1. Drilling Engineering - PE 311 Rock Failure Mechanisms

2. Rock Failure Mechanisms
Bits are designed to induce rock failure. Because rock failure can occur in different ways, depending on the formation and on downhole conditions, there are a large number of design variations among rolling cutter and fixed cutter bits. To evaluate these design variations and select a bit, we first need a basic understanding of how rocks fail and how formation conditions affect drilling performance.
The purpose of the design is to take advantage of the formation most efficient failure mechanisms.

3. Rock Failure Mechanisms The Stress/Strain Relationship
Stress is the internal force applied to a unit area of material. An analysis of the stresses acting on a particular object can become quite involved. For the purpose of this discussion, however, we can define three basic components of stress:
Compressive stress: a pushing or squeezing force;
Tensile stress: a pulling or elongating force;
Shear stress: a slicing or cleaving force.

4. Rock Failure Mechanisms The Stress/Strain Relationship
Strain is the deformation experienced by a material in response to an applied stress. This deformation may take one of two forms:
Elastic: If the applied stress is below the elastic limit of the material, the material returns to its original shape and size once the stress is removed.
Plastic: if the applied stress exceeds the material's elastic limit, the material experiences permanent deformation

5. Rock Failure Mechanisms The Stress/Strain Relationship
If rupture takes place before significant plastic deformation occurs, the material is described as brittle. If the material ruptures only after experiencing significant plastic deformation, it is considered ductile.

6. Rock Failure Mechanisms The Stress/Strain Relationship
If formation is under brittle failure, bits which have crushing and chipping actions are preferred. On the other hand, if formation is under ductile failure, bits which have gouging and scrapping actions are chosen.
All rocks exhibit brittle stage under atmosphere pressure. This is applicable for under balanced drilling conditions
Under high pressure, the failure mechanism transfers from brittle to ductile. This condition is for overbalanced drilling.

7. Rock Failure Mechanisms The Stress/Strain Relationship
At atmospheric pressure, sedimentary rocks are normally brittle. They become ductile, however, under high confining stress if there is no communication between the internal rock pore pressure and the surrounding pressure medium.

8. Rock Failure Mechanisms The Stress/Strain Relationship

9. Rock Failure Mechanisms Underbalanced Condition
If the pressure exerted by the fluid column is less than the pore pressure of the formation, the differential pressure is less than zero, and the well is being drilled in an underbalanced condition. This condition most often occurs when drilling with air, fresh water or muds weighing less than 8.6 lb/gal.
In underbalanced drilling, the rock exhibits brittle behavior — it has a relatively low failure strength and fractures very easily. Because the rock surface is in tension, it virtually explodes under the compressive loads of the bit. There is no downward pressure to promote chip hold-down, and so there is very little regrinding of already-drilled cuttings. This helps attain very high rates of penetration.

10. Rock Failure Mechanisms
Balanced Condition
When the pressure of the fluid column is equal to the pore pressure, the hole is in a balanced condition. This condition generally occurs when drilling with brine water or mud weighing 8.6 lb/gal.
Under balanced conditions, the rock is still in the brittle state and fractures relatively easily. The bottom of the hole is in pressure equilibrium, so there is minimal stress concentration present to either enhance or slow penetration rates. Penetration rates are generally slower than those experienced in an underbalanced drilling, because there is some chip hold-down resulting from cohesive forces between the rock cuttings, along with interference due to fluid viscosity.

11. Rock Failure Mechanisms Overbalanced Condition
In overbalanced drilling, the pressure of the mud column exceeds the formation pore pressure. In areas with normal pressure gradients, this condition occurs when the mud weight exceeds 8.6 Ib/gal. For safety reasons, overbalanced drilling is normal practice in most areas.
As the differential pressure increases in an overbalanced hole, the rock below the bit becomes increasingly strong and ductile. The hole bottom is in a state of compression, thus retarding fracture propagation caused by the bit. These factors, along with a high degree of chip hold-down, tend to slow penetration rates. If the differential pressure is too high, the mud can fracture the formation, resulting in lost circulation and possibly a blowout.

12. Rock Failure Mechanisms Overbalanced Condition

13. Rock Failure Mechanisms
Chip Hold Down
Penetration rate is also affected by a pressure-related phenomenon known as chip hold-down. Chip hold-down occurs when a mud filter cake or fine solids block fractures produced by the bit. This prevents the liquid phase of the mud from invading the fractures, and results in a positive pressure differential across the top surface of the chip. The hold-down force is equal to the area of the chip times the differential pressure

14. Rock Failure Mechanisms of Drag Bits
Introduction
Drag bits are designed to drill primarily by a wedging mechanism.
A vertical force is applied to the tooth as a result of applying drill collar weight to the bit, and a horizontal force is applied to the tooth as a result of applying the torque necessary to turn the bit. The result of these two forces defines the plane of thrust of the tooth or wedge. The cuttings are sheared off in a shear plane at an initial angle to the plane of thrust that is dependent on the properties of the rock.

15. Rock Failure Mechanisms of Drag Bits Mohr Failure Criterion

16. Rock Failure Mechanisms of Drag Bits Mohr Failure Criterion

17. Rock Failure Mechanisms of Drag Bits Mohr Failure Criterion
f: Angle to the direction of the compressive load

18. Rock Failure Mechanisms of Drag Bits Mohr Failure Criterion
Summing forces normal to the fracture plane gives
Where
dA3 = dAncosf and dA1 = dAnsinf
Making these substitutions in the force balance equation gives

19. Rock Failure Mechanisms of Drag Bits Mohr Failure Criterion
Summing forces parallel to the fracture plane gives
With dA3 = dAncosf dA1 = dAnsinf
These two equations represent graphically by the Mohr’s circle. Any combination between t and sn gives a new circle representing a new failure condition.
The rock will fail when the combination between WOB and shear force t gives a point out side the Mohr’s circle

20. Rock Failure Mechanisms of Drag Bits
Mohr’s Circle
Positive shear would cause a clockwise rotation of the element.
s12 is negative and s21 is positive
Compression is positive
Tensile is negative

21. Rock Failure Mechanisms of Drag Bits
Mohr’s Circle

22. Rock Failure Mechanisms of Drag Bits Mohr Failure Criterion
c = t - sntanq
q is the angle of internal friction
sn is the stress normal to the fracture plane
c is the cohesive resistance

23. Rock Failure Mechanisms of Drag Bits Mohr Failure Criterion
Example: A rock sample under a 2,000 psi confining pressure fails when subjected to a compressional loading of 10,000 psi along a plane that makes an angle of with the direction of the compressive load. Using the Mohr failure criterion, determine the angle of internal friction, the shear strength and the cohesive resistance of the material.

24. Rock Failure Mechanisms of Drag Bits Mohr Failure Criterion
Solution: the angle q and 2f must sum to 900. Thus the angle of internal friction is given by
q = 90 – 2(27) = 36 0
The shear strength is computed as follows
t = ½(s1 – s3)sin(2f) = ½(10,000 – 2,000)sin(540) = 3,236 psi
The stress normal to the fracture plane is
sn = ½(s1 + s3) – ½(s1 – s3)cos(2f) = 3,649 psi
The cohesive resistance can be computed
c = t - sntanq = 585 psi

25. Rock Failure Mechanisms of Rolling Cone Bits
Percussion or crushing action is the predominant mechanism present for the rolling cutter bits. Since these types of bits are designed for use in hard, brittle formations in which ROP tend to be low and drilling costs tend to be high, the percussion mechanism is of considerable economic interest.
The apparatus allowed the borehole pressure, rock pore pressure, and rock confining pressure to be varied independently. The apparatus was equipped with a static loading device which used an air-actuated piston to simulate constant force impacts similar to those produced in rotary drilling. Strain gauges and a linear potentiometer were used to obtain force displacement curves.

26. Rock Failure Mechanisms of Rolling Cone Bits

27. Rock Failure Mechanisms of Rolling Cone Bits

28. Rock Failure Mechanisms of Rolling Cone Bits
As load is applied to a bit tooth (A), the constant pressure beneath the tooth increases until it exceeds the crushing strength of the rock and a wedge of finely powdered rock then is formed beneath the tooth (B). As the force on the tooth increases, the material in the wedge compresses and exerts high lateral forces on the solid rock surrounding the wedge until the shear stress exceeds the shear strength of the solid rock and the rock factures (C).
The force at which fracturing begins beneath the tooth is called the threshold force. As the force on the tooth increases above the threshold value, subsequent fracturing occurs in the region above the initial fracture, forming a zone of broken rock (D).

29. Rock Failure Mechanisms of Rolling Cone Bits
At low differential pressure, the cuttings formed in the zone of broken rock are ejected easily from the crater (E). The bit tooth then moves forward until it reaches the bottom of the crater, and the process may be repeated (F, G).
At high differential pressures, the downward pressure and frictional forces between the rock fragments prevent ejection of the fragments (E’). As the force on the tooth is increased, displacement takes place along fracture planes parallel to the initial fracture (F’, G’). This gives the appearance of plastic deformation, and craters formed in the manner are called pseudo plastic craters.

30. Factors Affecting Penetration Rate
The most important variables affecting penetration rate that have been identified and studied included: bit type, formation characteristics, drilling fluid properties, bit operating conditions (WOB, and ROP), bit tooth wear, and bit hydraulics.

31. Factors Affecting Penetration Rate
Effecting of Bit Type
For rolling cutter bits, the initial ROP is often highest in a given formation when using bits with long teeth and a large cone offset angle. However, these bits are practical only in soft formations because of a rapid tooth destruction and decline in penetration rate in hard formations.
Drag bits are designed to obtain a given penetration rate. Drag bits give a wedging type rock failure in which the bit penetration per revolution depends on the number of blades and the bottom cutting angle. The diamond and PCD bits are designed for a given penetration per revolution by the selection of the size and number of diamonds or PCD blanks.

32. Factors Affecting Penetration Rate
Effecting of Formation Characteristics
The elastic limit and ultimate strength of the formation are the most important formation properties affecting ROP. The shear strength predicted by Mohr failure criteria sometimes is used to characterize the strength of the formation. To determine the shear strength from a single compression test, an average angle of internal friction of 350 was assumed. The angle of internal friction varies from about 30 – 400 form most rocks
The mineral composition of the rock also has some effect on ROP. Rocks containing hard, abrasive minerals can cause rapid dulling of the bit teeth. Rocks containing gummy clay minerals can cause the bit to ball up and drill in a very inefficient manner.

33. Factors Affecting Penetration Rate
Effecting of Formation Characteristics
The permeability of the formation also has a significant effect on the ROP. In permeable rocks, the drilling fluid filtrate can move into the rock ahead of the bit and equalize the pressure differential acting on the chips formed beneath each tooth. This would tend to promote the more explosive elastic mode of crater formation. it also can be argued that the nature of the fluids contained in the pore spaces of the rock also affects this mechanism since more filtrate volume would be required to equalize the pressure in rock containing gas than in a rock containing liquid.

34. Factors Affecting Penetration Rate
Effecting of Drilling Fluid Properties
The properties of drilling fluid reported to affect the ROP include: density, rheological flow properties, filtration characteristics, solids content and size distribution, and chemical composition.
Penetration rate tends to decrease with increasing fluid density, viscosity and solids content, and tends to increase with increasing filtration rate. The density, solid, and filtration characteristics of the mud control the pressure differential across the zone of crushed rock beneath the bit. The fluid viscosity controls the system frictional losses in the drillstring and thus the hydraulic energy available at the bit jets for cleaning. The most important factor out of the drilling fluid properties is the density. Changing density will change the overbalance. The ROP decreases as the overbalance increases.

35. Factors Affecting Penetration Rate Effecting of Operating Conditions

36. Factors Affecting Penetration Rate Effecting of Operating Conditions
When plotting ROP vs. WOB obtained experimentally with all other drilling variables held constant has the characteristic shape as shown:

37. Factors Affecting Penetration Rate Effecting of Operating Conditions

38. Factors Affecting Penetration Rate Effecting of Operating Conditions
No significant ROP is obtained until the threshold bit weight is applied (point a). ROP then increases rapidly with increasing values of WOB. For moderate value of bit weight, a linear curve is often observed (segment bc). However, at higher values of bit weight, subsequent increase in bit weight causes only slight improvements in ROP (cd). In some cases, a decrease in ROP is observed at extremely high value of WOB (de). This type of behavior often is called bit floundering. This poor response of ROP at high values of bit weight usually is attributed to less efficient bottomhole cleaning at higher rates of cuttings.

39. Factors Affecting Penetration Rate Effecting of Operating Conditions
A typical plot of ROP vs. rotary speed obtained with all other drilling variables held constant is shown. ROP usually increases linearly with low RPM. At higher values of RPM the response of ROP to increase RPM diminishes. The reason is due to the poor hole cleaning.

40. Factors Affecting Penetration Rate Effecting of Bit Diameters

41. Factors Affecting Penetration Rate Effecting of Bit Diameters
Generally, as the bit diameter increases, the applied weight on the bit is distributed over the larger area which consequently reduces the rate of penetration of the bit.