TY - JOUR

T1 - Percolation and dispersion of mass transport in saturated fracture networks

AU - Lin, Bih Shan

AU - Lee, Cheng Haw

N1 - Funding Information:
The authors would like to thank the National Science Council (NSC) and Radwaste Atomic Administration (RWA) for providing partial financial support of this study.

PY - 1998/12

Y1 - 1998/12

N2 - Dispersion and transport of mass in a fracture network is a percolation process. Macroscale 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 2> 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 2> 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.

AB - Dispersion and transport of mass in a fracture network is a percolation process. Macroscale 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 2> 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 2> 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.

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U2 - 10.1023/A:1008041302679

DO - 10.1023/A:1008041302679

M3 - Article

AN - SCOPUS:0032406429

VL - 12

SP - 409

EP - 432

JO - Water Resources Management

JF - Water Resources Management

SN - 0920-4741

IS - 6

ER -