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CAST Toolbox - Analytical Models - Ham et al. (2004)

{ref}``Ham et al. (2004)` is 2D horizontal model and provides an estimate of a steady-state plume length ($L_{max}$) using a point source. Ádditionally, the model explores the effects of longitudinal and transverse dispersivity on the steady state plume length.

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Ham et al. (2004)- conceptual set-up

Ham et al. (2004) provides the following explicit expression for $L_{max}$: $$ L_{max} = \frac{1}{4\pi}\frac{W^2}{\alpha_{TH}}\bigg(\frac{\gamma C_{ED}^\circ}{C_{EA}^\circ}\bigg)^2 $$

$W$ = Effective flow Width [L]<br>
$\alpha_{TH}$ = Horizontal transverse Dispersivity [L]<br>
$\gamma$ = Reaction stoichiometric ratio [ ]<br>
$C_{ED}^\circ$ = Contaminant (Electron Donor) concentration [ML$^{-3}$]<br>
$C_{EA}^\circ$ = Partner Reactant (Electron Acceptor) concentration [ML$^{-3}$]<br>

The model is based on the following assumptions:

  1. A point source with constant mass flow injection.
  2. An instantaneous reaction between an injected compound and a reactant in the ambient groundwater at the plume fringe.
  3. The domain in homogeneous, isotropic and fully saturated.

Using Ham et al. (2004) model in CAST

Single computing interface

The CAST user-interface for all the analytical models are identical. This is true for both single computing interface and multiple simulation interface. The identical interface simplifies the use of models in the CAST. Therefore, the extensive details on using the Liedl et al. (2005) model in CAST provided here can be used also for the Ham et al. (2004).

The difference in each model interface is the model specific parameters. This can be observed in the CAST screenshot below:

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name: ham2004_f2
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Ham et al. (2004)- input parameters

Once the input data is placed in the box, user needs to click on the Generate Graph to get the result. Results are obtained as an absolute number below the Generate Graph button and also graphically, which provides the field plume length data from the database. This allows a visual comparison of the model $L_{max}$ with the field data.

As explained in detail in Liedl et al. (2005) model , the resulting graph provides several interactive options to evaluate results.

Dynamically comparing model results - using sliders

Sliders are activated once the Generate Graph is clicked (see Interactive options in the Single computing interface). Sliders are provided for critical model parameters only. Sliders changes the model input parameters; for which the output $L_{max}$ appears in the graph. This enables a dynamic computation and visualization.

Multiple computing interface

The multiple computing interface of the Ham et al. (2004) model is identical to Liedl et al. (2005) model interface. The goal of the multiple computing interface is to develop several scenarios and compare the output of these scenarios with that of the field data. As can be observed in the screenshot below, users have an option to select the site(s) they would like to compare their scenarios with.

For clarification, the interface of multiple computing interface is provided in the screenshot below.

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name: ham2004_f3
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Options available with data input and result downloading in the multiple computing interface of CAST

(refham2004)=

Reference

Ham, P.A.S., Schotting, R.J., Prommer, H., Davis, G.B., (2004), Effects of hydrodynamic dispersion on plume lengths for instantaneous bimolecular reactions. Adv. Water Resour. 27, 803–813. https://doi.org/10.1016/j.advwatres.2004.05.008