PETE 411 Well Drilling

1. PETE 411Well Drilling Lesson 22 Prediction of Fracture Gradients

2. Prediction of Fracture Gradients Well Planning Theoretical Fracture Gradient Determination Hubbert & Willis Matthews & Kelly Ben Eaton Comparison of Results Experimental Frac. Grad. Determination Leak-off Tests Lost Circulation

3. Read:Applied Drilling Engineering, Ch. 6 HW #12Casing Designdue Nov. 1, 2002

4. NOTE:On all HW and Quizzes please put: * PETE 411/501 (or 411/502) * Name, written legibly * Number of HW or Quiz (on the outside) Thank you!

5. Well Planning Safe drilling practices require that the following be considered when planning a well: Pore pressure determination Fracture gradient determination Casing setting depth selection Casing design Mud Design, H2S considerations Contingency planning

6. Fig. 7.21

8. Formation Pressure and Matrix Stress Calculate: 1. Pore pressure, psi/ft , at 14,000 ft 2. Pore pressure, psi, at 14,000 ft 3. Matrix stress, psi/ft 4. Matrix stress, psi Given:Well depth is 14,000 ft. Formation pore pressure expressed in equivalent mud weight is 9.2 lb/gal. Overburden stress is 1.00 psi/ft.

9. Formation Pressure and Matrix Stress S = P + s overburden pore matrix stress = pressure + stress (psi) (psi) (psi)

10. Depth = 14,000 ft. Pore Pressure = 9.2 lb/gal equivalent Overburden stress = 1.00 psi/ft. Formation Pressure and Matrix Stress Calculations: 1. Pore pressure gradient = 0.433 psi/ft * 9.2/8.33 = 0.052 * 9.2 = 0.478 psi/ft 2. Pore pressure at 14,000 ft = 0.478 psi/ft * 14,000 ft = 6,692 psig

11. Formation Pressure and Matrix Stress psi psi/ft Calculations: 3. Matrix stress gradient, s/ D = 0.522 psi/ft

12. Formation Pressure and Matrix Stress Calculations: 4. Matrix stress (in psi) at 14,000 ft = 0.522 psi/ft * 14,000 ft s = 7,308 psi

13. Fracture Gradient Determination In order to avoid lost circulation while drilling it is important to know the variation of fracture gradient with depth. Leak-off tests represent an experimental approach to fracture gradient determination. Below are listed and discussed four approaches to calculating the fracture gradient.

14. Fracture Gradient Determination 1. Hubbert & Willis: where F = fracture gradient, psi/ft = pore pressure gradient, psi/ft

15. Fracture Gradient Determination 2. Matthews & Kelly: where Ki= matrix stress coefficient s= vertical matrix stress, psi

16. Fracture Gradient Determination 3. Ben Eaton: where S = overburden stress, psi g = Poisson’s ratio

17. Example A Texas Gulf Coast well has a pore pressure gradient of 0.735 psi/ft. Well depth = 11,000 ft. Calculate the fracture gradient in units of lb/gal using each of the above four methods. Summarize the results in tabular form, showing answers, in units oflb/gal and also in psi/ft.

18. Example - Hubbert and Willis 1. Hubbert & Willis: The pore pressure gradient,

19. Example - Hubbert and Willis Also,

20. Example - Hubbert and Willis = 0.8675 psi/ft Fmax = 16.68 lb/gal

21. Example 2. Matthews & Kelly In this case P and D are known, may be calculated, and is determined graphically. (i) First, determine the pore pressure gradient.

22. Example - Matthews and Kelly S = P + s s = S - P = 1.00 * D - 0.735 * D = 0.265 * D = 0.265 * 11,000 s = 2,915 psi (ii) Next, calculate the matrix stress.

23. Example - Matthews and Kelly Sn = Pn + sn n = “normal” 1.00 * Di = 0.465 * Di + 2,915 Di * (1 - 0.465) = 2,915 (iii) Now determine the depth, , where, under normally pressured conditions, the rock matrix stress, s would be 2,915 psi.

24. Example - Matthews and Kelly (iv) Find Ki from the plot on the right, for For a south Texas Gulf Coast well, Di = 5,449 ft Ki = 0.685

25. Example - Matthews and Kelly (v) Now calculate F:

27. Example Ben Eaton:

28. Variable Overburden Stress by Eaton At 11,000 ft S/D = 0.96 psi/ft

29. Fig. 5-5 At 11,000 ft g = 0.46

30. Example - Ben Eaton From above graphs, at 11,000 ft.: F = 0.9267 psi/ft = 17.82 lb/gal

31. Summary of Results Fracture Gradient psi.ftlb/gal Hubbert & Willis minimum: 0.823 15.83 Hubbert & Willis maximum: 0.868 16.68 Mathews & Kelly: 0.917 17.63 Ben Eaton: 0.927 17.82

32. Summary of Results Note that all the methods take into consideration the pore pressure gradient. As the pore pressure increases, so does the fracture gradient. In the above equations, Hubbert & Willis apparently consider only the variation in pore pressure gradient. Matthews & Kelly also consider the changes in rock matrix stress coefficient, and in the matrix stress ( Ki and si ).

33. Summary of Results Ben Eaton considers variation in pore pressure gradient, overburden stress and Poisson’s ratio, and is probably the most accurate of the four methods. The last two methods are actually quite similar, and usually yield similar results.

34. Similarities Ben Eaton: Matthews and Kelly:

35. 9 10 11 Pore Pressures 12 14 16 18

36. Experimental Determination of Fracture Gradient The leak-off test Run and cement casing Drill out ~ 10 ft below the casing seat Close the BOPs Pump slowly and monitor the pressure

38. 45 80 105 120 120 120 120 120 120 40 20

42. Experimental Determination of Fracture Gradient Example: In a leak-off test below the casing seat at 4,000 ft, leak-off was found to occur when the standpipe pressure was 1,000 psi. MW = 9 lb/gal. What is the fracture gradient?

43. Example Leak-off pressure = PS + DPHYD = 1,000 + 0.052 * 9 * 4,000 = 2,872 psi Fracture gradient = 0.718 psi/ft EMW = ?