Lagrangian Analysis of Nonreactive Pollutant Dispersion in Porous Media by Means of the Particle Image Velocimetry Technique

Abstract

An experimental technique based on image analysis was used to perform a Lagrangian description of passive pollutant particle motion in a three‐dimensional saturated porous medium. To allow for optical access, the experiment was carried out with Pyrex grains as the solid matrix and glycerol as the liquid phase in order to have two phases with the same refractive index. Statistical analysis of the experimental data allowed for estimation of velocity and displacement probability density functions (pdf), velocity component correlation functions, Lagrangian integral scales, and mechanical dispersion coefficient tensor components. The results obtained suggest that the longitudinal velocity component has a log normal pdf while the transversal component has a symmetrical pdf, which is nevertheless not Gaussian for high values of the kurtosis. Furthermore, the velocity components' autocorrelation functions are well represented by exponential laws, and the integral scale is dependent on filtration velocity and grain size. As foreseen in the theory the total displacement pdf shows the tendency to reach normal distribution after many integral scales. The evaluated dispersion coefficient tensor components are dependent on travel time; the components start from zero and reach an asymptotic value after several integral scales. Furthermore, the tensor is anisotropic, with the longitudinal component greater than the transversal one by about 1 order of magnitude. Comparison with other experimental data shows agreement at least for the longitudinal dispersion component. Dagan's linear theory has been used for comparing the analytical longitudinal component of the dispersion tensor with that obtained by means of the experiments.