Petroleum Engineering 405 Drilling Engineering

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1.11
Fracture Gradients
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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

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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
S P s
overburden pore
matrix stress pressure
stress (psi)
(psi) (psi)
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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
• 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

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Formation Pressure and Matrix Stress

• Calculations
• 3. Matrix stress gradient,

psi psi/ft
s / D 0.522 psi/ft
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Formation Pressure and Matrix Stress

• Calculations
• 4. Matrix stress at 14,000 ft
• 0.522 psi/ft 14,000 ft
• s 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/ft

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Fracture Gradient Determination

• 2. Matthews Kelly
• where Ki matrix stress coefficient
• s vertical matrix stress,
  psi

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Fracture Gradient Determination

• 3. Ben Eaton
• where S overburden stress, psi
• g Poissons ratio

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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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Example - Hubbert and Willis

• 1. Hubbert Willis
• The pore pressure gradient,

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Example - Hubbert and Willis

• Also,

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Example - Hubbert and Willis
0.8675 psi/ft Fmax 16.68 lb/gal
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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.

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Example - Matthews and Kelly

• (ii) Next, calculate the matrix stress.

S P s
s S - P 1.00 D - 0.735 D 0.265
D 0.265 11,000 s 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, s would be 2,915 psi.

Sn Pn sn
n normal 1.00 Di 0.465 Di 2,915
Di (1 - 0.465) 2,915
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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

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5,449
Depth, Di
0.685
Ki
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Example

• Ben Eaton

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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
• g 0.46

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Example - Ben Eaton

• From above graphs,
• at 11,000 ft.

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 si ).

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Summary of Results

• Ben Eaton considers
• variation in pore pressure gradient,
  overburden stress and
• Poissons 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

Matthews and Kelly
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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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