PETE 411

Well DrillingLesson 22

Prediction of Fracture Gradients

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 Lost Circulation

Read:

Applied Drilling Engineering, Ch. 6HW #12Casing Designdue Nov. 1, 2002

NOTE:

On all HW and Quizzes please put:

* PETE 411/501 (or 411/502)* Name, written legibly* Number of HW or Quiz

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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 Mud Design, H2S considerations Contingency planning

Fig. 7.21

Formation Pressure and Matrix StressGiven: 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 ft2. Pore pressure, psi, at 14,000 ft3. Matrix stress, psi/ft 4. Matrix stress, psi

Formation Pressure and Matrix Stressoverburden pore matrix stress = pressure + stress (psi) (psi) (psi) S = P + s

Formation Pressure and Matrix StressCalculations:

1. Pore pressure gradient= 0.433 psi/ft * 9.2/8.33 = 0.052 * 9.2= 0.478 psi/ft2. 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.

Formation Pressure and Matrix StressCalculations:3. Matrix stress gradient,psi

psi/ft s / D = 0.522 psi/ft

Formation Pressure and Matrix StressCalculations:

4. Matrix stress (in psi) at 14,000 ft

= 0.522 psi/ft * 14,000 ft

s= 7,308 psi

Fracture Gradient DeterminationIn 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 four approaches to calculating the fracture gradient.

Fracture Gradient Determination1. Hubbert & Willis:

where F = fracture gradient, psi/ft = pore pressure gradient, psi/ft

Fracture Gradient Determination2. Matthews & Kelly:

where Ki = matrix stress coefficient s = vertical matrix stress, psi

Fracture Gradient Determination3. Ben Eaton:

where S = overburden stress, psi g = Poissons ratio

ExampleA 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 four methods.

Summarize the results in tabular form, showing answers, in units of lb/gal and also in psi/ft.

Example - Hubbert and Willis1. Hubbert & Willis:

The pore pressure gradient,

Example - Hubbert and WillisAlso,

Example - Hubbert and Willis = 0.8675 psi/ft

Fmax = 16.68 lb/gal

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.

Example - Matthews and Kelly(ii) Next, calculate the matrix stress. S = P + ss = S - P = 1.00 * D - 0.735 * D = 0.265 * D = 0.265 * 11,000s = 2,915 psi

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 = normal1.00 * Di = 0.465 * Di + 2,915 Di * (1 - 0.465) = 2,915

Example - Matthews and Kelly(iv) Find Ki from the plot on the right, for

For a south Texas Gulf Coast well, Di = 5,449 ftKi = 0.685

Example - Matthews and Kelly(v) Now calculate F:

ExampleBen Eaton:

Variable Overburden Stress by EatonAt 11,000 ftS/D = 0.96 psi/ft

Fig. 5-5At 11,000 ftg = 0.46

Example - Ben EatonFrom above graphs, at 11,000 ft.:F = 0.9267 psi/ft = 17.82 lb/gal

Summary of Results Fracture Gradient psi.ft lb/galHubbert & Willis minimum: 0.823 15.83Hubbert & Willis maximum: 0.868 16.68Mathews & Kelly: 0.917 17.63Ben Eaton: 0.927 17.82

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 ).

Summary of Results Ben Eaton considers variation in pore pressure gradient, overburden stress and Poissons ratio,

and is probably the most accurate of the four methods. The last two methods are actually quite similar, and usually yield similar results.

SimilaritiesBen Eaton:Matthews and Kelly:

9101112141618Pore Pressures

Experimental Determination of Fracture GradientThe 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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Experimental Determination of Fracture GradientExample:In a leak-off test below the casing seat at 4,000 ft, leak-off was found to occur when the standpipe pressure was 1,000 psi. MW = 9 lb/gal.

What is the fracture gradient?

ExampleLeak-off pressure = PS + DPHYD = 1,000 + 0.052 * 9 * 4,000= 2,872 psi

Fracture gradient = 0.718 psi/ft

EMW = ?