American Journal of Oil and Chemical Technologies;
ISSN (online): 2326-6589; ISSN (print): 2326-6570
Volume X, Issue X, June 20XX
Field-Scale Simulation of WAG using Pore-Scale Network
Modelling
Suramairy, R1, Geiger, S2, Dijke, R3, Al-Dhahli, A4
Petroleum Engineering Department, Koya University, Kurdistan Region, Iraq.
2
Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh, UK.
3
Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh, UK.
4
Petroleum Develeopment, Oman.
ramyar.adnan@koya.edu.iq
1
Abstract:
In the recent years the interest in water alternating gas (WAG) increased as tertiary recovery method.
This method has been applied successfully in many fields around the world. The WAG process
results in three-phase flow zones in which its real mechanism still not well understood. Therefore; it
was important to understand and well describing the multi-phase flow properties (relative
permeability and capillary pressure) which controlling the WAG process.
In this study we used pore-scale network modeling to simulate WAG injection at field scale.
Network models being used as alternative for empirical methods since they are physically-based
tools which integrated all pore-scale mechanisms.
Unlike empirical approaches were have little physical basis. New developed network have been used
which integrated formation and collapse mechanism for oil clusters, representing more complexity of
pore structure in addition to implementing multiple displacement process. Three-phase relative
permeability and capillary pressure have been obtained by simulating network model which used for
our reservoir simulation model. We studied the effect of WAG on recovery factor by applying some
injection scenarios. Then we studied the effect of different WAG ratios on improving overall WAG
performance.
Keyword: Relative permeability, capillary pressure, three-phase, interfacial tension, residual,
ternary, ratio, breakthrough, clusters.
1. Introduction
In the recent years the interest in the Water-alternating –gas (WAG) increased as a recovery
method technique. This EOR technique has been successfully applied in several oil fields and
especially in the Middle East carbonate reservoirs to improve their recovery [10]. Since it has
been estimated that more than half of the world unrecovered reserve of oil contained in the
carbonate rocks in the middle east. WAG injection tends to improve the oil recovery through
contacting the unswept zones, especially the attic or cellar oil by segregation of the gas to the top
or the accumulation of the water to the bottom. WAG reduces the residual oil as a result of
injecting two fluids (gas and water), and three-phase zones may obtain lower remaining oil
saturation. In few words the WAG will improve the microscopic displacement [10].
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American Journal of Oil and Chemical Technologies;
ISSN (online): 2326-6589; ISSN (print): 2326-6570
Volume X, Issue X, June 20XX
Despite the remarkable progress in the WAG process results, but the real mechanism of the
three-phase flow which controls the process is still not well understood. The use of WAG must
be accompanied with well description of the multi-phase flow behaviour which is controlled by
relative permeability and capillary pressure. It is difficult and expensive to measure the relative
permeabilities and capillary pressure for the three-phase flow, in addition to the uncertainty
results present at low oil saturation [22]. The measurement of the relative permeabilities poses a
particular challenge, since there are an infinite number of different displacement paths. This
because three-phase displacement including various two independent saturations.
Thus, it is impractical to measure relative permeabilities for all three-phase displacement take
place in the reservoir [7]. Hence, empirical expression has been used to compute the relative
permeabilities and capillary pressure for the three-phase based on the available two-phase data
[5, 7, 21, 31, 32]. However, those empirical models have no or little physical basis and therefore;
fall to capture the oil flow at its low saturation and this indicates imprecise prediction of residual
oil. An alternative approach has been used to develop the physically-based three-phase network
models which integrate all the relevant pore-scale mechanism and tuned to match the two-phase
data in order to predict the relative permeablities and capillary pressure. This should improve the
understanding of the three-phase flow and minimizing the uncertainty during gas injection
projects. In the network models two or three dimensional noodles of wide pores connected by
narrower throats will be represented and will be used as simulation tool to predict the relative
permeabilities and capillary pressure [8, 9].
The first representation of the multiphase flow by the pore-networks was by Fatt in the 1950’s
[13, 14]. Recently, there has been growing interest in using the pore-scale modelling. In the last
years many of these models have been developed [16, 19, 25,26, 27, 29, 34].
The new model that will be used here has been developed to include thermodynamic criterion of
formation and collapse of the oil layers (van Dijke and Sorbie, 2007, van Dijke and Sorbie,
2003) which will be able to predict the residual oil accurately by capturing the flow of oil
film/layer which affects the relative permeability at low saturation. This model also offer the
possibility of mimic the complexity of the real pore structure by using inputs of geometrically
and topologically equivalent networks. In addition to that, the model has carried out the oil
clusters flow by multiple displacements as observed experimentally [30, 31] to give more
accurate prediction for the residual oil by giving more realistic phase distribution on the network
[2].
In this project we will use the network model reconstructed form the network constructed from
Berea sandstone to obtain the three-phase relative permeabilties and capillary pressure which
will be used in the simulator to understand the mechanism of the WAG in enhancing oil
recovery. Also we make a comparison between the oil-wet system and the water-wet system
through running several cases with different WAG scenarios.
This paper focuses on reviewing the literatures and studies carried out on WAG projects and
some of the statistical data that applied during real WAG projects and the results obtained from
that. Second chapter presenting the steps of obtaining input parameters for WAG simulation.
First we started with 3D network simulation to obtain three-phase properties (Kr and Pc)
necessary for running the reservoir model. Then the model will be run for some scenarios with
geological uncertainty model for Brugge field. Then investigating the factors effecting WAG
performance and comparison between network results and empirical methods. In the last chapter
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American Journal of Oil and Chemical Technologies;
ISSN (online): 2326-6589; ISSN (print): 2326-6570
Volume X, Issue X, June 20XX
we are reviewing the results for three-phase relative permeabilities and WAG simulation at field
scale and analysing those results. The chapter also highlighted the necessary points involving in
the results and important points for future work.
The main aim of this project is investigating the effect of water alternating gas (WAG) injection
as tertiary recovery method on the recovery factor in heterogeneous reservoirs by using sets of
relative permeabilities and capillary pressure obtained from pore-scale network model using
Brugge field reservoir model. The model also has been run to analyse the uncertainty during
WAG injection by comparing uncertainty raised from different relative permeabilities and
different geological models for Brugge field.
2. Methodology
2.1.
Network Model Discription
The developed model as described by [2] will be used since it is a physically-based simulation
tool. This model enables us to obtain the multi-phase flow functions at different rocks
wettability. Here we will briefly describe the main features of the model:
1. Thermodynamics criterion for capillary entry pressure for the formation and collapse of the
oil clusters has been applied. This will enable the model to accurate prediction of the residual
oil at low oil saturation since it succeed to capture the wetting films and flow of the oil that
affect the relative permeability.
2. Multiple displacement implementation which allows the accurate modelling of the
disconnected phase layers/clusters during high WAG floods. The multiple displacement
chain start begins with the invaded phase clusters and ends within connected phase to the
outlet and the favourable chain during three-phase flow will be found.
3. The model used realistic 3D networks which preserving the topology and pore-space shapes
that extracted from reconstructed method and CT images. The network consisting of pore
bodies (nodes) connected through narrower throats (bonds) this will enables easier
calculation of the intra-pore flow properties.
2.2.
Network validation
The validation of the networks has been performed and described in details [2]. We briefly
reviewing the validation process in this section as has been achieved. The results from both
experimentally and the predicted values from the network model which shows excellent
agreement. In the water-wet system the three-phase relative permeability of water and gas
predicted by the network model and compared to the results determined experimentally by [22]
and the conclusion of that was that, the gas is the less wetting phase therefore; its relative
permeability could be represented as a function of its own saturation. The non-zero gas relative
permeability could not be predicted at low gas saturation therefore; the perfect agreement has
been observed at high gas saturation figure (1). For the water phase which is the most wetting
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American Journal of Oil and Chemical Technologies;
ISSN (online): 2326-6589; ISSN (print): 2326-6570
Volume X, Issue X, June 20XX
phase in the system in which the relative permeability of the water will be the function of its
saturation figure (2)
Figure1. Comparison of gas relative
permeability by network model with the
experiment data of three-phase flow by
network model and with experimental [2]
Figure2.Comparison of water relative permeability
by network model with the experiment data of
three-phase flow by network model and with
experimental [2]
Figure1. Comparison of oil relative permeability by network model with the
experiment data of three-phase by network model and with experimental
flow [2]
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American Journal of Oil and Chemical Technologies;
ISSN (online): 2326-6589; ISSN (print): 2326-6570
Volume X, Issue X, June 20XX
2.3.
3D Network Simulation
We have run the network simulation to predict the three-phase properties (relative permeabilities
and capillary pressure). The realistic 3D pore-network extracted from the reconstructed pore
space of Berea sandstone which will be used as inputs data to our model. We used three
networks (A, B and C) table (1)APPENDIX. The simulation has been carried out for (water-wet)
system.
A- Initially the pores of the network are fully
saturated with water
B- Oil flooding
(Primary Drainage)
During the primary migration (Drainage), the
oil invades the pores of low capillary pressure.
The water could exist as films/layers.
C- Water Flooding
(Imbibition)
After the Drainage the wettability of the
system (pores) changed by altering the
contact angles. The second flood (Imbibition)
starts. The water will invade the oil in the
pores in which the water existed as films. The
oil clusters might be collapsed during that
flood
D- Gas injection
At this stage the gas will be injected into
the system. Here there is a possibility of
formation of oil clusters which separates
the water films and gas bulks. This could
be created if the gas invaded pores within
both oil bulks and water films
Figure 4. Displacement process takes place in network model during the 3D network simulation
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American Journal of Oil and Chemical Technologies;
ISSN (online): 2326-6589; ISSN (print): 2326-6570
Volume X, Issue X, June 20XX
3. Measurement of Relative permeabilities and Capillary pressure
3.1.
Two-phase flow
In order to initialize our reservoir model we need to compute the relative permeability for the
two-phase system. We run the network model for two different systems (gas-oil) and (oil-water)
systems. In the gas-oil system we injected oil into the network which originally saturated with
water. This enabled us to obtain the relative permeability of gas (Krg) and the capillary pressure
for that system (Pcgo). For the oil-water system, water injected into the pore of the networks
which are saturated with oil to the connate water saturation. At this level we determined the
water relative permeability (Krw) and the capillary pressure (Pcow) of the oil-water system.
Scaled Network
saturation Swi=0.2
0.15
Krw
0.1
0.05
0
0.2
0.3
0.4
0.5
0.6
0.7
Water saturation
Figure 5. Two phase relative permeability curve for network A
3.2.
Three-phase flow
To launch the simulation model for WAG injection the relative permeabilities of three-phase
flow should be provided. By simulating our network model, we were able to measure the threephase relative permeability which presented during the displacement process takes place in each
of the networks. Initially the network is fully filled with water (water-wet) rocks figure (4-A).
Then oil flooding begins to the network which represented the primary drainage of the oil from
the source rock to the reservoir. The invaded oil will fill the network pores up to the connate
water saturation (Swc) and displacing the water figure (4-B). This stage representing the initial
reservoir state. After that we have changed the contact angles to represent the wettability
alteration in the reservoir during ageing from water-wet to oil-wet. Then we ran the network
model within water flooding (Imbibition) in which production process modelled for the reservoir
within water injection figure (4-C).
The water injection continued up to the predetermined water saturation (Swi). At the final stage
the network simulation within gas injection (tertiary gas injection) has been performed in which
representing the production processes in the reservoir within the gas injection figure (4-D). This
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American Journal of Oil and Chemical Technologies;
ISSN (online): 2326-6589; ISSN (print): 2326-6570
Volume X, Issue X, June 20XX
process repeated for different paths of Sw to obtain reasonably set of data which will be able to
represent the three-phase relative permeability in the regions within the three-phase saturations in
the reservoir figure (6). The results of three-phase relative permeability will be discussed in the
next chapter.
Krw
Krg
Kro
Figure 6. Three-phase relative permeability curve for network A
4. Reservoir Model
Brugge filed is a complete synthetic field which was built from zero by (TNO). The geological
structure of this field consists of stretched half-dome in the east/west direction with a fault of
large boundary at the northern edge and an internal fault with 20° angle of modest throw at the
northern edge. The field dimensions are about (10x3) km. The original model which was highresolution composes of 20 million grid cells with each cell dimension of (50x50x0.25) m. This
model was gathered with properties including those properties used for the reservoir simulation
like (porosity, permeability, NTG, water saturation, etc.) all these properties was measured in
real fields in order to be able for generating well-log data. The original model was upscaled to a
450,000 grid cell which was performed arithmetically for the porosity and flow-based upscaling
for the permeability. This model formed the basis for the truth case for the further reservoir
simulations consisting of 60,000 grid cells [28].
The reservoir model used the “truth” case which consists approximately of (75x75x2.5) m grid
block size with total active grid-blocks of 327,067. This reservoir is under-saturated oil reservoir.
Total 30 wells presented 20 producers and 10 injectors figure (1)APPENDIX, all these wells had
only one perforation section during the first 10 years. After that three perforated sections have
been used in all the wells and this increased the well rates from 2,000 to 3,000 from the year 10
through the year 30 [28]. Table (3)APPENDIX shows main parameters for the reservoir
simulation model.
Three networks have been used which represented types of for the reservoir. These networks
have been selected based on their permeability distribution, figure (2)APPENDIX to provide
more heterogeneous system.
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American Journal of Oil and Chemical Technologies;
ISSN (online): 2326-6589; ISSN (print): 2326-6570
Volume X, Issue X, June 20XX
5. Results and Discussion
5.1.
Three phase relative permeabilities
The ternary diagrams in the figures (3, 4, 5)APPENDIX represent the three-phase relative
permeability which obtained by 3D network simulation for different saturation (Swi) paths for
water-wet system The most common feature for the all the three networks is that the low residual
oil could be achieved during gas injection. In the water-wet system high residual oil was
observed during the water injection than for gas injection figures (3, 4, 5) APPENDIX. This
related to the fact that during the water injection the oil layers might collapse and since in the
water-wet system the oil is the intermediate wetting phase. Therefore; the collapsed oil layers
will be surrounded by water wetting films leading to disperse the oil to smaller clusters which
reduce the connectivity between the oil clusters and more broken oil clusters trapped. Hence this
will result in high residual oil. During the gas injection more oil will be displaced and this
attributed to the oil phase which present as a layer phase sandwiched between water films and
gas bulks. This will give the possibility of formation of the oil clusters. However; the gas could
displace oil when invading pores fill with water films and oil bulks figure (4-D). As the water
saturation increase the less oil will be displaced by gas. This gives an indication that less oil
clusters connected to the outlets. The gas then start to displace water as it connected to the outlet
while the oil at this point trapped by water. At the last two saturation paths in network (A), gas
displaced directly water since oil phase disconnected and only water connected to outlets. In
network (C) it has been observed that gas displacing oil and water alternatively figures (3, 4, 5)
APPENDIX.
5.2.
Field-Scale WAG Injection
We used the Brugge field reservoir model and the relative permeabilities generated by simulating
the networks. We ran the model for (water-wet) system as stated in table (2)APPENDIX. We
investigated the effect of WAG injection on enhancing the recovery by applying some of the
scenarios listed in table (4) APPENDIX. For the water-wet system, the lowest recovery found
during injecting only gas figure (7). This related to the early gas breakthrough takes place in the
reservoir figure (8). It has been observed that most of the injected gas displacing oil in the upper
layers as a result of the gravity segregation before starting to escape and being produced which
reducing the recovery fig. (8). Implementing WAG injection showed improvement by (3%) in
recovery comparing to that one achieved by only water injection at one hydrocarbon pore
volume injection fig. (7).
In figure (8) the difference between red and black lines represents the additional oil recovered by
WAG. Recovery during water injection in WAG obtained more recovery for the same period
during only water injection and this attributed to the effect of the gas being used during WAG
which gives the raise for more oil to be displaced. After some periods, no significant increase
observed in WAG recovery comparing to water injection recovery. This related to the high
mobility of the gas and its low density which cause the gas to move to the top of the reservoir.
Therefore; gas breakthrough and more gas will be produced and this will reduce the recovery,
since the gas enhance the sweep efficiency if it trapped whereas; at this point it escapes and
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American Journal of Oil and Chemical Technologies;
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Volume X, Issue X, June 20XX
leaving residual oil. Therefore; the WAG cycles starting with water flood are more efficient than
those starting with gas flood figure (6).
Figure 7. Oil recovery for water-wet system using WAG scenario 7 stated in table (4)
Figure 3. Gas effect on recovery during WAG injection
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American Journal of Oil and Chemical Technologies;
ISSN (online): 2326-6589; ISSN (print): 2326-6570
Volume X, Issue X, June 20XX
5.3.
Effect of WAG Ratios
The effect of WAG ratios on the overall performance has been investigated during water-wet
system. We run the model with five WAG ratios (1:1, 1:2, 2:1, and 1:3, 3:1). The 1:1 WAG ratio
showed high recovery obtained by different ratios. WAG ratios with high water rate (3:1, 2:1)
overlapping each other and showed difference in recovery of about (10%) higher than (1:2, 1:3)
which are producing more gas figure (9).
FOE (fraction) of OOIP
0.6
0.5
0.4
0.3
WAG ratio 1:1
WAG ratio 2:1
WAG ratio 3:1
WAG ratio 1:2
0.2
0.1
0
0
0.5
1
1.5
2
2.5
Hydrocarbon pore volume injected
Figure 9. Oil recovery for different WAG ratios
6. Conclusion
We simulate WAG injection at field-scale to predict oil recovery by using pore-scale network
model which represent physically-based simulation tool. The new developed network model [2]
being used to simulate some WAG scenarios with the presence of uncertainty in relative
permeabilities and geological realisation of the Brugge field. We used three networks which
extracted from pore space reconstructed methods of Berea sandstone. Three-phase relative
permeabilities and capillary pressure obtained by simulating the pore-scale networks for waterwet system. The results showed that high residual oil obtained during water flooding than during
gas injection. This could be attributed to the snap-off of oil in the pores by the surrounding water
and which leads to break the oil layers into small clusters and trapped by water. While during gas
injection the formation of the oil clusters gives the possibility for more clusters to be connected
to the outlets of the pores and hence reducing the residual oil.
We then used the outputs (relative permeability and capillary pressure) to run the WAG
simulation at reservoir scale. The simulation results showed that lowest recovery achieved by
injecting only gas due to high gas mobility and lower density which moves to top of the reservoir
and breakthrough. The recovery could be improved by (3.5%) using WAG injection. WAG
scenarios started with water as first flood were more efficient. Many WAG ratios have been
applied and the (1:1) ratio showed more efficiency.
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American Journal of Oil and Chemical Technologies;
ISSN (online): 2326-6589; ISSN (print): 2326-6570
Volume X, Issue X, June 20XX
7. References:
[1] Al-Dhahli, A., Geiger, S., and van Dijke, M. I. J. (2011). "Three-Phase Pore-Network
Modelling for Mixed-Wet Carbonate Reservoirs." SPE Reservoir Characterisation and
Simulation Conference and Exhibition, Society of Petroleum Engineers, Abu Dhabi, UAE.
[2] Al-Dhahli, A., Geiger, S., and van Dijke, M. I. J. (2012). "Accurate Modelling of Pore-scale
Film and Layer Flow for Three-phase EOR in Carbonate Rocks with Arbitrary Wettability." SPE
Improved Oil Recovery Symposium, Society of Petroleum Engineers, Tulsa, Oklahoma, USA.
[3] Al-Ghanim, W., R. Gharbi, and M.K. Algharaib, Designing a Simultaneous Water
Alternating Gas Process for Optimizing Oil Recovery, in EUROPEC/EAGE Conference and
Exhibition. 2009, Society of Petroleum Engineers: Amsterdam, The Netherlands.SPE 120375MS.
[4] Andrews, J., M. Hettema, and T. Nesse, Injection Wells: A Case Study From the Statfjord
Field, in SPE Annual Technical Conference and Exhibition. 2004: Houston, Texas.SPE 90949.
[5] Baker, L .E. (1993). Three-Phase Relative Permeability of Water-Wet, Intermediate-Wet, and
Oil-Wet Sandstone. Seventh European Improved Oil Recovery Symposium, Moscow, Russia.
[6] Baojun, F., D. Xingjia, and Y. Cai, Pilot Test of Water Alternating Gas Injection in
Heterogeneous Thick Reservoir of Positive Rhythm Sedimentation of Daqing Oil Field. SPE
Advanced Technology Series, 1997. 5(1).
[7] Blunt, M. J. (2000). An Empirical Model for Three-Phase Relative Permeability. Soc. Pet.
Eng. J., 5 (4), 435-445.
[8] Blunt, M. J. (2001). "Flow in porous media - pore-network models and multiphase flow."
Current Opinion in Colloid & Interface Science, 6(3), 197-207.
[9] Blunt, M. J., Jackson, M. D., Piri, M., and Valvatne, P. H. (2002). "Detailed physics,
predictive capabilities and macroscopic consequences for pore-network models of multiphase
flow." Advances in Water Resources, 25(8-12), 1069-1089.
[10] Christensen, J. R., Stenby, E. H., and Skauge, A. (2001). "Review of WAG Field
Experience." SPE Reservoir Evaluation & Engineering (04).
[12] Fatt I. The network model of porous media I. Capillary pressure characteristics. Trans
AIME 1956;207:144_159.
[13] Fatt I. The network model of porous media II. Dynamic properties of a single size tube
network. Trans AIME 1956;207:160_163.
[14] Fatt I. The network model of porous media III. Dynamic properties of networks with tube
radius distribution. Trans AIME1956;207:164_181.
[15] Fenwick, D. H., and Blunt, M. J. (1998a). "Network Modeling of Three-Phase Flow in
Porous Media." SPE Journal, 3(1), 86-96.
[16] Fenwick, D. H., and Blunt, M. J. (1998b). "Three-dimensional modeling of three phase
imbibition and drainage." Advances in Water Resources, 21(2), 121-143.
[17] Forrest, J.K., et al., Samarang Field - Seismic To Simulation Redevelopment Evaluation
Brings New Life to an Old Oilfield, Offshore Sabah, Malaysia, in International Petroleum
Technology Conference. 2009: Doha, Qatar.SPE 13162
[18] Gorell, S.B., Modeling the Effects of Trapping and Water Alternate Gas (WAG) Injection on
Tertiary Miscible Displacements, in SPE Enhanced Oil Recovery Symposium. 1988: Tulsa,
Oklahoma.SPE 17340
11
American Journal of Oil and Chemical Technologies;
ISSN (online): 2326-6589; ISSN (print): 2326-6570
Volume X, Issue X, June 20XX
[19] Hui, M.-H., and Blunt, M. J. (2000a). "Pore-Scale Modeling of Three-Phase Flow and the
Effects of Wettability." SPE/DOE Improved Oil Recovery Symposium, Copyright 2000, Society
of Petroleum Engineers Inc., Tulsa, Oklahoma.
[20] Hui, M. H., and Blunt, M. J. (2000b). "Effects of wettability on three-phase flow in porous
media." Journal of Physical Chemistry B, 104(16), 3833-3845.
[21] Juanes, R., & Spiteri, E. (2004). Impact of Relative Permeability Hysteresis on WAG
Injection. SPE 89921.
[22] Oak, M. J. (1990). "Three-Phase Relative Permeability of Water-Wet Berea." SPE/DOE
Enhanced Oil Recovery Symposium, Tulsa, Oklahoma.
[23] Øren, P.-E., and Bakke, S. (2003). "Reconstruction of Berea sandstone and porescalemodelling of wettability effects." Journal of Petroleum Science and Engineering, 39(3-4),
177-199.
[24] Oren, P.-E., Bakke, S., and Arntzen, O. J. (1998). "Extending Predictive Capabilities to
Network Models." SPE Journal, 3(4), 324-336.
[25] Øren, P. E., Billiotte, J., and Pinczewski, W. V. (1994). "Pore-Scale Network Modelling of
Waterflood Residual Oil Recovery by Immiscible Gas Flooding." SPE/DOE Improved Oil
Recovery Symposium, 1994 Copyright 1994, Society of Petroleum Engineers, Inc., Tulsa,
Oklahoma.
[26] Paterson, L., Lee, J.-Y., and Pinczewski, W. V. (1997). "Three-Phase Relative Permeability
in Heterogeneous Formations." SPE Annual Technical Conference and Exhibition, 1997
Copyright 1997, Society of Petroleum Engineers, Inc., San Antonio, Texas.
[27] Pereira, G. G. (1999). "Numerical pore-scale modeling of three-phase fluid
flow:Comparison between simulation and experiment." Physical Review E, 59(4), 4229–4242.
[28] Peters, L., Arts, R., Brouwer, G., Geel, C., Cullick, S., Lorentzen, R. J., Chen, Y., Dunlop,
N., Vossepoel, F. C., Xu, R., Sarma, P., Alhuthali, A. H. H., and Reynolds, A. (2010). "Results
of the Brugge Benchmark Study for Flooding Optimization and History Matching." SPE
Reservoir Evaluation & Engineering(3), pp. 391-405.
[29] Piri, M., and Blunt, M. J. (2005a). "Three-dimensional mixed-wet random pore-scale
network modeling of two- and three-phase flow in porous media. I. Model description." Physical
Review E, 71(2), 026301.
[30] Sohrabi (2000) 'Pore scale study of water alternating gas (WAG) injection using highpressure micromodels with different conditions of wettability', SPE, (95594).
[31] Sohrabi (2001) 'Visualisation of Oil Recovery by Water Alternating Gas (WAG) Injection
Using High Pressure Micromodels - Oil-Wet & Mixed-Wet Systems', SPE, (71494-MS), pp.
1429-1435.
[32] Stone, H. L. (1970). Probability Model for Estimation Three- Phase Relative Permeability.
Journal of Petroleum Technology, 20, 214-218.
[33] Stone, H. L. (1973). Estimation of Three-Phase Relative Permeability and Residual Data,
Journal of Canadian Petroleum Technology, 12, 53-61.
[34] Suicmez, V. S., Piri, M., and Blunt, M. J. (2006). "Pore-Scale Modeling of Three-Phase
WAG Injection: Prediction of Relative Permeabilities and Trapping for Different Displacement
Cycles." SPE/DOE Symposium on Improved Oil Recovery, Society of Petroleum Engineers,
Tulsa, Oklahoma, USA.
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Volume X, Issue X, June 20XX
APPENDIX:
Table 1: pore networks parameters
Parameters
Networks
A
B
C
Number of Nodes
Number of Bonds
9315
16590
12786
21438
17657
28404
Permeability mD
1390
472.678
29.6618
Clay porosity %
0.0014
0.006506
0.2598
Net porosity %
Total porosity %
19.5281
19.5295
16.5346
16.5411
7.26506
7.52488
Formation Factor
28.9778
48.1238
329.337
Table 2: Properties of the wetting system
Wettability system
Contact angles
(degrees)
θow
θgo
θgw
Case
Water-wet
0-30
0
0-25.3
Figure1. Brugge field initial reservoir model
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Volume X, Issue X, June 20XX
Figure 2. Selection of networks based on porosity and permeability distribution for Brugge field
(Peters et al. 2010)
Table 3: Main reservoir simulation parameters
Parameters
Values
Pressure
2,466 psi @ 5577 ft depth
Oil water contact (OWC)
5498.5 ft
Free water level
5505 ft
Compressibility
3.5x10-8 psi-1
Producers and production rates
20 producers (5000 rb/d) @ 725 psi
Injectors and injection rates
10 injectors (10000 rb/d) @ 2611 psi
Water cut allowed
90%
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American Journal of Oil and Chemical Technologies;
ISSN (online): 2326-6589; ISSN (print): 2326-6570
Volume X, Issue X, June 20XX
Table 4: WAG injection scenario
Number
WAG
ratio
1
1:1
Scenario
First flood
Pure water injection
Water
2
1:1
Pure gas injection
Gas
3
1:1
21 WAG cycles (1 year water- 1 year gas)
Water
4
1:1
21 WAG cycles (1 year gas- 1 year water)
Gas
5
1:1
7 WAG cycles (3 years water- 3 years gas)
Water
6
1:1
7 WAG cycles (3 years gas- 3 years water)
Gas
7
1:1
4 WAG cycles (5 years water- 5 years gas)
Water
8
1:1
4 WAG cycles (5 years gas- 5 years water)
Gas
Kro
Krw
Krg
Figure 3. Network (A) Relative permeabilities
Figure 4. Network (B) Relative permeabilities
15
American Journal of Oil and Chemical Technologies;
ISSN (online): 2326-6589; ISSN (print): 2326-6570
Volume X, Issue X, June 20XX
Figure5. Network (C) Relative permeabilities
Figure 4: Oil recovery for water-wet system using WAG scenarios stated in table (4)
16