
Publication History:
This article was written
especially for "Crain's Petrophysical Handbook"
by E. R. Crain,
P.Eng in 2018.
This webpage version is the copyrighted intellectual
property of the author.
Do not copy or distribute in any form without explicit
permission. 
WATER WELL BASICS
Water is becoming the "New Oil". In many parts of the world,
safe drinkable fresh water is becoming scarce. Pollution,
population pressure, sea level rise, droughts, and floods
reduce available drinking water supplies, so Governments are
beginning to look at alternate sources, with industry
trailing far behind.
We use the term aquifer to describe the rock that contains
the water, as opposed to the word reservoir as used when the
rock contains oil or gas.
Water sources are divided between surface sources (streams,
springs, rivers, lakes) and underground, produced from
shallow or deep wells. From a petrophysical point of view,
we are interested only in the deep well category.
Water quality is divided, somewhat arbitrarily, into fresh,
brackish, and saline. Fresh water is defined as having less
than 1000 mg/liter total dissolved solids (TDS). Good
drinking water has less than 300 mg/liter TDS but many
shallow water wells run up past 500 mg/liter.
Water with more than 10,000 mg/liter TDS are termed saline
or salt water. Typical sea water has a salinity around
32,000 mg/liter, somewhat less in the Arctic regions.
Brackish water has a salinity between 1000 and 10,000
mg/liter TDS. Brackish waters are common, but need some treatment
before use and deep wells are needed to produce them.
Brackish water is often encountered during the drilling of
oil and gas wells. Rock and water samples, and petrophysical
well logs, are available from 10's of millions of oilfield
wells. Considerable technical data can be derived about such
aquifers and the water contained in them.
To put these salinities into terms of water resistivity (RW)
at 25C (77F), the fresh water cutoff of 1000 mg/l is about
5.5 ohmm, the brackish water cutoff of 10,000 mg/l is 0.55
ohmm, and typical seawater of 32,000 mg/l is 0.20
ohmm. Saturated salt water at 300,000 mg/l would have a RW
around 0.030 ohmm at 25C.
These values are near room temperature. Water resistivity
decreases with increased temperature, which in turn
increases with increased depth in the Earth. Arp's Equation
is used to convert water resistivity from one temperature to
another:
1:
FT = SUFT + (BHT  SUFT) / BHTDEP * DEPTH
2: KT1 = 6.8 for Fahrenheut units
KT1 = 21.5 for Celsius units
3: RW@FT = RW@TRW * (TRW + KT1) / (FT +
KT1)
TRW is the temperature at which the RW was measured. This
could be a lab (surface) temperature or a formation
temperature. FT is formation temperature OR any arbitrary
temperature for which an RW is needed.
Underground sources of drinking water (USDW) is the current
term used to cover fresh and brackish water resources that
could be exploited by drilled wells, in contrast to water
from surface sources such as lakes and rivers. The base of fresh water (BFW) is the true vertical
depth of the deepest aquifer that can produce water of a
specified TDS. BFW can be contoured to provide insight into
the disposition of USDW. Porositythickness and
permeabilitythickness maps can be generated from
petrophysical analysis results. These give volumetric and
productivity information that will aid water source
development.
Governments are taking more interest in USDWs. The US EPA
defines any aquifer with less than 10,000 mg/liter TDS as
potentially useful water for humans. Many aquifers in the
USA are protected by the EPA, which means that these
aquifers cannot be used for disposal of oilfield or
industrial
waste
water. Other restrictions on use may also be in
force in specific cases. Some aquifers are exempt from
protection rules due to existing licenses that permit
injection.
Water salinity usually increases with depth so shallower
aquifers are more likely to fall into the fresh and brackish
category. There are many exceptions. Meteoric water can
enter porous rock at its outcrop edge, bringing fresh or
brackish water to considerable depths. Examples are the
Black hills of South Dakota feeding meteoric water into the
Cretaceous reservoirs in northern tier States and southern
Alberta and parts of Saskatchewan. Another is the western
slopes of the Sierras feeding the adjacent deeper rocks in
California. Examples of interspersed brackish and saline
waters are not hard to find during oilfield evaluations.
Shallow water wells are logged by observation of the drill
cuttings and potential porous and permeable intervals are
noted. Copies of the report are given to the well owner and
to appropriate government agencies who assess and map aquifer quality
and thickness. A pumpdown test is used to determine flow
capacity in gallons or liters per minute.
Very few
petrophysical logs are run in shallow wells, although I ran
a single point resistivity log using a crowbar taped to the
end of the logging cable to find the porous interval in a
newly drilled town water well (way back in 1964). Potable
fresh water is high resistivity compared to clay and shale.
LOG ANALYSIS FOR WATER WELLS
In wells that have oilfield logs, there are some techniques that
are useful to evaluate water quality
and well performance.
The usual results from analysis of well logs are shale
volume (Vsh), total and effective porosity (PHIt, PHIe). Lithology (mineralogy), water
saturation (Sw), and permeability (Perm). The first three results tell us
how much water is present and what kind of rack it is in.
The last item can be used to estimate initial flow rate of
the water.
In water zones, we assume water saturation (Sw) is very near
100% and use that fact to calculate the apparent water
resistivity (Rwa). From that value, we can calculate the
equivalent sodium chloride salinity (WSa) of the water,
which in turn is a close approximation of the total dissolved solids (TDS).
Below are the details of the petrophysical analysis steps
required for a complete evaluation of aquifer and water
quality.
See
List of Abbreviations
for Nomenclature.
STEP 1: Calculate shale volume.
The most effective method is based on the gamma ray log:
1: Vshg = (GR 
GR0) / (GR100  GR0)
Adjust gamma ray method for young rocks using the
Clavier equation, if needed:
2: Vshc = 1.7 
(3.38  (Vshg + 0.7) ^ 2) ^ 0.5
To account for radioactive sands and volcanics, calculate Vsh from density
neutron crossplot
3:
Vshxnd = (PHIN  PHID) / (PHINSH  PHIDSH)
The minimum of these three values is shale volume Vsh.
The spontaneous potential (SP) method is not very useful in fresh and brackish
water zones.
STEP 2: Calculate total and effective porosity.
The best method available for modern, simple, log
analysis involves the shale corrected density neutron complex lithology crossplot
model.
Shale correct the density and neutron log data
and calculate total and effective porosity:
4: PHIdc = PHID
– (Vsh * PHIDSH)
5: PHInc = PHIN
– (Vsh * PHINSH)
6: PHIt
= (PHIN + PHID) / 2
7: PHIe
= (PHInc + PHIdc) / 2
This model is quite insensitive to variations in
mineralogy. A gas correction is needed for greater accuracy in gas zones, but
this will not affect the results in water zones. A graph representing this model
is shown below.
The shaly sand version of the
density neutron crossplot is not recommended because it underestimates porosity
in sands with heavy minerals.
If density or neutron are missing or density is
affected by rough hole conditions, choose a method from the
Handbook Index appropriate for the log curves
available.
Density Neutron Complex Lithology Crossplot
 Oil and Water cases,
or Gas zones with crossover.
STEP 3: Calculate mineralogy.
If the well penetrates a young sand shale sequence, this
step is not usually required as there are few heavy minerals
in the sands. In Lower Cretaceous and older rocks, choose a
method from the Handbook Index
appropriate for the log curves available.
STEP 4: Calculate permeability and flow
capacity.
If
the analysis is for water quality (salinity, TDS) only, this
step is not required. If the aquifer is being assessed for
injection of waste water or production of industrial or
drinking water, this step is essential.
Estimate
irreducible water saturation from porositysaturation
product using assumed Buckle's Number (KBICKL). Graph at
right shows the intimate relationship between porosity (vertical
axis), irreducible water saturation (horizontal axis),
permeability (diagonal lines), and Buckle's Number
(hyperbolic lines running from top left to lower right). A
constant Buckle's Number indicates a uniform rock type. The equation is:
8: SWir = KBUCKL / PHIe / (1  Vsh)
Calculate permeability from WyllieRose equation:
9: Perm = CPERM * (PHIe^6) / (SWir^2)
For
coarse to medium grained sands, KBUCKL = 0.0300 to 0.0500,
higher for fine grain, lower for carbonates. Default =
0.0400.
Default for CPRM = 100,000. Adjust to calibrate to core
permeability.
Flow capacity is:
10: Kh = Perm * (BASE  TOP)
Where TOP and BASE are measured depths of top and base of
this aquifer. Note that in a horizontal well, Kh is Perm
times the length of the wellbore exposed to the aquifer.
See
Initial Productivity Estimates to convert Kh to
a flow rate.
META/PERM Compare
Permeability Calculated from Various Methods
STEP 5: Calculate apparent water
resistivity at formation temperature.
In relatively clean rocks, the Archie model using
appropriate electrical properties is sufficient:
11: Rwa@FT = (PHIt ^ M) * RESD / A
It is useful to also calculate Rwa at 75F or 25C using Arp's equation, to allow us to
compare log derived values to lab water analysis reports or
water catalogs:
12: Rwa@75F = Rwa@fT * (FT+
6.8) / (75 +
6.8) with temperatures in
Fahrenheit
OR 13: Rwa@25C = Rwa@fT * (FT+ 21.5) / 275 +
21.5) with temperatures in Celsius
RECOMMENDED
PARAMETERS:
for
carbonates A = 1.00
M = 2.00 (Archie Equation as first published)
for sandstone A = 0.62
M = 2.15 (Humble Equation)
A = 0.81 M = 2.00 (Tixier Equation 
simplified version of Humble Equation)
Asquith (1980 page 67) quoted other authors, giving values for A
and M, with N = 2.0, showing the wide range of possible values:
Average sands A = 1.45 M = 1.54
Shaly sands
A = 1.65 M = 1.33
Calcareous sands
A = 1.45 M = 1.70
Carbonates
A = 0.85 M = 2.14
Pliocene sands S.Cal. A = 2.45 M = 1.08
Miocene LA/TX
A = 1.97 M = 1.29
Clean granular
A = 1.00 M = 2.05  PHIe
Equation 11 is not shale corrected.
If prospective water sands are quite shaly (Vsh > 0.25) or RSH
is very low (< 2.5 ohmm) the Simandoux equation can be
inverted to solve for RWa:
14: 2 / RESD = (PHIe ^ M) / (A * Rwa@FT * (1  Vsh) + Vsh
/ (2 * RSH)
15: Rwa@FT = xxxx
If you get this solved before I do, let me know the result.
META/RW Calculate RW
at formation temperature  5 methods.
Metric and English Units
STEP 6: Convert Rwa@FT to NaCl
equivalent (ppm) and TDS (ng/l)
Calculate formation temperature:
16: FT = SUFT + (BHT  SUFT) / BHTDEP * DEPTH
IF FT is Celsius, convert to Fahrenheit
17: THEN FT1 = 9 / 5 * FT + 32
18: OTHERWISE FT1 = FT
Using Crain's Equation inverted for water salinity WSa in
ppm NaCl equivalent:
19: WSa = 400000 / FT1 / ((RWa@FT) ^ 1.14)
An alternate method Baker Atlas (2002)
19A: WSa = 10 ^ ((3.562  (Log (RW@75
 0.0123))) / 0.955)
Convert WSa (ppm) to TDSa (mg/l) using the density of the water plus its
so;ute:
20: DENSw = 1.00 + (WSa * 2.16 / 1000000)
21: TDSa = WSa * DENSw
Note that 2.16 is the real density of halite – log bulk
density is 2.03 g/cc.
CAUTION:
If hydrocarbons are present, Rwa will be higher and
TDSa will be lower than the truth. Always investigate the
well history file, especially the sample log, for
indications of oil or gas in the interval to be studied.
The Bateman and Konen equation, and
the Kennedy equation, need Excel Solver to
solve for WSa. These equations use RW@75F, so Rwa#FT
would have to be converted to 75F as in equation 11.
Crain's equation matches other methods closely,
as shown in the graphs below.
Graph 1:
Rw Models  Red line = Crain, Black line
= Bateman and Konen, Blue line = Kennedy
Graph 2:
Cw Models  Red
line = Crain, Black line = Bateman and Konen, Blue line =
Kennedy.
The differences above 150,000 ppm NaCl have little impact on water
saturation.
META/SAL Compare RW
from NaCl Salinity (3 Methods)
LOG ANALYSIS EXAMPLE IN AQUIFER EVALUATION
This example shows
how conventional petrophysical analysis can assist in
evaluation of potential water wells. The salinity curve,
derived from the porosity and resistivity log data, can be
used to determine the base depth to any given water quality.
Track 1 contains gamma ray and caliper, Track 2 is deep
resistivity, Track 3 is density and neutron porosity. This
raw data is used to calculate shale corrected porosity
(Track 4), apparent water resistivity (Rwa in Track 5), and
salinity in Track 6. The right hand track shows the
lithology with shale volume shaded black. The salinity curve
is shaded between the curve and 10,000 ppm total dissolved
solids (TDS) to help identify useable water sources. Note
that TDS values in shaly zones seldom indicate useful water
zones.
