Vertically Oriented 2D Empirical Model for $L_{max}$ - Maier and Grathwohl (2006)ΒΆ

This 2D model, based on Maier and Grathwohl (2005), provides an estimate of a steady-state plume length ($L_{max}$ ) and analysed the sensitivity of the plume length with respect to biodegradation kinetics, flow velocity, transverse vertical dispersivity, the source and aquifer geometry and reaction stoichiometry.

Output from Maier And Grathwohl(2005) model

Maier and Grathwohl (2005) provides the following explicit expression for $L_{max}$:

$$ L_{max} = 0.5\frac{M^2}{\alpha_{Tv}} \bigg(\frac{\gamma C_{ED}}{C_{EA}}\bigg)^{0.3} $$

in which:

$M$ = Source Thickness [L], which is equal to Aquifer thickness ($A_t$) [L]
$\alpha_{Tv}$ = Vertical Transverse Dispersivity [L]
$\gamma$ = Reaction stoichiometric ratio [ ]
$C_{ED}^\circ$ = Contaminant (Electron Donor) concentration [ML$^{-1}$]
$C_{EA}^\circ$ = Partner Reactant (Electron Acceptor) concentration [ML$^{-1}$]

The model is based on the following assumptions:

  1. A uniform flow field in an aquifer of constant thickness is assumed.
  2. A completely contaminated aquifer thicknes (landfill or boundary source) is presumed.

Reference: U.Maier , P.Grathwohl 2005 . Numerical experiments and field results on the size of steady state plumes. https://doi.org/10.1016/j.jconhyd.2005.12.012