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Mobility Ratio Control in Water-flooded
Reservoir with Incidence of Oilfield ScaleA. S. A. Fadairo
a
aDepartment of Petroleum Engineering , Covenant University , Ota,
Nigeria
Published online: 06 Apr 2010.
To cite this article:A. S. A. Fadairo (2010) Mobility Ratio Control in Water-flooded Reservoirwith Incidence of Oilfield Scale, Petroleum Science and Technology, 28:7, 712-722, DOI:
10.1080/10916460902804689
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Petroleum Science and Technology, 28:712722, 2010
Copyright Taylor & Francis Group, LLC
ISSN: 1091-6466 print/1532-2459 online
DOI: 10.1080/10916460902804689
Mobility Ratio Control in Water-floodedReservoir with Incidence of Oilfield Scale
A. S. A. FADAIRO1
1Department of Petroleum Engineering, Covenant University, Ota, Nigeria
Abstract The process of precipitation and accumulation of oilfield scales aroundthe well bore vicinity are major ongoing flow assurance problems that may result in
formation damage. The phenomenon may negatively impact the success of a water-flooding project that majorly depends on mobility ratio.
A predictive model has been developed for estimating the mobility ratio of awater-flooded reservoir with possible incidence of oilfield scale. Results show that the
high mobility ratio encountered after water breakthrough does not only depend onthe increase in water saturation and relative permeability but on the magnitude of
oilfield scale saturation around the well bore.
Keywords mobility ratio, oilfield scale, permeability damage, porous media, pres-sure drop, skin factor
Introduction
Formation and deposition of scale in porous media due to extensive use of seawater
for oil displacement and pressure maintenance is a problem that results in permeability
damage after water breakthrough at reduced reservoir pressure (A. Fadairo et al., 2008a).
The phenomenon may provoke loss in productivity, injectivity, and efficiency of a water-
flooding scheme that is generally dependent on mobility ratio.
Several research works have developed models on permeability damage due to
migration of mineral scale particles in porous media and indicated that permeability
damage is more likely to be severe near the well bore. Among other authors, Rachon
et al. (1996) presented a relationship between initial permeability and instantaneous
permeability as a porosity exponential function. Civan et al. (1989) developed a power
law model that is valid for a solid mineral deposition inducing permeability reduction ofup to about 80%. Chang and Civan (1996) presented a relationship between the initial
permeability and instantaneous permeability as functions of altered porosity and initial
porosity, by assuming a power law of 3.0. Moghadasi et al. (2005, 2006) modified Civian
et al.s (2001) model by introducing variable parameters such as particle concentration in
the fluid, solid particles density against the depth, and time of invasion. A. Fadairo et al.
(2008, 2008b, 2009) recently presented an improved model of Moghadasi et al. (2005,
2006) and Civian et al.s (2001) formulation on formation permeability damage due to
mass transfer of particles flowing through the porous media. The improved model was
adapted to handle oilfield scale-induced permeability damage.
Address correspondence to A. S. A. Fadairo, Department of Petroleum Engineering, CovenantUniversity, KM 10 Idiroko Road, Ota, Nigeria. E-mail: [email protected]
712
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Mobility Ratio Control 713
Effect of oilfield scale-induced permeability on the success of a water-flooding
project that depends on mobility ratio has rarely been reported. Tahmasebi et al. (2007)
recently formulated an empirical correlation for predicting the permeability and apparent
mobility reduction due to calcium sulfate scale.
Mobility ratio is important in determining the success or failure of a water-flooding
project (Kumar et al. 2005; A. Fadairo et al., 2008a); hence, it is pertinent to determine
the key operational and reservoir/brine parameters that influence the mobility ratio of a
water-flooded reservoir.
This article presents a predictive tool for estimating mobility ratio of a water-flooded
reservoir with possible incidence of oilfield scale precipitation and accumulation. The
oilfield scale saturation around the well bore has been identified through the derivation
of the model as one of the key parameters that influences the mobility ratio after water
breakthrough.
The Model AssumptionsThe analytical expressions derived in this study are based on the following fundamental
and general assumptions:
1. Solid precipitates are uniformly suspended in an incompressible fluid.
2. The porous medium is homogeneous, isothermal, and isotropic.
3. The porous media contain a large number of pore spaces, which are interconnected
by a pore throat whose size is log-normally distributed.
4. The interaction forces between the medium and precipitated solid minerals are negli-
gible.
Formulation
Consider the simultaneous radial flow of oil and injected or produced water, saturated
with solid mineral scale particle at a location r, from the well bore. The total pressure
drop across the well bore is the summation of pressure drop due to flow of oil and water
and additional pressure drop due to scale deposition and around the well bore. That is,
PT DP(due to fluid) CP(due to scale deposition) (1)
PT DPw CPoC Ps (2)
PT D qww
2 hKKrwIn
rwater
rwellC
qoo
2 hKKroIn
roil
rwellC
qww
2 hKKrws (3)
Rearranging Eq. (3) we get:
PT D qww
2 hKKrw
In
rwater
rwellCs
C
qoo
2 hKKroIn
roil
rwell(4)
Multiply Eq. (4) by 2hKKrw
wto get:
2 hKKrwPT
wDqw
In
rwater
rwellCs
CqoMIn
roil
rwell(5)
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714 A. S. A. Fadairo
where
M(mobility ratio)D Krwo
Krow(6)
Dividing Eq. (5) by qoIn roilrwell , we get:
2 hKKrwPT
qowInroil
rwell
D qw
qoInroil
rwell
In
rwater
rwellCs
CM (7)
Rearranging Eq. (7) we get:
2 hKKrwPT
qowInroil
rwell
qw
qoInroil
rwell
In
rwater
rwellCs
D M (8)
Formation damage due to oilfield scale deposition during water-flooding results in
a positive skin effect around the well bore. The skin factor and pressure drop across
the skin due to oilfield scale deposition were expressed respectively by A. Fadairo et al.
(2008b) as follows:
Skin factor:
s D f1Ss.1Swi /3:0 1g In
rs
rw(9)
Pressure drop across the skin due to scale deposition:
Ps D qB
2 hKof1 Ss.1Swi /
3:0 1g Inrs
rw(10)
Inserting Eq. (9) into (8) and rearranging, we get:
M D 1
qoInroil
rwell
2 hKKrwPT
wqw
In
rwater
rwellC f1Ss.1Swi /
3:0 1g Inrs
rwell
(11)
The derivation of Eqs. (9) and (10) is expressed in detail in Appendix A.
Model Analysis
Computer software was developed for predicting the mobility ratio of a water-flooded
reservoir with possible incidence of mineral scale precipitation and deposition and es-timate instantaneous additional pressure drop and skin factor induced by oilfield scale
during water-flooding as a function of operational and reservoir/brine parameters.
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Mobility Ratio Control 715
Table 1
Amount of BaSO4 and SrSO4 precipitated as a
function of pore volume of seawater injected
Pore volume of
seawater injected, %
BaSO4 precipitate,
g/m3
0 0.0
10 71.0
20 65.0
30 58.0
40 48.0
50 42.0
60 32.0
70 25.0
80 18.0
90 10.0
100 0.0
(Source: Haarberg et al., 1992.)
The data of Haarberg et al. (1992) on scale formation shown in Table 1 and brine/
reservoir properties (Civan, 2001) listed in Table 2 were used as input for the model.
Discussion of Results
Flow rate of brine is the major parameter that influences the magnitude of flow impairment
and determines the success of any water-flooding project and this depends on the mobility
ratio. Figure 1 shows the effect of brine flow rate on the mobility ratio of a reservoir with
possible incidence of scale precipitation as pore volume of seawater injected increased.
Table 2
Fluid and reservoir base case properties used as
input in the scale prediction model
Pay thickness, h 26 m
Initial permeability 0.5922E-13 m2 (60 mD)
Initial porosity 0.05
Reservoir pressure 36,600 kPa
Bottom hole pressure 22,060 kPa
Reservoir temperature 353 K (80C)
Brine formation volume factor 1.7
Brine viscosity 0.0007 Pa-s
Hydrocarbon formation volume factor 1.2
Hydrocarbon viscosity 0.003
Connate water saturation 0.2
(Source: Civan, 2001.)
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716 A. S. A. Fadairo
Figure 1. Mobility ratio against pore volume of water injected at different flow rates of produced
water.
High mobility ratio occurs earlier for the high flow rate case than the lower flow rate case.
Therefore, reduction in produced water flow rate will generally decrease the mobility ratioand prolong the stable displacement of oil by water prior to significant flow impairment
caused by deposited oilfield scale, which promotes a high mobility ratio. From this figure
it can also be be observed that at low flow rate in the range of 0 m 3/day to 11.92 m3/day,
mobility ratio is less than one (M < 1) and approximately constant as pore volume
of injected water increased, indicating that the displacement of hydrocarbon by water is
approximately stable; therefore, the critical flow rate for bypassthat is, the rate at which
water or brine would under run the hydrocarbon in the form of a water tonguecan be
approximately determined for a water-flooded reservoir with possible incidence of scale
deposition around the well bore.
The mobility ratio and skin factor variation due to precipitation of sulfate scale for
different pore volumes of seawater injected in a reservoir during production are shownin Figure 2. From the figure it can be seen that there is a direct relationship between
the mobility and skin factor. The magnitude of positive skin determines the propensity
for water to bypass oil, causing unstable displacement in a water-flooded reservoir. The
skin factor increases as pore volume of seawater injected approaches a local maximum at
10% and begins to decrease beyond this pore volume. A similar trend was observed with
mobility ratio as shown in Figure 2. This observation may be due to a shift of equilibrium
from deposition to dissolution of scale beyond 10% pore volume; that is, deposited scale
experiences dissolution. The locations with high positive skin factors are most likely to
experience significant flow impairment by deposited scale and easily produce an unstable
displacement of hydrocarbon by water.Figure 3 corroborates Figure 2 where we observe that the mobility ratio is enhanced
by the presence of skin and as produced water rate increases.
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Mobility Ratio Control 717
Figure 2. Plot of mobility ratio and skin factor against pore volume of water injected at different
flow rates of produced water.
Figure 3. Plot of mobility ratio against pore volume of water injected.
Conclusion
The following conclusions were drawn from the results of this study:
1. The model developed has demonstrated that a high mobility ratio encountered after
water breakthrough in a water-flooded reservoir does not only depend on the increasein water saturation and relative permeability but on key operational and reservoir/
brine parameters such as fractional change in mineral scale concentration per unit
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718 A. S. A. Fadairo
change in pressure, viscosity of brine, formation volume factor of the brine, solid
scale density, brine/hydrocarbon ratio, brine flow rate, hydrocarbon flow rate, pressure
drawdown, reservoir temperature, reservoir thickness, brine and hydrocarbon velocity
against injection time, and radial distance.
2. The model has shown that mobility ratio is directly proportional to the flow rate of
produced water and positive skin factor induced by scale and inversely proportional to
flow rate of hydrocarbon. Low mobility ratio generally increases hydrocarbon recovery.
Reduction in water production rate would generally decrease the mobility ratio and
prolong the stable displacement of oil by water prior to significant flow impairment
by deposited oilfield scale that pronounce high mobility ratio.
3. Results of the study show that the control of mobility ratio after water breakthrough
is significantly dependent on oilfield scale saturation around the well bore during the
process of water-flooding. The mobility ratio of a water-flooded reservoir remains
constant until water breakthrough and achieves an increasing local maximum at 10%
pore volume injected water as the flow rate of produced water increases with a
significant jump beyond the critical flow rate observed at mobility ratio of 1. Similarresults corroborating the above were obtained with variation in skin factor.
4. The models could be used for diagnosis, evaluation, and simulation of a high mobility
ratio water-flooded reservoir and skin factor with possible incidence of oilfield scale
in a water-flooding scheme.
Acknowledgments
The author thanks Dr. Falode Olugbenga of University of Ibadan for his technical
contribution and Father-Heroes Consult Nig Ltd. for their financial support in carrying
out this research work.
References
Atkinson, G., Raju, K., and Howell, R. D. (1991). The thermodynamics of scale prediction.SPE Paper no. 21021, Society of Petroleum Engineers International Symposium on Oilfield
Chemistry, Anaheim, CA, February 2021, pp. 209215.
Chang, F. F., and Civan, F. (1996). Practical model for chemically induced formation damage.J. Petrol. Sci. Eng. 17:123137.
Civan, F. (2001). Modeling well performance under non equilibrium deposition condition. SPE
Paper no. 67234,SPE Production and Operations Symposium, OK, March 2427.
Civan, F., Knapp, R. M., and Ohen, H. A. (1989). Alteration of permeability by fine particle
processes.J. Petrol. Sci. Eng. 3:6579.
Fadairo, A., Ako, C. T., Omole, O., and Falode, O. (2009). Effect of oilfield scale on productivityindex. Adv. Sustain. Petrol. Eng. Sci. 1:295304.
Fadairo, A., Omole, O., and Falode, O. (2008a). Effect of oilfield scale deposition on mobility
ratio. SPE Paper no. 114488, CIPC/SPE International Conference, Calgary, Alberta, Canada,June 1619.
Fadairo, A., Omole, O., and Falode, O. (2008b). Modeling formation damage induced by oilfield
scales.J. Petrol. Sci. Tech. 27:14541465.Fadairo, A. S. A. (2004). Prediction of scale build up rate around the well bore (Nigeria). M.Sc.
Thesis, Department of Petroleum Engineering, University of Ibadan, Nigeria.
Haarberg, T., Selm, I., Granbakken, D. B., stvold, T., Read, P., and Schmidt, T. (1992). Scaleformation in reservoir and production equipment during oil recovery II: Equilibrium model.
SPE J. Prod. Eng. 7:847857.
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Mobility Ratio Control 719
Kumar, M., Hoang, V., Satik, C., and Rojas, D. H. (2005). High mobility water flood performance
prediction: Challenges and new insights. SPE Paper no. 97671 SPE International ImprovedOil Recovery Conference in Asia Pacific, Kuala Lumpur, Malaysia, December 56.
Moghadasi, J., Mller Steinhagen, H., Jamialahmadi, M., and Sharif, A. (2005). Model study on
the kinetics of oil field formation damage due to salt precipitation from injection. J. Petrol.
Sci. Eng. 46:299315.Moghadasi, J., Sharif, A., Kalantari, A. M., and Motaie, E. (2006). A new model to describe
particle movement and deposition in porous media. SPE Paper no. 99391, 15th SPE EuropeConference and Exhibition, Vienna, Austria, June 1215.
Rachon, J., Creusot, M. R., and Rivet, P. (1996). Water quality for water injection wells. SPE
Paper no. 31122, SPE Formation Damage Control Symposium, Lafayette, LA, February 1415, pp. 489503.
Tahmasebi, H. A., Azad, U., Kharrat, R., and Masoudi, R. (2007). Prediction of permeability
reduction rate due to calcium sulfate formation in porous media. SPE Paper no. 105105 15thSPE Middle East Oil and Gas Show and Conference, Kingdom of Bahrain, March 1114.
Appendix A
Instantaneous Permeability as a Result of Solid Scale Saturation Near
the Well Bore Region
Consider the radial flow of a fluid at constant rate q, saturated with solid-state particle at
a location r from the well bore. Assuming an idealized flow equation, A. Fadairo et al.
(2008a, 2008b) and A. S. A. Fadairo (2004) expressed the pressure gradient due to the
presence of scale in the flow path as follows:
dP
dr D
qwBww exp.3Kdep C t /
2Kihrs (A1)
where k is defined as formation damage coefficient1213. That is, k D exp(3Kdep
C t /
Instantaneous local porosity can be defined as the difference between the initial
porosity and damaged fraction of the pore spaces (Moghadasi et al., 2005, 2006; A.
Fadairo et al., 2008b, 2009):
That is,
s Di d (A2)
Therefore,
s Di
q2w
dC
dP
T
Bw w t k
42r2s h2Ki
(A3)
Damage fraction of the pore spaces d can be defined as the ratio of the volume of
scale deposited to bulk volume of the porous media or the fraction of minerals scale that
occupied the total volume of porous media (A. Fadairo et al., 2008a; Moghadasi et al.,
2006):
That is,
d Dvolume of minerals scale deposited
bulk volume of the porous media
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720 A. S. A. Fadairo
The volume of scale @V, which drops out and gets deposited in the volume element over
the time interval, @t, is given as follows (since @VD Flow rate Time interval; Civan,
2001; A. S. A. Fadairo, 2004; A. Fadairo et al., 2008a, 2008b):
dVDqw
dCdP
T
dPdt (A4)
where
dCdP
T
is defined as the change in saturated solid scale content per unit change in
pressure at constant temperature.
Hence, the change in porosity due to scale deposition over time interval is given as:
dd D
qw
dC
dP
T
dPdt
2 rsdrh (A5)
Substituting Eq. (A1) into Eq. (A5) and integrating the equation, we have
d D
q2
dC
dP
T
Bw w t k
4 2r2s h2Ki
(A6)
Substituting Eq. (A6) into Eq. (A2) and dividing both sides of equation by o, we have:
s
iD1
q2
dC
dP
T
B t k
42r2sh2Kii
(A7)
A. Fadairo et al. (2008b) recently expressed the fraction of mineral scale that occupied
the pore spaces at different radial distance from the well bore as follows:
Ss D
q2
dC
dP
T
Bw w t k
42r2s h
2
oKo.1 Swi /
(A8)
Rearranging Eq. (A8), we have:
oSs.1Swi /D
q2
dC
dP
T
Bw w t k
42 r 2s h2Ko
(A9)
where can be defined as porosity damage coefficient. That is,
Dexp.Kdep C t / (A10)
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Mobility Ratio Control 721
Substituting Eq. (A9) into Eq. (A7), we have:
DooSs.1Swi / (A11)
Dividing both sides of Eq. (A11) by o, we have:
s
oD1 Ss.1Swi / (A12)
Consider the relationship between the initial permeability and instantaneous permeability
as a function of altered porosity and initial porosity defined by Civian et al. (1990) as:
Ks
KoD
o
3(A13)
Instantaneous permeability induced by oilfield scale can be expressed after substituting
Eq. (A12) into (A13) as
Ks DKo1Ss.1Swi /3:0 (A14)
Equation (A14) expresses oilfield scale-induced permeability as a function of operational
parameters and reservoir/brine parameters.
The Skin Factor and Pressure Drop Across the Skin Due to
Scale Deposition
Formation damage due to oilfield scale deposition during water-flooding results in a
positive skin effect around the well bore.
The skin factor is a dimensionless variable used in petroleum field calculation toestimate the magnitude of skin effect or degree of damage in formation. The skin factor
can be expressed conventionally as:
s D
Ko
Ks1
In
rs
rw(A15)
Substituting Eq. (A13) into (A14), we have:
s D f1Ss.1Swi /3:0 1g In
rs
rw(A16)
Equation (A16) expresses the effect of oilfield scale buildup on skin factor at differentpore volumes of seawater injected. This equation has equally expressed the influence of
different operational and reservoir/brine parameters on the magnitude of skin effect.
Additional Pressure Drop across the Skin Due to Scale Deposition
Near the Well Bore
A positive skin factor causes additional pressure drop around the well bore vicinity. The
pressure drop across the skin Ps is the difference between the actual pressure in the
well bore when it is flowing and the pressure that would have been seen if the well were
undamaged. This can be expressed as:
Ps D qB
2 hKof1 Ss.1Swi /
3 1g Inrs
rw(A17)
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722 A. S. A. Fadairo
At initial production time, when tD 0, Ss D 0, the skin factor s D 0 and the additional
pressure drop across the skin due to scale deposition Ps D0.
Substituting Eq. (A16) into Eq. (A17), we have:
Ps D
qB
2 hKo s (A18)
Nomenclature
B formation volume factor
C salt concentration, g/m3
C(I) concentration at the well bore pressure, g/m3
C (P) concentration at the reservoir pressure, g/m3
dP change in pressure, Pa
F model parameter, sec1
h thickness, m
K permeability M2
Kdep deposition rate constant m3/g sec
Ki initial permeability, m2
Kro oil relative permeability
Krw water relative permeability
Ks instantaneous permeability, m2
jMj mobility ratio
P pressure, Pa
Ps additional pressure drop across the skin, Pa
PT total pressure, Pa
qo oil flow rate, m3
/dayqw water flow rate, m
3/day
roil radial distance covered by oil, m
rs radial distance covered by oilfield scale, m
rwater radial distance covered by water, m
rwell well bore radius, m
Ss saturation of sulfate (scale)
Swi connate water saturation
s skin factor
T temperature, K
t production time, sec
V volume of scale, m3
Greek Letters
activity coefficient
K permeability damage coefficient
porosity damage coefficient
w water viscosity, Pa-sec
o oil viscosity, Pa-sec
density, g/m3
instantaneous porosityd damaged fraction
o initial porosity