1. Well Design - PE 413 Chapter 1: Fracture Pressure

2. Physical Properties of Formation Materials
Young’s Modulus
A rock’s elastic properties are most often described by two different terms: Young’s modulus and Poisson’s ratio.
Young's Modulus E (Elastic modulus): is essentially an index of the rock’s resistance to external force. It is defined as the ratio of the applied stress to the resulting strain:
In other words, it is a coefficient of proportionality between uniaxial stress and strain. It has the same dimensions as pressure, and is typically measured in units of Pa or psi.

3. Physical Properties of Formation Materials
Young’s Modulus

4. Physical Properties of Formation Materials
Young’s Modulus
Higher values of Young's modulus indicate greater stiffness.
Therefore, a given amount of fracturing fluid will create a relatively long, narrow fracture in a rock having a high Young's modulus value.
If the Young's modulus varies from layer to layer, it might cause a complex width profile, with reduced widths in the layers of higher modulus values.
Soft formations are characterized by E values as low as 105 psi (Diatomite), while hard formations can have E values as large as107 psi (hard Limestone).

5. Physical Properties of Formation Materials
Poisson’s Ratio
Poisson's Ratio n: is defined as the ratio of the lateral strain demonstrated by a rock when subjected to a longitudinal load, divided by the amount of longitudinal strain caused by the same loading.
It is a dimensionless quantity, usually ranging from 0.15 to 0.35.
From a hydraulic fracturing standpoint, Poisson's ratio is primarily responsible for translating vertical stress into horizontal stresses.

6. Physical Properties of Formation Materials
Plane Strain Modulus
Plane Strain Modulus: Most of the equations used in fracturing contain only a certain combination of Young's modulus and Poisson's ratio, denoted by E':
The plane strain modulus is numerically very near to the Young's modulus, because the square of the Poisson's ratio can usually be neglected with respect to one.

7. Physical Properties of Formation Materials
Shear Modulus
Shear modulus: Some authors prefer to use the shear modulus, G, which can be easily calculated from the Young's modulus and the Poisson's ratio.
It is important to understand that the above properties are related to the elastic behavior of the rock.
They can be measured on a core sample using static or dynamic measurement methods, or in-situ, using dynamic (mostly sonic) methods.
The "static" and "dynamic" properties may be somewhat different.

8. Physical Properties of Formation Materials
1 m2 = e+15 mD
1kPa = psi
The common poisson’s ratio ranges between 0.25 to 0.4

9. Physical Properties of Formation Materials

10. Fracture Pressure (Minifrac Test)
1st injection cycle
2nD injection
cycle
flow-back
shut-in 1 2 3 4 5 6 8 7
Injection rate
Time
Bottomhole pressure
1. Breakdown pressure
2. Propagation Pressure
3. Ins. Shut-in Pressure
4. Closure Pressure

11. Fracture Pressure
Breakdown pressure: required to break down the formation and initiate fracture.
Propagation pressure: required to continually enlarge the fracture.
Instantaneous shut-in pressure (ISIP): required to just hold the fracture open.
If the PISIP is measured at the surface, then the bottom-hole instantaneous shut-in pressure is given:
PBISIP = PISIP + rgD
The fracture gradient is defined as:
FG = PBISIP/D

12. Physical Properties of Formation Materials
Linear Elasticity
For an isotropic and homogeneous material:
The strain in i direction can be calculated as follows:
From the above Eq., the stress in i direction can be expressed as:
where

13. Physical Properties of Formation Materials
Porous Media
For the porous media, some of the pores are interconnected, the fluid pressure helps to support compressive stresses exerted on an element of rock volume.
The equation describing an elastic body is:

14. Physical Properties of Formation Materials
Porous Media
If strain is restricted to the z direction (axial), then the strains in x and y direction, equal to zero.
The axial stress is now the overburden stress:
The strain and matrix stress:

15. Physical Properties of Formation Materials
Porous Media If
Vertical fractures must act against the x-stress. Therefore sx = pBISIP.
This equation can be use to predict the FG when information regarding the FG is not available.

16. Physical Properties of Formation Materials
Porous Media
A formation 3,000 m in depth exhibited a fracture gradient of 16 kPa/m when the formation pressure was 24,000 kPa. What is the fracture gradient when the formation pressure has declined to 10,000 kPa? Given the density of the overburden rm = 2,290 kg/m3.

17. Physical Properties of Formation Materials
Porous Media
Let , then:
Solving this equation give a = 0.56 and independent to formation pressure.
FG = 0.56(22.4) + ( )8 = 14 kPa/m = psi/ft.

18. Fracture Orientation
Fracture pressure is the pressure in the wellbore at which a formation will crack
The stress within a rock can be resolved into three principal stresses. A formation will fracture when the pressure in the borehole exceeds the least of the stresses within the rock structure. Normally, these fractures will propagate in a direction perpendicular to the least principal stress.

19. Fracture Orientation
At sufficient depths (usually below 1000 m or 3000 ft) the minimum principal stress is horizontal; therefore, the fracture faces will be vertical. For shallow formations, where the minimum principal stress is vertical, horizontal (pancake) fractures will be created.

20. Fracture Formation Pressure Definition and Mechanism

21. Fracture Formation Pressure Formation Integrity Test (FIT)
FIT is the method to test strength of formation, casing shoe, cement bond, by increasing bottom hole pressure to designed pressure.
The main reasons for performing formation integrity test (FIT) are:
To investigate the strength of the cement bond around the casing shoe.
To determine the fracture gradient around the casing shoe and then establish the upper limit of the primary well control for the open hole section.
To investigate well bore capability to withstand pressure below the casing shoe.

22. Fracture Formation Pressure Formation Integrity Test (FIT)

23. Fracture Formation Pressure
The Leak-off Test (LOT) – Limit Test - Formation Breakdown Test
The pressure at which formations will fracture when exposed to borehole pressure is determined by conducting one of the following tests:
• Leak-off test
• Limit Test
• Formation Breakdown Test

24. Fracture Formation Pressure
The Leak-off Test – Limit Test - Formation Breakdown Test
The procedure used to conduct these tests is basically the same in all cases. The test is conducted immediately after a casing has been set and cemented. The only difference between the tests is the point at which the test is stopped. The procedure is as follows:
1. Run and cement the casing string
2. Run in the drillstring and drillbit for the next hole section and drill out of the casing shoe
3. Drill ft of new formation below the casing shoe
4. Pull the drillbit back into the casing shoe (to avoid the possibility of becoming stuck in the openhole)

25. Fracture Formation Pressure
The Leak-off Test – Limit Test - Formation Breakdown Test
5. Close the BOPs at surface
6. Apply pressure to the well by pumping a small amount of mud (generally 1/2 bbl) into the well at surface. Stop pumping and record the pressure in the well. Pump a second, equal amount of mud into the well and record the pressure at surface. Continue this operation, stopping after each increment in volume and recording the corresponding pressure at surface.
7. Plot the volume of mud pumped and the corresponding pressure at each increment in volume.
8. When the test is complete, bleed off the pressure at surface, open the BOP rams and drill ahead

26. Fracture Formation Pressure
The Leak-off Test – Limit Test - Formation Breakdown Test
It is assumed in these tests that the weakest part of the wellbore is the formations which are exposed just below the casing shoe.
It can be seen in the next slide that when these tests are conducted, the pressure at surface, and throughout the wellbore, initially increases linearly with respect to pressure.
At some pressure the exposed formations start to fracture and the pressure no longer increases linearly for each increment in the volume of mud pumped into the well.
If the test is conducted until the formations fracture completely, the pressure at surface will often drop dramatically.

27. Fracture Formation Pressure
The Leak-off Test – Limit Test - Formation Breakdown Test

28. Fracture Formation Pressure
The Leak-Off Test
The “Leak-off test” is used to determine the pressure at which the rock in the open hole section of the well just starts to break down (or “leak off”). In this type of test the operation is terminated when the pressure no longer continues to increase linearly as the mud is pumped into the well.

29. Fracture Formation Pressure
The Limit Test (Or FIT)
The “Limit Test” is used to determine whether the rock in the open hole section of the well will withstand a specific, predetermined pressure. This pressure represents the maximum pressure that the formation will be exposed to while drilling the next wellbore section.

30. Fracture Formation Pressure The Formation Breakdown Test
The “Formation Breakdown Test” is used to determine the pressure at which the rock in the open hole section of the well completely breaks down.

31. Leak Off Test (LOT)

32. Fracture Formation Pressure
Example
While performing a leak off test, the surface pressure at leak off was 940 psi. The casing shoe was at a true vertical depth of 5010 ft and a mud weight of ppg was used to conduct the test. Calculate the maximum allowable mud weight.

33. Fracture Formation Pressure
Example
The Maximum bottom hole pressure during the leakoff test can be calculated from: hydrostatic pressure of column of mud + leak off pressure at surface
= (0.052 x 10.2 x 5010) = 3597 psi
The maximum allowable mud weight at this depth is therefore
= 3597 psi / 5010 ft = psi/ft = 13.8 ppg
Allowing a safety factor of 0.5 ppg,
The maximum allowable mud weight = = 13.3 ppg.

34. Fracture Formation Pressure Surface Leakoff Pressure Calculation
The anticipated surface leakoff pressure, Plo is given by:
Plo = Pff – 0.052rD + DPf
Where DPf is the frictional pressure loss in the well between the surface pressure gauge and the formation during the leakoff test. This equation is also used to compute the observed fracture pressure, Pff, from the observed leakoff pressure Plo.
The pressure required to initiate circulation is obtained by equation:

35. Fracture Formation Pressure Surface Leakoff Pressure Calculation
The anicipated slope line for the early leakoff test results is determined from the compressibility of the drilling fluid. The effective compressibility, ce, of drilling fluid composed of water, oil, and solids having compressibilities cw, co, and cs, respectively.
ce = cwfw + cofo + fsfs
Where fw, fo, and fw are the volume fractions of water, oil, and solids.

36. Fracture Formation Pressure Surface Leakoff Pressure Calculation
Compressibility is defined as
Therefore, the change in pressure due to the change in the volume of drilling fluid is

37. Fracture Formation Pressure Surface Leakoff Pressure Calculation
Example: The leakoff was conducted in 9.625’’ casing having an internal diameter of 8.835’’ which was cemented at 10,000 ft.
The test was conducted after drilling to 10,030 ft the depth of the first sand with an 8.5’’ bit. Drillpipe having an external diameter of 5.5’’ and an internal diameter of 4.67’’ was placed in the well to a depth of 10,000 ft for the test.
A 13.0 lbm/gal water based drilling fluid containing no oil and having a total volume fraction of solids of 0.2 was used. The gel strength of the mud was 10 lbf/100 ft2.
Verify the anticipated slope line and compute the formation fracture pressure.

38. Fracture Formation Pressure Surface Leakoff Pressure Calculation

39. Fracture Formation Pressure Surface Leakoff Pressure Calculation
The effective compressibility:
Ce = cwfw + cofo + csfs.
Ce = (3.0 x 10-6)(0.8) (0.2 x 10-6)(0.2)
Ce = 2.44 x 10-6 psi-1.

40. Fracture Formation Pressure Surface Leakoff Pressure Calculation
The capacity of the annulus, drillstring, and open hole are:
The volume of drilling fluid in the well is:

41. Fracture Formation Pressure Surface Leakoff Pressure Calculation
Thus, the predicted anticipated slope line is
The frictional pressure loss is assumed approximately equal to the pressure needed to break circulation. Since flow was down a drillpipe having a 4.67-in internal diameter, the pressure drop can be predicted as follows:
The fracture pressure:

42. Prediction of Fracture Pressure
Introduction
A potential hazard arises because an increase in mud weight may cause one of the exposed formations to fracture, resulting in loss of circulation.
When and where to set casing greatly depend on the pore pressure and fracture pressure.
Hubbert and Willis in 1957; Mattthew and Kelly in 1967; Eaton in 1967 are common accepted models that have been used to predict the Pff.
These methods can be used to estimate fracture pressures before the well is drilled.

43. Prediction of Fracture Pressure
Summary of Procedures

44. Prediction of Fracture Pressure
General Procedures
Fracture formation pressure is defined as:
The minimum stress, smin, is a function of matrix stress, sma.
Depending on how to handle the minimum stress, there are different correlations.

45. Prediction of Fracture Pressure Hubbert and Willis Equation
They introduced a principle: the minimum wellbore pressure required to extend an existing fracture was given as the pressure needed to overcome the minimum principle stress
Based on the experimental data from the laboratory, they suggested that the minimum principle stress in the shallow sediments is approximately one-third the matrix stress resulting from weight of the overburden

46. Prediction of Fracture Pressure Hubbert and Willis Equation

47. Prediction of Fracture Pressure Hubbert and Willis Equation
Example: Compute the maximum mud density to which a normally pressure U.S. gulf coast formation at 3000 ft can be exposed without fracture. Use the Hubbert and Willis equation for fracture extension. Assume an average surface porosity constant of 0.41, a porosity decline constant K of and an average grain density of 2.6 g/cm3.

48. Prediction of Fracture Pressure Hubbert and Willis Equation

49. Prediction of Fracture Pressure Hubbert and Willis Equation
Formation pressure
Fracture pressure

50. Prediction of Fracture Pressure Matthew and Kelley Correlation
Matthews and Kelley Correlation
Drilling experience showed that Hubbert and Willis method is not valid for deeper formation. Matthews and Kelley replaced the assumption that the minimum stress was one-third the matrix stress by
where Fs, the matrix stress coefficient, was determined empirically from field data taken in normally pressured formations.

51. Prediction of Fracture Pressure Matthew and Kelley Correlation
The cohesiveness of the rock matrix is usually related to the matrix stress and varies only with the degree of compaction.
Matthew and Kelley believed that the conditions necessary for fracturing the formation would then be similar to those for the normally compacted formation.
Fs varies with different geology conditions.

52. Prediction of Fracture Pressure Matthew and Kelley Correlation
The vertical matrix stress at normal pressure is calculated (subscript “n” is for normal pressure)
(sma)n = sobn – Pfn
For simplicity, Matthews and Kelley assumed that the average overburden stress is 1 psi/ft and an average normal pressure gradient is psi/ft. To calculate fracture pressure, they introduced the depth Di.
Di is the equivalent depth that have the same vertical matrix stress as the normal pressured formation of interest depth. In other words, Di will be smaller than the actual depth.

53. Prediction of Fracture Pressure Matthew and Kelley Correlation
Recall: (sma)n = sobn – Pfn
At the depth at which the abnormal pressure presents:

54. Prediction of Fracture Pressure
Figure 1: Equivalent normal pressure depth vs. Matrix stress ratio

55. Prediction of Fracture Pressure Matthew and Kelley Correlation
Example: A south Texas gulf coast formation at 10,000 ft was found to have a normal pore pressure of 8000 psig. Compute the formation fracture gradient using Matthews and Kelley correlation.

56. Prediction of Fracture Pressure Matthew and Kelley Correlation
From Fig 1, at Di = 3738 ft, Fs = 0.58
Note that one of the assumptions is that an average overburden stress gradient is 1. Therefore, the overburden stress or vertical stress
The fracture pressure gradient:

57. Prediction of Fracture Pressure Pennebaker Correlation
The Pennebaker correlation is similar to the Matthews and Kelley correlation.
Pennebaker called the coefficient Fs as the effective stress ratio and correlated this ratio with depth, regardless of pore pressure gradient. Thus, the actual depth of the formation always is used in the Pennebaker correlation.

58. Prediction of Fracture Pressure Pennebaker Correlation
Example: A south Texas gulf coast formation at 10,000 ft was found to have a pore pressure of 8,000 psi. Seismic records indicate an interval transit time of 100 ms/ft at a depth of 6,000 ft. Compute the formation fracture gradient using the Pennebaker correlation.

59. Prediction of Fracture Pressure Pennebaker Correlation

60. Prediction of Fracture Pressure Pennebaker Correlation
From the plot 6.48 at the depth of 10,000 ft, we can get the value of effective stress ratio Fs = 0.82.
Using the plot 6.49 at the depth of 10,000 ft and using the 6000-ft depth line for 100 ms/ft gives a value of vertical overburden gradient sob = 1.02 psi/ft.
smin = Fssma = Fs(sob - Pf) = 0.82(1.02 x 10, ) = 1,804 psig
The fracture pressure is calculated as
Pff = smin + Pf = 1, ,000 = 9,804 psig
The fracture pressure gradient is: 9,804 / 10,000 = 0.98 psi/ft

61. Prediction of Fracture Pressure Christman Correlation
Christman found that the matrix stress coefficient, Fs, could be correlated to the bulk density of the sediments.

62. Prediction of Fracture Pressure Christman Correlation
Example 3: apply the Christman correlation to calculate the fracture pressure gradient based on example 1 and 2. Pore pressure 6500 psig

63. Prediction of Fracture Pressure Christman Correlation
Bulk density
From the Christman Correlation gives
Fracture pressure gradient

64. Prediction of Fracture Pressure
Summary of Procedures
When planning a well the formation pore pressures and fracture pressures can be predicted from the following procedure:
1. Analyse and plot log data or d-exponent data from an offset (nearby) well.
2. Draw in the normal trend line, and extrapolate below the transition zone.
3. Calculate a typical overburden gradient using density logs from offset wells.
4. Calculate formation pore pressure gradients from equations.
5. Calculate the fracture gradient at any depth.