
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,
2020.
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 model is used to estimate porosity
when the density neutron crossplot method cannot be used,
due to lack of density log or bad density data caused by
rough hole conditions.. The sonic neutron crossplot method
works well when shale volume, matrix rock properties, and
sonic compaction effects are
accurately known. If both density and neutron logs are available, a superior
model that does not require matrix rock properties is the
Shale Corrected Density Neutron
Complex Lithology Crossplot Method. The Meta/Kwik
spreadsheet for this model is available at
Downloads and Spreadsheets.
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.
Since both logs
respond similarly to shale, the formulae do not have much accuracy
in very shaly sands.
Gas effect is similar to the density neutron crossplot, so gas
may be corrected for.
Sonic Neutron CrossplOT
POROSITY
Calculate
compaction correction for sonic.
For Metric units (usec/m)
1A: KCP = max (1, DTCSH / 328
OR For English units (usec/ft)
1B: KCP = max (1, DTCSH / 100
Calculate sonic porosity.
2: PHIS = (DTC  DTCMA) / (DTCW  DTCMA) / KCP
Calculate shale corrected sonic porosity:
3: PHISSH = (DTCSH  DTCMA) / (DTCW  DTCMA) / KCP
4: PHIsc = PHIS  Vsh * PHISSH
Calculate shale corrected neutron porosity:
5: PHInc = PHIN  Vsh * PHINSH
Check for gas crossover using PHInc and PHIsc.
If no gas crossover, that is
6: IF PHInc >= PHIsc
7: THEN E = 0.5  10 ^ (5 PHInc  0.3)
8: AND G = 0.146
9: AND PHIxsn = (G * PHInc  E * PHIsc) / (G  E)
If gas crossover occurs, that is:
10: IF PHInc < PHIsc
11: THEN PHIxsn = ((PHIsc ^ 2 + PHInc ^ 2) / 2) ^ 0.5
Where:
DTCSH = sonic log shale value for compaction correction (usec/ft
or usec/m)
KCP = compaction factor (fractional)
DTC = sonic log reading (usec/ft or usec/m)
DTCMA = travel time in rock matrix (usec/ft or usec/m)
DTCSH = sonic log reading in shale (usec/ft or usec/m)
DTCW = travel time in water (usec/ft or usec/m)
E = neutron pseudo matrix point
G = sonic pseudo matrix point
PHIN = neutron log reading (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.
Thismethod 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".
DTC = 300 usec/m
PHIN = 0.28
KCP = 1.00
DTCSH = 328 usec/m
PHINSH = 0.30
Vsh = 0.33
DTCMA = 182 usec/m
DTCW = 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
