Methods for evaluating cement bonding
Methods for evaluating cement bonding in a wellbore are provided. An example method for determining cement impedance includes generating one or more acoustic signals within a wellbore comprising a borehole fluid, a casing, and a cement layer. One or more reflections of the acoustic signals may be received from at least a portion of the wellbore, wherein each of the one or more reflections comprises an initial reflection portion and a resonance portion. At least one of the initial reflection portion and the resonance portion may be modified based, at least in part, on an attenuation response of the borehole fluid. An impedance of the cement layer may be determined by analyzing at least one of the modified initial reflection portion and the modified resonance portion.
1. A method for determining cement impedance, comprising:
generating one or more acoustic signals within a wellbore comprising a borehole fluid, a casing, and a cement layer;
receiving one or more reflections of the acoustic signals from at least a portion of the wellbore, wherein each of the one or more reflections comprises an initial reflection portion and a resonance portion;
modifying at least one of the initial reflection portion and the resonance portion based, at least in part, on an attenuation response of the borehole fluid; and
determining an impedance of the cement layer by analyzing at least one of the modified initial reflection portion and the modified resonance portion.
2. The method of claim 1 , further comprising determining the attenuation response of the borehole fluid.
3. The method of claim 2 , wherein determining the attenuation response of the borehole fluid comprises determining a frequency-dependent attenuation model for the borehole fluid.
4. The method of claim 3 , wherein determining the frequency-dependent attenuation model comprises using the following equation:
Loss in dB=20*log 10 ( e −αx )
wherein α corresponds to an attenuation coefficient and x corresponds to a distance traveled by the one or more acoustic signals through the borehole fluid.
5. The method of claim 4 , wherein determining the frequency-dependent attenuation model further comprises using the following linear equation:
α=α 0 +(α 1 *f )
wherein f corresponds to a frequency of the acoustic signal, α 1 corresponds to a slope of the attenuation model, and α 0 corresponds to an intercept of the attenuation model.
6. The method of claim 1 , wherein the modifying comprises multiplying each frequency component of at least one of the initial reflection portion and the resonance portion by e 2α f df , where α f corresponds to a borehole fluid attenuation coefficient, f corresponds to a frequency of the frequency component, and d corresponds to a standoff distance between the transducer and a wellbore casing.
7. The method of claim 1 , wherein the one or more acoustic signals are generated by an acoustic logging tool comprising a transducer positioned within the borehole fluid.
8. The method of claim 7 , wherein the acoustic logging tool comprises a rotating portion to which the transducer is coupled.
9. The method of claim 1 , further comprising transforming at least one of the initial reflection portions into a frequency domain by performing a Fast Fourier transform.
10. The method of claim 1 , wherein determining an impedance of the cement layer comprises determining a one-norm of the resonance portion normalized by a peak amplitude in the initial reflection portion or a one-norm of the initial reflection portion.
11. The method of claim 1 , wherein determining an impedance of the cement layer comprises determining a ratio of one-norms using the following equation:
r
=
(
norm
1
)
B
(
norm
1
)
A
wherein (norm 1 ) A corresponds to a one-norm of the initial reflection portion and (norm 1 ) B corresponds to a one-norm of the resonance portion.
12. The method of claim 11 , further comprising determining a ratio of one-norms model to describe a relationship between the ratio of one-norms and cement impedance.
13. The method of claim 12 , wherein determining the ratio of one-norms model comprises using the following equation:
log 10 r=pZ c +q
wherein r corresponds to the ratio of one-norms, p corresponds to a slope of the ratio of one-norms model, q corresponds to an intercept of the ratio of one-norms model, and z c corresponds to the cement impedance; and wherein p and q are determined using least squares fitting.
14. The method of claim 11 , wherein determining the ratio of one-norms model comprises simulating one or more acoustic reflections for at least two cement impedances.
15. The method of claim 13 , wherein determining the cement impedance comprises using the following equation:
=
(
log
10
r
meas
-
q
p
)
wherein r meas corresponds to the ratio of one-norms for each reflection of the one or more acoustic signals.
16. A method for determining cement impedance, comprising:
generating one or more acoustic signals within a wellbore comprising a borehole fluid, a casing and a cement layer;
receiving one or more reflections of the acoustic signals from at least a portion of the wellbore, wherein each of the one or more reflections comprise an initial reflection portion and a resonance portion;
modifying at least one of the initial reflection portion and the resonance portion based, at least in part, on an attenuation response of the borehole fluid;
computing a ratio of one-norms of the initial reflection portion and the resonance portion;
simulating one or more simulated acoustic reflections for one or more cement impedances based, at least in part, on the attenuation response of the borehole fluid, wherein each of the one or more simulated acoustic reflections have a simulated initial reflection portion and a simulated resonance portion;
computing a simulated ratio of one-norms of the simulated initial reflection portion and the simulated resonance portion; and
determining an impedance of the cement layer based, at least in part, on a comparison of the ratio of one-norms with the simulated ratio of one-norms.
17. The method of claim 16 , wherein computing a ratio of one-norms of the initial reflection portion and the resonance portion comprises using the following equation:
r
=
(
norm
1
)
B
(
norm
1
)
A
wherein (norm 1 ) A corresponds to a one-norm of the initial reflection portion and (norm 1 ) B corresponds to a one-norm of the resonance portion.
18. The method of claim 16 , wherein computing the simulated ratio of one-norms comprises using the following equation:
r
=
(
norm
1
)
B
(
norm
1
)
A
wherein (norm 1 ) A corresponds to a one-norm of the stimulated initial reflection portion and (norm 1 ) B corresponds to a one-norm of the stimulated resonance portion.
19. The method of claim 16 , wherein the one or more acoustic signals are generated by an acoustic logging tool comprising a transducer positioned within the borehole fluid.
20. The method of claim 19 , wherein the acoustic logging tool comprises a rotating portion to which the transducer is coupled.