Lab 10b supplement BSYSE 558 Groundwater Flow and Contaminant Transport
Partial Penetration, Superposition, and Bounded Aquifers
– The Use of WELLz
› Partial Penetration
–
When the open section of a well casing does not include the full thickness of the aquifer it penetrates,
the well is referred as partially penetrating
–
In reality, partial penetrating is the rule rather than the exception
–
Under partial penetrating conditions, the flow toward the pumping well will be 3-d due to the addition
of the vertical flow component, reflected by the upward inflection points in the time-drawdown
response
–
Numerous studies have been conducted to obtain solutions for flows toward partially penetrating
wells. Based on these studies, the effects of partial penetration will not significantly affect the
pumping test results if the observation well is located at some distance
where K is
the horizontal conductivity,
the vertical conductivity, and m the aquifer thickness
› Principle of Superposition
–
The diffusion equation is linear, i.e., it consists of a sum of linear terms—first degree in the dependent
variables and their derivatives. Compare the diffusion equation with Richards’ equation, one can
easily see that the former is linear while the latter nonlinear
(Diffusion equation)
(Richards’ equation)
–
Due to the linearity in the diffusion equation, the principle of superposition applies when using the
Theis equation, a solution to the diffusion equation. The principle of superposition states that, the
derivative of a sum of terms is equal to the sum of the derivatives of the individual terms
–
Expressed in terms of the pumping response, the principle of superposition signifies that, the total
effect resulting from multiple wells pumping simultaneously is equal to the sum of individual effect
caused by each of the wells acting separately
› Bounded Aquifers: Image-Well Theory
–
In reality, the assumption of an aquifer of infinite areal extent used in deriving most of the solutions
to the diffusion equation is often violated due to the physical presence of geological boundaries
–
The image-well theory permits treatment of aquifers limited in one or more directions and allows the
evaluation of the influence of aquifer boundaries on well flow; nonetheless, the additional assumption
of straight-line boundaries would have to be added
–
Assume formations A and B are in direct contact, with a well pumping from A, and B being
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Lab 10b supplement BSYSE 558 Ground-water Flow and Contaminant Transport
impermeable and serving as a no-flow boundary. The effect of a barrier (no-flow) boundary is to
increase the drawdown in the pumping well. The barrier boundary is simulated by the supposition that
formation A is infinite in areal extent and that an imaginary well is located across the real boundary
in B, on a line at right angle thereto and at the same distance from the boundary. If the image well
starts to pump at the same time and at the same rate as the real well, the boundary will evolve to a
ground-water divide
–
Similarly, if the aquifer is bounded by a stream serving as a constant head boundary, the effect of this
boundary is then to decrease the drawdown in the pumping well. A zero-drawdown at the constant
head boundary can be simulated by an imaginary well, located as previously described, with the
exception that this image well starts to recharge at the same time and at the same rate as the real well
–
The drawdown at any point in the real aquifer is the sum of the effects of the real and image wells
operating simultaneously, given by
(6.42)
where
and
are the well functions of the real, pumping well and the image well,
respectively. If the image well is a recharging well, the negative sign is used; if it is a discharging well,
the positive sign is used
–
When a well in a bounded aquifer is pumped, water levels in observation wells will initially decline
under the influence of the pumping well only; when the cone of depression reaches an exterior
boundary, deviation from the ideal response will be noted in the observation wells
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Lab 10b supplement BSYSE 558 Ground-water Flow and Contaminant Transport
About WELLz
(from WELLz version 1.0 README)
This directory contains the Windows version of WELLz. It has been developed and tested with Windows
95. The code installs automatically under Windows 95. Choose the RUN command (under the START button
on Windows 95, or under File menu on Windows 3.1x). Type ‘a:\setup’ or ‘b:\setup’ as appropriate. The code
operates as a normal Windows program. Details on operating the code are provided in Chapter 6. Here we
present a few additional details.
Files on the Disk
Several data files are provided on the disk. Each time a user selects File -- New, the data set “test” is loaded
into the Windows. This file is edited by the user for the problem at hand. When you select File -- Open, note
that test is there as “test.wzf”. There are two other files present on the disk “ex6_10.wzf” and “ex6_11.wzf”
which are the data files to run Examples 6.10 and 6.11. As you create new data sets, these are saved as with
the “wzf” extensions.
Adding and Labeling Contour Lines
The code lets you plot data points and label the contour lines for drawdown. For example, run “test” by
proceeding through the various data screens in order. The plot illustrates a pattern of circular drawdown with
no labels.
(1) To determine what contour lines are shown
Click ‘Options’ and select ‘Contour values’. You can either keep the default set of contours or provide your
own set of values by editing the ‘Contour values dialog’ box. Accept the values by clicking ‘OK’ and the plot
will reflect your choice of contour.
(2) To label contours or selected points
Click ‘Options’ and select ‘Label drawdown-values’. Click the mouse to add labels at appropriate points.
(3) To remove contour labels or other labels
If you save a dataset and later reopen it and edit parameters, the labels on the contour line will remain. The
old labels can be removed in one of two ways. With the contour plot in the Window, click ‘File’ and select
‘New’, which returns you to the first window, whereupon you run through the set of Windows and obtain a
new plot, or click ‘Editing’ and proceed to the last Window.
(4) Plotting precautions
For the plot to be prepared correctly, the region to be plotted must have coordinate locations greater than
zero. Stated another way, the coordinate axis (0, 0) should always be at the bottom left of the contour map.
It is possible to use negative well coordinates, but the contour plot cannot include these wells.
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Lab 10b supplement BSYSE 558 Ground-water Flow and Contaminant Transport
3000
Pumping well
(2250, 2250)
y-distance (m)
2000
1000
Pumping well
(750, 750)
0
0
1000
2000
3000
x-distance (m)
Fig. 1. (H4-P5) Map Showing the Location of the Pumping Wells.
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