资源环境科技发展态势分析平台

We develop a theoretical model for power law tailing behavior of transport in fractured rock based on the relative dominance of the decay rate of the advective travel time distribution, modeled using a Pareto distribution (with tail decaying as similar to time(-(1+alpha))), versus matrix diffusion, modeled using a Levy distribution. The theory predicts that when the advective travel time distribution decays sufficiently slowly (alpha<1), the late-time decay rate of the breakthrough curve is -(1+alpha/2) rather than the classical -3/2. However, if alpha>1, the -3/2 decay rate is recovered. For weak matrix diffusion or short advective first breakthrough times, we identify an early-time regime where the breakthrough curve follows the Pareto distribution, before transitioning to the late-time decay rate. The theoretical predictions are validated against particle tracking simulations in the three-dimensional discrete fracture network simulator dfnWorks, where matrix diffusion is incorporated using a time domain random walk.