Shale Content from 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 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