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Research ArticleMysteries behind the Low Salinity Water Injection Technique

Emad Waleed Al-Shalabi Kamy Sepehrnoori and Gary Pope

Department of Petroleum and Geosystems Engineering The University of Texas at Austin Austin TX 78712 USA

Correspondence should be addressed to Emad Waleed Al-Shalabi ealshalabiutexasedu

Received 25 October 2013 Accepted 22 April 2014 Published 25 May 2014

Academic Editor Alireza Bahadori

Copyright copy 2014 Emad Waleed Al-Shalabi et al This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Low salinity water injection (LSWI) is gaining popularity as an improved oil recovery technique in both secondary and tertiaryinjection modes The objective of this paper is to investigate the main mechanisms behind the LSWI effect on oil recovery fromcarbonates through history-matching of a recently published coreflood This paper includes a description of the seawater cyclematch and two proposed methods to history-match the LSWI cycles using the UTCHEM simulator The sensitivity of residual oilsaturation capillary pressure curve and relative permeability parameters (endpoints and Coreyrsquos exponents) on LSWI is evaluatedin this work Results showed thatwettability alteration is still believed to be themain contributor to the LSWI effect on oil recovery incarbonates through successfully historymatching both oil recovery and pressure drop dataMoreover tuning residual oil saturationand relative permeability parameters including endpoints and exponents is essential for a good data match Also the incrementaloil recovery obtained by LSWI is mainly controlled by oil relative permeability parameters rather than water relative permeabilityparametersThe findings of this paper help to gainmore insight into this uncertain IOR technique and propose amechanisticmodelfor oil recovery predictions

1 Introduction

Oil recovery from carbonate rocks is a challenge due to thehigh fracture density and the rock wettability state whichranges from mixed-wet to oil-wet One of the recentlyrecommended improved oil recovery (IOR) techniques islow salinity water injection (LSWI) which is believed toshift the wettability state of the rock towards more water-wetstate The LSWI technique has several advantages includinghigh efficiency in displacing light to medium gravity crudeoils ease of injection into oil-bearing formations availabilityand affordability of water and lower capital and operatingcosts compared to other IOR methods which leads tofavorable economics Other names proposed in the literaturefor the same mechanism are LoSal Smart Waterflood andAdvanced Ion Management The LSWI effect on oil recoveryfrom carbonates was shown both at laboratory scale and toa limited extent at field scale Although most researchersbelieve that wettability alteration is the main mechanism forthe LSWI on oil recovery from carbonates there are otherswho believe in the presence of other contributing mecha-nisms Therefore work is still progressing to understand the

chemical interactions in crude oil-brine-rock (COBR) in theporous media

TheLSWI effect on oil recovery from carbonate is not welladdressed compared to sandstone rocks due to the previousthoughts of relatingwettability alteration by low salinitywaterto the presence of clay which is not the case in carbonaterocks Nevertheless the effect of LSWI on oil recovery fromcarbonate rocks was investigated at laboratory scale usingboth spontaneous imbibition and coreflooding studies

Hoslashgnesen et al [1] concluded from their spontaneousimbibition experiments on reservoir limestone cores thatincreasing sulfate ion concentration at high temperature leadsto oil recovery increase due to the role of sulfate ion as awettability modifying agent for carbonate rocks frommixed-wet to water-wet state Webb et al [2] investigated the effectof sulfate on oil recovery from North Sea carbonate coresamples through spontaneous imbibition experiments Theyreported that seawater has the ability to alter wettabilityof the carbonate system to more water-wet state comparedto sulfate-free water Zhang et al [3] studied wettabilityalteration of North Sea chalk reservoirs in Ekofisk fieldshowing the effect of adding calcium andor magnesium

Hindawi Publishing CorporationJournal of Petroleum EngineeringVolume 2014 Article ID 304312 11 pageshttpdxdoiorg1011552014304312

2 Journal of Petroleum Engineering

ions at various temperaturesThey concluded that wettabilityalteration occurs if the imbibing water contains either Ca2+and SO

4

2minus or Mg2+ and SO4

2minus Moreover Strand et al[4] observed 15 increase in oil recovery from limestonecores when seawater was imbibed compared to seawater freeof sulfate Increased oil recovery using low salinity waterinjection in limestone formations was noticed by Fjelde [5]

Bagci et al [6] reported high oil recovery of 355 ofOOIP from their corefloods by using 2wtKCl on limestonecores and high pH effluent brine due to ions exchangereactions with the clay present in the rock They consideredwettability alteration as the reason behind recovering moreoil without further explanation Yousef et al [7] investigatedthe applicability of low salinity water injection (SmartWater-flood) on carbonate rocks for improving oil recovery by usingdifferent dilutions of seawater The results of corefloodingtests showed increasing oil recovery with stepwise dilutionof seawater upon which 18 incremental oil recovery wasachieved due to tertiary water injection Coreflooding experi-ments on both dolomite cores fromWest Texas and limestonecores from the Middle East were performed by Gupta et al[8] Experiments showed incremental 5ndash9 OOIP recoveryfrom both dolomite and limestone cores as a result of addingsulfate ions For limestone cores 7ndash9 OOIP was obtaineddue to reducing hardness of the injected water not the totaldissolved solids Another interesting finding is the 15 and20 OOIP by using borate (BO

3

3minus) and phosphate (PO4

3minus)as modified ions respectively In a later work Yousef etal [9] demonstrated that wettability alteration is the reasonbehind LSWI through NMR contact angle measurementand zeta potential studiesThe results showed that wettabilityalteration occurs through changing the surface charge fromthe zeta potential measurements and dissolution of CaSO

4

from NMR testsAl-Harrasi et al [10] provided direct evidence of low

salinity water flooding effect on oil recovery fromOmani car-bonate rocks through spontaneous and coreflooding exper-iments Wettability alteration was referred to as the reasonfor low salinity water injection with negligible reduction ininterfacial tension Also they reported that low salinity waterinjection by lowering the ionic strength hasmore pronouncedeffect on oil recovery from oil-bearing zone cores comparedto hardening the injected water Nevertheless the case is justthe opposite for StevnsKlint outcrop chalk cores because theyare more responsive to hardening of the injected low salinitywater as was reported by Romanuka et al [11] through theirspontaneous imbibition experiments

Extensive researchwas performed byAustad and cowork-ers [12ndash14] which showed the possibility of wettability alter-ation and enhancing oil recovery from carbonate rocks bymodifying the ionic composition in the injectedwaterWetta-bility alteration is the main and most acceptable mechanismfor the incremental oil recovery obtained from carbonaterocks using LSWI Wettability alteration in carbonate rocksusing smart water can be achieved by injecting water con-taining SO

4

2minus and either Ca2+ orMg2+ or both of them in thepresence of high temperatures (gt90∘C) It was proposed thatwith increasing temperature the affinity of sulfate to chalk

rock surface increases and sulfate adsorption occurs At thesame time Ca2+ adsorption increases as well as the initialpositive charge of the rock decreases Hence more excessCa2+ ions are present close to the surface which reacts withthe carboxylic material and releases some of themMoreoverwith increasing the temperature Mg2+ becomes more activeCa2+ substitution by Mg2+ occurs and sulfate becomes lessactive as it reacts with Mg2+ Otherwise CaSO

4precipitation

occurs which causes injection problems [13]The first ever LoSal application in carbonate reservoirs

was reported by Yousef et al [15] Two single-well chemicaltracer tests (SWCTT) were applied in an upper jurassiccarbonate reservoir using a diluted version of Qurayyah sea-waterThe tests resulted in about 7 saturation unitsrsquo reductionin the residual oil beyond conventional seawater injectionThe results obtained matched their previous experimentalworkwhich is encouraging to plan amultiwell demonstrationpilot

Only a few modeling works for carbonate rocks havebeen performed so far due to various reasons These reasonsinclude the complex chemical interaction in rock-oil-brineand the heterogeneity of carbonate rocks which complicateoil recovery predications by LSWI Also the uncertaintyin the controlling mechanism and the clash in some ofthe published experimental results shifted the focus onexperimental work rather than modeling work This paperincludes history-matching of Chandrasekhar and Mohantyrsquos[16] experimental work using theUTCHEMsimulator whichis a 3D multiphase flow transport and chemical floodingsimulator for black oil developed at The University of Texasat Austin

2 Experimental Data

Chandrasekhar and Mohanty [16] conducted several verticalcorefloods to investigate the low salinity water injection effecton oil recovery from Middle Eastern carbonate core plugsThe coreflood of our interest is the one with different injectedseawater dilutions Heterogeneous carbonate core plug wasused with average porosity and liquid permeability of 264and 759mD respectively The coreflood was conducted atreservoir temperature of 248∘F and atmospheric pressureat an injection rate of 1 ftday At each injection cycle theinjection rate was increased to 10 ftday to make sure thatthe oil maximum recovery was reached The brines usedwere field water of 179726 ppm and different diluted versionsof seawater of 43619 ppm by weight Rock properties andfluid properties are shown in Tables 1 2 and 3 The oilrecovery and pressure drop data are shown in Figures 1 and2 Here an increase in oil recovery is observed with stepwisedilution of the seawater by tertiary water injection Moredetails about the experimental work are described elsewhere[16]The UTCHEM software was used to history-match bothoil recovery and pressure drop dataThe pressure drop data ofeach injection cycle is matched just for the low injection rate(1 ftday) The second injection cycle is an exception wherethe pressure drop is matched for both injection rates (1 and10 ftday) because of the incremental oil recovery obtainedwith increasing the rate at 10 ftday in this cycle

Journal of Petroleum Engineering 3

Table 1 Reservoir core properties (Chandrasekhar and Mohanty2013 [16])

Pore Volume 158 ccPorosity 0264Permeability 759 mDDiameter 379 cmCross Sectional Area 1128 cm2

Length 53 cm119878119908i 03181119878119900119894

06819

Table 2 Field oil sample properties (Chandrasekhar and Mohanty2013 [16])

Oil propertiesViscosity (cp) at 248∘F 105Density (gcc) at 248∘F 0618API (degrees) 40

Table 3 Properties of various dilutions of seawater (248∘F) (Chan-drasekhar and Mohanty 2013 [16])

Water propertiesat 248∘FInjected watersalinity (ppm)

Water density(gcc)

Water viscosity(cp)

43619 09760 0260218095 09595 024643619 09464 0234218095 09448 0233

3 Simulation Data

This section includes both simulation model description andexperimental data analysis to obtain the simulation inputsneeded

31 Simulation Model Description A 2D Cartesian gridsystem was used with 10 times 1 times 10 grid blocks to simulatethe heterogeneous core plug for the coreflood The decisionon using a heterogeneous model is discussed later in theseawater cycle match section The heterogeneous model wasconsidered by generating permeability distribution with anarithmetic mean of 759mD and Dykstra Parsonrsquos coefficientof 085 A spherical variogram and a log normal permeabilitydistribution were used The 119910-direction correlation lengthwas assumed to be similar to the 119909-direction howevera high 119911-direction correlation length compared to the 119909-direction was chosen which generated vertical layers ofdifferent permeabilities (Figure 3) The simulation model hastwo horizontal wells injector at the bottom and producer atthe top Table 4 shows length width and height dimensionsfor the grid blocks We assumed a negligible capillary endeffect

0

10

20

30

40

50

60

70

8090

0 10 20 30 40 50 60

Cum

ulat

ive o

il re

cove

ry (

)

Water injected (PV)

Figure 1 Cumulative oil recovery curve for the coreflood conducted[16]

Water injected (PV)

0

5

10

15

20

25

30

0 10 20 30 40 50 60

Pres

sure

dro

p (p

si)

Figure 2 Pressure drop data for the coreflood conducted [16]

32 Experimental Data Analysis This section includes adescription of pressure drop data analysis and applicationof JBN method to find relative permeability curves for theseawater injected cycle

321 Pressure Drop Data Analysis As was previously men-tioned the analysis of the pressure drop curve (Figure 2)is performed for the 1 ftday injection rate except for thesecond cycle where the injection rate of 10 ftday resultedin additional oil recovery The water endpoint relative per-meability for each cycle at 1 ftday and even for the secondcycle at 10 ftday can be calculated using Darcyrsquos law andstabilized average pressure drop value The oil endpointrelative permeability was provided experimentally for theseawater cycle (119870lowast

119903119900= 0203) Table 5 summarizes the obtained

endpoint relative permeabilities for water and oil Table 5shows endpoint permeability calculation for the second cycleincluding both low salinity water injection and trappingnumber effects We can see a slight decrease in the waterendpoint relative permeability values for the LSWI effect inall injection cycles which indicates the presence of wettabilityalteration by LSWI


Table 4 Heterogeneous core model data

Parameter Value CommentsNumber of gridblocks 100 2D (10 times 1 times 10)

Grid block sizes(ΔI ΔJ ΔK) m

x-direction 1ndash10 Δx is 00033588my-direction 1-1 Δy is 0033588mz-direction 1ndash10 Δz is 00053m

Constant grid size in the x-y- and z-direction

Composite coremodel dimensions m 0033588m times 0033588m times 0053m Length times width times height

Table 5 Endpoint relative permeability data analysis

Oil viscosity 105 cPOil-water IFT 30 DynescmComposite core length 53 cm

Cross-sectional area 1128 cm2

Injection rate (main) 0045 ccmin119870119900119878119908119894119903119903

154 mDAbsolute brine permeability 759 mDInjection cycle Water viscosity (cP) Pressure drop (psi) 119896

119903119908

lowast119878119900119903

119896119903119900

lowast

First 026 720 0025 0329 0203Second 1 (LSWI effect) 0246 700 0024 0267Second 2 (trapping number effect) 0246 1890 0089 0163Third 0234 700 0023 0127Fourth 0233 720 0022 0127

322 JBN Method Johnson Bossler and Naumann (JBN)method was applied to find relative permeability curvesfor the seawater cycle The data obtained are shown inFigure 4 Coreyrsquosmodelwas fitted to find relative permeabilityendpoints and exponents for the seawater cycle Moreoverthe analysis was taken a step further to calculate the fractionalflow curve uponwhich bothmobility ratio and gravity effectsare considered The fractional flow in this case is defined as

119891119908=

119878119899119908119872119900[1 minus 119873

119900

119892(1 minus 119878)

119899119900 sin (120572)]

119878119899119908119872119900+ (1 minus 119878)

119899119900

(1)

The relative permeability data calculated from JBNmethod was fitted to an exponential function that wasused later to calculate the fractional flow curve throughmobility ratio calculations (Figure 5)The equation of relativepermeability ratio as function of saturation is given by

119870119903119900

119870119903119908

= 119886119890minus119887119878119908

(2)

The latter fractional flow curve (experimental) wasmatched with the analytical solution of fraction flow wherethe main matching parameters are 119899

119908of 13 and 119899

119900of 35

(Figure 6) The water and oil endpoint relative permeabilityvalues were obtained using pressure drop curve analysis fromTable 5The coreflood was conducted vertically which makessin(120572) equal to 1 The endpoint mobility ratio used is 047and the endpoint gravity number is 001 The definitions of

endpoint mobility ratio (119872119900) and endpoint gravity number(119873119900119892) are given by

119872119900=

119896119900

119903119908120583119900

119896119900

119903119900120583119908

119873119900

119892=

119896119896119900

119903119900Δ120588119892

119906120583119900

(3)

Nevertheless there is a mismatch between the BuckleyLeverett analytical solution compared to the experimen-tal data provided by Chandrasekhar and Mohanty [16](Figure 7) The main difference between the analytical solu-tion and the experimental data is the heterogeneity effectwhich is not taken into account in analytical solution addedto the capillary pressure effect Both of these effects can beconsidered using the UTCHEM simulator to history-matchthe data

4 Results and Discussion

This section covers seawater cycle history-matching andmethods used for thewettability alteration effectmatching fordifferent dilutions of seawater injected cycles

41 Seawater Cycle Match The final set of relative perme-ability curves for the seawater cycle as a result of pressuredrop analysis and JBN method is shown in Figure 8 Thefigure shows a weakly oil-wet rock where 119896

lowast

119903119900is 0203 119896lowast

119903119908

is 0025 119899119900is 35 119899

119908is 13 and the intersection point is at

about 05 water saturationThe heterogeneity effect was takeninto consideration by applying aDykstra Parson coefficient of


Injector

Producer

023

083

301

1090

3942

PERM

Z

000000

000000

000000

000800

000800

001600

001600002400 002400

003200

003200

003359

003359005300

004800

003600

002400

001200

Figure 3 Simulation model used in different runs with heterogeneous permeability

10E minus 06

10E minus 05

10E minus 04

10E minus 03

10E minus 02

10E minus 01

10E + 0002 03 04 05 06 07 08

Wat

er an

d oi

l rel

ativ

e

Experimental

perm

eabi

lity

curv

es (K

rw

KrwKrw Experimental Kro

Kro

Kro

)

Water saturation (Sw) (fraction)

Figure 4 Relative permeability data analysis using the JBNmethod(first cycle)

085 along with correlation lengths which resulted in verticallayers of different permeabilities as was previously shown inFigure 3 Moreover the capillary pressure contribution wasconsidered by applying Brooks-Corey model for imbibitioncapillary pressure for mixed-wet rocks as follows

(i) Water-wet part of capillary pressure curve (119878 lt 119878lowast) is

11987511988812

= CPC1radic120601

119896

(

119878lowast

119908minus 119878119908

119878lowast

119908minus 119878119908119903

)

EPC1

(4)

(ii) Oil-wet part of capillary pressure curve (119878 gt 119878lowast) is

11987511988812

= CPC2radic120601

119896

(

119878119908minus 119878lowast

119908

1 minus 119878119900119903minus 119878lowast

119908

)

EPC2

(5)

Table 6 Summary of relative permeability and capillary pressureparameters (seawater cycle)

Seawater cycle match parametersRelative permeability parameters

119896119903119908

lowast 0025 119899119908

13119896119903119900

lowast 0203 119899119900

35Capillary pressure parameters

CPC119908

2 EPC119908

2CPC119900

minus2 EPC119900

2119878lowast 05

where CPC is a parameter related to the maximum capillarypressure EPC is capillary pressure exponent and 119878

lowast isthe water saturation at zero capillary pressure value Thecapillary pressure curve used in matching oil recovery andpressure drop data along with summary of capillary pressureparameters and relative permeability parameters is presentedin Figure 9 and Table 6 respectively History-matching ofoil recovery and pressure drop data showed that the CPC

2

parameter controls the ultimate oil recovery value howeverCPC1controls the initial hump of the oil recovery and

the pressure drop data match It can be seen clearly thatthe capillary pressure does not contribute much to datahistory-matching Hence the capillary pressure is neglectedfor history-matching the successive dilutions of seawaterinjection

The results of history-matching of oil recovery and pres-sure drop data are depicted in Figures 10 and 11 respectivelyIn the latter figures two curves are presented for the homoge-neous 1D model with an average permeability and heteroge-neous models The history-matching shows the importance


000501

01502

02503

03504

04505

00 01 02 03 04 05 06 07Water saturation (fraction)

Experimental dataExpon (experimental data)

(KroK

rw) r

atio

y = 642154739e

R2 = 090

minus3079x

Figure 5 Relative permeability ratio versus water saturation (firstcycle)

00

02

04

06

08

10

0 01 02 03 04 05 06 07 08

Experimental dataAnalytical solution

Water saturation (Sw)

Wat

er fr

actio

nal fl

ow (f

w)

Figure 6 Fractional flow curve history-match (first cycle)

of heterogeneity incorporation to match reasonably the oilrecovery and pressure drop curves

42 Dilutions of Seawater Injected Cycles Match This sectionincludes history-matching of the LSWI cycles of Chan-drasekhar and Mohanty [16] coreflood using two proposedmethods

421 First Method In this method seawater cyclersquos relativepermeability parameters are used for the different dilutioncycles while only changing the residual oil saturation foreach cycle based on the reported values As expectedhistory-matching of data is not possible using this methodwhich validates the necessity of tuning relative permeabilityparameters for LSWI cycles because 119878

119900119903contribution by

itself is not enough This is supported by the findings of oilrecovery and pressure drop history-matching curves usingthis approach (Figures 12 and 13) It is worth mentioningthat the jump in the second cycle of pressure drop curve

000005010015020025030035040045050

00 10 20 30 40 50 60Water injected (PV)

Npd

(PV

)


Figure 7 Buckley Leverett analytical solution (first cycle)

0

005

01

015

02

025

0 02 04 06 08

Wat

er an

d oi

l rel

ativ

e pe

rmea

bilit

y cu

rves

(Krw

Kro

)


Kro

Krw

Figure 8 Relative permeability curves (first cycle)

minus3

minus2

minus1

0

1

2

3

0 02 04 06 08 1

Capi

llary

pre

ssur

e (ps

i)


Figure 9 Capillary pressure curve (first cycle)

(Figure 13) is due to the trapping number effect as theinjection rate was increased to 10 ftday without changing therelative permeability parameters

422 Second Method This method includes three approa-ches changing Coreyrsquos exponents only (first approach)


0

20

40

60

80

0 2 4 6 8 10

Cum

ulat

ive o

il re

cove

ry (

)

Cumulative water injected (PV)

Experimental dataHomogeneous modelHeterogeneous model

Figure 10 Oil recovery match for seawater cycle

0

5

10

15

20

25

30

Pres

sure

dro

p (p

si)

0 2 4 6 8 10Cumulative water injected (PV)


Figure 11 Pressure drop match for seawater cycle

0

20

40

60

80

100

0 10 20 30 40 50 60

Cum

ulat

ive o

il re

cove

ry (

)

Experimental data


Sor contribution

Figure 12 Cumulative oil recovery match using the first method

0102030405060708090

100

Pres

sure

dro

p (p

si)

0 10 20 30 40 50 60

Experimental data


Sor contribution

Figure 13 Overall pressure drop match using the first method

40

60

116 136 156 176 196

Cum

ulat

ive o

il re

cove

ry (

)

Experimental data


Kr and Sor contributionsSor contribution

Figure 14 LSWI effect on second cycle oil recovery match using thesecond method (third approach)

0

005

01

015

02

025

03

10E minus11 10E minus 09 10E minus 07 10E minus 05 10E minus 03Trapping number (Nc)

CDC modelExperimental

S or

Figure 15 Modeled CDC curve for the coreflooding experiment


0010203040506070809

1

0 02 04 06 08 1

Wat

er an

d oi

l rel

ativ

e pe

rmea

bilit

y cu

rves

(Krw

Kro

)


Krw (below NTlowast) Kro (below NTlowast)Krw (exceeding NTlowast) Kro (exceeding NTlowast)

Figure 16 Relative permeability curves before and after exceedingcritical119873

119879(second cycle-trapping number)

40

60

80

205 255 305 355

Cum

ulat

ive o

il re

cove

ry (

)


Experimental dataSor contributionSo Krr and contributions

Figure 17 Trapping number effect on second cycle oil recoverymatch using the second method (third approach)

0102030405060708090

100

Pres

sure

dro

p (p

si)

205 255 305 355Cumulative water injected (PV)


Figure 18 Trapping number effect on second cycle pressure dropmatch using the second method (third approach)

55

75

375 425 475 525 575

Cum

ulat

ive o

il re

cove

ry (

)



Figure 19 Third and fourth cycles oil recovery match using thesecond method (third approach)

Cum

ulat

ive o

il re

cove

ry (

)


0

20

40

60

80

100

0 10 20 30 40 50 60


Figure 20 Cumulative oil recoverymatch using the secondmethod(third approach)

0

102030405060708090

100

00 100 200 300 400 500 600

Pres

sure

dro

p (p

si)



Figure 21 Overall pressure drop match using the second method(third approach)


0010203040506070809

1

02 03 04 05 06 07 08 09 1

Wat

er an

d oi

l rel

ativ

e pe

rmea

bilit

y cu

rves

(Krw

Kro

)


05 06 08 0907

First cycle krwSecond cycle 1 krwSecond cycle 2 krwThird cycle krwFourth cycle krw

First cycle kroSecond cycle 1 kroSecond cycle 2 kroThird cycle kroFourth cycle kro

Figure 22 Relative permeability curves using the second method(third approach)

changing endpoint relative permeabilities only (secondapproach) and changing both Coreyrsquos exponents and end-point relative permeabilities (third approach) The first twoapproaches were not successful in history-matching pressuredrop and oil recovery data The third approach of thesecond method is applied on Chandrasekhar and Mohanty[16] coreflood by tuning relative permeability parametersincluding endpoints and Coreyrsquos exponents to match the datain each cycle starting with the second cycle The 119896

119903and 119878

119900119903

contributions curve for the LSWI effect on the second cycleis shown in Figure 14

The trapping number effect on the second cycle is con-sidered using the capillary desaturation curve (CDC) Therelation for adjusting residual oil saturation as a function oftrapping number was proposed by Pope et al [17] as follows

119878119897119903= 119878

high119897119903

+

119878low119897119903

minus 119878high119897119903

1 + 119879119897119873120591

119879119897

for 119897 = 1 119899119901 (6)

Figure 15 shows the modeled CDC curve for the secondcycle where the experimental trapping number calculated forthe injection rate of 10 ftday is matched using 119878

low119897119903

of 0267119878high119897119903

of zero 120591 of 082 and 119879119897parameter of 650000 The

detailed calculations of the CDC curve are listed in Table 7The effect of trapping number on relative permeabilityparameters was also considered using Delshad et alrsquos [18]proposed model as follows

119896119900

119903119897= 119896119900low

119903119897+

119878low1198971015840119903minus 1198781198971015840119903

119878low1198971015840119903minus 119878

high1198971015840119903

(119896119900high

119903119897minus 119896119900low

119903119897)

for 119897 1198971015840 = 1 119899119901

119899119897= 119899

low119897

+

119878low1198971015840119903minus 1198781198971015840119903

119878low1198971015840119903minus 119878

high1198971015840119903

(119899high119897

minus 119899low119897

)

for 119897 1198971015840 = 1 119899119901

(7)

Table 7 CDC curve parameters

119878119900119903 (high) 0000119878119900119903 (low) 026711987922(parameter) 650000

Tau (119873119879exponent) 082

119873119879

119878119900119903

100119864 minus 11 0267100119864 minus 11 0267100119864 minus 10 0266100119864 minus 09 0260500119864 minus 09 0242100E minus 08 0226100E minus 07 0122100119864 minus 06 0030500119864 minus 06 0009100119864 minus 05 0005100119864 minus 04 0001100119864 minus 03 0000

Table 8 Relative permeability parameters before and after exceed-ing critical119873

119879

Second cycle matching parameters trapping number effectBelow119873

119879

lowast (critical) Exceeding119873119879

lowast (critical)119899119908

17 119899119908

143119899119900

155 119899119900

155119896119903119908

lowast 0024 119896119903119908

lowast 0089119896119903119900

lowast 083 119896119903119900

lowast 083119878119900119903

0267 119878119900119903

0163119878119908119894119903119903

03181 119878119908119894119903119903

03181

In the previous equations the words ldquohighrdquo and ldquolowrdquo inthe superscripts indicate the value of the parameter at highand low trapping numbers respectively The values at hightrapping number are usually assumed and the values at lowtrapping number can be considered as the values obtainedthrough history-matching the effect of LSWI on the secondcycle It is worth mentioning that 119896119900

high

119903119897was assumed to be 02

due to the low water endpoint relative permeability of initialseawater cycle (0025) Table 8 and Figure 16 show two setsof relative permeability curves before and after exceeding thecritical trapping number The oil recovery and pressure dropmatch for trapping number effect on the second cycle areshown in Figures 17 and 18 respectively

The 119896119903and 119878

119900119903contributions curve for the third and

fourth cycles is depicted in Figure 19 The cumulative oilrecovery and the overall pressure drop curves using the thirdapproach of the second method are shown in Figures 20and 21 respectively Sets of relative permeability curves usedin history-matching using this approach are presented inFigure 22 and Table 9 The analysis showed that the core-flood of Chandrasekhar and Mohanty [16] was successfullymatched using the third approach of the second method


Table 9 Summary of relative permeability parameters (secondmethod-third approach)

Injection cycle 119896119903119908

119896119903119900

119899119908

119899119900

First cycle 0025 0203 130 350Second cycle (LSWIEffect) 0024 0830 170 155

Second cycle (trappingnumber effect) 0089 0830 143 155

Third cycle 0023 0850 200 153Fourth cycle 0022 0860 220 152

by tuning residual oil saturation and relative permeabilitycurves including endpoints and Coreyrsquos exponents

5 Summary and Conclusions

Oil recovery and pressure drop data for the coreflood ofChandrasekhar and Mohanty [16] were matched successfullyusing UTCHEMThemain findings of this work are summa-rized as follows

(i) Wettability alteration is still believed to be the contrib-utor to the LSWI effect on oil recovery from carbonaterocks

(ii) History-matching of the LSWI effect on oil recoveryis sensitive to residual oil saturation and relativepermeability curves

(iii) Tuning both relative permeability endpoints andCoreyrsquos exponents is essential for good history-matching of both oil recovery and pressure drop data

(iv) Neglecting capillary pressure effect on oil recoveryand pressure drop history-matching in case of LSWIis a plausible assumption even if the coreflood isconducted at reservoir rate of 1 ftday

(v) Oil relative permeability parameters are more sensi-tive to LSWI compared to water relative permeabilityparameters

(vi) The findings of this paper validate our previousfindings [19] uponwhich the two corefloods of Yousefet al [7] were history-matched

Moreover in light of the previous findings a simple inter-polation model can be implemented in UTCHEM andapplied to history-match both works of Yousef et al [7] andChandrasekhar and Mohanty [16] This is our next step tohavemore insight into the low salinity water injection (LSWI)mechanism before we propose our own mechanistic LSWImodel

Nomenclature

CPC Parameter related to the maximumcapillary pressure

EPC Capillary pressure exponent119896lowast

119903119897 Phase endpoint relative permeability

119899119897 Phase Coreyrsquos exponent

119878119897 Phase saturation

119878119897119903 Phase residual saturation

120590 Interfacial tension

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors wish to acknowledge useful discussions with KK Mohanty during the work This work was funded by AbuDhabi National Oil Company (ADNOC)

References

[1] E J Hoslashgnesen S Strand and T Austad ldquoWaterflooding ofpreferential oil-wet carbonates oil recovery related to reservoirtemperature and brine compositionrdquo in Proceedings of the 67thEuropean Association of Geoscientists and Engineers (EAGE rsquo05)pp 815ndash823 Madrid Spain June 2005 SPE-94166

[2] K J Webb C J J Black and G Tjetland ldquoA laboratory studyinvestigating methods for improving oil recovery in carbon-atesrdquo in Proceedings of the International Petroleum TechnologyConference pp 785ndash791 Doha Qatar November 2005 SPE-10506

[3] P Zhang M T Tweheyo and T Austad ldquoWettability alterationand improved oil recovery by spontaneous imbibition of seawa-ter into chalk impact of the potential determining ions Ca2+Mg2+ and SO4

2ndashrdquo Colloids and Surfaces A Physicochemical andEngineering Aspects vol 301 no 1ndash3 pp 199ndash208 2007

[4] S Strand T Austad T Puntervold E J Hoslashgnesen M Olsenand S M F Barstad ldquolsquoSmart Waterrsquo for oil recovery fromfractured limestone a preliminary studyrdquo Energy and Fuels vol22 no 5 pp 3126ndash3133 2008

[5] I Fjelde ldquoLow salinity water flooding experimental experienceand challengesrdquo in Proceedings of the Force RP Work ShopLow Salinity Water Flooding the Importance of Salt Content inInjection Water Stavanger Norway 2008

[6] S Bagci M V Kok and U Turksoy ldquoEffect of brine composi-tion on oil recovery by waterfloodingrdquo Petroleum Science andTechnology vol 19 no 3-4 pp 359ndash372 2001

[7] A A Yousef S Al-Saleh A Al-Kaabi and M Al-Jawfi ldquoLabo-ratory investigation of novel oil recovery method for carbonatereservoirsrdquo in Proceedings of the SPE Canadian UnconventionalResources and International Petroleum Conference pp 1825ndash1859 Alberta Canada October 2010 SPE-137634

[8] R Gupta P Griffin L Hu et al ldquoEnhanced waterflood formiddle east carbonates coresmdashimpact of injection water com-positionrdquo in Proceedings of the SPE Middle East Oil and GasShow and Conference Manama Bahrain 2011 SPE-142668

[9] A A Yousef S Al-Saleh andMAl-Jawfi ldquoImprovedenhancedoil recovery from carbonate reservoirs by tuning injectionwatersalinity and ionic contentrdquo in Proceedings of the SPE ImprovedOil Recovery Symposium Tulsa Okla USA 2012 SPE-154076

[10] A S Al-Harrasi R S Al Maamari and S Masalmeh ldquoLabo-ratory investigation of low salinity waterflooding for carbonatereservoirsrdquo in Proceedings of the SPE Abu Dhabi International


Petroleum Exhibition amp Conference Abu Dhabi UAE 2012SPE-161468

[11] J Romanuka J P Hofman D J Ligthelm et al ldquoLow salinityEOR in carbonatesrdquo in Proceedings of the SPE Improved OilRecovery Symposium Tulsa Okla USA 2012 SPE-153869

[12] D C Standnes and T Austad ldquoWettability alteration in chalk 2Mechanism for wettability alteration from oil-wet to water-wetusing surfactantsrdquo Journal of Petroleum Science and Engineeringvol 28 no 3 pp 123ndash143 2000

[13] P Zhang M T Tweheyo and T Austad ldquoWettability alterationand improved oil recovery in chalk the effect of calcium in thepresence of sulfaterdquo Energy and Fuels vol 20 no 5 pp 2056ndash2062 2006

[14] T Puntervold S Strand and T Austad ldquoWater flooding ofcarbonate reservoirs effects of a model base and natural crudeoil bases on chalk wettabilityrdquo Energy amp Fuels vol 21 no 3 pp1606ndash1616 2007

[15] A A Yousef J Liu G Blanchard et al ldquoSmart water floodingindustryrsquos first field test in carbonate reservoirsrdquo in Proceedingsof the SPE Annual Technical Conference and Exhibition SanAntonio Tex USA 2012 SPE-159526

[16] S Chandrasekhar and K K Mohanty ldquoWettability alterationwith brine composition in high temperature carbonate reser-voirsrdquo in Proceedings of the SPE Annual Technical Conferenceand Exhibition New Orleans La USA 2013 SPE-166280

[17] G A Pope W Wu G Narayanaswamy M Delshad M MSharma and P Wang ldquoModeling relative permeability effectsin gas-condensate reservoirs with a new trapping modelrdquo SPEReservoir Evaluation amp Engineering vol 3 no 2 pp 171ndash1782000

[18] M Delshad D Bhuyan G A Pope and L Lake ldquoEffect ofcapillary number on the residual saturation of a three-phasemicellar solutionrdquo in Proceedings of the SPE Enhanced OilRecovery Symposium Tulsa Okla USA 1986 SPE-14911

[19] E W Al-Shalabi K Sepehrnoori and M Delshad ldquoMecha-nisms behind low salinity water flooding in carbonate reser-voirsrdquo in Proceedings of SPEWestern Regional and AAPG PacificMeeting Monterey Calif USA 2013 SPE-165339

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



ions at various temperaturesThey concluded that wettabilityalteration occurs if the imbibing water contains either Ca2+and SO

4

2minus or Mg2+ and SO4

2minus Moreover Strand et al[4] observed 15 increase in oil recovery from limestonecores when seawater was imbibed compared to seawater freeof sulfate Increased oil recovery using low salinity waterinjection in limestone formations was noticed by Fjelde [5]

Bagci et al [6] reported high oil recovery of 355 ofOOIP from their corefloods by using 2wtKCl on limestonecores and high pH effluent brine due to ions exchangereactions with the clay present in the rock They consideredwettability alteration as the reason behind recovering moreoil without further explanation Yousef et al [7] investigatedthe applicability of low salinity water injection (SmartWater-flood) on carbonate rocks for improving oil recovery by usingdifferent dilutions of seawater The results of corefloodingtests showed increasing oil recovery with stepwise dilutionof seawater upon which 18 incremental oil recovery wasachieved due to tertiary water injection Coreflooding experi-ments on both dolomite cores fromWest Texas and limestonecores from the Middle East were performed by Gupta et al[8] Experiments showed incremental 5ndash9 OOIP recoveryfrom both dolomite and limestone cores as a result of addingsulfate ions For limestone cores 7ndash9 OOIP was obtaineddue to reducing hardness of the injected water not the totaldissolved solids Another interesting finding is the 15 and20 OOIP by using borate (BO

3

3minus) and phosphate (PO4

3minus)as modified ions respectively In a later work Yousef etal [9] demonstrated that wettability alteration is the reasonbehind LSWI through NMR contact angle measurementand zeta potential studiesThe results showed that wettabilityalteration occurs through changing the surface charge fromthe zeta potential measurements and dissolution of CaSO

4

from NMR testsAl-Harrasi et al [10] provided direct evidence of low

salinity water flooding effect on oil recovery fromOmani car-bonate rocks through spontaneous and coreflooding exper-iments Wettability alteration was referred to as the reasonfor low salinity water injection with negligible reduction ininterfacial tension Also they reported that low salinity waterinjection by lowering the ionic strength hasmore pronouncedeffect on oil recovery from oil-bearing zone cores comparedto hardening the injected water Nevertheless the case is justthe opposite for StevnsKlint outcrop chalk cores because theyare more responsive to hardening of the injected low salinitywater as was reported by Romanuka et al [11] through theirspontaneous imbibition experiments

Extensive researchwas performed byAustad and cowork-ers [12ndash14] which showed the possibility of wettability alter-ation and enhancing oil recovery from carbonate rocks bymodifying the ionic composition in the injectedwaterWetta-bility alteration is the main and most acceptable mechanismfor the incremental oil recovery obtained from carbonaterocks using LSWI Wettability alteration in carbonate rocksusing smart water can be achieved by injecting water con-taining SO

4

2minus and either Ca2+ orMg2+ or both of them in thepresence of high temperatures (gt90∘C) It was proposed thatwith increasing temperature the affinity of sulfate to chalk

rock surface increases and sulfate adsorption occurs At thesame time Ca2+ adsorption increases as well as the initialpositive charge of the rock decreases Hence more excessCa2+ ions are present close to the surface which reacts withthe carboxylic material and releases some of themMoreoverwith increasing the temperature Mg2+ becomes more activeCa2+ substitution by Mg2+ occurs and sulfate becomes lessactive as it reacts with Mg2+ Otherwise CaSO

4precipitation

occurs which causes injection problems [13]The first ever LoSal application in carbonate reservoirs

was reported by Yousef et al [15] Two single-well chemicaltracer tests (SWCTT) were applied in an upper jurassiccarbonate reservoir using a diluted version of Qurayyah sea-waterThe tests resulted in about 7 saturation unitsrsquo reductionin the residual oil beyond conventional seawater injectionThe results obtained matched their previous experimentalworkwhich is encouraging to plan amultiwell demonstrationpilot

Only a few modeling works for carbonate rocks havebeen performed so far due to various reasons These reasonsinclude the complex chemical interaction in rock-oil-brineand the heterogeneity of carbonate rocks which complicateoil recovery predications by LSWI Also the uncertaintyin the controlling mechanism and the clash in some ofthe published experimental results shifted the focus onexperimental work rather than modeling work This paperincludes history-matching of Chandrasekhar and Mohantyrsquos[16] experimental work using theUTCHEMsimulator whichis a 3D multiphase flow transport and chemical floodingsimulator for black oil developed at The University of Texasat Austin

2 Experimental Data

Chandrasekhar and Mohanty [16] conducted several verticalcorefloods to investigate the low salinity water injection effecton oil recovery from Middle Eastern carbonate core plugsThe coreflood of our interest is the one with different injectedseawater dilutions Heterogeneous carbonate core plug wasused with average porosity and liquid permeability of 264and 759mD respectively The coreflood was conducted atreservoir temperature of 248∘F and atmospheric pressureat an injection rate of 1 ftday At each injection cycle theinjection rate was increased to 10 ftday to make sure thatthe oil maximum recovery was reached The brines usedwere field water of 179726 ppm and different diluted versionsof seawater of 43619 ppm by weight Rock properties andfluid properties are shown in Tables 1 2 and 3 The oilrecovery and pressure drop data are shown in Figures 1 and2 Here an increase in oil recovery is observed with stepwisedilution of the seawater by tertiary water injection Moredetails about the experimental work are described elsewhere[16]The UTCHEM software was used to history-match bothoil recovery and pressure drop dataThe pressure drop data ofeach injection cycle is matched just for the low injection rate(1 ftday) The second injection cycle is an exception wherethe pressure drop is matched for both injection rates (1 and10 ftday) because of the incremental oil recovery obtainedwith increasing the rate at 10 ftday in this cycle




Length 53 cm119878119908i 03181119878119900119894

06819





Water density(gcc)

Water viscosity(cp)

43619 09760 0260218095 09595 024643619 09464 0234218095 09448 0233

3 Simulation Data



0

10

20

30

40

50

60

70

8090

0 10 20 30 40 50 60

Cum

ulat

ive o

il re

cove

ry (

)

Water injected (PV)


Water injected (PV)

0

5

10

15

20

25

30

0 10 20 30 40 50 60

Pres

sure

dro

p (p

si)


















119903119908

lowast119878119900119903

119896119903119900

lowast



119891119908=

119878119899119908119872119900[1 minus 119873

119900

119892(1 minus 119878)

119899119900 sin (120572)]

119878119899119908119872119900+ (1 minus 119878)

119899119900

(1)


119870119903119900

119870119903119908

= 119886119890minus119887119878119908

(2)


119908of 13 and 119899

119900of 35



119872119900=

119896119900

119903119908120583119900

119896119900

119903119900120583119908

119873119900

119892=

119896119896119900

119903119900Δ120588119892

119906120583119900

(3)





lowast

119903119900is 0203 119896lowast

119903119908

is 0025 119899119900is 35 119899




Injector

Producer

023

083

301

1090

3942

PERM

Z

000000

000000

000000

000800

000800

001600

001600002400 002400

003200

003200

003359

003359005300

004800

003600

002400

001200


10E minus 06

10E minus 05

10E minus 04

10E minus 03

10E minus 02

10E minus 01

10E + 0002 03 04 05 06 07 08

Wat

er an

d oi

l rel

ativ

e

Experimental

perm

eabi

lity

curv

es (K

rw


Kro

Kro

)





11987511988812

= CPC1radic120601

119896

(

119878lowast

119908minus 119878119908

119878lowast

119908minus 119878119908119903

)

EPC1

(4)


11987511988812

= CPC2radic120601

119896

(

119878119908minus 119878lowast

119908


119908

)

EPC2

(5)



119896119903119908

lowast 0025 119899119908

13119896119903119900

lowast 0203 119899119900


CPC119908

2 EPC119908

2CPC119900

minus2 EPC119900

2119878lowast 05



2





000501

01502

02503

03504

04505



(KroK

rw) r

atio

y = 642154739e

R2 = 090

minus3079x


00

02

04

06

08

10

0 01 02 03 04 05 06 07 08



Wat

er fr

actio

nal fl

ow (f

w)







000005010015020025030035040045050


Npd

(PV

)



0

005

01

015

02

025

0 02 04 06 08

Wat

er an

d oi

l rel

ativ

e pe

rmea

bilit

y cu

rves

(Krw

Kro

)


Kro

Krw


minus3

minus2

minus1

0

1

2

3

0 02 04 06 08 1

Capi

llary

pre

ssur

e (ps

i)






0

20

40

60

80

0 2 4 6 8 10

Cum

ulat

ive o

il re

cove

ry (

)




0

5

10

15

20

25

30

Pres

sure

dro

p (p

si)




0

20

40

60

80

100

0 10 20 30 40 50 60

Cum

ulat

ive o

il re

cove

ry (

)

Experimental data


Sor contribution


0102030405060708090

100

Pres

sure

dro

p (p

si)

0 10 20 30 40 50 60

Experimental data


Sor contribution


40

60

116 136 156 176 196

Cum

ulat

ive o

il re

cove

ry (

)

Experimental data




0

005

01

015

02

025

03



S or



0010203040506070809

1

0 02 04 06 08 1

Wat

er an

d oi

l rel

ativ

e pe

rmea

bilit

y cu

rves

(Krw

Kro

)





40

60

80

205 255 305 355

Cum

ulat

ive o

il re

cove

ry (

)




0102030405060708090

100

Pres

sure

dro

p (p

si)




55

75

375 425 475 525 575

Cum

ulat

ive o

il re

cove

ry (

)




Cum

ulat

ive o

il re

cove

ry (

)


0

20

40

60

80

100

0 10 20 30 40 50 60



0

102030405060708090

100

00 100 200 300 400 500 600

Pres

sure

dro

p (p

si)





0010203040506070809

1

02 03 04 05 06 07 08 09 1

Wat

er an

d oi

l rel

ativ

e pe

rmea

bilit

y cu

rves

(Krw

Kro

)


05 06 08 0907





119903and 119878

119900119903



119878119897119903= 119878

high119897119903

+

119878low119897119903

minus 119878high119897119903

1 + 119879119897119873120591

119879119897

for 119897 = 1 119899119901 (6)


low119897119903

of 0267119878high119897119903



119896119900

119903119897= 119896119900low

119903119897+

119878low1198971015840119903minus 1198781198971015840119903

119878low1198971015840119903minus 119878

high1198971015840119903

(119896119900high

119903119897minus 119896119900low

119903119897)

for 119897 1198971015840 = 1 119899119901

119899119897= 119899

low119897

+

119878low1198971015840119903minus 1198781198971015840119903

119878low1198971015840119903minus 119878

high1198971015840119903

(119899high119897

minus 119899low119897

)

for 119897 1198971015840 = 1 119899119901

(7)



Tau (119873119879exponent) 082

119873119879

119878119900119903



119879


119879



17 119899119908

143119899119900

155 119899119900

155119896119903119908

lowast 0024 119896119903119908

lowast 0089119896119903119900

lowast 083 119896119903119900

lowast 083119878119900119903

0267 119878119900119903

0163119878119908119894119903119903

03181 119878119908119894119903119903

03181


high



The 119896119903and 119878






119896119903119900

119899119908

119899119900














Nomenclature










Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Length 53 cm119878119908i 03181119878119900119894

06819





Water density(gcc)

Water viscosity(cp)

43619 09760 0260218095 09595 024643619 09464 0234218095 09448 0233

3 Simulation Data



0

10

20

30

40

50

60

70

8090

0 10 20 30 40 50 60

Cum

ulat

ive o

il re

cove

ry (

)

Water injected (PV)


Water injected (PV)

0

5

10

15

20

25

30

0 10 20 30 40 50 60

Pres

sure

dro

p (p

si)


















119903119908

lowast119878119900119903

119896119903119900

lowast



119891119908=

119878119899119908119872119900[1 minus 119873

119900

119892(1 minus 119878)

119899119900 sin (120572)]

119878119899119908119872119900+ (1 minus 119878)

119899119900

(1)


119870119903119900

119870119903119908

= 119886119890minus119887119878119908

(2)


119908of 13 and 119899

119900of 35



119872119900=

119896119900

119903119908120583119900

119896119900

119903119900120583119908

119873119900

119892=

119896119896119900

119903119900Δ120588119892

119906120583119900

(3)





lowast

119903119900is 0203 119896lowast

119903119908

is 0025 119899119900is 35 119899




Injector

Producer

023

083

301

1090

3942

PERM

Z

000000

000000

000000

000800

000800

001600

001600002400 002400

003200

003200

003359

003359005300

004800

003600

002400

001200


10E minus 06

10E minus 05

10E minus 04

10E minus 03

10E minus 02

10E minus 01

10E + 0002 03 04 05 06 07 08

Wat

er an

d oi

l rel

ativ

e

Experimental

perm

eabi

lity

curv

es (K

rw


Kro

Kro

)





11987511988812

= CPC1radic120601

119896

(

119878lowast

119908minus 119878119908

119878lowast

119908minus 119878119908119903

)

EPC1

(4)


11987511988812

= CPC2radic120601

119896

(

119878119908minus 119878lowast

119908


119908

)

EPC2

(5)



119896119903119908

lowast 0025 119899119908

13119896119903119900

lowast 0203 119899119900


CPC119908

2 EPC119908

2CPC119900

minus2 EPC119900

2119878lowast 05



2





000501

01502

02503

03504

04505



(KroK

rw) r

atio

y = 642154739e

R2 = 090

minus3079x


00

02

04

06

08

10

0 01 02 03 04 05 06 07 08



Wat

er fr

actio

nal fl

ow (f

w)







000005010015020025030035040045050


Npd

(PV

)



0

005

01

015

02

025

0 02 04 06 08

Wat

er an

d oi

l rel

ativ

e pe

rmea

bilit

y cu

rves

(Krw

Kro

)


Kro

Krw


minus3

minus2

minus1

0

1

2

3

0 02 04 06 08 1

Capi

llary

pre

ssur

e (ps

i)






0

20

40

60

80

0 2 4 6 8 10

Cum

ulat

ive o

il re

cove

ry (

)




0

5

10

15

20

25

30

Pres

sure

dro

p (p

si)




0

20

40

60

80

100

0 10 20 30 40 50 60

Cum

ulat

ive o

il re

cove

ry (

)

Experimental data


Sor contribution


0102030405060708090

100

Pres

sure

dro

p (p

si)

0 10 20 30 40 50 60

Experimental data


Sor contribution


40

60

116 136 156 176 196

Cum

ulat

ive o

il re

cove

ry (

)

Experimental data




0

005

01

015

02

025

03



S or



0010203040506070809

1

0 02 04 06 08 1

Wat

er an

d oi

l rel

ativ

e pe

rmea

bilit

y cu

rves

(Krw

Kro

)





40

60

80

205 255 305 355

Cum

ulat

ive o

il re

cove

ry (

)




0102030405060708090

100

Pres

sure

dro

p (p

si)




55

75

375 425 475 525 575

Cum

ulat

ive o

il re

cove

ry (

)




Cum

ulat

ive o

il re

cove

ry (

)


0

20

40

60

80

100

0 10 20 30 40 50 60



0

102030405060708090

100

00 100 200 300 400 500 600

Pres

sure

dro

p (p

si)





0010203040506070809

1

02 03 04 05 06 07 08 09 1

Wat

er an

d oi

l rel

ativ

e pe

rmea

bilit

y cu

rves

(Krw

Kro

)


05 06 08 0907





119903and 119878

119900119903



119878119897119903= 119878

high119897119903

+

119878low119897119903

minus 119878high119897119903

1 + 119879119897119873120591

119879119897

for 119897 = 1 119899119901 (6)


low119897119903

of 0267119878high119897119903



119896119900

119903119897= 119896119900low

119903119897+

119878low1198971015840119903minus 1198781198971015840119903

119878low1198971015840119903minus 119878

high1198971015840119903

(119896119900high

119903119897minus 119896119900low

119903119897)

for 119897 1198971015840 = 1 119899119901

119899119897= 119899

low119897

+

119878low1198971015840119903minus 1198781198971015840119903

119878low1198971015840119903minus 119878

high1198971015840119903

(119899high119897

minus 119899low119897

)

for 119897 1198971015840 = 1 119899119901

(7)



Tau (119873119879exponent) 082

119873119879

119878119900119903



119879


119879



17 119899119908

143119899119900

155 119899119900

155119896119903119908

lowast 0024 119896119903119908

lowast 0089119896119903119900

lowast 083 119896119903119900

lowast 083119878119900119903

0267 119878119900119903

0163119878119908119894119903119903

03181 119878119908119894119903119903

03181


high



The 119896119903and 119878






119896119903119900

119899119908

119899119900














Nomenclature










Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





















119903119908

lowast119878119900119903

119896119903119900

lowast



119891119908=

119878119899119908119872119900[1 minus 119873

119900

119892(1 minus 119878)

119899119900 sin (120572)]

119878119899119908119872119900+ (1 minus 119878)

119899119900

(1)


119870119903119900

119870119903119908

= 119886119890minus119887119878119908

(2)


119908of 13 and 119899

119900of 35



119872119900=

119896119900

119903119908120583119900

119896119900

119903119900120583119908

119873119900

119892=

119896119896119900

119903119900Δ120588119892

119906120583119900

(3)





lowast

119903119900is 0203 119896lowast

119903119908

is 0025 119899119900is 35 119899




Injector

Producer

023

083

301

1090

3942

PERM

Z

000000

000000

000000

000800

000800

001600

001600002400 002400

003200

003200

003359

003359005300

004800

003600

002400

001200


10E minus 06

10E minus 05

10E minus 04

10E minus 03

10E minus 02

10E minus 01

10E + 0002 03 04 05 06 07 08

Wat

er an

d oi

l rel

ativ

e

Experimental

perm

eabi

lity

curv

es (K

rw


Kro

Kro

)





11987511988812

= CPC1radic120601

119896

(

119878lowast

119908minus 119878119908

119878lowast

119908minus 119878119908119903

)

EPC1

(4)


11987511988812

= CPC2radic120601

119896

(

119878119908minus 119878lowast

119908


119908

)

EPC2

(5)



119896119903119908

lowast 0025 119899119908

13119896119903119900

lowast 0203 119899119900


CPC119908

2 EPC119908

2CPC119900

minus2 EPC119900

2119878lowast 05



2





000501

01502

02503

03504

04505



(KroK

rw) r

atio

y = 642154739e

R2 = 090

minus3079x


00

02

04

06

08

10

0 01 02 03 04 05 06 07 08



Wat

er fr

actio

nal fl

ow (f

w)







000005010015020025030035040045050


Npd

(PV

)



0

005

01

015

02

025

0 02 04 06 08

Wat

er an

d oi

l rel

ativ

e pe

rmea

bilit

y cu

rves

(Krw

Kro

)


Kro

Krw


minus3

minus2

minus1

0

1

2

3

0 02 04 06 08 1

Capi

llary

pre

ssur

e (ps

i)






0

20

40

60

80

0 2 4 6 8 10

Cum

ulat

ive o

il re

cove

ry (

)




0

5

10

15

20

25

30

Pres

sure

dro

p (p

si)




0

20

40

60

80

100

0 10 20 30 40 50 60

Cum

ulat

ive o

il re

cove

ry (

)

Experimental data


Sor contribution


0102030405060708090

100

Pres

sure

dro

p (p

si)

0 10 20 30 40 50 60

Experimental data


Sor contribution


40

60

116 136 156 176 196

Cum

ulat

ive o

il re

cove

ry (

)

Experimental data




0

005

01

015

02

025

03



S or



0010203040506070809

1

0 02 04 06 08 1

Wat

er an

d oi

l rel

ativ

e pe

rmea

bilit

y cu

rves

(Krw

Kro

)





40

60

80

205 255 305 355

Cum

ulat

ive o

il re

cove

ry (

)




0102030405060708090

100

Pres

sure

dro

p (p

si)




55

75

375 425 475 525 575

Cum

ulat

ive o

il re

cove

ry (

)




Cum

ulat

ive o

il re

cove

ry (

)


0

20

40

60

80

100

0 10 20 30 40 50 60



0

102030405060708090

100

00 100 200 300 400 500 600

Pres

sure

dro

p (p

si)





0010203040506070809

1

02 03 04 05 06 07 08 09 1

Wat

er an

d oi

l rel

ativ

e pe

rmea

bilit

y cu

rves

(Krw

Kro

)


05 06 08 0907





119903and 119878

119900119903



119878119897119903= 119878

high119897119903

+

119878low119897119903

minus 119878high119897119903

1 + 119879119897119873120591

119879119897

for 119897 = 1 119899119901 (6)


low119897119903

of 0267119878high119897119903



119896119900

119903119897= 119896119900low

119903119897+

119878low1198971015840119903minus 1198781198971015840119903

119878low1198971015840119903minus 119878

high1198971015840119903

(119896119900high

119903119897minus 119896119900low

119903119897)

for 119897 1198971015840 = 1 119899119901

119899119897= 119899

low119897

+

119878low1198971015840119903minus 1198781198971015840119903

119878low1198971015840119903minus 119878

high1198971015840119903

(119899high119897

minus 119899low119897

)

for 119897 1198971015840 = 1 119899119901

(7)



Tau (119873119879exponent) 082

119873119879

119878119900119903



119879


119879



17 119899119908

143119899119900

155 119899119900

155119896119903119908

lowast 0024 119896119903119908

lowast 0089119896119903119900

lowast 083 119896119903119900

lowast 083119878119900119903

0267 119878119900119903

0163119878119908119894119903119903

03181 119878119908119894119903119903

03181


high



The 119896119903and 119878






119896119903119900

119899119908

119899119900














Nomenclature










Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Injector

Producer

023

083

301

1090

3942

PERM

Z

000000

000000

000000

000800

000800

001600

001600002400 002400

003200

003200

003359

003359005300

004800

003600

002400

001200


10E minus 06

10E minus 05

10E minus 04

10E minus 03

10E minus 02

10E minus 01

10E + 0002 03 04 05 06 07 08

Wat

er an

d oi

l rel

ativ

e

Experimental

perm

eabi

lity

curv

es (K

rw


Kro

Kro

)





11987511988812

= CPC1radic120601

119896

(

119878lowast

119908minus 119878119908

119878lowast

119908minus 119878119908119903

)

EPC1

(4)


11987511988812

= CPC2radic120601

119896

(

119878119908minus 119878lowast

119908


119908

)

EPC2

(5)



119896119903119908

lowast 0025 119899119908

13119896119903119900

lowast 0203 119899119900


CPC119908

2 EPC119908

2CPC119900

minus2 EPC119900

2119878lowast 05



2





000501

01502

02503

03504

04505



(KroK

rw) r

atio

y = 642154739e

R2 = 090

minus3079x


00

02

04

06

08

10

0 01 02 03 04 05 06 07 08



Wat

er fr

actio

nal fl

ow (f

w)







000005010015020025030035040045050


Npd

(PV

)



0

005

01

015

02

025

0 02 04 06 08

Wat

er an

d oi

l rel

ativ

e pe

rmea

bilit

y cu

rves

(Krw

Kro

)


Kro

Krw


minus3

minus2

minus1

0

1

2

3

0 02 04 06 08 1

Capi

llary

pre

ssur

e (ps

i)






0

20

40

60

80

0 2 4 6 8 10

Cum

ulat

ive o

il re

cove

ry (

)




0

5

10

15

20

25

30

Pres

sure

dro

p (p

si)




0

20

40

60

80

100

0 10 20 30 40 50 60

Cum

ulat

ive o

il re

cove

ry (

)

Experimental data


Sor contribution


0102030405060708090

100

Pres

sure

dro

p (p

si)

0 10 20 30 40 50 60

Experimental data


Sor contribution


40

60

116 136 156 176 196

Cum

ulat

ive o

il re

cove

ry (

)

Experimental data




0

005

01

015

02

025

03



S or



0010203040506070809

1

0 02 04 06 08 1

Wat

er an

d oi

l rel

ativ

e pe

rmea

bilit

y cu

rves

(Krw

Kro

)





40

60

80

205 255 305 355

Cum

ulat

ive o

il re

cove

ry (

)




0102030405060708090

100

Pres

sure

dro

p (p

si)




55

75

375 425 475 525 575

Cum

ulat

ive o

il re

cove

ry (

)




Cum

ulat

ive o

il re

cove

ry (

)


0

20

40

60

80

100

0 10 20 30 40 50 60



0

102030405060708090

100

00 100 200 300 400 500 600

Pres

sure

dro

p (p

si)





0010203040506070809

1

02 03 04 05 06 07 08 09 1

Wat

er an

d oi

l rel

ativ

e pe

rmea

bilit

y cu

rves

(Krw

Kro

)


05 06 08 0907





119903and 119878

119900119903



119878119897119903= 119878

high119897119903

+

119878low119897119903

minus 119878high119897119903

1 + 119879119897119873120591

119879119897

for 119897 = 1 119899119901 (6)


low119897119903

of 0267119878high119897119903



119896119900

119903119897= 119896119900low

119903119897+

119878low1198971015840119903minus 1198781198971015840119903

119878low1198971015840119903minus 119878

high1198971015840119903

(119896119900high

119903119897minus 119896119900low

119903119897)

for 119897 1198971015840 = 1 119899119901

119899119897= 119899

low119897

+

119878low1198971015840119903minus 1198781198971015840119903

119878low1198971015840119903minus 119878

high1198971015840119903

(119899high119897

minus 119899low119897

)

for 119897 1198971015840 = 1 119899119901

(7)



Tau (119873119879exponent) 082

119873119879

119878119900119903



119879


119879



17 119899119908

143119899119900

155 119899119900

155119896119903119908

lowast 0024 119896119903119908

lowast 0089119896119903119900

lowast 083 119896119903119900

lowast 083119878119900119903

0267 119878119900119903

0163119878119908119894119903119903

03181 119878119908119894119903119903

03181


high



The 119896119903and 119878






119896119903119900

119899119908

119899119900














Nomenclature










Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










000501

01502

02503

03504

04505



(KroK

rw) r

atio

y = 642154739e

R2 = 090

minus3079x


00

02

04

06

08

10

0 01 02 03 04 05 06 07 08



Wat

er fr

actio

nal fl

ow (f

w)







000005010015020025030035040045050


Npd

(PV

)



0

005

01

015

02

025

0 02 04 06 08

Wat

er an

d oi

l rel

ativ

e pe

rmea

bilit

y cu

rves

(Krw

Kro

)


Kro

Krw


minus3

minus2

minus1

0

1

2

3

0 02 04 06 08 1

Capi

llary

pre

ssur

e (ps

i)






0

20

40

60

80

0 2 4 6 8 10

Cum

ulat

ive o

il re

cove

ry (

)




0

5

10

15

20

25

30

Pres

sure

dro

p (p

si)




0

20

40

60

80

100

0 10 20 30 40 50 60

Cum

ulat

ive o

il re

cove

ry (

)

Experimental data


Sor contribution


0102030405060708090

100

Pres

sure

dro

p (p

si)

0 10 20 30 40 50 60

Experimental data


Sor contribution


40

60

116 136 156 176 196

Cum

ulat

ive o

il re

cove

ry (

)

Experimental data




0

005

01

015

02

025

03



S or



0010203040506070809

1

0 02 04 06 08 1

Wat

er an

d oi

l rel

ativ

e pe

rmea

bilit

y cu

rves

(Krw

Kro

)





40

60

80

205 255 305 355

Cum

ulat

ive o

il re

cove

ry (

)




0102030405060708090

100

Pres

sure

dro

p (p

si)




55

75

375 425 475 525 575

Cum

ulat

ive o

il re

cove

ry (

)




Cum

ulat

ive o

il re

cove

ry (

)


0

20

40

60

80

100

0 10 20 30 40 50 60



0

102030405060708090

100

00 100 200 300 400 500 600

Pres

sure

dro

p (p

si)





0010203040506070809

1

02 03 04 05 06 07 08 09 1

Wat

er an

d oi

l rel

ativ

e pe

rmea

bilit

y cu

rves

(Krw

Kro

)


05 06 08 0907





119903and 119878

119900119903



119878119897119903= 119878

high119897119903

+

119878low119897119903

minus 119878high119897119903

1 + 119879119897119873120591

119879119897

for 119897 = 1 119899119901 (6)


low119897119903

of 0267119878high119897119903



119896119900

119903119897= 119896119900low

119903119897+

119878low1198971015840119903minus 1198781198971015840119903

119878low1198971015840119903minus 119878

high1198971015840119903

(119896119900high

119903119897minus 119896119900low

119903119897)

for 119897 1198971015840 = 1 119899119901

119899119897= 119899

low119897

+

119878low1198971015840119903minus 1198781198971015840119903

119878low1198971015840119903minus 119878

high1198971015840119903

(119899high119897

minus 119899low119897

)

for 119897 1198971015840 = 1 119899119901

(7)



Tau (119873119879exponent) 082

119873119879

119878119900119903



119879


119879



17 119899119908

143119899119900

155 119899119900

155119896119903119908

lowast 0024 119896119903119908

lowast 0089119896119903119900

lowast 083 119896119903119900

lowast 083119878119900119903

0267 119878119900119903

0163119878119908119894119903119903

03181 119878119908119894119903119903

03181


high



The 119896119903and 119878






119896119903119900

119899119908

119899119900














Nomenclature










Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

20

40

60

80

0 2 4 6 8 10

Cum

ulat

ive o

il re

cove

ry (

)




0

5

10

15

20

25

30

Pres

sure

dro

p (p

si)




0

20

40

60

80

100

0 10 20 30 40 50 60

Cum

ulat

ive o

il re

cove

ry (

)

Experimental data


Sor contribution


0102030405060708090

100

Pres

sure

dro

p (p

si)

0 10 20 30 40 50 60

Experimental data


Sor contribution


40

60

116 136 156 176 196

Cum

ulat

ive o

il re

cove

ry (

)

Experimental data




0

005

01

015

02

025

03



S or



0010203040506070809

1

0 02 04 06 08 1

Wat

er an

d oi

l rel

ativ

e pe

rmea

bilit

y cu

rves

(Krw

Kro

)





40

60

80

205 255 305 355

Cum

ulat

ive o

il re

cove

ry (

)




0102030405060708090

100

Pres

sure

dro

p (p

si)




55

75

375 425 475 525 575

Cum

ulat

ive o

il re

cove

ry (

)




Cum

ulat

ive o

il re

cove

ry (

)


0

20

40

60

80

100

0 10 20 30 40 50 60



0

102030405060708090

100

00 100 200 300 400 500 600

Pres

sure

dro

p (p

si)





0010203040506070809

1

02 03 04 05 06 07 08 09 1

Wat

er an

d oi

l rel

ativ

e pe

rmea

bilit

y cu

rves

(Krw

Kro

)


05 06 08 0907





119903and 119878

119900119903



119878119897119903= 119878

high119897119903

+

119878low119897119903

minus 119878high119897119903

1 + 119879119897119873120591

119879119897

for 119897 = 1 119899119901 (6)


low119897119903

of 0267119878high119897119903



119896119900

119903119897= 119896119900low

119903119897+

119878low1198971015840119903minus 1198781198971015840119903

119878low1198971015840119903minus 119878

high1198971015840119903

(119896119900high

119903119897minus 119896119900low

119903119897)

for 119897 1198971015840 = 1 119899119901

119899119897= 119899

low119897

+

119878low1198971015840119903minus 1198781198971015840119903

119878low1198971015840119903minus 119878

high1198971015840119903

(119899high119897

minus 119899low119897

)

for 119897 1198971015840 = 1 119899119901

(7)



Tau (119873119879exponent) 082

119873119879

119878119900119903



119879


119879



17 119899119908

143119899119900

155 119899119900

155119896119903119908

lowast 0024 119896119903119908

lowast 0089119896119903119900

lowast 083 119896119903119900

lowast 083119878119900119903

0267 119878119900119903

0163119878119908119894119903119903

03181 119878119908119894119903119903

03181


high



The 119896119903and 119878






119896119903119900

119899119908

119899119900














Nomenclature










Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0010203040506070809

1

0 02 04 06 08 1

Wat

er an

d oi

l rel

ativ

e pe

rmea

bilit

y cu

rves

(Krw

Kro

)





40

60

80

205 255 305 355

Cum

ulat

ive o

il re

cove

ry (

)




0102030405060708090

100

Pres

sure

dro

p (p

si)




55

75

375 425 475 525 575

Cum

ulat

ive o

il re

cove

ry (

)




Cum

ulat

ive o

il re

cove

ry (

)


0

20

40

60

80

100

0 10 20 30 40 50 60



0

102030405060708090

100

00 100 200 300 400 500 600

Pres

sure

dro

p (p

si)





0010203040506070809

1

02 03 04 05 06 07 08 09 1

Wat

er an

d oi

l rel

ativ

e pe

rmea

bilit

y cu

rves

(Krw

Kro

)


05 06 08 0907





119903and 119878

119900119903



119878119897119903= 119878

high119897119903

+

119878low119897119903

minus 119878high119897119903

1 + 119879119897119873120591

119879119897

for 119897 = 1 119899119901 (6)


low119897119903

of 0267119878high119897119903



119896119900

119903119897= 119896119900low

119903119897+

119878low1198971015840119903minus 1198781198971015840119903

119878low1198971015840119903minus 119878

high1198971015840119903

(119896119900high

119903119897minus 119896119900low

119903119897)

for 119897 1198971015840 = 1 119899119901

119899119897= 119899

low119897

+

119878low1198971015840119903minus 1198781198971015840119903

119878low1198971015840119903minus 119878

high1198971015840119903

(119899high119897

minus 119899low119897

)

for 119897 1198971015840 = 1 119899119901

(7)



Tau (119873119879exponent) 082

119873119879

119878119900119903



119879


119879



17 119899119908

143119899119900

155 119899119900

155119896119903119908

lowast 0024 119896119903119908

lowast 0089119896119903119900

lowast 083 119896119903119900

lowast 083119878119900119903

0267 119878119900119903

0163119878119908119894119903119903

03181 119878119908119894119903119903

03181


high



The 119896119903and 119878






119896119903119900

119899119908

119899119900














Nomenclature










Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0010203040506070809

1

02 03 04 05 06 07 08 09 1

Wat

er an

d oi

l rel

ativ

e pe

rmea

bilit

y cu

rves

(Krw

Kro

)


05 06 08 0907





119903and 119878

119900119903



119878119897119903= 119878

high119897119903

+

119878low119897119903

minus 119878high119897119903

1 + 119879119897119873120591

119879119897

for 119897 = 1 119899119901 (6)


low119897119903

of 0267119878high119897119903



119896119900

119903119897= 119896119900low

119903119897+

119878low1198971015840119903minus 1198781198971015840119903

119878low1198971015840119903minus 119878

high1198971015840119903

(119896119900high

119903119897minus 119896119900low

119903119897)

for 119897 1198971015840 = 1 119899119901

119899119897= 119899

low119897

+

119878low1198971015840119903minus 1198781198971015840119903

119878low1198971015840119903minus 119878

high1198971015840119903

(119899high119897

minus 119899low119897

)

for 119897 1198971015840 = 1 119899119901

(7)



Tau (119873119879exponent) 082

119873119879

119878119900119903



119879


119879



17 119899119908

143119899119900

155 119899119900

155119896119903119908

lowast 0024 119896119903119908

lowast 0089119896119903119900

lowast 083 119896119903119900

lowast 083119878119900119903

0267 119878119900119903

0163119878119908119894119903119903

03181 119878119908119894119903119903

03181


high



The 119896119903and 119878






119896119903119900

119899119908

119899119900














Nomenclature










Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119896119903119900

119899119908

119899119900














Nomenclature










Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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