Sonic Neutron Crossplot
The sonic neutron crossplot method involves the simultaneous solution of the sonic and neutron response equations for porosity. They are similar in form to the density neutron pair, and will not be repeated here.

Complex lithology is best suited to this method. Since both logs respond similarly to shale, the formulae do not have much accuracy in shaly sands.

Gas effect is similar to the density neutron crossplot, so gas may be corrected for.

Calculate compaction correction for sonic.
    1: KCP = max (1, CDTSH / (100 - 228 * (IF DEPTHUNIT$ = "METRIC)))

Calculate sonic porosity.
      2: PHIS = (DELT - DELTMA) / (DELTW - DELTMA) / KCP

Calculate shale corrected porosity:
      3: PHISSH = (DELTSH - DELTMA) / (DELTW - DELTMA) / KCP
      4: PHIsc = PHIS - Vsh * PHISSH
      5: PHInc = PHIN - Vsh * PHINSH

Calculate matrix offset (C) for neutron log, if needed, using offset formulae HERE. Since density data is not needed in this method, any arbitrary density porosity value can be used to calculate the matrix offset. This density porosity value should be the appropriate average porosity in the zone of interest.

Calculate neutron log value with matrix offset.
      6: PHINm = PHInc - C

Check for gas crossover using PHINm and PHIsc.
If no gas crossover, that is
      7: IF PHINm >= PHIsc
      8: THEN E = 0.5 - 10 ^ (-5 PHInc - 0.3)
      9: AND G = -0.146
    10: AND PHIxsn = (G * PHInc - E * PHIsc) / (G - E)

If gas crossover occurs, that is:
      11: IF PHINm < PHIsc
      12: THEN PHIxsn = ((PHIsc ^ 2 + PHInc ^ 2) / 2) ^ 0.5

WHERE:
  C = neutron log matrix offset (fractional)
  CDTSH = sonic log shale value for compaction correction (usec/ft or usec/m)
  KCP = compaction factor (fractional)
  DELT = sonic log reading (usec/ft or usec/m)
  DELTMA = travel time in rock matrix (usec/ft or usec/m)
  DELTSH = sonic log reading in shale (usec/ft or usec/m)
  DELTW = travel time in water (usec/ft or usec/m)
  E = neutron pseudo matrix point
  G = sonic pseudo matrix point
  PHIN = neutron log reading (fractional)
  PHINm = neutron log value offset for matrix effect (fractional)
  PHINSH = neutron log reading in shale (fractional)
  PHInc = porosity from neutron log corrected for shale (fractional)
  PHIS = porosity from sonic log (fractional)
  PHIsc = porosity from sonic corrected for shale (fractional)
  PHISSH = sonic porosity in shale (fractional)
  PHIxsn = porosity from sonic neutron crossplot (fractional)
  Vsh = shale volume (fractional)

COMMENTS:
The overall layout of the neutron sonic crossplot is shown below.


Chart for Sonic Neutron Porosity Model - shale corrected data must be entered

The gas correction represents a 45 degree line (in porosity units) on the crossplot. The method is best used in carbonates with or without gas, and is inappropriate for shaly sand.

Shear sonic data may be used in place of compressional sonic data. This is especially useful in cased holes where a shear sonic and neutron log can be run through casing.

NUMERICAL EXAMPLE:
1. Assume data for Sand "D".
DELT = 300 usec/m
PHIN = 0.28
KCP = 1.00
DELTSH = 328 usec/m
PHINSH = 0.30
Vsh = 0.33
DELTMA = 182 usec/m
DELTW = 616 usec/m
no matrix offset
PHIS = (300 - 182) / (616 - 182) / 1.0 = 0.27
PHISSH = (328 - 182) / (616 - 182) / 1.0 = 0.33
PHIsc = 0.27 - 0.33 * 0.33 = 0.16
PHInc = 0.28 - 0.33 * 0.30 = 0.18
E = -0.5 - 10 ^ (0-5 * 0.18 - 0.3) = 0.43
G = -0.146
PHIxsn = (-0.146 * 0.18 - 0.43 * 0.16) / (-0.146 - 0.54) = 0.165

MATRIX ROCK PROPERTIES


 

 

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