AdvectionDispersion

Advectiondispersion refers to the combined transport of solutes in a porous medium due to bulk fluid motion (advection) and spreading arising from velocity variations and molecular diffusion (dispersion). In groundwater hydrology and environmental engineering, the advection-dispersion equation is used to predict how contaminant plumes evolve as water moves through soils and rocks.

Advection is the transport of solute with the average groundwater flow, determined by Darcy velocity and the medium’s permeability. Dispersion describes the spreading of the solute beyond the pore water velocity, caused by differences in flow paths (mechanical dispersion) and molecular diffusion between adjacent pore spaces. Mechanical dispersion dominates at larger scales, while molecular diffusion is significant at small scales or long times. The combined effect leads to a spreading of the contaminant plume in the direction of flow and some transverse spreading.

The governing equation for a conservative (nonreactive) solute in one dimension is commonly written as ∂C/∂t + v ∂C/∂x = ∂/∂x (De ∂C/∂x), where C is concentration, v is average pore water velocity, and De is the dispersion coefficient, incorporating both mechanical dispersion and molecular diffusion. In porous media, De is often expressed as De = αL v + Dm, with αL the longitudinal dispersivity and Dm the molecular diffusion coefficient. For reactive systems, a retardation factor and decay terms may be included.

Limitations of the advection–dispersion framework include non-Fickian transport at large scales, anisotropy, sorption with nonlinear isotherms, and spatial heterogeneity. Extensions address time-dependent or anomalous diffusion and preferential flow. Applications span contaminant transport forecasting, risk assessment, and groundwater remediation design.