CHAPTER THIRTY-SEVEN: ANALYZING ANCIENT LOGS

TABLE OF CONTENTS
37.00 Introduction to this Chapter
37.01 Ancient Logging Tools
37.02 Shale Volume
37.03 Pore Volume
37.04 Porosity From The Neutron Log
37.05 Porosity from ES and Micrologs
37.06 Maximum Porosity Method
37.07 Lithology
37.08 Formation Water Resistivity
37.09 Water Resistivity From Catalog or DST Recovery
37.10 Water Resistivity From Water Zone (R0 Method)
37.11 Water Resistivity From Spontaneous Potential
37.12 Water and Hydrocarbon Saturation
37.13 Water Saturation from Archie Method
37.14 Water Saturation from Simandoux Method
37.15 Water Saturation from Dual Water Method
37.16 Water Saturation From Buckles Number
37.17 Water Saturation and Porosity from Ratio Method
37.18 Irreducible Water Saturation
37.19 Permeability and Productivity
37.20 Permeability From the Wyllie-Rose Method
37.21 Permeability From Porosity
37.22 Summarizing Results
37.23 Case Histories
1. Calibrating Ancient to Modern Logs (Shaly Sand)
2. Lake Maracaibo (Shaly Sand)
37.24 Modern Resistivity Inversion Software
37.25 In Conclusion
37.26 Exercise for Chapter Thirty-Seven
37.27 Bibliography for Chapter Thirty-Seven

Publication History: The majority of this Chapter can be found in Chapters One through Ten of this Handbook, and is gathered here to make it easier to assimilate. One of the case histories was presented as a poster session as "Quantitative Analysis of Older Logs For Porosity and Permeability, Lake Maracaibo, Western Flank Reservoirs, Venezuela" by E. R. (Ross) Crain, P.Eng. Manuel Garrido, Craig Lamb, P.Geol., Philip Mosher, P.Eng. presented at GeoCanada 2000, Calgary, AB, May 2000. This electronic edition created 20 Feb 2004.

CHAPTER THIRTY-SEVEN: ANALYZING ANCIENT LOGS

37.00 Introduction to this Chapter
Ancient logs are a great mystery to most people because they are not seen often and are usually discarded as useless. This latter opinion is far from the truth. Modern computer software for petrophysical analysis can glean considerable amounts of reservoir property data from these old logs, especially when the work is calibrated with core data and modern logs in nearby offset wells.

The term "ancient logs" is usually applied to the electrical survey (ES), microlog (MLC), and gamma ray neutron (GRN). These logs became available in the early 1930's and were in common use well into the late 1950's. At this time, induction (IES) and sonic (SL) logs gradually supplanted the ES and GRN. Early forms of the laterolog (LL7 and LL3) and microlaterologs (MLLC) were also developed to replace the ES and MLC in salt mud environments. In the early 1960's, induction and sonic log presentations were fairly primitive by today's standards, and some people consider them to be ancient logs also. A brief description of all logging tools, including ancient logs, can be found in Chapter Three.

By the mid 1960's, compensated neutron and density logs (scaled in porosity units), as well as borehole compensated sonic logs, were beginning to augment porosity determination. By the mid 1970's, "ancient" logging tools disappeared from North America, but similar tools were still being run in China, Soviet Union, and other areas that could not afford newer technology.

To put this in perspective, here is a brief history timeline. A more detailed history of well logging can be found in Chapter One

Many newer tools have evolved from the older ones since 1985. Various authors have specified alternate dates for these events - I have usually chosen the earliest.

Since the well files of the world are full of these ancient logs, we must learn to glean what we can from them. This chapter is a self contained coverage of how to analyze ancient logs to obtain shale volume, porosity, water saturation, permeability, and average reservoir properties. All of the material presented here can be found elsewhere in this Handbook - we have merely snatched the pertinent parts and assembled them in the correct order. Minor changes to the Usage Rules have been made to reflect the ancient log environment. Methods that were once common in pre-computer days have been excluded because we now have better ways to do the same job.

37.01 Ancient Logging Tools
The names and curve complement on older logs take a little study. The table below lists the curves available and a useful name for each. The illustrations following the table show typical log presentations from this era. Presentations were far from standard and it may take a little research to figure out who is where.

FIGURE 37.01: Comparison of ES, IES, and MLC in sand - shale sequence (shaded areas are relatively clean sandstones) - note separation between curves on MLC. Colour the separation bright red and count your net sand. Compare to net sand from SP or resistivity.

FIGURE 37.02: Logarithmic scaler for reading porosity from an unscaled neutron log. Draw vertical line on log at low porosity point (say porosity = 0.05) and another line at high porosity point (usually a shale - say porosity is 0.30). Align scaler between the two lines, setting 0.05 on scaler at low porosity line, and 0.30 on scaler on high porosity line. Skew scaler to obtain good fit. Mark other porosity points on log. Enlarge or reduce scaler in copier to fit smaller or larger logs. High and low porosity points are a matter of good judgment tempered by core or log analysis results from modern wells.

FIGURE 37.03: Typical GRN log with gamma ray (GR) and unscaled neutron log (NEUT). Use the scaler to draw a porosity scale on this log.

FIGURE 37.04: ES and GRN in gas over oil over water - Note 18'8" blind spot on lateral curve, which explains why we don't use it for quantitative work in computer programs. The blind spot on this lateral curve is at the top of the zone. This is the original electrode arrangement. It was soon inverted to put the blind spot on the bottom of the zone (inverse lateral arrangement). Also note backup scale on 16" and 64" normal. Draw oil-water contact on this log.

FIGURE 37.05: Laterolog (LL3), old style sonic (SL), and microlaterolog (MLLC) - note hybrid resistivity scale on LL and thin porosity streaks on MLLC not seen by other logs. Colour shale beds grey, colour porous streaks red.

There are special rules for picking the formation resistivity from the long normal (RESD in this book, Rt in most of the literature). These are empirical rules that work reasonably well and circumvent the need for bed thickness and borehole corrections. The rules are shown in the top half of Figure 37.06.

The lateral curve can also be used for handpicked data by following the special rules shown in the bottom half of Figure 37.06. Because the lateral curve has a blind spot over the bottom of every resistive zone, it cannot be used in computer aided log analysis.

FIGURE 37.06: Rules for estimating RESD (Rt) from long normal (R64) and lateral (R18)

37.02 Shale Volume
Shale is an imprecise term used to describe a rock composed of clay, silt, and bound water. The clay type and silt composition can vary considerably from one place to another. These can be determined from appropriate cross plots of PE, thorium, and potassium logs. The bound water volume varies with clay type, depth of burial, and burial history. Some shales have not lost as much water as others at similar depths and are called overpressured shales. Most shales are radioactive due to potassium and thorium, and sometimes due to uranium.

In ancient wells, the logs available for shale calculation are more limited than in modern wells. The usual curves are gamma ray, spontaneous potential, and shallow resistivity. Many ancient wells have been re-logged through casing with gamma ray, neutron, and thermal neutron decay (TDT) logs. There may even be modern logs such as spectral gamma ray, sonic (compressional and shear), compensated neutron, even resistivity. There may be a large number of suitable curves to choose from. Density logging through casing is exceedingly rare, so the density neutron crossplot method for shale volume will be unavailable.

Shale volume estimation is the first calculation step in a log analysis. All other calculations depend on the shale volume being known from this step.

STEP 1: Calculate shale volume from all available methods:
1: Vshg = (GR - GR0) / (GR100 - GR0)
2: Vshth = (TH - TH0) / (TH100 - TH0)
3: Vshs = (SP - SP0) / (SP100 - SP0)
4: Vshr = (logRESS - logRMAX) / (logRSH - logRMAX)

NOTE: Trim values between 0.0 and 1.0. If too many values fall outside this range, check the clean and shale parameters. Do not calculate methods which fail to pass all usage rules listed below.

STEP 2: Adjust gamma ray method for young rocks, if needed:
5: Vshc = 1.7 - (3.38 - (Vshg + 0.7) ^ 2) ^ 0.5

STEP 3: Take minimum of available methods:
6: Vsh = Min (Vshg, Vshth, Vshs, Vshr, Vshc)

*** PLEASE NOTE ***
YOU must choose the appropriate methods for each zone, but the minimum rule works well in most cases, provided the usage rules have been honored first.

USAGE RULES:
Use uranium corrected gamma ray (CGR) in preference to uncorrected GR
Do not use GR in radioactive sandstones or carbonates. Use Thorium curve from NGT for radioactive sandstone, and uranium corrected GR (CGR) curve for radioactive carbonates.
Do not use SP in fresh water formations, salt mud systems, high resistivity zones, or in carbonates.
Do not use the nonlinear young rock model unless there is some evidence that it is needed.
Resistivity method only works in hydrocarbon zones
On older gamma ray logs with no numerical scale, or logs scaled in ug Ra eqiv/ton, choose an arbitrary scale to match offset logs (eg 0 to 150 API units).
For SP logs, it is convenient to use a scale of 0 to 100 across the track, or any arbitrary scale (minus 80 to plus 20 is widely used).
GR and SP may need bed thickness corrections - see service company chartbooks.

If log analysis porosity is too low, calculated shale volume may be too high (or vice versa).

The shale in the zone may not have the same properties as nearby shales seen on the log. Therefore, some adjustments to shale properties might be necessary.

Shale can be structural, dispersed, or laminated. Shale volume calculations give averages over several feet. Different distributions will affect resistivity, porosity, and permeability differently, so these calculations will be affected by assumptions about distribution. Special rules for laminated shaly sands are required and are covered in Chapter Seventeen.

37.03 Pore Volume
The second calculation step in a log analysis is to find shale corrected porosity. Pore volume is the space in a rock filled with oil, gas, or water. Total porosity includes the bound water in the shale and is called PHIt. Effective porosity does not include bound water, and is called PHIe. When there is no shale, PHIe equals PHIt.

Logs read total porosity. All our analysis methods correct for shale, so the answers from any method presented below will give effective porosity. Some analysis methods NEED total porosity as an intermediate step, so you may also need to calculate it.

Raw log porosity, as presented in the field by the service company, does NOT take into account shale or lithology effects, so raw log readings should NEVER be used as answers. Log analysis MUST ALWAYS be done to find the correct porosity. All our analysis methods also account for matrix rock (lithology), but YOU may be required to define the rock type for some methods.

*** PLEASE NOTE ***
YOU MUST choose a method that is appropriate for the available data and for the rock type being analyzed.

37.04 Porosity From The Neutron Log
Old style gamma ray neutron (GRN) logs are unscaled neutron logs recorded in counts per second or API units. They are common in ancient wells. The log carries a gamma ray curve (GR) in the left hand track and a neutron curve (NEUT) in the right hand track. No borehole or casing corrections have been applied to these logs. Neutron log deflections to the left (lower count rate) represent higher porosity.

A large number of charts for specific tools, spacings, borehole conditions and rock types were available from service companies, such as the one shown in Figure 37.07. These may no longer be easily found today, and the semi-logarithmic approach described below works well except in very low porosity .

FIGURE 37.07: GNT/GNAM neutron porosity interpretation chart. Choose appropriate pivot point (top left) and pick low porosity point from log.

If no appropriate chart exists, it is expedient to use the "High porosity- Low porosity"
method. Select a high porosity point on the log (usually a shale) and assign it a porosity, based on offset wells with scaled neutron logs. This is PHIHI. Pick the count rate on the neutron log at this point - this is CPSHI (even though it is a low value). Choose a low porosity point on the log. Assign this a porosity value, again based on offset scaled porosity logs. This is PHILO. Pick the corresponding count rate on the log. This CPSLO, even though it is a larger number than CPSHI. Count rate is inversely proportional to porosity. Plot these points on semi-log graph paper as shown below in Figure 37.08.

FIGURE 37.08: Example of Porosity from Neutron Counts per Second - no shale correction

This graph has the same effect as using the logarithmic scaler shown in Figure 37.02. To use this plot in a calculator or computer instead of on a graph:

STEP 1: Put a scale on the unscaled neutron log
1: SLOPE = (log (PHIHI / PHILO)) / (CPSHI - CPSLO)
2: INTCPT = PHIHI / (10 ^ (CPSHI * SLOPE))
3: PHIn = INTCPT * 10 ^ (SLOPE * NCPS)

STEP 2: Correct scaled neutron porosity for shale effect
4: PHInc = PHIn – Vsh* PHINSH

USAGE RULES:
Use only if sonic and density log are unavailable or unusable.
Do not use in gas zones - very pessimistic results, correction for gas difficult.
The neutron log corrected for shale is one of the least accurate methods in shaly sands and should only be used if no other porosity data is available. This is common for wells drilled prior to 1957 or for wells logged through casing or drill pipe.
Old style neutron logs recorded in counts per second need to be scaled logarithmically between a high and a low porosity point, calibrated by core or modern logs from offset wells.
To calibrate to core porosity, adjust PHIHI, PHILO, PHINSH or Vsh to obtain a better match by trial and error. Appropriate crossplots may assist.

Scaled neutron logs are also common, having been run through casing sometime after the original logs were run. They will have a GR curve and a neutron porosity curve (PHIN in this Handbook), the latter may have lithology, borehole, or casing corrections already applied. If it does not have these corrections, service company charts are used to apply the corrections. Read the log heading carefully to determine what has already been done.

CAUTION: In dolomite zones, many so-called compensated cased hole neutron logs did not present a rational value for porosity. This appears to have been fixed in recent years. Always compare results in carbonates with offset open hole logs or core data.

37.05 Porosity from ES and Micrologs
There are a number of techniques for handling ancient logs like the old electrical survey (ES) and microlog (MLC). The ES log has 3 resistivity curves, the long normal or 64 inch normal (LN), the short normal or 16 inch normal (SN), and the 18' 8" lateral curve (not to be confused with a laterolog). The SN curve can be used as a shallow resistivity log (RESS in this Handbook) and the LN can be used as a deep resistivity (RESD in this Handbook). The ES log also has a spontaneous potential (SP) curve used to find shale volume or water resistivity in sand-shale sequences.

There are hundreds of charts used to perform borehole and bed thickness corrections to these curves. For typical fresh mud in an 8 inch (200 mm) borehole in a bed thicker than 8 feet, these corrections are small enough to be ignored. Charts for these corrections can be obtained on request from service companies.

The simplest porosity from resistivity method is to use the shallow resistivity and assume that the flushed zone water saturation is near 1.0.
1: PHIxo = (A / ((RXO / RMF@FT) * (SXO ^ N))) ^ (l / M)

USAGE RULES:
RXO is taken equal to the 16 inch normal (R16 or SN) or the microlog R1 value.
Use only if no other porosity log is available.
Not recommended in heavy oil or tar sands because SXO is low due to lack of invasion by mud filtrate.

The microlog has two very shallow resistivity curves, the 1 inch (R1 - solid line) and 2 inch (R2 - dashed line). This data can also be used in the following:
1: IF R2 > R1 (dashed curve is right side of solid curve)
2: THEN PHIml = 0.614 * ((RMF@FT * KML) ^ 0.61) / (R2 ^ 0.75)
3: OTHERWISE PHIml = 0

USAGE RULES:
Use only if no other porosity log is available.
Not recommended in heavy oil or tar sands because of lack of invasion by mud filtrate.

37.06 Maximum Porosity Method
In ancient wells, there may be no porosity logs of any kind. In addition, resistivity methods may be ineffective due to lack of invasion (heavy oil) or thin bed effects. The maximum porosity method is quite useful in shaly sands, but may not be helpful in a carbonate sequence.

FIGURE 37.09: Choosing PHIMAX from a plot of Vsh vs PHIe from offset well

STEP 1: Calculate PHImx
1: PHImx = PHIMAX * (1 - Vsh)

If there is no other porosity calculation method that works, then PHIe = PHImx.

Bad hole, bad cement, high shale volume, and statistical variations can cause erratic results when a scaled or unscaled neutron log is used, Values of porosity from any method should be trimmed by the following:
1: IF PHIe < 0
2: THEN PHIe = 0
3: IF PHIe > PHIMAX * (1 - Vsh)
4: THEN PHIe = PHIMAX * (1 - Vsh)

USAGE RULES:
Use always to trim excessive porosity due to wet shales or bad hole conditions.
Use as a porosity method in shaly sands.

This material balance prevents the sum of shale volume, porosity, and rock matrix from exceeding 100%, and prevents porosity in the sand fraction of a shaly sand from reaching ridiculous values. It is useful for estimating porosity in shaly sands where only an SP or gamma ray log is available.

CAUTION: Bear in mind that this approach provides a porosity value based only upon the shale content and the analyst's assumed maximum possible porosity. With offset well data for control this is not a bad approach for wells with a very limited log suite. It is often used in computer analysis of ancient logs. Because of its gross assumptions, a warning note should be annotated on the results, if the method is used in this manner.

37.07 Lithology
The third step in a log analysis is usually a lithology calculation. The log suite in an ancient well does not provide data suitable for such a calculation, unless some modern tools have been run through casing (such as the dipole shear sonic with a compensated neutron, or an induced gamma ray spectral log (GST) or equivalent. In most cases, the lithology description comes from core and sample descriptions, core analysis grain density, or log analysis in offset wells.

37.08 Formation Water Resistivity
The fourth step in a log analysis is to determine the water resistivity since most methods for computing water saturation require knowledge of this value. Water resistivity data can be sparse or overwhelming, depending on where you are working at the moment.

*** PLEASE NOTE ***
YOU must choose a water resistivity method appropriate to the available data.

37.09 Water Resistivity From Catalog or DST Recovery
Catalogs and lab reports usually provide results at 77'F (25'C) and this value must be transformed to a different value based on the formation temperature.

STEP 1: Calculate formation temperature:
1. GRAD = (BHT - SUFT) / BHTDEP
2: FT = SUFT + GRAD * DEPTH

STEP 2: Calculate water resistivity at formation temperature:
3: RW@FT = RW@TRW * (TRW + KT1) / (FT + KT1)

Where:
KT1 = 6.8 for English units
KT1 = 21.5 for Metric units

If water salinity is reported instead of resistivity, as may happen in reporting direct from the well site, convert salinity to resistivity with:
4: RW@FT = (400000 / FT1 / WS) ^ 0.88

NOTE: FT1 is in Fahrenheit

In some cases, salinity is reported in parts per million Chloride instead of the more usual parts per million salt (NaCl). In this situation convert Chloride to NaCl equivalent with:
5: WS = Ccl * 1.645

To covert a downhole RW to a surface temperature, reverse the terms in equation 3:
6: RW@SUFT = RW@FT * (FT + KT1) / (SUFT + KT1)

Where:
KT1 = 6.8 for English units
KT1 = 21.5 for Metric units

USAGE RULES:
Use in preference to other methods if data is available.
Do not use if DST recovery is small; the sample may be contaminated with mud filtrate.
Use data from last sample recovered from DST.
Use minimum value if more than one sample or catalog value is available.
Check chemical analysis for mud contamination.
Many people like to use Figure 37.09, on the following page, to manipulate RW, temperature, and salinity.
Compare measured lab or catalog RW values to RW from water zone method. Use your best judgment to choose one over the other.
Plot a graph of all available temperatures versus depth (eg from log headings, DST’s, temperature logs) to obtain BhT and GRAD by regression if needed. The line may not be straight. Most log heading values are too low due cooling from mud circulation. DST values may also be low if gas expansion occurred during the test.

FIGURE 37.10: RW, temperature, salinity chart

37.10 Water Resistivity From Water Zone (R0 Method)
If an obvious water zone exists, calculate water resistivity from the porosity and resistivity, as shown below.

STEP 1: Calculate water resistivity from an obvious water zone:
1: PHIwtr = (PHIDwtr + PHINwtr) / 2
2: RW@FT = (PHIwtr ^ M) * R0 / A

If there are no obvious water zones, calculate Rwa in all relatively clean porous intervals:
3: Rwa = (PHIe ^ M) * RESD / A

R0 is the resistivity of a known or obvious WATER layer and PHIwtr is the total porosity of the zone where R0 was chosen. RESD is the resistivity of any zone and PHIe is the porosity of that same zone.

If no obvious or known water zones exist, many zones may be calculated with the above equations and results scanned for low values which MIGHT be water zones. This is called the Rwa method instead of the R0 method, but the math is the same. Scan the list of Rwa values to find the minimum value of Rwa in clean, moderately high porosity zones close to the zone of interest. This Rwa value becomes RW@FT:

USAGE RULES:
Use in preference to SP method and to check catalog or DST values.
Use to find RW@FT in a clean water bearing zone only. Use the result (RW@FT) to calculate water saturation in nearby hydrocarbon zones.
Use to help calibrate A and M if RW@FT is known from DST or produced water.
Do not attempt to find RW@FT in low porosity (less than 5%) or where shale content is high (greater than 20%).
Do not attempt to find RW@FT in a hydrocarbon bearing zone.
If zones are not "obviously" wet, calculate Rwa in many zones and scan for the minimum value. This MAY be RW@FT, but remember, there may be NO water zones in the area of your calculation, or the minimum value may be too far away to be useful.
If there are no obvious water zones nearby, scan the well history cards or database for wells that tested water from the zone in nearby wells. Analyze logs from these wells to find RW@FT.
To find possible hydrocarbon zones, scan for zones with Rwa greater than three times the minimum expected value.
A shale corrected equation can be constructed by rearranging the Simandoux saturation equation.

37.11 Water Resistivity From Spontaneous Potential
If a good SP log is available, it may be used to calculate RW@FT, as shown below.

STEP 1: Calculate constants
1: GRAD1 = (BHT - SUFT) / BHTDEP
2: FT1 = SUFT + GRAD1 * DEPTH 3: KSP = 60 + 0.122 * FT1

NOTE: FT1 is in Fahrenheit

STEP 2: Calculate resistivity values
4: RSP = 10 ^ (-SSP / KSP)
5: IF RMF@FT > 0.1
6: THEN RMFE = 0.85 * RMF@FT
7: IF RMF@FT <= 0.1
8: THEN RMFE = (1.46 * RMF@FT - 5) / (337 * RMF@FT + 77)
9: RWE = RMFE / RSP
10: IF RWE > 0.12
11: THEN RW@FT = -(0.58 - 10 ^ (0.69 * RWE - 0.24))
12: IF RWE <= 0.12
13: THEN RW@FT = (77 * RWE + 5) / (146 - 337 * RWE)

USAGE RULES:
Do not use SP method in low porosity (less than 5%) or where shale content is high (greater than 20%).
SP method may not work well in a hydrocarbon bearing zone.
Do not use SP method in a carbonate or evaporite sequence.

The math for the SP model is pretty imposing but the charts are worse.

37.12 Water and Hydrocarbon Saturation
The fifth step in a log analysis is to find water saturation. Water saturation is the ratio of water volume to pore volume. Water bound to the shale is not included, so shale corrections must be performed if shale is present. We calculate water saturation from the effective porosity and the resistivity log. Hydrocarbon saturation is 1 (one) minus the water saturation.

All methods rely on work originally done by Gus Archie in 1940-41. He found from laboratory studies that, in a shale free, water filled rock, the Formation Factor (F) was a constant defined by:
1: F = R0 / Rw

He also found that F varied with porosity:
2: F = A / (PHIt ^ M)

For a tank of water, R0 = Rw. Therefore F = 1. Since PHIt = 1, then A must also be 1.0 and M can have any value. If porosity is zero, F is infinite and both A and M can have any value. However, for real rocks, both A and M vary with grain size, sorting, and rock texture. The normal range for A is 0.5 to 1.5 and for M is 1.7 to about 3.2. Archie used A = 1 and M = 2. In fine vuggy rock, M can be as high as 7.0 with a correspondingly low value for A. In fractures, M can be as low as 1.1. Note that R0 is also spelled Ro in the literature.

For shale-free rocks with both hydrocarbon and water in the pores, he also defined the term Formation Resistivity Index (I) as:
3: I = Rt / R0
4: Sw = (1 / I) ^ (1 / N)

Archie used an N of 2 and the usual range is from 1.3 to 2.6, depending on rock texture. It is often taken to equal M, but this is not supported by core data in all cases. Rearrangement of these four equations give the more usual Archie water saturation shown in the next section.

Shale corrections are applied by adding a shale conductivity term with an associated shale porosity and shale formation factor relationship. Numerous authors have explored this approach, leading to numerous potential solutions for water saturation. Two of the most common are given later in this Chapter.

*** PLEASE NOTE ***
Again, YOU must choose an appropriate method.

37.13 Water Saturation from Archie Method
The most common saturation method was developed by Gus Archie in 1941. It is widely used in all parts of the world and is suitable for carbonates, clean sands, and shaly sands where RSH is above 8 ohm-m. Where shale resistivity is low, the Archie method will be pessimistic in shaly sands.

STEP 1: Calculate water saturation:
1: Rwa = (PHIe ^ M) * RESD / A
2: SWa = (RW@FT / Rwa) ^ (1 / N)

Another way of stating this equation is:
3: SWa = (R0 / RFSD) ^ (1 / N)

The water saturation from the Archie method (SWa) is called the effective water saturation, SWe. To calculate Sxo, replace RESD with RESS and RW@FT with RMF@FT.

USAGE RULES:
RESD in older wells can come from the 64 jnch normal (R64 or LN) or from laterolog (RLL).
R64 and RLL may need borehole or bed thickness corrections - see service company chartbooks.
Do not use 18 foot lateral curve (RLAT or LT).
The Archie method should only be used when Vsh < 0.20 and RSH > 8.0. If Vsh is high or RSH is low, then SWa is too high and a shale corrected method should be used.
A quick look version of the Archie formula sets A = 1.0, M = 2.0 and N = 2.0.
3: SWa = (RW@FT / (PHIt ^ 2) / RESD) ^ 0.5
This formula can be calculated by mental arithmetic or on a scratch pad when needed, and is accurate enough for quick look work.
Calibrate water saturation to core by preparing a porosity vs SW graph from capillary pressure data. Adjust RW, A, M, N, PHIe until a satisfactory match is achieved.

37.14 Water Saturation from Simandoux Method
One of the first successful shale corrected methods is this one, proposed by P. Simandoux in 1963. It reduces to the Archie formula when Vsh = 0.

STEP 1: Calculate intermediate terms:
1: C = (1 - Vsh) * A * RW@FT / (PHIe ^ M)
2: D = C * Vsh / (2 * RSH)
3: E = C / RESD

STEP 2: Calculate quadratic solution for water saturation:
4: SWs = ((D ^ 2 + E) ^ 0.5 - D) ^ (2 / N)

The water saturation from the Simandoux method (SWs) is called the effective water saturation, SWe. To calculate Sxo, replace RESD with RESS and RW@FT with RMF@FT.

USAGE RULES:
Use Simandoux method when Vsh > 0.20 and RSH < 8.0. The dual water method may also be used and the choice is usually a personal preference.
The (2 / N) exponent in Equation 4 is an approximation and works when N is near 2. More sophisticated iterative techniques are available when N is far from 2.
Calibrate water saturation to core by preparing a porosity vs SW# graph from capillary pressure data. Adjust RW, A, M, N, RSH, Vsh, PHIe until a satisfactory match is achieved.

37.15 Water Saturation from Dual Water Method
Another common method, based on the cation exchange capacity equation proposed by Waxman and Smits, is the Schlumberger dual water model.

STEP 1: Calculate the apparent water resistivity in shale:
1: RWSH = (BVWSH ^ M) * RSH / A

RWSH is a constant for each zone. Note that this is the Archie equation applied to the shale zone.

STEP 2: Calculate the resistivity of the zone as if it were 100% wet:
2: C = 1 + (BVWSH * Vsh / PHIt * (RW@FT - RWSH) / RWSH)
3: Ro = A * RW@FT / (PHIt ^ M) * C

C can be larger than 1.0 if RW@FT is greater than RWSH.

STEP 3: Calculate total and effective water saturation:
4: SWt = (Ro / RESD) ^ (1 / N)
5: SWd = (PHIt * SWt - Vsh * BVWSH) / PHIe

This equation reverts to Archie when Vsh = 0. Schlumberger uses a term called SWb, which is the bound water expressed as a saturation, and is not the same as the SWd calculated above.

The water saturation from the Dual Water method (SWd) is called the effective water saturation, SWe. To calculate Sxo, replace RESD with RESS and RW@FT with RMF@FT.

USAGE RULES:
Use Dual Water method when Vsh > 0.20 and RSH < 8.0. The Simandoux method may also be used and the choice is usually a personal preference. Dual Water may be better than Simandoux when shale resistivity is very low, eg. less than 2 ohm-m.
The method is called the dual water method since there are two water resistivities being considered - the water in the pore space and the water bound to the shale. This is technically true of all shale corrected water saturation equations, but here the two terms are very explicitly exposed.
The term RWSH is the apparent water resistivity (Rwa) calculated from the resistivity and the apparent porosity of the shale. It is also inverted and referred to as the conductivity of bound water (Cwb) in some technical papers.
Exploration and development geologists often need to know how high the resistivity of a zone needs to be in order for it to be considered a potential hydrocarbon zone. The best way is to calculate the water zone resistivity (Ro) as shown above. Potential pay is indicated when RESD > 3 * Ro, water when RESD <= 2 * Ro.
Calibrate water saturation to core by preparing a porosity vs SW# graph from capillary pressure data. Adjust RW, A, M, N, RSH, Vsh, PHIe until a satisfactory match is achieved.

37.16 Water Saturation From Buckles Number
Most methods for calculating water saturation require the use of the resistivity log and a value for the formation water resistivity. In ancient wells, neither value may be available. The rule is based on the observation that the product of porosity and water saturation is constant for a particular zone, provided rock texture remains unchanged. The constant is called Buckles Number (KBUCKL) or the irreducible bulk volume water (BVWir).

FIGURE 37.11: Choose KBUCKL from a plot of log analysis porosity vs water saturation in an offset well, or from the same plot using cap pressure data.

Draw a hyperbolic line through the data and find its constant parameter (KBUCKL = PHIe * SWe .

STEP 1: Find Buckles number from special core analysis or from log analysis in a known clean pay zone that produces with zero initial water cut:
1: KBUCKL = PHIe * SWe (in a CLEAN zone which produces no initial water, or from capillary pressure data)

KBUCKL is a constant derived as above and used in the balance of the zone.

STEP 2: Solve for water saturation in each layer, but only if it is known to be a hydrocarbon zone:
2: IF Zone is hydrocarbon bearing
3: THEN SWp = KBUCKL / PHIe / (1 - Vsh)
4: OTHERWISE SWp = 1.00
5: IF SWp > 1.0
6: THEN SWp = 1.0

The water saturation from Buckles Number (SWp) is called the effective water saturation, SWe.

USAGE RULES:
Use as a saturation method only in pay zones at irreducible water saturation.
If zone is water bearing, set SWp to 1.00.
Use where RW@FT is not known.
Do not use in heterogeneous reservoirs unless KBUCKL is also varied to match rock description.
Buckles Number can be found by observing the porosity times water saturation product in pay zones where RW@FT is known, or where a water zone can be used to calibrate RW@FT.
KBUCKL can also be found from capillary pressure data by averaging the product of minimum wetting phase saturation and core plug porosity for a number of samples.
The (1 - Vsh) term can be replaced by (1 - Vsh^2) if needed.
Calibrate water saturation to core by preparing a porosity vs SW graph from capillary pressure data. Adjust KBUCKL, Vsh, PHIe until a satisfactory match is achieved.

37.17 Water Saturation and Porosity from Ratio Method
When no porosity data is available, saturation can be obtained by comparing the shallow and deep resistivity logs. This formula is not shale corrected but the chart in Figure 37.12 is.

STEP1: Calculate water saturation

1: SWrt = SXO * ((RXO / RESD) / (RMF@FT / RW@FT)) ^ (1 / N)

SWrt becomes SWe if there is no other method available.

STEP 2: Calculate porosity
2: PHIrt = (A / ((RESD / RW@FT) * (SWrt ^ N))) ^ (l / M)
3: PHIxo = (A / ((RESS / RMF@FT) * (SXO ^ N))) ^ (l / M)

USAGE RULES:
Use 64 inch normal or laterolog as RESD, use 16 inch normal or microlog as RESS.
Do not use lateral as RESD.
Use only if no other porosity log is available.
Do not use in heavy oil or tar sands because SXO is difficult to estimate.
See Figure 37.12 for a graphical solution to this formula, with additional shale correction if needed.

FIGURE 37.12: Graphical solution for Ratio method (with shale correction from SP)

37.18 Irreducible Water Saturation
Hydrocarbon zones with water saturation (Sw) above irreducible saturation (SWir) will produce some water along with hydrocarbons. This can occur in transition zones between the oil and water leg, or after water influx into a reservoir due to production of oil or gas or because of intentional water flooding.

The actual computed water saturation in an oil or gas zone above the transition zone IS the irreducible water saturation (or close enough for our work anyway). In a water zone, the actual water saturation is, of course 1.0 or 100% and this is not the irreducible saturation. Some permeability equations require irreducible water saturation as input to the math. So in water zones, we must estimate irreducible water saturation by working backwards through Buckles equation.

STEP 1: Find Buckles number from special core analysis or from log analysis in a known clean pay zone that produced initially with zero water cut.
1: KBUCKL = PHIe * SWe (in a CLEAN zone that produced initially with no water, or from core data)

STEP 2: Solve for irreducible water saturation in each zone.
2: IF zone is obviously hydrocarbon bearing
3: THEN SWir = SWe
4: OTHERWISE SWir = KBUCKL / PHIe / (1 - Vsh)
5: IF SWir > SWe
6: THEN SWir = SWe

USAGE RULES:
Use always in preparation for permeability calculations.
Buckles Number can be found by observing the porosity times water saturation product in pay zones where RW@FT is known, or where a water zone can be used to calibrate RW@FT. Data can also be found from capillary pressure data.
If SWe is greater than SWir, then the zone will produce with some water cut (if it produces anything at all).
If SWe is less than SWir, then the Buckles number for the layer is wrong.
The (1 - Vsh) term can be replaced by (1 - Vsh^2) if needed.
Calibrate water saturation to core by preparing a porosity vs SW graph from capillary pressure data. Adjust KBUCKL, Vsh, PHIe until a satisfactory match is achieved.

37.19 Permeability and Productivity
The sixth step in a log analysis is to estimate permeability and productivity. These values determine whether a zone is commercially attractive. There are a number of methods for calculating matrix permeability.

Although it is not a quantitative measure of permeability, the separation between the two microlog curves is an excellent indicator. This log is a common item in the well files of ancient wells.

*** PLEASE NOTE ***
You must choose a method appropriate to the available data:

37.20 Permeability From the Wyllie-Rose Method
The general form of this equation has been used by many authors, with various correlations between log and core data. Individual analysts routinely calibrate their core and log data to this equation.

STEP 1: Calculate permeability
1: PERMw = CPERM * (PHIe ^ DPERM) / (SWir ^ EPERM)

If we recall that SWir = KBUCKL / PHIe, we see that this equation is strictly a function of porosity if KBUCKL is a constant. However, KBUCKL varies with shale volume and grain size, so Perm will vary also.

The permeability from the Wyllie method (PERMw) is called the effective permeability, Perm. The result is in millidarcies. It can be calibrated to air, absolute, maximum, or Klinkenberg corrected permeability from core analysis. You should state which type of core analysis you calibrated to.

USAGE RULES:
Use anytime, usually when no core data is available.
Not reliable in fractures or heterogeneous reservoirs.
Calibrate to core by adjusting CPERM, DPERM, and EPERM. Sw, PHIe and Vsh calibration should have been accomplished earlier.