Page 46 - Applied Petroleum Geomechanics

Rock physical and mechanical properties 37

This equation can be rewritten, in terms of acoustic velocity, as the
following form:
1=V p 1=V m
f ¼ (2.8)
1=V f 1=V m
where V p , V m , and V f are the compressional velocities of the formation,
rock matrix, and pore fluid, respectively.
If pore spaces contain oil or gas, Dt will increase. Therefore, the porosity
calculated from Eqs. (2.6) and (2.7) is optimistic porosity, and corrections
for the gas or oil effect are needed. Fluid effect in high porosity formation
with high hydrocarbon saturation can be corrected by the following
empirical relations, respectively: for oil, f o ¼ 0.9f; for gas f g ¼ 0.7f.
The Wyllie equation (Eq. 2.7) represents consolidated and compacted
formations, generally for a porosity of less than 0.25 in sandstones. Un-
consolidated sandstones, such as those in the US Gulf Coast, Nigeria, and
Venezuela, often have much higher porosity (0.28e0.50). If this equation is
used in unconsolidated sandstones, the correction for the less compaction
effects is necessary. Additionally, the presence of clays within the sand
matrix will increase Dt by an amount proportional to the bulk-volume
fraction of the clay. The following empirical equation can be used for
calculating porosity in sandstones in which adjacent shale values (Dt sh )
exceed 100 ms/ft:

Dt Dt m 1
f ¼ (2.9)
Dt f Dt m C p
where C p is a “lack of compaction” correction factor, ranging commonly
from 1 to 1.3, with values as high as 1.8 occasionally observed (Raymer
et al., 1980). A variety of methods are used to estimate C p . The simplest
is to use the sonic compressional transit time observed in nearby shales
(Dt sh ,in ms/ft) divided by 100, or C p ¼ Dt sh =100.
Raymer et al. (1980) proposed an empirical velocity to porosity trans-
form for 0 < f < 0.37:
2
V p ¼ð1 fÞ V m þ fV f (2.10)
Raiga-Clemenceau et al. (1988) proposed another empirical relation-
ship of porosity and sonic transit time in a porous medium:

1=x
Dt m
f ¼ 1 (2.11)
Dt