**3.1.3 Testing method**

The rock drillability can be measured with a device for testing the rock drillability (shown in Fig.2). During the measurement, some weight is applied on the micro-bit by the function of a hydraulic pressure tank with the fixed poises, so that the weight on the micro-bit is kept at a constant value. The measured depth to be drilled to is set with the standard indicator, and the drilling time is logged with a stopwatch. Both the roller bit (bit of this kind has three rotating cones and each cone will rotate on its own axis during drilling) drillability and the PDC (the acronym of Polycrystalline Diamond Compact) bit drillability can be tested with the above-mentioned instrument, which is of the following standard data.

The diameter of the micro-bit is 31.75 mm.

Weight is 90±20 N on the roller bit and 500±20 N on the PDC bit.

The rotary speed is 55±1 r/min.

The total depth to be drilled to is 2.6 mm for the roller bit with a pre-drilled depth of 0.2 mm and 4 mm for the PDC bit with a pre-drilled depth of 1.0 mm.

During testing the rock drillability, the micro-bit is often checked so that each of the worn micro-bits should be replaced in time to ensure the testing accuracy. The testing points of drilling time for each tested side of a rock sample should be gained as many as possible and their average value is taken as the test value of the side. The grade value of each side drillability of the rock sample can be calculated by equation (16) with the test data of drilling time for each side of the rock sample.

Evaluation Method for Anisotropic Drilling Characteristics

Measured depth, m

No. of the cores from CCSD

of the Formation by Using Acoustic Wave Information 155

9 48 4.55 4.34 1.16 38 145 8.57 10.65 0.24 57 197 9.89 10.06 0.89 104 305 10.78 10.90 0.92 143 400 7.82 7.40 1.34 179 504 8.48 8.47 1.01 218 607 8.61 9.14 0.69 252 698 9.52 9.86 0.79 281 775 8.22 9.03 0.57 288 795 9.55 7.31 4.72 304 834 6.06 7.71 0.32 340 925 8.14 8.95 0.57 363 998 8.18 8.64 0.73 373 1027 7.93 8.77 0.56

It is observed clearly from Table 1 and Table 2 that the rock samples from CCSD have the anisotropic characteristics in the rock drillability. The rock drillability perpendicular to the bedding plan is different from that parallel to the bedding plane, whether it is for the roller bit or for the PDC bit. For the roller bit, indices of drillability anisotropy of the rock samples are ranged from 0.23 to 0.94, except the anisotropy indices of rock samples of 143# and 288#, which are 1.03 and 3.86 respectively. The case is similar to the PDC bit; indices of drillability anisotropy of the rock samples are between 0.24 and 0.92, except the anisotropy indices of rock samples of 9#, 143#, 179# and 288#, corresponding to 1.16, 1.34, 1.01 and 4.72, respectively. Generally, the rock drillability perpendicular to the bedding plan is less than that parallel to the bedding plane, so that the formation can be penetrated more easily in the

It is supposed that the formation is the transversely isotropic, and thus the acoustic anisotropy of the formation rock can be expressed by an acoustic anisotropy index ( *I*<sup>v</sup> ):

where *V*av and *V*ah are the acoustic velocities in rock along the directions perpendicular and

With the method of making the ultrasonic pulse penetrating through a rock sample, the acoustic velocities *V*av and *V*ah can be measured in laboratory. The ultrasonic testing

*IVV* v av ah = / (15)

Perpendicular to the bedding plane

Table 2. Experimental results of rock drillability with the PDC bit

direction perpendicular to the bedding plane.

parallel to the bedding plane of the formation respectively.

**3.2 Acoustic anisotropy of rock sample** 

**3.2.1 Definition** 

**3.2.2 Testing method** 

Rock drillability with the PDC bit (*K*dPDC) Rock

Parallel to the bedding plane drillability anisotropy index

Fig. 2. Testing device for rock drillability(Note: 1. Rock sample; 2. micro-bit; 3. cutting tray; 4. turbine rod; 5. lever; 6. weight; 7. meter for measuring depth; 8. bar with thread for adjusting lever; 9. worktable; 10. compaction bar with thread)

### **3.1.4 Experimental result and analysis**

Some testing results of rock drillability for the 14 core samples from CCSD are obtained in laboratory and shown in Table 1 and Table 2.


Table 1. Experimental results of rock drillability with the roller bit

9

10

5 6

Fig. 2. Testing device for rock drillability(Note: 1. Rock sample; 2. micro-bit; 3. cutting tray; 4. turbine rod; 5. lever; 6. weight; 7. meter for measuring depth; 8. bar with thread for

Some testing results of rock drillability for the 14 core samples from CCSD are obtained in

9 48 6.03 6.12 0.94 38 145 9.18 9.86 0.62 57 197 10.29 10.79 0.71 104 305 11.11 11.39 0.82 143 400 8.21 8.17 1.03 179 504 8.70 8.99 0.82 218 607 9.25 10.29 0.49 252 698 10.64 10.78 0.91 281 775 8.78 9.21 0.74 288 795 10.17 8.22 3.86 304 834 7.92 8.57 0.64 340 925 8.89 9.08 0.88 363 998 9.15 10.20 0.48 373 1027 8.12 10.21 0.23

Perpendicular to the bedding plane

Table 1. Experimental results of rock drillability with the roller bit

Rock drillability with the roller bit (*K*dRB) Rock

Parallel to the bedding plane

7 8

adjusting lever; 9. worktable; 10. compaction bar with thread)

**3.1.4 Experimental result and analysis** 

Measured depth, m

No. of the cores from CCSD

laboratory and shown in Table 1 and Table 2.

1

2 3

4

drillability anisotropy index


Table 2. Experimental results of rock drillability with the PDC bit

It is observed clearly from Table 1 and Table 2 that the rock samples from CCSD have the anisotropic characteristics in the rock drillability. The rock drillability perpendicular to the bedding plan is different from that parallel to the bedding plane, whether it is for the roller bit or for the PDC bit. For the roller bit, indices of drillability anisotropy of the rock samples are ranged from 0.23 to 0.94, except the anisotropy indices of rock samples of 143# and 288#, which are 1.03 and 3.86 respectively. The case is similar to the PDC bit; indices of drillability anisotropy of the rock samples are between 0.24 and 0.92, except the anisotropy indices of rock samples of 9#, 143#, 179# and 288#, corresponding to 1.16, 1.34, 1.01 and 4.72, respectively. Generally, the rock drillability perpendicular to the bedding plan is less than that parallel to the bedding plane, so that the formation can be penetrated more easily in the direction perpendicular to the bedding plane.

### **3.2 Acoustic anisotropy of rock sample**

### **3.2.1 Definition**

It is supposed that the formation is the transversely isotropic, and thus the acoustic anisotropy of the formation rock can be expressed by an acoustic anisotropy index ( *I*<sup>v</sup> ):

$$I\_{\rm v} = V\_{\rm av} \int V\_{\rm ah} \tag{15}$$

where *V*av and *V*ah are the acoustic velocities in rock along the directions perpendicular and parallel to the bedding plane of the formation respectively.

### **3.2.2 Testing method**

With the method of making the ultrasonic pulse penetrating through a rock sample, the acoustic velocities *V*av and *V*ah can be measured in laboratory. The ultrasonic testing

Evaluation Method for Anisotropic Drilling Characteristics

mechanism.

No. of the core from CCSD

Measured depth, m

**3.3 Correlations between** *I***r and** *I***v** 

are listed in Table 4.

of the Formation by Using Acoustic Wave Information 157

acoustic anisotropy indices of the rock samples are between 0.85 and 0.98, except the 363# and 373#, which are 0.77 and 0.76 respectively. For the test of the rock samples from CCSD, the rock acoustic velocity perpendicular to the bedding plan is less than that parallel to the bedding plane, as shown in Table 3. The main reason for this difference is that there are many fractures with different scales in the rock sample. When the acoustic wave penetrates through the fractures, the fractures cause a loss of the pulse energy so as to make the acoustic velocity reduce more quickly, on the other hand, the pulse energy is dissipated in the process of propagation. According to some progress in geophysics (Patrick & Richard, 1984), the fractures can play a role in guiding the wave when the elastic wave has propagated in the direction parallel to the bedding plane of the rock sample, and play a role in obstructing the wave when the elastic wave has propagated in the direction perpendicular to the bedding plane. Therefore, the propagation of the acoustic wave penetrating through the rock sample is probably controlled by such a kind of geophysical

plane (*Va*v)

Table 3. Experimental results of acoustic velocities of the rock samples

9 48 4387 4457 0.98 38 145 4442 5120 0.87 57 197 6365 6826 0.93 104 305 5431 5714 0.95 143 400 4410 4928 0.89 179 504 4568 4744 0.96 218 607 4177 4671 0.89 252 698 5805 5990 0.97 281 775 4776 5516 0.87 288 795 5142 5453 0.94 304 834 4392 5129 0.86 340 925 4325 5096 0.85 363 998 3816 4928 0.77 373 1027 3761 4930 0.76

With the experimental data in table 1 to table 3 and the corresponding calculations, it can be found that the rock drillability anisotropy is inherently related to the acoustic anisotropy of the rock samples. Therefore, exponential function, logarithmic function, polynomial function, and linear function, are used to make a regression analysis of the data obtained by experiments. With the matching & extrapolating effects of these regression functions comprehensively considered, exponential function is finally selected as the regression model of correlation between *I*<sup>r</sup> and *I*<sup>v</sup> . The results of regression calculations for the correlations

In Table 4, *I*rRB is denoted as the drillability anisotropy index of the rock sample with a roller bit, *I*vp as the acoustic anisotropy index of P-wave through the rock sample, Δ*K*dRB as

P-wave velocities of the rock samples, m/s Acoustic

the rock sample Perpendicular to bedding

Parallel to bedding plane (*Va*h)

anisotropy index of

system used in laboratory is shown in Fig. 3, in which the ultrasonic transducers can provide a frequency of 0.5 MHz and the butter and honey can be used as its coupling media. The pulse generator can generate electric pulses with a strength range of 1-300 V. The width and iteration frequency of the electric pulse can be adjusted and controlled. During testing, the signal generator makes an electric pulse signal which will touch off the emission end of the energy exchanger to generate ultrasonic pulses. The ultrasonic pulses (acoustic waves) propagating through the rock sample are incepted by the reception end of the energy exchanger. Finally, the propagation time and the signal strength of the ultrasonic pulses (acoustic waves) through the rock sample are logged by a digital memory oscillograph. In order to reduce the errors from the artificial operations, the emission end of the energy exchanger is aimed at its reception end as accurately as possible during testing. Before each test, the ultrasonic testing system should be calibrated using the aluminum rod to ensure the accuracy of the test results. Testing for each point of a rock sample is conducted for three times in the actual testing. The average value of the test data of three times for each point is taken as a final test result for the point of a rock sample. With the test data, the acoustic

$$V = \frac{l}{t - t\_0} \tag{16}$$

where *V* is the acoustic velocity; *l* is length of the rock sample, mm; *t* is propagation time of the acoustic wave, μs; and *t*<sup>0</sup> is delayed time of the testing system, μs.

Fig. 3. The ultrasonic testing system

### **3.2.3 Experimental result and analysis**

velocity may be calculated by the following equation:

Some ultrasonic test results of the 14 core samples from CCSD are logged with the above test method and with the ultrasonic testing system in laboratory, and the rock acoustic velocities shown in Table 3 can be calculated by equation (16).

It can be obviously observed from Table 3 that the rock samples from CCSD are of the rock acoustic anisotropy. The rock acoustic velocity perpendicular to the bedding plan is different from that parallel to the bedding plane. Based on the acoustic velocity data in Table 3, the acoustic anisotropy of the rock samples can be calculated by equation (15). The

system used in laboratory is shown in Fig. 3, in which the ultrasonic transducers can provide a frequency of 0.5 MHz and the butter and honey can be used as its coupling media. The pulse generator can generate electric pulses with a strength range of 1-300 V. The width and iteration frequency of the electric pulse can be adjusted and controlled. During testing, the signal generator makes an electric pulse signal which will touch off the emission end of the energy exchanger to generate ultrasonic pulses. The ultrasonic pulses (acoustic waves) propagating through the rock sample are incepted by the reception end of the energy exchanger. Finally, the propagation time and the signal strength of the ultrasonic pulses (acoustic waves) through the rock sample are logged by a digital memory oscillograph. In order to reduce the errors from the artificial operations, the emission end of the energy exchanger is aimed at its reception end as accurately as possible during testing. Before each test, the ultrasonic testing system should be calibrated using the aluminum rod to ensure the accuracy of the test results. Testing for each point of a rock sample is conducted for three times in the actual testing. The average value of the test data of three times for each point is taken as a final test result for the point of a rock sample. With the test data, the acoustic

0

*t t* <sup>=</sup> <sup>−</sup> (16)

**Computer**

*<sup>l</sup> <sup>V</sup>*

where *V* is the acoustic velocity; *l* is length of the rock sample, mm; *t* is propagation time of

Some ultrasonic test results of the 14 core samples from CCSD are logged with the above test method and with the ultrasonic testing system in laboratory, and the rock acoustic

**Rock sample Printer**

It can be obviously observed from Table 3 that the rock samples from CCSD are of the rock acoustic anisotropy. The rock acoustic velocity perpendicular to the bedding plan is different from that parallel to the bedding plane. Based on the acoustic velocity data in Table 3, the acoustic anisotropy of the rock samples can be calculated by equation (15). The

velocity may be calculated by the following equation:

Fig. 3. The ultrasonic testing system

**3.2.3 Experimental result and analysis** 

velocities shown in Table 3 can be calculated by equation (16).

the acoustic wave, μs; and *t*<sup>0</sup> is delayed time of the testing system, μs.

**Ultrasonic generator** 

acoustic anisotropy indices of the rock samples are between 0.85 and 0.98, except the 363# and 373#, which are 0.77 and 0.76 respectively. For the test of the rock samples from CCSD, the rock acoustic velocity perpendicular to the bedding plan is less than that parallel to the bedding plane, as shown in Table 3. The main reason for this difference is that there are many fractures with different scales in the rock sample. When the acoustic wave penetrates through the fractures, the fractures cause a loss of the pulse energy so as to make the acoustic velocity reduce more quickly, on the other hand, the pulse energy is dissipated in the process of propagation. According to some progress in geophysics (Patrick & Richard, 1984), the fractures can play a role in guiding the wave when the elastic wave has propagated in the direction parallel to the bedding plane of the rock sample, and play a role in obstructing the wave when the elastic wave has propagated in the direction perpendicular to the bedding plane. Therefore, the propagation of the acoustic wave penetrating through the rock sample is probably controlled by such a kind of geophysical mechanism.


Table 3. Experimental results of acoustic velocities of the rock samples
