Fast model based inversion of acoustic impedance of annulus behind casing

Patent metadata

Field	Value
Publication number	US-10012749-B2
Application number	US-201514887746-A
Country	US
Kind code	B2
Filing date	Oct 20, 2015
Priority date	Oct 20, 2014
Publication date	Jul 3, 2018
Grant date	Jul 3, 2018

Abstract

Techniques involve obtaining acoustic data from an acoustic logging tool, where the acoustic data includes waves reflected from the casing, the annular fill material, the formation, and/or interfaces between any of the casing, the annular fill material, and the formation. A crude casing thickness, tool position (e.g., eccentering), mud sound velocity may be estimated using the acoustic data. Techniques also involve computing a model spectra and an estimated casing thickness using a forward model and based on a crude casing thickness, an initial mud acoustic impedance, and an initial annular acoustic impedance, estimating a specular signal using the model spectra and the acoustic data in a first time window, computing a calibrated model signal using the estimated specular signal and computed model spectra, computing a misfit of the computed calibrated model signal and acoustic data in a second time window comprising the initial time window, and computing a correction update to one or more of the estimated casing thickness an estimated apparent annular acoustic impedance and an estimated mud acoustic impedance, based on the misfit. Techniques involve iteratively estimating the model spectra and the Jacobian curve, computing the specular signal, computing the misfit, and computing the update until the update is below a threshold. Outputs may include one or more of a casing thickness, an apparent acoustic impedance of the annular fill material, and the acoustic impedance of mud.

First claim

What is claimed is:

1. A method of determining properties of a wellbore in a formation, the wellbore comprising a casing and an annular fill material between the casing and the formation, the method comprising:
obtaining from an acoustic logging tool, acoustic data comprising acoustic waves reflected from the casing, the annular fill material, the formation, one or more interfaces between any of the casing, the annular fill material, and the formation, or combinations thereof;
computing a model spectra using a forward model and based on a crude casing thickness, an initial mud acoustic impedance, and an initial annular fill acoustic impedance;
estimating a specular signal using the model spectra and the acoustic data in a first time window;
computing a calibrated model signal using the estimated specular signal and computed model spectra;
computing a misfit of the computed calibrated model signal and acoustic data in a second time window comprising the initial time window;
computing a correction update to one or more of an estimated casing thickness, an estimated apparent annular fill acoustic impedance and an estimated mud acoustic impedance, based on the misfit;
iteratively estimating the model spectra, estimating the specular signal, computing the calibrated model signal, computing the misfit, and computing the update until the correction update is below a threshold; and
outputting one or more of a casing thickness, an apparent acoustic impedance of the annular fill material, and the acoustic impedance of mud.

2. The method of claim 1 , further comprising estimating a crude casing thickness, a tool position, and a sound velocity in mud between the acoustic logging tool and the casing, or combinations thereof, based on the acoustic data.

3. The method of claim 2 , wherein the crude casing thickness is determined based on a resonant frequency of the acoustic data.

4. The method of claim 3 , wherein estimating the crude casing thickness is based on

f
res

~

v

p
,
cas

2
⁢

⁢
casH

where f res is the resonant frequency, V p,cas is a compressional wave velocity of the casing, and casH is the casing thickness.

5. The method of claim 3 , wherein computing the crude casing thickness is determined based on time delays between successive echoes in the data.

6. The method of claim 2 , wherein the estimated tool position, the estimated mud sound velocity, or both, are estimated based on a time of flight estimation based on a time envelope of an initial reflection from an inner surface of the casing.

7. The method of claim 2 , wherein the estimated tool position, the estimated mud sound velocity, or both, are estimated using a Kalman filter.

8. The method of claim 1 , wherein estimating the model spectra comprises computing a table of waveforms over a plurality of model parameters comprising the crude casing thickness, an estimated tool position, an estimated sound velocity of mud between the acoustic logging tool and the casing, the initial annular fill acoustic impedance, the initial mud acoustic impedance, a casing diameter, material properties of the casing, material properties of the annular fill, and combinations thereof.

9. The method of claim 1 , wherein estimating the model spectra and the Jacobian curve is based on the relationship below:
A mod =diag(1·/ b r,f )[ b 1,f . . . b Nb,f ]°D res

where b r,f is a reference spectra and D res is a frequency delay operator that compensates for a delay in the reference spectra and the model spectra.

10. The method of claim 1 , wherein estimating the specular signal comprises reconstructing the specular signal over the time window using the relationship below:

R
t

⁡

(
S
)

=

W
t

⁢

{

diag
(

∑

m
=
1

N
b

⁢

⁢

(

D

res
,
m

i

∘

A

mod
,
m

)

)

⁢
S

}

where S is the specular signal in a time window t.

11. The method of claim 1 , wherein computing the specular signal comprises using a smoothing function.

12. The method of claim 1 , further comprising computing a calibrated model waveform based on the estimated specular signal.

13. A method comprising:
measuring an acoustic waveform at an acoustic transducer in a wellbore comprising casing and annular material, wherein the measured acoustic waveform is a reflection from the wellbore;
computing a crude casing thickness by processing the acoustic waveform;
determining an initial mud acoustic impedance of mud between the acoustic transducer and the casing and an initial annular fill acoustic impedance of the annular material;
using the estimated crude casing thickness, the initial mud acoustic impedance, and the initial annular fill acoustic impedance in a forward modeling to calculate a model spectra;
using the model spectra to calculate a specular signal;
using the model spectra and the specular signal to calculate a calibrated model signal;
using the model spectra and the calibrated model signal to compute a misfit of the calibrated model signal;
using the misfit to compute an update to one or more of the estimated casing thickness, the initial mud acoustic impedance, and the initial annular fill acoustic impedance; and
outputting one or more o

Assignees

• Schlumberger Technology Corp

Inventors

• Bose Sandip
• Zeroug Smaine
• Yang Jiaqi

Classifications

• E21B47/005

  Monitoring or checking of cementation quality or level · CPC title

• G01V1/306

  for determining physical properties of the subsurface, e.g. impedance, porosity or attenuation profiles · CPC title

• G01V1/50 Primary

  Analysing data · CPC title

• E21B47/0005

  Fixed Constructions · mapped topic