CHAPTER SIX: CALCULATING SHALE VOLUME

Table Of Contents
6.00 Introduction to This Chapter
6.01 Visualizing Shale Volume With Base Lines
6.02 Scaling the SP and GR Logs in Shale Volume Units
6.03 Scaling the Density Neutron Separation in Shale Volume Units
6.04 Borehole Corrections for Gamma Ray
6.05 Shale Volume from the Gamma Ray
6.06 Shale Volume From The Spectral Gamma Ray Log
6.07 Shale Volume from the Spontaneous Potential
6.08 Shale Volume from the Density Neutron Crossplot
6.09 Shale Volume Example
6.10 Shale Content from Density Neutron with Matrix Offset
6.11 Shale Content from Density Sonic Crossplot
6.12 Selecting the Minimum Shale Volume
6.13 Material Balance for Shale Content
6.14 Non Linear GR and SP Relationships
6.15 Selection of Shale Volume Method
6.16 Shale Volume Routines
6.17 Other Shale Volume Methods
6.18 Calibrating Shale Volume to Core and Sample Data
6.19 Total Organic Content TOC
6.20 In Conclusion
6.21 Exercises For Chapter Six
6.22 Bibliography For Chapter Six

TABLE 6.01 Summary of Shale Volume Methods

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Publication History: This Chapter formed Chapter Six of The Log Analysis Handbook, Pennwell 1986. Sections 6.17 and 6.18 were added and other updates made for this electronic edition Feb 2001. Section 6.19 added Jan 2008.

CHAPTER SIX: CALCULATING SHALE VOLUME

6.00 Introduction to This Chapter
Shale content, or volume of shale, is an important quantitative result of log analysis. It is relatively easy to find and does not require great accuracy. Several methods can be used, depending on the logs available. It is needed for correcting porosity and water saturation results for the effects of shale, and is an indicator of reservoir quality. Lower shale content usually indicates a better reservoir.

Visual log analysis methods for shale volume are covered in Sections 6.01 through 6.03. Remaining sections give mathematical solutions.

Some mathematical models require the volume of clay instead of the volume of shale, however the models used in this book do not. In our models, shale content is the sum of the dry clay, silt, and clay bound water in the formation.

Shale can be distributed in several different ways, as shown in Figure 6.00.

FIGURE 6.00: How Shale is Distributed in a Shaly Sand

Shale corrections are applied to porosity logs to determine effective porosity, as shown in the illustration above. Since shale contains some water, this water must be subtracted from the total porosity as measured by conventional logging tools. The mathematical method for finding shale volume is the same for all the shale distribution types, but the method for applying the shale correction to the porosity varies. The different approaches are described in Chapter Seven (Porosity) and Chapter Eight (Saturation).

The two most common shale indicating logs are the gamma ray (GR) and spontaneous potential (SP) logs. The units of measurement for GR are API units or counts per second, and for SP are millivolts.

The resistivity, neutron, and sonic are sometimes used individually, and the separation between density porosity and neutron porosity is also widely used. More rarely, the electromagnetic propagation attenuation curve is available and is an excellent shale indicator, especially in thin bedded (laminated) sand-shale sequences.

There are several flavours of gamma ray logs. The conventional natural gamma ray log is usually abbreviated GR or SGR and is the curve most commonly available. The natural gamma ray spectral log produces the same total gamma ray curve, usually abbreviated SGR. A second gamma ray curve, called CGR, has the gamma rays from uranium filtered off (sometimes abbreviated U-free GR). Thus CGR is always less than or equal to SGR. If a CGR is available, it should be used in preference to the SGR or GR logs.

The gamma rays from potassium, thorium, and uranium may be presented as separate curves, in addition to the SGR and CGR. They are usually calibrated in volumetric units (percent or ppm by rock volume) instead of counts per second or API units. These three curves can be used for mineral identification (see Chapter Nine) or as shale indicator curves.

6.01 Visualizing Shale Volume With Base Lines
Every log responds to shale in a particular way and each shale bed has its own unique log response. Although log readings in shale fluctuate from foot to foot, their average values will be fairly constant over a large area of the country.

Figure 6.01 illustrates the data for Classic Example 1, over clean and shaly sands. A base line for the SP is shown on the right hand side of the SP track. This line is called the shale base line or the shale line (SPl00).

FIGURE 6.01: Raw Data for Classic Example 1 with SP Baselines

The SP deflects to the left in clean sand. In the cleanest sand, the maximum SP reading to the left of the shale base line represents the clean SP line (SP0). Note that other sands may not develop an SP to the same degree as the cleanest sand. Therefore, they are either shaly sands or else they have fresher water in them. The proportion of shale can be estimated by observing the actual SP deflection with respect to the clean sand and shale base lines. For example, the sand at 1060m has developed an SP of about 50% of the maximum amplitude. Therefore, this zone is about 50% sand and 50% shale.

This is a rough approximation of shale content, but is often the only source of shale information in shaly sands on older logs where no gamma ray log exists.

SP base lines generally drift to the left or right due to changing electrical conditions at the well. Draw the base line to conform to the drift. Measure the SP deflection between the base line horizontally and not at right angles to the base line. Most log analysis computer programs have a method for correcting the SP drift. SP curves can also be normalized to make the maximum and minimum deflections equal in all wells by rescaling the curves in the computer. Some geological information may be lost if normalization is performed - some shaly sands may become too clean.

Note that if mud filtrate is saltier than the formation water, the SP shale base line will be on the left and the clean line will be on the right. This is the reverse of the normal situation. Figure 6.01 shows this in the upper sand at 1010 meters.

The gamma ray, like the SP, has a shale base line and a clean line. Estimation of shale content is done by observation of the gamma ray log with respect to the clean line (GR0) and the shale base line (GRl00). The base lines for the GR are shown in Figure 6.02.

FIGURE 6.02: Raw Data for Classic Example 1 with GR and Sonic Baselines

GR curves can also be normalized to make the maximum and minimum deflections equal in all wells by rescaling the curves in the computer. Some geological information may be lost if normalization is performed - some shaly sands may become too clean.

The shale base line for both the gamma ray and SP may alter with hole depth due to changes in logging instrumentation, hole size, mud properties, and varying shale character. Therefore, the shale base line should be chosen specifically in the shales immediately below the formation of interest. However, the clean line may have to be chosen quite some distance from the zone of interest if no clean sands may be nearby. If the well does not penetrate a shale below the zone of interest, the shale base line must be chosen from the nearest shale above the zone.

FIGURE 6.03: Raw Data for Classic Example 1 with Density and Neutron Baselines

There is no strong reason why the adjacent shales should represent the shale properties within the shaly sand, but the assumption is made that this is a good first approximation. Shale properties may need to be adjusted by comparing shale volume calculated from logs with core description, thin section point count data, X-ray diffraction data, or scanning electron microscope data. Discrepancies between log analysis porosity and core porosity may also indicate that shale base lines need to be adjusted.

The gamma ray log is the most useful indicator of shale content, with some minor exceptions, such as in radioactive sands or radioactive dolomite. It is available on most wells logged since 1957.

The sonic log also has a shale base line (DELTSH). It is the fairly straight section of the sonic log between l070 and l075m in our example. Shale content cannot be estimated elsewhere on the sonic log from this information alone. This value must be known so that porosity calculated from the sonic log can be corrected for shale. This is true also of the density (PHIDSH), neutron (PHINSH) and resistivity (RSH) logs, illustrated in Figures 6.01 and 6.03. It is therefore, helpful to document these values over the entire log interval for future reference.

6.02 Scaling the SP and GR Logs in Shale Volume Units
Having chosen the shale base line and the clean line for either or both the SP and GR, you can scale logs in units of shale content (Vsh). This is done by calling the clean line 0.0 Vsh and the shale base line l.0 Vsh as shown in Figures 6.04 and 6.05.

FIGURE 6.04: Shale Volume from SP	FIGURE 6.05 Shale Volume from GR

Then, linearly interpolate a finer scale between the 0 and 1.0 points - such as the 0.0, 0.2, 0.4, 0.6, 0.8, 1.0 scale shown in the examples. From this scale, the shale content (Vsh) can be read for any point on the log. For example:

The values derived from the SP are unreasonable considering the data available in two of the four zones. Therefore, the values should be discarded, or new base lines picked, as shown in Figure 6.01, and better Vsh values estimated. In this example, the SP resolution is too poor to be useful in Sand A, and the water resistivity versus filtrate resistivity contrast in Sand B prevents the use of the SP here.

6.03 Scaling the Density Neutron Separation in Shale Volume Units

Similarly, the separation between the density and neutron porosity logs can be scaled in shale units, as shown in Figure 6.06. A scaler must be made equal in length to the distance between PHINSH and PHIDSH. The scale should be marked with 0.0 Vsh at PHINSH and 1.0 Vsh at the PHIDSH point. Slide the zero end of the scaler along the neutron log to read Vsh at each point desired.

FIGURE 6.06: Shale Volume from Density Neutron Separation

For example:

If this procedure is used in a shaly sand, the density neutron log must be in sandstone units, and if used in a limestone section, the log must be in limestone units.

Do not use this method in gas zones, dolomite, or anhydrite sections. See Chapter Seven for details on converting limestone to sandstone scales and vice versa. If density data is not in porosity units, see Chapter Seven for a method to generate porosity data from density readings.

6.04 Borehole Corrections for Gamma Ray
If the hole size varies between intervals within the zone to be analyzed, or the shale zone used to pick the GRl00 value, then hole size correction to the GR is needed. Corrections for the SP are seldom used even though some effect of hole size and mud properties may be seen. Complex correction charts are available in the literature, but are not usually included in computer programs or hand analysis.

1: IF DEPTHUNIT$ # "METRIC"
2: THEN GRc = GR * (l + 0.04 * (MWT - 8.3)) * (l + 0.06 * (CAL - 8))
3: IF DEPTHUNIT$ = "METRIC"
4: THEN GRc = GR * (1 + 0.000322 * (MWT - 1000)) * (1 + 0.0024 * (CAL - 203))
5: IF MWT = Null
6: OR IF BITZ = Null
7: OR IF CAL = Null
8: THEN GRc = GR

WHERE:
CAL = caliper log reading (hole size) (in or mm)
GR = gamma ray log reading (API units)
GRc = gamma ray log reading corrected for borehole size and mud weight (API units)
MWT = mud weight (lb/US gal or Kg/m3)

COMMENTS:
The fixed constants in these formulae may need to be varied for some logging tools. A chart indicating corrections for more complex situations and the associated mathematical formulae are shown in Figure 6.07, courtesy of Dresser Atlas. If mud properties are unknown, the usual solution is to do nothing and use the GR value as is.

RECOMMENDED PARAMETERS:
None. Default value for MWT is usually 10 lb/USgal or 1250Kg/m3

NUMERICAL EXAMPLE:
See Section 6.09.

FIGURE 6.07: Borehole Corrections for Gamma Ray

6.05 Shale Volume from the Gamma Ray
The response equation for the gamma ray log follows the classical form:

GR = PHIe * Sxo * GRw (water term)
+ PHIe * (1 - Sxo) * GRh (hydrocarbon term)
+ Vsh * GRsh (shale term
+ (1 - Vsh - PHIe) * Sum (Vi * GRi) (matrix term)

WHERE:
GRh = log reading in 100% hydrocarbon
GRi = log reading in 100% of the ith component of matrix rock
GR = log reading
GRsh = log reading in 100% shale
GRw = log reading in 100% water
PHIe = effective porosity (fractional)
Sxo = water saturation in invaded zone (fractional)
Vi = volume of ith component of matrix rock
Vsh = volume of shale (fractional)

Both GRw and GRh are zero. GRi is equal to the background radiation in non-shaly rock and is called GR0 in this book. GRsh is the log reading in shale, called GR100 here. The effect of porosity is very small, so that term also is assumed to be zero. The response equation thus reduces to:

GR = Vsh * GR100 + (1 - Vsh) * GR0

When solved for Vsh, this equation becomes:

Vshg = (GR - GR0) / (GR100 - GR0)

Thus, the algebraic formula to solve for shale volume from the gamma ray is a linear interpolation between the minimum and maximum log readings.

1: Vshg = (GR - GR0) / (GR100 - GR0)

WHERE:
GR = gamma ray log reading in zone of interest corrected for borehole size (API units)
GR0 = gamma ray log reading in l00% clean zone (API units)
GRl00 = gamma ray log reading in l00% shale (API units)
Vshg = shale volume from gamma ray log (fractional)

COMMENTS:
Use CGR, if available, in preference to GR or SGR curves. The gamma ray method for shale volume is preferred in the majority of cases. The exceptions are radioactive dolomites and sandstones, and zones which contain feldspar and its derivatives, such as kaolinite. Use of the data from the natural gamma ray spectroscopy log helps to resolve these cases. See following sections.

RECOMMENDED PARAMETERS:
Range Default

GR0 10 to 45 15 API units
GR100 80 to 150 115 API units

NUMERICAL EXAMPLE:
See Section 6.09.

6.06 Shale Volume From The Spectral Gamma Ray Log
The algebraic formula to solve for shale volume from the gamma ray spectrolog is in the same form as the normal gamma ray.

1: Vshth = (TH - TH0) / (TH100 - TH0)

WHERE:
TH = gamma ray spectrolog reading in zone of interest, thorium only (ppm)
TH0 = gamma ray thorium reading in 100% clean zone (ppm)
TH100 = gamma ray thorium reading in 100% shale (ppm)
Vshth = shale volume from thorium curve of gamma ray spectrolog (fractional)

COMMENTS:
The gamma ray spectrolog thorium curve for shale volume is preferred in dolomites and sandstones which are radioactive due to uranium content, and zones which contain feldspar and its derivatives, such as kaolinite.

1: Vshk = (K - K0) / (K100 - K0)

WHERE:
K = gamma ray spectrolog reading in zone of interest, potassium only (percent)
K0 = gamma ray potassium reading in 100% clean zone (percent)
K100 = gamma ray potassium reading in 100% shale (percent)
Vshk = shale volume from potassium curve of gamma ray spectrolog (fractional)

COMMENTS:
The gamma ray spectrolog potassium curve for shale volume is an alternative method in dolomites and sandstones, which are radioactive due to uranium content. It cannot be used in zones which contain feldspar and its derivatives, such as kaolinite.

Other methods of using spectrolog data have been presented and are discussed fully in Chapter Nine. Two formulae commonly seen are:

1. Wfel = (TH / THCL - K / KCL) / (THFEL / THCL - KFEL / KCL)
2. Wcl = (TH / THFEL - K / KFEL) / (THCL / THFEL - KCL / KFEL)

WHERE:
K = potassium log reading (percent)
KCL = potassium log reading in 100 % clay (percent)
KFEL = potassium log reading in 100 % feldspar (percent)
TH = thorium log reading (ppm)
THCL = thorium log reading in 100 % clay (ppm)
THFEL = thorium log reading in 100 % feldspar (ppm)
Wcl = weight of clay (fractional)
Wfel = weight of feldspar (fractional)

Volumetric fractions of clay and feldspar can be obtained from the density of each constituent. The method is only practical if the potassium and thorium clay values are represented effectively by the log readings in shale. I have no experience with this method, so I cannot recommend it with confidence,

RECOMMENDED PARAMETERS:

Range Default
TH0 0 to 5 0 ppm
TH100 10 to 15 10 ppm
FEL0 0 to 0.5 0 percent
FEL100 2.0 to 2.5 2 percent

NUMERICAL EXAMPLE:
See Section 6.09.

6.07 Shale Volume from the Spontaneous Potential
The algebraic formula to solve for shale volume from the SP log is a linear interpolation between the minimum and maximum log readings, similar to the GR solution.

1: Vshs = (SP - SP0) / (SP100 - SP0)

WHERE:
SP = spontaneous potential log reading in zone of interest (mv)
SP0 = spontaneous potential log reading in 100% clean zone (mv)
SP100 = spontaneous potential log reading in shale (mv)
Vshs = shale volume from spontaneous potential (fractional)

COMMENTS:
The SP method is the second most popular approach to shale volume. The SP is reduced by high resistivity, often associated with hydrocarbons or tight zones, so these may appear too shaly by this approach. The method has poor resolution in zones with fresh formation water, or in wells drilled with salty mud. The method works well in radioactive sands, but not in carbonates.

In older charts and technical papers, the SP is called the pseudo static SP (PSP) and SP0 is called the static SP (SSP). The same formula was used for shale volume as given above, with SP100 taken as zero. The result is always called ALPHA, the SP reduction factor, and was often equated to shale volume:

1: Vsh = ALPHA = PSP / SSP

This formula is no longer commonly used.

RECOMMENDED PARAMETERS:
Range Default
SP0 -100 to -45 -80 mv
SP100 -10 to +10 0 mv

NUMERICAL EXAMPLE:
See Section 6.09.

6.08 Shale Volume from the Density Neutron Crossplot
The response equation for the density log in porosity units follows the classical form:

PHID = PHIe * Sxo * PHIDw (water term)
+ PHIe * (1 - Sxo) * PHIDh (hydrocarbon term)
+ Vsh * PHIDsh (shale term)
+ (1 - Vsh - PHIe) * Sum (Vi * PHIDi) (matrix term)

WHERE:
PHIDh = log reading in 100% hydrocarbon
PHIDi = log reading in 100% of the ith component of matrix rock
PHID = log reading
PHIDsh = log reading in 100% shale
PHIDw = log reading in 100% water
PHIe = effective porosity (fractional)
Sxo = water saturation in invaded zone (fractional)
Vi = volume of ith component of matrix rock
Vsh = volume of shale (fractional)

The response equation for the neutron porosity log also follows the classical form:

PHIN = PHIe * Sxo * PHINw (water term)
+ PHIe * (1 - Sxo) * PHINh (hydrocarbon term)
+ Vsh * PHINsh (shale term)
+ (1 - Vsh - PHIe) * Sum (Vi * PHINi) (matrix term)

WHERE:
PHINh = log reading in 100% hydrocarbon
PHINi = log reading in 100% of the ith component of matrix rock
PHIN = log reading
PHINsh = log reading in 100% shale
PHINw = log reading in 100% water
PHIe = effective porosity (fractional)
Sxo = water saturation in invaded zone (fractional)
Vi = volume of ith component of matrix rock
Vsh = volume of shale (fractional)

The following assumptions are made:
PHIDw = PHIDh = PHINw = PHINh = 1.0, PHIDi = PHINi = 0.0. Sxo = 1.0

Then by subtracting the two equations and solving for Vsh, we get:

Vshx = (PHIN - PHID) / (PHINSH - PHIDSH)

Thus, the algebraic formula to solve for shale volume from the density neutron crossplot is a linear interpolation of the separation between the density and neutron porosity log curves.

1: Vshx = (PHIN - PHID) / (PHINSH - PHIDSH)

WHERE:
PHID = density log porosity reading in zone of interest (fractional)
PHIDSH = apparent density porosity in shale (fractional)
PHIN = neutron log reading in zone of interest fractional)
PHINSH = neutron log reading in 100% shale (fractional)
Vshx = shale volume from density neutron crossplot (fractional)

COMMENTS:
Shale volume from the density neutron crossplot should only be attempted in oil or water bearing shaly sands, not in dolomite, anhydrite, or gas zones. This is because the separation between the two curves is not a function of shale in these cases. The density neutron will help resolve shale volume in radioactive sands (like granite wash formations) provided the zone is known to be sandstone. It will not help resolve a radioactive dolomite.

If matrix density is not the same as the log units see Section 6.10.

If the density neutron data is recorded in percentage units instead of fractional units, convert the data to fractions by dividing each value by 100. If percentage data is used in error, the results will still be correct, but Vsh will be in fractional units.

RECOMMENDED PARAMETERS:
Range Default
PHIDSH -0.03 to +0.10 0.00
PHINSH 0.10 to 0.40 0.30

NUMERICAL EXAMPLE:
See Section 6.09.

6.09 Summary of Shale Volume Methods (With Worked Examples)
Assume data from Sand "D" of Classic Example 1:

1. Vsh from gamma ray log:
Vshg = (75 - 45) / (135 - 45) = 0.33

2. Vsh from spontaneous potential log:
Vshs = (-50 - (-90)) / (0 - (-90)) = 0.44

3. Vsh from density neutron crossplot:
Vshx = (0.28 - 0.12) / (0.30 - 0.03) = 0.59

4. Vsh from gamma ray spectrolog thorium curve:
Vshth = (5 - 0) / (10 - 0) = 0.50

5. Vsh from gamma ray spectrolog potassium curve:
Vshk = (1.5 - 0) / (3 - 0) = 0.44

6. If hole size was 400 mm at the shale point, and mud weight was 1250 Kg/m3, the GR log would read low and a correction would be needed:
GR100 = 135 * (1 + 0.000322 * (1250 - 1000))*(1 + 0.0024*(400 - 203)) = 217 API units
Vshg = (75 - 45) / (217 - 45) = 0.18

This is approximately one half the value without the hole correction applied.

6.10 Shale Content from Density Neutron with Matrix Offset
The previous method described for density neutron data (Section 6.08) assumes the clean line for the crossplot is identical to the units of the density neutron log (i.e. sandstone or limestone). If you wish the clean line to be at a matrix value other than that for the log units, both neutron and density data must be shifted to account for this matrix change.

A chart illustrating the construction of the shale content lines on a density neutron crossplot is given in Figure 6.08. This is the normal density neutron crossplot for determination of porosity and shale volume in the shaly sand model when the sand fraction is made up of quartz.

FIGURE 6.08: Shale Volume from Density Neutron Crossplot

A matrix offset is needed if the sand contains heavy minerals in place of some or all of the quartz. The matrix offset translates the origin along a 45 degree line for CNL data, and at a steeper angle for SNP data. This is equivalent to the solution of the two response equations in Section 6.08, with PHIDi and PHINi not equal to zero, but determined from knowledge of the actual rock description.

Reconstitute density data from density porosity log.
1: DENS = (PHID * 1.00 + (1 - PHID) * (2.65 + 0.06 * (IF LOGUNIT$ = "LIMESTONE"))) * (1 + 999 * (IF DEPTHUNIT$ = "METRIC"))

Calculate density porosity for desired matrix and fluid values.
2: PHIDm = (DENSMA - DENS) / (DENSMA - DENSW)

Calculate density offset for this matrix and fluid.
3: D = PHIDm - PHID

Calculate neutron offset for same matrix.
4: C = D - 0.25 * D * (IF NEUTRONTYPE$ = "SNP")

Calculate neutron log reading for same matrix.
5: PHINm = PHIN - C

Adjust shale values for offset
6: PHIDSHm = PHIDSH + D
7: PHINSHm = PHINSH - C

Calculate shale content.
8: Vshxm = (PHINm - PHIDm) / (PHINSHm - PHIDSHm)

WHERE:
C = neutron log offset (fractional)
D = density log offset (fractional)
DENS = density log reading (kg/m3 or gm/cc)
PHID = density log reading (fractional)
PHIDm = density log reading in zone of interest (fractional)
PHIDSH = apparent density porosity in shale (fractional)
PHIDSHm = density log reading in 100% shale in zone of interest (fractional)
PHIN = neutron log reading in zone of interest (fractional)
PHINm = neutron log reading correction for matrix offset (fractional)
PHINSH = neutron log reading in 100% shale fractional)
PHINSHm = neutron log reading in 100% shale corrected for matrix offset (fractional)
DENSMA = matrix density (kg/m3 or gm/cc)
DENSW = fluid density (kg/m3 or gm/cc)
Vshxm = shale volume from density neutron crossplot corrected for matrix offset (fractional)

COMMENTS:
If density log is in density units, skip Step 1. The analyst should review the discussion of density and neutron log porosity in Chapter Seven before using this method. The comments in Section 6.08 also apply.

RECOMMENDED PARAMETERS:
Range Default
PHIDSH -0.03 to +0.10 0.00
PHINSH 0.10 to 0.40 0.30

See Chapter Seven for additional parameters.

NUMERICAL EXAMPLE:
1. Using data for Sand "D".
PHID = 0.12
PHIDSH = 0.03
PHIN = 0.28
PHINSH = 0.30
Units = Sandstone
desired DENSMA = 2740 Kg/m3

DENS = (0.12 * 1.00 + (1 - 0.12) * (2.65)) * 1000 = 2452 Kg/m
PHIDm = (2740 - 2452) / (2740 - 1000) = 0.165
D = 0.165 - 0.12 = + 0.045
C = - 0.045
PHINm = 0.28 - 0.045 = 0.235
PHIDSHm = 0.03 + 0.045 = 0.075
PHINSHm = 0.30 - 0.045 = 0.255
Vshxm = (0.235 - 0.165) / (0.233 = 0.075) = 0.39

This result agrees more closely with GR and SP data and suggests the matrix offset was reasonable and necessary. The value with no offset applied was 0.59 from the previous example.

6.11 Shale Content from Density Sonic Crossplot
Separation between the density and neutron logs is a common method for calculating shale content because the two logs are often recorded simultaneously on one log. Thus, this approach is easy to use.

The sonic density combination is also practical, since the separation in porosity units, is often proportional to shale content. The response equations used are analogous to those for the density neutron example, and are not repeated here (see Sections 6.08 and 6.10 for details). However, the two curves are seldom presented on one log, so visual or manual methods are seldom seen.

Neutron sonic separation is not useful, as the separation is not usually a function of shale content.

For the sonic density shale calculation, perform the following steps.

Reconstitute density data from density porosity log.
1: DENS = (PHID * 1.00 + (1 - PHID) * (2.65 + 0.06 * (IF LOGUNIT$ = "LIMESTONE"))) * (1 + 999 * (IF DEPTHUNIT$ = "METRIC"))

Calculate density porosity for desired matrix and fluid values.
2: PHIDm = (DENSMA - DENS) / (DENSMA - DENSW)

Calculate density offset for this matrix and fluid.
3: D = PHIDm - PHID

Adjust shale value for offset.
4: PHIDSHm = PHIDSH + D

Calculate compaction correction for sonic data.
5: CP = max (1, CDTSH / (100 + 228 * (IF DEPTHUNIT$ = "METRIC"))

Calculate sonic log total porosity.
6: PHIS = (DELT - DELTMA) / (DELTW - DELTMA) / CP

Calculate sonic log shale porosity.
7: PHISSH = (DELTSH - DELTMA) / (DELTW - DELTMA) / CP

Calculate shale content from density sonic crossplot.
8: Vshxt = (PHIS - PHIDm) / (PHISSH - PHIDSHm)

WHERE:
CDTSH = shale travel time for compaction correction (fractional)
CP = compaction correction (fractional)
D = density log offset (fractional)
DELT = sonic log reading (usec/ft or usec/m)
DELTMA = sonic travel time in matrix (usec/ft or usec/m)
DELTSH = sonic travel time in shale (usec/ft or usec/m)
DELTW = sonic travel time in water (usec/ft or usec/m)
DENS = density log reading (kg/m3 or gm/cc)
DENSMA = matrix density (kg/m3 or gm/cc)
DENSW = fluid density (kg/m3 or gm/cc)
PHID = density log reading (fractional)
PHIDm = density log reading corrected for matrix offset (fractional)
PHIDSH = apparent density porosity in shale (fractional)
PHIDSHm = density log reading in 100% shale corrected for matrix offset (fractional)
PHISSH = apparent sonic porosity in shale (fractional)
PHIS = total porosity derived from sonic log (fractional)
Vshxt = shale volume from sonic density crossplot (fractional)

COMMENTS:
The analyst should review discussions of sonic log porosity in Chapter Seven before using the sonic density crossplot method for shale volume calculations. This is the least accurate shale volume method in shallow shaly sands.

The sonic density crossplot method is useful in radioactive sands, but not appropriate in carbonates. It may work in gas zones if invasion is very shallow, but it is not recommended.

An alternative method using sonic density data was used when the density log was first introduced in the 1960’s. The formula is:
1: Vshq = Q = (PHIS - PHID) / PHIS

The Q method is obsolete, yet some examples exist in technical papers or well files and may still be used in some computer programs in local areas. It assumes that the value of the density log in shale (PHIDSH) is zero, which may be incorrect, and that PHIS = PHISSH which is seldom true.

RECOMMENDED PARAMETERS:
Range Default
PHIDSH - 0.03 to +0.10 0.00
DELTSH (English) 75 to 140 100
DELTSH (Metric) 225 to 460 328

See Chapter Seven for additional parameters.

NUMERICAL EXAMPLE:
1. Data from Sand "D" of Classic Example 1:
Metric units:
PHID = 0.12
PHIDSH = 0.03
DELT = 300 usec/m
DELTSH = 328 usec/m
DELTW = 616 usc/m
DELTMA = 182 usec/m (sandstone)
DENSMA = 2650 Kg/m3 (no matrix offset)

CP = 328 / (100 + 228) = 1.0
PHIS = (300 - 182) / (616 - 182) / 1.0 = 0.27
PHISSH = (328 - 182) / (616 - 182) / 1.0 = 0.34
Vshxt = (0.27 - 0.12) / (0.34 - 0.03) = 0.48
Vshq = Q = (0.27 - 0.12) / (0.27) = 0.55

2. Equivalent English units example:
PHID = 0.12
PHIDSH = 0.03
DELT = 91 usec/ft
DELTSH = 100 usec/ft
DELTW = 189 usec/ft
DELTMA = 55.5 usec/ft

CP = 100 / (100) = 1.0
PHIS = (91 - 55.5) / (189 - 55.5) / 1.0 = 0.27
PHISSH = (100 - 55.5) / (189 - 55.5) / 1.0 = 0.34
Vshxt = (0.27 - 0.12) / (0.34 - 0.03) = 0.48
Vshq = Q = (0.27 - 0.12) / (0.27) = 0.55

6.12 Selecting the Minimum Shale Volume
The usual approach for deciding which of the several available shale volume results to use is to find the minimum value of the feasible results. Feasible results do not include answers from the crossplot methods if gas crossover occurs. The minimum is chosen because most errors for any one method tend to increase the apparent shale volume. For example radioactive sandstone would appear very shaly from the gamma ray but reasonable from the SP and density neutron crossplot.

1: IF PHIN < PHID
2: THEN shx = 10^6
3: Vsh = min (Vshg, Vshs, Vshx)

WHERE:
PHID = density log reading (fractional)
PHIN = neutron log reading (fractional)
Vsh = shale volume from minimum method (fractional)
Vshg = shale volume from gamma ray method (fractional)
Vshs = shale volume from SP method (fractional)
Vshx = shale volume from density neutron crossplot method (fractional)

COMMENTS:
This algorithm needs to be modified to include the methods actually used to calculate shale volume, so that the minimum reflects the actual method.

6.13 Material Balance for Shale Content
The material balance for shale content prevents impossible values and should be applied to each shale volume method used.

1: IF Vsh < 0.0
2: THEN Vsh = 0.0
3: AND VshNEG = VshNEG + 1
4: IF Vsh > 1.0
5: THEN Vsh = 1.0
6: AND VshPOS = VshPOS + 1

WHERE:
Vsh = shale content from any method (fractional)
VshNEG = counter for Vsh less than zero
VshPOS = counter for Vsh greater than one

COMMENTS:
If too many values fall below zero or above 1.0, the analyst should review the choice of clean and shale base lines. Less than 10% of all individual data points should fall outside the material balance constraints. Vsh from the density neutron crossplot will always be negative if gas crossover occurs. In this case, an alternate method should be used. Improper matrix offsets may also cause erroneous gas crossover.

6.14 Non-Linear GR and SP Relationships
Various studies have shown that the GR, and in some cases the SP, is not a linear prediction of shale volume. Various formulae are used to modify the linearly derived shale volume to obtain a more satisfying answer. Since shale volume is needed only to the nearest 5%, these formulae are often found only in computer programs.

Schlumberger Clavier equation.
1: IF NONLINSWITCH$ = "CLAVIER"
2: THEN Vshc = 1.7 - (3.38 - (Vsh + 0.7) ^ 2) ^ 0.5

Dresser tertiary equation.
3: IF NONLINSWITCH$ = "TERTIARY"
4: THEN Vshc = 0.083 * (2 ^ (3.7 * Vsh) - 1)

Dresser older rock equation.
5: IF NONLINSWITCH$ = "OLDERROCKS"
6: THEN Vshc = 0.33 * (2 ^ (2 * Vsh) - 1)
7: OTHERWISE Vshc = Vsh

WHERE:
Vsh = shale content from GR or SP (fractional)
Vshc = shale content corrected for non-linear effects (fractional)

COMMENTS:
Vsh must be within the range of 0.0 to 1.0 before applying these formulae. The Clavier equation is a good compromise between the tertiary and older rock equations. Figure 6.09 illustrates these curves.

FIGURE 6.09: Non-Linear Adjustments to Shale Volume

RECOMMENDED PARAMETERS:
None.

NUMERICAL EXAMPLE:
Assume Vsh = 0.50 (50%).

1. Clavier equation:
Vshc = (1.7 - (3.38 - (0.50 + 0.7) ^ 2) ^ 0.5 = 0.30

2. Tertiary equation:
Vshc = 0.083 * (2 ^ (3.7 * 0.50) - 1) = 0.15

3. Older rocks equation:
Vshc = 0.33 * (2 ^ (2 * 0.50) - 1) = 0.33

6.15 Selection of Shale Volume Method
These methods provide some independent approaches to calculating shale volume, as well as a number of correction factors which could be applied. If the results differ significantly from each other, then the log scales should be checked, the shale and log picks reviewed in an attempt to reconcile the differences. If no reconciliation can be made, discard the least trustworthy result. In order of preference, it is suggested you use:

1. Vsh from GR (if sandstone or carbonate is not radioactive).
2. Vsh from density neutron (only if hole conditions are good and there is no gas crossover and no dolomite).
3. Vsh from SP (only if SP has sufficient character or resolution to be believed).
4. Vsh from sonic density crossplot (not the Q method).
5. Vsh from minimum of above if there is no reason to prefer one method over another.
6. Use linear methods unless local correlations have shown a need for a non-linear relationship.

Answers should be rounded to the nearest 5% (0.05 fractional) for hand calculations, and to the nearest percent (0.01 fractional) for computer work. Set negative values to zero and those greater than 1.0 equal to 1.0. Too much precision in an imprecise number is unnecessary and confusing.

List the shale content results beside the zones on the log, or on a separate data sheet such as was done for Classic Example 1 in Figure 6.10. Column headings may be changed to suit your own needs. Review these results to verify that you can achieve answers similar to those presented here.

FIGURE 6.10: Calculated Shale Volume for Classic Example 1

Computer generated plots of the results for the mixed lithology example are displayed in Figure 6.11. The crossplot shale values are not valid because heavy minerals affect the results.

FIGURE 6.11: Comparison of Shale Calculation Methods for Mixed Lithology Example

6.16 Shale Volume Routines
The simplest routine uses the gamma ray and the material balance algorithm only.

A more complete routine would perform GR borehole corrections, use all methods for which curves were available, test for the minimum, and do the non-linear correction requested.

This routine would approximate that used in most service company computer programs. Other Vsh algorithms could be added, but the VshMIN routine would need to be revised to agree with the changes.

An intelligent computer program could use the set of rules in Section 6.15 and the previously described algorithms to calculate shale volume from the best method with little intervention from the user.

6.17 Other Shale Volume Methods
A number of useful shale volume methods have more restricted application than the more common methods described earlier. The four listed below have proved useful on particular projects that needed help. The reader should take a moment to define the parameters and work a hypothetical numerical example.

The electromagnetic propagation attenuation curve works well, especially in thinly bedded sand-shale sequences. Attenuation increases with shale volume.

1. Vshept = (ATTEN - ATTEN_CLN) / (ATTEN_SHL - ATTEN_CLN)

The deep resistivity sometimes can be used but shale volume will be too high in water zones or swept zones when the water is fairly salty (WS > 50000 ppm NaCl), so another method, such as the SP or GR, should be used as well. Resistivity decreases with higher shale volume. The method is very useful in shallow shaly sands where kaolinite or feldspar makes the gamma ray read high. For the resistivity log method, the use of the logarithm of the resistivity log values (and base line values) works better than linear values, as follows:

1. Vshrd = (log(RESD) - log(RESD_CLN)) / (log(RESD_SHL) - log(RESD_CLN))

Note that RESD_CLN is greater than RESD_SHL

In many shaly sands that are invaded with normal drilling mud filtrate (Rmf >= 0.30 ohm-m), the shallow resistivity may be a good shale indicator. Again, this is a very useful method in feldspathic sandstones, and there is better bed resolution than the deep resistivity. Do not use microlog or microspherically focused log as RESS.

1. Vshrs = (log(RESS) - log(RESS_CLN)) / (log(RESS_SHL) - log(RESS_CLN)

Some newer neutron logs produce a capture cross section curve (SIGMA) which mimics a gamma ray log in shaly sands:

1. Vshsig = (SIGMA – SIG0) / (SIG100 – SIG0)

All cased hole thermal decay time logs display a SIGMA curve as one of the primary measurements. Although there are hydrocarbon effects, the curve can sometimes be used to overcome problems with the gamma ray log, such as uranium precipitation on casing or tubing, or missing GR log.

The equations reproduced in Table 6.01 provide most of the known relationships for calculating shale volume. This material is reprinted courtesy of Dresser Atlas.

TABLE 6.01: Other Shale Volume Methods

TABLE 6.01: Other Shale Volume Methods

6.18 Calibrating Shale Volume to Core and Sample Data
One measure of a good log analysis is that results should match ground truth reasonably well. In the case of shale volume calculations, ground truth is usually rather sparse and, if present, may be qualitative instead of quantitative.

Sample descriptions are available on many wells. These will contain a written description of the rock chips extracted from the drilling mud. The description will include dominant mineralogy, accessory minerals, cementing minerals, grain size or texture, pore geometry, porosity estimate, and hydrocarbon shows. Shale or clay, if present, will be mentioned, sometimes with a volumetric estimate in percent. This work is done by observation through a microscope. Samples can be re-logged quantitatively after the initial review.

Samples are well mixed by the mud circulation so these descriptions include rock chips from a fairly large interval. In addition, cavings from above the sampled interval will continue to contaminate deeper samples. Samples also take a long time to reach the surface, so their source depth is not perfectly established. The time taken to reach the surface is called the lag time. Lag time is calculated by comparing estimated borehole volume with mud pump capacity and speed. It is checked periodically by adding a chemical tracer to the mud and measuring how long it takes to detect the tracer back at the surface.

A good wellsite geologist will correlate his description to the shape of the drilling time log. Later, the sample depths may be adjusted to the open hole logs, especially gamma ray, resistivity and density logs. The geologist will also eliminate most caving from the descriptions.

FIGURE 6.12: Typical Sample Description Log

Your log analysis should show 80 to 100% shale where the geologist shows “shale” or “siltstone”. The results should show 0 to 10% shale where the samples indicate clean sandstone, limestone, dolomite, anhydrite, salt, or mixtures of these minerals. Some shale should show on your analysis where the samples contain shale or clay minerals. A precise match is probably impossible due to the inherent limitations of sample descriptions. At least the samples will eliminate calculation of shale when in fact the zone is a radioactive sandstone or dolomite.

Core