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A Layer-Integrated Model of Solute Transport in Heterogeneous Media

Published online by Cambridge University Press:  03 June 2015

Hung-En Chen ,
Hui-Ping Lee ,
Shih-Wei Chiang ,
Tung-Lin Tsai  and
Jinn-Chuang Yang
Hung-En Chen
Affiliation:
Department of Civil Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 30010, Taiwan
Hui-Ping Lee
Affiliation:
Department of Civil Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 30010, Taiwan
Shih-Wei Chiang*
Affiliation:
Agricultural Engineering Research Center, 196-1 Chung Yuan Road, Chungli 32061, Taiwan
Tung-Lin Tsai
Affiliation:
Department of Civil and Water Resources Engineering National Chiayi University, 300 Syuefu Road, Chiayi 60004, Taiwan
Jinn-Chuang Yang
Affiliation:
Department of Civil Engineering and Disaster Prevention and Water Environment Research Center, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 30010, Taiwan
*
*Corresponding author. Email: [email protected]
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Abstract

This study presents a numerical solution to the three-dimensional solute transport in heterogeneous media by using a layer-integrated approach. Omitting vertical spatial variation of soil and hydraulic properties within each layer, a three-dimensional solute transport can be simplified as a quasi-three-dimensional solute transport which couples a horizontal two-dimensional simulation and a vertical one-dimensional computation. The finite analytic numerical method was used to discretize the derived two-dimensional governing equation. A quadratic function was used to approximate the vertical one-dimensional concentration distribution in the layer to ensure the continuity of concentration and flux at the interface between the adjacent layers. By integration over each layer, a set of system of equations can be generated for a single column of vertical cells and solved numerically to give the vertical solute concentration profile. The solute concentration field was then obtained by solving all columns of vertical cells to achieve convergence with the iterative solution procedure. The proposed model was verified through examples from the published literatures including four verifications in terms of analytical and experimental cases. Comparison of simulation results indicates that the proposed model satisfies the solute concentration profiles obtained from experiments in time and space.

Keywords

65C2065M99Layer-integrated modelgroundwatersolute transportfinite analytic methodhet-erogeneous media
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 6 , December 2014 , pp. 699 - 717
Copyright
Copyright © Global-Science Press 2014

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References

[1]Al-Niami, A. N. S. and Rushton, K. R., Dispersion in stratified porous-media-analytical solu-tions, Water Resour Res., 15(5) (1979), pp. 1044–1048.Google Scholar
[2]Chen, C. J., Naseri-Neshat, H. and Ho, K. S., Finite-analytic numerical solution of heat transfer in two-dimensional cavity flow, Numer. Heat Trans., 4(2) (1981), pp. 179–197.Google Scholar
[3]Chen, Y. M., Xie, H. J., Ke, H. and Chen, R. P., An analytical solution for one-dimensional contaminant diffusion through multi-layered system and its applications, Environ. Geol., 58(5) (2009), pp. 1083–1094.Google Scholar
[4]Didierjean, S., Maillet, D. and Moyne, C., Analytical solutions of one-dimensional macrodispersion in stratified porous media by the quadrupole method: Convergence to an equivalent homogeneous porous medium, Adv. Water Resour., 27(6) (2004), pp. 657–667.Google Scholar
[5]Hung, M. C., Hsieh, T. Y., Tsai, T. L. and Yang, J. C., A layer-integrated approach for shallow water free-surface flow computation, Commun. Numer. Meth. Eng., 24(12) (2008), pp. 1699–1722.CrossRefGoogle Scholar
[6]Hwang, J. C., Chen, C. J., Sheikhoslami, M. and Panigrahi, B. K., Finite analytic numerical-solution for two-dimensional groundwater solute transport, Water Resour Res., 21(9) (1985), pp. 1354–1360.Google Scholar
[7]Kim, C. K. and Lee, J. S., A 3-dimensional PC-based hydrodynamic model using an ADI scheme, Coast Eng., 23(3-4) (1994), pp. 271–287.Google Scholar
[8]Kuo, Y. C., Huang, L. H. and Tsai, T. L., A hybrid three-dimensional computational model of groundwater solute transport in heterogeneous media, Water Resour. Res., 44(3) (2008).Google Scholar
[9]Lai, C. J. and Yen, C. W., Turbulent free-surface flow simulation using a multilayer model, Int. J. Numer. Meth. Fl., 16(11) (1993), pp. 1007–1025.Google Scholar
[10]Lardner, R. W. and Cekirge, H. M., A new algorithm for 3-dimensional tidal and storm-surge computations, Appl. Math. Model., 12(5) (1988), pp. 471–481.CrossRefGoogle Scholar
[11]Leij, F. J. and Vangenuchten, M. T., Approximate analytical solutions for solute transport in 2-layer porous-media, Transport Porous Med., 18(1) (1995), pp. 65–85.CrossRefGoogle Scholar
[12]Li, C. W. and Gu, J., 3d layered-integrated modelling of mass exchange in semi-enclosed water bodies, J. Hydraul. Res., 39(4) (2001), pp. 403–411.Google Scholar
[13]Li, Y. C. and Cleall, P. J., Analytical solutions for contaminant diffusion in double-layered porous media, J. Geotech. Geoenviron., 136(11) (2010), pp. 1542–1554.CrossRefGoogle Scholar
[14]Li, Y. S. and Zhan, J. M., An efficient 3-dimensional semiimplicit finite-element scheme for simulation offree-surface flows, Int. J. Numer. Meth. Fl., 16(3) (1993), pp. 187–198.Google Scholar
[15]Lin, L., Yang, J. Z., Zhang, B. and Zhu, Y., A simplified numerical model of 3-d groundwater and solute transport at large scale area, J. Hydrodyn., 22(3) (2010), pp. 319–328.Google Scholar
[16]Lin, W. L., Haik, Y., Bernatz, R. and Chen, C. J., Finite analytic method and its applications: A review, Dynam. Atmos Oceans, 27(1-4) (1998), pp. 17–33.CrossRefGoogle Scholar
[17]Liu, C. X., Ball, W. P. and Ellis, J. H., An analytical solution to the one-dimensional solute advection-dispersion equation in multi-layer porous media, Transport Porous Med., 30(1) (1998), pp. 25–43.Google Scholar
[18]Liu, C. X., Szecsody, J. E., Zachara, J. M. and Ball, W. P., Use of the generalized integral transform method for solving equations of solute transport in porous media, Adv. Water Resour., 23(5) (2000), pp. 483–492.CrossRefGoogle Scholar
[19]Liu, G. and Si, B. C., Analytical modeling of one-dimensional diffusion in layered systems with position-dependent diffusion coefficients, Adv. Water Resour., 31(2) (2008), pp. 251–268.Google Scholar
[20]Neville, C. J., Compilation of Analytical Solutions for Solute Transport in Uniform Flow, S. S. Padadopulos & Associateds, Bethesda, MD, 1994.Google Scholar
[21]Reggio, M., Hess, A. and Ilinca, A., 3-d multiple-level simulation of free surface flows, J. Hydraul. Res., 40(4) (2002), pp. 413–423.Google Scholar
[22]Sudicky, E. A., Gillham, R. W. and Frind, E. O., Experimental investigation of solute transport in stratified porous-media. 1. The nonreactive case, Water Resour Res., 21(7) (1985), pp. 1035–1041.Google Scholar
[23]Taigbenu, A. E. and Onyejekwe, O. O., A flux-correct green element model of quasi threedimensional multiaquifer flow, Water Resour Res., 36(12) (2000), pp. 3631–3640.CrossRefGoogle Scholar
[24]Tang, Y. and Aral, M. M., Contaminant transport in layered porous-media. 1. General-solution, Water Resour Res., 28(5) (1992), pp. 1389–1397.Google Scholar
[25]Tsai, T. L., Yang, J. C. and Huang, L. H., An accurate integral-based scheme for advection- diffusion equation, Commun. Numer. Meth. Eng., 17(10) (2001), pp. 701–713.Google Scholar
[26]Tsai, W. F. and Chen, C. J., Unsteady finite-analytic method for solute transport in groundwater-flow, J. Eng. Mech-Asce., 121(2) (1995), pp. 230–243.Google Scholar
[27]Tsai, W. F., Lee, T. H., Chen, C. J., Liang, S. J. and Kuo, C. C., Finite analytic model for flow and transport in unsaturated zone, J. Eng. Mech-Asce., 126(5) (2000), pp. 470–479.Google Scholar
[28]Xia, C. L. and Jin, Y. C., Multilayer averaged and moment equations for one-dimensional open-channelflows, J. Hydraul. Eng-Asce., 132(8) (2006), pp. 839–849.Google Scholar
[29]Yakirevich, A., Borisov, V. and Sorek, S., A quasi three-dimensional model for flow and transport in unsaturated and saturated zones: 1. Implementation of the quasi two-dimensional case, Adv. Water Resour., 21(8) (1998), pp. 679–689.Google Scholar
[30]Zhan, H. B., Wen, Z. and Gao, G. Y., An analytical solution of two-dimensional reactive solute transport in an aquifer-aquitard system, Water Resource Res., 45 (2009), pp. W10501.Google Scholar
[31]Zhan, H. B., Wen, Z., Huang, G. H. and Sun, D. M., Analytical solution of two-dimensional solute transport in an aquifer-aquitard system, J. Contam. Hydrol., 107(3-4) (2009), pp. 162–174.Google Scholar
[32]Zhao, C. B., Xu, T. P. and Valliappan, S., Numerical modeling of mass-transport problems in porous-media-a review, Comput. Struct., 53(4) (1994), pp. 849–860.Google Scholar