Page 43 - Applied Petroleum Geomechanics

34 Applied Petroleum Geomechanics

Bender et al. (1996), and the Ocean Drilling Program (ODP, 2008). Dr.
Terry Miller obtained the shallow density correlation based on the measured
porosity and density data. Miller’s shallow density method (KSI/Halliburton
internal research published by Zhang et al., 2008 with KSI’s permission)
addresses the problem that in deepwater, the shallow sediments may have
very high porosities and thus low densities cannot be correctly described
using seismic interval velocities. Using shallow porosity data from
Ostermeier et al. (2001) and the Ocean Drilling Program, the Miller
shallow porosity can be expressed in the following form:
f ¼ f þ f e kd 1=n (2.3)
a
s
b
where f s is the shallow porosity; f a þ f b is the mudline porosity, d is the
depth below the mudline in ft, and k and n are empirically determined pa-
rameters that provide the reasonable fit to the data.
The porosity data can then be applied to calculate near mudline bulk
density, r s , directly by the following relationship:
r ¼ r ð1 f Þþ r f s (2.4)
w
m
s
s
where r m is the average density of the sediment grains (typically 2.65 g/cm 3
for shales); r w is the density of formation water (typically 1.03e
3
1.05 g/cm ).
Fig. 2.3 plots the measured porosity data in the deepwater Gulf of
Mexico locations versus Miller’s near mudline density correlation obtained
from Eqs. (2.3) and (2.4), using f a ¼ 0.35, f b ¼ 0.35, k ¼ 0.0035,
3
3
r m ¼ 2.675 g/cm , r w ¼ 1.05 g/cm , and n ¼ 1.09 (Zhang et al., 2008). In
a similar region where has a low formation density at the shallow depth,
Eqs. (2.3) and (2.4) may be applicable after certain calibrations to the local
core tests or density log data.

2.2 Porosity

2.2.1 Porosity from density, velocity, and resistivity
Porosity (f) is an important property to analyze volumes of the oil and gas
reservoirs. It is defined to be the ratio of a volume of void spaces within a
rock to the total bulk volume of the rock, i.e.,

V pores
f ¼ (2.5)
V rock
where V pores and V rock are the volumes of pores and the rock, respectively.