Flow‐dependence of matrix diffusion in highly heterogeneous rock fractures

Diffusive mass transfer in rock fractures is strongly affected by fluid flow in addition to material properties. The flow‐dependence of matrix diffusion is quantified by a random variable (“transport resistance”) denoted as β [ T / L ] and computed from the flow field by following advection trajectories. The numerical methodology for simulating fluid flow is mesh‐free, using Fup basis functions. A generic statistical model is used for the transmissivity field, featuring three correlation structures: (i) highly connected non‐multi‐Gaussian; (ii) poorly connected (or disconnected) non‐multi‐Gaussian; and (iii) multi‐Gaussian. The moments of β are shown to be linear with distance, irrespective of the structure, after approximately 10 integral scales of ln T . Percentiles of β are found to be linear with the mean β when considering all three structures. Taking advantage of this property, a potentially useful relationship is presented between β percentiles and the fracture mean water residence time that integrates all structures with high variability; it can be used in discrete fracture network simulations where T statistical data on individual fractures are not available.