Proposal: optional exfiltration conductance for RIV, GHB, LAK & SFR

[tandreasr]

Hi again,
this is meant as a proposal for introducing an optional exfiltration conductance for the above mentioned boundary conditions. We often have the application case, that infiltration conductance (head/stage of boundary condition > groundwater head) is differnt from exfiltration conductance (HBound<Head) and currently there is no way in MF6 to simulate this behaviour.

My favourite solution would be a keyword in OPTIONS specifying, whether exfiltration conductance is read from a separate column in the PERIOD data.

Another simpler but still sufficient way would be to specify just an exfiltration factor in OPTIONS applied to the conductance when exfiltration takes place.

What do you think about it?

Thanks & best regards
Andreas

[langevin-usgs]

Are there any publications on this that you could reference here?

[AlastairBlack]

Id second this suggestion as a helpful addition that we would make use of. As for reference, the earliest that aware of would be K.R.Rushton & L.M.Tomlinson, 1979, Possible mechanisms for leakage between aquifers and rivers. Journal of Hydrology Volume 40, Issues 1–2, Pages 49-65 https://doi.org/10.1016/0022-1694(79)90087-8.

Figure 2b in this paper is what I believe is being proposed (2a and 2c already possible in RIV and SFR) but may be other options also.

We would use this functionality as commonly desired to have easier inflow to rivers where flows come through base and sides. Where as in ex-filtration flow is generally down through bed sediment only.
The fact that we presently have an elevation that provides a decoupling of Q from stage relative to cell head is helpful, but an option for a different conductance under exfil could be useful in some settings.

Thanks
Al Black

[tandreasr]

Hi Chris,
so you've already got a reference you asked for from Alastair :-)
I actually wanted to make very similiar explanations as Alastair just did for possible reasons of application. Mainly its due to the fact that exfiltration from groundwater into the river usually takes place through the higher parts of the river bed (where colmation at least in smaller rivers is usually less signifikant), resulting in a higher == better conductivity.
In contrast infiltration to groundwater mainly goes through the more heavily polluted lower river bed parts.
The same obviously applies for lakes.
Thanks & regards
Andreas

[Huite]

I can second this request. It's seems to be relatively common in groundwater modelling in the Netherlands to make a distinction between between infiltration and exfiltration. (Among the Deltares changes for iMODFLOW, an "infiltration factor" for the river package has been added.)

Unfortunately, there appears to be very little scientific literature on this subject. I believe there are at least two physical processes at play for exfiltration versus infiltration:

1. Different flow lines: flow through the sides, effectively a much larger cross-sectional flow area in exfiltration situations when heads are higher, as @AlastairBlack mentions.
2. Low hydraulic conductivity of bed sediments if fine particulate matter clogs a surface water bed -- compare with e.g. sand filters in water treatment and "filter cake" formation.

The second process can lead to very significant resistance build-up. This is quite clear for the surface water distribution network in Dutch polders: in these cases, the surface water stage can be meters higher than the surrounding land (behind a levee). Yet nearby piezometers show no influence from the surface water, suggesting resistances in the order of thousands of days and very little infiltration. (I wonder whether in exfiltration situation some "hydraulic failure" occurs in the bed, opening the bed again.)

The infiltration systems for drinkwater production in the Dutch coastal dunes is another good example, and includes actual measurements of fluxes. Pre-filtrated river water is infiltrated in (large) ponds, flows through the phreatic aquifer, and is abstracted via horizontal drains, making sure there's enough travel time to rid the water of pathogens. Though the water is pre-filtrated, a "cake" builds and infiltration fluxes measurably decrease over the years, with a large fraction of the water infiltrating via the sides of the ponds after some time. Unsurprisingly, the higher the head difference between pond and drain, the more frequent these ponds get clogged and to be emptied for maintenance.

So there has been some research, but it's of a relatively practical nature, with reports in Dutch.

Here are some sources from a quick search on Google scholar, by checking who cites the paper @AlastairBlack mentions:

Transient Leakance and Infiltration Characteristics during Lake Bank Filtration
https://ngwa.onlinelibrary.wiley.com/doi/abs/10.1111/j.1745-6584.2008.00510.x
(My take-away: clogging appears to matter, and it's complicated.)

Field evidence of a dynamic leakage coefficient for modelling river–aquifer interactions
https://www.sciencedirect.com/science/article/pii/S0022169407005021
(Essentially no surprises: scouring event apparently increases flow, viscosity and thereby temperature matters, wetted perimeter changes over time.)

This article from my colleague Joost actually contains exactly the plot you'd want... and shows no difference between infiltration and exfiltration over a range of ~1.4 m!

(Edited:) Viscosity plays something of a role, but because the measurements are for a single season, there won't be large temperature and viscosity variation.

Investigating summer flow paths in a Dutch agricultural field using high
frequency direct measurements
https://www.sciencedirect.com/science/article/pii/S0022169414008531

To end on a practical note, for basic rivers, the behavior can be relatively easily achieved in current modflow6 by adding drainage on top of the river with a drainage elevation equal to the river stage. Maybe you could do the same with the other packages by making use of the water mover, but it seems like an awful hassle.

[JoerivanEngelen]

FYI, for those who are trying to implement this in their models now:
Here's a paper written by Willem Zaadnoordijk explaining how to achieve this by combining the GHB (or RIV) package with a DRN package.

Zaadnoordijk, W. (2009). Simulating Piecewise-Linear Surface Water and Ground Water Interactions with MODFLOW. Ground Water.
https://ngwa.onlinelibrary.wiley.com/doi/10.1111/j.1745-6584.2009.00582.x