Cement evaluation
Systems and methods of evaluating well cementation are disclosed. In certain embodiments, a tool is lowered into a casing surrounded by an annular material within a wellbore. An emitter of the tool emits an acoustic signal at a first pitch angle selected to excite a mixed-mode Lamb wave comprising a symmetric extensional (Sn) mode and an asymmetric flexural (An) mode of a Lamb wave in the casing. A receiver of the tool that is disposed at a first distance from the emitter receives a portion of the Lamb wave that has leaked from the casing at approximately the first distance.
1. A system for evaluating well cementation, comprising:
a body configured to be lowered into a casing within a wellbore;
an emitter configured to emit an acoustic signal and coupled to the body at a pitch angle and frequency band selected to excite a mixed-mode Lamb wave comprising a symmetric extensional (S n ) mode and an asymmetric flexural (A n ) mode in the casing;
wherein the pitch angle is selected to primarily excite a single dominant S 0 mode and a single dominant A 0 mode of the Lamb wave in the casing; and
a first receiver coupled to the body at a first distance from the emitter and configured to receive a portion of the Lamb wave that has leaked from the casing at approximately the first distance and calculate a first moment (EM1) of an energy distribution between points n 1 and n 2 of the mixed mode (S 0 , A 0 ) portion of the first waveform, given by the equation:
EM
1
=
-
∑
n
1
n
2
(
n
-
n
0
)
n
φ
2
∑
n
1
n
2
φ
2
.
2. The system of claim 1 , wherein the pitch angle is within a range of 20-30 degrees from perpendicular to the casing.
3. The system of claim 1 , wherein the first receiver is coupled to the body at a first catch angle that is approximately equal to the pitch angle.
4. The system of claim 3 , wherein the pitch angle and the first catch angle can be changed while the system is disposed within the wellbore.
5. The system of claim 1 , wherein the pitch angle is selected to primarily excite a single dominant S 0 mode and a single dominant A 0 mode of the Lamb wave in the casing.
6. The system of claim 1 , further comprising a pulse-echo transceiver coupled to the body at a pulse-echo angle that is less than 5 degrees from perpendicular to the casing.
7. The system of claim 1 , further comprising one or more second receivers coupled to the body at one or more second respective distances from the emitter.
8. A method of evaluating well cementation, comprising steps:
lowering a tool into a casing surrounded by an annular material within a wellbore;
causing an emitter of the tool to emit an acoustic signal at a pitch angle selected to excite a mixed-mode Lamb wave comprising a symmetric extensional (S n ) mode and an asymmetric flexural (A n ) mode of a Lamb wave in the casing;
wherein the pitch angle is selected to primarily excite a single dominant S 0 mode and a single dominant A 0 mode of the Lamb wave in the casing; and
receiving, with a first receiver of the tool that is disposed at a first distance from the emitter, a portion of the Lamb wave that has leaked from the casing at approximately the first distance and calculating a first moment (EM1) of an energy distribution between points n 1 and n 2 of the mixed mode (S 0 , A 0 ) portion of the first waveform, given by the equation:
EM
1
=
-
∑
n
1
n
2
(
n
-
n
0
)
n
φ
2
∑
n
1
n
2
φ
2
.
9. The method of claim 8 , wherein the pitch angle is within a range of 20-30 degrees from perpendicular to the casing.
10. The method of claim 8 , further comprising steps:
receiving, with a transceiver of the tool, a pulse-echo waveform;
estimating a pulse-echo acoustic impedance based in part on the pulse-echo waveform;
plotting the pulse-echo acoustic impedance vs. the EM1; and
classifying the annular material as well-bonded lightweight cement or water by comparing the plot of the pulse-echo acoustic impedance vs. the first moment of the EM1 to a predetermined reference boundary.
11. The method of claim 10 , wherein the reference boundary is determined from analysis of the acoustic impedance and the EM1 of the energy data in a portion of the wellbore that is known to have a free casing.
12. The method of claim 10 , wherein the reference boundary is determined by lab experiments, computational modeling, analysis of pulse-echo acoustic impedance vs. the first moment plots from one or more other wellbores, or a combination thereof.
13. The method of claim 10 , wherein:
the step of receiving a portion of the Lamb wave comprises receiving a plurality of portions of the Lamb wave with a plurality of receivers of disposed at a respective plurality of distances from the emitter;
the step of calculating the EM1 comprises calculating a respective plurality of EM1s for each portion of the Lamb wave received by the plurality of receivers;
the step of plotting the pulse-echo acoustic impedance vs. the EM1 comprises plotting the respective plurality of EM1s; and
the step of classifying the annular material comprises comparing the plots of the respective plurality of EM1s against a plurality of predetermined boundaries respectively associated with the plurality of receivers.