THE FINANCIAL
SIGNIFICANCE OF OPTIMUM WELLSITE LOCATION
Dr. William M. Turner
INTRODUCTION
Hydrologists and water supply engineers know it is desirable to drill production wells
in an aquifer having high transmissivity rather than low transmissivity.
Transmissivity is a number that describes how rapidly ground water moves in the
aquifer. Wells in high transmissivity aquifers will produce more water than wells in
low transmissivity aquifers. Higher capacity wells means fewer wells and lower
operation and maintenance costs and less pipeline.
There are two compelling reasons to locate wells in high transmissivity aquifers.
1. For a given production rate the well in
the high transmissivity aquifer will have a less drawdown than a similar well in a low
transmissivity aquifer. Less drawdown will translates into lower pumping costs
because the energy required to lift the water to the surface is less.
2. For similar maximum possible drawdown,
the well in the higher transmissivity aquifer has the higher production capacity.
Thus, for large water requirements that are greater than the production capacity of a
single well, fewer wells will be needed if they are located in an aquifer with high
transmissivity to meet the water requirement. Savings in capital investment in wells
and equipment and maintenance will be realized by drilling fewer high capacity wells.
THE IMPORTANCE OF AQUIFER HETEROGENEITY
Very few aquifers have reasonably uniform hydraulic properties. With uniformity,
it makes little difference from a well production viewpoint where a well is located.
One location is just as good as another.
However, most aquifers do not have uniform hydraulic properties.
Alluvial, limestone, volcanic aquifers have a wide range in transmissivity.
Commonly, transmissivity changes within very short distances. The statistical
distribution of transmissivity has been studied for a number of
aquifers. AGW scientists have examined the statistical distribution of
transmissivity for six aquifers. These studies are found in our reference library.
Supkow (1973) studied the transmissivity distribution of alluvial aquifer in the Tucson
Basin aquifer in the State of Arizona in the arid American Southwest. Figure 1 shows the location of the Tucson Basin within the State of
Arizona.
In the Tucson Basin, aquifer heterogeneity results from alluvial materials that were
deposited on a preexisting erosional surface with a dendritic drainage network. This
erosional surface is known locally as the "Rillito" surface.
STATISTICAL SIGNIFICANCE
Supkow (1973) found the probability density function (pdf) for the frequency
distribution of transmissivity in the Tucson Basin
alluvial aquifer is given by:
f(T) = 1/le ^{T/l} for T>0
f(T) = 0
otherwise
where,
T = transmissivity
l = mean value of transmissivity.
The cumulative probability of drilling well into an alluvial aquifer with a specified
transmissivity is given by:
You can see that areas of high transmissivity are very scarce and areas of low
transmissivity are very numerous. In fact, only 16 percent of the Tucson Basin
aquifer has transmissivities in excess of 100,000 gallons per day per foot (gpd/ft) (1,242
m^{2}/d), whereas 52 percent of the aquifer has transmissivities less than 40,000
gpd/ft (497 m^{2}/d).
This means that if you select well locations in the
Tucson Basin at random, your chance of finding a poor location is excellent and your
chance of finding a good location is very poor. Table 1 shows
data used to determine the cumulative probability density function in the Tucson
Basin. Figure 2 is a graph of the cumulative probability
density function.
Because the alluvial aquifer in the Tucson Basin consists of heterogeneous,
channelfill deposits, the aquifer transmissivity is highly variable everywhere.
Just because the aquifer has a transmissivity of 30,000 gpd/ft (373 m^{2}/d) at a
particular well site, does not mean that a well drilled 200 feet (61 m) away will have the
same transmissivity.
Shortterm aquiferperformance tests only sample the part of the aquifer near the well
site. A short distance away from a well, the aquifer transmissivity will be
significantly different.
Because the PDF in the Tucson Basin is exponential, locating a well is not like
flipping a coin. If you were flipping a coin, 50 percent of wells would encounter
part of the aquifer with a transmissivity greater than some average, and 50 percent would
find an aquifer with a transmissivity less than the average.
Because the PDF for alluvial aquifers and karst aquifers is exponential, you have a
greater probability of finding parts of an aquifer with values smaller than the average
than of finding part of an aquifer with a transmissivity grater than the average.
In the Tucson Basin, for example, the average value of transmissivity is about 52,000
gpd/ft (645 m^{2}/d). Only 36.8 percent of the transmissivities within the
aquifer are greater than the average, whereas 63.2 percent are less than the
average.
These percentages hold true for any exponential distribution. For example, if you
substitute the average transmissivity of the Tucson Basin aquifer for T_{2} in the
cumulative probability formula and "0" is substituted for T_{1}, you can
see that for any area with an exponential distribution of transmissivity, your probability
of finding transmissivity values less than the average is always 63.2 percent and your
probability of finding transmissivity values greater than the average is always 36.8
percent.
The ratio of 63.2 and 36.8 percent is 1.72. This means that your probability of
our finding a part of the aquifer with a transmissivity of less than the average is nearly
twice that of finding a part of the aquifer with a transmissivity greater than the
average.
In the same way, you can demonstrate that the probability of finding transmissivity
values that are smaller than onehalf the average value is 39.4 percent and your
probability of finding transmissivity values that are greater than twice the average value
is 13.5 percent. This gives a ratio of 2.91. This means that the probability
of your finding transmissivity values having smaller than onehalf the average value is
nearly three times greater than your probability of finding transmissivity values greater
than double the average transmissivity.
This discussion is important because when you select a well site, you are not
interested in the average transmissivity value of the aquifer. You must be
interested in the extreme high value of transmissivity. But, because of the
exponential probability distribution of transmissivity within the aquifer, the most
probable transmissivity values are in the extreme low range.
You may want to believe that some parts of an aquifer are homogeneous and that some
parts have transmissivity distributions that are other than normal. However, there
is no known physical evidence that any part of any aquifer is homogeneous.
Different performance characteristics of adjacent wells are known to all hydrologists and
water engineers. This demonstrates nonhomogeneous conditions.
OTHER ALLUVIAL AQUIFERS
Rao (1991) studied the statistical properties of the transmissivity
distribution for the Shallow Alluvial aquifer of the Roswell Artesian Basin of New Mexico,
also in the arid American Southwest. Figure 3 shows the
location the Roswell Basin in the State of New Mexico. You can find a more
detailed description of Rao's work on the Shallow
Alluvial aquifer revised by Turner (1999) in our reference library.
Based on the data compiled by Rao (1991), and reviewed by Turner (1999), a
statistically significant lognormal PDF was determined for the Shallow Alluvial aquifer of
the Roswell Basin.
Turner (1999) has analyzed transmissivity data from the alluvial
aquifer of the Estancia Basin of central New Mexico. Figure 4
shows the location of the Estancia Basin. You can find a more detailed
description of this work on the Alluvial aquifer of
the Estancia Basin in our reference library.
Turner (1999) found a statistically significant lognormal PDF for this alluvial aquifer
also.
THE REASON FOR OPTIMUM WELLSITE LOCATION
Now that you have at your disposal equations giving the probability distribution of
transmissivities in alluvial basins, you should place this information to use and select
optimum well sites where the aquifer will have the highest transmissivity.
Unfortunately, the PDF is a frequency distribution and not an areal distribution.
You cannot locate an optimal well site simply by knowing the frequency distribution.
The PDF says nothing about where the high transmissivity zones are located within a
particular area. Therefore, unless you have some a priori information about
the spatial distribution of transmissivity within an area, any exploration drilling
program, other than a complete saturation drilling scheme, is doomed because the
probability of finding the highest transmissivity values in any area is small regardless
of the size or location of the area.
DOCUMENTED EXAMPLE
The following documented example shows the economic losses associated with uncertainty
in the areal distribution of transmissivity within the Tucson aquifer. The project
was conducted some years ago. Only the costs have increased. The costs are in
US Dollars.
In 1969, the Tucson Water Department conducted an exploratory drilling program along
the eastern boundaries of Townships 16 and 17 East of Range 1 South, south of Tucson,
Arizona. The drilling program at that time cost $30,000 and consisted of 5
mudrotary, drilled holes, 5.5 inches (14 cm) in diameter and 1,000 feet (305 m)
deep.
On the basis of grainsize analysis and electric logs of the test holes, only one site
was judged to be suitable for a production well. Subsequently, a production well was
drilled and constructed at this site. Thus the exploration costs for this well were
$30,000 not including the cost of electric logging and well completion.
To assist in evaluating the economic impact of uncertainty in the areal distribution of
transmissivity within an alluvial aquifer, AGW scientists performed a computer simulation
of a hypothetical aquifer having an approximate exponential transmissivity frequency
distribution. Our hypothetical model is not the same model we developed for the
Tucson Basin. The hypothetical model contains a variable grid spacing in which the
nodes in the central part of the model are spaced 100 feet (30 m) apart. Nodes
farther from the central part of the model had progressively wider spacing up to 12,800
feet (3,900 m) at the boundary of the model. The areal extent of the model was
51,900 by 51,000 feet (15,819 by 15,545 m). This is sufficiently large to eliminate
boundary effects during a simulated aquiferperformance test at locations within the
model.
The model simulates a paleoriver channel filled with wellsorted clastic material
surrounded by bands of lower permeability rock. The frequency distribution of
transmissivity is approximately exponential.
We placed hypothetical wells at different locations within the model and pumped them
for 1,000 days at each location at the rate of one million gallons per day (3,785 m^{3}/d).
We also pumped a well in the center of the paleoriver channel deposits at 2
million gallons per day (7,570 m^{3}/d).
The simulations showed that the well in the center of the paleoriver channel, pumping
at 2 million gallons per day (mgd) (7,570 m^{3}/d), has less drawdown than the
hypothetical well that misses the channel by only 300 feet (91 m) and that produces 1 mgd
(3,875 m^{3}/d).
If we did not know the areal distribution of transmissivity in the hypothetical model,
we would have only a 19 percent probability of locating a well site anywhere in the zone
of highest transmissivity. Uncertainty in the areal distribution of transmissivity
has a very significant economic cost that can be evaluated in the following way.
COST OF FAILURE
Suppose that two entrepreneurs each decides to exploit the water resources in an area
having aquifer properties similar to those of the hypothetical model. Assume that
each entrepreneur has exactly the same total water requirements and that each wants to
minimize his well investment cost. Assume further that one entrepreneur knows where
the zone of high transmissivity is located; but, the other does not. The probability
that the knowing entrepreneur will put his wells in the zone of high transmissivity is 100
percent. The probability that the unknowing entrepreneur will do the same is less
than 19 percent.
In terms of pumping costs over the long run, the unknowing entrepreneur will suffer
only slightly as compared to the knowing entrepreneur. For similar drawdowns, two
wells in poor locations are required to pump the same quantity of water as one well in the
optimum location.
In terms of capital investment, the unknowing entrepreneur must invest at least twice
as much scarce money in well drilling, pumps, equipment, pipeline and maintenance as the
knowing entrepreneur. This estimate is conservative because the proportion of low
transmissivity areas in the model is less than it would be in a truly exponential
distribution. That is, much of the area given a transmissivity value of 10,000
gpd/ft (124 m^{2}/d) would be assigned lower values if the distribution were more
nearly exponential.
Based on the experience of the hypothetical entrepreneurs, we can now
proceed to estimate the economic loss to a typical reallife entrepreneur resulting from
uncertainty in transmissivity distribution, namely the City of Tucson Water
Department. The Tucson Water Department released the following cost data in 1971:
ITEM

COST
USD/ACRE FOOT 
COST
USD/1000 CUBIC METERS 
Power 
$ 7.02 
$ 5.69 
Well Construction 
$ 1.80 
$ 1.46 
Equipment, insurance, land maintenance and administration 
$ 15.60 
$ 12.65 
TOTAL 
$ 24.72 
$ 19.80 
The Tucson Water Department purchased its own welldrilling rig because
it could reduce welldrilling costs by 50 percent. The future costs of producing
water, exclusive of power costs, will be about $16.50 per acrefoot ($13.38 per 1000 m^{3}).
Projected water demand for the following 10 years indicted an increase in demand of
about 5,000 acre feet per year (6,166 m^{3}/y). The total additional water
expected to be pumped over the 10year period is about 275,000 acrefeet (339 million
cubic meters). The total nonpower cost to the city as an unknowing entrepreneur of
producing this water at 1971 rates will be about $4,537,500 over the 10 years.
If the Tucson Water Department were a knowing entrepreneur and could put all of its
future wells in optimum locations, based on the conservative estimate of the previously
described hypothetical model, the Water Department could produce the same quantity of
water with half the number of wells. This would cut the nonpower costs of producing
the additional water almost in half at a savings of about $8.00 per acrefoot ($6.48 per
1,000 cubic meters). Over the 10 years ending in 1981, the savings would amount to
about $2 million.
This $2 million represents a real cost to the government and the ratepayer that can be
avoided. The $2 million is the cost of uncertainty in not knowing the precise
transmissivity distribution in the aquifer at any location.
KARST AQUIFERS
The discussion here has primarily focused on alluvial aquifers. Two
limestone karst aquifers have been studied in detail: the San Andres Limestone and the
Madera Limestone aquifers in New Mexico, U.S.A.
The statistical distribution of transmissivity of both of these aquifers was determined
using a rich data set developed from aquiferperformance tests performed by many
hydrogeologists over the past 50 years. The studies dealing with the San Andres Limestone and the Madera Limestone are detailed in our reference
library.
In both cases, lognormal probability density functions describe the statistical
distribution of transmissivity within the limestone aquifers. The discussion
relating to groundwater exploration in alluvial aquifers applies equally to limestone
aquifers.
THERMONIC INVESTIGATION
If you are the unknowing entrepreneur, the part of investment that you must make above
the investment of the knowing entrepreneur represents the cost of uncertainty caused by
the exponential transmissivity distribution of the aquifer. The cost of uncertainty
in the areal distribution of transmissivity within an aquifer is a cost that can easily be
avoided. By making a simple, inexpensive Thermonic geophysical survey and using
other modern geological and geophysical methods to determine the areal distribution of
transmissivity within an aquifer under investigation, the uncertainty in the distribution
of transmissivity can be reduced to zero.
The Thermonic survey in the aquifer is a negligible expense to eliminate the
uncertainty in transmissivity distribution. This eliminates large unnecessary
cost. Even if you are ultraconservative and estimate that a Thermonic survey could
reduce the number of required wells by only one, the savings of the cost of the well and
future operations and maintenance cost of the single well could pay for the cost of the
survey plus royalties. In fact, the cost of the Thermonic survey plus royalties or
annual fees are, in part, deferred costs paid for by ratepayers rather than up front costs
for new wells needing hard to find money.
The many successes of integrated groundwater exploration surveys including Thermonic
surveys are detailed in our case histories.
