CEMENT BOND EVALUATION USING EARLY
REFRACTED ARRIVALS
Rama Rao V. N.
Earth Resources Laboratory
Department of Earth, Atmospheric, and Planetary Sciences
Massachusetts Institu~e of Technology
Cambridge, MA 02139
Batakrishna MandaI
Halliburton Energy Services
Houston, TX
Arthur C. H. Cheng
Western Atlas Logging Services
Houston, TX
and
Earth Resources Laboratory
Dept. of Earth, Atmospheric, and Planetary Sciences
Massachusetts Institute of Technology
Cambridge, MA 02139
M. N afi Toksoz
Earth Resources Laboratory
Department of Earth, Atmospheric, and Planetary Sciences
Massachusetts Institute of Technology
Cambridge, MA 02139
9-1
Rao et al.
ABSTRACT
The cement bond evaluation tool is a device used to examine the integrity of cement
bonding to the casing. A conceptual tool operating between 80-200 kHz is considered
here, with a transmitter and two receivers, oriented parallel to the axis of the borehole and next to the casing. The compressional head wave in the casing, excited by
the transmitter, will be the first arrival to be measured by the two receivers in most
situations. With both receivers on the same side of the transmitter, the attenuation of
this wave in traveling between the two receivers is dependent on the properties of the
medium immediately outside the casing. The radially layered borehole was modeled as a
layered plane medium for large operating frequency. A spectral integral approach (complete wave synthesis) was used to compute the response at the receiver locations, which
then provided attenuations. Different parameters, such as transducer separation (1-12
in), annulus thickness (0-6 in), annulus impedance (free pipe to good cement), casing
thickness (0.25-0.45 in), standoff distance (0.5-1 in) and source frequency (80-200 kHz)
were varied in the evaluation of the operation of the tool. The parameter studies based
on the theoretical computations revealed that free pipe could be distinguished from the
presence of cement in a variety of situations. Additionally, lower bounds on receiver
separations are given for reliable operation of the tool.
INTRODUCTION
Cement bond evaluation tools attempt to identify the presence of cement behind the
casings using transmitters and receivers inside the casing. Cement bond logs have been
used in the oil industry for more than three decades using sonic frequency (e.g., Walker,
1962, 1968; Pardue, et aI., 1963; Gollwitzer and Masson, 1982) and for more than
a decade using ultrasonic frequency (e.g., Froelich, et aI., 1981; Havira, 1982). In this
paper, we conduct numerical computations to evaluate the effect of different parameters
of cement bonding to the casing.
The tool considered here is operating at ultrasonic frequency, and has a transmitter
and two receivers that are parallel to the axis of the borehole and that are next to the
casing. The two receivers are on the same side of the transmitter and the separation
between the transmitter and the closest receiver is the same as that between the two
receivers. The ratio of the earliest arrival at the two receivers is used to determine the
attenuation of this wave traveling between the two receivers. Since it is a ratio of two
response measurements, it is independent of the source power. This attenuation varies
with the thickness and material properties of the casing, the cement and the formation.
The sensitivity of the attenuation of the earliest arrival to layers outside the casing is
used in characterizing the nature of the bond between the casing and the cement.
9-2
Cement Bond Evaluation
MODEL
The wavetypes that are recorded at the receivers include early refracted arrivals (compressional and shear), a reflected mud arrival and a direct (Stoneley) arrival. The arrival
of concern is the refracted compressional arrival that impinges on the casing wall at near
critical angles and travels along the casing wall as a compressional lateral wave in the
steel and then radiates at near critical angles in a conical wavefront to the receivers
COberall, 1973 ).
The operation of the tool is evaluated by computing the attenuation predicted by
a model of the tool. The variation in the attenuation of the first arrival in traveling
between the two receivers is examined as various model parameters are varied. This is
used to elicit bounds of operation and sensitivity levels of the tool.
Assumptions
• The cylindrically layered borehole was modeled with plane layers. The typical operating frequencies of such tools are around 100 kHz. At such high frequencies the
radial curvature of the borehole can be neglected. Hence, the offset-independent,
horizontally stratified, seismo-acoustic model, OASES (Schmidt and Tango, 1986),
was used to compute the effects of wave propagation between the source and receiver. The model is shown in Figure 1. There are two plane layers, the casing
and the cement, which are bound by two half spaces, the drilling mud on one side
and the formation on the other.
• All media were modeled as being lossless. The attenuation of the first arrival is
due to radiation into the formation and mud and due to spreading between the
two receivers. The radiation to the formation depends on the coupling between
the casing and the formation provided by the annulus material.
PARAMETER VARIATION
The attenuation is computed as the following parameters are varied.
1. Source frequency, Ricker wavelets with center frequencies from 80-200 kHz in
steps of 20 kHz.
2. Annulus material properties, considering air, water, and weak and strong
cement (the terms weak and strong cement are used specifically to indicate cement
types with P impedances of 3 x 10 6 and 6 x 10 6 kg/m 2 s, respectively).
3. Annulus thickness, h, in the range 0.1-6 in.
4. Casing thicknesses,
Ct,
of 0.25, 0.35 and 0.45 in.
5. Transducer separation, A"TR, in the range 1-12 in (ArTR = Ar12)'
9-3
Rao et al.
6. Standoff distances, X, of 0.5 and 1 in.
As the parameters are varied, the receiver responses for a wideband impulse is predicted using OASES. This result is then bandpass-filtered for Ricker source wavelets
of different center frequencies. The ratio of amplitudes of the first arrival at the two
receivers is then computed to arrive at the apparent attenuation of the compressional
head wave in traveling between the two receivers. In all attenuation plots, computed results are marked with 'o's or '+'s, with a least squares fit solid line drawn through them.
The attenuation corresponding to the 80 kHz Ricker source wavelet is plotted as a thick
grey line and the attenuations of the six subsequent center frequencies are plotted as
thin black lines. Increasing the center frequencies leads to increased attenuations, with
the 200 kHz response being the most attenuated. Also included are results for different
annulus thickness and the media. The material properties used in the simulations are
given in Table 1.
Casing Thickness Effects
The attenuations are computed from the time responses at the two receivers for various
annulus and casing thicknesses and are shown in Figures 2, 3 and 4. They show the
computed first arrival attenuations for 0.25, 0.35 and 0.45 in thick casings, respectively.
For most cases, attenuations are insensitive to annulus thickness greater than 1 in.
As expected, the attenuations in cement are greater than that in air or water as there is
stronger coupling and more efficient energy leakage into the formation. Attenuations in
air and water increase with increasing casing thickness. However, this change is 1 dB at
80 kHz and 3 dB at 200 kHz. Thus, a more consistent performance in different casings
can be expected at lower frequencies. The change in attenuation is a function of the
change in the ratio of casing thickness to compressional wavelength in the casing, which
is smaller for lower frequencies.
In weak cement, attenuations decrease as casing thickness changes from 0.25 to
0.35 in and then increase as it changes from 0.35 to 0.45 in. In contrast, strong cement
attenuations decrease with increasing casing thickness. The attenuations are the result
of the interaction of the casing, cement and formation, and exhibit undulations for
different casing thicknesses and different layer properties.
Transducer Separation Effects
The transmitter-near receiver separation (b.rTR) and the near receiver-far receiver separation (b.r12) are assumed to be the same. The term 'transducer separation' refers
to the numerical value of both separations. The attenuations for different transmitter
receiver separations are analyzed in two ways.
First, two transducer separations of 3 and 6 in are considered for a range of annulus thicknesses (0.1-6 in) when the annulus medium is strong cement. This gives a
highly resolved attenuation profile with annulus thickness, as shown in Figure 5. The
9-4
(
Cement Bond Evaluation
attenuations for 80 and 100 kHz at 3 in separation are not plotted due to the difficulty in identifying the amplitude of the first arrival. The profile of attenuation with
annulus thickness exhibits variations at small annulus thicknesses, which levels out for
thicknesses greater than 1 in.
In the second case, the attenuations for a range of transducer separations, 1-12 in,
are calculated for two specific annulus thicknesses, 0.5 and 1 in. Here, four different
types of annulus media are considered. The attenuation profiles for 80 and 200 kHz
alone are plotted for an annulus thickness of 0.5 in in Figure 6, and for 1 in in Figure 7.
Attenuation increases linearly with transducer separation. Furthermore, the increase in
attenuation with transducer separation is low for air and water (0.35 dB per in change
of separation) compared to weak cement (0.7 dB/in) and strong cement (1.25 dB/in).
The erratic results for small separations are explained below. Figure 8 shows a plot
of traveltimes of the various wavetypes in traveling from the source to the near receiver
for different separations. This plot shows that at transmitter-near receiver separations
(6rTR) less than 1.30 in, the direct arrival (thin solid line) is the first arrival at the near
receiver, while at larger separations it is the compressional refracted arrival (thick solid
line). The threshold separation is given by equating the traveltimes of the two paths.
6r
6r - -2X tan e,,12
-=
"'1'
2X
+---,--
"'2
"'1
cos
e" 12
(1)
where e,,12 is the compressional critical angle between the mud and the steel casing.
Further, below 0.26 in separation, there are no refracted waves. Between 0.26 and 0.53
in only compressional refracted arrivals are present and above 0.53 in both refracted
wavetypes are present. This is indicated in Figure 8 as different shaded regions. Thus
at small separations, both receivers do not consistently measure the same wavetype in
the first arrival. This accounts for the erratic attenuation profile in Figures 6 and 7.
While a minimum transmitter-near receiver separation of 1.3 inches ensures that the
compression arrival is the first arrival at both receivers, larger separations are required
to ensure that the overlap with succeeding arrivals is minimized. Thus the attenuation
estimates become consistent beyond a separation of 4 in at 80 kHz and 3 in at 200 kHz.
This can also be seen as those transducer separations beyond which the leading arrival
is separated from the next arrival by a time separation greater than the width of the
Ricker wavelet (about 12 /.LS for 80 kHz and 5 /.LS for 200 kHz).
Stand-Off Distance Effects
The attenuations for two different stand-off distances are calculated and plotted in
Figures 9 and 10, with the results for 0.5 and 1 in stand-off distances, respectively.
With all parameters being the same, a change in stand-off distance from 0.5 to 1 in
produces no change in attenuation levels. Moving all transducers away from the casing
simultaneously changes the signal strength that they measure, but does not change
their relative strengths. In this theoretical experiment, we assumed the same standoff
distances for the transmitter and receivers.
9-5
Rao et al.
CONCLUSIONS
A theoretical parametric study of the operating ranges of a cement bond evaluation tool
was conducted over a wide range of parameters using frequency-wavenumber integration
techniques, with the following results.
• Attenuation levels in free pipe (air and water in the annulus) are at least 2 dB
lower than those in poor to good cement (weak and strong cement) in a wide
variety of situations. Thus the presence or absence of cement can be detected
with a tool of the type discussed here.
• Attenuation in weak cement is at least 2 dB less than that in the strong cement
considered here. Thus it is possible to distinguish the quality of cement bond
using this tool.
• Transducer separations, t:.TTR, need to be greater than 4 inches when operating at
80 kHz, and 3 inches, when operating at 200 kHz, to produce reliable attenuation
results.
• Casing thickness changes the measured attenuation with the change being a function of frequency. The lower source frequencies tend to be insensitive to casing
thicknesses and produce consistent attenuation in different casings.
• Increasing transducer separations lead to increased attenuations with the increase
being proportional to the impedance of the annulus material.
• Changes in standoff distance do not affect the attenuation profiles.
ACKNOWLEDGMENTS
This work was supported by the Borehole Acoustics and Logging Consortium at the
Massachusetts Institute of Technology and by the Gas Research Institute, Chicago.
9-6
Cement Bond Evaluation
REFERENCES
Froelich, B., Dumont, A., Pittman, D., Seeman, 1981, B., and Ravira, M.,1981, Ultrasonic imaging of material mechanical properties through steel pipe, IEEE Ultrasonics
Symposium.
Gollitzer, L. R., and Masson, J. P., 1982, The cement bond tool, SPWLA Annual
Logging Symposium.
Ravira, R. M., 1982, Ultrasonic cement bond evaluation, SPWLA Annual Logging Symposium, Corpus Christi, TX.
Pardue, G. R., Morris, R. L. Gollwitzer, L. R., and Moran, J. R.,1963, Cement Bond
Log-A Study of cement and, casing variables, J. Pet. Tech., 545-555.
Schmidt, R. and Tango, G, 1986, Efficient Global Matrix approach for the computation
of synthetic seismograms, Geophys. J. Roy. astr. Soc., 84,331-359.
Uberall, R., 1973, Surface Waves in Acoustics, in Physical Acoustics-Principles and
Methods, 10, Academic Press, New York, NY.
Walker, T., 1962, Case histories of bond logging, Oil and Gas Journal.
Walker, T., 1968, A full-wave display of acoustic signal in cased holes, J. Pet. Tech.,
811-24.
9-7
Rao et al.
Medium
Medium
no. i
1
2
3
4
Water
Steel pipe
Air
Water
Weak cement
Strong cement
Formation
Table 1- Material Properties
Compressional
Shear
speed f3i
speed "'i
(mls)
(mls)
1500
5800
330
1500
1500
3000
4200
-
3200
-
866
1800
2424
Density
Pi
(kglm 3 )
1000
7900
1
1000
2000
2000
2000
(
9-8
Cement Bond Evaluation
Transmitter
Near receiver
Far receiver
Annulus
Figure 1: Schematic of the model.
9-9
Rao et at.
Air channel
Water channel
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4
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024
6
Weak cement channel (P Impedance =3.0)
6
Strong cement channel (P impedance = 6
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-9
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~-11
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..
.
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246
024
Channel thickness [inch]
6
Channel thickness [inch]
Figure 2: Casing thickness variation: c, = 0.25 in; Annulus thickness H = 0.3; 0.6,
0.9, 2, 3, 4, 5 and 6 in; Annulus = air; water, weak cement and strong cement;
Transducer separations t,.rTR=t,.r12 = 6 in; Stand-off distance X = 0.5 in; Ricker
source wavelet center freq. = 80-200 kHz, in steps of 20 kHz, with 80 kHz result
shown in gray (multiply attenuations in the plot by 2 for attenuation in units of
dB/ft).
9-10
Cement Bond Evaluation
Air channel
Water channel
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.
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.
2
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6
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Channel thickness [inch]
2
4
6
Channel thickness [inch]
Figure 3: Casing thickness variation: c, = 0.35 in; Annulus thickness H = 0.3, -0.6,
0.9, 2, 3, 4, 5 and 6 in; Annulus = air, water, weak cement and strong cement;
Transducer separations Ll.rTR=Ll."12 = 6 in; Stand-off distance X = 0.5 in; Ricker
source wavelet center freq. = 80-200 kHz, in steps of 20 kHz, with 80 kHz result
shown in gray (multiply attenuations in the plot by 2 for attenuation in units of
dB/ft).
9-11
Rao et al.
Air channel
Water channel
-4,----------,
-4,----------,
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.
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.
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c
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024
6
-12'-----'-------'~--...J
o
2
4
6
(
Weak cement channel (P Impedance =3.0)
Strong cement channel (P impedance =6
-6,------------,
-6,---.,.--------,
-7
-7
.
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6
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2
4
6
Channel thickness [inch]
Channel thickness [inch]
Figure 4: Casing thickness variation: c, = 0.45 in; Annulus thickness H = 0.3, 0.6,
0.9, 2, 3, 4, 5 and 6 in; Annulus = air, water, weak cement and strong cement;
Transducer separations D.rTR=D.r12 = 6 in; Stand-off distance X = 0.5 in; Ricker
source wavelet center freq. = 80-200 kHz, in steps of 20 kHz, with 80 kHz result
shown in gray (multiply attenuations in the plot by 2 for attenuation in units of
dB/ft).
9-12
Cement Bond Evaluation
Source-receiver spacing = 3 [inch]
Source-receiver spacing = 6 [inch]
-9
-4
-5
-6
in
0".
c
o
.~
::l
C
Q)
;j'
- 10 L---'---'----'-----'----'-_-'--'---'---'-.J
10-1
10°
Channel thickness [inch]
_ 15 L---'---'----'----'---'-_-'--'----'---'-.J
10-1
10°
Channel thickness [Inch]
Figure 5: Transducer separation variation: fl1"TR=fl1"12 = 3 and 6 in; Annulus thickness
H = 0.1-6 in; Annulus = strong cement, Casing thickness = 0.35 in; Stancl-off
distance X = 0.5 in; Ricker source wavelet center freq. = 80-200 kHz, in steps of 20
kHz, with 80 kHz result shown in gray (multiply attenuations in the left plot by 4
and the right plot by 2 for attenuation in units of clB/ft).
9-13
Rao et al.
Air channel
"
-5 .
OJ
:>
«
-5
.
+
.
+
-15
+
+
-10 .
..
<=
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10
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4
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2
4
6
8
10
(
Weak cement channel (P Impedance = 3.0)
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~-10
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OJ
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.
., .... ,
-10 .
<=
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"iii
+
:>
<=
.$
«
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+
0
-20 .. :1:"
-20
.
(
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o 2
4
6
8
10
Transducer separation [inch]
-25 '--~_--'-_-'-_~_~---.J
o 2 4 6 8 10
Transducer separation [inch]
Figure 6: 'Transducer separation variation: f1"TR=f1r12 = 1-12 in; Annulus thickness
H = 0.5 in; Annulus = air, water, weak cement and strong cement; Casing thickness
= 0.35 in; Stand-off distance X = 0.5 in; Ricker source wavelet center freq. = 80
kHz (gray lines with '0') and 200 kHz (black lines with '+').
9-14
Cement Bond Evaluation
Water channel
Air channel
0
_5.
-5
iii'
0
+
c:
+
0
~
+
"c:
2-15·
+
-15
:;:
+
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+
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2
4
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6
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10
··0··
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iii'
4
6
8
10
Strong cement channel (P impedance = 6
Or-~----------,
Weak cement channel (P Impedance = 3.0)
Or-~--------,
-5
2
o
-10 ....
!!.-10
c:
~
+
"
c:
~ -15
-15
..:
+
.
0
-20 . +
-20
_25l-_~_~---,~---',----'::--J
o
2
4
6
8
10
Transducer separation [inch]
-25 L-----"_---':_---:-_--:-_:':-----'
o 2 4 6 8 10
Transducer separation [inch]
Figure 7: Transducer separation variation: ll.rTR=ll.r12 = 1-12 in; Annulus thickness
H = 1 in; Annulus = air, water, weak cement and strong cement; Casing thickness
= 0.35 in; Stand-off distance X = 0.5 in; Ricker source wavelet center freq. = 80
kHz (gray lines with '0') and 200 kHz (black lines with '+').
9-15
Rao et al.
Travel times of various wavetypes
6,-----,------,-.,.-------,--,-------r------",----,
• 0
..
..... .
.• .
~"
o·
............ ,,-
5
o
o
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c
=c
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w
:/
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.
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......
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f-
pomp. and shear refracted wave~
11IylqQmR~1r~faqtga
a
a
20
60
40
Time [micro sec]
Figure 8: Theoretical traveltimes of various wavetypes.
9-16
80
100
120
Cement Bond Evaluation
Air channel
Water channel
-3r---~--~------'
-3r---~--~~--,
-4
-4
-5
~
15a -6
"
-6 ............. - ...
.
=>
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g
-< -7
..
-8
-7
..
_9l.--_~
o
2
-6
__
_ _..J
~~
4
-9
6
Weak cement channel (P Impedance = 3.0)
0
4
2
6
Strong cement channel (P impedance = 6
-6r--~---~----'
-6r---~---~----'
-7
-7
..
"
-8 .~.
-8
-9
W -9
!!.
..
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'iiia -10
.;;
=>
.
g::t:=::=::=::=::=:1
~
2
n
;;:-11 .
-12
..
-11
-12
o
o
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-13 ...,,:: ...
-13
. ..
n
_14L-_ _
o
_ _....J
6
Channel thickness [inch]
~
2
~
_14L-_ _
o
4
_ _....J
2
4
6
Channel thickness [inch]
~
~
Figure 9: Stand-off distance variation: X = 0.5 in; Annulus thickness H = 0.3, 0.6,
0.9, 2, 3, 4, 5 and 6 in; Annulus = air, water, weak cement and strong cement;
Transducer separations 6.TTR=D.'·12 = 6 in; Casing thickness Ct = 0.35 in; Ricker
source wavelet center freq. = 80-200 kHz, in steps of 20 kHz, with 80 kHz result
shown in gray (multiply attenuations in the plot by 2 for attenuation in units of
dB/ft).
9-17
Rao et al.
Air channel
Water channel
-3r---~-------,
-3r----------,
-4
-4 ....
.
-5
_-5
co
:!2.
"a -6
"
j"g
-6
~
"" -7
.
-7
-6
-6
-9'----'----'------'
4
2
o
6
_9 ' - - - - ' - - - - - - ' - - - - '
o
Weak cement channel (P Impedance = 3.0)
co
4
6
Strong cement channel (P impedance = 6
-6r------------,
-6r-----------,
-7
-7
-6
:!2.
2
:~
.
(
-6
-9
-9
§
~-10
(
"
2"
;;:-11
-12
-12
-13
-13
-14 '-----'--.----'--------'
2
4
6
o
Channel thickness [inch]
.
.... ;
.
':==::==::==::==::==*
·u~··~"..~.
-14 ' - - - - - ' - - - - - - ' - - - - - - - - '
o
6
Figure 10: Stand-off distance variation: X = 1 in; Annulus thickness H = 0.3, 0.6,
0.9 , 2, 3, 4, 5 and 6 in; Annulus = air, water, weak cen1ent and strong cen1entj
Transducer separations LlTTR=Ll"12 = 6 in; Casing thickness c, = 0.35 in; Ricker
source wavelet center freq. = 80-200 kHz, in steps of 20 kHz, with 80 kHz result
shown in gray (multiply attenuations in the plot by 2 for attenuation in units of
dB/ft).
9-18