heriot-watt university tony peters - kerr- mcgee (north sea ltd) · supervisors – tony peters -...
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Heriot-Watt University
Institute of Petroleum Engineering
Supervisors – Tony Peters - KERR- MCGEE (North Sea Ltd)
Gillian Pickup (Heriott-Watt)
MSc Petroleum Engineering
Project Report 2004/2005
Rohan Corlett
“Relative Permeability Upscaling
From Water-Oil Ratio Plot”
- 2 -
Declaration:
I Rohan Corlett confirm that this work submitted for assessment is my own and is
expressed in my own words. Any uses made within it of words of other authors in any
form (eg. Ideas, equations, figures text, tables, programs) are properly acknowledged at
the point of their use. A list of the references employed is included.
Signed…………………………………………………………..
Date………………………………………….
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ACKNOWLEDGEMENTS
I would like to express my sincere thanks to my project supervisors, Tony Peters, Kerr
McGee North Sea U.K Ltd, Aberdeen, and Gillian Pickup, Heriot-Watt University for
their support, comments and knowledge throughout this project.
I would also like to thank Richard Todd, John Baillie, Sarah Brady, Kerr McGee North
Sea U.K Ltd and Jasper Schmidt, Horizon Energy Partners BV, for their involvement and
guidance.
- 4 -
SUMMARY
Dynamic upscaling especially in highly heterogeneous reservoir models is a very
challenging procedure and it is often hard to produce good history matches.
This report investigates the validity of a novel dynamic upscaling technique that only
requires knowledge of fluid properties (oil and water) and production history to generate
relative permeability pseudos that can be applied to full field simulation models to achieve
a history match.
The report
• Describes the background and method to the proposed technique.
• details the simulation study performed to investigate the validity of the technique
for a range of reservoir and fluid types
• Applies technique to north sea field
The results from the simulation studies showed good agreement with the fine scale models
indicating that this was a viable technique. The method was then applied to a full field
model which achieved excellent history matches to watercut.
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TABLE OF CONTENTS
INTRODUCTION ............................................................................................... - 7 -
1 UPSCALING TECHNIQUE .................................................................... - 8 -
1.1 Background................................................................................................................................... - 8 -
1.1.1 – The Water-Oil Ratio ............................................................................................................... - 8 -
1.1.2 Background –Fractional Flow ................................................................................................. - 10 -
1.1.3 Background – Mobile Hydrocarbon ........................................................................................ - 10 -
1.1.4 Background – Corey Functions ............................................................................................... - 11 -
1.2 Upscaling Technique Method .................................................................................................... - 12 -
2 SIMULATION STUDY INVESTIGATION ............................................. - 15 -
2.1 Introduction ................................................................................................................................ - 15 -
2.2 Model boundary effects ............................................................................................................. - 15 -
2.3 Homogeneous Models ................................................................................................................ - 17 -
2.3.1 Fine Scale model ..................................................................................................................... - 17 -
2.3.2 Coarse grid model ................................................................................................................... - 20 -
2.3.3 Results ..................................................................................................................................... - 20 -
2.3.4 Pseudo Adjusting ..................................................................................................................... - 22 -
2.4 Varying Rock curves .................................................................................................................. - 28 -
2.5 Heterogeneous Models ............................................................................................................... - 30 -
2.5.1 Model with High Permeability Streak ..................................................................................... - 30 -
2.5.2 Heterogeneous model .............................................................................................................. - 32 -
2.5.3 Viscous model ......................................................................................................................... - 39 -
3 APPLICATION OF TECHNIQUE TO A NORTH SEA FIELD .............. - 42 -
4 CONCLUSIONS ................................................................................... - 46 -
5 References ................................................................................................................................... - 47 -
6 Appendix ..................................................................................................................................... - 48 -
- 6 -
TABLE OF FIGURES
Figure 1 - Typical Water-Oil Ratio Plot ........................................................................... - 8 -
Figure 2 - Examples of North Sea Field WOR Plots ........................................................ - 9 -
Figure 3 - Fraction Flow Curve Generated From WOR Plot ......................................... - 13 -
Figure 4 - Matching of fractional flow curves ................................................................ - 14 -
Figure 5 - Model showing different well locations ........................................................ - 16 -
Figure 6 - WOR plots for production wells in different locations ................................. - 16 -
Figure 7 - WOR for Homogeneous model ..................................................................... - 18 -
Figure 8 - Fractional flow curve matching for homogeneous model ............................. - 19 -
Figure 9 - Corey curves from Nw = 1.51 & No = 1.82, that were inputted in to Coarse
scale model ..................................................................................................................... - 19 -
Figure 10 - FOPT vs FWCT for coarse and fine models................................................ - 20 -
Figure 11 - Comparison of WWCT ................................................................................ - 21 -
Figure 12 – BHP match .................................................................................................. - 22 -
Figure 13a & b - Pseudo relative permeability curve and comparison of FOPT vs. FWCT . -
23 -
Figure 14 - Pseudo relative permeability curves where Krw &Kro are constant ........... - 24 -
Figure 15 - FWCT vs. FOPT comparison of fine and coarse with adjusted pseudos. ... - 25 -
Figure 16a & b - Pseudo curves with reduced water mobility and FWCT comparison for
COARSE Model with adjusted pseudo .......................................................................... - 26 -
Figure 17a & b - Pseudo curves and FWCT comparison for coarse with adjusted pseudo .. -
27 -
Figure 18 - WWCT comparision .................................................................................... - 28 -
Figure 19 - WOR plot and FOPT vs FWCT comparision .............................................. - 29 -
Figure 20 - WOR plot for heterogeneous model with high permeability streak ............ - 30 -
Figure 21 - Fw curve matching for high perm streak model .......................................... - 31 -
Figure 22 - FOPT vs. FWCT comparison for model with High permeability layer ...... - 31 -
Figure 23 - WOR plot for Hetrogeneous model ............................................................. - 32 -
Figure 24 - Satuartion profile showing coning ............................................................... - 33 -
Figure 25 - Saturation profiles after 13 & 14 years showing coning ............................. - 34 -
Figure 26 - WOR for model with Kv/Kh = 1 ................................................................. - 34 -
Figure 27 – WOR plot for Heterogeneous model........................................................... - 35 -
Figure 28 - Curve matching ............................................................................................ - 36 -
Figure 29 - FOPT vs. FWCT comparison for Heterogeneous model ............................. - 37 -
Figure 30 - Curve matching to flood front saturation, Swf. ........................................... - 38 -
Figure 31 - Simulation performance ............................................................................... - 38 -
Figure 32 – Comparison of WOR plot for models with high permeability in different
layers ............................................................................................................................... - 40 -
Figure 33 – Curve matching viscous model ................................................................... - 40 -
Figure 34 - FOPT vs FWCT comparison for viscous model .......................................... - 41 -
Figure 35 – WOR for North Sea Fulmar oil reservoir .................................................... - 43 -
Figure 36 - Curve match to WOR .................................................................................. - 43 -
Figure 37 – Relative permeability curves that were inputted into full field model ........ - 44 -
Figure 38 - watercut match for well ............................................................................... - 44 -
Figure 39 - Watercut match for well in same reservoir .................................................. - 45 -
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Introduction
Reservoir simulation models are routinely used to predict the future performance of a
reservoir under different depletion and operating scenarios. To produce a reliable
characterisation of a reservoir, reservoir engineers and geoscientists need to build multi-
million geocellular models, which require a great deal of time and processing power for
flow simulations. The use of less complex models with a reduced number of cells is
therefore preferred, and is generally referred to as “upscaling”. Upscaling results in the
loss of important property information. Static reservoir properties, such as porosity, net-
to-gross, and initial water saturation are relatively straightforward to upscale. However,
the upscaling of dynamic properties such as absolute permeability (horizontal & vertical),
capillary pressure, and relative permeability tend to be more difficult. Dynamic upscaling
requires accurate reservoir description and fine scale simulation studies to generate
“pseudo” relative permeabilities that can be applied to full field models.
This report investigates the validity of a novel dynamic upscaling technique that only
requires knowledge of fluid properties (oil and water) and production history to generate
relative permeability pseudos that can be applied to full field simulation models to achieve
a history match. The technique is only applicable to undersaturated oilfields that have a
production history with a developing watercut.
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1 Upscaling Technique
This section describes the upscaling technique.
1.1 Background
1.1.1 – The Water-Oil Ratio
Many North Sea Oil fields exhibit a strong water-oil ratio (WOR) production trend. That is
a semi-log plot of:
Water Production Rate vs. Cumulative Oil Production [ 1]
Oil Production Rate
exhibits a linear trend that, in theory, can be extrapolated to an ultimate recovery for a
given watercut cutoff. Figure 1 is an example of a typical water-oil plot. In it, a linear
trend is observed for WOR > 0.4. From the extrapolation of the WOR trend an ultimate
recovery of around 4.5 MMbbls can calculated for a 95% watercut cutoff.
0.01
0.1
1
10
100
- 1,000,000 2,000,000 3,000,000 4,000,000 5,000,000 6,000,000
Cumulative Oil Production
Historical
Production
WOR
Extrapolation
WOR =19
95% watercut
WA
TE
R-O
IL R
atio
v/v
Ultimate Recovery
4.5 MMbbls
Figure 1 - Typical Water-Oil Ratio Plot
- 9 -
There is debate in the reservoir engineering community about the validity of the water-oil
ratio plot for predicting ultimate economic recovery from a reservoir [2]. Some of the
standard reservoir engineering reference books [3] [4] do not describe the water-oil ratio plot
as a tool for predicting ultimate recovery from a reservoir.
Example WOR plots for four actual North Sea Fields are shown in Figure 2 [5]. It can be
seen that linear trends are clearly discernible during periods of stable reservoir conditions.
Figure 2 - Examples of North Sea Field WOR Plots
0.01
0.10
1.00
10.00
100.00
Cum Oil
WO
R
WOR
0.0
0.1
1.0
10.0
100.0
Cum Oil bbl
WO
R
WOR
Consistent WI
Management
0.01
0.10
1.00
10.00
100.00
Cum Oil
WO
R
0
50000
100000
150000
200000
250000
300000
WOR
Field Injection
Late Time WOR
Upturn due to Low Water
injection
Small field, aquifer support
Auk WOR
0.001
0.01
0.1
1
10
100
Cum Oil
WO
R
WOR Monthly
Successful Infill Drilling campaign, WOR not valid, fractured reservoir ?
- 10 -
1.1.2 Background –Fractional Flow
The fractional flow of water (Fw), at any point in the reservoir is defined as:
Fw = QwBw / (QwBw + QoBo)…………………………………EQ. 1
Where (in field units)
, Qw = Water flow rate (stb/d)
Qo = Oil flow rate (stb/d)
Bw = Water formation volume factor (rb/stb)
Bo = Oil formation volume factor (rb/stb)
For displacement in a horizontal reservoir, and neglecting capillary pressure the fractional
flow equation can also be written as:
Fw = 1 / [1 + (μw/krw)*(kro/μo)]……………………………EQ. 2
Where, μo = Viscosity of oil
μw = Viscosity of water
krw = relative permeability to water
kro = relative permeability to oil
1.1.3 Background – Mobile Hydrocarbon
For a given porosity unit, the mobile hydrocarbon pore volume (HCPV) is defined as
(1-Swc-Soirr)…………………………………...………EQ. 3
Where
Swc = Initial water saturation
Soirr = irreducible oil saturation to water
- 11 -
1.1.4 Background – Corey Functions
Pore scale fractional flow information is usually measured during laboratory coreflooding
tests on cores taken from the reservoir. In the absence of such information, reservoir
engineers often generate relative permeability data (for use in reservoir simulation) using
Corey functions.
Corey functions are defined as:[6]
Relative permeability of Oil:
Kro =Kro (end point)* [(1-Sw-Soirr)/(1-Swc-Soirr)]No……………EQ. 4
Relative permeability of Water:
Krw = Krw (end point)*[(Sw-Swi)/(1-Swi-Soirr)]Nw……………EQ. 5
Where, Kro = Relative permeability of Oil
Krw = Relative permeability of Water
Krw (end point) = end point on water relative permeability curve
Kro (end point) = end point on oil relative permeability curve
No = Corey exponent for Oil
Nw = Corey exponent for water
The reservoir engineer uses different oil and water exponent to generate curves suitable for
the rock wettability and oil/water viscosity ratio.
- 12 -
1.2 Upscaling Technique Method
The upscaling technique simply converts field scale fractional flow to relative
permeability data that can be used in full field simulation models. It uses the base
assumption that the linear trend on the water oil ratio plot both extrapolates to the ultimate
recovery from the reservoir and accurately predicts the future fractional flow of the
reservoir. For the technique to be appropriate the WOR for the field must have exhibited a
linear trend (after initial rollover).
Workflow
FOPT = cumulative production
At connate water saturation oil is immobile, therefore:
When,
Sw = Swc, FOPT = 0
Then Sw=1-Soirr FOPT = Ultimate Recovery
Intermediate saturation values are determined for FOPT values from the following
approximation:
Sw = Swi + (FOPT/Ultimate Cumulative recovery)*(1-Swi-Soirr) …………EQ. 6
For each intermediate Sw value, the oil rate and water rates can be calculated directly from
the WOR plot. Hence a fractional flow curve can be generated from EQ. 1 (Figure 3) for
historic and future Sw.
- 13 -
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00Sw
Fw
Fractional flow curve
Swi
HCPV
FOPT0 Ultimate recovery
(1- Soirr)
Swf
Figure 3 - Fraction Flow Curve Generated From WOR Plot
The flood front saturation, Swf, is defined as the tangency point on the fractional flow
curve [4]. Relative permeabilities are then calculated for Saturation values between Swi
and 1-Soirr. Corey functions are then used to match the fractional flow for the saturation
range only when a linear trend on the WOR plot is observed (and predicted) [by
application of Equations 2,4,5]. Figure 4 shows the resultant match (note no match to the
FW prior to WOR linearity has been attempted)
- 14 -
Curve Matching
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80Sw
Fw
0.1
1
10
100
1000
WO
R
Fw (from rel perm)
Fw from WOR
Series1
WOR
Start of linear WOR,
corresponds to the point at
which Fw curves are matched
Figure 4 - Matching of fractional flow curves
The relative permeabilities used to obtain the match are then inputted into the coarse scale
model.
This upscaling technique should produce good recovery and water cut matches from the
point that the fractional flow curves are matched.
- 15 -
2 Simulation Study Investigation
2.1 Introduction
The validity of this proposed upscaling technique was evaluated through a number of
simulations for different geological realisations. To investigate the technique a fine scale
model was run to produce the production data needed for the upscaling procedure. The
produced pseudos were then inputted into a coarse grid model with identical geometry as
the fine scale model and the performances were compared. The first tests that were carried
out used simple 3-dimensional homogeneous models. Further tests were performed where
parameters like heterogeneity, fluid viscosity and geometry were varied. This section
details the study.
2.2 Model boundary effects
As previously stated from real production data the WOR plot will tend towards a linear
straight line. To ensure the simulation models simulations truly reflected pore scale
fractional flow a study was performed to investigate effects that model boundaries might
have on production profiles (FW).
A fine scale simulation models was constructed. It was homogeneous and was run with an
injector / producer pair with injection controlled on a 100% voidage replacement basis.
Sensitivities investigating the effects that producer location has on the well’s WOR were
performed. (Figure 5 shows the position of each production relative to the injector). The
WOR plots for each well location are shown in Figure 6 It can clearly be observed that
when the producer is near the rear boundary of the model there is a large upturn in the
- 16 -
WOR plot. However, as the distance from the rear boundary to the producer is increased
the WOR plot tends more towards a straight line.
Figure 5 - Model showing different well locations
WOR Plots
0.1
1
10
100
1000
2000000 2500000 3000000 3500000 4000000 4500000 5000000 5500000 6000000
FOPT (STB)
Ln
WO
R
Well 1 Well 2
Well 3 Well 4
Well 5 Well 6
Figure 6 - WOR plots for production wells in different locations
From this it was concluded that the upturn on the WOR plots from the simulation is an
effect of the boundaries. When carrying out the simulation investigation only fine scale
Inj W 1 W 2 W 3 W 4 W 5 W 6
- 17 -
models that have a relatively straight line WOR plots were used (i.e. distances from
boundaries were adjusted to ensure correct pore scale fractional flow was being
represented in the well’s production).
2.3 Homogeneous Models
2.3.1 Fine Scale model
The first test was carried out using a simple 3-dimensional homogeneous model with 119
x 21 x 7 fine grid blocks. The properties of the fine grid blocks are shown in Table 1.
Property Value
Porosity, φ 0.2
Permeability 100mD
Viscosities, µo 0.48 cP
µw 0.312 cP
Formation factors, Bo 1.348 rb/bbl
Bw 1.05 rb/bbl
Grid Block sizes, dx 64.3 ft
dy 59.5 ft
dz 14.4 ft Table 1 - Fine scale model parameters
The rock relative permeabilities were derived from the Corey equation, where, values for
the Corey exponents of Nw = 2 and No = 2 were used. The end points on the relative
permeability curves were Krw = 0.362 and Kro = 0.65. The model used saturation values
of Swi = 0.35 and Swoirr = 0.25. Capillary pressure was zero.
Situated in the model were two wells: the producer producing 5000 rb/d and an injector
injecting at 100% voidage replacement. Both wells were completed vertically through the
entire reservoir interval. Further details of the fine scale simulation model are available in
Appendix A. The simulation was run for approximately 90 years in order to achieve a
water cut of 99%. The output data was used to produce a WOR for the fine scale
simulation, see Figure 7.
- 18 -
WOR Plot
y = 0.0006046256e0.0000014739x
0.1
1
10
100
1000
4000000 4500000 5000000 5500000 6000000 6500000 7000000 7500000 8000000 8500000 9000000
FOPT (STB)
WO
R
WOR
Extrapolation
Ultimate Recovery
8.4 MMbbls
WOR = 150
99% watercut
Equation of Extraploated line
Figure 7 - WOR for Homogeneous model
It was observed that there was a slight deviation from the straight line extrapolation due to
the effect of the model’s boundaries. The values at which the WOR plot began to deviate
from the straight line to the last point were discarded and new values of FOPT for values
of WOR were determined from the equation of the extrapolated straight line.
The fractional flow from the simulation was calculated and plotted along side the
fractional flow curve from the relative permeabilities. The fractional flow curve was
adjusted until the curves matched from the point that the WOR linear trend starts. Figure
8, shows the match that was achieved using Corey exponents of Nw = 1.51 and No = 1.83.
- 19 -
Curve Matching
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80Sw
Fw
0.1
1
10
100
1000
WO
R
Fw (from rel perm)
Fw from WOR
WOR
Extraploation of WOR
Fw curves are matched to
start of linear WOR, with
Corey exponents of Nw = 1.51
& No = 1.83
Figure 8 - Fractional flow curve matching for homogeneous model
The subsequent Corey curves for water and oil are also shown in Figure 8. These are the
relative permeability curves that were inputted into the coarse grid model. The above plots
shows one of the potential limitations of the technique – when a straight line on WOR is
only achieved at high watercuts.. This limitation is perceived as not many North Sea
reservoirs are homogeneous and a WOR trend is usually observed at watercuts below 50%
(Figure 2).
Corey curves
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80Sw
Kr
Psuedo Kro
Krw
Figure 9 - Corey curves from Nw = 1.51 & No = 1.82, that were inputted in to Coarse scale model
- 20 -
2.3.2 Coarse grid model
A coarse grid model with 17 x 3 x 1 grid blocks equating to a 7 x7 x 7 coarsening system
was built ensuring that it had the same STOIIP, reservoir properties and interwell
distances as the fine same model. The WOR generated relative permeabilities were
inputted into the coarse grid and the model run for the same number of years. The
performance of the coarse scale model was then compared to the fine scale model.
2.3.3 Results
2.3.3.1 Oil Production Total vs. Field Water Cut Total
The achieved cumulative production vs. watercut plot match is shown in Figure 10.
Performance Match
0.1
1
10
100
1000
2000000 3000000 4000000 5000000 6000000 7000000 8000000 9000000
FOPT (STB)
WO
R
0
0.2
0.4
0.6
0.8
1
1.2
WOR
Fine
Coarse
Extrapolation
Start of match at
watercut of 78%
corresponds to start
of WOR linear trend
Figure 10 - FOPT vs FWCT for coarse and fine models
From the plot it can be seen that the coarse model shows a very good match for water cut
values above approximately 80%. As this upscaling technique is aimed at mature fields
- 21 -
that have high water cuts, this match is very satisfactory. When the WOR was plotted on
the same graph it could be seen that the WOR plot first begins to tend towards a linear
straight line at approximately WOR = 4, this corresponds to a FOPT value of 5900000
STB. This is the same FOPT value that the Fine and Coarse (FOPT vs FWCT) curves
begin to match. This shows that the extrapolated WOR data can be used to generate
accurate pseudos for a coarse homogeneous model of a high water cut field.
2.3.3.2 Watercut vs. Time
The watercut vs. time match is shown in Figure 11. it can be seen that there was early
water breakthrough in the coarse model due to numerical dispersion in the coarse grid
blocks. However the curves began to match at higher water cut values corresponding to
the point at which the WOR plot began to turn over towards a linear straight line.
FWCT
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
WW
CT
Time (Days)
FINE
PSEUDO - COARSE
Figure 11 - Comparison of WWCT
2.3.3.3 Bottom Hole Pressure
The coarse and the fine scale bottom hole pressures do not match (Figure 12. However,
they do follow the same trend and shape. If the scale is refined to 20 days, see Figure 12,
- 22 -
it can be seen that the divergence occurs during the first 2 days. This was assumed to be
due to numerics because the fine scale cells better manage the pressure transients near the
producer.
BHP
4500
4700
4900
5100
5300
5500
5700
0 5000 10000 15000 20000 25000
BH
P (
ps
ia)
Time (Days)
FINE
PSEUDO - COARSE
BHP
4500
4700
4900
5100
5300
5500
5700
0 2 4 6 8 10 12 14 16 18 20
BH
P (
psia
)
Time (Days)
FINE
PSEUDO - COARSE
Figure 12 – BHP match
2.3.4 Pseudo Adjusting
To achieve a better match to the fine model at lower water cuts the relative permeabilities
for saturations less than the flood front saturation will have to be altered. A number of
different techniques were investigated to try to obtain a better match in the early time.
There is early water break through in the coarse model. This is due to numerical
- 23 -
dispersion; therefore, the main aim was to adjust the relative permeabilities to compensate
for the increasing numerical dispersion during upscaling. The first technique investigated
the effect of using straight line relative permeability curves for saturation values below
Swf ( see Figure 13a&bfor pseudo and resultant match)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1000000 2000000 3000000 4000000 5000000 6000000 7000000 8000000 9000000
FOPT
FW
CT
Fine
Coarse - Straihtline Rel perms
Coarse
Figure 13a & b - Pseudo relative permeability curve and comparison of FOPT vs. FWCT
This was seen to promote early water breakthrough however the curves began to match at
a lower water cut values, FWCT = 0.55. It was therefore decided to increase the mobility
of the oil and at the same time reduce the mobility of the water to hopefully gain more
production before the water broke through to the producing well. This was achieved by
- 24 -
keeping Kro and Krw constant ie. Kro = 0.65 and Krw =0 for saturation values above Swi.
The pseudo curves are shown in Figure 14.
Figure 14 - Pseudo relative permeability curves where Krw &Kro are constant
The effect of this was investigated by incrementally increasing the saturation value by 1%
from Swi at which Kro and Krw were to remain constant. This was done to simulate a
piston-like displacement at low saturations. It was observed that the best match was
obtained when Kro and Krw were constant from Swi to Sw = 0.4 (see Figure 15). The
early water breakthrough had clearly been delayed and the coarse model curve now
matches the fine model curve at a FWCT of 40%.
- 25 -
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1000000 2000000 3000000 4000000 5000000 6000000 7000000 8000000 9000000
FOPT
FW
CT
2/2 - Fine (119x21x7)
Coarse
Coarse - Kro & Krw constant to Sw=0.4
Figure 15 - FWCT vs. FOPT comparison of fine and coarse with adjusted pseudos.
The next technique was designed to reduce the mobility of the water so that more oil could
be produced before the water broke through. Kro remained a straight line and Krw was
reduced at different saturations, (the pseudo curves are shown in Figure 16a). The best
match was achieved when Sw = 0.5, Krw = 0.05 (see Figure 16b). Again the water
breakthrough had been delayed, however, not by as much as the previous technique, but its
curves also matched at approximately a FWCT = 40%.
- 26 -
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1000000 2000000 3000000 4000000 5000000 6000000 7000000 8000000 9000000
FOPT
FW
CT
2/2 - Fine (119x21x7)
Coarse
Coarse - Krw reduced
Figure 16a & b - Pseudo curves with reduced water mobility and FWCT comparison for COARSE
Model with adjusted pseudo
The last technique used a combination of the two previous techniques. Kro and Krw
constant to Sw = 0.4 and at Sw = 0.5, Kro = 0.05 (see Figure 17a). This reduced the water
breakthrough further and the curves began to match at FWCT = 0.3.
- 27 -
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1000000 2000000 3000000 4000000 5000000 6000000 7000000 8000000 9000000
FOPT
FW
CT
2/2 - Fine (119x21x7)
Coarse
Coarse - Combination
Figure 17a & b - Pseudo curves and FWCT comparison for coarse with adjusted pseudo
This investigation has shown that providing the pseudo-relative permeability curves generated
from the upscaling technique are maintained for saturations greater than Swf, then the rest of
the pseudo curves can be adjusted to gain a better match in the early time without affecting the
late time match.
Comparing the production well’s water cut for the fine model with the coarse model with the
adjusted pseudos it can be seen from Figure 18, that there is still some early water
breakthrough, however, the curves begin to match at reduced water cut values.
- 28 -
FWCT
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
WW
CT
Time (Days)
FINE
COARSE - PSEUDO ADJUSTED
Figure 18 - WWCT comparision
2.4 Varying Rock curves
In the previous test Corey functions of Nw = 2 and No = 2 were used to generate the rock
curves that were applied to the fine scale homogeneous model. The next investigation
looked at the effect of using different Corey exponents and the ability to obtain a match.
For this investigation Corey exponents of Nw = 5 and No = 2 were used. These Corey
functions for water and oil are typical values for a water wet system. The model’s
geometry, geology and properties matched exactly the previous one. This model was run
for the same number of years to obtain a 99% water cut, and from the output data FOPT vs
log WOR was plotted. From Figure 19 it was observed that the WOR plot was similar to
the previous example. There was a slight deviation from the straight line at the end,
assumed to be due to boundary effects of the model. It was noted that the start of the
straight line was at a greater WOR, WOR = 5, than the previous example, where WOR =
3.5. From this it was inferred that if a match was produced, then, because of this the
performance plot of FOPT vs. FWCT for the fine and coarse models would begin to match
at a greater FWCT than the previous example.
- 29 -
A match to the fractional flow curves was achieved using Corey exponents of Nw = 1.70
and No = 1.81 (see Appendix B for curve matching plot).
The respective relative permeabilities produced were applied to the coarse scale model and
the performance plots compared.
Simulation Performance comparison
0.1
1
10
100
1000
3000000 4000000 5000000 6000000 7000000 8000000 9000000
FOPT (STB)
WO
R
0
0.2
0.4
0.6
0.8
1
1.2
FW
CT
WOR
Coarse
Fine
Extrapolation WOR plot
Match at 82%
watercut
Figure 19 - WOR plot and FOPT vs FWCT comparision
As previously anticipated the curves did match at a higher FWCT of Approximately 82%.
Again the FOPT where the two curves begin to match is the same as the start of the WOR plot
linear straight line. It was concluded that the value of the WOR where the linear straight-line
starts is related to the FWCT where the two curves match. The lower the WOR value that the
plot tends to a straight-line, the lower the FWCT the curves will begin to match. In practice,
the WOR plot straight line starts at a lower WOR than these previous two examples have
shown. Therefore, to prove this further, the next stage of the investigation was to produce
models where the turn over to the linear straight line could be observer at lower WOR
- 30 -
2.5 Heterogeneous Models
2.5.1 Model with High Permeability Streak
In order to try to reduce the WOR value at which the plot turns over to a straight line some
heterogeneity was introduced into the model. A high permeability horizontal layer of
1000mD was introduced to the centre of the fine scale model. This was done to promote
water breakthrough into the producer so that the linear WOR could be reached sooner.
The models rock curves were produced from Corey exponents of 5 and 2 for water and oil
respectively. The model had 199x49x7 fine grid blocks all other parameters remained the
same as the previous two models expect for this 1000mD layer. The WOR plot is shown
in Figure 20 below. The straight line linear WOR begins now at approximately WOR =
2.5.
Water Oil ratio
y = 0.02580927798767e0.00000035350136x
0.1
1
10
100
1000
50
00
00
0
70
00
00
0
90
00
00
0
11
00
00
00
13
00
00
00
15
00
00
00
17
00
00
00
19
00
00
00
21
00
00
00
23
00
00
00
25
00
00
00
FOPT
WO
R
WOR
Extrapolation of linearWOR
Equation of Extrapolated line
Ultimate Recovery
24MMbbls
WOR = 150
99% watercut
Figure 20 - WOR plot for heterogeneous model with high permeability streak
The fractional flow curves were matched to the start of the WOR linear trend using Corey
Exponents of Nw =0.96 and No = 2.16 (see Figure 21).
- 31 -
Curve Matching
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.30 0.40 0.50 0.60 0.70 0.80Sw
Fw
0.1
1
10
100
1000
WO
R
Fw (from relperm)
Fw from WOR
WOR
Figure 21 - Fw curve matching for high perm streak model
The performance plot of FOPT vs FWCT showed that the curves began to match at a
FWCT = 0.7, a better match in the early time could be achieved by manually adjusting the
pseudos, see section 2.3.4. Again this simulation study has shown that the lower the value
of WOR that the plot begins to tend to a straight line the lower the FWCT that the curves
begin to match.
Simulation Performance comparison
0.1
1
10
100
1000
0 5000000 10000000 15000000 20000000 25000000FOPT
WO
R
0
0.2
0.4
0.6
0.8
1
1.2
FW
CT
Fine - 1000mD high permstreak
Coarse
Match from 70%
watercut
Match better match in early
time could be achieved by
adjusting pseudos (see
homogeneous model)
Figure 22 - FOPT vs. FWCT comparison for model with High permeability layer
- 32 -
2.5.2 Heterogeneous model
The next simulation study introduced some more heterogeneity into the model to
determine if this had the effect of further lowering the start of the linear WOR plot. The
model’s parameters and geometry remained the same as the previous example but the
permeability within each layer was varied. The table below shows each layer’s
permeability.
Layer Number Permeability, mD
1 200
2 400
3 50
4 100
5 1000
6 300
7 200 Table 2 - Layer permeabilities
Figure 23, shows the WOR plot, it can be seen that the addition of this heterogeneity had
lowered the start of the linear straight line to approximately a WOR of 0.5.
0.1
1
10
100
1000
8000000 10000000 12000000 14000000 16000000 18000000 20000000 22000000 24000000
FOPT
WO
R
WOR - Kv/Kh = 0.1
Expon. (WOR - Kv/Kh = 0.1)
Figure 23 - WOR plot for Hetrogeneous model
Inflection point Deviation due to
boundary effects
- 33 -
It was observed that there was an inflection point on the WOR plot not long after the start
of the linear straight line and a deviation at the end of the plot. The deviation at the end is
assumed to be due to boundary effects, as this has been observed in other models. The
point of concern was the inflection near the start of the plot. To try to discover the cause
of this increase in FWCT, the models saturation profiles were investigated.
2.5.2.1 Coning
The saturation profiles clearly showed that there is a degree of coning in the model. This
coning occurred after approximately 10 years, from observing FWCT vs. Time this
corresponded to an increase in water cut. (see Appendix B).
Figure 24 - Satuartion profile showing coning
To further investigate the effect of coning and vertical connectivity on the WOR plot the
models vertical permeability was increased, Kv/Kh = 1. The saturation profiles in Figure
25 show a high degree of coning
Coning
- 34 -
Figure 25 - Saturation profiles after 13 & 14 years showing coning
The effect of this coning can clearly be seen on the WOR plot in Figure 26. Increasing
Kv/Kh in the model has resulted in the turn over to a linear straight line becoming more
gradual. The linear WOR was clearly visible then there was a large inflection on the plot.
This increase in FWCT occurred at the same time, approximately 13 years (see appendix
for FWCT vs Tme) when the physical coning was visible in the model’s saturation
profiles. Due to this large extent of coning it would be very hard to obtain a match with a
coarse pseudo.
WOR
0.1
1
10
100
8000000 10000000 12000000 14000000 16000000 18000000 20000000 22000000 24000000 26000000
FOPT
WO
R
WOR - Kv/Kh = 1
Extrapolation Linear WOR
Inflection point due to coning
Figure 26 - WOR for model with Kv/Kh = 1
Coning
- 35 -
In order to try to reduce the effect of the coning within in the model the vertical
permeability was reduced to Kv/Kh = 0.05. The WOR plot in Figure 27 showed that the
model was still being affected by coning and boundaries.
Water Oil ratio
y = 0.00083862308351e0.00000053500568x
0.1
1
10
100
1000
50
00
00
0
70
00
00
0
90
00
00
0
11
00
00
00
13
00
00
00
15
00
00
00
17
00
00
00
19
00
00
00
21
00
00
00
23
00
00
00
25
00
00
00
Cum Oil
Qw
/Qo
WOR -SIMULATION
Extrapolationof WOR
Linear trend
starting at
WOR >0.4
Ultimate
Recovery
22MMbbls
WOR = 150
99% watercut
Figure 27 – WOR plot for Heterogeneous model
The linear straight-line was extrapolated to a WOR = 150 to achieve a 99% watercut. The
resulting fractional flow curves were then matched from the start of the WOR linear trend.
- 36 -
Curve Matching
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80Sw
Fw
0.1
1
10
100
1000
WO
R
Psuedo Krw
Psuedo Kro
Fw (from rel perm)
Fw from WOR
WOR Extrapolated
Figure 28 - Curve matching
The Corey Exponents used to achieve this match were Nw = 3.4 and No = 1.9. The
relative permeabilities were inputted into the coarse scale model. The permeability for the
coarse scale model was determined from the Harmonic average of the fine scale model
layer’s permeabilites.
Kh = SUM (ti) / SUM (ti/Ki) …………EQ. 7
Where, Kh = Harmonic average
ti = Layers thickness
Ki = Layers permeability
The Harmonic average permeability that was inputted into the coarse model was 185 mD.
- 37 -
Simulation performance
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
5000000 7000000 9000000 1.1E+07 1.3E+07 1.5E+07 1.7E+07 1.9E+07 2.1E+07 2.3E+07FOPT (STB)
FW
CT
5/2 - Fine Hetrogeneous
3.4/1.9 - Coarse
Early water
breakthrough in fine
model due to coning Misalignment in late
time due to
boundary effects in
coarse scale model
Figure 29 - FOPT vs. FWCT comparison for Heterogeneous model
The performance curves did not match in the early time because there was early water
break - through in the fine scale model due to the coning. However after the coning has
stopped the curves began to match at around 40% water cut. There was a misalignment
that occurred at approximately 80%, this was assumed to be boundary effects in the coarse
scale model.
The plot showed that the fine scale model had an earlier water breakthrough than the
coarse, therefore the mobility of the water in the coarse scale would have to be increased
to obtain a better match in the early time. It was decided to match only the curves to the
flood front saturation, Swf, on the fractional flow curve. This in effect would increase the
mobility of the water.
Figure 30 shows the fractional flow curves matched from the flood front saturation, Swf =
0.65. A match was obtained using Corey exponents of Nw = 1.85 and No = 1.7.
- 38 -
Curve Matching
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80Sw
Fw
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00Fw (from relperm)Fw from WOR
Psuedo Krw
Psuedo Kro
Curves matched
to flood front
saturation,Swf
Figure 30 - Curve matching to flood front saturation, Swf.
Simulation Performance
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 5000000 10000000 15000000 20000000 25000000FOPT
FW
CT
5/2 - Fine Hetrogeneous
1.85/1.7 - Coarse Matched toshock front
Figure 31 - Simulation performance
- 39 -
The simulation performance curves in Figure 31 showed that the water breakthrough in
the coarse scale model was at approximately the same as the fine scale model. Matching
the fractional flow curve from Swf had compensated for the effect of the coning in the fine
scale model.
2.5.3 Viscous model
The next investigation looked at the effect of increasing the viscosity of the oil within the
model. The Model was the same as the previous example with the high permeability
streak in the middle except the viscosity of the oil was increased from μ = 0.48 cP to μ =
1.48. The WOR plot is shown in Figure 32. This model had a viscous-dominated flood;
the permeability heterogeneity dispersed the flood front, so that breakthrough occurred
earlier. There is a large deviation from the linear WOR this again is due to coning which
was observed on the saturation profiles. To try to omit this coning effect the high
permeability layer was place at the top of the model.
- 40 -
WOR
0.1
1
10
100
1000
0 5000 10000 15000 20000 25000
FOPT 10^3 (STB)
WO
R
WOR - High perm layer in middle
WOR - high perm layer at top
Deviation from linear
WOR due to coning
Figure 32 – Comparison of WOR plot for models with high permeability in different layers
The WOR plot showed that this did reduce the coning effect but did not get rid of it
completely. A small amount of coning downwards was observed in the saturation profile.
Placing the high permeability layer at the top of the model also had the effect of reducing
the start of the linear WOR.
Curve matching
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.30 0.40 0.50 0.60 0.70 0.80
Sw
Fw
0.1
1
10
100
1000
Fw (from relperm)
Fw from WOR
ExtraploatedWOR
Figure 33 – Curve matching viscous model
- 41 -
The fractional flow curve match in Figure 33 was achieved using corey exponents of Nw
= 1.95 and No = 1.55.
The performance curves below in Figure 34 showed that a good match was achieved in the
late time from about a water cut of 75%. The mismatch in the early time was again
because of the early water breakthrough in the fine scale model due to the coning.
Simulation Performance
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 5000 10000 15000 20000 25000
FOPT 10^3
FW
CT
Fine - VISC
1.95/1.55 - Coarse
Mismatch due to coning
and boundary effects
Figure 34 - FOPT vs FWCT comparison for viscous model
- 42 -
3 Application of Technique to A North Sea Field
The upscaling technique was applied to production data from a well in a North Sea Fulmar
oil reservoir. The well’s water-oil ratio plot used is shown in Figure 35. The effects of
varying areal sweep patterns on the well’s WOR are clear. The WOR was extrapolated
from a linear trend during a period of sustained water injection. Figure 36 shows the match
to the WOR generated fractional flow. Figure 37 shows the generated relative
permeability curves that were inputted in the field full field simulation model. The
achieved watercut match for the well is shown in Figure 38. The watercut match of a well
that drained the same reservoir zone is shown in Figure 39. Both matches are good,
especially as no other adjustment to the model was made after application of the pseudo.
The early time matches could be improved by modifying the low water saturation parts of
the pseudo (as used in section 2.3.4 of this report to perfect the homogeneous model
match) or adjust other model parameters (e.g. irreducible oil saturation).
- 43 -
Water Oil Ratio
0.1
1
10
100
4000000
5000000
6000000
7000000
8000000
9000000
10000000
11000000
12000000
Cumultive Well production
Qw
/Qo
0
10000
20000
30000
40000
50000
60000
70000
80000Well WOR
Water Injection
Expon. (Extrap)
WOR Extrapolation from a period of
sustained water injection
Figure 35 – WOR for North Sea Fulmar oil reservoir
Curve matching
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80
Sw
Fw
0.1
1
10
100
1000
Fw (from relperm)
Fw from WOR
Fw from WOR
WOR
Figure 36 - Curve match to WOR
- 44 -
0.00
0.20
0.40
0.60
0.80
1.00
- 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80
Sw
Kr
Psuedo Krw
Psuedo Kro
Fw (from rel perm)
Fw from WOR
Figure 37 – Relative permeability curves that were inputted into full field model
Figure 38 - watercut match for well
- 45 -
Figure 39 - Watercut match for well in same reservoir zone
- 46 -
4 Conclusions
• The WOR is a valid tool to predict future reservoir waterflood performance for
North Sea fields with developing watercuts
• Fine scale simulation studies have shown that when upscaling care must be taken
to eliminate boundary or near wellbore effects that are not true rock fractional flow
characteristics.
• Where a WOR trend occurs at high watercuts the approach shall only provide good
matches at the corresponding watercuts. In this instance improvements to the
match can be achieved by the manual introduction of a small shockfront to the
relative permeability curve.
• The investigated technique to generate pseudo relative permeability curves for use
in field models is shown to be valid and a non time consuming that does not
require detailed reservoir characterisation.
• The approach is valid for both heterogeneous and homogeneous reservoirs with
both favourable and unfavourable fluid mobility ratios.
- 47 -
5 References
[ 1] Willhite, G.P.W, “Waterflooding”, SPE textbook series VOL:3
[2] Miles, A, “Fractional Flow Approach to Performance Prediction in Mature Water-Flooded Fields”
DTI Oil & Gas Directorate, August 2002 (http://ior.rml.co.uk/issue1/articles/art-2.htm)
[3] Dake, L.P, “The Practice of Reservoir Engineering” (Revised Edition)
[4] Dake, L.P, “Fundamentals of Reservoir Engineering”
[5] Petroleum Production Reporting System, DTI Oil & Gas
http://www.og.dti.gov.uk/pprs/full_production.htm
[6] Stiles, J, “Using Special Core Analysis in Reservoir engineering – Relative Permeability &
Capillary Pressure”, Course notes, Dec 1994
[7] Darman, N.H, G.E Pickup and K.S Sorbie, “A Comparison of Two-phase Dynamic Upscaling
methods Based on Fluid Potentials”, Computational Geosciences 6: 5-27, 2002
[8] Azoug, Y, “The Performance of Pseudofunctions in the Upscaling Process”, SPE 80910, presented
at SPE Production and Operations Symposium, Oklahoma, March 2003
[9] Okano, H, “Quantification of Uncertainty in Relative Permeability for Coarse-Scale Reservoir
Simulation”, SPE 94140, Europec/EAGE Annnual Conference, Madrid, June 2005.
- 48 -
6 Appendix
- 49 -
Appendix A
Eclipse Input File – Fine Homogeneous Model
--
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
-V2_2.DATA
--
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
-- SIMPLE FINE SCALE MODEL
-- FOR UPSCALING STUDY
-- Model (119x21x7)
--
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
--
--
-- Authors: Rohan Corlett & Tony Peters
-- Date:25 July 2005
-- ECLIPSE: v2004
--
--
========================================================================
======
RUNSPEC
--
========================================================================
======
--
========================================================================
======
NOECHO
TITLE
Fine Scale Model
DIMENS
-- NX NY NZ
119 21 7 /
OIL
WATER
FIELD
TABDIMS
--Sat.Tabs PVT.Tabs Sat.Nodes Pres.Nodes FIP.Regs Rs.Nodes
Sat.EndPt.Tabs
1 1 50 50 15 25 3
/
EQLDIMS
--Equil.Regs Depth.Nodes Depth.Nodes Tracer.Tabs Depth.Nodes
1 10 10 0 0 /
REGDIMS
--FIP.Regs Sets.FIP.REGS
1 /
- 50 -
WELLDIMS
--No.Wells No.Cons.Per.Well No.Groups No.Wells.Per.Group
2 25 1 2 /
VFPPDIMS
-- MXMFLO MXMTHP MXMWFR MXMGFR MXMALQ NMMVFT
/
VFPIDIMS
-- MXSFLO MXSTHP NMSVFT
/
START
1 'JUL' 2005 /
NSTACK
25 /
UNIFOUT
UNIFIN
--NOSIM
-------------------------------------------------------
-- Set relative paths for INCLUDE files
GRID
--
MESSAGES
9* 1000 /
--PSEUDO
--
EQUALS
'TOPS' 10000 1 119 1 21 1 1 /
'DX' 64.3 1 119 1 21 1 7 /
'DY' 59.5 1 119 1 21 1 7 /
'DZ' 14.3 1 119 1 21 1 7 /
'PORO' 0.20 1 119 1 21 1 7 /
'NTG' 1.0 1 119 1 21 1 7 /
'PERMX' 100 1 119 1 21 1 7 /
/
COPY
'PERMX' 'PERMY' /
'PERMX' 'PERMZ' /
/
MULTIPLY
'PERMZ' 0.1 1 119 1 21 1 7 /
/
--
========================================================================
======
INIT
PROPS
--
========================================================================
======
--
========================================================================
======
SWOF
- 51 -
------------------------------------------------
-- Corey func nw=2 no=2 Krw=0.362 Kro=0.65
------------------------------------------------
-- Sw Krw Kro Pc
0.3500000 0.0000000 0.6500000 0.0000000
0.3600000 0.0002263 0.6179063 0.0000000
0.3700000 0.0009050 0.5866250 0.0000000
0.3800000 0.0020363 0.5561563 0.0000000
0.3900000 0.0036200 0.5265000 0.0000000
0.4000000 0.0056563 0.4976563 0.0000000
0.4100000 0.0081450 0.4696250 0.0000000
0.4200000 0.0110863 0.4424063 0.0000000
0.4300000 0.0144800 0.4160000 0.0000000
0.4400000 0.0183263 0.3904063 0.0000000
0.4500000 0.0226250 0.3656250 0.0000000
0.4600000 0.0273763 0.3416563 0.0000000
0.4700000 0.0325800 0.3185000 0.0000000
0.4800000 0.0382363 0.2961563 0.0000000
0.4900000 0.0443450 0.2746250 0.0000000
0.5000000 0.0509063 0.2539063 0.0000000
0.5100000 0.0579200 0.2340000 0.0000000
0.5250000 0.0692891 0.2056641 0.0000000
0.5480000 0.0886991 0.1657663 0.0000000
0.5500000 0.0905000 0.1625000 0.0000000
0.5600000 0.0997763 0.1466563 0.0000000
0.5700000 0.1095050 0.1316250 0.0000000
0.5800000 0.1196863 0.1174063 0.0000000
0.5900000 0.1303200 0.1040000 0.0000000
0.6000000 0.1414063 0.0914063 0.0000000
0.6100000 0.1529450 0.0796250 0.0000000
0.6200000 0.1649363 0.0686563 0.0000000
0.6300000 0.1773800 0.0585000 0.0000000
0.6400000 0.1902763 0.0491563 0.0000000
0.6500000 0.2036250 0.0406250 0.0000000
0.6600000 0.2174263 0.0329063 0.0000000
0.6700000 0.2316800 0.0260000 0.0000000
0.6800000 0.2463863 0.0199063 0.0000000
0.6900000 0.2615450 0.0146250 0.0000000
0.7000000 0.2771563 0.0101563 0.0000000
0.7100000 0.2932200 0.0065000 0.0000000
0.7200000 0.3097363 0.0036563 0.0000000
0.7300000 0.3267050 0.0016250 0.0000000
0.7400000 0.3441263 0.0004063 0.0000000
0.7500000 0.3620000 0.0000000 0.0000000
/
--
========================================================================
======
ROCK
-- pref Cr
-- psia 1/psi
5905 3.1E-06 /
PVTW
-- pref Bw Cw visw
-- psia rb/bbl 1/psi cp
5905 1.050 3.0E-06 0.312 /
PVDO
-- psia Bo viso
-- rb/bbl cP
2040 1.421 0.380
- 52 -
3000 1.392 0.405
4000 1.368 0.431
5000 1.354 0.459
5910 1.342 0.480
6500 1.334 0.49
/
GRAVITY
-- Surface Densities for Oil Water and Gas
-- API Water=1 Air=1
44.28 1.0474 1.0570 / Platform
RSCONST
-- GOR pref
-- Mcf/bbl psia
0.502 2040 /
--
========================================================================
======
REGIONS
--
========================================================================
======
SATNUM
17493*1 /
FIPNUM
17493*1 /
EQLNUM
17493*1 /
--
========================================================================
======
SOLUTION
--
========================================================================
======
EQUIL
--
--DATUM PRES WOC CAP.PRES GOC CAP.PRES RSVD RSVD EQUIL
--DEPTH DATUM FT @WOC FT @GOC TABLE TABLE ACC
11351 5910 11351 0 0 0 0 0 10
/
-------------------------------------------------------
RPTSOL
'RESTART=2' 'FIP=3' /
--
========================================================================
======
--
========================================================================
======
SUMMARY
SEPARATE
- 53 -
RPTONLY
FOPR
FWPR
FOPT
FWCT
--
WBHP
'W1' 'PR1' /
WWCT
'W1' 'PR1' /
FVPT
FVIT
WPI
'W1' 'PR1' /
--
--
--
========================================================================
======
SCHEDULE
--
========================================================================
======
-- Reporting
RPTRST
'BASIC=4' /
RPTSCHED
/
WELSPECS
'PR1' 'G1' 81 11 1* 'OIL' 7* /
'W1' 'G1' 11 11 1* 'WAT' 7* /
/
COMPDAT
'PR1' 1* 1* 1 7 'OPEN' 2* 0.508 3* 'Z' 1* /
'W1' 1* 1* 1 7 'OPEN' 2* 0.508 3* 'Z' 1* /
/
-- qo qw qg ql rb/d bhp
WCONPROD
'PR1' 'OPEN' 'RESV' 1* 1* 1* 1* 5000 2100 /
/
WPIMULT
'W1' 10 /
'PR1' 10 /
/
WCONINJ
'W1' 'WAT' 'OP' 'RESV' 1* 0 1.0 FVDG 10000 /
/
TSTEP
30*1
11*30
/
TSTEP
- 54 -
12*30
12*30
12*30
12*30
/
TSTEP
12*60
12*60
12*60
12*60
/
TSTEP
12*100
12*100
/
TSTEP
10*365
20*365
40*365
/
END
--
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
-- END OF FILE
--
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
- 55 -
--
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
-- V2_2_C_PS.DATA
--
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
-- PSEUDO COARSE GRID CROSS-SECTIONAL MODEL
-- FOR UPSCALING STUDY (Nw = 1.16, No = 2.06)
--
--
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
--
-- Simple Coarse Grid
-- for use in pseudo upscaling study
--
-- Authors: Rohan Corlett & Tony Peters
-- Date: 26 Jul 2005
-- ECLIPSE: v2004
--
========================================================================
======
RUNSPEC
--
========================================================================
======
--
========================================================================
======
NOECHO
TITLE
Simple Coarse Model
DIMENS
-- NX NY NZ
17 3 1 /
OIL
WATER
FIELD
TABDIMS
--Sat.Tabs PVT.Tabs Sat.Nodes Pres.Nodes FIP.Regs Rs.Nodes
Sat.EndPt.Tabs
1 1 50 50 15 25 3
/
EQLDIMS
--Equil.Regs Depth.Nodes Depth.Nodes Tracer.Tabs Depth.Nodes
1 10 10 0 0 /
REGDIMS
--FIP.Regs Sets.FIP.REGS
1 /
WELLDIMS
--No.Wells No.Cons.Per.Well No.Groups No.Wells.Per.Group
2 25 1 2 /
VFPPDIMS
-- MXMFLO MXMTHP MXMWFR MXMGFR MXMALQ NMMVFT
- 56 -
/
VFPIDIMS
-- MXSFLO MXSTHP NMSVFT
/
START
1 'JUL' 2005 /
NSTACK
25 /
UNIFOUT
UNIFIN
--NOSIM
-------------------------------------------------------
-- Set relative paths for INCLUDE files
GRID
--
MESSAGES
9* 1000 /
--PSEUDO
--
EQUALS
'TOPS' 10000 1 17 1 3 1 1 /
'DX' 450 1 17 1 3 1 1 /
'DY' 417 1 17 1 3 1 1 /
'DZ' 100 1 17 1 3 1 1 /
'PORO' 0.20 1 17 1 3 1 1 /
'NTG' 1.0 1 17 1 3 1 1 /
'PERMX' 100 1 17 1 3 1 1 /
/
COPY
'PERMX' 'PERMY' /
'PERMX' 'PERMZ' /
/
MULTIPLY
'PERMZ' 0.1 1 17 1 3 1 1 /
/
--
========================================================================
======
INIT
PROPS
--
========================================================================
======
--
========================================================================
======-----------------------
------------------------------------------------
--
SWOF
------------------------------------------------
-- Corey func nw=1.51 no=1.83 Krw=0.362 Kro=0.65
- 57 -
------------------------------------------------
-- Sw Krw Kro Pc
0.3500000 0.0000000 0.6500000 0.0000000
0.3600000 0.0013856 0.6204967 0.0000000
0.3700000 0.0039428 0.5916183 0.0000000
0.3800000 0.0072691 0.5633673 0.0000000
0.3900000 0.0112196 0.5357467 0.0000000
0.4000000 0.0157105 0.5087591 0.0000000
0.4100000 0.0206849 0.4824077 0.0000000
0.4200000 0.0261010 0.4566954 0.0000000
0.4300000 0.0319266 0.4316254 0.0000000
0.4400000 0.0381353 0.4072010 0.0000000
0.4500000 0.0447057 0.3834256 0.0000000
0.4600000 0.0516194 0.3603027 0.0000000
0.4700000 0.0588608 0.3378360 0.0000000
0.4800000 0.0664160 0.3160292 0.0000000
0.4900000 0.0742729 0.2948864 0.0000000
0.5000000 0.0824208 0.2744118 0.0000000
0.5100000 0.0908500 0.2546096 0.0000000
0.5200000 0.0995516 0.2354844 0.0000000
0.5300000 0.1085176 0.2170411 0.0000000
0.5400000 0.1177407 0.1992845 0.0000000
0.5500000 0.1272143 0.1822201 0.0000000
0.5600000 0.1369319 0.1658535 0.0000000
0.5700000 0.1468879 0.1501905 0.0000000
0.5800000 0.1570769 0.1352375 0.0000000
0.5900000 0.1674938 0.1210013 0.0000000
0.6000000 0.1781340 0.1074890 0.0000000
0.6100000 0.1889929 0.0947085 0.0000000
0.6200000 0.2000664 0.0826681 0.0000000
0.6300000 0.2113506 0.0713769 0.0000000
0.6400000 0.2228417 0.0608450 0.0000000
0.6500000 0.2345362 0.0510834 0.0000000
0.6600000 0.2464307 0.0421042 0.0000000
0.6700000 0.2585220 0.0339213 0.0000000
0.6800000 0.2708072 0.0265505 0.0000000
0.6900000 0.2832832 0.0200097 0.0000000
0.7000000 0.2959473 0.0143206 0.0000000
0.7100000 0.3087969 0.0095095 0.0000000
0.7200000 0.3218293 0.0056095 0.0000000
0.7300000 0.3350422 0.0026659 0.0000000
0.7400000 0.3484332 0.0007473 0.0000000
0.7500000 0.3620000 0.0000000 0.0000000
/
--
========================================================================
======
ROCK
-- pref Cr
-- psia 1/psi
5905 3.1E-06 /
PVTW
-- pref Bw Cw visw
- 58 -
-- psia rb/bbl 1/psi cp
5905 1.050 3.0E-06 0.312 /
PVDO
-- psia Bo viso
-- rb/bbl cP
2040 1.421 0.380
3000 1.392 0.405
4000 1.368 0.431
5000 1.354 0.459
5910 1.342 0.480
6500 1.334 0.49
/
GRAVITY
-- Surface Densities for Oil Water and Gas
-- API Water=1 Air=1
44.28 1.0474 1.0570 / Platform
RSCONST
-- GOR pref
-- Mcf/bbl psia
0.502 2040 /
--
========================================================================
======
REGIONS
--
========================================================================
======
SATNUM
51*1 /
FIPNUM
51*1 /
EQLNUM
51*1 /
--
========================================================================
======
SOLUTION
--
========================================================================
======
EQUIL
--
--DATUM PRES WOC CAP.PRES GOC CAP.PRES RSVD RSVD EQUIL
--DEPTH DATUM FT @WOC FT @GOC TABLE TABLE ACC
11351 5910 11351 0 0 0 0 0 10
/
-------------------------------------------------------
RPTSOL
'RESTART=2' 'FIP=3' /
- 59 -
--
========================================================================
======
--
========================================================================
======
SUMMARY
SEPARATE
RPTONLY
FOPR
FWPR
FOPT
FWCT
--
WBHP
'W1' 'PR1' /
WWCT
'W1' 'PR1' /
FVPT
FVIT
FOIP
--
--
--
========================================================================
======
SCHEDULE
--
========================================================================
======
-- Reporting
RPTRST
'BASIC=4' /
RPTSCHED
/
WELSPECS
'PR1' 'G1' 12 2 1* 'OIL' 7* /
'W1' 'G1' 2 2 1* 'WAT' 7* /
/
COMPDAT
'PR1' 1* 1* 1 1 'OPEN' 2* 0.508 3* 'Z' 1* /
'W1' 1* 1* 1 1 'OPEN' 2* 0.508 3* 'Z' 1* /
/
-- qo qw qg ql rb/d bhp
WCONPROD
'PR1' 'OPEN' 'RESV' 1* 1* 1* 1* 5000 2100 /
/
WPIMULT
'W1' 10 /
'PR1' 10 /
/
WCONINJ
'W1' 'WAT' 'OP' 'RESV' 1* 0 1.0 FVDG 10000 /
- 60 -
/
TSTEP
30*1
11*30
/
TSTEP
12*30
12*30
12*30
12*30
/
TSTEP
12*60
12*60
12*60
12*60
/
TSTEP
12*100
12*100
/
TSTEP
10*365
40*365 /
END
--
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
-- END OF FILE
--
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
- 61 -
Appendix B – curve matching
Curve Matching for Homogeneous Model
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80
Sw
Fw
0.1
1
10
100
1000
Fw (from relperm)
Fw fromWOR
WOR -Extraploated
WOR -Extraploated
Expon.(WOR -Extraploated)
- 62 -
FWCT vs. TIME
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 2 4 6 8 10 12 14 16 18 20
FW
CT
Time (years)
FINE - Hetrogeneous model
Increasing watercut
due to coning
Coning in Heterogeneous model Kv/Kh = 0.1
FWCT vs. TIME
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 2 4 6 8 10 12 14 16 18 20
FW
CT
Time (years)
FINE - Hetrogeneous modelKv/Kh = 1
Increasing watercut
due to coning
Coning in Heterogeneous model Kv/Kh = 1