Stresses Caused by Bit Loading at the Center of the Hole

1961 ◽  
Vol 1 (03) ◽  
pp. 177-183
Author(s):  
J.B. Cheatham ◽  
J.C. Wilhoit
Keyword(s):  
Stress Distribution ◽  
Pore Pressure ◽  
Cylindrical Cavity ◽  
Brittle Failure ◽  
Permanent Deformation ◽  
Confining Pressure ◽  
Radius Of Curvature ◽  
Oil Well ◽  
Large Radius ◽  
Bit Loading

Abstract Although an oil well is a long cylindrical hole with an irregular bottom, it appears likely that the nature of the stress concentration at the bottom of the hole can be ascertained from an analysis of the stresses around a short cylindrical cavity with rounded corners and smooth bottom. Such a cavity is studied primarily because it leads more readily to a solution to the problem by the use of stress functions in this paper the stress distribution around a short cylindrical cavity subjected to bit loading, overburden and drilling fluid pressures is determined by means of an analytical solution which approximately satisfies the boundary conditions of the problem. From this solution the stresses at the corner of the hole are calculated to be about 35 per cent lower than comparable results obtained by photoelastic and relaxation analyses. This difference is apparently due to the large radius of curvature at the corner of the cavity in the present analysis. Since good agreement is obtained between the results of this analysis and the stresses calculated for a similar loading on a semi-infinite elastic solid, it is concluded that the bit action in the region near the center of the hole is not appreciably affected by the presence of the sides of the hole. Introduction Much has been written concerning drilling "under down-hole conditions" and pertaining to the stress distribution in the rock at the bottom of an oil well. For example, it is known that identical rocks can be drilled more rapidly at the surface than under subsurface conditions of pressure and stress. Information on the behavior of rocks under loading can be obtained from triaxial test data. From such tests it is found that rocks exhibit brittle failure when the confining pressure and pore pressure are equal, but the mode of failure may change to ductile as the difference between the confining pressure and the pore pressure is increased. Brittle failure implies that there is very little permanent deformation before fracture, whereas ductile failure indicates that permanent deformation takes place before fracture. Some rocks are ductile at differential pressures of 5,000 psi, but other rocks are brittle even at differential pressures of more than 50,000 psi.

Strength of Oil Well Cements at Downhole Pressure-Temperature Conditions

1965 ◽  
Vol 5 (04) ◽  
pp. 341-347 ◽  
Author(s):  
John Handin
Keyword(s):  
Pore Pressure ◽  
Triaxial Compression ◽  
Test Chamber ◽  
Confining Pressure ◽  
Effect Of Temperature ◽  
Oil Well ◽  
Effective Pressure ◽  
Confining Pressures ◽  
The Difference ◽  
Cement Strength

Abstract Triaxial compression tests with independently applied external confining pressures and internal pore pressures show that the ultimate compressive strengths of representative oil well cements are nearly linear functions of effective pressure the difference between external and internal pressures on the jacketed cylindrical specimens (to 15,000 psi). The strengths are little affected by the test temperature to 350F (not to be confused with the curing temperature). At an effective pressure of 15,000 psi, strengths are in the range of 30,000 to 50,000 psi, comparable to those of sedimentary rocks under similar conditions. The cements become very ductile even under low effective pressures; permanent shortenings of 30 per cent or more are attainable without rupture. Introduction Since the pioneering work of Richart, Brandtzaeg and Brown on the failure of cement under combined compressive stresses, it has been recognized that ultimate compressive strength is greatly enhanced by the application of confining pressure. More recently, McHenry showed that the strength of concrete was a linear function of the effective pressure (the difference between the external confining pressure on a jacketed specimen and the internal fluid pore pressure) at least for a range of 0 to 1,500 psi. The effect of temperature had not been investigated, and no previous systematic triaxial compression testing of materials used for oilwell cementing seems to have been done. The present work was suggested by the late J. M. Bugbee who stated that "consideration of the common application of high-pressure hydraulic fracturing to the initial completion or recompletion of wells, and the large pressure drawdowns in some producing wells, particularly those in abnormally high-pressure gas-condensate reservoirs, raises the question of what is a suitable cement strength for various completions. The intuitive belief exists that cement strength need be no greater than formation strength. Tests should, however, be conducted at downhole conditions."The ultimate compressive strengths of rocks penetrated by the borehole must rise several fold with increasing depth. This marked enhancement of strength is due to the influence of the effective pressure, the total weight per unit area of the overburden less the hydrostatic pore pressure. (The effect of temperature due to the geothermal gradients is relatively small for depths to 30,000 ft.) A significant comparison of the strengths of rocks and cements at downhole conditions requires knowledge of the confined compressive strengths of cements as well. EXPERIMENTAL PROCEDURES The theory and technique of triaxial compression testing are fully discussed in earlier reports. Briefly, cylindrical specimens 1-in. long and 0.5-in. in diameter are jacketed in thin copper tubes of negligible strength, placed in the test chamber and subjected to an external confining pressure of kerosene and loaded axially by the piston at a strain rate of 1 per cent per minute. Pore pressures of water (or kerosene) are applied independently through the hollow piston and are maintained constant during the shortening of the specimen. Tests at sensibly 0 pore pressure are arranged so that any free water in the cement can escape to the atmosphere. (If egress of water were denied, pore pressure would rapidly attain the value of the external confining pressure because of reduction of pore space.) The test chamber can be heated for high-temperature experiments. Unless other-wise noted, the cement samples were air dried for about a week. Recorded during a test are pore and confining pressures, shortening and axial differential force (total force less the product of the confining pressure and the area of the piston). SPEJ P. 341ˆ

Duplex Spread Blade Method for Cutting Hypoid Gears with Modified Tooth Surface

1998 ◽  
Vol 120 (3) ◽  
pp. 441-447 ◽  
Author(s):  
K. Kawasaki ◽  
H. Tamura
Keyword(s):  
Cutting Edge ◽  
Tooth Surface ◽  
Radius Of Curvature ◽  
Large Radius ◽  
Ring Gear ◽  
Circular Arc ◽  
Hypoid Gears ◽  
Manufacturing Method ◽  
Straight Line

In this paper, a duplex spread blade method for cutting hypoid gears with modified tooth surface is proposed. The duplex spread blade method provides a rapid and economical manufacturing method because both the ring gear and pinion are cut by a spread blade method. In the proposed method, the nongenerated ring gear is manufactured with cutting edge that is altered from the usual straight line to a circular arc with a large radius of curvature and the circular arc cutting edge produces a modified tooth surface. The pinion is generated by a cutter with straight cutting edges as usual. The main procedure of this method is the determination of the cutter specifications and machine settings. The proposed method was validated by gear manufacture.

Strength and Deformation Characteristics of Stabilized Silty Soil

2012 ◽  
Vol 594-597 ◽  
pp. 512-515
Author(s):  
Zheng Rong Zhao ◽  
Hong Xia Yang
Keyword(s):  
Internal Friction ◽  
Brittle Failure ◽  
Yellow River ◽  
Strain Curve ◽  
Friction Angle ◽  
Confining Pressure ◽  
Alluvial Plain ◽  
The Yellow River ◽  
Stress Strain Curve ◽  
Silty Soil

Combined with the silty soil characteristics of the Yellow River alluvial plain and the subgrade filling of Ji-He expressway, the paper discusses silty soil, stabilized silty soil strength and stress-stain characteristics through the indoor triaxial shear test. The results show that the remodeling silty soil has obvious peak, brittle failure, low residual strength after being destroyed and the stress-strain curve shows a softening type in confining pressure 100kPa lower stress level. In the confining pressure 400kPa higher stress level, soil samples peak is not obvious,mainly plastic failure and the stress-strain curve is close to a hardening type. Compared to mixed with 8% lime, stabilized silty soil of mixed with 4% cement and 4% lime shows that the partial stress peak is more obvious when destroyed and the residual strength is drastically reduced and more incline to brittle failure. In different the age, compared to mixed with 8% lime, stabilized silty soil of mixed with 4% cement and 4% lime shows that internal friction angle becomes larger and cohesion improves gradually whose amplitude is much larger than internal friction angle. Therefore, a more effective way to stabilize the silty soil of the Yellow River alluvial plain is to select silty soil mixed with 4% cement and 4% lime.

Résonateur ouvert en géométrie sphérique

1980 ◽  
Vol 58 (1) ◽  
pp. 80-86 ◽  
Author(s):  
Gilles Duret ◽  
Gérard Zepp ◽  
Alain Wick
Keyword(s):  
Radius Of Curvature ◽  
Large Radius ◽  
Open Resonators

Most of the approximate theories of the spherical open resonators are insufficient, except for the very large radius of curvature. It is often necessary to consider other cases. The theory we have developed is applicable for any curvature and aperture of the mirrors. This theory also allows study of multi-dielectric cavities. This method is accurately studied in detail in this paper.

Experimental investigation of the effect of compliant pores on reservoir rocks under hydrostatic and triaxial compression stress states

2019 ◽  
Vol 56 (7) ◽  
pp. 983-991
Author(s):  
Hua Yu ◽  
Kam Ng ◽  
Dario Grana ◽  
John Kaszuba ◽  
Vladimir Alvarado ◽  
...  
Keyword(s):  
Pore Pressure ◽  
Triaxial Compression ◽  
Matrix Material ◽  
Volumetric Strain ◽  
Confining Pressure ◽  
Differential Pressure ◽  
Sandstone Sample ◽  
Stress States ◽  
Rock Springs ◽  
Stage 1

The presence of compliant pores in rocks is important for understanding the stress–strain behaviors under different stress conditions. This paper describes findings on the effect of compliant pores on the mechanical behavior of a reservoir sandstone under hydrostatic and triaxial compression. Laboratory experiments were conducted at reservoir temperature on Weber Sandstone samples from the Rock Springs Uplift, Wyoming. Each experiment was conducted at three sequential stages: (stage 1) increase in the confining pressure while maintaining the pore pressure, (stage 2) increase in the pore pressure while maintaining the confining pressure, and (stage 3) application of the deviatoric load to failure. The nonlinear pore pressure – volumetric strain relationship governed by compliant pores under low confining pressure changes to a linear behavior governed by stiff pores under higher confining pressure. The estimated compressibilities of the matrix material in sandstone samples are close to the typical compressibility of quartz. Because of the change in pore structures during stage 1 and stage 2 loadings, the estimated bulk compressibilities of the sandstone sample under the lowest confining pressure decrease with increasing differential pressure. The increase in crack initiation stress is limited with increasing differential pressure because of similar total crack length governed by initial compliant porosity in sandstone samples.

scholarly journals Experimental Study of Stress-Seepage Coupling Properties of Sandstone under Different Loading Paths

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Xi Chen ◽  
Wei Wang ◽  
Yajun Cao ◽  
Qizhi Zhu ◽  
Weiya Xu ◽  
...  
Keyword(s):  
Elastic Modulus ◽  
Pore Pressure ◽  
Complex Loading ◽  
Friction Angle ◽  
Confining Pressure ◽  
Triaxial Tests ◽  
Compression Tests ◽  
Biot Coefficient ◽  
Cyclic Loading And Unloading ◽  
Loading And Unloading

The study on hydromechanical coupling properties of rocks is of great importance for rock engineering. It is closely related to the stability analysis of structures in rocks under seepage condition. In this study, a series of conventional triaxial tests under drained condition and hydrostatic compression tests under drained or undrained condition on sandstones were conducted. Moreover, complex cyclic loading and unloading tests were also carried out. Based on the experimental results, the following conclusions were obtained. For conventional triaxial tests, the elastic modulus, peak strength, crack initiation stress, and expansion stress increase with increased confining pressure. Pore pressure weakened the effect of the confining pressure under drained condition, which led to a decline in rock mechanical properties. It appeared that cohesion was more sensitive to pore pressure than to the internal friction angle. For complex loading and unloading cyclic tests, in deviatoric stress loading and unloading cycles, elastic modulus increased obviously in first loading stage and increased slowly in next stages. In confining pressure loading and unloading cycles, the Biot coefficient decreased first and then increased, which indicates that damage has a great impact on the Biot coefficient.

Testing Study on the Effects of Water Content on Permeability for Coal

2014 ◽  
Vol 580-583 ◽  
pp. 201-204
Author(s):  
Chun Hui Zhang ◽  
Xiao Pan Xu
Keyword(s):  
Water Content ◽  
Pore Pressure ◽  
Coal Sample ◽  
Channel Wall ◽  
Confining Pressure ◽  
Liaoning Province ◽  
Air Drying ◽  
Slippage Effect

To obtain the effects of water content on the permeability of coal, briquette specimen were obtained from Wulong Mine, Liaoning Province. The permeability of the air drying, bounding water and saturating specimens were tested with self-made equipment respectively, and the effects of water content on permeability for coal were studied. The results showed that: (1)The permeability of specimens decreases with confining pressure increasing, and the air drying and bounding water specimens take on obvious slippage effect. However the saturated specimens never take on slippage effects. It is because the channels of saturated coal sample are occupied by water. When the gas goes through specimens, gas never is absorbed. Collision between gas and the channel wall decreases, and the slippage effect disappears. (2) With water content increasing, the permeability of specimens decreases. (3)The permeability of specimens increases when pore pressure increases.

Experimental and Computational Investigation of Shaped Film Cooling Holes Designed to Minimize Inlet Separation

2020 ◽  
Author(s):  
Fraser B. Jones ◽  
Dale W. Fox ◽  
David G. Bogard
Keyword(s):  
Film Cooling ◽  
Velocity Ratio ◽  
Tangential Velocity ◽  
Velocity Fields ◽  
Radius Of Curvature ◽  
Large Radius ◽  
Combustion Gases ◽  
Shaped Hole ◽  
Manufacturing Technologies ◽  
Film Cooling Holes

Abstract Film cooling is used to protect turbine components from the extreme temperatures by ejecting coolant through arrays of holes to create an air buffer from the hot combustion gases. Limitations in traditional machining meant film cooling holes universally have sharp inlets which create separation regions at the hole entrance. The present study uses experimental and computational data to show that these inlet separation are a major cause of performance variation in crossflow fed film cooling holes. Three hole designs were experimentally tested by independently varying the coolant velocity ratio (VR) and the coolant channel velocitty ratio (VRc) to isolate the effects of crossflow on hole performance. Leveraging additive manufacturing technologies, the addition of a 0.25D radius fillet to the inlet of a 7-7-7 shaped hole is shown to significantly improve diffuser usage and significantly reduce variation in performance with VRc. A second AM design used a very large radius of curvature inlet to reduce biasing caused by the inlet crossflow. Experiments showed that this “swept” hole design did minimize biasing of coolant flow to one side of the shaped hole and it significantly reduced variations due to varying VRc. RANS simulations at six VR and three VRc conditions were made for each geometry to better understand how the new geometries changed the velocity field within the hole. The sharp and rounded inlets were seen to have very similar tangential velocity fields and jet biasing. Both AM inlets created more uniform, slower velocity fields entering the diffuser. The results of this paper indicate large improvements in film cooling performance can be found by leveraging AM technology.

scholarly journals Intragranular deformation mechanisms in calcite deformed by high-pressure torsion at room temperature

2020 ◽  
Vol 114 (2) ◽  
pp. 105-118
Author(s):  
Roman Schuster ◽  
Gerlinde Habler ◽  
Erhard Schafler ◽  
Rainer Abart
Keyword(s):  
High Pressure ◽  
Twin Boundary ◽  
Brittle Failure ◽  
Room Temperature ◽  
High Pressure Torsion ◽  
Confining Pressure ◽  
Temperature Deformation ◽  
Orientation Relationships ◽  
High Confining Pressure ◽  
Confining Pressures

AbstractPolycrystalline calcite was deformed to high strain at room-temperature and confining pressures of 1–4 GPa using high-pressure torsion. The high confining pressure suppresses brittle failure and allows for shear strains >100. The post-deformation microstructures show inter- and intragranular cataclastic deformation and a high density of mechanical e$$ \left\{01\overline{1}8\right\} $$011¯8 twins and deformation lamellae in highly strained porphyroclasts. The morphologies of the twins resemble twin morphologies that are typically associated with substantially higher deformation temperatures. Porphyroclasts oriented unfavorably for twinning frequently exhibit two types of deformation lamellae with characteristic crystallographic orientation relationships associated with calcite twins. The misorientation of the first deformation lamella type with respect to the host corresponds to the combination of one r$$ \left\{10\overline{1}4\right\} $$101¯4 twin operation and one specific f$$ \left\{01\overline{1}2\right\} $$011¯2 or e$$ \left\{01\overline{1}8\right\} $$011¯8 twin operation. Boundary sections of this lamella type often split into two separated segments, where one segment corresponds to an incoherent r$$ \left\{10\overline{1}4\right\} $$101¯4 twin boundary and the other to an f$$ \left\{01\overline{1}2\right\} $$011¯2 or e$$ \left\{01\overline{1}8\right\} $$011¯8 twin boundary. The misorientation of the second type of deformation lamellae corresponds to the combination of specific r$$ \left\{10\overline{1}4\right\} $$101¯4 and f$$ \left\{01\overline{1}2\right\} $$011¯2 twin operations. The boundary segments of this lamella type may also split into the constituent twin boundaries. Our results show that brittle failure can effectively be suppressed during room-temperature deformation of calcite to high strains if confining pressures in the GPa range are applied. At these conditions, the combination of successive twin operations produces hitherto unknown deformation lamellae.

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