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.