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PETE 625 Well Control

2. Contents. Allowable Wellbore Pressures Rock Mechanics Principles Hooke's Law, Young's Mudulus, Poisson's Ratio Volumetric Strain, Bulk Modulus, Compressibility Triaxial Tests. . 3. Contents cont'd. Rock Mechanics Principles (con't.) Rock Properties from Sound Speed in Rocks' Mohr's C

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PETE 625 Well Control

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    1. PETE 625 Well Control Lesson 9 Fracture Gradients

    2. 2 Contents Allowable Wellbore Pressures Rock Mechanics Principles Hooke’s Law, Young’s Mudulus, Poisson’s Ratio Volumetric Strain, Bulk Modulus, Compressibility Triaxial Tests

    3. 3 Contents – cont’d Rock Mechanics Principles (con’t.) Rock Properties from Sound Speed in Rocks’ Mohr’s Circle Mohr-Coulomb Failure Criteria

    4. Assignments HW # 5: Ch 2, Problems 21- 30 due Friday, June 18 HW # 6: Ch 3, Problems 1- 10 due Wednesday, June 23 HW # 7: Ch 3, Problems 11- 20 due Monday, June 28 Read: Chapter 3

    5. 5 Fracture Gradients Read: “Fracture gradient prediction for the new generation,” by Ben Eaton and Travis Eaton. World Oil, October, 1997. “Estimating Shallow Below Mudline Deepwater Gulf of Mexico Fracture Gradients,” by Barker and Wood.

    6. 6 Lower Bound Wellbore Pressure Lower bound of allowable wellbore pressure is controlled by: Formation pore pressure Wellbore collapse considerations This sets the minimum “safe” mud weight.

    7. 7 Upper bound allowable wellbore pressure may be controlled by: The pressure integrity of the exposed formations (fracture pressure) The pressure rating of the casing The pressure rating of the BOP Chapter 3 deals with fracture gradient prediction and measurement Upper Bound Wellbore Pressure

    8. 8 Fracture Gradients May be predicted from: Pore pressure (vs. depth) Effective stress Overburden stress Formation strength

    9. 9 Rock Mechanics How a rock reacts to an imposed stress, is important in determining Formation drillability Perforating gun performance Control of sand production Effect of compaction on reservoir performance Creating a fracture by applying a pressure to a wellbore!!!

    10. 10 Elastic Properties of Rock

    11. 11 Elastic Properties of Rock

    12. 12 Elastic Properties of Rock The vertical stress at any point can be calculated by:

    13. 13 Elastic Properties of Rock Hooke’s Law: s = E e

    14. 14 Hooke’s Law

    15. 15 Typical Elastic Properties of Rock

    16. 16 Poisson’s Ratio Poisson’s Ratio = transverse strain/axial strain m = -(ex/ez) Over the elastic range, for “most metals”, m ~ 0.3 Over the plastic range, m increases, and may reach the limiting value of 0.5

    17. 17 Volumetric Strain

    18. 18 Bulk Modulus and Compressibility values in rock

    19. 19 Shear Modulus (G) G is the ratio of shear stress to shear strain G is intrinsically related to Young’s modulus and Poisson’s ratio G = t/g = E/[2*(1+m)]

    20. 20 Bulk Modulus (Kb) Kb is the ratio between the average normal stress and the volumetric strain Kb can be expressed in terms of Young’s modulus and Poisson’s ratio. Kb = average normal stress/ volumetric strain Kb = E/[3*(1-2m) = [(sx+ sy+sz)/3]/ev

    21. 21 Bulk Compressibility (cb) cb is the reciprocal of the bulk modulus cb = 1/Kb = 3*(1-2m)/E = ev / [(sx+ sy+sz)/3]

    22. 22 Metals and Rocks Metallic alloys usually have well- defined and well-behaved predictable elastic constants.

    23. 23 Metals and Rocks In contrast, rock is part of the disordered domain of nature. It’s response to stress depends on (e.g.): Loading history Lithological constituents Cementing materials Porosity Inherent defects

    24. 24 Metals and Rocks Even so, similar stress-strain behavior is observed. Triaxial tests include confining stress

    25. 25 Rock Behavior Under Stress

    26. 26 Young’s Modulus for a Sandstone

    27. 27 Transverse Strains for SS in Fig. 3.5

    28. 28 Example 3.1 Using Fig. 3.5, determine Young’s Modulus and Poisson’s ratio at an axial stress of 10,000 psi and a confining stress of 1,450 psi. From Fig 3.5, the given stress conditions are within the elastic range of the material (e.g. linear stress-strain behavior)

    29. 29 Solution

    30. 30 Rock Properties Rocks tend to be more ductile with increasing confining stress and increasing temperature Sandstones often remain elastic until they fail in brittle fashion. Shales and rock salt are fairly ductile and will exhibit substantial deformation before failure

    31. 31 Rock Properties Poisson’s ratio for some plastic formations may attain a value approaching the limit of 0.5 Rocks tend to be anisotropic, so stress-strain behavior depends on direction of the applied load.

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    41. 41 Hydraulic Fracturing Hydraulic fracturing while drilling results in one form of lost circulation (loss of whole mud into the formation). Lost circulation can also occur into: vugs or solution channels natural fractures coarse-grained porosity

    42. 42 For a fracture to form and propagate: The wellbore pressure must be high enough to overcome the tensile strength of the rock. must be high enough to overcome stress concentration at the hole wall must exceed the minimum in situ rock stress before the fracture can propagate to any substantial extent.

    43. 43 In Situ Rock Stresses

    44. 44 In Situ Rock Stresses

    45. 45 In Situ Rock Stresses

    46. 46 In Situ Rock Stresses The above stressed block is analgous to a buried rock element if the material assumptions remain valid. Using the book’s nomenclature for overburden stress and substituting Terzaghi’s effective stress equation leads to:

    47. 47 In Situ Rock Stresses

    48. 48 Fig. 3.13

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