Page 146 - Introduction to Petroleum Engineering

GEOMECHANICAL MODEL 133
7.6 GEOMECHANICAL MODEL

The mechanical behavior of rocks in the subsurface can be modeled using geome-
chanical models. Parameters used in geomechanical modeling include Poisson’s
ratio (ν), Young’s modulus (E), uniaxial compaction (Δh), and horizontal stress
(σ ). This set of geomechanical parameters can be estimated using the IFM.
H
Poisson’s ratio and Young’s modulus depend on the frequency of the vibration.
Dynamic Poisson’s ratio and dynamic Young’s modulus are obtained from
measurements of compressional and shear velocities. Static Poisson’s ratio and
static Young’s modulus are measured in the laboratory using measurements on
cores. Static measurements more accurately represent mechanical properties
of reservoir rock. Consequently, it is worthwhile to be able to transform from
dynamic to static properties.
Dynamic Poisson’s ratio (ν ) is given in terms of compressional (P‐wave) velocity
d
and shear (S‐wave) velocity as
05V 2 −V 2
.
ν = 2 P 2 S (7.31)
d
V P −V S
Once an estimate of dynamic Poisson’s ratio is known, it can be combined with shear
modulus to estimate dynamic Young’s modulus (E ):
d
E = ( 21 +ν d G ) * (7.32)
d
Static Poisson’s ratio (ν ) is calculated from dynamic Poisson’s ratio using the
algorithm s

v = aν b d + c (7.33)
s
where a, b, c are dimensionless coefficients. Coefficients a, b are functions of effec-
tive pressure p , which can be estimated from the IFM as
e
p = p con −α p (7.34)
e
where p is pore pressure. Confining pressure p at depth z is estimated from the
con
overburden pressure gradient γ as
OB
p con = γ OB z (7.35)

The Biot coefficient α is the ratio of the change in pore volume to the change in bulk
volume of a porous material in a dry or drained state (Mavko et al., 2009). The Biot
coefficient α is estimated in the IFM from the Geertsma–Skempton correction

 K 
1
α =−  IFM  (7.36)
 K m 
Static Poisson’s ratio is equal to dynamic Poisson’s ratio when a = 1, b = 1, c = 0.