Geoscience Reference
In-Depth Information
Here P
c
is defined by the fluid buoyancy term,
ʔ
)gh, where h is the height above the free
water level. This equation gives a useful basis
for forward modelling water saturation, given
some known rock and fluid properties.
For practical purposes we often want to esti-
mate the S
w
function from well log data. There
are again several approaches to this
(Worthington
2001
gives a review), but the sim-
plest is the power law function which has the
same form as the J-function:
(
ˁ
Silty
sandstone
1
Clean uniform
sandstone
J(S
w
)
0
0
1
h
d
S
w
S
w
¼
C
:
ð
3
:
38
Þ
A significant issue in reservoir modelling is
how the apparent (and true) saturation height
function is affected by averaging of well data
and/or upscaling of the fine-scale geological
model data.
To illustrate these effects in the reservoir
model, we take a simple case. We must first
define the
free water level
(FWL) - the fluid
water interface in the absence of rock pores, i.e.
resulting only from fluid forces (buoyancy and
hydrodynamic pressure gradients). The effect of
rock pores is to introduce another factor (capil-
lary forces) on the oil-water distribution, so that
the oil-water contact is different from the free
water level.
A simple model for this behaviour is given by
the following saturation-height function:
Fig. 3.42
Example capillary pressure J-functions
We can expand the P
c
equation to include the
fluid properties:
P
c
SðÞ
¼
˃
p
ϕ=
cos
ʸ
JSðÞ
k
ð
3
:
35
Þ
where
˃
¼
interfacial tension
ʸ
¼
interfacial contact angle
J(S
w
)
Leverett J-junction.
Rearranging this we obtain the J-function:
¼
1
=
2
P
c
S
ðÞ
˃
k
ϕ
JSðÞ
¼
ð
3
:
36
Þ
cos
ʸ
Figure
3.42
shows two example J-functions
for contrasting rock types.
To put this more simply, we could measure and
model any number of capillary pressure curves,
P
c
¼
h
i
2
=
3
p
k
S
w
¼
S
wi
þ
ð
1
S
wi
Þ
0
:
1
h
=ϕ
ð
3
:
39
Þ
f(S). However, the J-function method allows
a number of similar functions to be normalized
with respect to the rock and fluid properties and
plotted with a single common curve.
Figure
3.43
shows example curves, based on
this function, and illustrates how at least 10 m
variation in oil-water contact can occur due to
changes in pore throat size. In general, for a high
porosity/permeability rock OWC
FWL. How-
ever, for low permeability or heterogeneous
reservoirs the fluid contact will vary considerably
as
3.7.2 Saturation Height Functions
There are a number of ways of plotting the P
c
¼
f(S) function to indicate how saturation varies
with height in the reservoir. The following equa-
tion is a general form of the P
c
equation, includ-
ing all the key rock and fluid terms.
a
function
of
rock
properties,
and
OWC
FWL.
Further difficulties in interpretation of these
functions come with upscaling or averaging
saturations from heterogeneous systems. For
example, suppose you had a thinly-bedded reser-
voir comprising alternating rock types 2 and 4
(Fig.
3.43
), then the average saturation-height
6
¼
1
=
2
¼
ˁ
w
ˁ
o
ð
Þ
gh
k
ϕ
S
wn
b
ð
3
:
37
Þ
˃
ʸ
cos
