Dispersion in doublet-type flows through highly anisotropic porous formations

Steady doublet-type flow takes place in a porous formation, where the log-transform of the spatially variable hydraulic conductivity is regarded as a stationary random field of two-point autocorrelation. A passive solute is injected at the source in the porous formation and we aim to quantify the resulting dispersion process between the two lines by means of spatial moments. The latter depend on the distance between the lines, the variance of and the (anisotropy) ratio between the vertical and the horizontal integral scales of. A simple (analytical) solution to this difficult problem is obtained by adopting a few simplifying assumptions: (i) a perturbative solution, which regards as a small parameter, of the velocity field is sought; (ii) pore-scale dispersion is neglected; and (iii) we deal with a highly anisotropic formation . We focus on the longitudinal spatial moment, as it is of most importance for the dispersion mechanism. A general expression is derived in terms of a single qua...