Geoscience Reference
In-Depth Information
laminated rock - a cross-bedded aeolian sandstone
(Fig.
4.10
), oil becomes trapped in the high perme-
ability layers upstream of low permeability layers
due to water imbibition into the lower permeability
layers (Huang et al.
1995
).
The chosen flow rate for this experiment was
at typical reservoir waterflood rate (around
0.1 m/day). This trapped oil can be mobilised
either by reducing the capillary pressure (e.g.
by modifying the interfacial tension by use of
surfactant chemicals) or by increasing the flow
rate, and thereby the viscous forces. Alterna-
tively, a modified flow strategy favouring flow
along the rock layers (parallel to bedding) would
result in less capillary trapping and a more effi-
cient waterflood. In the more general case, where
the rock has variable wettability the effects of
capillary/viscous interactions become more com-
plex (e.g. McDougall and Sorbie
1995
; Huang
et al.
1996
; Behbahani and Blunt
2005
).
(a) Calculate the upscaled horizontal and
vertical single-phase permeability using
averaging.
(b) Calculate selected values for the
upscaled two-phase relative permeabil-
ity curves, assuming steady-state capil-
lary equilibrium conditions. Use the
flow functions shown in Fig.
4.11
,as
tabulated below, with water saturation,
S
w
; relative permeability to water, krw;
relative permeability to oil, krow; cap-
illary pressure, P
c
(bars). Choose P
c
values of 0.05 and 0.3 (shown in bold).
Exercise 4.1
Permeability upscaling for a simple layered
model.
The simple repetitive layered model
showninFig.
4.11
canbeusedtoillus-
trate single and multi-phase permeability
upscaling using the “back of the enve-
lope” maths. We assume the two layers
are regular and of equal thickness. Rock
type 1 has a permeability of 100md and
rock type 2 has a permeability of
1,000md.
Table for rock type 1 (100 mD)
Table for rock type 2 (1,000 mD)
Sw
krw
krow
Pc
Sw
krw
krow
Pc
0.2092
0.0
0.9
10.0
0.05432
0.0
0.9
10.0
0.209791
0.0000004
0.897752
2.744926
0.055066
0.0
0.897752
0.976926
0.212154
0.000009
0.888792
0.938248
0.058048
0.000016
0.888792
0.333925
0.215108
0.000038
0.877668
0.590923
0.059
0.000023
0.887
0.3
0.221016
0.000151
0.855673
0.372172
0.061777
0.000065
0.877668
0.210311
0.226
0.0003
0.839
0.3
0.069234
0.000259
0.855673
0.132457
0.238740
0.000943
0.791683
0.201984
0.091604
0.001618
0.791683
0.071887
0.256464
0.002413
0.730655
0.147628
0.113974
0.004141
0.730655
0.052541
0.26828
0.003771
0.691590
0.127213
0.119
0.005
0.718
0.05
0.32736
0.015084
0.515190
0.080120
0.128888
0.006471
0.691590
0.045275
0.38644
0.033939
0.368967
0.061135
0.203456
0.025884
0.515190
0.028515
0.44552
0.060336
0.250969
0.050461
0.278024
0.058239
0.368967
0.021758
0.449
0.062
0.245
0.05
0.352592
0.103536
0.250969
0.017959
0.5046
0.094275
0.159099
0.043483
0.42716
0.161775
0.159099
0.015476
0.56368
0.135756
0.091074
0.038504
0.501728
0.232956
0.091074
0.013704
0.62276
0.184779
0.044366
0.034742
0.576296
0.317079
0.044366
0.012365
0.68184
0.241344
0.016099
0.031781
0.650864
0.414144
0.016100
0.011311
0.74092
0.305451
0.002846
0.029380
0.725432
0.524151
0.002846
0.010456
0.8
0.3771
0.000000
0.027386
0.8
0.6471
0.000000
0.009747
