Simulation of Non-Ergodic Transport in 2-D Heterogeneous Anisotropic Media

Abstract

The development of a plume of pollutant in a two-dimensional heterogeneous medium with anisotropy in the correlation structure of the transmissivity (T) field is studied. In particular, we analyze the dispersion of the plume when the mean flow is tilted with respect to the principal directions of anisotropy. Of special interest is the angle between the main axes of the developed plume compared to the direction of the mean flow. T is considered locally isotropic, but the anisotropy in the correlation structure leads to anisotropic effective transmissivity. Dispersion is analyzed using a particle tracking scheme in a Monte Carlo framework.

When flow is tilted with respect to the directions of anisotropy, stochastic theories based upon ergodicity conclude that the plume gets oriented in the mean flow direction. In our non-ergodic simulations, for each single realization the plume gets oriented in an angle that is offset from the mean flow direction. The mean of the offset angles from the different realizations is again offset towards the direction of maximum anisotropy, as ergodicity is not achieved in our simulated domain.

Comparing the plume evolution for each realization, a wide range of plume configurations is found both in terms of displacement of the center of mass and in dispersion around these centers (plume sizes). A statistical analysis of the ensemble average of the plumes for the 500 realizations is also carried out. The plume obtained from ensemble averaging is oriented closer to the mean flow direction than the average offset angle for the different plumes considered separately. This work poses some important questions regarding the different types of plume averaging within a stochastic framework.