**5. Case study**

166 Acoustic Waves – From Microdevices to Helioseismology

Based on the previous section 3, a calculation model has been established to predict rock

Where *K*dv is the rock drillability perpendicular to the bedding plane of the formation;

China, we can get such coefficients as *C*1=0.05246, *C*2=-0.76732, *C*3=32.977, *C*4=-4.950.

**4.3 Evaluation method of rock drillability anisotropy based on acoustic wave** 

time interval of acoustic wave perpendicular to the bedding plane of the formation.

transformation of the formation coordinates to the bottom hole coordinate.

 α

is the angle between hole axis and normal of the formation;

arccos cos cos sin sin cos( )

is azimuth, degree or radian;

*<sup>f</sup>* is azimuth of the formation tendency, degree or radian.

2. Making an initial guess for the acoustic wave velocity *vP*,0 .

6. Comparing the P-wave group velocity with the measured velocity.

Otherwise, we should repeat step 2 to step 7 until they are matched.

rock drillability anisotropy index can be established by using equation (46).

ω

φ

inclination & azimuth of hole.

equation (44), respectively.

4. Calculating phase angle by equation (43).

plane of the formation is shown in figure 7.

where

φ

ω

procedures:

degree or radian;

the time interval of acoustic wave in the same direction, us/m; *Cj* (*j*=1,2,3,4) are the regression coefficients based on the experimental data and the survey data in drilling engineering. For example, by the regression analysis based on some oilfield data in west

From equations (46) and (47), it is shown that the key point for the evaluation of rock drillability anisotropy is how to obtain the rock drillability perpendicular to the bedding plane of the formation which depends on the time interval of acoustic wave in the same direction. Thus, the evaluation of rock drillability anisotropy comes down to determine the

Provided that the formation is of the transversely isotropy and has the symmetry axis perpendicular to the bedding plane of the formation, the angle between hole axis and the formation normal can be calculated by the following formula which is derived from

> = −− β

When rock anisotropy parameters of a hole section is known, its acoustic wave velocity perpendicular to the bedding plane of the formation can be calculated by the following

1. Calculating group angle according to stratigraphic dip angle & up dip direction, and

3. Reading shear wave velocity from shear wave logging or calculating it by equation (46).

5. Calculating phase velocity and group velocity of the P-wave by equation (41) and

7. If group velocity of the P-wave matches the measured velocity, *vP*,0 is what we find.

The flow chart for inversion of the acoustic wave velocity perpendicular to the bedding

The rock drillability can be calculated by equation (47) after obtaining the time interval of the acoustic wave perpendicular to the bedding plane of the formation. Thus, the profile of

α

β

β

 φφ*<sup>f</sup>* (48)

α

is stratigraphic dip, degree or radian;

is hole inclination,

1 dv 2

<sup>r</sup> 2*CK C I* <sup>+</sup> = (46)

Δ*t* is

*K CC t* dv 3 4 =+ Δ ln( ) (47)

**4.2 Prediction model of rock drillability anisotropy** 

drillability anisotropy of the formation:

Based on some well logging data and drilling information from Qinghai oilfield in west China, the case study is presented in this section to verify the evaluation method for the anisotropic drilling characteristics of the formation to a certain extent.

Based on these data in table 5, rock drillability anisotropy of the fromation and its anisotropic drilling characteristics can be calculated by using the evaluation method described above. The inversion result of shale anisotropy parameters is shown in table 6.


Table 5. Well drilling & logging information from some completed wells at the Honggouzi conformation in Qinghai oilfield

Evaluation Method for Anisotropic Drilling Characteristics

Honggouzi conformation in Qinghai oilfield

evaluated quantificationally by using the oilfield data.

drillability anisotropy of the formation in drilling engineering.

**6. Conclusion** 

formations to be drilled.

shown in figure 9.

of the Formation by Using Acoustic Wave Information 169

shown in Fig.7 and the well logging data of acoustic wave. Thus, the rock drillability anisotropy of the formation can be calculated by equations (46) & (47), and the corresponding anisotropic drilling characteristics can be evaluated by equations (8) & (9), as

Fig. 9. The evaluation results of anisotropic drilling characteristics of the formation at the

The orthotropic formation and the transversely isotropic formation are the typical formations encountered frequently in drilling engineering. Based on rock-bit interaction model, the two parameter equations have been derived for us to calculate the anisotropic drilling characteristics of them as soon as rock drillability anisotropy of the formations is

The correlation between rock drillability anisotropy and acoustic wave anisotropy of the formation can be matched to each other by an exponential function which is of the best extrapolative performance and relativity. Coefficients in the model are various for different

To a certain extent, the research results presented here have shown a new way for us to evaluate conveniently rock drillability anisotropy of the formation by using well logging or seismic data. Case study shows that this evaluation method is better for applications of rock


Table 6. The inversion result of shale anisotropy parameters for the Honggouzi conformation

From the data in the table 6, we can see that the shale is of strong rock anisotropy. The acoustic wave front of the shale section is shown in figure 8.

Fig. 8. Acoustic wave front of the shale section of the Honggouzi conformation

Based on the wave front of the shale shown in Fig.8, the rock anisotropy parameters of the formation at any measured depth, ε and δ , can be approximately calculated by the following equations:

$$\begin{aligned} \mathcal{E} &= V\_{\text{sh}} \mathcal{E}\_{\text{c}} \\ \mathcal{S} &= V\_{\text{sh}} \mathcal{S}\_{\text{c}} \\ V\_{\text{sh}} &= (\mathbf{2}^{\Delta GR \cdot \text{C}\_{\text{sur}}} - \mathbf{1}) / (\mathbf{2}^{\text{C}\_{\text{sur}}} - \mathbf{1}) \\ \Delta GR &= (GR - GR\_{\text{min}}) / (GR\_{\text{max}} - GR\_{\text{min}}) \end{aligned} \tag{49}$$

where ε and δ are rock anisotropy parameters of the formation at any measured depth; ε*c* and δ*<sup>c</sup>* are rock anisotropy parameters of the shale section; *V* sh is the shale content, %; *GR* is gamma ray value; *GR*max is the maximum value of gamma ray; *GR*min is the minimum value of gamma ray; *G*cur is the Hilchie index whose value is 3.7 for the Neogene Stratigraphy and 2 for old strata.

After obtaining the rock anisotropy parameters( ε andδ ), we can calculate the acoustic wave perpendicular to the bedding plane of the formation by using the inversion method

4029.1 1.6833 1.6098 98.6153

From the data in the table 6, we can see that the shale is of strong rock anisotropy. The

δ

root-mean-

square (m/s)

, can be approximately calculated by the

(49)

), we can calculate the acoustic

ε*c*

ε

acoustic wave front of the shale section is shown in figure 8.

Table 6. The inversion result of shale anisotropy parameters for the Honggouzi

Fig. 8. Acoustic wave front of the shale section of the Honggouzi conformation

ε and δ

sh

*V*

After obtaining the rock anisotropy parameters(

ε

δ

*sh c sh c*

 δ

Δ ⋅

 ε

*V V*

Based on the wave front of the shale shown in Fig.8, the rock anisotropy parameters of the

= <sup>=</sup> =−− Δ= − −

cur cur

*GR GR GR GR GR*

(2 1) (2 1)

*GR G G*

min max min

are rock anisotropy parameters of the formation at any measured depth;

ε andδ

wave perpendicular to the bedding plane of the formation by using the inversion method

( )( )

*<sup>c</sup>* are rock anisotropy parameters of the shale section; *V* sh is the shale content, %; *GR* is gamma ray value; *GR*max is the maximum value of gamma ray; *GR*min is the minimum value of gamma ray; *G*cur is the Hilchie index whose value is 3.7 for the Neogene

*v*P,0 (m/s)

formation at any measured depth,

Stratigraphy and 2 for old strata.

following equations:

where ε and δ

and δ

conformation

shown in Fig.7 and the well logging data of acoustic wave. Thus, the rock drillability anisotropy of the formation can be calculated by equations (46) & (47), and the corresponding anisotropic drilling characteristics can be evaluated by equations (8) & (9), as shown in figure 9.

Fig. 9. The evaluation results of anisotropic drilling characteristics of the formation at the Honggouzi conformation in Qinghai oilfield
