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# 1.

11

Well Planning
Hubbert & Willis
Matthews & Kelly
Ben Eaton
Comparison of Results
Leak-off Tests

Well Planning
Safe drilling practices require that the
following be considered when
planning a well:
Pore pressure 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
Formation Pressure and Matrix Stress

S =S PP +

overburden pore matrix
stress
= pressure + stress 1.11- 5
Formation Pressure and Matrix Stress
Depth = 14,000 ft.
Pore Pressure = 9.2 lb/gal equivalent
Calculations:
Overburden stress = 1.00 psi/ft.

= 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
Formation Pressure and Matrix Stress

Calculations:
S P psi
S P
or psi/ft
D D D
S P
i.e., 1.000 0.478 psi / ft
D D D

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

Calculations:

= 7,308 psi

## In order to avoid lost circulation while

drilling it is important to know the variation

## Leak-off tests represent an experimental

determination. Below are listed and
discussed three approaches to calculating

1 2P
1. Hubbert & Willis: Fmin 1
3 D
1 P
Fmax 1
2 D
where F = fracture gradient, psi/ft
P
D

K i P
F
D D

## where Ki = matrix stress coefficient

= vertical matrix stress, psi

3. Ben Eaton:

S P P
F *
D 1 D

= Poissons ratio

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.
Example - Hubbert and Willis

## 1. Hubbert & Willis: 1 2P

Fmin 1
3 D
P psi
D ft

1 psi
Fmin 1 2 *0.735 0.823
3 ft
Example - Hubbert and Willis

Also,
0.823 psi/ft
Fmin
psi/ft
0.052
lb/gal

## Fmin 15.83 lb/gal

Example - Hubbert and Willis

1 P 1
Fmax 1 1 0.735
2 D 2

= 0.8675 psi/ft

## Fmax = 16.68 lb/gal

Example

P K i
2. Matthews & Kelly F
D D
In this case P and D are known, may be
calculated, and K i is determined graphically.

## (i) First, determine the pore pressure gradient.

P
0.735 psi / ft (given )
D
Example - Matthews and Kelly

## S=P+ S overburden, psi

matrix stress, psi

=S-P
= 1.00 * D - 0.735 * D P pore pressure, psi
D depth , ft
= 0.265 * D
= 0.265 * 11,000
= 2,915 psi
Example - Matthews and Kelly

## (iii) Now determine the depth, D i , where,

under normally pressured conditions, the
rock matrix stress, would be 2,915 psi.
Sn = Pn + n n = normal
1.00 * Di = 0.465 * Di + 2,915
Di * (1 - 0.465) = 2,915

2,915
Di 5,449 ft
0.535
Example -
Matthews and
Kelly

the plot on the
right, for
Di = 5,449 ft

## For a south Texas

Gulf Coast well,
Ki = 0.685
Example - Matthews and Kelly
K i P
(v) Now calculate F: F
D D

0.685 * 2,915
F 0.735
11,000
0.9165 psi / ft
0.9165
F 17.63 lb / gal
0.052
5,449
Depth, Di

0.685

## Fracture Gradients Ki 1.11- 22

Example

Ben Eaton:

S P P
F *
D 1 D

S
? ?
D
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, S P P

F
D D 1 D
at 11,000 ft.:
S
0.96 psi / ft; 0.46
D

0.46
F 0.96 0.735 0.735
1 0.46
F = 0.9267 psi/ft
= 17.82 lb/gal
Summary of Results

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
As the pore pressure increases, so does

## In the above equations, Hubbert & Willis

apparently consider only the variation in
Kelly also consider the changes in rock
matrix stress coefficient, and in the
matrix stress ( Ki and i ).

Summary of Results

## Ben Eaton considers

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.
Similarities

Ben Eaton:

S P P
F *
D 1 D

Ki P
F
D D

## Matthews and Kelly:

Experimental Determination of

## 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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