Modeling Mechanical Dispersion by Using the Method of Advective Transport Phenomena, a First Step

Mechanical dispersion is driven by a variance in velocity rather than by the concentration gradient in the classical Fickian model. The groundwater community needs a theoretical development for this that offers a practical way to implement it (Konikow 2025). The method of Advective Transport Phenomena (De Lange 2020) describes mechanical dispersion based on the spread of water particles generated at sub-model scale by advective flow through zones with conductivity different from that of the overall aquifer, leading to a new parameter in the dispersive mass flux which is added to the advective mass flux computed at model scale similar to the existing approach in numerical modeling. The new parameter, called dispersive volume shift, is determined only by the traveled distance and the aquifer heterogeneity described by the horizontal and the vertical characteristic length and the log conductivity variance. The dispersive mass flux combines the dispersive volume shift and the concentration difference which is proportional to the traveled distance per time step. Using a spreadsheet model, the longitudinal concentration distribution in a traveling plume is simulated in a homogeneous aquifer and in a heterogeneous aquifer. The latter case shows asymmetry in the plume growth which is not produced by a classical Fickian model. Developments are still needed for application in general numerical modeling.