Relating flow channelling to tracer dispersion in heterogeneous networks

Flow channelling is a well-documented phenomenon in heterogeneous porous media and is widely recognised to have a substantial effect on solute transport. The goal of this study is to quantify flow channelling in heterogeneous, two-dimensional, pipe networks and to investigate its relation with dispersion. We explored the effect of pore size heterogeneity and correlation length by, respectively, varying the normalised standard deviation of the pipe diameter distribution and imposing an exponential variogram to their spatial distribution. By solving the flow equations, we obtained a complete description of the volumetric flow and pressure gradient fields in each network realisation. Both fields displayed lineations but their preferential directions were roughly perpendicular to each other. We estimated their multifractal dimension spectra and showed that the correlation dimension was a reliable quantitative indicator of flow channelling. We then simulated solute dispersion in these networks using a previously published method. We observed that flow channelling corresponded to an increase of the asymptotic dispersion coefficient and a lengthening of the pre-asymptotic period. We conclude at the existence of a strong, but not exactly one-to-one, relation between the asymptotic longitudinal dispersion coefficients and the correlation dimension of the flow field.