Geoscience Reference
In-Depth Information
The final important question to address is:
Which reservoir or rock unit do we want to
average? There are many related concepts used
to define flowing rock intervals - flow units,
hydraulic units, geological units or simply “the
reservoir”. The most succinct term for defining
the rock units in reservoir studies is the Hydraulic
Flow Unit (HFU), which is defined as represen-
tative rock volume with consistent petrophysical
properties distinctly different from other rock
units. There is thus a direct relationship between
flow units and the 'model elements' introduced
in the preceding chapter.
volumes and flow units in Chap.
4
when we
look at upscaling, but first we need to understand
permeability.
3.2
Understanding Permeability
3.2.1 Darcy's Law
The basic permeability equation is based on the
observations and field experience of Henri Darcy
(1803-1858) while engineering a pressurized
water distribution system in the town of Dijon,
France. His equation relates flow rate to the head
of water draining through a pile of sand (Fig.
3.4
):
Exercise 3.2
Additive properties
Additivity
involves a mathematical
function in which a property can be
expressed as a weighted sum of some inde-
pendent variable(s). The concept is impor-
tant to a wide range of statistical methods
used in many science disciplines. Additiv-
ity has many deeper facets and definitions
that are discussed in mathematics and sta-
tistical literature.
It is useful to consider a wider selection
of petrophysical properties and think
through whether they are essentially addi-
tive or non-additive (i.e. multiplicative)
properties.
What would you conclude about these
terms?
Net-to-gross ratio
Fluid saturation
Permeability
Porosity
Bulk density
Formation resistivity
Seismic velocity, V
p
or V
s
Acoustic Impedance, AI
Q
¼
KA
ð
ʔ
H
=
L
Þ
ð
3
:
3
Þ
where
Q
¼
volume flux of water
¼
K
constant of hydraulic conductivity or coef-
ficient of permeability
A
¼
cross sectional area
ʔ
H
¼
height of water column
L
¼
length of sand column
From this we can derive the familiar Darcy's
Law - a fundamental equation for flow in porous
media, based on dimensional analysis and the
Navier-Stokes equations for flow in cylindrical
pores:
¼
k
ʼ
∇
u
ð
P
þ ˁ
gz
Þ
ð
3
:
4
Þ
Water
Δ
H
Sand
L
Abbaszadeh et al. (
1996
) define the HFU in
terms of the Kozeny-Carmen equation to extract
Flow Zone Indicators which can be used quanti-
tatively to define specific HFUs from well data.
We will return the definition of representative
Q
Fig. 3.4
Darcy's
experiment
