  • Rev Recd Date: 22 June 2016
  • Publish Date: 31 May 2017
    Abstract

  • Abstract

    To quantify the non-Fickian transport in porous media, a linear function was employed to characterize the relationship between the dispersivity and migration distance, a mathematical model LAF(Linear-Asymptotic Function) was presented, solute transport tests in one-dimensional glass column were carried out, and the accuracy of LAF was contrasted with the traditional ADE (advection-dispersion equation) models according to experimental data. The results show that, although the flow satisfies Darcy’s law, there are some differences between the experimental values and the fitted values obtained from the ADE model treating the dispersivity as a constant(the maximal error value being 1.57 g/L).#br##br##br##br#The simulation accuracy is enhanced when the dispersivity is treated as a linear function of LAF:#br##br# the maximal error value is 0.62 g/L. It can better simulate solute transport in the homogeneous finite column. These conclusions have been obtained in homogeneous media. The situation is more complicated in heterogeneous porous media, and the mechanism needs further research.

    Abstract

    To quantify the non-Fickian transport in porous media, a linear function was employed to characterize the relationship between the dispersivity and migration distance, a mathematical model LAF(Linear-Asymptotic Function) was presented, solute transport tests in one-dimensional glass column were carried out, and the accuracy of LAF was contrasted with the traditional ADE (advection-dispersion equation) models according to experimental data. The results show that, although the flow satisfies Darcy’s law, there are some differences between the experimental values and the fitted values obtained from the ADE model treating the dispersivity as a constant(the maximal error value being 1.57 g/L).#br##br##br##br#The simulation accuracy is enhanced when the dispersivity is treated as a linear function of LAF:#br##br# the maximal error value is 0.62 g/L. It can better simulate solute transport in the homogeneous finite column. These conclusions have been obtained in homogeneous media. The situation is more complicated in heterogeneous porous media, and the mechanism needs further research.
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    • References(15)
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    魏峰, 王全九, 周蓓蓓. 考虑尺度效应的瞬时输入溶质运移模型及解析解[J]. 农业工程学报，2014, 30(16): 129-135.
    [2]
    SHARMA P K, OJHA C S P, SWAMI D, et al. Semi-analytical solutions of multiprocessing non-equilibrium transport equations with linear and exponential distance-dependent dispersivity[J]. Water Resources Management, 2015,29(14): 5255-5273.
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    GELHARL W, WELTY W, REHFELDT K R. A critical review of data on field-scaledispersion in aquifers[J]. Water Resources Research, 1992, 28: 1955–1974.
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    王子亭.对流-弥散问题的随机过程方法[J].石油大学学报,1996,20(6):29-31.
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    GELHAR L W, WELTY C, REHFELDT K R. Acritical review of data on filed-scale dispersion in aquifers[J].Water Resources Research, 1992, 28(7): 1955-1974.
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    黄康乐. 多孔介质水动力弥散尺度效应研究—现状与展望[J]. 水文地质工程地质, 1991, 18(3): 25-26.
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    PICKENS J F, GRISAK G E. Modeling of scale-dependent dispersion in hydrogeologic systems[J].Water Resources Research, 1981, 17(6): 1701-1711.
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    PANG L P, HUNT B. Solutions and verification of a scale-dependent dispersion model[J]. Journal of Contaminant Hydrology, 2001, 53(1/2): 21-39.
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    VAN GENUCHTEN MTh, WIERENGA P J. Mass transfer studies in sorbing porous media I. Analytical solutions[J]. Soil Science Society of America Journal, 1976, 40 (4): 473-480.
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    张德生. 土壤溶质运移数学模型研究[D]. 西安：西安理工大学, 2004.
    [11]
    高光耀.考虑弥散尺度效应与不动水体的反应性溶质运移动力学模型及半解析解[J].水动力学研究与进展:A辑，2010,25(2):207-208.
    [12]
    PANG L P, HUNT B. Solutions and verification of a scale-dependent dispersion model[J]. Journal of Contaminant Hydrology,2001,53: 21–39.
    [13]
    VAN GENUCHTEN M T, PARKER J C. Boundary conditions for displacementexperiments through short laboratory soil columns[J]. Soil Science Society of America Journal, 1984, 48: 703–708.
    [14]
    ZHOU L,SELIM H M. Scale-dependent dispersion in soils: An overview[J]. Advances in Agronomy, 2003, 80: 223–263.
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    YOU Kehua, ZHAN Hongbin. New solutions for solute transport in a finite column with distance-dependent dispersivities and time-dependent solute sources[J].Journal of Hydrology, 2013,487: 97-97.
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    [1]
    魏峰, 王全九, 周蓓蓓. 考虑尺度效应的瞬时输入溶质运移模型及解析解[J]. 农业工程学报，2014, 30(16): 129-135.
    [2]
    SHARMA P K, OJHA C S P, SWAMI D, et al. Semi-analytical solutions of multiprocessing non-equilibrium transport equations with linear and exponential distance-dependent dispersivity[J]. Water Resources Management, 2015,29(14): 5255-5273.
    [3]
    GELHARL W, WELTY W, REHFELDT K R. A critical review of data on field-scaledispersion in aquifers[J]. Water Resources Research, 1992, 28: 1955–1974.
    [4]
    王子亭.对流-弥散问题的随机过程方法[J].石油大学学报,1996,20(6):29-31.
    [5]
    GELHAR L W, WELTY C, REHFELDT K R. Acritical review of data on filed-scale dispersion in aquifers[J].Water Resources Research, 1992, 28(7): 1955-1974.
    [6]
    黄康乐. 多孔介质水动力弥散尺度效应研究—现状与展望[J]. 水文地质工程地质, 1991, 18(3): 25-26.
    [7]
    PICKENS J F, GRISAK G E. Modeling of scale-dependent dispersion in hydrogeologic systems[J].Water Resources Research, 1981, 17(6): 1701-1711.
    [8]
    PANG L P, HUNT B. Solutions and verification of a scale-dependent dispersion model[J]. Journal of Contaminant Hydrology, 2001, 53(1/2): 21-39.
    [9]
    VAN GENUCHTEN MTh, WIERENGA P J. Mass transfer studies in sorbing porous media I. Analytical solutions[J]. Soil Science Society of America Journal, 1976, 40 (4): 473-480.
    [10]
    张德生. 土壤溶质运移数学模型研究[D]. 西安：西安理工大学, 2004.
    [11]
    高光耀.考虑弥散尺度效应与不动水体的反应性溶质运移动力学模型及半解析解[J].水动力学研究与进展:A辑，2010,25(2):207-208.
    [12]
    PANG L P, HUNT B. Solutions and verification of a scale-dependent dispersion model[J]. Journal of Contaminant Hydrology,2001,53: 21–39.
    [13]
    VAN GENUCHTEN M T, PARKER J C. Boundary conditions for displacementexperiments through short laboratory soil columns[J]. Soil Science Society of America Journal, 1984, 48: 703–708.
    [14]
    ZHOU L,SELIM H M. Scale-dependent dispersion in soils: An overview[J]. Advances in Agronomy, 2003, 80: 223–263.
    [15]
    YOU Kehua, ZHAN Hongbin. New solutions for solute transport in a finite column with distance-dependent dispersivities and time-dependent solute sources[J].Journal of Hydrology, 2013,487: 97-97.
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