engleski

Flow and travel time statistics in highly heterogeneous porous media

In this paper we present flow and travel time ensemble statistics based on a new simulation methodology Adaptive Fup Monte Carlo Method (AFMCM). As a benchmark case, we considered two-dimensional steady flow in a rectangular domain characterized by multi-Gaussian heterogeneity structure with an isotropic exponential correlation and lnK variance up to 8. Advective transport is investigated using the travel time framework where Lagrangian variables (e.g. velocity, transverse displacement or travel time) depend on space, rather than time. We find that Eulerian and Lagrangian velocity distributions diverge for increasing lnK variance due to enhanced channeling. Transverse displacement is a non-normal for all and control planes close to the injection area, but after xIY=20 was found to be nearly normal even for high . Travel time distribution deviates from the Fickian model for large lnK variance and exhibits increasing skewness and a power-law tail for large lnK variance, the slope of which decreases for increasing distance from the source ; no anomalous features are found. Second moment of advective transport is analyzed with respect to the covariance of two Lagrangian velocity variables: slowness and slope which are directly related to the travel time and transverse displacement variance which are subsequently related to the longitudinal and transverse dispersion. We provide simple estimators for the Eulerian velocity variance, travel time variance, slowness and longitudinal dispersivity as a practical contribution of this analysis. Both 2-parameter models considered (the advection-dispersion equation and the log-normal model) provide relatively poor representations of the initial part of the travel time pdf in highly heterogeneous porous media. We identify the need for further theoretical and experimental scrutiny of early arrival times, and the need for computing higher order moments for a more accurate characterization of the travel time pdf. A brief discussion is presented on the challenges and extensions for which AFMCM is suggested as a suitable approach.

flow; travel time; highly heterogeneous porous media; adaptive multi-resolution approach; Monte-Carlo

Art. no. W07402.