
Publication History:
This article is based on
Chapter 7 of "The Log Analysis Handbook" by E. R. Crain, P.Eng., published by Pennwell Books 1986 Updated 2004.
This
webpage version is the copyrighted intellectual
property of the author.
Do not copy or distribute in any form without explicit
permission. 
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 ^ (05 * 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
