Linking mean pore velocity and dispersivity to pore velocity distribution by advection–dispersion and stream tube modeling

A large set of experimental solute tracer breakthrough data (corresponding to more than 350 individual tracer breakthrough curves) in eight granular filter materials, were used to investigate the links between solute dispersivity and the shape of the pore velocity—relative pore area distributions for the materials. Solute dispersivity values and the shape of the pore velocity—relative pore area distributions were determined by fitting the breakthrough data to the advection–dispersion equation and to the stream tube modeling (STM), respectively. For the STM calculations, stream tube diameter and average stream tube flow rate were allowed to vary between individual stream tubes. Shape parameters e.g., mean, coefficient of variation, skewness and excess kurtosis for the STM-based pore velocity—relative pore area distributions were subsequently calculated. Comparisons between dispersivity and shape parameter values showed strong correlation between dispersivity, coefficient of variation, skewness and excess kurtosis. These results also indicated a universal relationship between dispersivity, skewness and excess kurtosis across all materials and breakthrough curves. This relationship will assist in modelling of experimental data which cannot be characterized by a single or a limited number of pore velocities but require continuous pore velocity distributions. Results further indicated, that the shape of the observed pore velocity—relative pore area distributions could be well approximated by a log-normal distribution.