Download - 1.11 Fracture Gradients
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Fracture Gradients 1.11- 1
1.11
Fracture Gradients
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Fracture Gradients 1.11- 2
Prediction of Fracture Gradients
Well PlanningTheoretical Fracture Gradient Determination
Hubbert & WillisMatthews & KellyBen EatonComparison of Results
Experimental Frac. Grad. DeterminationLeak-off Tests
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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
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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
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Formation Pressure and Matrix Stress
PS
overburden pore matrix stress = pressure + stress (psi) (psi) (psi)
S = P +
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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
Depth = 14,000 ft.
Pore Pressure = 9.2 lb/gal equivalent
Overburden stress = 1.00 psi/ft.
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Formation Pressure and Matrix Stress
Calculations:
3. Matrix stress gradient,
psi
psi/ft
/ D = 0.522 psi/ft
PS
DD
P
D
Sor
ft/psi478.0000.1D
P
D
S
D.,e.i
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Fracture Gradients 1.11- 8
Formation Pressure and Matrix Stress
Calculations:
4. Matrix stress at 14,000 ft
= 0.522 psi/ft * 14,000 ft
= 7,308 psi
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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 three approaches to calculating the fracture gradient.
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Fracture Gradient Determination
1. Hubbert & Willis:
where F = fracture gradient, psi/ft
= pore pressure gradient, psi/ftD
P
D
P21
3
1Fmin
D
P1
2
1Fmax
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Fracture Gradient Determination
2. Matthews & Kelly:
where Ki = matrix stress coefficient
= vertical matrix stress, psi
D
P
D
KF i
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Fracture Gradient Determination
3. Ben Eaton:
where S = overburden stress, psi
= Poisson’s ratio
D
P
1*
D
PSF
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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 three methods.
Summarize the results in tabular form, showing answers, in units of lb/gal and also in psi/ft.
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1. Hubbert & Willis:
The pore pressure gradient,
F1
31 2*0.735 0.823
psi
ftmin
D
2P1
3
1Fmin
P
D0.735
psi
ft
Example - Hubbert and Willis
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Also,
lb/galpsi/ft
0.052
psi/ft0.823Fmin
lb/gal 15.83Fmin
Example - Hubbert and Willis
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Example - Hubbert and Willis
D
P1
2
1Fmax 735.01
2
1
= 0.8675 psi/ft
Fmax = 16.68 lb/gal
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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.
D
K
D
PF i
iK
Example
)given(ft/psi735.0D
P
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Example - Matthews and Kelly
(ii) Next, calculate the matrix stress.
ft ,depthD
psi ,pressure poreP
psi ,stress matrix
psi ,overburdenS
S = P +
= S - P = 1.00 * D - 0.735 * D = 0.265 * D = 0.265 * 11,000 = 2,915 psi
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Example - Matthews and Kelly
(iii) Now determine the depth, , where, under normally pressured conditions, the
rock matrix stress, would be 2,915 psi.
iD
Sn = Pn +n n = “normal”
1.00 * Di = 0.465 * Di + 2,915
Di * (1 - 0.465) = 2,915
ft449,5535.0
915,2Di
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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
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Example - Matthews and Kelly
(v) Now calculate F:D
P
D
KF i
735.0000,11
915,2*685.0F
ft/psi9165.0
gal/lb63.17052.0
9165.0F
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0.685
5,449
Ki
Dep
th, D
i
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Fracture Gradients 1.11- 23
Example
Ben Eaton:
D
P
1*
D
PSF
??D
S
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Variable Overburden Stress by Eaton
At 11,000 ft
S/D = 0.96 psi/ft
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Fig. 5-5
At 11,000 ft
= 0.46
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Example - Ben Eaton
From above graphs,
at 11,000 ft.:D
P
1D
P
D
SF
46.0;ft/psi96.0D
S
735.046.01
46.0735.096.0F
F = 0.9267 psi/ft = 17.82 lb/gal
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Summary of Results
Fracture Gradient
psi.ft lb/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
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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 i ).
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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 three methods. The last two methods are actually quite similar, and usually yield similar results.
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Similarities
Ben Eaton:
D
P
1*
D
PSF
Matthews and Kelly:
D
P
D
KF i
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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
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