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# 10. Fracture Gradients - cont'd - PETE 625 Well Control...

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PETE 625 Well Control Lesson 10 Fracture Gradients - cont’d

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2 Fracture Gradients - cont’d Radial and Tangential Stresses near the Wellbore Stresses in Rock near Wellbore Effect of Anisotropic Stresses Onshore vs. Offshore Fracture Gradients Fracture Gradients in Inclined Wellbores Oil Based and Water Based Drilling Fluids
Assignments 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

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4 Fracture Gradients Read: Ch. 3, and also “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.
5 Fig. 3.21 - Stress concentrations around a borehole in a uniform stress field Tension Additional compression

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6 Fig. 3.22 - Induced stresses in the presence of a biaxial-stress field
7 Example 3.4 Given: Formation depth = 10,000’ Poisson’s ratio = 0.22 Pore pressure grad = 0.433 psi/ft Hole diameter = 9.0 in Mud density = 8.33 ppg Overburden stress grad. = 1.00 psi/ft

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8 Example 3.4 - Part 1 1. Estimate the horizontal stress if the rock behaves in an elastic manner Solution: σ H = ( μ /(1- μ ))*( σ ob - p p ) + p p ….Eq 3.21b σ H = (0.22/(1 - 0.22)) * (1*10,000 - 0.433*10,000) + 4,330 σ H = 5,929 psi
9 Example 3.4 – Part 1 - cont’d Effective horizontal stress σ eH = σ H - α *p p If α = 1.0 and p p = 4,330 psig Then, σ He = 5,929 – 4,330 σ eH = 1,599 psi

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10 Example 3.4 – Part 2 2. Estimate the tangential and radial stresses at the borehole wall if the horizontal stresses are equal. σ r = p w Eq. 3.24 σ r = 4,330 psig σ t = σ H1 + σ H2 - p w - 2( σ H1 - σ H2 ) cos2 θ ... Eq. 3.25 = 5,929 + 5,929 - 4,330 - 0 = 7,528 psig σ r p w
11 Example 3.4 – Part 2 – cont’d The corresponding effective stresses are: σ re = 4,330 - 4,330 = 0 psi σ te = 7,528 - 4,330 = 3,198 psi

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12 Example 3.4- Part 3 3. What are the radial and tangential stresses 2.0 ft from the wellbore centerline? ) psig 929 , 5 away, (far psig 985 , 5 330 , 4 0 . 24 5 . 4 0 . 24 5 . 4 1 929 , 5 p r r r r 1 H 2 2 2 2 ft 2 , t w 2 2 w 2 2 w H ft 2 , t = σ = - + = σ - + σ = σ psig 873 , 5 330 , 4 0 . 24 5 . 4 0 . 24 5 . 4 1 929 , 5 p r r r r 1 2 2 2 2 ft 2 , r w 2 2 w 2 2 w H ft 2 , r = + - = σ + - σ = σ Radial Stress: Eq. 3.31 Tangential Stress: Eq. 3.32
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