HR: 0830h
AN: H11D-0890    [PDF]
TI: Predicting Plume Development of Reactive Solutes Using an Analytical Transport Model
AU: * Ham, P
EM: p.a.s.ham@citg.tudelft.nl
AF: TU Delft, Stevinweg 1, Delft, 2600GA Netherlands
AU: Schotting, R
EM: r.j.schotting@citg.tudelft.nl
AF: TU Delft, Stevinweg 1, Delft, 2600GA Netherlands
AU: Prommer, H
EM: Henning.Prommer@csiro.au
AF: TU Delft, Stevinweg 1, Delft, 2600GA Netherlands
AB: Transversal dispersion is considered to be the controlling mixing process in many cases where contaminant plumes attenuate naturally. An analytical model is presented, which describes the transport of a reactant $B$ continuously injected at the origin through a 2-D domain initially filled with a reactant $A$. Moreover a simple, instantaneous chemical reaction of the form $A + B \rightarrow AB$ is considered. The flow domain is a porous medium, the aquifer assumed homogeneous with steady, uniform flow. Explicit steady state solutions (in the limit $t\rightarrow\infty$) are presented for the distributions of reactants and products in $x-y$ space in the form of the modified Bessel function of zeroth order and second kind. From this a solution is presented to quantify the length of a plume given a few basic (geo)hydrological parameters. It is proven that zeroth or first order approximations to the Bessel function, in the limit $0.1 > \beta > 1$ and $0.01 > \beta > 0.1$ respectively, where $\beta = \alpha_T / \alpha_L$; $\alpha_L=1$, accurately represent plume lengths. Furthermore it is shown that in the first case plume length does not depend on longitudinal dispersivity $\alpha_L$, but only on pre-defined (geo)hydrological parameters, including $\alpha_T$. This result infers that in many practical situations the influence of $\alpha_L$ upon plume length is negligible. In the latter case, the plume length is written as a function of both $\alpha_T$ and $\alpha_L$. The assumption that $\alpha_L$ is only important for the transient development of the plume, is verified through the use of a numerical solution. Results demonstrate that for values of $\beta$ close to unity plume growth is rapid and largely linear, quickly reaching an asymptotic value. For $0.01 > \beta > 0.1$, plume growth demonstrates real longitudinal dispersive effects, growth rate being considerably slower.
DE: 1800 HYDROLOGY
DE: 1829 Groundwater hydrology
DE: 1831 Groundwater quality
DE: 1832 Groundwater transport
SC: Hydrology [H]
MN: 2003 Fall Meeting