1. Lesson 22 Prediction of Fracture Gradients
PETE 411 Well 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 #12 Casing Design due 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
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.
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

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

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

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

12. Formation Pressure and Matrix Stress
Calculations:
4. Matrix stress (in psi) at 14,000 ft
= 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 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 of lb/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
= psi/ft
Fmax = 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
(ii) Next, calculate the matrix stress.
S = P + s
s = S - P
= 1.00 * D * D
= * D
= * 11,000
s = 2,915 psi

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

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

31. Summary of Results Fracture Gradient psi.ft lb/gal
Hubbert & Willis minimum:
Hubbert & Willis maximum:
Mathews & Kelly:
Ben Eaton:

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 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 = psi/ft
EMW = ?