\ I /
United States
Environmental Protection
Agency
Robert S. Kerr Environmental
Research Laboratory
Ada OK 74820
Research and Development
EPA/600/S2-85/066 Aug. 1985
Project Summary
Upconing of a Salt/Fresh-
Water Interface Below a
Pumping Well
Jan Wagner and Douglas Kent
Analytical solutions for the upconing
of an abrupt salt-water/fresh-water in-
terface beneath a pumping well and for
the concentration profile across a mov-
ing interface are developed for two
types of upconing problems. The first
considers the position of the interface
and the salinity of the pumped water
for a specified pumping rate. The sec-
ond type of problem addresses the
pumping schedules to prevent saliniza-
tion of a well or to reach a predeter-
mined salinity in the pumped water.
An interactive Fortran computer code
has been developed to obtain solutions
to both types of problems. The user is
provided with options to modify the
definition of a given problem, and,
therefore, can gain some insight into
the effects of geometry and physical
properties on the rate and extent of up-
coning and the salinization of a well.
This Project Summary was devel-
oped by EPA's Robert S. Kerr Environ-
mental Research Laboratory, Ada, OK,
to announce key findings of the re-
search project that is fully documented
in a separate report of the same title
(see Project Report ordering informa-
tion at back).
Introduction
The full report presents an analytical
solution for the upconing of an abrupt
salt-water/fresh-water interface below a
pumping well. Dispersion phenomena
arising from the displacement of a mov-
ing interface or a finite transition zone
between the invading and displaced flu-
ids can be superimposed on the analyti-
cal solution for the position of an abrupt
interface. An interactive FORTRAN com-
puter code has been developed that en-
ables the user to modify parameters
and to control the computational se-
quence. This interactive approach en-
ables the user to gain insight into the
effects of geometry and physical prop-
erties on the rate and extent of upcon-
ing and salinization of a well.
Mathematical Development
McWhorter (1972) presented the
equations that describe the flow in satu-
rated aquifers which are underlain by a
zone of saline water and pointed out the
difficulties in obtaining solutions to
these problems. The complexity of the
flow phenomenon has led many investi-
gators to idealize the system as a fresh-
water zone separated from an underly-
ing salt-water zone by a sharp interface.
In other words, the two fluids are as-
sumed to be immiscible. Schmorak and
Mercado (1969) followed this approach
and accounted for the mixing of the two
fluids by superimposing the effects of
dispersion on the transient solution for
the position of an abrupt interface.
For the case of upconing beneath a
pumping well partially penetrating a rel-
atively thick confined aquifer as shown
in Figure 1, Schmorak and Mercado
(1969) presented Bear and Dagan's so-
lution for the position of the interface as
a function of time and radial distance
from the pumping well as
x(r.t) =
2i;(Ap/p)Kxd
1
1
(1)
(1 + R2)1'2 [(1 + T)2 + R2]1'2
where R and T are dimensionless dis-
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Validity
of Linear
Approxi-
mation
= Xc, + Zo
Figure 1. Upconing of an abrupt interface below a pumping well
tance and time parameters defined by
, 1/2
and
(AP/p)Kz
(2)
(3)
Other notations are defined as follows
(also refer to Figure 1):
d = distance from the bottom of
the well to the initial interface
elevation (L)
KX,KZ = horizontal and vertical perme-
abilities, respectively (L/t)
Q = well pumping rate (L3/t)
r = radial distance from well axis
(L)
t = time elapsed since start of
pumping (t)
X = rise of the interface above its
initial position (L)
Ap/p = dimensionless density differ-
ence between the two fluids,
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elevation and the dispersion concept
should be limited to the zone below the
critical depth. The complex mixing and
flow phenomena above the critical
depth, near the well screen, and within
the well pipe are approximated empiri-
cally using the approach followed by
Schmorak and Mercado (1969).
The average dimensionless concen-
tration of the transition zone above the
critical rise, e(X > Xcr), is approximated
as one-half the concentration at the crit-
ical depth, or
e(X > Xcr) = 0.5 e(Xcr)
(7)
The concentration in the pumped water,
ew, is determined from dilution of the
average transition-zone concentration
above the critical depth with displaced
fluid, or
Xcr)
(8)
where cp is an interception coefficient, or
the fraction of transition zone fluid in
the total volume pumped.
Computer Program
Two types of upconing problems are
considered. The first involves the de-
scription of the expected interface ele-
vation and the salinity of the pumped
water as a function of time for a given
pumping rate. The second problem ad-
dresses the maximum rate at which a
well can be pumped without exceeding
a specified salinity in the pumped water.
Both types of problems are included in
an interactive computer code. Data are
required under two modes of opera-
tion—"Basic Input Data" and "Edit".
Basic input data are required to initi-
ate a new problem using the UPCONE
program. The data entries include the
problem title, the physical properties of
the aquifer and the two fluids, and the
geometry of the system. The user is
prompted for the required data through
a series of input commands.
Once the basic input data have been
entered, the problem as currently de-
fined is listed and the program enters
the "Edit" mode. The edit commands
can be used to redefine the problem,
execute elevation or pumping rate cal-
culations, or terminate the program.
The program has been written in an
unextended version of FORTRAN 77
and has been installed on microcom-
puters running under CP/M-80 and
MS-DOS as well as variety of minicom-
auters and mainframe machines. The
major modifications in code to imple-
ment the program on a given system is
the assignment of logical devices.
Guidelines for these types of modifica-
tions are clearly identified in the source
code.
References
Bear J. and D. K. Todd. 1960. "The Tran-
sition Zone Between Fresh and Salt
Waters in Coastal Aquifers." Contri-
bution No. 29, Water Resources Cen-
ter, University of California, Berkeley,
CA.
McWhorter, D. B. 1972. "Steady and Un-
steady Flow of Fresh Water in Saline
Aquifers." Water Management Tech-
nical Report No. 20, Engineering Re-
search Center, Colorado State Univer-
sity, Fort Collins, CO.
Schmorak, S. and A. Mercado. 1969.
"Upconing of Fresh Water-Sea Water
Interface Below Pumping Wells, Field
Study," Water Resources Research,
Vol. 5, No. 6, pp. 1290-1311.
Jan Wagner and Douglas C. Kent are with Oklahoma State University, Stillwater,
OK 74078.
Carl G. Enfield is the EPA Project Officer (see below).
The complete report, entitled "Upconing of a Salt/Fresh-Water Interface
Below a Pumping Well," (Order No. PB 85-215341 /A S; Cost: $11.50, subject
to change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Robert S. Kerr Environmental Research Laboratory
U.S. Environmental Protection Agency
P.O. Box 1198
Ada, OK 74820
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