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Simulation of Immiscible WAG Injection in a Stratified Reservoir Characterization of WAG Performance
Poster · April 2019
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Jan Inge Nygård
Pål Østebø Andersen
University of Stavanger (UiS)
University of Stavanger (UiS)
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Simulation of Immiscible WAG Injection in a Stratified
Reservoir - Characterization of WAG Performance
Jan Inge Nygård1, Pål Østebø Andersen1,2
1 Department of Energy Resources, University of Stavanger
2 The National IOR Centre of Norway, University of Stavanger
Abstract
Results
Water-Alternating-Gas (WAG) is a well-established EOR process where gas and water are injected in
alternating fashion. Good volumetric sweep is achieved as water and gas target both the oil residing in low
and high portions of the reservoir, respectively. Other important features in three-phase hysteretic flow
include phase trapping which is believed to be more strongly associated with the gas phase. With these
aspects in mind a vast simulation study has been performed investigating immiscible WAG injection focusing
on mechanisms such as mobility, gravity, injected volume fractions, reservoir heterogeneity, gas entrapment
and relative permeability hysteresis. A horizontally layered reservoir is considered where oil is displaced by
water and gas alternately injected towards a producer. The model is a modified black-oil type, where
hysteresis in the gas phase is modeled using Land’s model for trapping and Carlsens model for relative
permeability hysteresis. It is seen that gravity segregation in uniform models and increased heterogeneity in
no-gravity models both lead to lower oil recovery. However, in heterogeneous models, gravity can divert flow
from high permeable layers into low permeable layers and improve recovery. Hysteresis lowers gas mobility
and hence improves gas-oil mobility ratio and reduces gravity segregation. The first effect is always positive,
but the second is mainly positive in more uniform reservoirs where gravity segregation has a negative effect
on recovery. In heterogeneous reservoirs, reducing gravity segregation can lead to that the oil in low
permeable layers remains unswept.
In addition to demonstrating the role of the various parameters we derive a characteristic
dimensionless number to scale these mechanisms and predict recovery trends. This number is effectively a
WAG mobility ratio, termed M*, expressing how well the injected fluid mixture is able to displace oil whether
it is due to fluid mobilities, heterogeneity or other effects. At a value of M* near 1 optimal recovery is
achieved, while logarithmic increase of M* reduces recovery.
We consider non-gravity flow first and four models where FH ranges from 1.0 (homogeneous) to 13 (highly heterogeneous),
and find that M* gives a good match. MWAG is used as reference and correspond to M* when FH=1 and FG=1.
Figure 3: Scaling of recovery factor (RF) data under no-gravity no-hysteresis conditions
Next, we showcase some simulation sets comparing the effect of hysteresis with and without gravity:
Effect of hysteresis – No gravity
Effect of hysteresis - With gravity
Objectives
• Develop a characteristic dimensionless number that can describe WAG performance
• Consider the interplay of mobility, gravity, heterogeneity and relative permeability
hysteresis, and how these may alter optimal WAG injection scheme
Methods
We consider a model:
Figure 1: System geometry
where relative permeabilities are defined by Corey formulation, which are averaged across
the full saturation interval (1) and then used to define twophase mobility ratios (2) as
follows:
Figure 4: The role of hysteresis under no-gravity
conditions. Mwag (left) and M* (right)
(1)
Figure 5: The role of hysteresis under gravityinfluenced conditions. Mwag (left) and M* (right)
Overall match of all simulation cases / sets:
(2)
And finally, we show an overview of all simulation results plotted with MWAG (left) and M* (right). Note how
the data are much more collected with M*, with the reduced scatter of the datapoints.
Hysteresis: We apply the ‘WAGHYSTR’ model to simulate hysteresis effects in which Land’s
parameter C have been set to 1.0, and the secondary drainage factor α to 2.5. The
significance of these with regards to gas relative permeability is illustrated in Figure 2,
where it becomes apparent that lower values of C indicates that a larger portion of the gas
phase becomes trapped while higher values of alpha indicates stronger hysteretic effect for
a given amount of gas trapped.
Figure 2: The role of hysteresis parameters C (left) and α (right) on gas relative permeability
To represent the lowered relative permeability of the gas phase we update (2) with
alterations to Sorg and krogmax from C and alpha, respectively.
Conclusions
Heterogeneity: To indicate how heterogeneity increases the effective mobility ratio we
define a heterogeneity multiplier Fh which is based on arithmetic and harmonic averages of
the horizontal permeabilities:
•
•
•
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In uniform models (FH=1), gravity led to segregation and lower recovery factor (RF). For the no-gravity models RF
declined with increases in heterogeneity (FH>1)
In heterogeneous models, gravity was a positive mechanism compared to no-gravity cases as injection fluids were
diverted into low-permeable layers giving higher RF
Hysteresis lowers gas mobility and hence improves gas-oil mobility ratio and reduces gravity segregation. The first effect
is always positive, but the second is mainly positive in more uniform reservoirs where gravity segregation has a negative
effect on recovery. In heterogeneous reservoirs, reducing gravity segregation can lead to that the oil in the low
permeable layers remains unswept
It is important to investigate the interplay between gravity and hysteresis on optimization procedures for WAG, as these
were observed to have differing impacts on recovery individually than when combined
WAG performance can be characterized by just one dimensionless number, M*. Accordingly RF can be predicted just
knowing M*, and the impact of model input parameters on RF can be directly associated with how they affect M*
The scaling number accounts for water-oil and gas-oil mobility ratio, reservoir heterogeneity, gravity effects from both
water and gas phases, relative permeability hysteresis, and the applied WAG ratios (changes rw)
Gravity: We represent gravity effect through Fg, where a1 and a2 are fitting parameters
while NG is a ratio between the residence and segregation time of injected fluids, which Is
affected by parameters as vertical permeability, density difference and individual phase
mobilities:
•
Matching parameter M*: Characteristic dimensionless number that incorporates mobility,
gravity, heterogeneity and hysteresis, where rw is the injected volume fraction of water:
Acknowledgement
Contact information
The authors acknowledge the Research Council of Norway and the industry
partners, ConocoPhillips Skandinavia AS, Aker BP ASA, Vår Energi AS, Equinor
ASA, Neptune Energy Norge AS, Lundin Norway AS, Halliburton AS,
Schlumberger Norge AS, Wintershall Norge AS, and DEA Norge AS, of The
National IOR Centre of Norway for support.
E-mail: nygaard.janinge@gmail.com
LinkedIn:
www.linkedin.com/in/janingenygaard
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