Geoscience Reference
In-Depth Information
The following function was found to capture
the characteristic vertical permeability of this
system (Ringrose et al.
2003
):
3.7
Saturation Modelling
3.7.1 Capillary Pressure
V
m
Vmc
k
mud
k
sand
k
v
¼
k
sand
ð
3
:
31
Þ
An important interface between the static and
dynamic models is the definition of initial water
saturation. There are numerous approaches to this
problem, and in many challenging situations anal-
ysis and modelling of fluid saturations requires
specialist knowledge in the petrophysics and res-
ervoir engineering disciplines. Here we introduce
the important underlying concepts that will enable
the initial saturation model to be linked to the
geological model and its uncertainties.
The initial saturation model is usually based
on the assumption of capillary equilibrium with
saturations defined by the capillary pressure
curve. We recall the basic definition for capillary
pressure:
P
c
¼
where V
mc
is the critical mudstone volume frac-
tion (or percolation threshold).
This formula is essentially a re-scaled geo-
metric average constrained by the percolation
threshold. This is consistent with the previous
findings by Desberats (
1987
) and Deutsch
(
1989
) who observed that the geometric average
was close to simulated k
v
for random shale
systems, and also noted percolation behaviour
in such systems. This equation captures the per-
colation behaviour (the percolation threshold is
estimated for the geometry of a specific deposi-
tional system or facies), while still employing a
general average function that can be easily
applied in reservoir simulation.
The method has been applied to a full-field
study by Elfenbein et al. (
2005
) and compared to
well-test estimates of anisotropy (Table
3.5
). The
comparison showed a very good match in the
Garn 4 Unit but a poorer match in the Garn 1-3
Units. This can be explained by the fact that the
lower Garn 1-3 Units have abundant calcite
cements (which were modelled in the larger-
scale full-field geomodel), illustrating the impor-
tance of understanding both the thin large-scale
barriers and the inherent sandstone anisotropy
(related to the facies and bedding architecture).
P
non
‐
wetting phase
P
wetting
‐
phase
P
c
¼
½
fS
ðÞ
ð
3
:
32
Þ
The most basic form for this equation is given
by:
p
ϕ=
AS
wn
b
P
c
¼
k
ð
3
:
33
Þ
That is, capillary pressure is a function of the
wetting phase saturation and the rock properties,
summarized by
and k. The exponent b is
related to the pore size distribution of the rock.
Note the use of the normalised water saturation:
ϕ
S
wn
¼
ð
S
w
S
wi
Þ=
ð
S
wor
S
wi
Þ
ð
3
:
34
Þ
Table 3.5
Comparison of simulated kv/kh ratios with well test estimates from the case study by Elfenbein et al. (
2005
)
Modelled k
v
/k
h
:
Geometric average
of simulation model
Modelled k
v
/k
h
:
Geometric average
of well test volume
Well test k
v
/k
h
:
Analytical estimate Comments
Tyrihans South, well test in well 6407/1-2
Reservoir unit
Garn 4
0.031
0.043
<
0.05
Test of Garn 4 interval
Garn 3
0.11
Producing interval uncertain
Garn 2
0.22
Complex two-phase flow
Garn 1
0.11
Tyrihans North, well test in well 6407/1-3
Garn 4
0.025
Garn 3
0.123
0.19
0.055
Test of Garn 1 to 3 interval
Garn 2
0.24
Analytical gas cap
Garn 1
0.12
Partial penetration model
