Magnetic resonance imaging experiments for the verification of a stochastic transport theory
Abstract
Magnetic resonance imaging techniques were investigated means to obtain experimental data for the verification of a stochastic transport theory. Gradient imaging techniques were applied to obtain one-dimensional concentration images and two- and three-dimensional velocity images during flow in homogeneous and aphoristic heterogeneous porous media. Concentration and velocity field measurements in an aphoristic heterogeneous model were used to evaluate the applicability of the stochastic transport 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 numerical results did not match the experimental data. While the results showed general agreement, the stochastic model appeared to 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 are insignificant relative to terms containing doublet cross correlations. Measured velocity covariances were compared to the velocity covariance determined from the first-order solution to the flow equation. The first-order relation was shown to be in general agreement with the measured covariance; however, it did not accurately predict the detailed covariance structure in the aperiodic heterogeneous model. In particular, it was not able to predict the observed negative correlation in the measured covariance. Notwithstanding, it was concluded that higher-order corrections may improve the agreement between measured and theoretical velocity covariance. Velocity imaging experiments were also performed to determine if velocity imaging techniques could be applied to evaluate the closure scheme of a recursive perturbation solution to the Eulerian transport problem. A three-dimensional image was made of the velocity field in one section of a homogeneous model to estimate the relative magnitude of two- and three-point velocity correlation functions. No definitive conclusions were drawn from the preliminary results since the data from a single image produced too small a sample size for the determination of reliable correlation functions. This work can easily be extended to further investigate the accuracy of the closure scheme.
Degree
Ph.D.
Advisors
Greenkorn, Purdue University.
Subject Area
Chemical engineering|Mechanical engineering|Mechanics
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.