Well Design – Spring 2013
Well Design - PE 413
Chapter 1: Fracture Pressure
Prepared by: Tan Nguyen
Well Design – Spring 2013
Fracture Formation Pressure
Definition and Mechanism
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.
Prepared by: Tan Nguyen
Well Design – Spring 2013
Fracture Formation Pressure
Definition and Mechanism
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.
Prepared by: Tan Nguyen
Well Design – Spring 2013
Fracture Formation Pressure
Definition and Mechanism
Prepared by: Tan Nguyen
Well Design – Spring 2013
Fracture Formation Pressure
The Leak-off Test – 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
Prepared by: Tan Nguyen
Well Design – Spring 2013
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 5 - 10 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)
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Well Design – Spring 2013
Fracture Formation Pressure
The Leak-off Test – Limit Test - Formation Breakdown Test
5. Close the BOPs (generally the pipe ram) 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. Plot the volume of mud pumped and the
corresponding pressure at each increment in volume.
Prepared by: Tan Nguyen
Well Design – Spring 2013
Fracture Formation Pressure
The Leak-off Test – Limit Test - Formation Breakdown Test
7. When the test is complete, bleed off the pressure at surface, open the BOP
rams and drill ahead
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.
Prepared by: Tan Nguyen
Well Design – Spring 2013
Fracture Formation Pressure
The Leak-off Test – Limit Test - Formation Breakdown Test
Prepared by: Tan Nguyen
Well Design – Spring 2013
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.
Prepared by: Tan Nguyen
Well Design – Spring 2013
Fracture Formation Pressure
The Limit Test
The
“Limit
Test”
is
used
to
determine whether the rock in the
open hole section of the well will
withstand
predetermined
a
specific,
pressure.
This
pressure represents the maximum
pressure that the formation will be
exposed to while drilling the next
wellbore section.
Prepared by: Tan Nguyen
Well Design – Spring 2013
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.
Prepared by: Tan Nguyen
Well Design – Spring 2013
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
10.2 ppg was used to conduct the test. Calculate the maximum allowable mud
weight.
Prepared by: Tan Nguyen
Well Design – Spring 2013
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) + 940 = 3597 psi
The maximum allowable mud weight at this depth is therefore
= 3597 psi / 5010 ft = 0.718 psi/ft = 13.8 ppg
Allowing a safety factor of 0.5 ppg,
The maximum allowable mud weight = 13.8 - 0.5 = 13.3 ppg.
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Well Design – Spring 2013
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:
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Well Design – Spring 2013
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.
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Well Design – Spring 2013
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
Prepared by: Tan Nguyen
Well Design – Spring 2013
Fracture Formation Pressure
Surface Leakoff Pressure Calculation
Example: The leakoff test shown in Fig. 6.53 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 lbm/100 ft2. Verify
the anticipated slope line shown in Fig. 6.53 and compute the formation
fracture pressure.
Prepared by: Tan Nguyen
Well Design – Spring 2013
Fracture Formation Pressure
Surface Leakoff Pressure Calculation
Prepared by: Tan Nguyen
Well Design – Spring 2013
Fracture Formation Pressure
Surface Leakoff Pressure Calculation
Prepared by: Tan Nguyen
Well Design – Spring 2013
Fracture Formation Pressure
Surface Leakoff Pressure Calculation
Prepared by: Tan Nguyen
Well Design – Spring 2013
Fracture Formation Pressure
Surface Leakoff Pressure Calculation
Prepared by: Tan Nguyen
Well Design – Spring 2013
Prediction of Fracture Pressure
Hubbert and Willis Equation
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
Pff   min  Pf
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
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Well Design – Spring 2013
Prediction of Fracture Pressure
Hubbert and Willis Equation
Pff 
Pff 
Pff 
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 ma
3
 Pf
 ob  Pf
3
 ob  2 Pf
3
 Pf
Well Design – Spring 2013
Prediction of Fracture Pressure
Hubbert and Willis Equation
Example 1: 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 0.000085 and an
average grain density of 2.6 g/cm3.
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Well Design – Spring 2013
Prediction of Fracture Pressure
Hubbert and Willis Equation
 ob  gr g DS 
g r g  r l o
K
1  e
 ob  0.052  2.6  8.3  3000 
 ob  2660 psi
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 KDS

0.0522.6  1.0748.33  0.41
1  e 0.0000853000
0.000085


Well Design – Spring 2013
Prediction of Fracture Pressure
Hubbert and Willis Equation
Formation pressure
Pf  0.465  3000  1395 psi
Fracture pressure
Pff 
Pff 
 ob  2 Pf
3
2660  2  1395
 1817 psi
3
Prepared by: Tan Nguyen
Well Design – Spring 2013
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
 min  F  ma
where the stress coefficient was determined empirically from field data taken in
normally pressured formations.
Prepared by: Tan Nguyen
Well Design – Spring 2013
Prediction of Fracture Pressure
Matthew and Kelley Correlation
The vertical matrix stress at normal pressure is calculated (subscript “n” is for
normal pressure)
(ma)n = obn – Pfn
For simplicity, Matthews and Kelley assumed that the average overburden stress
is 1 psi/ft and an average normal pressure gradient is 0.465 psi/ft. To calculate
abnormal fracture pressure, they introduced the depth Di. Di is the equivalent
normal pressure depth which represents for the abnormally pressured formation
of interest depth.
Prepared by: Tan Nguyen
Well Design – Spring 2013
Prediction of Fracture Pressure
Matthew and Kelley Correlation
(ma) n  1 Di  0.465Di  0.535Di
At the depth at which the abnormal pressure presents:
( ma )n  ob  Pf D  Pf
Di 


0.535
0.535
0.535
Prepared by: Tan Nguyen
Well Design – Spring 2013
Prediction of Fracture Pressure
Figure 1: Equivalent
normal pressure depth
vs. Matrix stress ratio
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Well Design – Spring 2013
Prediction of Fracture Pressure
Matthew and Kelley Correlation
Example 2: A south Texas gulf coast formation at 10,000 ft was found to have a
pore pressure of 8000 psig. Compute the formation fracture gradient using
Matthews and Kelley correlation.
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Well Design – Spring 2013
Prediction of Fracture Pressure
Matthew and Kelley Correlation
Di 
D  Pf
0.535

10,000  8,000
 3,738 ft
0.535
From Fig 1, at Di = 3738 ft, F = 0.59
 min  F  ma  F  ob  Pf   0.5910,000  8,000  1,180 psig
Note that one of the assumptions is that an average overburden stress
gradient. Therefore, the overburden stress or vertical stress  v  D
The fracture pressure gradient:
Pff 
1
 min  Pf   1 1,180  8,000  0.918 psig / ft
D
10,000
Prepared by: Tan Nguyen
Well Design – Spring 2013
Prediction of Fracture Pressure
Pennebaker Correlation
The Pennebaker correlation is similar to the Matthews and Kelley correlation.
 min  F  ma
Pennebaker called the coefficient F 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, which is shown in
Fig. 6.48.
Prepared by: Tan Nguyen
Well Design – Spring 2013
Prediction of Fracture Pressure
Pennebaker Correlation
Prepared by: Tan Nguyen
Well Design – Spring 2013
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.
Prepared by: Tan Nguyen
Well Design – Spring 2013
Prediction of Fracture Pressure
Pennebaker Correlation
Prepared by: Tan Nguyen
Well Design – Spring 2013
Prediction of Fracture Pressure
Pennebaker Correlation
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Well Design – Spring 2013
Prediction of Fracture Pressure
Pennebaker Correlation
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Well Design – Spring 2013
Prediction of Fracture Pressure
Christman Correlation
Christman found that the stress coefficient could be correlated to the bulk density of
the sediments.
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Well Design – Spring 2013
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
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Well Design – Spring 2013
Prediction of Fracture Pressure
Christman Correlation
  0 e  KD  0.45e 0.00008510,000  0.192
Bulk density
rb  rl  1   r g  1.074  0.192  1  0.1922.6  2.31 g / cm3
From Fig. 2
F  0.8
 min  F  ma  F  ob  Pf   0.89,436  6,500  2,348 psig
Fracture pressure gradient
Pff 
1
 min  Pf   1 2348  6500  0.88 psig / ft
D
10,000
Prepared by: Tan Nguyen
Well Design – Spring 2013
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.
Prepared by: Tan Nguyen
Well Design – Spring 2013
Prediction of Fracture Pressure
Summary of Procedures
Prepared by: Tan Nguyen