2-fracture gradients

8/10/2019 2-fracture gradients

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MPWE

Well Drill ing

Prediction of

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

Lost Circulation


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Read:

Applied Drilling Engineering, Ch. 6


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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


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Formation Stresses &

Pressure


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Fig. 7.21


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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 ft3. Matrix stress, psi/ft

4. Matrix stress, psi


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+= PS

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

S = P +


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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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Calculations:

3. Matrix stress gradient,

psi

psi/ft

/ D = 0.522 psi/ft

+= PS

DDP

DSor +=

( ) ft/psi478.0000.1D

P

D

S

D.,e.i ==


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Calculations:

4. Matrix stress (in psi) 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 fourapproaches to calculating the fracture

gradient.


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1. Hubbert & Willis:

where F = fracture gradient, psi/ft

= pore pressure gradient, psi/ft

= overburden stress, psiD

P

+=D

P

D

F2

3

1min

+=D

P

D

F

2

1max


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Hubbert & Willis

Predicts a higher fracture gradient inabnormal pressure and lower fracture

gradient in subnormal pressure

formations.

Found not applicable in soft rock

countries (GOM, northern North Sea),

Mathews and Kelly modified this model


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where F = fracture gradient, psi/ft

= pore pressure gradient, psi/ftDP

+=

D

P21

3

1Fmin

+=D

P1

2

1Fmax


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2. Matthews & Kelly:

where Ki = matrix stress coefficient

= vertical matrix stress, psi

D

P

D

KF i

+

=


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Fracture Gradient by Matthews & Kelly

Calculate the Matrix stressAssume normal

compaction (PPG=.465 psi/ft) andOverburden stress 1psi/ft.

Determine the equivalent Depth Di

corresponding to the assumed normalcompaction

Determine Ki from Ki Vs Depth graph for thefield under consideration

Determine FG using Matthews & Kelly Eqn.


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Matthews & Kelly

Can only be used if fracture data of nearby wells are available for which a graph

of Ki against depth can be established.


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3. Ben Eaton:

where S = overburden stress, psi = Poissons ratio

D

P

1

*

D

PSF +

=


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Fracture Gradient by Etons

Establish Pore Pressure Depth graph forthe field

Establish Density Depth graph and convert

to an Overburden Stress - depth graph(multiply density by 0.4335 to convert to psi/ft)

Establish a Poisson's Ratio Depth graph

Use Etons Equation to predict FG for futurewells


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Ben Eaton

Most Widely used.Modification of Hubbert & Willis

(Overburden stress and Poissons ratio

are assumed to be variablesPoissons ratio for a given field should

be fairly constant and may be

determined from previous offset wellsdata


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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/galusing each of the above four methods.

Summarize the results in tabular form, showinganswers, in units oflb/gal and also in psi/ft.


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The pore pressure gradient,

( )F 13

1 2 *0.735 0.823 psift

min= + =

+=

D

2P1

3

1Fmin

P

D0.735

psi

ft=

Example - Hubbert and Willis


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Also,

F 0.823 psi / ft

0.052psi / ft

lb / gal

min=

F 15.83 lb / galmin=



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+= DP

12

1Fmax ( )735.0121 +=

= 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

(iii) Now determine the depth, , where,

under normally pressured conditions, therock matrix stress, would be 2,915 psi.

iD

Sn = Pn + n n = normal1.00 * Di = 0.465 * Di + 2,915

Di * (1 - 0.465) = 2,915

ft449,5535.0

915,2Di ==


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Example -

Matthews andKelly

(iv) Find Ki fromthe 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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Example

Ben Eaton:

D

P

1

*

D

PSF +

=

??D

S ==

V i bl O b d St b


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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==

( ) 735.0

46.01

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 doesthe 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 thematrix stress ( K i and i ).


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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 four methods. The last two

methods are actually quite similar, andusually 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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910

1112

1416

18

Pore Pressures

E i t l D t i ti f


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Experimental Determination of

Fracture Gradient

The leak-off test

Run and cement casing

Drill out ~ 10 ftbelow the casing seat

Close the BOPs

Pump slowly and

monitor the pressure


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Fracture Gradient

Example:

In a leak-off test below the

casing seat at 4,000 ft, leak-off

was found to occur when thestandpipe pressure was 1,000

psi. MW = 9 lb/gal.

What is the fracture gradient?


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2-fracture gradients

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