Geologic units in ground water models
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REPRESENTING GEOLOGIC UNITS IN GROUND WATER MODELS
There are two basic approaches to representing geology in a 3-D ground water model:
1. Grid Conforms to Hydrostratigraphic Boundaries Create a grid where layers
conform to the contacts of stratigraphic, or hydrostratigraphic units. In many
cases, grid layer boundaries conform to the contacts bounding a stratigraphic unit,
and there are additional grid layers within the stratigraphic unit. Use zones within
the layers based on the distribution of hydraulic conductivity in each stratigraphic
unit. This approach creates a model that resembles the geology. It can result in a
grid with layers that abruptly change thickness or that pinch out. These effects
may cause problems with convergence of the model, although they can be
successfully included in some cases.
2. Effective Hydrostratigraphy Create a grid with layers that are flat-lying or that
vary only slightly in elevation. Determine the stratigraphic units that occur within
each cell and determine the effective horizontal and vertical conductivities that
represent those units. The grid layers are essentially the hydrostratigraphic
equivalents of the stratigraphic units they contain. This approach creates a model
that represents the effective hydrostratigraphy, but it may appear to differ from
the stratigraphy. Models created with this approach can converge more quickly
and reliably than models created where the layer thickness varies abruptly.
Models formulated using this approach require calculations of effective hydraulic
conductivity at each grid block, and this can be more difficult to formulate than a
model where the grid matches the hydrostratigraphy.

Simple methods for determining the effective vertical and horizontal
hydraulic conducitvities of layered media are given at the end of these
notes.
Surfer can be used to create layers that define the contact between two geologic units.
The surfer .grd files can then be imported to represent geologic units in GWV. This
approach facilitates representing aquifer systems using grids that conform to the
hydrostratigraphy.
Advice for making a large model Large ground water models of complicated
areas that run properly can be extremely frustrating to create. The strategy for success is
to first adopt a relatively simple representation of the field area. This model may be
much smaller, or cruder compared to the level of detail that you ultimately want, but the
important thing is that you get it to run successfully and obtain meaningful results
relatively quickly. Use those results to gain some insight into the problem, then add
some features that make the model more realistic and run it again. If it runs properly,
evaluate the results and increase the complexity or size. If there is a problem, then
simplify the model and try again. Maybe even simplify back to the previous case until
you have identified and solved the problem. This strategy of incrementally advancing the
size or sophistication of a model, and incrementally retreating to overcome small
problems, will work for nearly any type of modeling effort
Try to avoid the temptation of creating a large, detailed model on your first attempt, even
if you think you know how to do this. Problems in large, complex models can be
Geologic units in ground water models
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extremely difficult to find. As a result, you may think you can save some time by
avoiding the simple, preliminary models, but you may waste your entire effort if you are
unable to get the big model to work properly.
SOME SURFER RECIPES
Here are some techniques for creating SURFER .grd files that represent geologic
conditions.
1. Unit of uniform thickness
Say the formation is 50 units thick relative to topography. Start with a .grd file
representing topography.
Use Grid/Math with file A as the topography grid file
C=A-50
Use C as the lower contact of the upper unit, or the upper contact of the lower
unit.
You can also use this procedure for creating units of uniform thickness in the
subsurface.
Try this:

Use x,y,upper in test points to create a grid file representing the
upper surface.

Make a lower contact 50 units below the upper one.
2. Unit bounded by a planar, dipping contact.
Intersect the unit with 3 boreholes.
Digitize the boreholes and enter coordinates into SURFER
Grid/Data and use “polynomial regression” as the interpolation method. The
default for this interpolation method is to fit the points with a plane.

Try this using 3 points.xls
Geologic units in ground water models
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3. Unit that pinches out
laterally.
Subtract lower surface from upper surface to get isopach map
The isopach map will have negative elevations where the unit has pinched out
(this is what we are assuming anyway).
Make the negative isopach values equal to zero this way:
Map A is the isopach
C = 0.5*(A+(SQRT(A*A)))
C is the isopach with zero values
This procedure essentially takes each cell value and adds it to the absolute value
of the cell value, then divides by 2. You should convince yourself that negative
values go to zero and positive values are left unchanged by this procedure.
Now make map A the original upper surface, and map B the isopach map with
zero thicknesses that you have just created. Do this
C=A-B
And map C will be the lower surface of the unit that pinches out. Notice that this
procedure will create a continuous surface across the map area. The pinch-out is
produced where the upper and lower bounding surfaces are at the same
elevation—the thickness of the unit is zero here.
Note that Modflow will generate an error when the thickness of a layer is zero.
To avoid this, you will want to modify the procedure outlined above to make the
surfaces have slightly different elevations, instead of the exact elevations. Do this
by subtracting a small amount from the elevation of the lower layer.

Try this by creating an upper surface and lower surface by gridding the
points in test pts.xls. You want to create a lens between the upper and
lower surfaces. Assume that the upper surface extends beyond the lens.

You will make a total of six grids to get the final result. The grids are
shown on the following page.
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Upper contact.grd
Use as contact where upper<lower
Isopach.grd
Upper surface – isopach w/ 0s
Lower contact.grd
Ignore where lower>upper
isopach where negative values are set to 0
Upper surface – isopach –1
The bowl-shape is the lower contact of the pinched out unit
Edges are the same as upper contact contact, so thickness of
pinched-out unit is zero
Thickness of pinched
out unit is 1 where
unit is absent to
satisfy MODFLOW
Geologic units in ground water models
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4. Contact that is a subdued expression of topography.
There are probably a variety of ways to do this, but here is a procedure that seems
to work fairly well. Be sure to check the results for your case to make sure the
procedure has created the surfaces you expect.
Import the file containing the elevations of streams, which you generated using
GV4 and StreamBC.xls. Make a grid in Surfer to produce a surface that includes
the stream elevations and interpolated values between them.
Make an isopach map of the difference between the ground surface and the
gridded stream surface.
Saprolite should be somewhat thinner than indicated by the thicknesses on this
map. I multiplied the isopach by 0.3 to get thickness that reached maximum
values under ridges of about 25 m. Subtract this new isopach map from
topography. The thickness of the saprolite is zero at the streams using this
procedure.
The contact between saprolite and transition zone is then obtained by subtracting
the modified isopach from the map of the ground surface.
Disclaimer: Be sure to recognize that this is only a suggested approach for creating a
surface. Geometries of the contact between saprolite and rock are difficult to
characterize, and any approach that is used must be verified.
topography
Surface resembling
topography but with lower
amplitudes
Cross-section
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5. Control points
The best way to create stratigraphic layers in a model is by interpolating between control
points where locations of contacts are known. This information could be available from
borehole data and outcrops, for example.
Keep in mind that you will still need to check the gridded layers to be certain that you
have created what you are intending to create.
You may want, or need, to use several of the methods outlined above to create an
accurate representation of the subsurface.
One more reminder: Always begin by testing the methods you use
with simple examples to understand how they work. Then
gradually increase complexity and check for proper functioning as
you go.
Geologic units in ground water models
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Effective Conductivity Parallel to Layers
h1
h1
h
h2
K1
b1
K2
K
h
h2
Ke
Q1
b2
bT
b3
Q2
3
Q3
x
Layered media
Equivalent homogenous media
The volmetric flow through each layer (y is the width of the area through which flow
occurs)
Q1 = -y b1 K1 (h/x)
Q2 = -y b2 K2 (h/x)
Q3 =-y b3 K3 (h/x)
(1a)
(1b)
(1c)
QT = -y bT Ke (h/x)
(2)
Assume that the flows through the layered media and the equivalent media are equal
Q1 + Q2 + Q3 = QT
(3)
Substituting (1) and (2) into (3)
-y bT Ke (h/x) = -y b1 K1 (h/x) - y b2 K2 (h/x) - y b3 K3 (h/x)
cancelling and dividing by bT gives the effective hydraulic conductivity.
Ke =
1
{b1 K1 + b2 K2 + b3 K3 }
bT
(4)
This is simpler when written in terms of transmissivity, T=Kb
Te = T1 + T2 + T3
(5)
Geologic units in ground water models
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Effective Conductivity Normal to Layers
h1
h1
h2
h14
h14
h4
h4
h3
q
K1
b1
K2
K3
b2
b3
Ke
q
bT
Equivalent homogeneous media
Layered media
According to Darcy’s Law, the flux through each layer is
h  h1
h
b
q1   K1 2
  K1 12 ;
or
h12  q1 1
b1
b1
K1
h3  h2
h
  K2 23 ;
b2
b2
h  h3
h
q 3   K3 4
  K3 34 ;
b3
b3
and
h  h1
h
q e   Ke 4
  Ke 14 ;
bT
bT
q 2   K2
or
or
or
b2
K2
b
h34  q 3 3
K3
h23  q 2
h14  q e
bT
Ke
where h23 is shorthand for the head drop across layer 2, etc. Assuming that the head
drop across the equivalent media is the same as the total drop across the layers
b
b
b
b
h14  h12  h23  h34 ;
or q e T  q1 1  q 2 2  q 3 3
Ke
K1
K2
K3
But the flux through each layer is the same, and they are equal to the flux through the
equivalent layer, so
n
bT
bT
Ke =
or for n layers Ke = 
 b1
b2
b 
i=1  bi 
 3
 
 
K2
K3 
 K1
 Ki 
Geologic units in ground water models
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