Recharge Rates in $L_{max}$: 2D Empirical Model – Birla et al. (2020)

Output from Birla et al.(2020) model

Birla et al.(2020) provides the following explicit expression for $L_{max}$:

$$ L_{emp} = \big(1 - 0.047M^{0.404} R^{1.883} \big)\frac{4M^2}{\pi^2 \alpha_{Tv}}\ln\bigg(\frac{4}{\pi} \frac{\gamma C_{ED}+C_{EA}}{C_{EA}}\bigg) $$

in which:

$M$ = Source Thickness [L], which is equal to Aquifer thickness ($A_t$) [L]
$\alpha_{Tv}$ = Vertical Transverse Dispersivity [L]
$R$ = Recharge Rate [LT$^{-1}$]
$\gamma$ = 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. Steady-state condition in a homogeneous and isotropic aquifer.
  2. Add more:

Reference:

Birla, s., Yadav, P.K., Mahalawat, P., Haendel, F., Liedl, R., Chahar, B. 2020. Influence of recharge rates on steady-state plume lengths. Jour. Contam. Hydrol. https://doi.org/10.1016/j.jconhyd.2020.103709