Scale and directional dependence of macrodispersivities in colonnade networks

Abstract

Macrodispersion in discrete colonnade network models is investigated using a series of Monte Carlo type numerical experiments. The numerical simulations consider fluid flow and advective transport through a square flow region of a two‐dimensional network of hexagonal colonnades. Macrodispersivities are calculated as a function of the scale and orientation of the square flow region within the larger, parent geometry. Particle tracking, with flux‐weighted tracer injection and monitoring, is used to generate experimental residence time distributions (RTDs). The method of moments is used to characterize the longitudinal tracer spreading. The simulated RTDs are utilized to examine the macrodispersive behavior in colonnade networks (column diameter, 1 m) with lognormally distributed fracture apertures (b, in millimeters). The network models are assumed to consist of open fractures with μln b = −1.945 and σln b = 0.896; this translates to an equivalent continuum log‐conductivity variance (σln K2) of 3.67. Based on an ensemble average of 100 realizations, the slope for spatial variance versus scale of observation ranges from 3.15 to 3.36 m for varying orientations of the hydraulic gradient. For ensemble‐averaged data, the varying orientations appear to have little effect on the macrodispersive behavior. For single‐realization experiments, the computed macrodispersivities are directionally dependent at a length scale as large as 30 times the column diameter (and probably much beyond). The computed asymptotic and preasymptotic macrodispersivities are compared with available stochastic solutions for two‐dimensional isotropic heterogeneity in the horizontal plane. The ensemble‐based numerical data are in excellent agreement with the solutions of Dagan (1984, 1988) and Gelhar and Axness (1983). However, for individual realizations, nonergodic behavior is clearly apparent in the near‐source, evolving region of transport, and the numerical data are quite variable between realizations. The study provides important insight on applicability of stochastic continuum theories to discrete colonnade network models having σln K2 much greater than 1.