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Uncertainty propagation of hydrodispersive transfer in an aquifer: an illustration of one-dimensional contaminant transport with slug injection

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Abstract

It is evident that the hydrodynamic dispersion coefficient and linear flow velocity dominate solute transport in aquifers. Both of them play important roles characterizing contaminant transport. However, by definition, the parameter of contaminant transport cannot be measured directly. For most problems of contaminant transport, a conceptual model for solute transport generally is established to fit the breakthrough curve obtained from field testing, and then suitable curve matching or the inverse solution of a theoretical model is used to determine the parameter. This study presents a one-dimensional solute transport problem for slug injection. Differential analysis is used to analyze uncertainty propagation, which is described by the variance and mean. The uncertainties of linear velocity and hydrodynamic dispersion coefficient are, respectively, characterized by the second-power and fourth-power of the length scale multiplied by a lumped relationship of variance and covariance of system parameters, i.e. the Peclet number and arrival time of maximum concentration. To validate the applicability for evaluating variance propagation in one-dimensional solute transport, two cases using field data are presented to demonstrate how parametric uncertainty can be caught depending on the manner of sampling.

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References

  • Bear J (1972) Dynamics of fluids in porous media. American Elsevier Publishing Company, New York

    Google Scholar 

  • De Josselin De John G (1958) Longitudinal and transverse diffusion in granular deposits. Trans Am Geophys Union 39(1):67

    Google Scholar 

  • Fetter CW (1999) Contaminant Hydrogeology. Prentice Hall, Englewood Cliffs

    Google Scholar 

  • Freeze RA, Cherry JA (1979) Groundwater. Prentice Hall, Englewood Cliffs

    Google Scholar 

  • Gardner RH, O’Neill RV (1983) Parameter uncertainty and model predictions: a review of Monte Carlo results. In: Beck MB, Van Straten G (eds) In uncertainty, forecasting of water quality. Springer, New York

    Google Scholar 

  • Leveinen J (2000) Composite model with fractional flow dimensions for well test analysis in fractured rocks. J Hydrol 234(3–4):116–141

    Article  Google Scholar 

  • Myers RH (1971) Response surface methodology. Allyn and Bacon, Boston

    Google Scholar 

  • NRC (1989) A review of techniques for propagating data and parameter uncertainties in high-level radioactive waste repository performance waste repository performance assessment models. NUREG/CR-5393 (SAND89-1432), Nuclear Regulatory Commission, USA

  • Ogata A (1970) Theory of dispersion in a granular medium. US Geological Survey Professional Paper 411-I

  • Perkins TK, Johnson OC (1963) A review of diffusion and dispersion in porous media. Soc Pet Eng J 3:70–84

    CAS  Google Scholar 

  • Picken JF, Grisak GE (1981) Scale-dependent dispersion in a stratified granular aquifer. Water Resour Res 17(4):1191–1211

    Article  Google Scholar 

  • Sauty JP (1980) An analysis of hydrodispersive transfer in aquifers. Water Resour Res 16(1):145–158

    Article  Google Scholar 

  • Schaibly JH, Shuler KE (1973) Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients, II. Application. J Chem Phys 59:3879–3888

    Article  CAS  Google Scholar 

  • Shih DCF (2004) Uncertainty analysis: one-dimensional radioactive nuclide transport in a single fractured media. Stoch Environ Res Risk Assess 18:198–204

    Article  Google Scholar 

  • Shih DCF, Chuang WS, Chang SS, Kuo MC, Lin GF (2002) Uncertainty analysis for corrosion depth of nuclear spent fuel canister, Waste Management’02, Session 39B, paper #575, 24–29 February 2002, Tucson, AZ/USA

  • Shih DCF, Lin GF (2006) Uncertainty and importance assessment using differential analysis: an illustration of corrosion depth of spent nuclear fuel canister. Stoch Environ Res Risk Assess 20:291–295

    Article  Google Scholar 

  • Throne PD, Newcomer DR (1992) Summary and evaluation of available hydraulic property data for the Hanford site unconfined aquifer system. US DOS DE-AC06-76RLO 1830, Pacific Northwest Laboratory, PNL-8337/UC-402,403

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Acknowledgments

The support of the Department of Geosciences of National Taiwan University and the Institute of Nuclear Energy Research (AEC) of Taiwan are gratefully acknowledged.

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Authors and Affiliations

  1. Department of Geosciences, National Taiwan University, Taipei, Taiwan, ROC

    David Ching-Fang Shih, Yue-Gau Chen & Yih-Min Wu

  2. Department of Civil Engineering, National Taiwan University, Taipei, Taiwan, ROC

    Gwo-Fong Lin

  3. Institute of Nuclear Energy Research, AEC, Lungtan, Taiwan, ROC

    David Ching-Fang Shih

  4. P·O. Box 3-7, Lungtan, 32546, Taiwan, ROC

    David Ching-Fang Shih

Authors
  1. David Ching-Fang Shih
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  2. Yue-Gau Chen
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  3. Gwo-Fong Lin
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  4. Yih-Min Wu
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Correspondence to David Ching-Fang Shih.

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Shih, D.CF., Chen, YG., Lin, GF. et al. Uncertainty propagation of hydrodispersive transfer in an aquifer: an illustration of one-dimensional contaminant transport with slug injection. Stoch Environ Res Risk Assess 23, 613–620 (2009). https://doi.org/10.1007/s00477-008-0246-2

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  • DOI: https://doi.org/10.1007/s00477-008-0246-2

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