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Percolation and Dispersion of Mass Transport in Saturated Fracture Networks

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  • Bih-Shan Lin
  • Cheng-Haw Lee

Abstract

Dispersion and transport of mass in a fracture network is a percolation process. Macro-scale dispersion is related to travel time, distance, mass distribution and fracture geometry. This article presents a stochastic, discrete fracture model in conjunction with percolation theory to investigate the dispersion phenomenon and the power law relationship between mean square travel paths displacement 〈 r2 〉 and particle travel time t. For imposed boundary conditions, particle dispersion is simulated to observe percolation thresholds and dispersion trends in different network structures. Simulation results demonstrate that the critical exponent values of t in the percolated networks are extremely close to the theoretical value of 1.27 and occur at certain percolation factors. Below these percolation factors, the exponents of t increase with decreasing percolation factors, above these percolation factors, exponents decrease with increasing percolation factors. In our simulated cases, the proportionality between 〈 r2 〉 and time t is given by t raised to a power between 1.27 and 1.66, depending on the fracture pattern. The coefficient of anisotropic dispersion tensor increases with increasing distance. The percolation process is related to travel time and distance, and cannot be interpreted as a Fickian diffusive process. Copyright Kluwer Academic Publishers 1998

Suggested Citation

  • Bih-Shan Lin & Cheng-Haw Lee, 1998. "Percolation and Dispersion of Mass Transport in Saturated Fracture Networks," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 12(6), pages 409-432, December.
    • Handle: RePEc:spr:waterr:v:12:y:1998:i:6:p:409-432
    DOI: 10.1023/A:1008041302679
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    Cited by:

    1. Konstantinos Moutsopoulos & Vassilios Tsihrintzis, 2009. "Analytical Solutions and Simulation Approaches for Double Permeability Aquifers," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(3), pages 395-415, February.

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