Page 144 - Introduction to Petroleum Engineering

PETROELASTIC MODEL 131
development of geologic models, preparing an image of the geologic structure, iden-
tifying faults and folds, and designing wellbore trajectories.

7.5 PETROELASTIC MODEL

Seismic attributes can be related to one another using a petroelastic model. One
example of a petroelastic model, the integrated flow model (IFM) (Fanchi, 2009, 2010),
is used in reservoir simulation software to conduct studies of fluid flow in porous
media. The IFM is based on the assumptions that temperature does not significantly
affect rock properties, and rock properties are elastic. The elasticity assumption is rea-
sonable in regions where rock failure does not occur over the range of pressure and
temperature encountered during the life of a reservoir. The IFM is presented here.

7.5.1 IFM Velocities
The seismic attributes compressional velocity (V ), shear velocity (V ), and associated
P
S
acoustic impedances (Z , Z ) are calculated in the IFM using the relations
P S
S * 4 G *
*
V = , S = * (7.19)
K +
P ρ * 3

G *
V = (7.20)
S
ρ *
V
Z = ρ* , Z = ρ* V S (7.21)
S
P
P
where S* is stiffness, K* is bulk modulus, G* is shear modulus, and ρ* is bulk density.
Bulk density accounts for both pore volume occupied by fluids and volume of rock
grains in the bulk volume. The equation for bulk density is
ρ* = (1 − φ ρ ) m + φρ f (7.22)
where ϕ is porosity, ρ is rock matrix grain density, and ρ is fluid density. Fluid
f
m
density for different fluids occupying pore space is
ρ = ρ S o + ρ S w + ρ S g (7.23)
o
g
f
w
where ρ is fluid density of phase ℓ and S is saturation of phase ℓ. Subscripts o, w, and
ℓ
ℓ
g stand for oil, water, and gas, respectively.
The ratio V /V of compressional velocity to shear velocity is
P S
(
*
V K + 4 G / * 3 ) 4 K*
P = = + (7.24)
V G* 3 G*
S
The ratio V /V is greater than 43/ since the moduli K* and G* are greater than zero.
P S