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1、精品论文The Research on Teeth Invade Bottomhole Rock Basing onUnified Strength TheoryLI Wei, YAN Tie, Li Siqi5(Petroleum Engineering, Northeast Petroleum University, Heilongjiang Daqing 163318) Abstract: Considering the condition of the bottom hole pressure, basing on unified strength theory to analyze
2、the mechanical process of teeth invade rock, build bottomhole rock intrusive equation with unified strength parameters and give intrusive coefficient without the impact of axial load, invasion depth and bit angle. The equation considers the impacts of intermediate stress on intrusive coefficient.10T
3、he results of the equation and Mohr-Coulomb strength theory are identical when b equals to 0.Analyze the impact of angle of internal friction, fluid column pressure, pore pressure and bit angle onintrusive coefficient. The results show that with b, angle of internal friction and bit angle, fluid col
4、umn pressure and pore pressure increasing, the intrusive coefficient increases, increases exponentially, increases linearly and decreases linearly respectively.15Keywords: Unified strength theory; bit tooth; intrusive coefficient; drilling engineering0IntroductionThe teeth of cone bit impact bottomh
5、ole rock under drill pressure is one of basic characteristics in its rock breaking mechanism1-2. Physical and mechanical properties of20bottomhole rock change significantly under joint action of overlying formation pressure, horizontal stress, pore pressure, fluid column pressure and so on. The mech
6、anism which the teeth of cone bit invade bottomhole rock is still not very clear3-5.At present, the research at home and abroad is mainly about its invasive process by single shear strength theory (Mohr-Coulomb Formula) under atmospheric conditions in door, they lack25of the analysis under high pres
7、sure conditions in bottom2, 6, 7. Mohr-Coulomb Formula ignoredthe influence of intermediate principal stress, it is bound to make the calculation results of invasion deep of bottom rock deviate from the actual value. Yu Maohong professor started to study the strength theory systematically in the 196
8、0s and finally proposed a new unified strength theory8-9. The unified strength theory covers single shear and double shear strength theory, forms30a set of complete theoretical system, and has many successful application examples in domestic and foreign10-12. In this paper, based on unified strength
9、 theory, study the teeth invade bottomhole rock problem. The study has important significance to rich mechanical rock breaking theory and to promote the researches on rock breaking mechanism of cone bit under complex drilling conditions in deep formation.351The unified strength theory in form of Moh
10、r-Coulomb1.1The unified strength theoryBased on the double shear unit, professor Yu Maohong has established a new theory which is suitable for geotechnical material. It is defined as when the influence function reaches a certain limit value, the material begins to be damaged. The influencing functio
11、n is about two large shear40stress and normal stress which act on double shear cell cube. The expressions in principal stressform of unified strength theory are,- 9 -F = 1 (b 2 + 3 )1+ b= t ， 1 + 321 + （1a）Brief author introduction:LI Wei,（1979-)，M， Eng.D，Associate Professor, Main Research Oil & Gas
12、 WellEngineering Mechanics. E-mail: cyypingF = 1 + b 2 1+ b3= t ， 1 + 321 + （1b）Where: b is the effect coefficient of intermediate principal shear stress, is tensile and45compressive intensity ratio of rock material and tis uniaxial tensile strength, MPa. c0is thecohesive force. 0is the angle of int
13、ernal friction. They are strength indexes which aredetermined by Mohr-Coulomb test. The relationship of , t = 1 + sin 01 sin0andc0 , 0is as follows.（2a）t = 2c0 cos01 sin0（2b）50By equation (1) and equation (2), we can get principal stress expressions which represented by rock strength parameters.F =
14、b 2 + 3 1+ sin0= 2c0 cos0 ， 1 + 3 1 31 1 + b1 sin01 sin0 2 sin 02 2（3a）F = 1 + b 2 1 + b 31 + sin01 sin0= 2c cos01 sin0， 2 1 + 32 1 32sin 0（3b）1.2Mohr-Coulomb form55Introduce the factor m, = m (22 1+ 3 )（4）From equation (3) and equation (4), we can get as follows. 1 3 = ( 1 + 3 ) sin 1 + 2c1 cos 1 ，
15、 1 3 = ( 1 + 3 ) sin 2 + 2c2 cos 2 ，m 1m 1（5a）（5b）60Where:sin1= b(1 m) + (2 + b + bm) sin 02 + b + b sinc1 =2(1 + b)c0 cos0(2 + b + b sin )cos0 , 0 1 ,sin2= b(m 1) + (2 + b + bm) sin02 + b b sinc2 =2(1 + b)c0 cos0(2 + b b sin )cos0 , 0 1 ,1 、 c1 、2 、 c2 are unified strength parameters.Then get the u
16、nified strength theory formula. It is consistent with strength criterion in form.Equation (5) has considered the impact of the middle shear stress on rock strength.652The intrusion equation in the process of teeth invading bottomhole rock2.1Mechanics analysis in the process of teeth invading bottomh
17、ole rockThe process of teeth invading rock under drill pressure in drilling engineering can besimplified as Figure 1. The teeth with 2angle invades rock under the effect of axial load P and70bottomhole rock is under the effect of horizontal crustal stress Hh , drilling fluid columnpressurePm and por
18、e pressurePP . Load P on teeth blade surface forms shear force 1 andnormal force 1 . When the load increases to a certain critical value, the rock on the side of theblade surface represents a shear failure. The included angle of shear failure surface and bottomsurface is .75Figure1. The force analys
19、is of a single tooth invading bottomhole rockThe normal stress 1of rock are,and shear stress 1which tooth blade surface acts on shear surface80=11 =Pi +1 sin2hi +1 sinPi +1 sinsin( + )cos( + )（6）（7）2hi +1 sinThe normal stress 2and shear stress 2which all kinds of pressure in bottom act onshear failu
20、re surface of rock are, = ( Hh + Pm ) ( Hh Pm ) cos 2 P2 2 2 p = ( Hh Pm ) sin 2852 2（8）（9）Then the total normal stress and the total shear stress on shear failure surface ofbottomhole rock are,902.2Intrusion equation = 1 + 2 = 1 + 2（10）（11）From equation (5), we can get failure condition of rock on
21、blade side is, tan = CWhere: C 、 are unified strength parameters of bottomhole rock on blade side.（12）From equation (10), (11) and (12), we can get,95 =pi +1sin cos( + + ) + ( Hh Pm ) (sin 2 + cos 2 tan ) 2hi +1sin cos (Hh+ Pm ) P2 p2 tan （13） is the function of . Derive equation (13) and let it equ
22、al to zero. We can get, = + （14）4 2 is maximum value now. By analyzing equation (14), we can know shear failure100surface of bottomhole rock appears on the surface with the dip angle + first. When4 2 + is less than90 , the rock can occur shear crushing; When + is greater than90 ,rock is in a state o
23、f comprehensive compression, leap forward type intrusion doesnt occur. From equation (13) and (14), we can get,105pi +1 =hi +14C sin cos ( Hh Pm ) sin 2 + (2 Hh + 2Pm 4Pp ) sin sin 1 sin( + ) K （15）It is shown that if the horizontal stress of formation, fluid column pressure and pore pressure are co
24、nstant, the ratio of load and invasion depth of teeth in every leap forward is a constant K. Itis the invasion coefficient in bottom. From equation (5) and (15), we can get,110Where:K = 4c1 sin cos1 ( Hhpi +1 = Khi +1 Pm ) sin 2 + (2 Hh+ 2Pm（16）， 4Pp ) sin sin 1m 11151201 sin( + 1 )4c sin cos ( P )
25、sin 2 + (2 + 2P 4P ) sin sin 22HhmHhmp2m 1K =，1 sin( + 2 )Equation (16) is the intrusion equation of teeth invading rock in bottom. It is also theintrusion equation of atmospheric condition if remove the environmental impact of bottomhole pressure. The invasion coefficient isnt affected by axial loa
26、d, invasion depth and other parameters. It is an important constant to describe the intrusion resistance ability of bottomhole rock.3Indoor experiments and result analysis3.1Experimental device and methodThe experimental device is mechanical rock breaking simulation and analysis system which is deve
27、loped by efficient rock breaking drilling technology laboratory, as shown in Figure 2. The main functions of device include intrusion crushing experiments with different rate of loading and different shape heads, cutting various alloy teeth experiments with different load and rotation speed and rota
28、ry rock breaking experiments with various sizes of drill bits. The range of axial loadis 030 kN, the range of rotation speed is 0500 r/min, the stroke of rock breaking tool is 0400mm. The size range of rock sample is 0300mm0300mm0400mm.125Figure 2. Mechanical rock breaking simulationand analysis sys
29、temFigure 3. Use chisel teeth in intrusion experiment130135140145There are two kinds of teeth invading experiments. One is under the normal temperature and pressure, the other is under the confining pressure. Teeth are chisel and bit angle is divided intothree kinds, they are 10、15and 、20. In oil an
30、d gas well engineering, sandstone is commondrilling formation, so it is selected as sample lithology. Its physical and mechanical parameters are as follows. Volume density is 2.54g/cm3, elastic modulus is 9.8103MPa, compressing strength is 72.62MPa, cohesive force is 8.13MPa and angle of internal fr
31、iction is 23. The testingsurface of sample is polished by grinding wheel before the experiment. The size of sample is determined according to the experimental needs.3.2The experimental results and analysisWhen bit angle is 10, horizontal stress is 25.4MPa, fluid column pressure is 11.5MPa and pore p
32、ressure is 10MPa. In this condition, draw the theoretical analysis curves of intrusion coefficient and angle of internal friction, as shown in Figure 4. The intrusion coefficient is increasing with the angle of internal friction exponentially with different b value. Different b value is correspondin
33、g to different invasion coefficient. It increases with the increasing of b value. This is because inthe unified strength theory, different b valuerepresents different strength theories. Whenb=0, the strength theory is Mohr-Coulomb. ItFigure 4. The curve between intrusion coefficient andangle of inte
34、rnal friction150155is in the lower limit of strength theory and the intrusion coefficient is small. When b=1, the strength theory is double shear strength theory. It is in the upper limit strength theory and the intrusion coefficient is big. The greater the invasion coefficient is, the greater the d
35、ifficulty of teeth invading rock is, the greater the invasion resistance strength is. In the same angle of internal friction, the invasion coefficient in bottom with b=0 is more than it in normal pressure with b=1. This shows that when the axial load is the same, the invasion depth in bottom is obvi
36、ously less than it in normal pressure. It means that the pressure environment in bottomhole will greatly reduce the penetration rate of cone bit.In order to further explain the influence of pressure environment in bottomhole on intrusion160165170coefficient, analyze the relation curve of fluid colum
37、n pressure, pore pressure and intrusion coefficient, as shown in Figure 5 and Figure 6. At this time, the bit angle is 10 and the horizontal stress is 25.4MPa. Figure 5 shows that intrusion coefficient increases and invasiondepth decreases with the increasing of fluid column pressure in borehole. Th
38、is is consistent with the actual drilling conditions. When the fluid column pressure increases, the chip hold down effect of bottomhole rock is obvious, the strength of rock increases and penetration rate declined obviously. Based on the effective stress principle, skeleton stress will decline with
39、the increase of pore pressure. The reduction of compaction degree of rock will improve the rock breaking efficiency and penetration rate of cone bit. The theoretical analysis and experimental values are both consistent with the fact in Figure 6. When b=0, the theoretical intrusion coefficient value
40、is minimum. When b=1, it is maximum. The experimental values in Figure 5 and Figure 6 is mostclose to but slightly higher than the theoretical value of the intrusion coefficient with b=0.Figure 5. The curve between intrusion coefficient andfluid column pressureFigure 6. The curve between intrusion c
41、oefficient andpore pressureIn order to analyze the influence of teeth on intrusion coefficient, do a single tooth intrusion experiment respectively in normal temperature and pressure and in bottomhole, as shown inFigure 7 and Figure 8.175Figure 7. The curve between intrusion coefficient and bit angl
42、e in doorFigure 8. The curve between intrusion coefficient and bit angle in bottomholeThe larger the bit angle is, the blunter the teeth are, the weaker the invasion ability is. The theoretical calculation value and experimental value in Figure 7 and Figure 8 show that the intrusion coefficient of r
43、ock increases exponentially with the increase of bit angle. The intrusion coefficient in bottomhole is significantly greater than it in normal pressure with the same bit angle.1801851901952002052102152202254Conclusion1. Based on unified strength theory, establish the intrusion equation of teeth invading bottomhole rock with parameters of unified strength theo
