1.11 fracture gradients

Fracture Gradients 1.11- 1

1.11

Fracture Gradients


Prediction of Fracture Gradients

Well PlanningTheoretical Fracture Gradient Determination

Hubbert & WillisMatthews & KellyBen EatonComparison of Results

Experimental Frac. Grad. DeterminationLeak-off Tests


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


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



PS

overburden pore matrix stress = pressure + stress (psi) (psi) (psi)

S = P +



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.



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



Calculations:

4. Matrix stress at 14,000 ft

= 0.522 psi/ft * 14,000 ft

= 7,308 psi


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.



1. Hubbert & Willis:

where F = fracture gradient, psi/ft

= pore pressure gradient, psi/ftD

P

D

P21

3

1Fmin

D

P1

2

1Fmax



2. Matthews & Kelly:

where Ki = matrix stress coefficient

= vertical matrix stress, psi

D

P

D

KF i



3. Ben Eaton:

where S = overburden stress, psi

= Poisson’s ratio

D

P

1*

D

PSF


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.


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


Also,

lb/galpsi/ft

0.052

psi/ft0.823Fmin

lb/gal 15.83Fmin




D

P1

2

1Fmax 735.01

2

1

= 0.8675 psi/ft

Fmax = 16.68 lb/gal


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


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



(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


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



(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


0.685

5,449

Ki

Dep

th, D

i


Example

Ben Eaton:

D

P

1*

D

PSF

??D

S


Variable Overburden Stress by Eaton

At 11,000 ft

S/D = 0.96 psi/ft


Fig. 5-5

At 11,000 ft

= 0.46


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


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


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 ).


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.


Similarities

Ben Eaton:

D

P

1*

D

PSF

Matthews and Kelly:

D

P

D

KF i


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

1.11 fracture gradients

Documents

dp1dp sf

pore pressure

pore pressure

fracture gradient

matrix stress

overburden

fracture gradients1

matrix stresscalculations