한국지하수토양환경학회지:지하수토양환경 (Journal of Soil and Groundwater Environment)

  • 제13권6호
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  • Pages.40-49
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  • 2008
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  • 1598-6438(pISSN)
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  • 2287-8831(eISSN)
한국지하수토양환경학회 (Korean Society of Soil and Groundwater Environment)
권호 표지

디스크소스로부터 NAPL의 확산손실에 관한 수학적 모델

Mathematical Models on Diffusive Loss of Non-Aqueous Phase Organic Solvents from a Disk Source

  • 발행 : 2008.12.31
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초록

평평한 fractures에서 공극을 가진 모암으로의 NAPL 확산을 수치적인 방법으로 해석하였다. 2D와 3D에 대한 일회성 디스크 소스와 3D 연속 디스크소스에 대한 모델은 Caralaw and Jaeger(1959)의 이론을 바탕으로 개발하였다. 3D 연속 디스크소스에 대해 공극모암으로 확산되는 NAPL의 총량을 계산할 수 없기 때문에 확산이 반구형으로 이루어진다고 가정하여 등농도선의 합을 이용하여 공극모암으로 확산되는 NAPL의 총량을 계산하였다. 수치적 계산에 따르면 2D 대비 3D의 경우에 NAPL 손실 시간이 현저히 빠른 것으로 나타났으며, 디스크 소스의 중심점에서 normalized된 농도는 일회성 디스크 소스는 시간에 따라 감소하고, 연속 디스크 소스는 증가하는 것으로 나타났으며, 시간과 공간에 따라 확산율은 감소하는 것으로 나타났다. 그리고 NAPL의 mass 손실은 1에 도달하지 못하였으며, 이는 연속 디스크 소스를 semi-infinite로 가정하고 적분했기 때문이다. 확산에 의해 사라지는 시간은 소스의 크기 및 모암 공극률 크기 증가에 비례해서 지수함수적으로 증가하고, 반면 NAPL의 용해성이 증가하면 감소하는 것으로 나타났다.

Matrix diffusion from planar fractures was studied mathematically and through physical model experiments. Mathematical models were developed to simulate diffusion from 2D and 3D instantaneous disk sources and a 3D continuous disk source. The models were based on analytical solutions previously developed by Carslaw and Jaeger (1959). The mathematical simulations indicated that the 2D scenario produces significantly different results from the 3D scenario, the time for mass disappearance is significantly larger for continuous sources than for instantaneous sources, the normalized concentration generally decreased over time for instantaneous sources while it increased over time for continuous sources, diffusion rates decrease significantly over time and space, and the normalized mass loss from the source zone never reaches 1 for continuous sources due to the semi-infinite integral. The simulations also showed that disappearance times increase exponentially with increasing source radii and matrix porosity, and decrease with increasing aqueous-phase NAPL solubilities.

키워드

참고문헌

  1. Abriola, L.M., and George, F, P., 1985, A multiphase approach to the modeling of porous media contamination by organic compounds: 1) Equation development. 2) Numerical Simulation, Water Resources Research, 21(1), 11-26 https://doi.org/10.1029/WR021i001p00011
  2. Abriola, L.M., Kurt, D.P., and Catherine, A. Peters, 1995, Persistence., and interphase mass transfer of organic contaminants in the unsaturated zone: Experimental observations and mathematical modeling, Vadose Zone Hydrology : Cutting Across Disciplines, Kerney Foundation Conference, Davis, CA
  3. Bear, J., 1972, Dynamics of fluids in porous media, New York; American Elservier Publishing Company, 764
  4. Carslaw, H.S. and Jaeger, J.C. 1959, Conduction of heat in solids, Second Edition, Clarendon Press, Oxford
  5. Cherry, J.A., 1984, Groundwater Contamination. Mineralogical Association of Canada Short Course in Environmental Geochemistry, 10, M.E. Fleet (Ed.)
  6. Crank, J., 1956, The Mathematics of Diffusion, Oxford University Press
  7. Doherty, R.E., 2000, A history of the production and use of carbon tetrachloride, tetrachloroethylene, trichloroethylene and 1,1,1-trichloroethane in the United States: Part 1 - historical background; carbon tetrachloride and tetrachloroethylene, Journal of Environmental Forensics, 1, 69-81 https://doi.org/10.1006/enfo.2000.0010
  8. Eckberg, D.K. and Daniel, K.S., 1984, Nonsteady three-phase immiscible fluid distribution in porous media, Water Resources Research 20, 1, 1891-1897 https://doi.org/10.1029/WR020i012p01891
  9. Feenstra, S., 1984, Groundwater contamination by dense nonaqueous phase liquid chemicals, Geological Association of Canada, Annual Meeting, May 14-16, 1984, London, Ontario
  10. Grisak, G.E. and Pickens, J.F. 1980, Solute transport through fractured media. 1. The effect of matrix diffusion, Water Resources Research, 16(4), 719-730 https://doi.org/10.1029/WR016i004p00719
  11. Grisak, G.E. and Pickens, J.F. 1981, An analytical solution for solute transport through fractured media with matrix diffusion, Journal of Hydrology, 52, 47-57 https://doi.org/10.1016/0022-1694(81)90095-0
  12. James, V.B., 1981, Large time solutions for temperatures in a semi-infinite body with a disk heat source, Int. J. Heat Mass Transfer, 24, 155-164 https://doi.org/10.1016/0017-9310(81)90104-6
  13. Kueper, B.H. and Mcwhorter, D.B. 1991, The hehaviour of dense, non-aqueous phase liquids in fractured clay and rock, Ground Water, 29(5), 716-728 https://doi.org/10.1111/j.1745-6584.1991.tb00563.x
  14. Kueper, BH., Wealthall, G. P., Smith, J.W.N., Lehame, S.A., and Lemer, D. N., 2003, An illustrated handbook of DNAPL transport and fate in the subsurface, Enviornment Aciency
  15. Miller, D.W., 1984, Groundwater Contamination : A Special Report. American Assoc. for Advancement of Science. Washington, D.C., 25
  16. Pankow, J.F. and Cherry, J.A. 1996, Dense chlorinated solvents and other DNAPLs in groundwater: History, behavior, and remediation, Waterloo Press
  17. Parker, B.L., J.A. Gillham, J.A. and Cherry, J.A., 1994, Diffusive disappearance of immiscible phase organic liquids in fractured geologic media, Ground Water, 32(5), 805-820 https://doi.org/10.1111/j.1745-6584.1994.tb00922.x
  18. Parker, B. L., Cherry, J. A., and Gillham, R. W., 1996, The effect of molecular diffusion on dnapl behavior in fractured porous media. Chapter 12 In: Dense Chlorinated Solvents and Other DNAPLs in Groundwater. J. F. Pankow and J. A. Cherry (eds.). Portland, OR: Waterloo Press
  19. Parker, B.L., Mcwhorter, D.B., and Cherry, J.A., 1997, Diffusive loss of non-aqueous phase organic solvents from idealized fracture networks in geologic media, Ground Water, 35(6), 1077-1088 https://doi.org/10.1111/j.1745-6584.1997.tb00180.x
  20. Dickson, S.E. and Thomson, N.R., 2003, Dissolution of entrapped DNAPLs in variable aperture fractures: Experimental data and empirical model, Environ. Sci. Technol., 37(18), 4128-4137 https://doi.org/10.1021/es026275r
  21. Silliman S.E., Berkowitz, B., Simunek J., and Genuchten M. Th., 2001, Fluid flow and solute migration within the capillary fringe, Ground Water, 40(1), 76-84 https://doi.org/10.1111/j.1745-6584.2002.tb02493.x
  22. Smith, J.E. and Gillham, R.W., 1999, Effects of solute concentration-dependent surface tension on unsaturated flow: Laboratory sand column experiments, Water Resources Research, 35(4), 973-982 https://doi.org/10.1029/1998WR900106