Prediction of Fracture Pressure

Well Design – Spring 2013

Prepared by: Tan Nguyen

Well Design - PE 413

Chapter 1: Fracture Pressure

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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.

Fracture Formation Pressure Definition and Mechanism

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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.


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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

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

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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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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.


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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.


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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.

Fracture Formation Pressure The Leak-Off Test

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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.

Fracture Formation Pressure The Limit Test

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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.

Fracture Formation Pressure The Formation Breakdown Test

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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.

Fracture Formation Pressure Example

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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.

Fracture Formation Pressure Example

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The anticipated surface leakoff pressure, Plo is given by:

Plo = Pff – 0.052D + Pf

Where Pf 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:

Fracture Formation Pressure Surface Leakoff Pressure Calculation

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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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Compressibility is defined as

Therefore, the change in pressure due to the change in the volume of drilling

fluid is


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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.


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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

Prediction of Fracture Pressure

fff PP min

Hubbert and Willis Equation

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fma

ff PP 3

ffob

ff PP

P

3

32 fob

ff

PP


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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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SKDolgSgob e

Kg

Dg

1

3000000085.01000085.0

41.033.8074.16.2052.030003.86.2052.0

eob

psiob 2660


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Formation pressure

psiPf 13953000465.0

Fracture pressure

32 fob

ff

PP

psiPff 18173139522660


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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 the stress coefficient was determined empirically from field data taken in

normally pressured formations.

maF min

Matthew and Kelley Correlation

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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.


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iiinma DDD 535.0465.01)(

At the depth at which the abnormal pressure presents:

535.0535.0535.0)( ffobnma

i

PDPD


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Figure 1: Equivalent

normal pressure depth

vs. Matrix stress ratio

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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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Note that one of the assumptions is that an average overburden stress

gradient. Therefore, the overburden stress or vertical stress

The fracture pressure gradient:

ftPD

D fi 738,3

535.0000,8000,10

535.0

From Fig 1, at Di = 3738 ft, F = 0.59

psigPFF fobma 180,1000,8000,1059.0min

Dv

ftpsigPD

P fff /918.0000,8180,1000,1011

min


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The Pennebaker correlation is similar to the Matthews and Kelley correlation.

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.

Pennebaker Correlation

maF min

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Prediction of Fracture Pressure Pennebaker Correlation

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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.

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Christman found that the stress coefficient could be correlated to the bulk density of

the sediments.

Christman Correlation

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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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192.045.0 000,10000085.00 ee KD

Bulk density

3/31.26.2192.01192.0074.11 cmgglb

From Fig. 2

8.0F

psigPFF fobma 348,2500,6436,98.0min

Fracture pressure gradient

ftpsigPD

P fff /88.065002348000,1011

min


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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.

Summary of Procedures

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Prediction of Fracture Pressure Summary of Procedures

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Prediction of Fracture Pressure