2d Vertical Unsaturated modeling with mod Van Genuchten

Hello
I am a fairly new FeFlow user looking for advice on unsaturated, vertical flow modeling. The goal of the model is to more effectively model perched water tables in the unsaturated zone. I am attempting to model a pit slope using the modified Van Genuchten modeling. The model has constant head boundaries on either edge, 2nd order flux recharge BC at the dumps and seepage face boundaries along the pit slope. Values for unsaturated porosity, residual saturation and hydraulic conductivity are assigned by unit. The following modified Van Genuchten parameters were recommended to me for dealing with the pit slope as values for “fractured, porous rock”:

Sr = (n-Sy)/n 
? = 1.10
A = 40 (my max element size, although it sounds like other posts suggest to lower this value? Does lowering this value below element size maintain accuracy?)
n = 1.15 
m = 0.145

Using these values I am having some trouble obtaining convergence during steady-state calibration. The stability of the model has been decreasing significantly with any introduction of anisotropy or increased in recharge flux boundary condition.

Has anyone attempted a similar scenario and has any insight into more effective mod VG parameters for pit slopes, particularly values for fractured, hard rock that might improve convergence?

Any insight on increasing the stability of the model, with reasonable parameters would be extremely helpful. Or any literature on this specific topic would be of great interest, especially regarding parameter estimation for n, m and ?. I am also open to trying other approaches as well.

Thank you in advance for any help.

Hello,

The first question is what you are trying to model. If your are only using the unsaturated approach to get a better approximation of the water table and you do not vary the parameters in space then the parameters you choose should not affect this result very much because at this point all parameters should give the same solution.
But keep in mind that this is valid only for steady state computations. In transient computations the unsaturated properties are controlling the watering/dewatering processes in the unsaturated zone and will effect your modelling results.

About the parameters you use:
residual asturation Sr has to be <1 (typical values for porous media are in a range of 0.001 to 0.05
The parameter A in the Van Genuchten relationship can be intepretated as 1/hc where hc is the capillary rise. Typical values for hc are for example about 0.3 m for sand and about 2.0 m for loam. Thinking of a fractured media you can try to describe A with the diameter d of the bigger fracture in your rock. If think of the fractures as tubes the capillarry rise could be estimated as:
hc [m] = 3e-5/d[m]
So your value of A seems to be quiet large but could be realistic.

You are right that values of A less then your vertical mesh discretization could cause some numreical problems, because then a node is (more or less) dry or wet.

If you have problems with the model stability you could try to use some othe values for m and n: try to smooth the capillary pressure curve. Maybe some bigger values will help.
If you use the modified Van Genuchten function you can seperately define the relative conductivity function. To my experience small values of the parameter delta give more stable solutions (but delta < 1 is not physically correct!).

Maybe also a mesh refinement (in the region of the water table) could help with the convregence, but I would first try the parameter variation above.

Good luck
Zebra