PERMFILE43377

• Permit No: M1999002
• IBM Index Class Name: Permit File
• Doc Date: 6/18/1999
• Doc Name: SONIC LOG DATA HELP DETERMINE FORMATION STRENGTH
• Section_Exhibit Name: OBJECTORS EXHIBITS
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• Archive: No

TECHNOLOGY
Fig 5
Table 7
The changing slopes for
tests with low lateral stress
levels correspond to the
cun•ed portion of Wyllie's
plots of acoustical wave ve-
locity where stress levels
were low.
At higher lateral stresses,
the modulus value in the
strength test plots becomes
constant.
This condition is analo-
gous to Wyllie's terminal ve-
locity.
Peaks in the strength test
plots continue to increase at
greater lateral stress levels
even though the modulus
value remains constant.
Pock strength parameters
based nn acoustical wave ve-
locities must be evaluated at
stress levels less than termi-
nal conditions, in which
both strength and velocity
values vary with stress.
Stress region
The ruck properties in the
stress region less than termi-
nal conditions are the basis
for converting mck strengths
behveen dynamic and static
values. Dynamic values are
based on acoustical velocit}~
data; static values are based
on rock Failure tests in a
press. The following are
three characteristics of these
rock properties:
• The relationship be-
hveen shear modulus and
stress is a straight line.
In studies with friable
sands at stress levels less
than terminal conditions, a
straight-line plot of shear
modulus es. vertical stress
t}'as used to calculate rock
properties.' This plot was
developed from compres-
sional acoustic wave data,
assuming the average bulk
modulus value in the sands
remained constant.
This procedure is analo-
gous to working with partial
differentials in which onl}~
the change in shear modulus
with stress is considered.
The procedure obtained
good results because the
predicted fracture pressure;
agreed with empirical data
reported in the literature.
• There is a common
point (a,0) on the Shea;
modulus vs. stress on the
Mohr-Coulomb plots (Fig.
3).
The horizontal axis of the
Ivtohr-Coulomb strength
plot is the stress vertical to
the plane of failure in rock
samples subjected to com-
pression strength tests at
different lateral stress condi-
tions.
The vertical axis plots the
shear stress along the plane
of failure.
The strength of cohesion,
or cementation, is the value
on the Mohr-Coulomb line
at zero vertical stress. A
strength test measures the
stress conditions when the
sample fails. The negative
vertical stress is significant.
if the effect of the negative
vertical stress (a) is equal to
the strength of cementation,
then the shear strength is
zero.
The test plots in Fig. 2
confvm that the shear mod-
ulus coordinates are the
same as these shear strength
coordinates, assuming the
cun~es were obtained in
compressional tests with tri-
axial equipment.
The slopes for that case
would be Young's modulus
values. No compression
would be required for the
sample to fail if shear
strength is zero.
Therefore, the test plot of
interest would lie on the
horizontal axis, and the val-
ue of Young's modulus for a
horizontal line is zero. Also,
the shear modulus should
approach zero when
Young's modulus approach-
es zero, in accord with Equa-
tion 1. The assumptions are
that the bulk modulus has a
finite value and that the rock
is homogeneous and isotro-
pic.
• The stress required to
reach terminal velocity de-
creases as the stren~th of the
rock increases.l' 7 From
these data, estimates of ter-
minal stress thresholds for
rocks of different strengths
are plotted in Fig. 4.
Shear modulus
11'uerker rep. rted data for
a limited number of lime-
stone samples used to con-
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vert the >fohr-Coulomb
strength plMS to shear mod-
ulus values (Table I).7
The following iterative
procedure is used to calcu-
late shear modulus values
using porosity fraction, bulk
densih•, and the Mohr-Cou-
lomb equation data for each
sample:
• Calaflate the travel time
(the reciprocal of velocity) of
a compressional acoustic
wave going through the rock
at terminal stress (Equation
2).` (lt is assumed the sam-
ple pores are filled with
brine.)
• Calcul.tte the combined
dynamic modulus at the ter-
minal stress (Equation 3).'
• Calculi:e the combined
dynam
psf an,
sonabla
lion 4)
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lus, K,
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