
Publication History:
This article is based on
Chapter 6 of "The Log Analysis Handbook" by E. R. Crain, P.Eng., published by Pennwell Books 1986 Updated 2004,
2020.
This
webpage version is the copyrighted intellectual
property of the author.
Do not copy or distribute in any form without explicit
permission. 
Shale Content from Sonic Density 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 also
proportional to shale content (as well as mineral effects).
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 * KD1 + (1  PHID) *
KD2
Where:
KD1 = 1.00 gm/cc English units 1000 kg/m3 Metric Units
KD2 = 2.65 gm/cc English units 2650 kg/m3 Metric Units
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: KCP = max (1, CDTSH / KS3
Where: KS3 = 100 for English units, 328 for Metric
units
Calculate
sonic log total porosity.
6: PHIS = (DTC  DTCMA) / (DTCW  DTCMA) / KCP
Calculate sonic log shale porosity.
7: PHISSH = (DTCSH  DTCMA) / (DTCW  DTCMA) / KCP
Calculate
shale content from density sonic crossplot.
8: VSHxsd = (PHIS  PHIDm) / (PHISSH  PHIDSHm)
9: VSHxsd = Min(1, Max(0, VSHxsd))
Where:
CDTSH = shale travel time for compaction correction (usec/ft or usec/m)
KCP = compaction correction (fractional)
D = density log offset (fractional)
DTC = sonic log reading (usec/ft or usec/m)
DTCMA = sonic travel time in matrix (usec/ft or usec/m)
DTCSH = sonic travel time in shale (usec/ft or usec/m)
DTCW = 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)
VSHxssd = shale volume from sonic density crossplot (fractional)
COMMENTS:
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.
"Q" METHOD (OBSOLETE)
An
alternative method using sonic density data was used when
the density log was first introduced in the 1960’s.
It is the same as the standard sonic density model, but assumes that
PHIDSH =0.00 and PHISSH = PHIS. This is seldom true, so the model
should not be used.
The formula is:
9: VSHq = Q = (PHIS  PHID) / PHIS
10: VSHq = Min(1, Max(0, VSHq))
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.
RECOMMENDED
PARAMETERS:
Range Default
PHIDSH  0.03 to +0.10 0.00
DELTSH (English) 75 to 140 100
DELTSH (Metric) 225 to 460 328
NUMERICAL
EXAMPLE:
1. Data from Sand "D" of Classic Example 1:
Metric units:
PHID = 0.12
PHIDSH = 0.03
DTC = 300 usec/m
DTCSH = 328 usec/m
DTCW = 616 usc/m
DTCMA = 182 usec/m (sandstone)
DENSMA = 2650 kg/m3 (no matrix offset)
KCP = 328 / (100 + 228) = 1.0
PHIS = (300  182) / (616  182) / 1.0 = 0.27
PHISSH = (328  182) / (616  182) / 1.0 = 0.34
VSHxsd = (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
DTC = 91 usec/ft
DTCSH = 100 usec/ft
DTCW = 189 usec/ft
DTCMA = 55.5 usec/ft
KCP = 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
