Advective Transport Phenomena to Better Understand Dispersion in Field and Modeling Practice

The absence of recent research on dispersion in engineering applications indicates the need for a description that is more focused on field and modeling practice. Engineers may benefit from simple calculation tools allowing them to understand the processes encountered in the field. Based on a conceptual model for advective transport through an elongated conductivity zone, for example, in fluvial sediments, explicit expressions are presented for macro-scale phenomena: (1) the different travel distances of water particles traveling in laminar flow through and adjacent to a single zone with conductivity higher or lower than that of the aquifer; (2) the affected thickness of the bundle of flowlines; (3) the distinction of inflow, outflow, and through-flow sections; (4) the development of a plume front vs. that of a tail; (5) conservation of mass causing water particles to travel both slower and faster than the aquifer average velocity while passing a single zone. The spread derived from a spatial distribution in a field experiment relates to the geometric mean of the spreads of the plume front and tail. The results obtained for a single conductivity zone are expanded for a general aquifer that is characterized by stochastic parameters. A fundamental new expression describes the dispersive mass flux as the product of the advective volume shift and the related local concentration difference. Contrary to Fickian theory, the dispersive mass flux in both the front and tail of a plume in highly heterogeneous aquifers is limited. In modeling, the advective volume shift is proportional to the cell size.