Characterizing Aquifers - Hydrogeology: Objectives, Methods, Applications - page 159

div(K* gradh) = S s ∂h/∂t + q
where S s is storativity, ∂h/∂t is the variation in hydraulic head, and q is
discharge
In addition to this equation governing the fl ow of water, other equations
describing the movement of pollutants can be used. The models then take
into account a substance's molecular diffusion in water (independent of
fl ow) and kinematic dispersion in pores (which depends on fl ow). Diffusion
and dispersion are actually combined in the general term dispersion.
Dispersion therefore has transversal and longitudinal components. Within
the rock, water circulates at a velocity that varies from the edges to the
center of a pore according to a parabolic curve, due to friction. Figure 88
shows a point source of pollution evolving as a dispersion front. Convection
(or advection) is the transport of material by fl ow.
It is also necessary to take into account the interactions between the
pollutant and the solid grains of the aquifer. One can compare conserved
(or conservative) pollutants to evolving (or non-conservative) pollutants.
Deterministic models present both a cognitive value in terms of the
behavior of the hydrosystem (confi rmation of the parameters used and of
their spatial distribution), and management value. MODFLOW is a very
common model distributed by Waterloo.
Figure 88 Dispersion of a tracer (or a pollutant) in intergranular spaces.
Figure 89 shows an example of piezometric reconstruction in the
fl uvioglacial cone of Pontarlier (Doubs), based on the given grid.