Dispersion and connectivity in flow through fractured networks

A stochastic modeling technique in a 2-D discrete fracture network with two orthogonal sets of fractures has been developed to observe mass transport dispersion, and to investigate the scaling law related to the mean square displacement of particle travel time, with various percolation probabilities. A law with a fractal dimension for dispersion in the discrete fracture network is estimated by analyzing the random walk with percolation theory, and by using the particle tracking method. Emphasis is placed on understanding how fracture connectivity influences dispersion in flows through fractured networks. Simulation results show that the distribution of masses is skewed or multimodal due to the low interconnection of fractures, and has an approximately Gaussian distribution at the high level of interconnection. Dispersion in fractured media is affected by the connectivity of fractures. Based on percolation theory analysis, numerical results show that there exists a threshold for fracture interconnectivity when the percolation factor is increased. In the case near the percolation threshold, a ratio exists between the mean square displacement of travel paths <r2> and time <t> raised to the power value of 1.23, which agrees with the theoretic value of 1.27. Above the percolation threshold, an increasing percolation probability increases the slope of the scaling relationship between Ln <rL> vs. Ln <f> in our study cases. An increasing connectivity of fractures decreases the variation of standard deviation in dispersion.