If you have only one layer in a model, then flow is always parallel to the layer. There will be NO potential for VERTICAL flow no matter how you stress the model.
In order to define vertical components of flow, you need vertical "stacks" of cells.
If you have only two layers, you can calculate either an upward or downward gradient of one magnitude (that is you cannot calculate a stronger gradient at one level versus another). With only 2 layers, you cannot calculate convergent flow.
If you want a detailed map of complicated vertical flow patterns, you will need to have numerous nodes in the vertical direction.
Items to consider as you define the vertical character of your grid:
PURPOSE OF MODEL
- REGIONAL / LOCAL?
- Units are likely to be grouped ("lumped") in vertical sections in regional models and represented in more detail in local models. Of course, the nature of the question for which the model is developed will strongly influence the need (or not) for more detail in the vertical direction.
- PARTIAL PENETRATION?
- Obviously you may wish to include vertical
layers so that you can specifically define the open interval of a well in
the model, but if the affect of partial penetration is important to you,
it will be essential to include additional layers in order to define the
head gradients and flow paths.
schematic field condition around a partially penetrating well:
representation in a single layer numerical model:
- AQUITARD STORAGE?
- Some models (including MODFLOW) allow
you to define an aquitard without using cells. This is done by describing
a resistance between layers. Such a feature can control the leakage rate
between aquifers, but cannot be used to keep track of storage in the aquitard.
If such storage is important to your problem, you will need to represent
the aquitard with cells, perhaps several vertical cells to allow representation
of the migration of the pressure gradient vertically through the aquitard.
conditions when aquitard is defined without using cells:
benefits of using multiple layers to represent aquitard:
- FUTURE TRANSPORT MODELING?
- This issue includes aspects of all the issues above. In order to track contamination which may follow paths that include significant vertical components, several cells need to be stacked in the vertical direction. If an aquitard is represented only by a resistance, then the contaminants will arrive instantly (albeit perhaps at a low rate) in the adjacent aquifer. In order to represent travel time through an aquitard, a number of cells need to represent it vertical extent.
- GEOLOGIC LOGS
- Examine geologic logs and build a three-dimensional stratigraphy. Then determine how the system can be simplified and units can be grouped or "lumped". Remember that even if the geology is homogeneous enough to be simulated as a homogeneous material, vertical components of flow may exist due to the geometry and character of the boundary conditions and the stresses, so vertical discretization may be necessary.
- GEOPHYSICS
- Use geophysical logs and surveys to enhance the work with geologic logs.
- Consider the natural vertical gradients in the area and determine if they are important to your problem. Define enough layers (vertical stacks of nodes) to sufficiently represent the variation of vertical gradients.
- The original version of MODFLOW would not
allow grid cells to "re-wet" if the head had dropped below the bottom of a
cell in a previous iteration. These cells would become impermeable. The modern
MODFLOW accommodates this feature. If you are working with the old version,
or another code that behaves similarly, you may have to make shallow units
thick in order to keep them from completely dewatering. Of course, this means
that you will not evaluate vertical components of flow in that zone.
permanently impermeable zone if re-wetting option is not used, even if the well is turned off:
- MODFLOW offers two options, the latter being more representative of field conditions, but the former may be used to expedite the modeling, obtain a rough approximation, or to be compatible with another software function performed in the project:
- CONSTANT LAYER THICKNESS / VARIABLE PROPERTIES
- VARIABLE LAYER THICKNESS / CONSTANT PROPERTIES
- MODFLOW connects layers explicitly, consequently you do not need to be concerned about truncation errors in a matrix solution for vertically adjacent cells.
Smaller layer thickness with more numerous layers will provide more accuracy, but one wonders how small is small enough?