Examination of stochastic dispersion theory by MRI in aperiodic porous media

Magnetic resonance imaging techniques were applied to obtain concentration and velocity field measurements during flow in an aperiodic heterogeneous porous medium. These measurements were used to evaluate the applicability of a stochastic perturbation theory and the validity of the assumptions underlying its derivation. A comparison of experimental moment data to the first and second moments of simulated mean concentration distributions showed that the theory did not match the experimental data. While the results showed general agreement, the stochastic model appeared to slightly overpredict the experimentally observed mixing behavior Discrepancies between experimental and numerical results were attributed to the assumption that triplet correlation terms involving fluctuating velocities and fluctuating concentration ape insignificant relative to terms containing doublet cross-correlations. Measured velocity covariances were compared to the velocity covariance determined front the first-order solution to the flow equation. The first-order relation agreed generally with the measured covariance, but did not accurately predict the detailed covariance structure in the aperiodic heterogeneous model.