
Publication History:
This article is based on
Chapter 9 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. 
Lithology from Matrix
TRAVEL TIME
"Slowness" is the new word for sonic or acoustic travel
time. The inverse of slowness is speediness or velocity. We
continue to use travel time in this Handbook  it's hard to
teach old dogs new tricks.
The
apparent matrix travel time can be calculated in a similar fashion
to the matrix density, again by rearrangement of the response
equation.
Calculate Matrix
1: IF Vsh + PHIe < 0.95
2: THEN DTCms = (DTC  PHIe * DTCW  Vsh *
DTCSH) / (1  PHIe  Vsh)
3: OTHERWISE DTCma = DTC
Calculate mineral volumes (relative to each other)
4: Min1 = (DTCma  DTC2) / (DTC1  DTC2)
5: Min2 = 1.00  Min1
Calculate mineral volumes (relative to total rock volume)
6: Vrock = (1.0  Vsh  PHIe)
7: Vmin1 = Min1 * Vrock
8: Vmin2 = Min2 * Vrock
WHERE:
DTC = sonic log reading (usec/ft or usec/m)
DTCma = computed matrix travel time (usec/ft or usec/m)
DTC1 = matrix travel time for first mineral (usec/ft or usec/m)
DTC2 = matrix travel time for second mineral (usec/ft or usec/m)
DTCSH = sonic log reading in shale (usec/ft or usec/m)
DTCW = sonic log reading in water (usec/ft or usec/m)
PHIe = effective porosity from any method (fractional)
Vsh = volume of shale (fractional)
Vrock = rock volume (fractional)
Vmin1 = true volume of first mineral (fractional)
Vmin2 = true volume of second mineral (fractional)
Min1 = relative volume of first mineral (fractional)
Min2 = relative volume of second mineral (fractional)
COMMENTS:
This
equation breaks down with high values of PHIe + Vsh, so we set
DELTma = DELT when PHIe + Vsh > 0.95.
This
model is not very sensitive in carbonates  the matrix density model
is better, if data is available.
The
matrix travel time can be obtained graphically from the chart below.
Sonic neutron crossplot to find DELTma
NUMERICAL
EXAMPLE:
1. Assume
Sand D in Example 1.
DTC = 300 usec/m
DTCSH = 328 usec/m
Vsh = 0.33
DTCW = 616 usec/m
PHIe = 0.11
DCTma = (300  0.11 * 616  0.33 * 328) / (1  0.11  0.33) = 229
usec/m
This
value falls in the impossible area and is too high because the sonic
log reads high compared to effective porosity found from the density
neutron crossplot. If porosity was 0.16, the matrix travel time
would be 183 usec/ft (close to the sandstone value).
This
is another quality control indicator, and in this example
demonstrates a lack of coherence between the sonic and density
neutron data, when the matrix, shale and fluid assumption are as
given above. Either these parameters, or the log data, or the whole
rock model are in error.
Sonic Lithology Codes
Lithology codes are more difficult to generate with sonic data then
with density data.
SlithCode  Sonic Lithology Codes
DELTma 


English 
Metric 
SlithCode 
usec/ft 
usec/m 

< 41 
< 134  
 
41  45 
134  147 
DOLO 
45  49 
147  160 
LIME 
49  51 
160  167 
ANHY 
51  58 
167  190 
QRTZ 
58  65 
190  213 
 
65  68 
213  223 
SALT 
68  72 
223  236 
 
72  76 
236  249 
SYLV 
76  80 
249  262 
CARN 
80  120 
262  393 
COAL
(only if trigger set) 
120  124 
393  406 
SULF 
> 124 
> 406  
 
if Vsh >
0.85 

SHLE 
COMMENTS:
The bad
hole code does not intervene in sonic calculations.
Should
not be used in shallow unconsolidated sandstones.
SONIC PARAMETERS
