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Journal of Natural Gas Science and Engineering 39 (2017) 1e15

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Journal of Natural Gas Science and Engineering

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Scale formation in porous media and its impact on reservoirperformance during water flooding

Sassan Hajirezaie a, *, Xingru Wu a, Catherine A. Peters b

a Mewbourne School of Petroleum & Geological Engineering, University of Oklahoma, OK, USAb Department of Civil and Environmental Engineering, Princeton University, USA

a r t i c l e i n f o

Article history:Received 3 September 2016Received in revised form24 January 2017Accepted 26 January 2017Available online 31 January 2017

Keywords:Mineral scale formationPorous mediaMultivariate regression analysisStatistical and graphical analysis

* Corresponding author.E-mail address: [email protected] (S. H

http://dx.doi.org/10.1016/j.jngse.2017.01.0191875-5100/© 2017 Elsevier B.V. All rights reserved.

a b s t r a c t

Water flooding is the most widely used improved oil recovery technique, and many other methods, suchas chemical methods, are based on water flooding performance. If the injected water is not compatiblewith the formation water, scaling and other solid deposition would occur, which can reduce the for-mation permeability and transmissibility of the reservoir. The objective of this research is to model thein-depth reservoir formation damage as a result of scaling and to simulate its impact on reservoir per-formance. Literature survey shows that the development of a theoretical model for estimation ofpermeability and porosity reduction is of practical importance.

In this paper, two models based on barium concentration were proposed to estimate permeabilityreduction in porous media as a result of scale deposition. Model development was conducted by using216 experimental data points from literature covering various thermodynamic properties and reservoirconditions, and statistical and graphical error analyses were employed to evaluate the accuracy of theproposed models.

The results showed that the proposed models are capable of predicting permeability alteration causedby scale deposition with absolute average relative errors less than 1% compared with the experimentaldata. In addition, the values of root mean square error and coefficient of determination were found to benearly 0.1 and 0.95 for the high barium concentration model and 0.06 and 0.94 for the normal bariumconcentration model. Moreover, error distribution curves of the developed models showed that themodels do not have any significant error trend under different reservoir and thermodynamic conditions.

A synthetic field was used to simulate the injection and production performance of an incompatiblewater flooding operation to better study the impact of scaling issue on reservoir performance. Inparticular, the impacts of scale deposition on reservoir properties and injection pressure were investi-gated. The results of numerical simulation indicated that scale formation could reduce the reservoirporosity from 0.2 to nearly 0.07. Moreover, the injection bottom hole pressure needed for the operationincreases significantly up to nearly 19,000 psi when the reservoir is affected by scale formation.

© 2017 Elsevier B.V. All rights reserved.

1. Introduction

Waterflooding technique is often used to maintain the reservoirpressure and improve oil recovery after primary depletion. How-ever, inorganic scale formation may occur if the injected water isincompatible with the in-situ formation water, which may result inmineral precipitation (Merdhah et al., 2007). For example, seawa-ters have high concentrations of anions such as SO4

2� while for-mation waters are usually rich in cations such as Ba2þ, Ca2þ and

ajirezaie).

Sr2þ. Mixing these waters during water flooding processes maylead to precipitation and deposition of various minerals such asBaSO4, CaSO4 and SrSO4 when their concentrations exceed the ca-pacity of the solvent in dissolving these solutes (Merdhah and Badr,2008). In waterflooding processes, scale formation occurs any-where from the reservoir porous media up to the surface throughpipelines and facilities (Moghadasi et al, 2004).

Scale formation tendency is evaluated by using saturation index(SI) defined as follows (Kan et al, 2005):

SI≡ log 10�ion activity product

KspðT; PÞ�

(1)

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As an example, for barite, which forms based on the followingreaction:

Ba2þ þ SO2�4 /BaSO4 (2)

Saturation index would be:

SIBarite ¼ Log

24ðaBa2þ Þ�aSO2�

4

�Ksp;Barite

35¼ Log

24�Ba2þ�hSO2�

4

iðgBa2þÞ

�gSO2�

4

�Ksp;Barite

35 (3)

In Eqn. (3), aBa2þ and aSO2�4

represent the ionic activity of bariumand sulfate, respectively and [Ba

2þ] and [SO42�] denote the molality

of these ions. Ksp,Barite is the solubility product of barite as a functionof temperature and pressure; all in SI units. gBa2þ and gSO2�

4are the

activity coefficients of barium and sulfate, respectively, which arefunctions of ionic strength, temperature and pressure and can bedetermined by Pitzer theory (Pitzer, 1973).

Bethke (Nghiem et al, 2004; Bethke, 2007) proposed thefollowing expression for mineral precipitation (or dissolution) rate:

rb ¼ Abkb

1� Qb

Keq;b

!b ¼ 1;…;Rmn (4)

In Eqn. (4), k b is the rate constant, Ab is the reactive surface area

Table 1Statistical description of the experimental dataset.

Inputs/Outputs Min Ma

Injection rate, ft3/min 3.02 � 10�4 10�

Reservoir Temperature,�F 122 176Fluid Pressure Difference, psi 100 200Injection Period, min 10 120Barite Solubility, ppm 137 162Pore Volume, ft3 3.98 � 10�4 5.2Kf/Ki 0.812 0.9

Fig. 1. Sensitivity analysis ba

of mineral b, Keq,b is the chemical equilibrium constant which canbe found as a function of temperature in the literature (Delany andLundeen, 1994; Kharaka et al, 1988) and rb is the reaction rate, all inSI units. The term Qb

Keq;b in Eqn. (4) is the saturation index of thereaction. If the saturation index is less than unity, mineral precip-itation occurs. When the saturation index is one, the reaction is atequilibrium.

Qb is the activity product formineral b and can be determined bythe following equation:

Qb ¼Ynaq

k¼1

avkbk (5)

where, ak is the activity of component k and vkb is the stoichiometrycoefficient. The following expression shows the relationship be-tween the activity of and molality of components:

ai ¼ gimi i ¼ 1;…;naq (6)

In Eqn. (6), mi is themolality of component i and gi is the activitycoefficient which can be calculated based on B-dot model (Bethke,1996) as follows:

Log gi ¼ � Ayz2iffiffiI

p

1þ _aiByffiffiI

p þ BI (7)

where _ai is the ion size parameter, Ag, Bg and B are functions of

x Mean Standard deviation

3 6.31 � 10�4 1.87 � 10�4

152 22.5150 40.965 34.6

0 758 6368 � 10�4 4.66 � 10�4 4.23 � 10�5

99 0.94 0.04

sed on pore radius ratio.

Table 2Model constants at high barium concentration (2200 ppm) and normal bariumconcentration (250 ppm).

Constant High barium concentration(2200 ppm)

Normal barium concentration(250 ppm)

A0 �1.69 � 102 �1.33 � 101

A1 1.14 7.89 � 10�1

A2 �1.51 �7.61 � 10�2

A3 1.69 � 102 6.06A4 �1.04 � 10�1 �5.45 � 10�1

A5 1.09 � 10�1 9.40 � 10�2

Table 3Statistical parameters of permeability reduction model using 216 data points.

Barium Concentration Ea (%) Er (%) RMSE R2

High Concentration of BariumTraining Set 0.777 �0.013 0.023 0.949Validation Set 0.906 �0.002 0.027 0.943Total 0.889 �0.021 0.102 0.948Normal Concentration of BariumTraining Set 0.011 0.412 0.014 0.941Validation Set 0.409 0.026 0.014 0.942Total 0.427 �0.005 0.056 0.941

S. Hajirezaie et al. / Journal of Natural Gas Science and Engineering 39 (2017) 1e15 3

temperature and I is the ionic strength calculated as follows:

I ¼ 12

Xnaq

k¼1

mkz2k (8)

where zk is the ionic charge of the kth ion.As it was mentioned earlier, Ab is the reactive surface area of

mineral b. It is known that in high porosity sandstones, the acces-sible fraction of reactive minerals is around one third while thisvalue can be as small as one fifth for shaly sandstones (Peters,2009). The following mole change based equation is used forcalculating the reactive surface area:

Ab ¼ A0b

Nb

N0b

(9)

where Ab is the reactive surface area of mineral b at current time, A0b

is the reactive surface area at time zero, Nb is the moles of mineral bper unit grid block volume at current time and N0

b is defined at timezero.

The following expression is used to calculate the change inporosity resulting from mineral dissolution/precipitation:

bf ¼ f* �Xnm

b¼1

Nb

ƿb�

N0b

ƿb

!(10)

where, bf is the reference porosity when dissolution/precipitation isincluded, f* is the reference porosity without mineral dissolution/precipitation and ƿ is the molar density of mineral b.

The following equation shows the relationship betweenpermeability ratio and thickness of precipitation at a specificporosity:

K2

K1¼ X6

1� f1

1� f1X2

2(11)

where X refers to the pore radius ratio before and after precipita-tion. Fig. 1 shows the severity of permeability reduction as a resultof scale deposition for variable formations. The figure shows that

permeability ratio decreases significantly when the thickness ofprecipitation increases.

The rest of this article is made of two sections. In the first sec-tion, we study scale precipitation in porousmedia andwe develop amodel for predicting permeability reduction resulting from scaleprecipitation in porous media. One novelty of this work is consid-ering a wider range of parameters compared to other studies(Moghadasi et al, 2004; Chang and Civan, 1997; Ghaderi et al.,2009; Naseri et al., 2015; Zahedzadeh et al, 2014; Moghadasiet al, 2003; Moghadasi et al, 2002; Abouie et al, 2016; Abouie,2015). In addition, we quantify the relative impact of physical pa-rameters that affect permeability reduction in porous media. In thesecond section of the paper, we study the impact of mineral pre-cipitation at a larger scale by focusing on reservoir properties andwell performance that are altered because of scale formation.

2. Model development and validation

The development of a comprehensive correlation between themechanisms of scaling tendency and porous media propertiesrelated to productivity is vital. In this study, a model based onmultivariate regression analysis was developed for determining thepermeability reduction in reservoir resulting from mineral scaledeposition. Based on the availability of experimental data, bariumsulfate was considered as the main scale in this study. To achievethis objective, 216 experimental data points covering a wide rangeof thermodynamic and reservoir conditions were collected fromthe literature (Merdhah and Badr, 2008). The statistical descriptionof experimental data used in this study is illustrated in Table 1. 80%of the data points were used for constructing the model and 20% ofthe data points were used to validate the model.

A synthetic field was used to simulate the injection and pro-duction performance of an incompatible water flooding operationto better study the impact of scaling issue on reservoir perfor-mance. In order to quantify the impact of barium sulfate depositionon formation damage and reservoir performance, a brine rich inbarium was mixed with a brine rich in sulfate. The barium richbrine represents the formation water while the sulfate rich brinerepresents the seawater.

Experimental data in the literature show that temperature andthroughput of brine are among the parameters that have directeffect on permeability reduction resulting from scale deposition.Temperature has a direct effect on dissolution/precipitation reac-tion rate. Precipitation rate differs from the case in which fluid ismoving fast over a small surface area during a specific time periodto the case in which fluid velocity is controlled by a large surfacearea. We propose the following functionality between permeabilityreduction and the aforementioned parameters in which the powervalues were found empirically:

KfKi

��T

16; PV

14inj

�(12)

where KfKi

stands for the permeability ratio, T denotes temperatureand PVinj is the injected pore volume.

A combination of pressure, salt solubility and available porevolume of themedium also affects scaling behavior. Pressure has aneffect on the solubility product of the salt and also affects the ki-netics of deposition. The pressure difference indicates the pressurechange across the core samples that were used in the originalexperimental work in which a pressure transducer with a digitaldisplay was used to measure this parameter. Solubility of themineral plays a significant role in the scaling tendency of the mixedfluids and can be found in literature at different conditions (Blount,1977). Finally, the available pore volume of the medium has a close

Fig. 2. Cross-plot of the proposed model for permeability ratio at the high barium concentration of 2200 ppm.

Fig. 3. Cross-plot of the proposed model for permeability ratio at the normal barium concentration of 250 ppm.


relationship with the amount of volume available for solid depo-sition as it can be an indicator of the reactive surface area of themineral. The following relationship was found to exist between thementioned group and the corresponding permeability impairment:

KfKi

� ðDP$VP$SBaSO4Þ (13)

where DP denotes the pressure difference, VP is the pore volume ofporous medium and SBaSO4 stands for the barite solubility.

In order to develop an accurate predictive model, multivariateregression using least square error method was utilized.

Experimental data from literature (Merdhah and Badr, 2008)was used for model development. Four different formation watersas well as two different seawaters (Barton and Angsi seawaters)were considered in the original experimental work. The cores were

from Malaysia with diameters and lengths of 1 inch and 3 inches,respectively. The porosity of samples was 0.32 on average and thepermeability ranged from 12.3 to 13.87 mD. Two formation watersincluded high and normal concentrations of calcium and strontiumfor studying calcium and strontium sulfates and two formationwaters included high and normal concentration of barium forstudying barium sulfate precipitation. The composition of thesedifferent waters can be found in the original work (Merdhah andBadr, 2008). In this study, the two different barium concentra-tions of 2200 ppm and 250 ppm were considered and two corre-sponding models were developed. These two concentrations arerepresentative for low and high barium concentrations. Among the216 data points,108 data points belong to a barium concentration of2200 ppm and 108 data points belong to a barium concentration of250 ppm. After analyzing the experimental data and statisticalanalysis, the following model was developed for predicting

Fig. 4. Error distribution plot of the model at the barium concentration of 2200 ppm.


permeability reduction in porous media as a result of barium sul-fate scale formation:

expKfKi

¼ A0 þ A1T

1=6 þ A2ðQtÞ1=4 þ A3LnðVPÞ

þ A4LnðSBaSO4Þ þ A5LnðDPÞ (14)

where Q is the injection rate and t is the injection duration. Theunits for all the mentioned parameters are the same as reported inTable 1. A0, A1, A2, A3, A4, and A5 are empirical coefficients obtainedfrommultivariate regression analysis, and their values are shown inTable 2 for barium concentrations of 2200 ppm and 250 ppm,respectively.

The proposed model performance was evaluated using statistics

Fig. 5. Error distribution plot of the model a

and the results are summarized in Table 3. The description of sta-tistical analysis is provided in the Appendix.

The error analysis indicates that the regressed models are validfor these experiments on barium sulfate scale formation. The cross-plots for these two concentrations are shown in Fig. 2 and Fig. 3 andthe error distribution plots are shown in Fig. 4 and Fig. 5,respectively.

Additionally, relevancy factor (Hajirezaie et al, 2015; Tohidi-Hosseini et al, 2016) was utilized to investigate the impact ofeach input parameter on permeability impairment. A larger abso-lute value of relevancy factor (r) between an input and outputmeans the greater impact of that input on the output. Relevancyfactor is defined based on the following equation:

t the barium concentration of 250 ppm.

Fig. 6. Relative impact of input parameters on permeability reduction.

rinpk;

kfki

i

¼

Pni¼1

�inpk;i � inpk;avg

�kfki

i�kfki

avg

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPn

i¼1

�inpk;i � inpk;avg

�2Pni¼1

kfki

i�kfki

avg

2s (15)


In this equationKf

Ki

iand

Kf

Ki

avg

denote the ith and average

values of predicted permeability ratio, respectively. K denotes theinput variables (injected pore volume, temperature, pressuregradient, barite solubility and pore volume of the medium). inpk,irepresents the ith value of the kth input and inpk,avg is the averagevalue of the kth input.

The results of relevancy factor analysis are depicted in Fig. 6. Theanalysis shows that the injected pore volume and barite solubilityare important parameters in controlling the permeability reduc-tion. This is because a larger amount of solid crystals can bedeposited and consequently, a larger portion of the pores and

Fig. 7. Sensitivity analysis b

throats are plugged.In order to compare the results of models with experimental

data, two sensitivity analyses based on temperature for the highbarium concentration model and pressure for the normal bariumconcentration were conducted. Fig. 7 shows the results of sensi-tivity analysis based on temperature. In this case, pressure differ-ence is 100 psig and barium concentration is 2200 ppm. Based onthe model predictions, permeability decreases by decreasing tem-perature and increasing the number of injected pore volumes. Ascan be seen in Fig. 7, these results are confirmed by the experi-mental data.

In the second case, a sensitivity analysis based on pressure wasconducted as shown in Fig. 8. In this case, temperature was 50 �C

ased on temperature.

Table 4Reservoir properties.

Property Value

Grid 30 � 30 � 1Grid block sizes Dx ¼ Dy ¼ 20 ft Dz ¼ 150 ftPermeability in all directions 300 mDPorosity 0.2Depth of reservoir top 9500 ftReservoir temperature 161 �FInitial reservoir pressure 4800 psi at 9600 ftRock compressibility 3 � 10�6 psi�1

Table 5Hydrocarbon components and properties.

Component Composition Molecular weight (g/mol) Critical pressure (psia) Critical temperature (�F)

CO2 0.0023 44.01 1071.30 87.89N2 0.0063 28.01 492.31 �232.51CH4 0.3624 16.04 667.78 �116.59C2H6 0.0279 30.07 708.34 90.104C3H8 0.0225 44.09 615.76 205.97C4H10 0.0204 58.12 532.58 297.35C5H12 0.0139 72.15 479.81 380.20C6H14 0.0166 86.00 477.16 453.83C7þ 0.5277 300.00 208.59 1096.85

Table 6Chemical reaction properties (Christy and Putnis, 1993; Hubbard et al, 2014).

Property Value

Barium molality in formation aqueous phase 0.007 MSulfate molality in seawater 0.028 MActivation energy of barite precipitation reaction 22 kJ/molBarite reactive surface area 900 m2/m3 of bulk volume of minerallog of barite reaction rate constant at 25 �C �8 mol/m2sLog of barite chemical equilibrium constant �9.97

Fig. 8. Sensitivity analysis based on pressure difference.



and barium concentration was 250 ppm. As can be seen, there is agood agreement between the trends of experimental data andmodel predictions.

3. The effect of scale deposition on reservoir performance

Numerical simulation is used to study scale deposition in thereservoir and its effect on reservoir performance. The features ofGEM-GHG reservoir simulator were used for reservoir modeling inthis study. GEM is an advanced EOS based compositional simulatorthat is able to model multi-phase multi-component flow. GHG wascoupled with GEM tomodel phase equilibrium between gas, oil andaqueous phase, dispersive and convective flow in porous media,kinetics of mineral precipitation and dissolution and chemicalequilibrium between aqueous components (Nghiem et al, 2004).Although this fully coupled geochemical compositional simulatorwas mainly designed for CO2 sequestration processes, we haveapplied the features of this simulator to model scale formationduring water flooding processes. A quarter of five-spot water in-jection pattern is used in themodel, and themain input parametersare summarized in Table 4. The reservoir fluid components andcompositions are shown in Table 5. Barium sulfate was consideredto be the precipitating mineral in the reservoir as a result of waterinjection.Water quality from a real case (Bethke, 2007) andmineralprecipitation reaction properties are shown in Table 6. The relativepermeability curves are shown in Fig. 9. Production was continuedfor nine years and the production well was constrained by a min-imum bottom hole pressure of 2500 psi and maximum surface

Volume of barite precipitation ¼ 2132381 gmolbarite �233:39gbarite1gmolbarite

new porosity ¼ old porosity� reduced pore volumeinitial pore volume

new porosity ¼ 0:2� 12000f t3 � 3923:36f t3

12000f t3¼ 0:135

Fig. 9. The relative permeability curves of water and oil obtained by using the Stone m

liquid rate of 300 bbl/day. The injection well was constrained to amaximum water rate of 340 bbl/day and subjected to a largemaximum bottom hole pressure to ensure a constant injection rate.

Figs. 10e14 demonstrate the process of barite mineral deposi-tion by injecting sulfate rich seawater to barium rich formationwater at the injection pore volumes of 0.2, 0.4 and 0.6, respectively.As can be seen in Figs. 10 and 11, barium concentration decreaseswhile sulfate concentration increases during the course of flooding.As can be observed in Figs. 12 and 13, the locations of porosityreduction in the reservoir are directly related to the mineraldeposition of barite within the reservoir. In other words, whereverbarite scaling occurs, porosity reduction is observed. In addition, itcan be noted that the porosity reduction wave is propagated in aradial manner from the injection well towards the production wellwhich is the same as themovement of the ions. Moreover, as can beseen in some of the grid blocks, porosity drops down from 0.2 tonearly 0.07, which significantly affects the reservoir performance.Fig. 14 illustrates the water saturation profile within the reservoirduring the course of injection.

Here, we attempt to calculate the porosity reduction for one ofthe grid blocks (13, 21,1). Initially, the pore volume of the grid blockis 12,000 ft3. The profile of barite precipitation shows that theamount of precipitation after 0.6 pore volume of water injection is2,132,381 gmol in the mentioned grid block. Since the molecularweight and density of barite are 233.3876 g/mol and 4479.61 kg/m3, respectively, we are able to measure the volume of the pre-cipitates by performing the following calculations:

� 1kg1000g

� 1m3barite

4479:61 kgbarite� 35:31f t3

1m3 ¼ 3923:36f t3

odel. Kro ¼ krocwS�o [krow@Sw/(krocw (1-S�w))][(krog@Sg/krocw (1-S�g )] (Stone, 1970).

Fig. 10. Profiles of barium concentration during water flooding; a. Barium concentration after 0.2 pore volume of water injection, b. Barium concentration after 0.4 pore volume ofwater injection, c. Barium concentration after 0.6 pore volume of water injection.


which is shown by the corresponding color in Fig. 13cIt should be mentioned that in this section, permeability alter-

ation is modeled as a function of porosity reduction based on theCarman-Kozeny equation as follows:

kk0

¼f

f0

31� f0

1� f

2

where k0 is the initial permeability and k is the current perme-ability, f0 is the initial porosity and f is the current porosity.

However, the permeability alteration is not shown here. Instead, itsinfluence is taken into account in calculating injection pressurechanges as presented in the following sections.

In the next step, two scenarios were designed for performingwater flooding to evaluate the impact of barite scaling on the in-jection performance. In one case, pure water was injected into thereservoir and the ionic components were not considered to exist inthe reservoir aqueous phase. The well constraints were designed toallow a constant oil production rate of 300 bbl/day. The bottomholepressure needed for maintaining this constant rate is plotted inFig. 15. As can be observed, the injection bottom hole pressure

Fig. 11. Profiles of sulfate concentration during water flooding; a. Sulfate concentration after 0.2 pore volume of water injection, b. Sulfate concentration after 0.4 pore volume ofwater injection, c. Sulfate concentration after 0.6 pore volume of water injection.


increases up to nearly 5500 psi. In the second scenario, the for-mation water and seawater properties reported in Table 6 wereconsidered to form the aqueous phase and the injection water. Thesame oil rate was enforced and the results are shown in the samefigure. As can be observed, in this case the injection bottom holepressure needed for the operation increases significantly up tonearly 19,000 psi. These results are in close agreement with the realoil field experience in Siri offshore oil field in Persian Gulf(Moghadasi et al, 2002) where water flooding project was stoppedafter 6 years as the water injection rate decreased from 9100 to2200 bbl/day as a result of scaling issue. Here, we ensured a con-stant injection rate to determine the bottom hole pressure neededfor this operation. This means that care should be takenwhilewater

flooding projects are designed. Ignoring the scaling issue and im-pacts of mineral deposition in the reservoir will significantly affectthe success of the water injection process.

4. Conclusions

In this study, 216 experimental data points were employed todevelop two predictive models for permeability reduction inporous media resulted from barium sulfate precipitation. 80% of thedata points were used for constructing the models and 20% of thedata points were used to validate the models. The statistical anal-ysis indicates that the models at high and normal barium concen-trations accurately estimate permeability reduction in porous

Fig. 12. Profiles of moles of barite during water flooding; a. Moles of barite after 0.2 pore volume of water injection, b. Moles of barite after 0.4 pore volume of water injection, c.Moles of barite after 0.6 pore volume of water injection.


media by showing total regression coefficients of 0.948 and 0.941,respectively. Graphical error analyses including cross plots anderror distribution curves show that not only the models are in goodagreement with experimental data points, but also they do not havea significant error trend when permeability reduction ranges fromzero to 20%. Studying the relative impact of input parameters in-dicates that the impact of injected pore volume on permeabilityreduction is larger than that of pressure and temperature. Inaddition, a synthetic field was used to simulate the injection andproduction performance of an incompatible water flooding opera-tion to better study the impact of scaling issue on reservoir per-formance. Comparing the reservoir performance before and afterscale deposition shows thatmixing 0.007M barium from formationwater with 0.028 M sulfate from seawater reduces the porosityfrom 0.2 to nearly 0.07. In particular, the results show that injectionbottom hole pressure needed for the operation increases

significantly from 4800 up to nearly 19,000 psi when the reservoiris affected by scale formation.

Acknowledgement

The authors would like to thank the Computer Modeling Groupand the University of Oklahoma for their support.

Nomenclature

ai Ion size parameterak Activity of component kaBa2þ Barium ion activityA0b Mineral reactive surface area at time zero

Ab Reactive surface area of mineral b at current time[Ba2þ] Barite molality

Fig. 13. Profiles of reservoir porosity during water flooding; a. Reservoir porosity after 0.2 pore volume of water injection, b. Reservoir porosity after 0.4 pore volume of waterinjection, c. Reservoir porosity after 0.6 pore volume of water injection.


Ea Average Absolute Percentage Relative ErrorEi Percentage Relative ErrorEr Average Percentage Relative ErrorI Ionic strengthinpk,avg The average value of the kth inputinpk,I The ith value of the kth inputk input variablesKeq,b Chemical equilibrium constantKf/Ki Permeability damage ratioKf

Ki

avg

The average value of predicted permeability ratioKf

Ki

i

The ith value of predicted permeability ratio

Ksp Solubility productmi Molality of component iN0b Moles of mineral b per unit grid block volume at time zero

Nb Moles of mineral b per unit grid block volume at currenttime

PVinj Pore volume injectedDP Pressure differenceQ Injection rateQb Activity product of mineral bR2 Coefficient of DeterminationRMSE Root Mean Square Errorrb Reaction rate[SO42�] Sulfate molalitySBaSO4 Solubility of BaSO4SI Saturation indext Injection durationT Temperatureu Fluid velocityvkb Stoichiometry coefficients of the aqueous species

Fig. 14. Profiles of water saturation during water flooding; a. Water saturation after 0.2 pore volume of water injection, b. Water saturation after 0.4 pore volume of water injection,c. Water saturation after 0.6 pore volume of water injection.


VP Pore VolumeX pore radius ratiozk Ionic charge of the kth ionbf Reference porosity when dissolution/precipitation is

includedf* Reference porosity without mineral dissolution/

precipitationǷ Molar density of mineral bgBa2þ Barium activity coefficient

gSO42� Sulfate activity coefficient

gi Activity coefficient of component i

Appendix

Statistical analysis

To evaluate the quality of matching, the following statisticalparameters have been measured.

Fig. 15. The impact of scale deposition in reservoir on injection bottom hole pressure at a constant oil production rate. The bottom hole pressure needed for maintaining theconstant production rate increases up to nearly 19,000 psi when scale formation is considered in the simulations.


1Average Percentage Relative Error (APRE):

Er ¼ 1n

Xni¼1

Ei (16)

where Ei is Percentage Relative Error and is the relative deviation ofa predicted value from the corresponding experimental value. It isdefined based on the following equation:

Ei ¼

264Kf

Ki

exp

�Kf

Ki

rep:=pred

Kf

Kiexp

375� 1000i ¼ 1;2;3;…;n (17)

where Kf

Kiiexp is the experimental permeability ratio and Kf

Kiirep:=pred

stands for the represented/predicted permeability ratio. Kf denotesthe final permeability and Ki stands for the initial permeability.

2Average Absolute Percentage Relative Error (AAPRE):

Ea ¼ 1n

Xni¼1

jEij (18)

3Root Mean Square Error (RMSE):

RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1n

Xni¼1

Kf

Kiiexp � Kf

Kiirep:=pred

2vuut (19)

4 Coefficient of Determination (R2):

R2 ¼ 1�Pn

i¼1

Kf

Kiiexp � Kf

Kii rep:=pred

2

Pni¼1

0@Kf

Kii rep:=pred � Kf

Ki

1A2 (20)

where

0@Kf

1A is the experimental data mean.
Ki
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