Quasi-static Stoneley slowness estimation
A method and system for producing a Quasi-Static Stoneley Slowness log. The method for producing a Quasi-Static Stoneley Slowness log may comprise recording a pressure wave at a receiver; determining a slowness-frequency range with an information handling system from the pressure wave, processing a frequency-domain semblance, extracting a Stoneley Dispersion, minimizing a misfit between theoretical and the Stoneley Dispersion, and identifying Quasi-Static Stoneley slowness from the Stoneley Dispersion. The well measurement system for producing an Quasi-Static Stoneley Slowness log and shear slowness anisotropy may comprise a downhole tool, a vehicle, and an information handling system. Wherein the information handling system may be operable to record a pressure wave at a receiver, determine a slowness-frequency range with an information handling system from the pressure wave, process a frequency-domain semblance, extract a Stoneley Dispersion; minimize a misfit between theoretical and the Stoneley Dispersion; and identify Quasi-Static Stoneley slowness from the Stoneley Dispersion.
1. A method for producing a Quasi-Static Stoneley Slowness log comprising:
disposing a downhole tool into a borehole, wherein the downhole tool includes:
at least one transmitter configured to generate a pressure wave; and
at least one receiver; configured to record the pressure wave;
determining a slowness-frequency range with an information handling system,
processing a frequency-domain semblance from the slowness-frequency range;
extracting a Stoneley Dispersion from the frequency-domain semblance;
minimizing a misfit between a theoretical low-frequency Stoneley dispersion model and the Stoneley Dispersion; and
identifying Quasi-Static Stoneley slowness from the Stoneley Dispersion in real time.
2. The method of claim 1 , further comprising:
finding borehole characteristics;
performing a forward model with borehole characteristics; and
building a low-frequency Stoneley Dispersion Model.
3. The method of claim 1 , wherein the extracting the Stoneley Dispersion comprises identifying a maximum semblance/coherence value at a frequency.
4. The method of claim 1 , further comprising displaying the Quasi-Static Slowness in a log.
5. The method of claim 2 , wherein the borehole characteristics comprises mud slowness or mud density.
6. The method of claim 2 , wherein the low-frequency Stoneley Dispersion Model is created from D ST (f,R,DTM,ρ mud ,DTC,DTS,ρ fm ,ANI,INV,TL), where f is frequency, R is borehole radius, ρ mud is mass density of mud, ρ fm is formation respectively; DTS is formation shear, DTC is compressional wave slowness, DTM is mud slowness, ANI are anisotropy parameters of the formation, INV are invasion parameters, and TL are parameters of a tool model.
7. A method for producing Quasi-Static Stoneley Slowness log comprising:
disposing a downhole tool into a borehole, wherein the downhole tool includes:
at least one transmitter configured to generate a pressure wave; and
at least one receiver; configured to record the pressure wave;
inputting known borehole characteristics into an information handling system;
creating a forward model with the information handling system from the known borehole characteristics;
building a low-frequency Stoneley Dispersion Model;
minimizing a misfit between a predicted Stoneley waveform and a measured Stoneley waveform to estimate final Stoneley dispersion by maximizing a coherence value between the predicted Stoneley wave form and the measured Stoneley waveform; and
identifying Quasi-Static Stoneley Slowness from the estimate final Stoneley dispersion in real time.
8. The method of claim 7 , wherein the borehole characteristics comprises mud slowness or mud density.
9. The method of claim 8 , wherein the building a low-frequency Stoneley Dispersion Model is created from D ST (f,R,DTM,ρ mud ,DTC,ρ fm ,s feature ,a,b,TL) where f is frequency, R is borehole radius, ρ mud is mass density of mud, ρ fm is formation respectively; DTS is formation shear, DTC is compressional wave slowness, DTM is mud slowness, ANI are anisotropy parameters of the formation, INV are invasion parameters, and TL are parameters of a tool model, s feature is a feature point in a dispersion curve at a specific frequency point, a and b are parameters that account for the effect of anisotropy and invasion.
10. The method of claim 7 , further comprising propagating a waveform from a first receiver to a second receiver with at least one trial parameter.
11. The method of claim 7 , wherein the minimizing the misfit between predicted and measured Stoneley waveform data comprises maximizing a coherence value between the predicted and measured Stoneley waveform data.
12. The method of claim 7 , wherein the minimizing the misfit between predicted and measured Stoneley waveform data comprises maximizing the energy of a stacked waveform of the predicted and measured Stoneley waveform data.
13. The method of claim 7 , comprising displaying the Quasi-Static Stoneley Slowness on a log.
14. A well measurement system for producing a Quasi-Static Stoneley Slowness log and shear slowness anisotropy for a vertically transversely isotropic formation comprising:
a downhole tool wherein the downhole tool includes:
at least one transmitter configured to generate a pressure wave; and
at least one receiver; configured to record the pressure wave;
a vehicle, wherein the downhole tool is attached by a conveyance to the downhole tool; and
an information handling system operable to determine a slowness-frequency range from the pressure wave; process a frequency-domain semblance from the slowness-frequency range; extract a Stoneley Dispersion from the frequency-domain semblance; minimize a misfit between a theoretical low-frequency Stoneley dispersion model and the Stoneley Dispersion; and identify Quasi-Static Stoneley slowness from the Stoneley Dispersion.
15. The well measurement system of claim 14 , wherein the information handling system is operable to obtain a formation shear slowness anisotropy for a tilted transversely isotropic formation.
16. The well measurement system of claim 14 , wherein the information handling system is operable to compute a Stoneley Effective formation shear modulus is found with
μ
ST
=
1
(
s
ST
static
2
-
DTM
2
)
(
1
-
r
tool
)
ρ
mud
-
r
tool
μ
tool
.
17. The well measurement system of claim 14 , wherein the information handling system is operable to compute a formation shear anisotropy is found with
ξ
=
μ
ST
-
μ
qSV
2
μ
qSV
ξ is the apparent formation shear anisotropy observed by Stoneley waves, μ qSV is shear modulus for vertically polarized shear waves calculated from dipole data processing , and μ ST is the Stoneley Effective formation shear modulus.
18. The well measurement system of claim 15 , wherein the formation density and a layer dip angle is computed from
λ
=
η
(
sin
2
θ
8
-
cos
2
θ
)
+
ξ
cos
2
θ
(
1
+
2
η
)
cos
4
θ
-
(
1
+
2
ξ
)
cos
2
θsin
2
θ
+
sin
4
θ
8
where λ is the true shear slowness anisotropy of the rock formation, η is the apparent shear slowness anisotropy obtained from dipole processing, and ξ is the apparent formation shear anisotropy observed by Stoneley waves.
19. The well measurement system of claim 18 , wherein an apparent shear slowness anisotropy is found with
η
=
μ
SH
-
μ
qSV
2
μ
qSV
where η is the apparent shear slowness anisotropy obtained from dipole processing, μ qSV is shear modulus for vertically polarized shear waves, and μ SH is the shear modulus for horizontally polarized shear waves propagation in the borehole axis.