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Geomechanics Considerations in Enhanced Oil RecoveryTadesse
Weldu Teklu, Waleed Alameri, Ramona M. Graves, Azra N. Tutuncu, and
Hossein Kazemi, ColoradoSchool of Mines, and Ali M. AlSumaiti, The
Petroleum Institute
Copyright 2012, Society of Petroleum Engineers
This paper was prepared for presentation at the SPE Canadian
Unconventional Resources Conference held in Calgary, Alberta,
Canada, 30 October–1 November 2012.
This paper was selected for presentation by an SPE program
committee following review of information contained in an abstract
submitted by the author(s). Contents of the paper have not
beenreviewed by the Society of Petroleum Engineers and are subject
to correction by t he author(s). The material does not necessarily
reflect any position of the S ociety of Petroleum Engineers,
itsofficers, or members. Electronic reproduction, distribution, or
storage of any part of this paper without the written consent of
the Society of Petroleum Engineers is prohibited. Permission
toreproduce in print is restricted to an abstract of not more than
300 words; illustrations may not be copied. The abstract must
contain conspicuous acknowledgment of SPE copyright.
Abstract
Geomechanics plays significant role in decisions regarding all
phases of exploration and production of oil and gas.Specifically,
geomechanics influences prospect appraisal, field development, and
primary, secondary, and tertiary productionactivities. Injection of
enhanced oil recovery (EOR) fluids such as polymer, steam and gas/
2CO affect reservoir stress re-distribution and re-orientation in
the field. Hence geomechanics studies need to be conducted in every
step of the EOR
processes, from EOR screening to abandonment.
This paper reviews geomechanical issues related to polymer,
steam and hydrocarbon gas/ 2CO continuous and water-alternating-gas
flooding both in sandstone and carbonate formations. A number of
published laboratory and field case studieswill be presented and
discussed in regard to geomechanics issues. The geomechanical
effects pertinent to waterflooding andEOR processes in
unconventional reservoirs such as shale reservoirs and oil sands
will also be discussed. Finally, reservoir
properties affected by stress changes and how to incorporate it
in reservoir modeling will be discussed.
1. IntroductionDeveloping EOR schemes involves high financial
risks and uncertainties. Careful screening the EOR type is required
beforeembarking with any costly specialized laboratory
investigation, EOR analysis/simulation, pilot study or field
implementation.The main technical parameters considered in EOR
screening are fluid properties (API gravity, viscosity, composition
andfluid compressibility), remaining volume (remaining oil
saturation, porosity, net thickness and areal extent),
lithology,
permeability, depth, and temperature (Taber et al. , 1997).
Overburden stress is highly related with the depth of the
reservoir;similarly porosity and permeability are strong functions
of in situ stress, pore pressure and their alteration resulted by
theEOR process and the associated production. Moreover, the
remaining volume is related with the pore pressure hence
theeffective in situ stresses. The temperature contrast between the
injectant and the reservoir also affects the stress field of
thereservoir. Therefore, in addition to the above mentioned
reservoir parameters, geomechanical properties play important
roleon deciding which type of EOR should be applied to maximize
recovery.
Reservoir deliverability is related to interactions between
changing fluid pressure, reservoir in situ stresses, and fracture
permeability during production and injection. Cold injection such
as miscible and immiscible gas injection, waterflooding
and microbial injection might lead to near well contraction and
reduction of stresses that may lead to fracturing. Coldinjection
such as polymer injection might increase the stress due to high
fluid viscosity and reduction of the formation
permeability (pore throat blockage) whereas thermal processes
may lead to rock expansion and rising lateral stresses
withincreased chance of inter-well shear fractures, seal breach,
fault reactivation or rock failure. Formation/rock failure can be
in
Mode I or Mode II , in the form of tensile failure or shear
failure. Tensile failure occurs when tensile stress exceeds
rocktensile strength and shear failure occurs when shear stress
exceeds the rock shear resistance strength. Therefore,geomechanical
assessment starting from analytical failure models such as
Mohr-Coulomb failure criteria to more advancedgeomechanical
analysis (coupled fluid flow and geomechanics simulation) should be
examined in making a decision onviable EOR type, managing the field
effectively and improving the recovery (Qobi et al. , 2010).
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2. Geomechanics considerations in secondary recovery
(waterflooding)Waterflooding is by far the most widely used method
to increase oil recovery. In addition to parameters such as
well
placement and well type, optimal rate selection is essential to
improve water flooding performance (Alhuthali et al. ,
2007).Injection rate is related with stress distribution near
wellbore or in the reservoir according to the well-known Terzaghi
Law(Terzaghi, 1943) that relates effective stress ( eff ) with pore
pressure ( p ) as in Eq. 1 :
...................................................................................................(1)eff
p Where is Biot’s coefficient and is stress.
Biot coefficient is also strong function of stress changes (Mese
and Tutuncu, 2000) and is calculated by
1
.....................................................................................................(2)b
grain
K
K
Where bK and grainK are bulk and grain modulus respectively.
Waterflooding experiment performed by Muralidharan et al.
(2005), both on fractured and un-fractured sandstone core
atdifferent stress condition (uniaxial, triaxial and hydrostatic
stress), show that fluid flow from fracture dominates when
theapplied confining stress is small ( Fig. 1, a ); on the other
hand fluid flow from matrix may increase as applied stress
increases(Fig. 1, b ). This could be due to conformance
modification as water flows into the matrix with increasing
confining stress .
Therefore, recovery may be improved by operating at an optimal
stress condition by varying the injection rate. Similarobservations
were noticed during 2CO flooding as will be discussed in Section 5
.
Fig. 1 - Effect of stress on fluid flow in fracture and matrix
at different injection rate (Muralidharan et al. , 2005).
A recent numerical study by Fakcharoenphol et al. (2012) shows
that, waterflood-induced stress change improves oilrecovery in
shale reservoirs. The synergestic effect of reservoir cooling and
pore pressure increase during waterflooding cansignificantly
trigger rock failure, potentially reactivating healed natural
fractures and creating new microfractures ( Fig. 2 ).These
microfractures could create flow paths for hydrocarbons inside the
matrix, thus, improving the fracture-matrixinterface area and
increasing hydrocarbon production from the matrixes. Similarly,
analytical study by Kocabas (2006) showsthat, in porous medium with
stiff materials (such as carbonate reservoirs), cooling by
waterflooding creates large-scale tensilestress and may induce new
fractures (or propagate existing ones far into the reservoir).
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Fig 2 - Mohr diagram for stress change during water injection
(Fakcharoenphol et al. , 2012).
In an experimental study, Zekri and Chaalal (2001) investigated
the effect of thermal shocks in a carbonate cores. Thecooling
thermal shock can happen as a result of stress and strain change
caused by abrupt cooling during waterflooding.Fractured and
un-fractured carbonate outcrop cores from Hafeet Mountain, Al-Ain,
UAE, were used to study the effect ofcooling. Porosity and
permeabilities of several samples, fractured and un-fractured, were
measured before and after abruptcooling. The carbonate core samples
were cut into six small disks of 25.4mm diameter and 5mm thickness
for repeatability.Scanning Electron Microscope (SEM) and CT
scanning were performed to characterize pore size and shape prior
and afterthe thermal shock. They concluded: (1) Cooling generally
results in permeability reduction for un-fractured cores and
haslittle or no effect on tight ( 0.1 md k ) limestone cores. (2)
Cooling improve permeability of fractured cores. (3) Bothheating
and cooling cause a reduction in the fracture gradient; however,
the effect is more pronounced for cooling. Therefore,appropriate
coupling of geomechanics and fluid flow is necessary to capture
these impacts on oil recovery.
3. Geomechanics considerations in polymer floodingPolymer
flooding can enhance recovery by improving sweep efficiency
(conformance) of conventional water flooding. Theworld’s largest
polymer flood was implemented at Daqing, China, beginning in 1995.
According to a study by Wang et al. (2008), 23.3% of total
production from the field, as of 2007, was attributed to polymer
flooding. Polymer flooding isexpected to boost the ultimate
recovery of the field to more than 50% OOIP (10 to 12% more than
conventional waterflooding). The type of polymer used in Daqing is
a high-molecular-weight, partially hydrolyzed polyacrylamides
(HPAMs)(Wang et al. , 2008). Reservoir properties including
reservoir lithology, stratigraphy, heterogeneity, remaining oil
saturation,well pattern and well distance, polymer properties such
as resistance to degradation, tolerance to reservoir salinity
andhardness, polymer retention, rheology and compatibility with
other chemicals are among the critical factors that impact
thedesign of the polymer flooding (Wang et al. , 2008; Seright et
al. , 2009). In addition to the aforementioned factors, Wang etal.
(2008) investigated the effect of injection rate on recovery of 12
years of polymer flooding at Daqing field. According totheir study,
despite the fact that high injection rate might give higher
production at the earlier period ( Fig. 3 ), ultimatelylower
injection rate gives slightly better recovery and lower water cut.
They recommend 0.14 – 0.20 pore volume/ year(PV/yr) polymer
injection rate. The dependence of ultimate recovery on injection
rate could be related to stress changesspecifically due to
increased pore pressure near injection wells or increased
resistance factor and residual resistance factor.
Resistance factor is a quantitative measure of mobility
reduction during the propagation of the polymer solution in the
porousmedia, while the residual resistance factor is a measure of
permeability reduction after the polymer treatment (Wang et al.
,2008). Similarly, laboratory investigation of sulfonated polymer
injection on 100 to 600 md carbonate cores at reservoirconditions,
the resistance factor was 5 to 8 and residual resistance factor was
1.24 to1.34 (Han et al. , 2012).
S h e a r s
t r e s s
Increase pressure
Decrease temperature
Effective normal stress
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Fig. 3 - Changes in oil-production rate vs. injection rate (Wang
et al. , 2008).
Khodaverdian et al. (2010) investigated experimentally and
numerically the geomechanical effects of polymer flooding in
anunconsolidated sand, viscous oil reservoir. A major concern
related to polymer flooding in unconsolidated sand is the
potential of shear failure, which could lead to fault
reactivation, casing failure, well loss, and containment loss.
Undesirableshear failure or fracture propagation in polymer
flooding could happen due to: (1) Impurity and solids present in
the injectionfluid can plug the sand face over time leading to
fracturing. (2) High in-situ oil viscosity and low polymer mobility
can causefracturing. (3) Production could cause compaction and
subsidence (Dominguez and Willhite, 1977; Seright et al. , 2009;
Hanet al. , 2012). Fractures preferentially propagate into lower
permeability layers; therefore if there is small or no stress
contrast
between shale and sand, the fracture will predominantly
propagate into the shale. Fracturing could be detrimental
especially ifit can lead to containment loss when the stress
contrast between the sand and caprock is small.
Khodaverdian et al. (2010) further determined the possible
fracture mechanism and net propagation pressure from
theirexperimental study. They have derived an empirical equation to
determine equivalent fracture toughness as an input to
theirnumerical modeling. Lab determined effective stress value was
upscaled into field scale. A simulator with capability ofmodeling
sand plasticity, shear failure, finite deformations coupled with
two-phase flow was used for their numerical studymonitoring the
rock deformation, pressure, saturation, and stress among other
parameters throughout the injection period.The model has one
vertical injector well and a horizontal production well to check
the occurrence of any shear failure during
polymer injection due to pore pressure changes. Their study
showed that there is a potential for large-scale shear failure
inunconsolidated formations during polymer or high-viscosity-fluid
flooding.
Similar experimental study by Zhou et al. (2010) showed that
viscous/polymer flooding in unconsolidated formation induces planar
fractures. About 40% absolute permeability increments were reported
due to a decrease in effective stress caused byshear dilation.
Axial pressure, radial pressure, injection pressure, and axial
displacement were measured. The relationship
between propagation pressure and confining stress was also
determined in unconsolidated sands by a series of physical
modelmeasurements.
4. Geomechanics consideration in thermal EORThermal stress
change in the formation during waterflooding, steam injection,
polymer-augmented waterflooding, and gasinjection can induce
thermoelastic stresses to alter the magnitude and direction of
principal stress ( max min, , and v ).Similarly, pore pressure
change and sand production in oil sands can cause poroelastic
alterations as well as changes in theeffective stresses . These
stress changes may cause thermal strains (during thermal EOR) that
can eventually lead to rupture orshear failure (Hojka et al. ,
1993; Dusseault, 1993; Qobi et al. , 2010).
Benzagouta and Amro (2009) conducted an experimental study on
Arab D, one of the prolific oil bearing carbonateformations among
Middle East reservoirs, and showed that increase in effective
stress and temperature result permeabilityreduction. They conducted
core flooding measurements at various temperatures (25, 50, 75 and
100 oC) and effective stresses (725 to 4,000 psi). SEM analyses and
core flooding experiments show permeability reduction with
increasing effective stress (Fig. 4 ) and temperature ( Fig. 5 ).
Hence, operators should be aware of these phenomena during
secondary and tertiaryrecovery operations. Steam flooding might
lead to permeability reduction for low temperature (shallow)
reservoirs as
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reported by Benzagouta and Amro (2009); However, typically
temperature-induced stress changes are near-wellbore phenomena as
permeability is less sensitive at reservoir temperature (> 60
oC) as can be seen in Fig. 5 .
The reduction of permeability versus effective stress and
temperature is shown in Fig. 4 and 5 , respectively. The
initialtemperature, stress, and permeability of the sample were 25
oC, 725 psi and 300 md. All permeability changes werenormalized
with respect to the permeability at initial conditions (i.e., k =
300 md). Similar experimental observations werereported by other
researchers (Sanyal et al. , 1974; Muralidharan et al. , 2005;
Ferno et al. , 2010).
Fig. 4 - Permeability reduction percentage vs. effective stress
atconstant temperature (Benzagouta and Amro, 2009).
Fig. 5 - Permeability reduction percentage vs. temperature
atconstant effective stress (Benzagouta and Amro, 2009).
A study by Sanyal et al. (1974) reported 60% to 88% permeability
reduction with increasing temperature in consolidatedsandstone
formations. The decrease in permeability with increasing effective
stress is caused by the reduction of pore spacedue to decreasing
modulus of elasticity. Another study by Muralidharan et al. (2005)
and Ferno et al. (2010) also show
permeability reduction with increasing effective stress of
fractured and un-fractured sandstone and carbonate cores.
Allreviewed studies show that, despite the variation in the level
of reduction, permeability reduces with increase in effectivestress
(uniaxial stress, triaxial and hydrostatic stress). And the
reduction in permeability is more pronounced for fracturedcores
compared to un-fractured ones.
Cyclic Steam Stimulation (CSS), Steam Assisted Gravity Drainage
(SAGD) and Cold Heavy Oil Production with Sand(CHOPS) are the
current leading thermal EOR process for bituminous unconsolidated
sand reservoirs. SAGD increasesreservoir pressures and temperatures
sufficiently to cause shear failure within and beyond the growing
steam chamber in oilsands. This shear failure results increase in
bulk volume, a phenomenon called “dilation”. The associated
increase in
permeability in oil sands can reach up to ten-fold of the
original vertical permeability. The increase in permeability
withrespect to original permeability (normalized permeability)
versus volumetric strain (dilation), ,v for a triaxial
measurementon both vertical and horizontal cores from Athabasca oil
sand is shown in Fig. 6 (Collins, 2007). The permeability and
porosity can be related to volumetric strain, ,v in modeling
coupled systems as will be discussed in Section 6 .
In SAGD, in addition to enhancement of production due to
increase in permeability and mobility, pore pressures ahead of
thesteam chamber also substantially increases promoting the growth
of the steam chamber (Collins, 2007; Yale et al. , 2010) .The
direction of steam chamber propagation is dictated by the stresses
acting on the rock matrix that is a function of thereservoir depth
and the tectonic loading. According to study by Collins (2007),
SAGD would be more efficient if steam isinjected at higher rates
resulting in shear failure and improved permeability. Hence,
detailed geomechanical study could helpin determining an optimal
steam injection rate to improve recovery by increasing
permeability.
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Fig. 6 - Absolute permeability increase during triaxial tests
(Collins, 2007).
5. Geomechanics and geochemical considerations in hydrocarbon
gas and CO 2 floodingMiscible hydrocarbon gas and carbon dioxide
(
2CO ) flooding are effective means of enhanced oil recovery for
light oil
carbonate and sandstone reservoirs. Similar to waterflooding
discussed in Section 2 , gas flooding can causes stress
re-distribution. The stress change can be triggered by reservoir
temperature cooling or pore pressure fluctuations, especially
inwater-alternating-gas (WAG) flooding (Rui et al. , 2009).
Moreover, geochemical effect of 2CO injection, such as
dissolution
of carbonates during 2CO flooding (Ross et al. , 1982) or
asphaltene deposition (Patel et al. , 1987) could alter the
stressdistribution.
Dissolution results from a reaction of 2CO and water (brine) to
form carbonic acid 2 3(H CO ) and subsequently forming
bicarbonate ion 3(HCO ) . The bicarbonate forms a weak acid in a
precence of water (brine) and dissolves calcites in
carbonate rocks. The 2CO - invoked dissolution of formation
minerals is highly dependent on lithology -- mainly calcite
3(CaCO ), dolomite 3 2(CaMg CO ) , and anhydrite 4(CaSO ) .
Ross et al. (1982) investigated the dissolution effect on
permeability of a number of U.K. and North Sea calcareous
sandstonecores. They observed significant permeability improvements
(up to five-fold) due to dissolution of carbonates during
2COinjection. Despite the expected improvement in recovery as a
result of permeability increase, there could be drawbacks --well
instability, subsidence, and early 2CO breakthrough. Dissolution
effect is greater for calcite compared to dolomite and iseven
greater in chalks (Madland et al. , 2006; Korsnes et al. ,
2008).
Compaction during primary production and later due to “ water
weakening of chalk ” during water injection caused more than7.8
meter of subsidence in the Ekofisk Field, in the Norwegian sector
of the North Sea (Sylte et al. , 1999). In chalkformations, as in
Ekofisk, water reduces yield stress and increases rock
compressibility. Based on field and laboratorymeasurements, water
weakening is the main cause of compaction in Ekofisk (Sylte et al.
, 1999). In addition to waterweakening , dissolution may also
weaken chalk formations. Korsnes et al. (2008) showed that the
volumetric strain during
2CO flooding could increase 1.5 to 3.3 times that of
waterflooding.
Alam et al. (2011) studied the impact of 2CO flooding on two
major oil bearing chalk formations, the Ekofisk and Tor of theSouth
Arne field in Danish North Sea. Porosity, permeability, carbonate
content, surface area, wettability, compressional andshear wave
velocity, and triaxial compression measurements were among the
petrophysical and mechanical properties studied
before and after 2CO flooding. For the triaxial compression
experiments, waterflooded and 2CO flooded cores were used.
Wettability was measured using 2T relaxation times before and
after 2CO flooding. The experiments indicated that permeability,
porosity, formation stiffness, and specific surface area decreased
while wettability remained the same.
Mohamed et al. (2011) similarly discussed supercritical 2CO
flooding experiments on limestone cores. Calcium, magnesium,and
sodium content, and permeability of the limestone cores were
measured before and after core flooding. The permeabilityof the
cores remained the same when NaCl – brine was injected while
injection of 2CaCl – brine promoted rock dissolution.
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Patel et al. (1987) showed that in carbonate reservoir of the
Denver unit, Wasson Field, contrary to the expected 2CO injectivity
increase compared to water flooding, the 2CO injection rate was
lower than water injection rate. Similarly, Rogers
and Grigg (2001) observed injectivity loss in many carbonate
fields during 2CO flooding. The injectivity loss might becaused by
a combination of pore compaction, asphaltene deposition, rock
dissolution and re-precipitation, particle migration,wettability
alteration, relative permeability change (Patel et al. , 1987;
Rogers and Grigg, 2001; Rui et al. , 2009), andeffective
permeability reduction due to stress change in
fractured/un-fractured reservoirs (Rui et al. , 2009).
If fractures are present in the reservoir, 2CO might flow along
the fracture and cause early breakthrough and hence cause low
displacement efficiency. Moreover, pore pressure might fluctuate
to some extent during 2CO injection. This pore pressurefluctuation
causes fluctuation in effective stress leading to rock deformation
and reduction in permeability of both matrix andfracture. The
decrease in permeability coupled with multi-phase flow can cause a
decrease in well productivity in stresssensitive formations . The
fracture aperture (induced or natural fracture) is strongly
dependent on the normal stress across thefracture.
Rui et al. (2009) studied the effect of effective stress on
displacement efficiency in 2CO flooding in low-permeability
fractured reservoirs. The flow rate distribution between
fracture and matrix was obtained by flowing 2CO at different
effectivestress as shown in Fig. 8 and as discussed in Section 2 .
Because the fractional reduction in fracture permeability is
greaterthan the reduction in matrix permeability ( Fig. 7 ), more
2CO flows in the matrix at higher effective stress (Fig. 8 ) up to
anoptimal level. Therefore, displacement efficiency could be
improved with increasing effective stress , Fig. 9 .
Fig. 7 - Reduction in permeability vs. effective stress for
matrix and fracture of a core (Rui et al. , 2009).
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Fig. 8 - Flow rate distribution at effective stress (Rui et al.
,2009).
Fig. 9 - Displacement efficiency for three different fractured
coresat different effective stress: PC2 ≈ 3 md, MK3 ≈ 30md and HW1
≈ 306 md, and fracture permeability of 1md for the three cores
(Ruiet al. , 2009).
The reason for the disproportionately large reduction in the
fractures permeability compared to the matrix permeability is
thatthe permeability reduction of matrix cores depends on the pore
deformation; however, the permeability reduction of afractured core
depends on fracture parameters such as fracture aperture, fracture
density, fracture orientation, fracture length,and shear stress
effects. Hence, as effective stress increases, the fracture is much
easier to deform than the pores. Similar to
permeability, fracture aperture was observed to decrease with
increasing effective stress (Rui et al. , 2009). As shown in Fig.9,
increasing the effective stress can restrain gas channeling in the
fracture in the core -- leading to improvement in sweepefficiency
in the matrix and improved oil recovery. However, beyond a
threshold effective stress sweep efficiency will start todecrease
due to the reduction in effective permeability.
The 2CO EOR projects can serve as great 2CO sequestration
reservoirs because of their cost and proven fluid containment(seal
integrity); however, in highly fractured reservoirs more detailed
study is required. Chiaramonte et al. (2011) studied theeffect of
fracture presence and geomechanical parameters during 2CO EOR and
sequestration project in a Tensleep
Formation. They have also investigated the constraints on the
volume of 2CO injected and flow rates to avoid the sealintegrity
problems using a coupled geomechanics and fluid flow simulator.
They concluded that 2CO injection was not agood EOR process due to
the highly fractured nature of the formation. Also, critically
stressed minor faults in the caprockmay lead to seal integrity
problems. Hence, a detailed rock mechanical, geomechanical, and
fracture measurements arenecessary to evaluate potential hazards to
the reservoir.
Another issue during 2CO or gas flooding EOR projects is proper
monitoring of the flood front to determine suitable infill
production and injection wells. Wang et al. (1996) discussed the
use of high resolution time-lapse cross-well seismic surveyduring
2CO flooding to monitor the 2CO movement. As 2CO displaces the
original reservoir fluid, it causes a reduction in the
bulk modulus that can be monitored form of seismic measurements
of compressional velocity ( ) pV and shear velocity ( ).sV Wang et
al. (1996) performed a rock physics study using a carbonate
reservoir core at in situ stress conditions. According totheir
study, if the stress increment after 2CO flooding is neglected, the
compressional and shear velocities predicted using theGassmann
(1951) fluid substitution analysis would be considerably high as
studied by Nolen-Hoeksema et al. (1995), andmay lead to unrealistic
2CO front tracking interpretations. Hence, geomechanic parameters
should be incorporated inmonitoring the fluid movement in gas or CO
2 flooding EOR operations.
6. Geomechanics and fluid flow couplingAs mentioned in the
previous sections, geomechanics plays a very important role during
primary, secondary and tertiary oil
production periods. To account for such effects, the governing
equations of fluid flow and geomechanics should be coupled,which
can be accomplished by partial or full coupling numerical
techniques.
In partial coupling techniques, the fluid flow and geomechanics
governing equations are solved separately and the
relevantinformation is exchanged between them at a user-specified
time interval. This method is computationally efficient as the
fluid
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flow can be computed at a refined time steps (on the order of
days) compared to geomechanics time steps (on the order ofmonths)
(Minkoff et al. , 2004). In addition to the time step flexibility,
partial coupling is convenient to implement differentcomputational
grid size and grid spacing. The flow simulator includes only the
reservoir whereas the geomechanics modelmay extend further in the
lateral and vertical directions. Hence, the flow spatial domain is
typically a subset of thegeomechanics domain.
In linear-elasticity models, Eq. 3 and Eq. 4 can be used to
update permeability and porosity once the total volumetric strain
,,v is updated.
01 (1 )1
...............................................................................................(3)
v
n
e
1
...............................................................................................(4)v
Bnk Ae
Where 0 is the initial porosity, n and nk are the porosity and
permeability values at time-level ‘ n’, and 1n and 1nk are porosity
and permeability values at time-level ‘ n+1 ’. A and B are
coefficients specific to the formation of interest, andcan be
determined by experiments (Minkoff et al. , 2004; Yale et al. ,
2010).
As an approximation, t he change in effective stress within the
reservoir can be estimated using Eq. 5 based on the
“uniaxialstrain” assumption for isotropic rocks.
01 2 3 ........................................(5)1 1h v b p p K
T T
In fully coupled numerical techniques, fluid flow and
geomechanics governing equation can be solved iteratively (Settari
andMourits, 1994; Chin et al. , 2002) or simultaneously (Gutierrez
et al. , 2001; Chin et al. , 2000; Charoenwongsa et al. ,
2010).Full coupling approaches, although claimed to be robust, are
computationally expensive. However, as in the case of
chalkreservoirs (Madland et al. , 2006; Korsnes et al. , 2008),
unconsolidated oil sand (Khodaverdian et al. , 2010; Collins,
2007;Dusseault, 1993), highly fractured reservoirs (Bagheri and
Settari, 2008), shale reservoirs (Fakcharoenphol et al. , 2012),
and
2CO flooding (Pan et al. , 2009; Chiaramonte et al. , 2011),
most reservoirs are highly stress sensitive; therefore, it
isimperative to carry out the relevant simulation using a
fully-coupled technique. Fully coupled techniques can be solved
by
parallel computing techniques .
7. ConclusionsThe following conclusions are in conjunction with
geomechanical considerations regarding steam , gas and polymer
injectionEOR processes:
Experimental studies on fractured and un-fractured sandstone and
carbonate cores, with uniaxial, triaxial, orhydrostatic stress
loading conditions, indicate that fluid flow in fractures dominates
when the applied confiningstress is small.
Stress changes during high injection rate steam flooding in oil
sands may cause thermal strains that can lead torupture or shear
failure. The recovery may be improved as a result of up to a
ten-fold increase in permeability. Thecurrent industrial yardstick
to evaluate steam flooding performance does not account for the
shear failure advantageat higher injection rates.
Cooling that may happen during intermittent waterflooding in
water-alternating-gas injection may improve permeability in
fractured cores and reduce permeability in un-fractured cores.
However, the main effect of coolingthermal shocks is reduction of
the fracture gradient.
Injectivity loss has been observed in many fields during
continuous or intermittent water-alternating-gas flooding.This is
due to combined effects of dissolution , asphaltene deposition,
wettability change, permeability reduction, andeffective stress
reduction.
During 2CO injection, pore pressure fluctuations in
low-permeability fractured reservoirs may lead to fluctuation
ineffective stress , which could cause reduction in permeability of
matrix and fractures.
Acknowledgments The authors would like to thank Abu Dhabi
National Oil Company (ADNOC), The Petroleum Institute (PI), Abu
Dhabi,Center for Earth Materials, Mechanics, and Characterization
(CEMMC), the Unconventional Oil and Gas Institute (UNGI),and
Marathon Center of Excellence for Reservoir Studies (MCERS) at
Colorado School of Mines for their support of thisstudy.
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NomenclaturebK bulk modulus, M/(Lt
2), psi or MPa
grainK bulk modulus, M/(Lt2), psi or MPa
pV compressional velocity, L/t), m/s
sV shear velocity, L/t), m/s
k permeability, L 2, mdnk permeability at ‘n’ time-level, L 2,
md
1nk permeability at ‘n+1’ time-level, L 2, md p pore pressure,
M/(Lt 2), psiT current temperature, T, oR
0T reference temperature for stress-strain equilibrium state at
time zero, T,oR
Greek Letters
Biot’s poroelastic coefficient, dimensionless coefficient of
linear thermal expansion of fluid, 1/T, 1/ oR
v volumetric strain, dimensionless0 initial porosity,
dimensionlessn porosity at ‘n’ time-level, dimensionless
1n porosity at ‘n+1’ time-level, dimensionless
stress, M/(Lt2), psi or MPa
eff effective stress, M/(Lt2), psi or MPa
h horizontal stress, M/(Lt2), psi or MPa
v overburden stress, M/(Lt2), psi or MPa
min minimum principal stress, M/(Lt2), psi or MPa
max maximum principal stress, M/(Lt2), psi or MPa
Poisson’s ratio, dimensionless
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