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Economic'Well Spacing for an

Industrial water Supply

A Thesis Submitted to

The Faculty of
MICHIGAN STATE COLLEGE
of

AGRICULTURE AND APPLIED SCIENCE

by

E. A. Moulder
W
Candidate for the Degree of

Bachelor of Science

June 1948

ACKN UWIJSDGELLEN T3

The writer wishes to express his appreciation for the advice and
assistance given by Professor F. Theroux, Professor of Civil Engineering
at lfiichigan State College, the staff of the Ground. Yater Division of the
United States Geological Survey office in Lansing, Mr. Black, Engineer
for the Board of Water and Electric Light Commissioners of Lansing,
bun Harold WOrden, Cooke well supplies representative for the Lansing

area, and to the staff of the Layne—Vorthern Company of Lansing, Michigan.

C}Ob)t\

CONTENTS

Introduction

Condition of Problem . . . . . . . . . . . . . . . . .
Collection of data . . . . . . . . . . . . . . . . . .
Expected Geologic Conditions to be encountered . . . .
Static Water Level estimates . . . . on . . . . . . .
Selection of Storage and Transmissibility coefficients
Spacing Study . . . . . . . . . . . . . . . . . . . . .
Cost Estimates for Various well Combinations . . . . .
Summary and Conclusions . . . . . . . . . . . . 1 . . .

Bibliography . . . . . . . . . . . . . . . . . . . . .

ILLUSTRATIONS

Map of proposed site . . . . . . . . . . . . . . . . .
Lansing and East Lansing map showing well locations . .
Typical water level recorder chart . . . . . . . . . .
LOgarithmic "Type Curve" . . . . . . . . . . . . . . .
Adjusted drawdown graph . . . . . . . . . . . . . . . .
Logarithmic graph of drawdown . . . . . . . . . . . . .

Geologic Cross Section of Saginaw Formation . . . . . .

Page No.
. l
. l
. 2
. 4
. 8
. 16
. 25
. 30
. 33
Figure
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2
3
4
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6
7

INTRODUCTION

The ever increasing use of ground water for municipal and industrial
supplies has brought about the need for workable methods for estimating
well performance.

In the past the procedure of obtaining a sufficient supply of water
from the ground consisted of tapping a water bearing formation and ex?
tracting the desired amount of water frdm it. The growth of communities
and industries and hence the increased need for larger quantities of
water has brought out the fact that these ground reservoirs are not inex-
haustible. The over-development of certain areas has proven costly and
could have been avoided if proper spacing of wells had been predetermined.

The problem of economically spacing wells and forecasting their
performance will be discussed in this report and a step by step proce-
dure involving a typical problem will be presented.

This problem is intended to illustrate what can be done to utilize
data normally available to the designer in well built up districts. It
is recognized that in many instances the data may not be as complete as
that used here, but on the other hand the information used here is not
nearly as complete as it could be.

It has been a common failure of many industries to choose locations
for their plants without proper consideration as to where or how they
were going to obtain sufficient quantities of water. Many'plants have
been forced to abandon their sites for more suitable ones, just for
that reason: 'The paper industry of central Michigan is an excellent
example of what may happen if prOper water supply planning is not

utilized. Several plants have chosen sites where apparently there was

'water in sufficient quantities to last forever, but an investigation would
reveal that the number of abandoned wells far exceeds the number of
producing ones. Without further investigation it is evident that any
forecast that may have been made in regard to the long-time out put of
these wells was expensively inaccurate.

If this example were an outstanding one there would be little need
for modification of the present methods used in regard to well field
design, but it is not the exception; it is quite general throughout the
United States.

“While this report does not attempt to solve all the problems, or
even most of the problems of the well designer, I believe sincerely that
it is a step in the right direction.

The problem presented will attempt to illustrate in general a pro-
cedure to use in applying several formulas and basic principles devised
by a number of investigators; it will not attempt to derive these
formulae or delve into their theories. References will be made for
further study, and to substantiate the methods used herein. It is also
realized by the writer that many specific problems as to specifications

have been omitted in hopes of amplifying the main objective.

PROBLEM

Conditions of problem

 

A suitable site for a large bakery is to be investigated to deter-
mine whether the bakery may obtain a suitable ground water supply of
its own. Also, the cost of obtaining will be compared to purchasing
township water. The site chosen is the N% of the SW% of sec. 24 ex-
cluding railroad right of way prOperty, and is as shown by Figure 1. It
is assumed that the bakery has an option on the property and is con—
sidering construction of their plant here.

Collection of data

 

By a thorough canvass of the surrounding area, as much information
regarding existing wells as possible is obtained. Information as to
the log of the materials encountered in drilling these wells is often
obtainable from the owner or the driller. The pumping rates of surround-
ing areas, likely to have effect on the field, are obtainable from the
records kept by the municipal and industrial water works Operators.
Water level measurements are often kept by Government agencies.

_Locations of abandoned wells for possible observation wells may be
found by this canvass. A very important place to check is the Ground
Water Division of the United States Geological Survey, and also the
State Geological Survey, for that area. They collect such data as is
mentioned above, including water level measurements, and also have per-
meability and other figures based on pumping tests conducted in the
area. They also offer advice in the method of obtaining these figures

by the use of pumping tests.

 

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The small home wells have valuable information too. The amount of
casing in the well is indicative of the depth to rock. The quality of
the water may be tested to check its contents and uniformity. The ease
of obtaining depth to water may be helpful. Core samples from drillings
may be used for laboratory tests. Libraries and newspaper files are
excellent sources for obtaining records of old wells, and often mentioned
are water levels at various times which may lead to an estimate of the
rate of decline of the water table. If time is available, talks with
old-timers or drillers may add little bits of obscure data that may fit
well into the overall picture.

This investigation includes all such bits of information and an at-
tempt to correlate these in a logical manner to their best advantage.
Expected Geologic Conditions to be encountered

A geologie cross section was drawn using the logs of existing wells
and projecting them on an assumed plane perpendicular to the earth's
surface with its line of intersection as indicated on the map of Figure 2.
The wells that indicate only the bedrock surface are wells whose complete
logs were not obtainable. The bed rock level was obtained by taking the
elevation at which the drive casing was "landed". A method that is not
usable in a report of this kind consists of making a 3-dimensional
model, using a map of the area for a base and soda straws erected
perpendicular to the map's surface at each well location. By using
different color paints for different types of strata, and painting
the straws using a convenient scale for elevation, the resulting model

gives a very enlightening picture of the different stratas.

Analysis of Geology and_proof or suggestion of interconnection

The cross-sectional diagram (Figure 7) will be used for estimating
the following:

I The depth to the water-bearing formation.

II The thickness of the water bearing formation, and hence the

total depth of the well.

III The depth to bedrock, and hence the casing setting.

IV Hydraulic connection between the various other well fields.

Taking the above items in order, a brief discussion will be made of
each to point out the reasons for selecting the estimated values.

The depth to the tOp of the water bearing sandstone throughout the
cross section shows that its elevation varies between 780 M. S. L. and
758 M. S. L. It is quite probable the elevation at the proposed site
will fall somewhere in between these values. It is also reasonable to
assume that the elevations nearest the site are more apt to be correct.
A straight line drawn between the two adjacent wells shown should give
a value close enough for estimating purposes, so the estimated elevations
will be taken as 770 for all ‘wells in the field.

The water bearing strata which is found in this area is the Saginaw
sandstone. It is apparent from the logs shown that there are layers of
shale present which do not seem to be continuous; but are found only in
lens form. This condition seems to be quite general throughout the
entire Saginaw formation, as pointed out by several geologists. The
shales are relatively impermeable, and the sandstone is bounded by these
shale layers at approximate depths of 770 and 460. The estimated

thickness above the limestone of the water bearing formation or aquifer

will be taken as 200, allowing for the shale lenses. The total depth of
the well then may be determined by taking the difference between the ground
elevation of the estimated bottom of the aquifer, or 400 feet.

The depth to bed rock, or to the base of the drift, is normally
where the well casing is set. The well driller is more likely to bid the
contract lower if he is sure of approximately how much casing the well
will require. The depth that will be estimated will be 60 feet, and was
obtained by the same method as was used in estimating the depth of the
water-bearing formation.

The fact that the shale formations cannot be traced from wells for
only a short distance leads to the conclusion that they "pinch out" and
leave the sandstone formation hydraulically connected. It is further
apparent from the cross—section that the sandstone may be traced can!
pletely through the area at the same elevation. This uninterrupted
ground water reservoir is then not only the source of supply for the
proposed well field of the problem, but is also the same source for the
Industrial and Municipal water supplies of the Greater Lansing Area.
This fact must be taken into consideration, as it will have a direct
bearing on the static water levels in the entire area. Further proof
and a more thorough discussion will be given later concerning the
interference to be expected from other well fields when an analysis
of the Water Level data is made.

Static water Level estimates

 

Information regarding past water levels was collected from various
sources, and from these an attempt will be made to predict future exp
pected conditions. Perhaps a brief history of the ground water develop-

ments will give a better basis for the reasoning to be used.

.5-

Prior to 1885, privately owned shallow wells furnished most of the
domestic supply for the Lansing area. At this time the public supply
was started using shallow wells drilled in a sand formation. Ten years
later the first tells penetrating the sandstone were drilled to a depth
of approximately 150 feet. By 1915 various other locations had wells
penetrating the sandstone to a maximum total depth of 350 feet. The 1920
average daily withdrawal amounted to about 4.7 M. G. D., and by 1930 the
rate had almost doubled. Finally, by 1944, the Lansing water supply
system had reached 14 M. G. D. average rate, drawing from 91 wells.

East Lansing and Michigan State College's rates also increased rapidly.
Michigan State College is using approximately 1.5 M. G. D., and East
Lansing .7 M. G. D. Other considerable withdrawals of water are made
by the industries and air-conditioned buildings.

Picture this vast underground reservoir supplying this tremendous
amount of water. Its ability to transmit water is limited by the cross-
sectional area of the aquifer, its permeability, and its hydraulic
gradient. Consequently, when the rate of pumping of an area exceeds
its transmitting properties it can only result in a decrease in head or
lowering of pumping levels. It is evident from the water level records
in the Lansing area that this condition exists. An example can be shown
by the use of an old newspaper clipping which gage the static water level
of the hichigan State College number 3 well as 1.5 feet from the top of
the ground in February, 1905. The water level in this well now is ap-
proximately 40 feet. From the same source the Lansing well on Townsend
Street was reported as having a static of 2 feet the same year. Its

present level is about 35 feet, and it is quite some distance from any

large pumping. Some of the water levels in the Lansing Area nearer the
more heavily pumped sectors are over 100 feet from the top of the ground.
Recent installations of the Landell Metropolitan Area's wells will
probably have increased effects on the lowering of the water table.

By numerous computations using pumping rates of the various fields
and expected increases due to new fields, estimates of the proposed
bakery site could be made. It is felt by the author that such computa-
tions would not be warranted on this particular problem; so estimates
will be based on water level records taken in the immediate vicinity of
this site.

At present there is a 10-inch'well located on the property selected
for the investigation which was originally put down as a natural gas
test well, and later the casing pulled to the base of the drift and the
hole sealed off at a depth of 455 feet. There is a water level recording
instrument on this well maintained by the United States Geological Survey
since November, 1945. A continuous record has been kept of the fluctua-
tions of the water level in this well since that time. A typical chart
showing the fluctuations over a period of a week is shown in Figure 3.

During this period of record the water level in this well has varied
between 28 feet and 48 feet. It is apparent from a study of these
graphs that the level is most affected by pumping in the vicinity.
Positive proof of interference from the College wells will be shown
later in the results of the pumping test. To show proof of interference
from the nearest Lansing well field (Riverside hell Field) a period is
taken when the College wells remain at a comparatively steady rate, and

when the next nearest field or the city's Pere Marquette field also

remain at a steady rate. The data is tabulated below:

1948 Ma? luggage amaze
Jan. 45 M. G. appx. 47.7 0.5
Feb. 45 M. G. appx. 45.0 6.8
Mar. 45 M. G. appx. 51.9 0.7

From these pumping records it is shown that while the College wells
remained relatively constant and the PM field's rate decreased 2.7 from
January to February, and then again increased their rate by 6.9 million
gallons, that the Riverside field had a sizeable increase in pumping.
This increase in pumping of 6.3 million gallons from January, 1948 to
February, 1948 was accompanied by a lowering of the level in the
recording observation well. During the month of January the water
level averaged about 45 feet from the measuring pointéburing February,
the average level was about 47 feet, and went as low as 48.1 feet.
During the month of March it recovered to an average level of 45 feet
again. V

It would seem from this analysis that the effects of adjacent pump-
ing should be taken into consideration in estimating a safe assumed static
for the proposed well field.

Taking the months when the heaviest pumping occurred in adjacent
fields and comparing them to the water level in the observation well,
should give an indication as to what the lowest expected level should be.
During July and August of 1946, the total pumpage of the Lansing's City
wells reached a maximum. for the year of 545 million gallons and 526
million gallons. During this period the Riverside field pumped the
largest quantity (82 million gallons) for the period of water level

recording. At this time the observation well reached an all time IOW’

with a depth to water of 48.5 feet. The heaviest pumpage for 1947 also
occurred during the months of July and August, with a total pumpage of
486 million gallons and 579 million gallons, respectively. The high
during August, 74 million gallons, which was 8 milli
pumpage figure for the Riverside field occurred/less than in 1946.
During this period the low water level was recorded as 47.5 feet from
the measuring point.

The measuring point in all cases was taken at a point 2.2 feet above
the surface of the ground. The ground at this point has an elevation of
approximately 865 feet.

From the above observed data it would seem that the maximum expected
depth to water during the year would be about 48 to 49 feet, and the aver-
age would fall somewhere between 28 and 48 feet. By an inepection of all
the data recorded it appears that the average would fall between 35 and
40 feet. In view of the installations of new township and city wells
within the Lansing area, and an inspection of the last year's data, an
average depth of about 40 feet would appear to be a very reasonable
figure. Allowing for slightly increased rates during the next few years
a design figure will_be placed on the safe side and taken as 45 feet
from the ground surface, or at an elevation of 820 feet M. S. L.

Selection of storage and transmissibility coefficients

 

Essentially, there are two basic methods for determining permeability
of ground water formations; the "Equilibrium Method" and the "Non-
equilibrium method." The equilibrium method makes the basic assumption
in its formulas that the cone of depression around the discharging well
has reached equilibrium (steady-state flow of water). The non-equilibrium
method does not depend on the cone of depression reaching equilibrium,

and also introduces the factors of time and elasticity. This last method

may also be applied to the recovery of the water level in the vicinity
of a discharging well, after the discharge of the well has stopped.
For a more complete comparison of the methods, the reader is referred
to “Geological Survey'water-Supply Paper 887".

During the month of January, 1948, a controlled pumping test was
conducted at Michigan State College under the direction of the United
States Geological Survey. 'With the permission of the Lansing office this
data was made available for use in determining the water-bearing charac-
teristics to be used in this problem. The observations made from the
water level recorder located on this site (shown in Figure 1) are the
water levels to be used in computing the transmissibility and storage
coefficients.

The non-equilibrium formula recently developed under the direction
.of Thais is based on the assumption that Darcy's law is analogous to the
law of the flow of heat by conduction, and thus the mathematical theory
of heat-conduction is largely applicable to hydraulic theory. The

Theis' non—equilibrium formulu is:

- 114.6 ’ -
8 - "vf'J 1.81r25 ——-—e Ed“
Tt

Theis, C. V., the relation between the lowering of the piezometric
surface and the rate and duration of discharge of a well using ground-
water storage: American Geophys. Union Trans. 1935, pps. 519-524 where
s is the drawdown, in feet, at any point in the vicinity of a well pumped
at a uniform rate; Q is the discharge of the well, in gallons per minute;
T is the coefficient of transmissibility of the aquifer in gallons per

day, through each strip extending the height of the aquifer, under a unit

-1o-

gradient-this is the average field coefficient of permeability multiplied
by the thickness of the aquifer; r is the distance from the pumped well

to the point of observation, in feet; 3 is the coefficient of storage of
the aquifer; and t is the time the well has been pumped in days.

The coefficient of transmissibility is defined as the number of
gallons of water that will move in one day through a vertical strip of
the aquifer one foot wide and having the full height of the aquifer with
a hydraulic gradient of 100%.

The coefficient of storage is defined as the volume of water, measured
in cubic feet, released from storage in each vertical column of the aquifer
having a base one foot square when the artesian head is lowered one foot.

The assumptions under which this formula is valid are as follows:

1. The water-bearing formation is equally permeable in all

directions. .

2. The formation is of infinite areal extent.

3. The wells penetrate the full thickness of the formation.

4. The coefficient of transmissibility is constant at all places

and at all times.
5. The formations release water from storage instantaneously with
a decline in water level.

Any divergence of actual field conditions from these idealized assump-
tions result in variations and inconsistencies in the alignment of the
observed data.

The solution of the integral is greatly simplified by the use of
graphs, a method devised by Theis, and will be demonstrated in the solution

of the equation.

The eXponential integral in equation (1) is replaced by the term
W(u)'which is read "well-function of u" and the equation is reawritten

as follows:

5: gfii‘fl ‘w(u)
The value of the integral is given by the following series:

W(u) = -O.577216 - log e U + U - U2 + U3 - U4

272': 37'3"! 473; (2)
Where u 1': My (3)

Values of W(u) for values of u between 10"LS and 9.9 are given in
Table 1. To avoid repeated solutions for u a "type curve" of values of u
versus W(u) are plotted on logarithmic paper as shown in Fig. 3. By

putting equations (1) and (3) in the following form:

8 : 23%] W(u) (4)

g3 35%;] u (5)

it is seen that s is related to r 2/t as W(u) is to u. By plotting the
test data values of the drawdown 8 against the distance from pumped well
to observation well squared over the corresponding time (r 2/t) on
logarithmic tracing paper, the resulting curve should match the "type
curve" where its correSponding values are in proportion. By selecting a

"matching point" on the two curves and rewriting the equations as follows:

 

‘1‘ : 114.6} W01) (6)
and
S : u T (7)

m

the values for transmissibility and storage can be solved for directly.

-12-

The controlled pumping test that was run on the college number 12
well was conducted as follows:

I All wells were held constant prior to test until the recording

chart on the observation well showed relative stabilization.
(No appreciable change in water level.)

II Baily chart installed on recording instrument to make possible

closer check on time factor.

III Number 12 pump shut off and exact time noted. Other wells

held constant.

IV Recorder changed at 24 hour intervals.

V After being off for 48 hours approximately, number 12 pump

'was again started and as before the exact time was noted.

VI Daily charts were maintained on the observation well until

the magnitude of the water level changes due to the resumed
pumping were so small as to be obscured by other fluctuations.

VII The distance between the two wells was obtained.

Using the non-equilibrium method the data will be analyzed. Here-
after the data collected during the period that the pump was off will
be referred to as the "recovery data" and the data collected during the
period after the pump resumed operation will be referred to as the
"drawdown data".

The recovery data was first analyzed. The procedure followed was
to extract the values of the water levels from the recorder chart and
their corresponding times and put them in tabular form, selecting points
at various time intervals to give fairly even spacing when plotted on
logarithmic paper. The values for s were computed by assuming the

depth to water at the start of the test to be static level, 8 is then

the difference between the water levels during the test and the assumed
static level. The time is converted to minutes, using the time the

pump went off as zero minutes. Another column is computed for the

r 2/t values by squaring the distance in feet from pumped well to ob—
servation well and multiplying by 1440 to convert the time from days to
minutes, and dividing by each selected time. These values were plotted
and values for T and S determined for comparison with the drawdown
computations. 0f the two sets of data, the greatest weight was assigned
to the drawdown data, because the extension of the recovery curve was
thought to be more accurate than the assumed static used in the recovery
data. The procedure will be outlined for the analysis of the drawdown
data in detail as these values will be used in the subsequent design.
This method in general is the same used on the recovery data.

The solid line of figure 5 is a reproduction of-the observed data
on the drawdown test. The dashed line represents the trend of the water
level if no change in pumpage had occurred. This extended curve was
obtained as follows:

I The plotted curve for 3 versus r 2/t of the recovery data was
superimposed on the type curve, matching the two curves as
closely as possible, keeping their coordinate axes parallel.

The observed data curve was extended by tracing the type curve
to the desired point. Values of s were then extracted from

this extended portion and plotted with their corresponding

times on figure 5 as shown by the X-marks. Through these points
the extended curve was drawn. The values for the adjusted
drawdown s are now obtainable by scaling the distance between

the two lines. Putting the required data in tabular form for

 

-14-

convenience of plotting we have:

(1) (2) (3) (4) (S)
t 3
DATE HOUR MIN. ADJ. D/D r 2/t RATE OF PUMPING
Q
Jan. 19 2:00 p 0 O V’3 200
Jan. 19 2:30 p 30 .02 1.96 x.108 200
Jan. 19 3:30 p 9o .07 6.53 x 107 200

From the values of (4) and (5) the graph shown in figure 6 was
plotted on transparent logarithmic paper. Superimposing this plotted
data on the type curve of figure 4 keeping the coordinate axes parallel
the best "fit" was obtained; that is, the Spot at which the most points
bearing the greatest weight fell on the type curve. The first few points
were assigned less weight than the following points because of the lag
in reaction of the observation well, a slight error in the time element
would be magnified, and the variable rate of pumping that is likely to
occur until a relatively constant pumping level is reached. The last
few points were also assigned less weight because their decreasing rate
of change had diminished to the point where other pumping effects in the
area were likely to be of greater magnitude than that of the tested
discharging well.

The fitting of the type curve to the plotted points is shown by the
dashed line of figure 6. The next step is the selection of a "match"
point, or a point that is common to both curves. This point was selec-
ted as shown by the cross at a point on the type curve (figure 6) where
the value u : 0.1 for convenience in computing. The values of both
graphs at this point were noted and recorded for use in solving the

following equations for T & S:

 

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5
Where 0 = 200 CPU, w(u) : 1.82, s : 4.65 feet
T : 114.6 x 200 x 1.82 : 9,000 0,p,D. feet
4.657
and S :

2.2
1.84 r 2/t
Where 1). : 0.1, T = 9,000, r 2/t : 2.4 x 109

s = 0.1 x 9000 : 2.02 x 10-4
10 x 03 X 0-

To relate the transmissibility to the more common term of permea-
ility, the value for T can be divided by the thickness of the formation
to give the average permeability.

Pav. : if.
M

Where T Z 9000 and M 2 200 feet assumed permeable thickness.

Pav. = 2ggg.= 45 GPD per square foot per feet of hydraulic gradient.

The value obtained from the recovery data for T and S were 8750 and
1.66 x 10‘4 which were reasonably close. If both the recovery and drawdown
data were weighted equally, the average values would be used as the
accepted ones. For the reasons mentioned previously the values obtained
from the drawdown will be used as the accepted ones for further design.

A tabulation of the data thus far obtained will now be made for use
in the analysis of the spacing of the wells and selection of the most
economical grouping.

Estimated depth of each well . . . . . . . . . . . . 400 feet

(all ground elevations assumed filled in to 855 MSL)

Estimated length of casing required . . . . . . . . 60 feet

-16-

Estimated depth to t0p of water-bearing formation . . . 95 feet
Estimated depth to water . . . . . . . . . . . . . . . 45 feet
Computed coefficient of Transmissibility . . . . . . . 9000
Computed coefficient of Storage . . . . . . . . . . . . 2.02 x 10"4

Spacing study

 

The site for the proposed well field is about 2600 feet long and
1300 feet wide at its widest part. To come well within state health
specifications the wells will be located 300 feet away from any boundary
and will be kept in a line lengthwise of the field. The spacing between
the two outermost wells will be held to a maximum distance of 2000 feet.
Several combinations of well groupings will be investigated and the
unit cost of water for each determined. An analysis of these values will
be used in selecting the most economical design.
The basic assumptions to be used in the computations of the various
well combinations are as follows:
I All wells drawing from storage for a 6 months period. (No
appreciable recharge to the aquifer)
II Dewatering of the aquifer to be avoided by limiting effective
drawdown to 40 feet in all wells.
III Behavior of the water levels in the wells will corresponde to
theoretical conditions of non-equilibrium method.
IV 8 hour pumping day to furnish total amount.
V Values for T and S determined will hold true for all wells.
The assumption made of no recharge to the aquifer for 6 months may
sound severe, but quite often drought periods have lasted for this length

of time.

It has been noted by well Operators in the Lansing area that the
wells that have pumping levels constantly below the top of the aquifer
progressively fall off in yield. It is thought that this is caused
partly from the dewatering of the sandstone and a subsequent incrusta—
tion of the dewatered portion of the formation decreasing its ability
‘to pass water. For this reason a suggested remedy for this situation
will be incorporated in this design. By limiting the effective or daily
average drawdown to a point somewhere above the top of the aquifer, the
formation should not become dewatered for any long period of time, and
hence incrustation and drops in yield due to this should be held at a
minimum.

The computed water levels will probably be somewhat in error from
what actually would occur; however, their relative behavior should
corresponde very closely. The safety factor included throughout should
take care of any errors. Computed values for water levels using similar
data have been found to agree within 10% in artesian formation near
Fulkin, Texas. Other investigations throughout the country have closely
approximated this value, through careful analysis of the data available
to them.

The pr0posed bakery is assumed to be in Operation for an 8-hour day
and consequently their demand will be for that period. Reservoirs could
be used for balancing the supply, but for the sake of estimating the
8—hour period will be used. The amount withdrawn during this 8-hour
period should be the maximum for the day, regardless of the number of
hours of pumping.

In many cases the coefficients of transmissibility and storage may

be checked from other tests or more observations of the same test. The

-13-

values obtained here were the only ones available in the area, so they
will be the accepted ones.

Computations:

 

General formula for computing the drawdown in any one of a group of

wells:

81 3 S1.1 * S2-1 + S3-1 * + SnLl

82 81-2 + 82-2 “ 83-2 + " Sn-z

Sn = Sl-n + $2_n + SBdn + + Sn-N
'which is read as follows: the drawdown in well one is equal to the
drawdown effect of pumping of number one on number one, plus the effect

of number 2 on number 1, plus the effect of number 3 on number 1, etc.

Where 5 : 114.6 Q'W(u2

T (4)

and'W(u) varies as before with u

 

‘where u 2 1.87 r28 (3)
Tt—-_

let c : 114.6 Mu) (8)
T

Now 8 : c Q

or in the general equation

Sn-N = Cn-N QN

By the use of equations (3) and (8) c values will be computed for a
six months (183 days) period for various radii, using a 14 inch diam. well.

u = 1.87 r25 = 1.87 x 2.02 x 10-"?2 = 2.30 x 10'10r2
Tt 9000 x 183

C I 114.6 Win) : 0.0 1273 "(11)
9000

 

-19-

C Values for Various Radii

 

 

Table 2
r r2 u WKu) C
7/12 . .34. 7.80 x 10-11 22.70 .289
100 1.0 x 104 2.30 x 10-0 12.41 -.158
250 6.25 x 104 1.43 x 10-5 10.58 .135
500 2.5 x 105 5.73 x 10-5 9.19 .117
667 4.45 x 105 1.02 x 10"4 8.61 .109
750 5.62 x 105 1.29 x 10-4 8.38 .107
1000 1.00 x 106 2.30 x 10-4 7.80 .099
1333 1.78 x 106 4.10 x 10-4 7.22 .092
1500 2.25 x 106 5.16 x 10"4 6.99 .089
2000 4.00 x 106 9.18 x 10"4 6.42 .082

 

Values of‘W(u) taken.from Table 1.

To find the maximum pumping rate that will produce an effective
drawdown of 40 feet at the end of the 6 months design period, the Q rate
value will be the rate for a 24-hour pumping period. It is seen, then,
that for 8 hours three times this rate could be pumped. The actual
drawdown, pumping at this rate, will be different from the design value
and will be computed later to determine the pumping level for chossing
a pump.

For the purpose of illustration and comparison of rates, the first

computation will be for the yeild from one well under these conditions.

-20-

Eq. for 24 hour pumping 8: 00

or Q :.E
c

or for 8 hour pumping

3/3ng orQ:§__-_‘-"_
C c

where s 2 40 feet and c from table is .289

Q = 3 x 40 a 414 G.P.M.

To obtain 8 hour rate, 3 x s or 120 will be used for value of 5.

Because closer spacing gives lesser yields, the maximum space of
2000 feet between outer wells will be utilized in the following computa-
tions:

For 2 wells spaced 2000 feet apart

 

Because both wells are affected similarly, one equation is needed as

the Q values are equal:

31 g 51-1 + 52-1
31 = c1-1‘3 *' c2—1Q
s1 = Q (01-1 + c2-1)
Substituting 120 = Q (.289 + .082)
Q =.%§$1 = 324 G. P. M. per well Field Value
2 x 324 = 648 G.P.M.

3 Wells 1000 feet apart

 

In this case the two outside wells will have the same rate, but the
inside rate will be less. Therefore, two equations are required.

I 81 = c1-1 01 + c2-1 Q2 * °3-1 Q3 “here 81 = Q3
II 82

01-2 01 + C2-2 Q2 + c3_2 Q3
1_ 120 = (.289 + .082) 01 + .099 Q2
II 120 : 2(.099) Q. + .289 02

 

ii--.‘ A

.21-

 

I 120 : .371 01 + .099 Q2
2 225 2 .371 010+ .542 Q2 II x 1.88
105 Z .443 Q2 subtract I from 2
.44}
Q1 = Q3 = 258 G. P. M. . substituting Field Value

2(258) + 237 = 753 e. p. m

4 Wells 667 feet apart

 

Two pairs of similar wells, two unknown Q values, so there are two
equations. As before the general equations hold true, but due to simi-
larity of spacing, requires less equations. The method is now made
clear so hereafter the equations will be shortened, showing only the
direct substituting equations.

1 120 z (.289 + .082) 01 + (.109 + .092) 02

II 120 = (.109 + .092) 01 + (.289 + .109) 02
2 222 : .371 01 + .735 Q2 II x 1.85

subtracting I from 2

Q2 : 102 : 191 Go Po M0
.53?

Substituting Field Value
Q1 = 220 G. P. M.

2(191) + 2(220) _ 822 0. P. M.

5 Wells 500 feet apart

 

I 120 ; (.289 + .082) 01 + (.117 + (.117 + .089) 02 + .099 Q3
II 120

(.117 + .089) 01 + (.289 + (.289 + .099) 02 g .117 Q3

III 120

(2 x .099) 01 + (2 x .117) 02 + .289 03
I 120 = .371 01 + .206 02 + .099 Q3
2 216 : .371 Q; + .699 02 + .210 Q, II x 1.80

 

IV 96 = + .493 Q2 + .111 Q3 subtract I from 2

.. 3.8.4111 .. l

-22-

 

I 120 z .371 01+ .206 02 + .099 Q3
3 225 :- .371 0;). .439 Q? +§42 0; III x 1.88
V 105 = + .233 02 + .443 0,3 subtract 1 from 3

IV 96 = 6493 Q2 "" 0111 Q3

 

5 222 = .493gg + .937 03 v x 2.12
126 = + .826 Q3 subtract IV from 5
Q =126=1
3 .826 53 G P u
Q2 = 160 G. P. M. substituting
Q1 . 194 0. P. M. substituting

Field values
153 + 2(160) + 2(194) - 861 G.P.M.

Since the field values or rate obtainable from each well group‘
rapidly approaches a constant yield as the number of wells increases,
it would seem advisable to stop at this point, analyze the values ob-
tained, and select the most practical group.

The only apparent method for making an economical selection would
be a comparative cost study.

A necessary factor to consider in determining the power required is
the pumping level, or the distance the pump is required to lift the water
from the ground. Computations for estimating this value for each well
group considered will now be made.

The difference between an 8—hour pumping period at the daily rate and
the 6 months pumping period at the same rate should give the reduction
of the non-pumping water level in the well over the 6 months period.

This reduction of water level should then also be applicable to the

pumping level for the 8-hour rate. By adding this difference to the

 

.23-

pumping level for 8 hours at the 8-h0ur rate, the pumping level at the
end of 6 months is obtained. As the rate of decline after the first
few hours approaches a straight line function, the mean of the two levels
is expressed in equation form: (the average pumping level)
Average pumping level = Pumping level at 6 months + pumping level at
8 hours, divided by 2.

For 1 well

 

S1 = Cl—l QL = 0289 x"fl%fl = 40.0 (6 months period)
. 414 '
81 = 01-1 QL = .208 x”... : 28.7 (8 hour period)
3 iio3 feet

(difference in level during 6 months)

53 01-1' Qh a .208 x 414 - 86.1 feet (actual level at 8 hours)

86.1 + 11.3 = 97.4 ' (actual level after 6 months)

In
H
II

Average : 97.4 g 86.1 I 91.8, or approximately 92:
So the pumping level below ground surface would be 92 feet plus the
original static of 45 feet, or 137 feet.

For 2 wells

 

8l 2 ('289 + “082) 2%5 : 40.0 (6 months period)

31 : (.208 + .007) (lgfl) : 23.2 (8 hour period)
I678
(difference in level during 6 months period)
s3 = (.208 + .007) 324 = 69.6 (actual level at 8 hours)
51 a 69.6 + 16.8 a 86.4 (actual level at 6 hours)

Average = 86.4 + 69.6 a 78 feet
2

 

Pumping level below ground surface is 78 + 45 3 123 feet
Similarly the pumping levels were obtained for 3, 4, and 5 wells.

Since the method used was generally the same, the actual computations

-24-

will be omitted and their results will be tabulated below with those
for 1 and 2. The additional computed data obtained thus far will also
be included in the following table.

Assuming elevated storage to furnish 30# pressure or 69.30 head
(alright for one story construction), the height above the ground to
discharge water to storage will be taken as a constant value of 70
feet. Disregarding friction losses in valves and pipe, the total

design head will be assumed to be 70 feet, plus the pumping level.

 

 

TABLE 3

No. of Field Field Average Average Total
Value Value Rate per well Appx P. L. Head

wells GEM GPD GPM feet feet
1 414 199,000 414 137 207

2 648 311,000 324 123 193

3 753 362,000 251 115 185

4 822 395,000 205 112 182

5 861 414,000 172 101 171

 

The values shown in Table 3 are the necessary ones for selection
of the pumps to be used. To get present day pump costs, this table was
taken to Mr. WOrden, the Cooke Company's pump representative for this
area, for the selection of pumps required and their prices. From inter-
views with various peOple connected with estimating costs ofiwell water,
estimates for the rest of the costs involved in the system were ob-

tained. A need for an average rate of 350,000 G. P. D. will arbitrarily

.25-

be chosen for use in choosing the most economical combination of wells.

To estimate the total cost of suoplying water to the bakery, only
the factors related to the transmission of water to the elevated stor-
age will be considered. This is to demonstrate their relative cost to
buying the water from the township.

Cost Estimates for Various Jell Combinations

 

Case I - 1 well

Cost pf Hell

 

 

The pump selected for the first combination was a 30 hip., oil

lubricated, 4 stage 12 inch pump 1% inch shaft, 6 inch column.

 

 

Unit Price
Pump and motor $2400
tell and pump installed 4000
hell house 500
Meters and electric installations 1000
$7900
haintenance, 5% 395
Engineering, Int. on investment, 8 Misc.

20% 1580

Total 89875.00

The life of the pump, well, etc. is estimated to be 20 years, so

the annual depreciation is

2§g§,°r 8493.75

Using a 300 day working year, the total number of gallons pumped
will be

300 x daily rate : 300 x 199,000 : 50.7 million gallons

-26-

The depreciation cost per 1,000 gallons is then found by dividing
the yearly depreciation by the number of gallons in thousands or:

493-75 = :
35:755 vOoOO9739

The power cost was computed by the use of the tables in Anderson's
hater tell handbook. Similar tables are available to the well designer
in numerous other handbooks. At the same time that the pump selections
were made, their efficiencies were noted and will be those used below.

Pump efficiency 79%, Motor efficiency 87%, Wire to water efficiency:
.87 x .79 = .69 or 69% from the table in the handbook.

For efficiency of 69%, 0.4550 KW hours / 1000 gallons is required
for a 100 foot head. The total head or field head for Case 1 is 207
feet so,

égg x .4550 3 0.942 KW hours / 1000 gallons

Using a unit price of $0.02 per KW hour,

.02 x .942 : 30.01884 / 1000 gallons power cost

The total cost per 1000 gallons may then be found by adding the
depreciation cost to the power cost.

.9739 + 1.884 = 2.858 cents / 1000 gallons

Using the same method, the costs per 1000 gallons were obtained for
the other four combinations of wells. Included in the estimates involv-
ing more than 1 well was the added cost of transmission main necessary
to bring the water to the reservoir.

As the method is illustrated, only the final values will be presented.
These will be found in the following table along with the cost of ob-
taining the additional water from the township for those combinations

not producing the desired quantity. The cost of township water is es-

timated to be 10.6 cents / 1000 gallons, based on present rates.

~27-

 

TABLE 4

(l) (2) (3) (4) (S) (6) (7)

No. Daily Amt. pur- Cost of Cost of Cost of Total

of Field Rate chased purchased pumped pumped cost/day
wells 1000 GPD from twp. ‘water/day water/1000 gals. water/day dollars

1000 GPD dollars cents dollars

1 199 151 16.00 2.858 5.69 21.69

2 311 39 4.14 3.104 9.65 13.79

3 361 O 0 3.233 11.32 11.32

4 394 0 0 3.695 12.92 12.92

5 414 0 0 3.687 12.90 12.90

 

Inspection of column (7) of Table 4 indicates the most economical
well combination to be the third one from the top. The reason for the
decrease in cost of the 5 well group over the 4 well group was caused
by the selection of pumps. To fit the 4 well combination, the pumps
available were not designed for high efficiency under the given con-
ditions. Other conditions being equal, there would be a gradual in-
crease in the cost per day rate for each additional well over three.

Using the 3 well combination, the possibility of spacing them
closer together will be investigated. The equations for the 3 well
combination were adjusted to determine the well yields for 500 feet
Spacing and 100 foot spacing. The computations were carried on in the
same manner as previously illustrated and the design value obtained.
The comparison in cost by redicing the space between them is as shown

in Table 5 o

—28—

 

TABLE 5
(1) (2) (3) (4) (5) (6) (7)
Well Daily Field Amt. from Cost of Cost of Cost of Total Cost
Spacing rate twp. twp water pumped water pumped water day
feet 1000 GPD 1000 GPD per day per 1000 gals per day dollars
dollars cents dollars
1000 361 0 0 3.233 11.32 11.32
500 340 10 1.06 3.229 11.19 12.25
100 292 58 6.16 3.319 9.68 15.84

 

It is noted, that even though the cost of transmission main is cut
in half the increased head and requirement of additional water makes the
1000 foot spacing the cheapest.

It is noted from column (5) of the above table that the cost per
1000 gallons for the 500 foot spacing is the minimum cost. Theoreti-
cally, then, spacing of the 3 wells at a distance between 500 and 1000
feet where the daily rate would be exactly 350,000 gallons would be
the ideal locations. It is the opinion of the writer that this degree
of accuracy is not warranted in this problem, as the difference between
actual and assumed conditions are quite likely to be in error.

The final design values for the supply will be as follows:

I Three 14 inch diameter wells to a depth of 400 feet.

II feat of 14 inch casing; remainder-open hole.

III Spaced 1000 feet apart; no well closer than 300 feet to the

property line.

IV 3 deep well 8 inch turbine pumps, having 1 inch shaft, 5 inch

column, 8 stage, and a 15 h.p. electric motor. Pump, 81%
efficient, motor, 87% efficient. 3 phase, 440 volts, 60

cycle, A. C. U. S. Motor.

-2 9-

V 4 inch transmission main to 6 inch main discharging to
elevated storage or system.

VI 6 inch emergency line from township supply for fire protec—
tion and major breakdowns.

VII Capacity of elevated storage tank, 100,000 gallons.

-30-

SUMMARY AND CONCLUSIONS

The methods outlined in a publication by the American'Water Works
Association entitled "Standard Specifications for Deep Wells" will be
the basis for a comparison study. The section entitled "Testing for
Yield and Drawdown" states, "In most instances the maximum capacity of
the test pump should be equal to the maximum quantity of water that it
is anticipated the well will produce, and not merely equal to the
capacity of the pump that is planned for permanent use."

They indicate that this information may be used in the future for
ordering larger pumping equipment, or in the design of adjacent wells.
This information could be very misleading to the untrained owner of
the well. As was pointed out in the design problem, the presence of
adjacent wells, if improperly located, could produce costly results
if the producing properties were assumed to be the same. As to pump-
ing the well at its maximum capacity for a basis of what can be ex-
pected in the future, no considerations of the lowering in pumping
levels has been mentioned. If the formation is unable tocbtain
sufficient recharge to meet the withdrawals the pumping level declines.
Quite often wells that have passed these shortterm pumping tests have
suffered losses in yields. The procedure usually followed is to lower
the pump-bowl settings to prevent a loss of yield. Constant recession ’
of the water level finally results in a loss of yield to the point
where the withdrawal of water balances the recharge rate.

The preliminary design, as outlined in this report, offers a
method of determining the safe yield of a formation, and hence the

removal of these undesirable series of events.

 

The ad
may not be
with a fee
expected.

Care

run cont
levels 5
After 0
levels

Creasi1

the s<
EHnOtui
one I!

is C'

the

thq

in

tc

The accuracy to which the values were carried out in this problem
may not be used as the absolute eXpected figures, but should be used
with a feeling of security that they are the worst conditions to be
expected.

Careful observations during construction of the wells should be
made, and corrections made where assumed values differ from actual
ones. It would also be desirable upon completion of the wells to
run controlled pumping tests on the various wells and observing water
levels in the adjacent wells for a check on the preliminary values.
After completion of the system, frequent and regular checks of water
levels would give valuable information as to the possibility of in-
creasing the capacity of the field.

For economy in selection of proper spacing, it would seem that
the set of conditions that most closely approximates the desired
amount of water would be the cheapest. This conclusion might be the
one made from inspecting columns (2) and (7) of Tables 4 and 5. It
is conceivable, though, by the redmction of cost for smaller pumps
and the decreased size of well necessary, that a greater number of
wells might offer a greater long-time saving. The wells in this
problem were all assumed to be 14 inch; however, it is more economical
to design the size of the well to fit the size of the pump desired, as
the yield is only slightly decreased by a decrease in the diameter of
the well.

Comparatively few industries keep complete records of their well
installations or Operation figures. These records are vitally needed
to make an investigation for expansion of the system, tracing contami-

nation, and in making repairs or changes in the present system.

 

Other problems may be solved using similar methods of attack; among
these are locating boundaries of preglacial valleys, locating desirable
localaties for well fields, and determining sources of recharge. A

bibliography will be included for further study of related subjects.

BIBLIOGRAPHY

Meinzer, 0. E.,
Hydrology, Physics of the Earth, IX, First Edition, McGraw-Hill Book
Company, New York, 1942.
Leverett, Frank and Taylor, F. B.,
The Pleistocene of Indiana and Michigan, U. S. Geological Survey.
Theis, C. V.,
The source of water derived from wells. Civil Engineering, Vol. 10,
No. S, May 1940. I
Whnzel, L. K.,
The Theim method for determining permeability of water-bearing
materials. U. S. Geological Survey'Water Supply Paper 679-A, 1936.
Brown, G. F.,
Geologic Factors affecting the Perennial Yield of Artesian Aquifers
in Three Areas in Mississippi, Economic Geology, Vol. XL, N0. 3,

May, 1945 o

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

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