An exact nonlinear correction to transverse macrodispersivity for transport in heterogeneous formations

The random, two‐dimensional, and steady in time Eulerian velocity field is assumed to be given. It pertains to flow through heterogeneous porous media of spatially variable permeability. Advective transport of a passive scalar is modeled by the Lagrangian approach by seeking the statistical moments of the trajectory of a tagged particle. The trajectories' variances and the associated dispersion coefficients are evaluated by a perturbation expansion in the velocity variances and by Corrsin's conjecture. First‐order results obtained in the past show that for flow through porous formations of log‐permeability, two‐point covariance of finite integral scale, the transverse dispersion coefficient tends asymptotically to zero. In contrast, Corrsin's conjecture leads to a finite dispersion coefficient, quadratic in the velocity variance. To investigate this effect, an exact nonlinear correction to the transverse dispersion coefficient is derived for a normal velocity field. It is shown that this term tends to zero asymptotically, in contrast with the result based on Corrsin's conjecture. Furthermore, an illustrative computation shows the transport‐related nonlinear correction to be small at any time.