 Density Neutron 'SHALY SAND" Crossplot CAUTION The  Density Neutron Shaly Sand Crossplot Porosity Model shown below assumes that the sandstone is pure quartz plus clay. This assumption is seldom true as most sandstones are composed of quartz plus other mineraks, all of them heavier than quartz. In these cases the calculated porosity is pessimistic, so DO NOT use this model unless the sand is pure quartz plus clay. If heavy minerals are present,a
Shaly Sand with Matrix Offset model may wotk, but the Density Neutron Complex Lithology Crossplot Porosity Model is far superior to any other model. STANDARD 'SHALY SAND" Crossplot MODEL
Very rapid methods for estimating porosity from density and neutron log data are available, based on extensive use of assumptions. They are easily memorized and should be used with mental arithmetic or calculators. The approach simulates the results from chartbooks, but more detailed formulae should be used in computers, as discussed later in this chapter.

Read comments below BEFORE using this model. In shaly sands, convert logs into sandstone units and enter the uncorrected density and neutron log readings into the following equations:

If no gas crossover exists, that is,
3: IF PHIN >= PHID
4: THEN PHIxdn = (PHID * PHINSH - PHIN * PHIDSH) / (PHINSH - PHIDSH)

If gas crossover is present, that is,
5: IF PHIN < PHID
6: THEN PHIxdn = ((PHIN ^ 2 + PHID ^ 2) / 2) ^ 0.5

Where:
PHID = density porosity log reading (fractional)
PHIdc = density log porosity corrected for shale (fractional)
PHIN = neutron porosity log reading (fractional)
PHInc = neutron log porosity corrected for shale (fractional)
PHIDSH = density log shale porosity (fractional)
PHINSH = neutron log shale porosity (fractional)
PHIxdn = porosity from density neutron crossplot (fractional) COMMENTS:
Do not gas or shale correct the density or neutron data before using this method.

This method calculates the shale correction based on the density neutron crossplot shale volume (Vshx).  If this is not the shale volume method you want to use, DO NOT USE THIS POROSITY METHOD.

This method is pessimistic if heavy minerals exist in the sandstone. Since nearly every sandstone contains minerals other than quartz to some degree (such as mica, volcanic rock fragments, dolomite or calcite cement), the shaly sand model is almost ALWAYS PESSIMISTIC. Methods listed below are also better. However, this shaly sand model has been very widely used and it can still be found in every computer-aided log analysis package. I strongly recommend NOT using this model. Quick Density Neutron Porosity in Any Rock
An alternate quick look method for shaly sand or carbonates is:
7: PHIdc = PHID - Vsh * PHIDSH
8: PHInc = PHIN - Vsh * PHINSH
9: IF PHInc < 0
10: THEN PHInc = 0
11: PHIxdn = PHIdc + (PHInc - PHIdc) / 3

Where:
PHID = density porosity log reading (fractional)
PHIdc = density log porosity corrected for shale (fractional)
PHIN = neutron porosity log reading (fractional)
PHInc = neutron log porosity corrected for shale (fractional)
PHIDSH = density log shale porosity (fractional)
PHINSH = neutron log shale porosity (fractional)
PHIxdn = porosity from density neutron crossplot (fractional)
Vsh = shale volume (fractional) COMMENTS:
This formula is effective even in gas zones and is based on the premise that the neutron log sees deeper into the zone than the density log, and thus has more gas effect.

Shale corrections could create apparent gas crossover and this may be real or an artifact of excessive correction. Check against known data from the well if shale correction creates crossover. RECOMMENDED PARAMETERS: Range Default PHIDSH -0.03 to +0.12 0.00 PHINSH 0.10 to 0.40 0.30 NUMERICAL EXAMPLE:
1. Data for Shaly Sand "D"
PHID = 0.12
PHIN = 0.30
PHIDSH = 0.03
PHINSH = 0.30
PHIxdn2 = (0.12 * 0.30 - 0.28 * 0.03) / (0.30 - 0.03) = 0.100

The shale volume was 0.59 using this data. Since this value is too high compared to the shale content from the GR, the porosity from this method will be too low.

2. If this porosity is unacceptably low, use the complex lithology formula with Vsh of your choice, as shown below. Given Vsh = 0.33 from GR, with other data as before, then:
PHInc = 0.30 - 0.33 * 0.30 = 0.20
PHIdc = 0.12 - 0.33 * 0.03 = 0.11
PHIxdn = (0.20 + 0.11) / 2 = 0.155

3. The alternate quick method gives, for Sand "D"
PHInc = 0.30 - 0.33 * 0.30 = 0.20
PHIdc = 0.12 - 0.33 * 0.03 = 0.11
PHIxdn3 = 0.11 + (0.20 - 0.11) / 3 = 0.140 Shaly Sand Crossplot (Density Neutron) with Matrix Offset
This method is more long-winded than the quick method and accounts for matrix offset to an arbitrary user defined matrix value.

Reconstitute density data from density porosity log.
12: DENS = (PHID * KD1 + (1 - PHID) * KD2

Where:
English Units   Metric Units    Log Scale
KD1       1.00                 1000               All
KD2       2.65                 2650           Sandstone
KD2       2.71                 2710           Limestone
KD2       2.87                 2870           Dolomite

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

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

Calculate neutron offset for same matrix:
14: C = KN4 * D

Where:
KN4 = 1.00 for CNL   0.75 for SNP neutron log

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

16: PHIDSHm = PHIDSH + D
17: PHINSHm = PHINSH - C

Calculate porosity where there is no gas crossover, that is:
18: IF PHINm >= PHIDm
19: THEN PHIxdn = (PHIDm * PHINSHm - PHINm * PHIDSHm) / (PHINSHm - PHIDSHm)

If gas crossover occurs:
20: IF PHINm < PHIDm
21: THEN PHIxdn4 = ((PHINm ^ 2 + PHIDm ^ 2) / 2) ^ 0.5

Where:
KD5 = 1.00 English units, 1000 Metric units
C = neutron log offset (fractional)
D = density log offset (fractional)
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 in zone of interest (fractional)
PHIDm = density log reading corrected for matrix offset (fractional)
PHIDSH = density log reading in 100% shale (fractional)
PHIDSHm = density log reading in 100% shale corrected for matrix offset (fractional)
PHIN = neutron log reading in zone of interest (fractional)
PHINm = neutron log reading corrected for matrix offset (fractional)
PHINSH = neutron log reading in 100% shale (fractional)
PHINSHm = neutron log reading in 100% shale corrected for matrix offset (fractional)
PHIx = density neutron porosity with matrix and gas correction applied (fractional)
PHIxdn = shaly sand crossplot porosity corrected for matrix offset

The graphical solution to these equations is shown below. Chart for Estimating Shale Corrected Porosity From Density Neutron Crossplot - Shaly Sand Model
The "Sand Point" can be shifted to account for Matrix Offset COMMENTS
Note that this method, while called the shaly sand crossplot method, will work for any lithology, providing it is constant over the computed interval (shale may vary but not the mineral mixture). Shale content is implicitly corrected by use of PHINSH and PHIDSH. The method does not use the Vsh value calculated by any other method.

The gas correction is usually applied automatically when crossover of the density and neutron logs occurs. In shaly or dolomitic sands, crossover may be inhibited by the nature of the lithology, so the analyst may impose the corrections if gas is known to be present. The analyst must select the matrix density towards which the gas correction should be applied.

Because the shale volume is implied instead of an explicit input parameter, I do not recommend this method. RECOMMENDED PARAMETERS: Range Default PHIDSH -0.03 to +0.10 0.00 PHINSH 0.20 to 0.40 0.30 DENSMA (English) 2.65 to 2.87 2.71 DENSMA (Metric) 2650 to 2870 2710 NUMERICAL EXAMPLE:
1. Assume data for Sand "C"
PHID = 0.33
PHIN = 0.24 (gas crossover occurs)
DENSMA = 2680 kg/m3
DENSW = 1000 kg/m3
D = 0.02
C = -0.02
PHIDm = 0.33 + 0.02 = 0.35
PHINm = 0.24 - 0.02 = 0.22

PHIxdn4 = ((0.22 ^ 2 + 0.35 ^ 2) / 2) ^ 0.5 = 0.30

2. Assume data from Sand "D" and impose gas correction manually, since there is no gas crossover, due to shaliness.
PHID = 0.12
PHIN = 0.28
DENSMA = 2680 kg/m3
DENSW = 1000 kg/m3
D = 0.02
C = -0.02
PHIDm = 0.12 + 0.02 = 0.14
PHINm = 0.28 - 0.02 = 0.26
PHIDSHm = 0.03 + 0.02 = 0.05
PHINSHm = 0.30 = 0.02 = 0.28

PHIxdn4 = (0.12 * 0.28 - 0.26 * 0.05) / (0.28 - 0.05) = 0.11

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