CN111794689B - Design method of sound insulation structure and drill collar - Google Patents
Design method of sound insulation structure and drill collar Download PDFInfo
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- CN111794689B CN111794689B CN202010714715.9A CN202010714715A CN111794689B CN 111794689 B CN111794689 B CN 111794689B CN 202010714715 A CN202010714715 A CN 202010714715A CN 111794689 B CN111794689 B CN 111794689B
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- 238000009413 insulation Methods 0.000 title claims abstract description 46
- 238000000034 method Methods 0.000 title claims abstract description 42
- 238000013461 design Methods 0.000 title claims abstract description 11
- 230000004323 axial length Effects 0.000 claims abstract description 29
- 238000001228 spectrum Methods 0.000 claims description 17
- 230000003595 spectral effect Effects 0.000 claims description 5
- 238000004088 simulation Methods 0.000 claims description 4
- 239000012530 fluid Substances 0.000 claims description 3
- 238000010183 spectrum analysis Methods 0.000 claims description 3
- 238000005553 drilling Methods 0.000 description 14
- 238000002955 isolation Methods 0.000 description 4
- 230000003628 erosive effect Effects 0.000 description 3
- 238000005259 measurement Methods 0.000 description 3
- 230000008569 process Effects 0.000 description 3
- 238000005516 engineering process Methods 0.000 description 2
- 230000007774 longterm Effects 0.000 description 2
- 238000004519 manufacturing process Methods 0.000 description 2
- 230000001902 propagating effect Effects 0.000 description 2
- 239000002002 slurry Substances 0.000 description 2
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 2
- 238000010146 3D printing Methods 0.000 description 1
- 230000015572 biosynthetic process Effects 0.000 description 1
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- 230000006835 compression Effects 0.000 description 1
- 238000007906 compression Methods 0.000 description 1
- 230000007797 corrosion Effects 0.000 description 1
- 238000005260 corrosion Methods 0.000 description 1
- 230000003247 decreasing effect Effects 0.000 description 1
- 230000006870 function Effects 0.000 description 1
- 230000005484 gravity Effects 0.000 description 1
- 239000012212 insulator Substances 0.000 description 1
- 230000001788 irregular Effects 0.000 description 1
- 230000009191 jumping Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
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- 230000005404 monopole Effects 0.000 description 1
- 230000003287 optical effect Effects 0.000 description 1
- 230000000737 periodic effect Effects 0.000 description 1
- 239000003208 petroleum Substances 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
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- 102220222088 rs781696878 Human genes 0.000 description 1
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- E—FIXED CONSTRUCTIONS
- E21—EARTH OR ROCK DRILLING; MINING
- E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B17/00—Drilling rods or pipes; Flexible drill strings; Kellies; Drill collars; Sucker rods; Cables; Casings; Tubings
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- E—FIXED CONSTRUCTIONS
- E21—EARTH OR ROCK DRILLING; MINING
- E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B47/00—Survey of boreholes or wells
- E21B47/12—Means for transmitting measuring-signals or control signals from the well to the surface, or from the surface to the well, e.g. for logging while drilling
- E21B47/14—Means for transmitting measuring-signals or control signals from the well to the surface, or from the surface to the well, e.g. for logging while drilling using acoustic waves
- E21B47/18—Means for transmitting measuring-signals or control signals from the well to the surface, or from the surface to the well, e.g. for logging while drilling using acoustic waves through the well fluid, e.g. mud pressure pulse telemetry
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- Environmental & Geological Engineering (AREA)
- Fluid Mechanics (AREA)
- General Life Sciences & Earth Sciences (AREA)
- Geochemistry & Mineralogy (AREA)
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Abstract
The invention discloses a design method of a sound insulation structure and a drill collar, wherein the method comprises the following steps: acquiring a drill collar wave signal sent by a sound source with a source distance TR received by a drill collar without a grooved structure; determining the number n of cavities to be arranged between the inner wall and the outer wall of the drill collar without the grooved structure according to the drill collar wave signals and the source distance; the cavities are arranged along the axial direction and are of hollow structures; determining the axial length of each cavity in the n cavities according to the number n of the cavities; wherein the distance between every two adjacent cavities is 2 times of the larger axial length of the two adjacent cavities.
Description
Technical Field
The disclosure relates to the technical field of oil logging, in particular to a design method of a sound insulation structure and a drill collar.
Background
The drill collar is located at the lowest part of the drill string and is the main component of the lower drilling assembly. The drill rod is mainly characterized by large wall thickness (generally 38-53mm, which is equivalent to 4-6 times of the wall thickness of the drill rod), and large gravity and rigidity. The drill collar has the main functions of applying bit pressure to the drill bit, ensuring necessary strength under a compression condition, reducing vibration, swing, jumping and the like of the drill bit, enabling the drill bit to work stably and controlling well deviation.
When the acoustic logging-while-drilling instrument works, a sound source excites a guided wave which propagates along the drill collar. If the sound insulation treatment is not carried out, the drill collar wave can dominate in the measurement signal, so that the measurement of the formation wave velocity is seriously interfered. To date, there are two main acoustic isolation techniques while drilling, one being a method of periodic notching between the transmitting and receiving transducers to block the wave propagating along the drill collar, e.g., the inner, outer or both surfaces of the drill collar can be notched simultaneously; the other design scheme is that the effective sound insulation stop band is widened by combining drill collars with different cross-sectional areas and different inherent stop bands, wherein the length of the drill collars is larger than the wavelength of sound waves, and for example, the sound insulation is realized by combining variable-diameter drill collars with the length of the drill collars being larger than the wavelength.
The water hole of the acoustic logging-while-drilling instrument is used as a channel for slurry circulation, and the slurry is always circulated in the whole drilling process. When the mud meets irregular abrupt cross sections (such as grooves on the inner wall of the drill collar and reducing positions on the inner wall of the drill collar), eddy currents can be generated, and long-term erosion can cause corrosion or cracks to be generated on sound insulation positions of the drill collar of the acoustic logging while drilling instrument. The drill collar strength is weakened due to long-term erosion, and drilling safety accidents can be caused in severe cases. In addition, the acoustic wave while drilling instrument is expensive in manufacturing cost, and great economic loss is caused because the acoustic wave while drilling instrument cannot be repaired when the erosion damage is caused.
Disclosure of Invention
The embodiment of the disclosure provides a design method of a sound insulation structure, which is applied to a drill collar without a groove structure and comprises the following steps:
acquiring a drill collar wave signal transmitted by a sound source with a source distance TR received by a drill collar without a groove structure;
determining the number n of cavities to be arranged between the inner wall and the outer wall of the drill collar without the grooved structure according to the drill collar wave signals and the source distance; wherein n is a natural number; the cavities are arranged along the axial direction and are of hollow structures;
determining the axial length of each cavity in the n cavities according to the number n of the cavities;
wherein the distance between every two adjacent cavities is 2 times of the larger axial length of the two adjacent cavities.
In an exemplary embodiment, the method further comprises the following features:
determining the number n of cavities to be arranged between the inner wall and the outer wall of the drill collar without the grooved structure according to the drill collar wave signals and the source distance, and the method comprises the following steps:
calculating a frequency spectrum curve of the drill collar wave signal according to the drill collar wave signal;
determining a minimum sound insulation frequency fmin and a maximum sound insulation frequency fmax according to the frequency spectrum curve;
determining the axial maximum length L _ max and the axial minimum length L _ min of the cavity according to fmin and fmax;
and determining the number n of the cavities according to the source distance TR, the axial maximum length and the axial minimum length of the cavities.
In an exemplary embodiment, the method further comprises the following features:
the frequency spectrum curve of the drill collar wave signal is calculated according to the drill collar wave signal, and the method comprises the following steps:
and carrying out frequency spectrum analysis on the drill collar wave signals, and carrying out FFT to obtain the frequency spectrum curve.
In an exemplary embodiment, the method further comprises the following steps:
the determining of the minimum sound insulation frequency fmin and the maximum sound insulation frequency fmax according to the spectrum curve comprises:
and determining the frequencies corresponding to the two maximum amplitude values on the frequency curve as fmin and fmax.
In an exemplary embodiment, the method further comprises the following features:
determining the maximum axial length L _ max and the minimum axial length L _ min of the cavity according to fmin and fmax, comprising:
l _ max and L _ min are calculated according to the following equations:
L_max＝v/4fmin；L_min＝v/4fmax；
wherein v represents the propagation velocity of the collar wave signal.
In an exemplary embodiment, the method further comprises the following features:
determining the number n of the cavities according to the source distance TR, the axial maximum length and the axial minimum length of the cavities, and comprising the following steps:
calculating the number n of cavities according to the following formula:
in an exemplary embodiment, the method further comprises the following features:
determining the axial length of each cavity in the n cavities according to the fmin, the fmax and the number n of the cavities, and the method comprises the following steps:
the axial length L of each cavity is determined as followsi：
fstep＝(fmax-fmin)/n；
Wherein i is an integer, and 0< i is not more than n.
In an exemplary embodiment, the method further comprises the following features:
the method for acquiring the drill collar wave signal sent by the sound source with the TR source distance received by the drill collar without the grooved structure comprises the following steps:
by establishing a three-dimensional finite difference model or a finite element model of the drill collar without the grooved structure in a fluid domain, a drill collar wave signal received by the numerical simulation three-dimensional finite difference model or the finite element model is used as a drill collar wave signal sent by a sound source with a source distance TR received by the drill collar without the grooved structure.
In an exemplary embodiment, the method further comprises the following features:
the cavity is annular in shape.
The disclosure also provides a drill collar, which comprises a drill collar without a groove structure and a sound insulation structure;
the sound insulation structure comprises a plurality of cavities, wherein the cavities are hollow structures positioned between the inner wall and the outer wall of the drill collar without the notch structure;
the cavities are axially arranged between the inner wall and the outer wall of the drill collar without the grooved structure, and the distance between every two adjacent cavities is 2 times of the larger axial length of the two adjacent cavities;
the number n of the cavities and the axial length of each cavity are determined according to a design method of the sound insulation structure.
Drawings
Fig. 1 is a flowchart of a method for designing a sound insulation structure according to an embodiment of the present disclosure.
FIG. 2 is an example of a spectral plot of a drill collar wave having a source spacing TR in accordance with an embodiment of the present disclosure.
FIG. 3 is an example of a logging device according to an embodiment of the present disclosure.
Fig. 4a is an example of a time-domain waveform of a sound insulation structure according to an embodiment of the disclosure.
Fig. 4b is an example of a spectral curve of a sound insulation structure according to an embodiment of the present disclosure.
Fig. 4c is an example of a sound attenuation curve of a sound insulating structure according to an embodiment of the present disclosure.
FIG. 5 is an example of a drill collar that is an embodiment of the present disclosure.
Detailed Description
To make the objects, technical solutions and advantages of the present disclosure more apparent, embodiments of the present disclosure will be described in detail below with reference to the accompanying drawings. It should be noted that the embodiments and features of the embodiments in the present application may be arbitrarily combined with each other without conflict.
Fig. 1 is a flowchart of a design method of a sound insulation structure according to an embodiment of the present disclosure, where the sound insulation structure belongs to a drill collar, the drill collar further includes a drill collar without a grooved structure, and the sound insulation structure includes a cavity disposed between an inner wall and an outer wall of the drill collar without the grooved structure.
As shown in fig. 1, the method for designing a sound insulation structure of the present embodiment includes:
s11, obtaining a drill collar wave signal sent by a sound source with a source distance TR received by the drill collar without the grooved structure.
S12, determining the number n of cavities to be arranged between the inner wall and the outer wall of the drill collar without the grooved structure according to the drill collar wave signals and the source distance, wherein the cavities are arranged along the axial direction and are of a hollow structure.
S13, determining the axial length of each cavity in the n cavities according to the number n of the cavities, wherein the distance between every two adjacent cavities is 2 times of the larger axial length of the two adjacent cavities.
The drill collar without the grooving structure refers to a drill collar with the inner wall and the outer wall of the drill collar without grooves and diameter change.
In an exemplary embodiment, the n cavities may be axially arranged in an order of increasing or decreasing axial length; in other exemplary embodiments, the n cavities may be axially out of order.
In an exemplary embodiment, determining the number n of cavities to be arranged between the inner wall and the outer wall of the drill collar without the grooved structure according to the drill collar wave signal and the source distance comprises:
calculating a frequency spectrum curve of the drill collar wave signal according to the drill collar wave signal;
determining a minimum sound insulation frequency fmin and a maximum sound insulation frequency fmax according to the frequency spectrum curve;
determining the axial maximum length L _ max and the axial minimum length L _ min of the cavity according to fmin and fmax;
and determining the number n of the cavities according to the source distance TR, the axial maximum length and the axial minimum length of the cavities. Wherein n is a natural number.
In an exemplary embodiment, the minimum and maximum sound isolation frequencies may be determined in other ways; or the axial maximum and minimum lengths of the cavities may be determined in other ways; such as by empirical values, simulation, measurement, etc.
In an exemplary embodiment, said calculating a spectral profile of said collar wave signal from said collar wave signal comprises:
and carrying out frequency spectrum analysis on the drill collar wave signals, and carrying out FFT to obtain the frequency spectrum curve.
The determining of the minimum sound insulation frequency fmin and the maximum sound insulation frequency fmax according to the frequency spectrum curve comprises the following steps:
and determining the frequencies corresponding to the two maximum amplitude values on the frequency curve as fmin and fmax.
The acoustic isolation frequency here is the frequency that prevents acoustic signals from propagating on the drill collar.
In an exemplary embodiment, determining the maximum axial length L _ max and the minimum axial length L _ min of the cavity from fmin and fmax comprises:
l _ max and L _ min are calculated according to the following equations:
L_max＝v/4fmin；L_min＝v/4fmax；
wherein v represents the propagation velocity of the collar wave signal, typically 5900 m/s.
In an exemplary embodiment, the axial maximum and minimum lengths may be calculated using a modified form of the above equation, or other equations.
In an exemplary embodiment, determining the number of cavities n based on the source distance TR, the maximum axial length and the minimum axial length of the cavities comprises:
calculating the number n of cavities according to the following formula:
wherein the content of the first and second substances,
indicating that 2 × TR/(L _ min + L _ max) is rounded down, e.g. to
The result of rounding down was 12.
In an exemplary embodiment, the number of cavities may be calculated using a modified equation of the above equation, or other equations.
In an exemplary embodiment, determining the axial length of each of the n cavities based on fmin and fmax and the number of cavities n comprises:
the axial length L of each cavity is determined as followsi：
fstep＝(fmax-fmin)/n；
Wherein i is an integer, and 0< i is not more than n.
In one exemplary embodiment, acquiring a drill collar wave signal from an acoustic source having a source distance TR received by a drill collar without a grooved structure, comprises:
by establishing a three-dimensional finite difference model or a finite element model of the drill collar without the grooved structure in a fluid domain, a drill collar wave signal received by the numerical simulation three-dimensional finite difference model or the finite element model is used as a drill collar wave signal sent by a sound source with a source distance TR received by the drill collar without the grooved structure.
In an exemplary embodiment, the cavity is annular in shape; the ring shape is easy to process during production. In other embodiments, the cavity may be other shapes, such as oval, hexagonal, etc.
Embodiments of the present disclosure are described in detail below with reference to specific design examples.
Assuming that the acoustic source distance TR of the acoustic drilling tool is 2000m, the outer diameter D of the drill collar is 6.75in (in represents inch, 1 inch is 25.4mm), and the inner diameter D of the water hole is 3.3 in. Firstly, a three-dimensional finite difference algorithm is adopted to theoretically simulate a theoretical waveform curve (shown in figure 2) of a drill collar without a notch, so that two sound insulation frequencies corresponding to the maximum value of the frequency spectrum capable of covering a sound insulation stop band are obtained, wherein fmin is 6.6kHz, and fmax is 16.3 kHz. From the sound insulation formula L v/4f, the axial length L _ max of the maximum and minimum annular cavities is 223mm, L _ min is 90 mm. Thereby determining the number n of the annular cavities, 4000/313, 12.
And determining the sound insulation frequency step length fstep to be 0.808kHz according to the formula fstep to be (fmax-fmin)/n. And dividing the sound insulation interval at equal intervals according to the frequency spectrum step to obtain f _0, f _1, … and f _ n. The values are:
f_0＝6.6kHz，f_1＝7.408kHz，f_2＝8.216kHz，f_3＝9.024kHz，f_4＝9.832kHz，f_5＝10.64kHz，f_6＝11.448kHz，f_7＝12.256kHz，f_8＝13.064kHz，f_9＝13.872kHz，f_10＝14.68kHz，f_11＝15.488kHz，f_12＝16.296kHz
calculating the axial length of the n annular cavities according to a sound insulation formula L ═ v/4 f:
L0＝223mm，L1＝199mm，L2＝180mm，L3＝163mm，L4＝150mm，L5＝139mm，L6＝129mm，L7＝120，L8＝113mm，L9＝106mm，L10＝100mm，L11＝95mm，L12＝90mm。
according to the method, a sound-insulation logging-while-drilling device with the outer diameter of 6.75 inches (shown in figure 3) is designed, the device comprises a monopole transmitting transducer T, n annular cavities are formed in a drill collar, and M receiving transducers (R1, R2, … and Rm) are adopted as a receiving device.
In petroleum drilling, acoustic logging-while-drilling instruments (such as 4.75in, 6.75in, 8in and 9in) with different outer diameter sizes are generally adopted, and the method is suitable for designing the acoustic insulator while drilling of drill collars with different sizes.
The processing mode of the cavity structure in the drill collar can be two, one is to open a groove on the outer surface of the drill collar and then carry out welding technology on the outer surface; and the other one adopts the 3D printing technology to directly process the drill collar.
Fig. 4a is an example of a time domain waveform of a numerically simulated non-grooved and sound insulating structure according to an embodiment of the disclosure. In fig. 4a, the black solid line is the waveform of the drill collar without the notch, and the black dotted line is the waveform of the drill collar designed according to the present disclosure. FIG. 4b is a spectrum curve example of the sound insulation structure according to the embodiment of the present disclosure, the black solid line is a spectrum curve of a drill collar without a notch, the black dotted line is a spectrum curve of a drill collar designed by the method, and compared with the visible inherent stop band of a drill collar wave of a drill collar without a notch, the inherent stop band of the drill collar wave is 11-14 kHz, and the sound insulation stop band of the drill collar designed by the present disclosure is widened to 8-15 kHz. Fig. 4c is an example of a sound attenuation curve of the sound insulation structure according to the embodiment of the disclosure, and it can be seen from the graph that the maximum sound insulation amount can reach-28 dB/m in a sound insulation stop band of a drill collar wave, compared with a relative sound attenuation curve of a drill collar without a notch.
FIG. 5 is an example of a drill collar of an embodiment of the present disclosure, as shown in FIG. 5, including a non-grooved structure drill collar and a sound isolation structure;
the sound insulation structure comprises a plurality of cavities, wherein the cavities are hollow structures positioned between the inner wall and the outer wall of the drill collar without the notch structure;
the cavities are axially arranged between the inner wall and the outer wall of the drill collar without the grooved structure, and the distance between every two adjacent cavities is 2 times of the larger axial length of the two adjacent cavities;
the number n of the cavities and the axial length of each cavity are determined according to the design method of the sound insulation structure in the embodiment of the disclosure.
It will be understood by those skilled in the art that all or part of the steps of the above methods may be implemented by instructing the relevant hardware through a program, and the program may be stored in a computer readable storage medium, such as a read-only memory, a magnetic or optical disk, and the like. Alternatively, all or part of the steps of the above embodiments may be implemented using one or more integrated circuits. Accordingly, each module/unit in the above embodiments may be implemented in the form of hardware, and may also be implemented in the form of a software functional module. The present disclosure is not limited to any specific form of combination of hardware and software.
The foregoing is only a preferred embodiment of the present disclosure, and there are certainly many other embodiments of the present disclosure, which will become apparent to those skilled in the art from this disclosure and it is therefore intended that various changes and modifications can be made herein without departing from the spirit and scope of the disclosure as defined in the appended claims.
Claims (10)
1. A design method of a sound insulation structure is applied to a drill collar without a groove structure and comprises the following steps:
acquiring a drill collar wave signal sent by a sound source with a source distance TR received by a drill collar without a grooved structure;
determining the number n of cavities to be arranged between the inner wall and the outer wall of the drill collar without the grooved structure according to the drill collar wave signals and the source distance; wherein n is a natural number; the cavities are arranged along the axial direction and are of hollow structures;
determining the axial length of each cavity in the n cavities according to the number n of the cavities;
wherein the distance between every two adjacent cavities is 2 times of the larger axial length of the two adjacent cavities.
2. The method of claim 1, determining from the collar wave signals and source spacing, a number n of cavities to be disposed between an inner wall and an outer wall of the non-grooved structure collar, comprising:
calculating a frequency spectrum curve of the drill collar wave signal according to the drill collar wave signal;
determining a minimum sound insulation frequency fmin and a maximum sound insulation frequency fmax according to the frequency spectrum curve;
determining the axial maximum length L _ max and the axial minimum length L _ min of the cavity according to fmin and fmax;
and determining the number n of the cavities according to the source distance TR, the axial maximum length and the axial minimum length of the cavities.
3. The method of claim 2, said calculating a spectral profile of said collar wave signal from said collar wave signal, comprising:
and carrying out frequency spectrum analysis on the drill collar wave signals, and carrying out FFT to obtain the frequency spectrum curve.
4. The method of claim 2, wherein determining a minimum soundproofing frequency fmin and a maximum soundproofing frequency fmax from the spectral curves comprises:
and determining the frequencies corresponding to the two maximum amplitude values on the frequency curve as fmin and fmax.
5. The method of claim 2, determining an axially maximum length L _ max and an axially minimum length L _ min of said cavity from said fmin and fmax, comprising:
l _ max and L _ min are calculated according to the following equations:
L_max＝v/4fmin；L_min＝v/4fmax；
wherein v represents the propagation velocity of the collar wave signal.
6. The method of claim 2, determining the number of cavities, n, from the source distance, TR, the axially maximum length, and the axially minimum length of the cavities, comprising:
calculating the number n of cavities according to the following formula:
7. the method of claim 2, determining an axial length of each of the n cavities based on the fmin and fmax and the number of cavities n, comprising:
the axial length L of each cavity is determined as followsi：
fstep＝(fmax-fmin)/n；
Wherein i is an integer, and 0< i is not more than n.
8. The method as claimed in claim 1, wherein obtaining the drill collar wave signals from the acoustic source with the source distance TR received by the drill collar without the grooved structure comprises:
by establishing a three-dimensional finite difference model or a finite element model of the drill collar without the grooved structure in a fluid domain, a drill collar wave signal received by the numerical simulation three-dimensional finite difference model or the finite element model is used as a drill collar wave signal sent by a sound source with a source distance TR received by the drill collar without the grooved structure.
9. The method of claim 1, comprising:
the cavity is annular in shape.
10. A drill collar, characterized by:
the drill collar comprises a drill collar without a notch structure and a sound insulation structure;
the sound insulation structure comprises a plurality of cavities, wherein the cavities are hollow structures positioned between the inner wall and the outer wall of the drill collar without the notch structure;
the cavities are axially arranged between the inner wall and the outer wall of the drill collar without the grooved structure, and the distance between every two adjacent cavities is 2 times of the larger axial length of the two adjacent cavities;
wherein the number n of cavities and the axial length of each cavity are determined according to the method of any one of claims 1-9.
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| CN103352692B (en) * | 2013-07-31 | 2015-04-15 | 中国石油大学(华东) | Optimized design method of reducing sonic system sound insulator of acoustic logging-while-drilling drill collar |
| CN105257282A (en) * | 2015-09-28 | 2016-01-20 | 中国科学院声学研究所 | Acoustic logging-while-drilling transmitting unit and device thereof |
| CN105888655B (en) * | 2016-05-05 | 2021-07-06 | 中国海洋石油集团有限公司 | While-drilling sound wave sound insulation structure |
| CN207004508U (en) * | 2017-07-20 | 2018-02-13 | 西南石油大学 | A kind of acoustic logging-while-drillidevice device |
| CN209398415U (en) * | 2018-11-29 | 2019-09-17 | 中国科学院声学研究所 | A kind of acoustic logging while drilling acoustic isolater of depth-graded cutting |
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