Vertical (lateral) boundaries to emulate an "infinite" 3D theoretical model

[Kenneth Ugalde]

Dear all,

I'm developing some groundwater 3D (re)circulation analytical theoretical models for a horizontally infinite porous medium, with boundaries at both the bottom (impermeable/no flow) and the top (free surface/water table and confined/impermeable - depending on aquifer type). While the (re)circulation flow of the basic model, with no background flow (U=0), is supposed to only vanish at infinity, under background flow (U>0), the (re)circulation cell is supposed to have finite dimensions.

To check their goodness-of-fit, I'm planning to prepare various numerical models with MODFLOW (later, probably also some lab-scale sandbox physical models too).

I will set the bottom boundary as "no flow" (impermeable), the top boundary being "no flow" (impermeable: confined) or "free surface" (water table), depending on the aquifer type to simulate. Both upgradient/downgradient and lateral vertical boundaries, being "artificial boundaries" [1, p.14],  I will set them as "constant head" (fixed hydrostatic pressure), to simulate the natural background gradient outside the (re)circulation cell.

My doubt arises from the finite nature of the grid. While I can set top/bottom boundaries equivalent to reality, I'm not sure how to proceed laterally. Of course, I will use the analytical models to have a solid clue on the lateral distances at which the effect of my (re)circulation cell vanishes or is almost negligible*.

But I'm afraid that if I prepare a grid not long/wide enough [2, Ch.23.6.1], the "constant head" boundaries might interfere with the (re)circulation flow and deform the geometry of my (re)circulation cell in a not-negligible way, thus not being able to match it to the cell length/width as previously calculated with the analytical models.

On the other hand, if I prepare a VERY LONG/WIDE grid, the computation effort/time might be toooooo much.

Thus, I'm thinking about preparing a grid slightly longer/wider than the previously calculated "almost negligible" width and length from the analytical models. And then assigning very high hydraulic conductivity values to the elements just before the boundaries, to somehow "emulate" a vanishing flow field (i.e., acting as a "cushion" between the "constant head" boundaries and the "negligible" flow field of the outer shell of the (re)circulation cell).

Any similar experiences?

Comments or critiques (constructive, please)...

...or bibliographic references about the specific problem?

(*) I will first have to decide what I consider negligible (e.g., where the (re)circulation flow is less than a fraction X of the total (re)circulation flow).

[1]  USGS (2001) "System and Boundary Conceptualization in Ground-Water Flow Simulation", Techniques of Water-Resources Investigations of the United States Geological Survey, Book 3, Applications of Hydraulics, Chapter B8. https://pubs.usgs.gov/twri/twri-3_B8/pdf/twri_3b8.pdf

[2] Delleur, J. W. (2007) "The Handbook of groundwater engineering" (2nd ed.), CRC Press / Taylor & Francis. DOI: https://doi.org/10.1201/9781420006001.