Ultrasonic logging methods and apparatus for automatically calibrating measures of acoustic impedance of cement and other materials behind casing
View Patent ↗Methods and apparatus for in situ, continuous, automatic, and real-time acoustic impedance calibration of a transducer in an acoustic logging system. By taking the frequency characteristics of the ultrasonic transducer which are present in the internal casing reflection and convolving them with the frequency characteristics of the casing being logged, a theoretical model is created with a theoretical acoustic impedance fluid producing a theoretical free pipe signal at each measure point. The measured signal is then compared to the theoretical free pipe signal thereby yielding a calibrated acoustic impedance value for at each measure point. The only model employed is in the theoretical calculation of spectrum characteristics of free pipe.
1. A method for using an acoustic logging system comprising an acoustic transducer and a processor cooperating with said acoustic transducer to obtain a calibrated measure of acoustic impedance in a cased borehole, the method comprising:
at a measure point, measuring a composite response signal with said transducer;
at said measure point, determining a theoretical free pipe response of said transducer with said processor by:
determining an ultrasonic transducer transfer function from said composite response function after filtering to remove casing reverberations;
determining a casing transfer function;
convolving said ultrasonic transfer function with said casing transfer function to obtain a total transfer function; and
determining said theoretical free pipe response by inverse Fourier transforming said total transfer function; and
combining said composite response signal with said theoretical free pipe response signal to obtain said calibrated measure of acoustic impedance.
2. The method of claim 1 wherein said casing transfer function is determined according to the equation:
TR
=
AZ
in
-
DZ
out
-
CZ
in
Z
out
+
B
CZ
in
Z
out
-
DZ
out
-
AZ
in
+
B
where
TR=the casing transfer function,
Z in =the acoustic impedance of fluid within the casing and is measured,
Z out =the acoustic impedance of fluid outside of the casing and is estimated, and
A, B, C and D are terms computed from known or measured parameters.
3. The method of claim 2 wherein said terms A, B, C and D are determined according to the equations:
A
=
cosh
(
ξ
T
hc
)
B
=
-
Z
cas
sinh
(
ξ
T
hc
)
C
=
-
1
Z
cas
cosh
(
ξ
T
hc
)
D
=
cosh
(
ξ
T
hc
)
where
Z cas =the casing acoustic impedance which is a known constant,
T hc =casing thickness determined by from frequency of the reverberations of the casing, and
ζ=(a+jβT hc ) is a propagation constant,
where
α=a known attenuation constant of the casing
j=a normalization constant, and
β=the delay constant and is known.
4. The method of claim 1 further comprising:
obtaining a plurality of said calibrated measure of acoustic impedance at a measure points located axially along and azimuthally around said borehole;
with said plurality of said calibrated measures of acoustic impedance, generating a two dimensional map of acoustic impedance.
5. A method for using an acoustic logging system comprising an acoustic transducer and a processor cooperating with said acoustic transducer to determine a theoretical value of free pipe in a cased borehole, the method comprising:
at a measure point, measuring a composite response signal with said transducer disposed within said borehole; and
with said processor:
determining an ultrasonic transducer transfer function from said composite response function after filtering to remove casing reverberations;
determining a casing transfer function;
convolving said ultrasonic transfer function with said casing transfer function to obtain a total transfer function; and
determining said theoretical free pipe response by inverse Fourier transforming said total transfer function.
6. The method of claim 5 wherein said casing transfer function is determined according to the equation:
TR
=
AZ
in
-
DZ
out
-
CZ
in
Z
out
+
B
CZ
in
Z
out
-
DZ
out
-
AZ
in
+
B
where
TR=the casing transfer function,
Z in =the acoustic impedance of fluid within the casing and is measured,
Z out =the acoustic impedance of fluid outside of the casing and is estimated, and
A, B, C and D are terms computed from known or measured parameters.
7. The method of claim 6 wherein said terms A, B, C and D are determined according to the equations:
A
=
cosh
(
ξ
T
hc
)
B
=
-
Z
cas
sinh
(
ξ
T
hc
)
C
=
-
1
Z
cas
cosh
(
ξ
T
hc
)
D
=
cosh
(
ξ
T
hc
)
where
Z cas =the casing acoustic impedance which is a known constant,
T hc =casing thickness determined by from frequency of the reverberations of the casing, and
ζ=(α+jβT hc ) is a propagation constant,
where
α=a known attenuation constant of the casing
j=a normalization constant, and
β=the delay constant and is known.
8. An acoustic logging system comprising:
an acoustic transducer configured to measure a composite response signal at a plurality of measure points in a borehole; and
a processor cooperating with the acoustic transducer, wherein the processor is:
configured and programmed to receive the measured composite response signal from the transducer;
programmed to compute a theoretical free pipe response of the transducer; and
programmed to combine the measured composite response signal and the theoretical free pipe response of the transducer to obtain a calibrated measure of acoustic impedance;
wherein the processor is programmed to compute the theoretical free pipe response by:
filtering the measured composite response signal to remove casing reverberations;
computing an ultrasonic transducer transfer function from the filtered composite response function;
computing a casing transfer function;
convolving the ultrasonic transfer function with the casing transfer function to obtain a total transfer function; and
computing the theoretical free pipe response by computing an inverse Fourier transform of the total transfer function.
9. The acoustic logging system of claim 8 wherein the casing transfer function is computed according to the equation:
TR
=
AZ
in
-
DZ
out
-
CZ
in
Z
out
+
B
CZ
in
Z
out
-
DZ
out
-
AZ
in
+
B
where
TR=the casing transfer function,
Z in =the acoustic impedance of fluid within the casing and is measured,
Z out =the acoustic impedance of fluid outside of the casing and is estimated, and
A, B, C and D are terms computed from known or measured parameters.
10. The acoustic logging system of claim 9 wherein the terms A, B, C and D are computed according to the equations:
A
=
cosh
(
ξ
T
hc
)
B
=
-
Z
cas
sinh
(
ξ
T
hc
)
C
=
-
1
Z
cas
cosh
(
ξ
T
hc
)
D
=
cosh
(
ξ
T
hc
)
where
Z cas =a known, constant casing acoustic impedance,
T hc =casing thickness determined from a measured casing reverberation frequency, and
ζ=(α+jβT hc ), a propagation constant,
where
α=a known attenuation constant of the casing
j=a normalization constant, and
β=a known delay constant.