We investigate the combined effects of network scale flow variability and retention due to matrix-diffusion on the scaling behavior of transport through fractured media. Two of the principal mechanisms controlling the transport of solutes through fractured low-permeability media are broad distributions of flow velocities and retention times in the solid matrix. We study the relative impact of these two processes under different initial conditions using a set of three-dimensional discrete fracture network simulations. We use these simulations to develop and calibrate an upscaled continuous time random walk (CTRW) approach for advective transport based on an Ornstein-Uhlenbeck model for the particle velocities that accounts for the fracture-matrix coupling using a compound Poisson process. This CTRW model can be conditioned on the initial solute distribution and allows to observe late-time scaling behavior at distances beyond what is feasible to observe using high-fidelity direct numerical simulations. We determine that the initial distribution of particles leads to marked differences in the persistent long-term scale behavior in the solute travel time distributions, even those undergoing retention due to matrix diffusion through implementation and analysis of the model.

我们研究了由于基质扩散引起的网络规模流量变化和保留对通过裂缝介质传输的缩放行为的综合影响。控制溶质通过裂缝性低渗透介质传输的两个主要机制是固体基质中流速和保留时间的广泛分布。我们使用一组三维离散裂缝网络模拟来研究这两个过程在不同初始条件下的相对影响。我们使用这些模拟来开发和校准基于 Ornstein-Uhlenbeck 模型的对流传输的放大连续时间随机游走 (CTRW) 方法，该模型用于解释使用复合泊松过程的裂缝 - 矩阵耦合的粒子速度。该 CTRW 模型可以以初始溶质分布为条件，并允许在超出使用高保真直接数值模拟观察可行范围的距离上观察后期缩放行为。我们确定粒子的初始分布导致溶质传播时间分布中持久的长期尺度行为的显着差异，即使是那些通过模型的实施和分析因基质扩散而被保留的粒子。