Fracture Gradient - Part I
description
Transcript of Fracture Gradient - Part I
![Page 1: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/1.jpg)
Fracture Gradients
By Dr. Eissa shokir
![Page 2: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/2.jpg)
Prediction of Fracture Gradients4Well Planning4Theoretical Fracture Gradient Determination4Hubbert & Willis4Matthews & Kelly4Ben Eaton4Comparison of Results
4Experimental Frac. Grad. Determination4Leak-off Tests
![Page 3: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/3.jpg)
Well Planning
4Safe drilling practices require that the following be considered when planning a well:
4 Pore pressure determination4 Fracture gradient determination4 Casing setting depth selection4 Casing design
![Page 4: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/4.jpg)
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 ft2. Pore pressure, psi, at 14,000 ft3. Matrix stress, psi/ft
4. Matrix stress, psi
![Page 5: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/5.jpg)
Formation Pressure and Matrix Stress
σ+= PSoverburden pore matrix
stress = pressure + stress(psi) (psi) (psi)
S = P + σ
![Page 6: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/6.jpg)
Formation Pressure and Matrix Stress
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.
![Page 7: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/7.jpg)
Formation Pressure and Matrix Stress
Calculations:3. Matrix stress gradient,
psi
psi/ft
σ / D = 0.522 psi/ft
σ+= PS
DDP
DSor σ
+=
( ) ft/psi478.0000.1DP
DS
D.,e.i −=−=
σ
![Page 8: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/8.jpg)
Formation Pressure and Matrix Stress
Calculations:
4. Matrix stress at 14,000 ft
= 0.522 psi/ft * 14,000 ft
σ = 7,308 psi
![Page 9: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/9.jpg)
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 experimentalapproach to fracture gradient determination. Below are listed and discussed three approaches to calculating the fracture gradient.
![Page 10: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/10.jpg)
Fracture Gradient Determination
1. Hubbert & Willis:
where F = fracture gradient, psi/ft
= pore pressure gradient, psi/ftDP
⎟⎠⎞
⎜⎝⎛ +=
DP21
31Fmin
⎟⎠⎞
⎜⎝⎛ +=
DP1
21Fmax
![Page 11: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/11.jpg)
Fracture Gradient Determination
2. Matthews & Kelly:
where Ki = matrix stress coefficientσ = vertical matrix stress, psi
DP
DKF i +
σ=
![Page 12: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/12.jpg)
Fracture Gradient Determination
3. Ben Eaton:
where S = overburden stress, psiγ = Poisson’s ratio
DP
1*
DPSF +⎟⎟
⎠
⎞⎜⎜⎝
⎛γ−
γ⎟⎠⎞
⎜⎝⎛ −
=
![Page 13: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/13.jpg)
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 three methods.
Summarize the results in tabular form, showing answers, in units of lb/gal and also in psi/ft.
![Page 14: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/14.jpg)
1. Hubbert & Willis:
The pore pressure gradient,
( )F 13
1 2 *0.735 0.823 psiftmin = + =
⎟⎠⎞
⎜⎝⎛ +=
D2P1
31Fmin
PD
0.735 psift
=
Example - Hubbert and Willis
![Page 15: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/15.jpg)
Also,
⎟⎟⎠
⎞⎜⎜⎝
⎛=
lb/galpsi/ft0.052
psi/ft0.823Fmin
lb/gal 15.83Fmin =
Example - Hubbert and Willis
![Page 16: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/16.jpg)
Example - Hubbert and Willis
⎟⎠⎞
⎜⎝⎛ +=
DP1
21Fmax ( )735.01
21
+=
= 0.8675 psi/ft
Fmax = 16.68 lb/gal
![Page 17: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/17.jpg)
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.
DK
DPF iσ+=
σiK
Example
)given(ft/psi735.0DP
=
![Page 18: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/18.jpg)
Example - Matthews and Kelly
(ii) Next, calculate the matrix stress.
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
====
ft ,depthDpsi ,pressure porePpsi ,stress matrix
psi ,overburdenSσ
S = P + σ
σ = S - P= 1.00 * D - 0.735 * D= 0.265 * D= 0.265 * 11,000
σ = 2,915 psi
![Page 19: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/19.jpg)
Example - Matthews and Kelly
(iii) Now determine the depth, , where, under normally pressured conditions, the rock matrix stress, σ would be 2,915 psi.
iD
Sn = Pn + σn n = “normal”1.00 * Di = 0.465 * Di + 2,915
Di * (1 - 0.465) = 2,915
ft449,5535.0915,2Di ==
![Page 20: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/20.jpg)
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
![Page 21: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/21.jpg)
Example - Matthews and Kelly
(v) Now calculate F:DP
DKF i +
σ=
735.0000,11
915,2*685.0F +=
ft/psi9165.0=
gal/lb63.17052.0
9165.0F ==
![Page 22: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/22.jpg)
0.685
5,449
Ki
Dep
th, D
i
![Page 23: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/23.jpg)
Example
Ben Eaton:
DP
1*
DPSF +⎟⎟
⎠
⎞⎜⎜⎝
⎛γ−
γ⎟⎠⎞
⎜⎝⎛ −
=
??DS
=γ=
![Page 24: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/24.jpg)
Variable Overburden Stress by Eaton
At 11,000 ftS/D = 0.96 psi/ft
![Page 25: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/25.jpg)
Fig. 5-5
At 11,000 ftγ = 0.46
![Page 26: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/26.jpg)
Example - Ben Eaton
From above graphs,at 11,000 ft.:
DP
1DP
DSF +⎟⎟
⎠
⎞⎜⎜⎝
⎛−
⎟⎠⎞
⎜⎝⎛ −=
γγ
46.0;ft/psi96.0DS
=γ=
( ) 735.046.01
46.0735.096.0F +⎟⎠⎞
⎜⎝⎛
−−=
F = 0.9267 psi/ft= 17.82 lb/gal
![Page 27: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/27.jpg)
Summary of Results
Fracture Gradientpsi.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
![Page 28: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/28.jpg)
Summary of Results
4 Note that all the methods take into consideration the pore pressure gradient. As the pore pressure increases, so does the fracture gradient.
4 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 σi ).
![Page 29: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/29.jpg)
Summary of Results
4 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.
![Page 30: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/30.jpg)
Similarities
Ben Eaton:
DP
1*
DPSF +⎟⎟
⎠
⎞⎜⎜⎝
⎛γ−
γ⎟⎠⎞
⎜⎝⎛ −
=
Matthews and Kelly:
DP
DKF i +
σ=
![Page 31: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/31.jpg)
![Page 32: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/32.jpg)
Experimental Determination of Fracture Gradient
The leak-off test
4 Run and cement casing4 Drill out ~ 10 ft
below the casing seat4 Close the BOPs4 Pump slowly and
monitor the pressure
![Page 33: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/33.jpg)
![Page 34: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/34.jpg)
![Page 35: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/35.jpg)
![Page 36: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/36.jpg)
![Page 37: Fracture Gradient - Part I](https://reader033.fdocuments.in/reader033/viewer/2022052306/5465a565af795997368b4ea0/html5/thumbnails/37.jpg)