MATLAB MODULE TO DELINEATE ZONES OF CONTRIBUTION
Developed by Roseanna M. Neupauer, University of Colorado
Description:
Two MATLAB functions have been written to produce plots of zones of contribution,
lines of constant head, and streamlines. One function, capzone.m, is used for a
homogeneous aquifer with uniform flow and with one pumping well; and the other
function, hydcont.m, is used for a homogeneous aquifer with uniform flow and with a
pumping well and injection well pair. The user can vary the pumping (and injection) rate,
aquifer transmissivity, ambient hydraulic gradient, orientation of the ambient flow, and
separation distance between the pumping and injection wells. These functions allow for
rapid calculation and visualization of the zones of contribution for various sets of
parameters, providing students with a simple tool that enables them to observe the effects
of the parameter values on the size and shape of the zone of contribution.
Usage:
To use either of the functions, open Matlab and change to the directory that contains the
two functions. This can be done most easily by browsing for the appropriate directory
using the browsing window (selected by left-clicking on the gray button with ellipsis on
the right side of the tool bar). To run capzone.m, type, at the command prompt:
capzone(Q,T,dhds,theta,xmin,xmax,ymin,ymax,cboxx,cboxy)
and hit the return key. Here, Q is the pumping rate (L3/T), T is transmissivity (L/T), dhds
is ambient hydraulic gradient, theta is the orientation angle that the ambient flow
direction makes with the horizontal (x) axis (in degrees) with positive in the
counterclockwise direction, xmin and xmax are the minimum and maximum value of the
plot domain in the horizontal (x) direction, ymin and ymax are the minimum and
maximum value of the plot domain in the vertical (y) direction, pflag is a flag denoting
whether or not to display parameter values on the plot (use 1 to display parameter values,
and 0 to not display parameter values), and cboxx and cboxy are optional N-length
vectors containing the x- and y-coordinates of the outline of the contaminated region.
The pumping well is assumed to be at (0,0), with ambient flow from right to left.
Consistent length and time units are assumed. As an example, typing
capzone(30,8,0.01,15,-100,400,-250,250,1)
at the command prompt (and hitting the return key) produces the plot shown in Figure 1.
With the length units in meters and the time units in days, the pumping rate is 30 m3/s,
transmissivity is 8 m2/d, ambient hydraulic gradient is 0.01 m/m, the orientation of the
ambient flow is 15o above the horizontal axis, the plotted region is -100 m to 400 m in the
horizontal direction and from -250 m to 250 m in the vertical direction, and the
parameters are printed on the plot. The dotted black lines on the plot represent
streamlines (p. 312 of Charbeneau, 2000), solid blue lines represent the potentiometric
surface (superposition of the drawdown calculated using the Theis equation and a
linearly-sloping ambient potentiometric surface), and the dashed red line represents the
boundary of the zone of contribution (equation 6.4.1 in Charbeneau, 2000).
Figure 1. Example of results of capzone.m.
To run hydcont.m, type, at the command prompt:
hydcont(Q,T,dhds,theta,L,xmin,xmax,ymin,ymax,cboxx,cboxy)
and hit the return key. Here, Q is the pumping rate (L3/T), T is transmissivity (L/T), dhds
is ambient hydraulic gradient, theta is the orientation angle that the ambient flow
direction makes with the horizontal (x) axis (in degrees) with positive in the
counterclockwise direction, L is one half of the distance between the pumping and
injection wells, xmin and xmax are the minimum and maximum value of the plot domain
in the horizontal (x) direction, ymin and ymax are the minimum and maximum value of
the plot domain in the vertical (y) direction, pflag is a flag denoting whether or not to
display parameter values on the plot (use 1 to display parameter values, and 0 to not
display parameter values), and cboxx and cboxy are optional N-length vectors containing
the x- and y-coordinates of the outline of the contaminated region. The pumping and
injection wells are assumed to be at (-L,0) and (L,0), respectively, with ambient flow
from right to left. Consistent length and time units are assumed. As an example, typing
hydcont(30,8,0.01,0,100,-100,400,-250,250,1)
at the command prompt (and hitting the return key) produces the plot shown in Figure 2.
With the length units in meters and the time units in days, the pumping rate is 30 m3/s,
transmissivity is 8 m2/d, ambient hydraulic gradient is 0.01 m/m, the orientation of the
ambient flow is 0o (aligned with the horizontal axis), the pumping well is located at (100m, 0m) and the injection well is located at (100m, 0m), the plotted region is -250 m to
250 m in the horizontal direction and from -150 m to 150 m in the vertical direction, and
the parameters are printed on the plot. The dashed black lines on the plot represent
streamlines (p. 314 in Charbeneau, 2000), the blue lines represent the potentiometric
surface (p. 314 in Charbeneau, 2000), and the dashed red line represents the boundary of
the zone of contribution (equation 6.4.4 in Charbeneau, 2000). The zone of contribution
is only plotted if the flow direction is aligned with the horizontal axis. In other cases, the
size and shape of the zone of contribution can be observed by the direction of streamlines
as shown in Figure 3. The boundary of the zone of contribution for the pumping well
occurs between the streamlines that reach the boundary at x=-250 m and those that
terminate at the pumping well (PW), while the boundary of the zone of contribution for
the injection well occurs between the streamlines that reach the boundary at x=250 m and
those that terminate at the injection well (IW).
Reference
Charbeneau, R.J., Groundwater Hydraulics and Pollutant Transport, Prentice Hall, 2000.
Figure 2. Example of results of hydcont.m with flow aligned with the horizontal axis.
Figure 3. Example of results of hydcont.m with flow not aligned with the horizontal axis.