Rock Mechanical Properties
The Most Critical For Stimulation
Stress & Strain
F
F
Observations
Length will decrease
Radius will increase
L1
L2
F
Stress
A
r2
r1
Stress & Strain
F
Strain is the change in the
shape
It can be positive or negative
Strain in length is (-)
L
L
F
L
L
r2
Strain in radius is (+)
r
r
r1
Poisson’s Ratio
It is the ratio between the two strains
F
F
r
r
L
L
L
L
r
r
ORTHOGONAL - NORMAL
L
L
r2
r1
Young’s Modulus
F
Stress
A
It is the ratio between stress
and strains in the longitudinal
direction
F
Stress
E
A
L
Strain
L
F
F
L
L
L
L
r
r
r2
r1
Relationship between Acoustic Velocity and Elastic Moduli
Particle
Motion
Particle
Motion
Wave
Direction
Wave
Direction
Compressional Velocity (P- Wave)
Shear Velocity (S- Wave)
Computation of Elastic Properties from Logs
Three log inputs are used: ts, tc, and b
t s v p
2
R 2 2
t c v s
2
2
b
G 13,474 2
t s
R 2
2R 2
G 3R 4
E
R 1
2
2
2
2
Three log inputs are used: ts, tc, and b
FORMATION STRESSES
z = Po
Z
H = h + t
+ ( * P p )* (1 )
h = Po *
1-
1-
h
H
Parameters Needed for Stress Calculations
Overburden
Po POBW *Wdepth POBR * (TVD Wdepth )
Biot Constant
Biot A B * t
Pore Pressure
Worldwide Experience
A= 0.64
B = 0.854
Pp Pgrad current *
Pgrad Original * (1
) * TVD
max
max
Deviated wells
r=(
x + y
=(
2
4
2
x - y
)(1 - R2 ) + (
)(1+ 3 R4 - 4 R2 ) cos 2
2
2
r
r
r
4
2
2
+ xy (1+ 3 R4 - 4 R2 ) sin 2 + P w R2
r
r
r
x + y
x - y
)(1+ R2 ) - (
)(1+ 3 R4 ) cos 2
2
2
r
r
4
2
- xy (1+ 3 R4 ) sin 2 - P w R2
r
r
2
zz
y
4
2
r
2
R
R
z = z - [2( x - y ) 2 cos 2 + 4 xy 2 sin 2 ]
r
r
x
Poisson’s Ratio Varies With Lithology
0.45
Poisson's Ratio
0.40
0.35
0.30
PR qtz
0.25
PR clay
0.20
PR dolo
0.15
0.10
50
PR lime
PR coal
60
70
80
90
100
110
120
130
Compressional T (sec/ft)
For Internal Use Only
107
140
150
160
Young’s Modulus Estimates
Multiply E/Dens by Rock Density (g/cc)
6.00
E qtz
E clay
5.00
E dolo
E lime
E/Dens
4.00
E coal
3.00
2.00
1.00
0.00
50
60
70
80
90
100
110
120
Compressional t (sec/ft)
For Internal Use Only
108
130
140
150
160
Thank You
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