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 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 ohm-m, the brackish water cutoff of 10,000 mg/l is 0.55 ohm-m, and typical seawater of 32,000  mg/l is 0.20 ohm-m. Saturated salt water at 300,000 mg/l would have a RW around 0.030 ohm-m 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. Porosity-thickness and permeability-thickness 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 pump-down 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.

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.

 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 porosity-saturation 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 Wyllie-Rose 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

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 ohm-m) 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)

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.
Image courtesy Aptian Technical.

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