13.Movilidad Scale.

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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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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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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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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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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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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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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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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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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

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