• Mathematical Models on Diffusive Loss of Non-Aqueous Phase Organic Solvents from a Disk Source
  • Yoon, In-Taek;S.E., Dickson;
  • GeoSystem Research Corp.;Department of Civil Engineering, McMaster University;
  • 디스크소스로부터 NAPL의 확산손실에 관한 수학적 모델
Abstract
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.

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.

Keywords: Fracture;Matrix diffusion;Disk source;Mathematical model;NAPL;

Keywords: 공극모암;확산;디스크 소스;수치모델;

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This Article

  • 2008; 13(6): 40-49

    Published on Dec 31, 2008