RESEARCH· ·1970·

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mation, both of Cretaceous age, consist of fine- to
n1edium-grained sandstone intercalated with siltstone
and shale. l\1ost of the artesian wells are completed in
sandstone in the upper part of the Fox Hills and in the
lower part of the I-Iell Creek, but a substantial number
of wells obbtin water from the upper part of the
Hell Creek, ·and a few itap beds of sandstone near the
base of the overlying Tongue River l\1ember of the
Fort Union Formation of Tertiary age. An excellent
description of these formations and a summary of the
stratigraphy is av~tilable in Denson and Gill (1965, p.
7-9) and Johnson and J(unkel ( 1959).
The artesian head measured in wells perforated in
the upper part of the Fox flills Sandstone and in the
lower part of the I-Iell Creek Formation, in the southwest
corner of l\1ercer County, is contoured in figure 1.
Wells· completed in the upper part of the Hell Creek,
in general, have lower heads and presumably represent
n different aquifer system. Probably most wells tap
only part of the sandstone beds forming these aquifer
systems.
HYDRAULIC PROPERTIES·
Methods of determining the hydraulic properties of
aquifers by using a flowing artesian well were devised by
Jacob and Lohman (1952). They developed equations
for a graphical solution for transmissivity and the
storage coefficient for short periods of flow, and a
simpler equation for straight-line graphical solutions
that gives accurate results with slightly longer periods of
flow. The formulas for the straight-line solutions are:
T
264
!l(sw/Q) and
CROFT AND WESOLOWSKI
(1)
S=2.1X10- 4 T(tfrw 2 ) 0 , or (2)
2.1 X 10-
s 4 T(tfrw 2 )
logto -l [sw/Q/!l(sw/Q)] 1 (3)
in which
T=coefficient of transmissivity, in gallons per day
per foot,
S=storage coefficient,
Sw=drawdown, in feet,
Q=flow rate, in gallons per minute,
t =time between beginning of flow and flow
measurement, in minutes, and
7'w=effective radius of the well through the aquifer,
in feet.
The values, Sw/Q, are plotted on the linear scale on semilog
paper, and the corresponding values of tfrw 2 are
plotted on the logarithmic scale. The slope, ll(sw/Q), is
the change in Sw/Q over one log cycle of tfrw 2 • The value,
(tfrw 2 ) 0, (equation 2) is taken at the point' (sw/Q) =0.
When the slope of the curve is steep, equation 3 is used
B191
to · a void large extrapolation errors. In this case, the
values of tfrw 2 and Sw/Q are arbitrarily selected from a
specific point on the line.
Eleven flow tests were conducted on wells in Mercer
and Oliver Counties in the summer of 1968. The hydraulic
properties of the aquifers derived from graphical
solution using formulas 1, 2, and 3 are given in table 1.
After each flow test was completed, a check of the
calculated value for Twas made using the Theis (1935,
p. 522) recovery formula. The formula is:
264Q 1
T=-,- log 10 tjt , ( 4)
8
in which
Q =the weighted average discharge, in gallons per
minute, .
t =the time since discharge started, in minutes,
t' =the time since discharge stopped, in minutes,
and
s' =the residual drawdown, in feet.
The results of the recovery tests are given in table 1.
In addition, recovery tests were made on 27 other wells
in the fall of 1967 and the summer of 1968 for which
it was not practicable to make flow tests. The data
plots of many recovery tests have a slight, gradual
change in slope, probably due to pressure-sensitive
leaks in the well casings. In general the changes
in the plot were not serious enough to invalidate the
results.
RESULTS OF AQUIFER TESTS
The results of the 49 flow and recovery tests made in
l\1ercer and Oliver Counties are summarized in table
1. The values obtained for transmissivity range from
13 to 3,100 gpd (gallons per day) per foot and average
510 gpd per foot. The average was obtained by using
the average results of the flow test an~ the recovery
test as one value. The values for permeabilities (table
1) were obtained by dividing the thickness of the
aquifer, obtained from a driller's log or electric log of
the well, into the value for transmissivity. The permeabilities,
which average 16 gpd per square foot, are
comparable to the values obtained by Taylor (1968, p.
16) for the Fox Hills Sandstone and the Hell Creek
Formation in the Northern Powder River valley,
l\1ontana. The mean permeabilities obtained by Taylor
ranged from 2.8 to 21.4 gpd per square foot.
The. artesian storage coefficient is proportional to the
thickness of the aquifer and generally ranges frmn 10- 3
to about 10- 5 • Values for the storage coefficient calculated
from field tests ranged from 1.r X 10- 13 to 3.8 X lQ- 4 •
However, those values smaller than 10- 5 are probably
not realistic. Because the effective well radius, rw, appears
as .rw 2 in equations 2 and 3, a slight error in rw
would have considerable effect on the accuracy of S.