Equivalent porosity estimates for Colonnade Networks

Using a particle‐tracking procedure, numerical simulations are performed to evaluate the asymptotic limits and the length scale requirements for equivalent porosity estimates of discrete colonnade networks. The simulation results are used to determine differences between the scale requirements for equivalent hydraulic conductivities and porosities. The directional dependence of the equivalent porosity is investigated using a polar plot. For a continuous network of hexagonal colonnades with uniform apertures, the asymptotic porosity estimates become directionally dependent; the numerical values compare favorably with those based on theoretical considerations. With uniform apertures, the porosity values drop sharply whenever a fracture set is perpendicular to the applied gradient and thereby becomes nonconductive. With lognormally distributed apertures, the effect of a particular fracture set's being perpendicular to the gradient is overshadowed by the effect of distributed velocities, and the asymptotic limit for the equivalent porosity ellipse approaches that of a circle. For colonnade network models with filled or unfilled apertures, the computed length scale requirements for equivalent porosity approximation are slightly smaller than those for equivalent hydraulic conductivity. The study provides guidance in selecting an acceptable block size for use in a continuum model of ground water flow and transport through colonnade networks.