Geology Reference
In-Depth Information
V
cl
SOLID PHASE
Time-Average
(Wyllie) Mixing
Aspect Ratio Model
α
sand
α
clay
Mineral Parameters
KUSTER-TOKSOZ
theory
Porosity (Phi
t
)
Dry Rock Moduli
CALIBRATION
to measured V
p
Fluid Parameters
GASSMANN's EQUATION
V
p
, V
s
,
ρ
Figure 8.36
Schematic view of the Xu-White (
1995
) model.
Owing to the possibility of parameterising differ-
ent porosity types, the Xu
White model has found
application in carbonates and an extension of the
Xu
-
White model has been presented by Xu and
Payne (
2009
). This proceeds by dividing the total por-
osity into four types: (1) clay-related pores, as in the
Xu
-
7.0
6.0
-
White model, but generally only a small fraction
of the porosity as most carbonates are quite clean; (2)
interparticle pores, as in the the Xu
Wyllie's Equation
White model; (3)
microcracks, which have low aspect ratios and make
the rock weaker; and (4) stiff pores, rounded moldic
or vuggy porosity, typically formed by a dissolution
process, with high aspect ratio. These pore types are
added into an effective medium model in the same
way as the Xu
-
5.0
α
=0.13
4.0
3.0
White model.
Figure 8.39
shows an
example of calculated P wave velocity as a function of
porosity and pore type. As with Xu
-
α
=0.01
2.0
White, the model
predicts rock frame properties and Gassmann substi-
tution is used to calculate the fluid-filled response,
with the following refinement. The microcracks have
very low local permeability because of their very small
size. Pore fluid tends to be trapped in the microcracks
and is unable to reach equilibrium as the seismic wave
passes through, thus violating the assumptions of the
-
1.0
0
0.1
0.2
0.3
0.4
Porosity
177
Figure 8.37
Xu-White (
1995
) model results for a clean sand with
varying pore aspect ratio.
