Fuel 119 (2014) 111–119

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Fuel

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Parametric study to develop an empirical correlation for undersaturatedcrude oil viscosity based on the minimum measured input parameters

0016-2361/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.fuel.2013.11.044

⇑ Corresponding author. Tel.: +968 24142558; fax: +968 24141354.E-mail address: farouqsm@yahoo.com (F.S. Mjalli).

Majda Al-Balushi, Farouq S. Mjalli ⇑, Talal Al-Wahaibi, Yahya Al-Wahaibi, Abdul Aziz Al-HashmiDepartment of Petroleum and Chemical Engineering, Sultan Qaboos University, P.O.Box 33, Al-Khoud, P.C. 123, Oman

h i g h l i g h t s

� Published correlations forundersaturated oil viscosity wereevaluated and compared.� A new correlation was developed for

the bubble point oil viscosity.� The developed undersaturated oil

viscosity correlation outperformedpublished models.

g r a p h i c a l a b s t r a c t

a r t i c l e i n f o

Article history:Received 15 September 2013Received in revised form 13 November 2013Accepted 18 November 2013Available online 2 December 2013

Keywords:ViscosityBubble point pressureUndersaturatedOmani crude oil

a b s t r a c t

In this study, the correlations published in the literature for predicting undersaturated oil viscosity datahave been evaluated based on field-measured data collected from PVT reports for different Omani fields.It was found that most of these correlations provide good prediction for undersaturated Omani crude oilviscosity with Bergman and Sutton [1] being the best. Then, evaluation analysis was carried out usingboth calculated bubble point pressure and bubble point oil viscosity data and adopting publishedcorrelations for these two parameters. It was found that the calculated bubble point pressure have insig-nificant effect on the predicted viscosity; therefore it was indicated that the correlations published byStanding [2] and Al-Shammasi [3] can be used to predict bubble point pressure in case of lack of thesedata. On the other hand, the calculated bubble point oil viscosity was found to have a significant effecton the calculated undersaturated oil viscosity. Therefore, a new correlation for this parameter wasdeveloped by applying the genetic algorithm optimization methodology on the collected experimentaldata. The validation test indicated that the correlation developed in this study for bubble point oilviscosity outperformed all the correlations available in the literature. Hossain et al. [4] correlation provedto have the best prediction for the undersaturated oil viscosity, while the Standing [2] correlation is rec-ommended for predicting the bubble point pressure. On the other hand, the newly developed correlationgave the best performance for predicting the bubble point oil viscosity.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction determines how easily the fluid can flow through the porous med-

Viscosity is defined as a measure of fluid resistance to flow. It isone of the important fluid properties in oil industry since it

ia. It is important to be predicted at the initial stages of well devel-opment since it plays an important role in well test interpretation,well problem analysis, determination of oil reserves, design of sur-face and subsurface facilities, etc.

Oil samples from new wells are usually sent for experimentalPVT analysis from which detailed compositional and PVT

Table 1The published undersaturated oil viscosity correlations.

Authors Samples origin No. of datapoints used

Correlation

Kouzel [7] Worldwide 3593 lo ¼ lobe 5:50318�10�5þ3:77163�10�5l0:278obð Þðp�pbÞ½ �

Standing [8] United States 52 lo ¼ lob þ 0:001ðp� pbÞð0:024:l1:6ob þ 0:038l0:56

ob ÞVazquez and Beggs

[9]Worldwide 600 PVT reports lo ¼ lobðp=pbÞ

E

E ¼ 2:6:p1:187 expð�11:513� 8:98� 10�5:pÞKhan et al. [10] Saudi Arabia 75 bottom hole

sampleslo ¼ lobe9:6�10�5ðp�pbÞ

Al-Khafaji et al. [11] Middle East 300 oil samples lo ¼ lob þ 10F

F ¼ �0:3806� ð0:1845� APIÞ þ ð0:004034� API2Þ�ð3:716� 10�5 � API3Þ þ 1:11 logðp� pbÞ

Abdul-Majeed et al.[12]

North Africa and Middle East 253 lo ¼ lob þ 10G

G ¼ 1:9311� 0:89941 lnð5:614RsbÞ � ð0:001194API2Þþ9:2545� 10�3API lnð5:614RsbÞ�5:2106þ 1:11 logðp� pbÞ

Kartoat-modjo andSchmidt [13]

Southeast Asia, North America,Middle East and Latin America

3588 lo ¼ 1:00081lob þ 0:001127ðp� pbÞ � 0:006517l1:8148ob þ 0:038l1:590

ob Þ

Labedi [14] Libya 91lo ¼ lob � 1� p

pb

� �10�2:488l0:9036

odp0:6151

b

100:01976:API

� �� �

De Ghetto et al. [15] Mediterranean Basin, Africa, ArabianGulf and North Sea

3700Extra heavy oil: lo ¼ lob � 1� p

pb

� �10�2:19l1:055

od :p0:3132b

100:0099:API

� �� �Heavy oil: lo ¼ 0:9886:lob þ 0:002763ðp� pbÞð�0:01153:l1:7933

ob þ 0:0316:l1:5939ob Þ

Medium oil: lo ¼ lob � 1� ppb

� �10�3:8055l1:4131

od :p0:6957b

10�0:00288API

� �� �Entire oil samples: lo ¼ lob � 1� p

pb

� �10�1:9l0:7423

od :p0:5026b

100:0243:API

� �� �

Pertosky and Farshad[16]

Gulf of Mexico 126 PVT reports lo ¼ lob þ 1:3449� 10�3ðp� pbÞ:10K

K ¼ �1:0146þ 1:3322 logðlobÞ � 0:4876 log ðlobÞ2 � 1:15036 log ðlobÞ

3

Almehaideb [17] United Arab Emirates 15 Reservoirs lo ¼ lobppb

� �L

L ¼ 0:134819þ 1:94345� 10�4:Rsb � 1:93106� 10�9:R2sb

Elsharkawy andAlikha [18]

Middle East 254 Oil samples lo ¼ lob þ 10�2:0771ðp� pbÞðl1:19279od :l�0:40712

ob :p�0:7941b Þ

Elsharkawy andGharbi [19]

Kuwait 805 lo ¼ lob þMðp� pbÞM ¼ ð�5612þ 9481:lod � 1459:l2

od þ 81:l3odÞ:10�8

Dindoruk andChristman [20]

Gulf of Mexico More than 100PVT reports

lo ¼ lob þ 6:334� 10�5ðp� pbÞ:10O

O ¼ 0:776644115þ 0:987658646 logðlobÞ � 0:190564677 logðRsbÞþ9:147711� 10�3:lob logðRsbÞ � 1:9111� 10�5ðp� pbÞ

Kulchanya-vivat [21] Worldwide 1968 lo ¼ lobqoqob

� �aqob tr ¼ �61:5246 ln q3

ob þ 709:6163 ln q2ob � 2717:621 ln qob þ 3455:599pb tr ¼ 0:0365 ln p2

b � 0:29579 ln pb þ 0:19966ztr

¼ qob tr þ pb tra ¼ eð0:12572:z3trþ0:04923:z2

trþ0:7801�ztrþ2:3724Þ

Hossain et al. [4] Worldwide 390 lo ¼ lob þ 0:004481ðp� pbÞð0:555955l1:068099ob � 0:527737l1:063547

ob ÞBergman and Sutton

[1]Worldwide 10,248 lo ¼ lobeaðp�pbÞb

a ¼ 6:5698� 10�7 ln ðlobÞ2 � 1:48211� 10�5 lnðlobÞ þ 2:27877� 10�4

b ¼ 2:24623� 10�2 lnðlobÞ þ 0:873204Isehunwa et al. [22] Niger Delta More than 400

oil reservoirslo ¼ lobe1:02�10�4ðp�pbÞ

112M

.Al-Balushi

etal./Fuel

119(2014)

111–119

M. Al-Balushi et al. / Fuel 119 (2014) 111–119 113

properties are reported to the operators. However, this is both timeconsuming and cost-intensive. In addition they are dependent onthe availability of the samples which are not always available,especially from exploration wells. Presently, oil companies usethe tuning of validated EOS in their calculations and simulationpackages [5]. These equations require compositional analysis fromPVT reports [6], which makes them redundant since the idea is toavoid this costly requirement. Therefore, the idea of finding empir-ical correlations that depend on the other handy oil propertiescame through many decades ago.

Crude oil viscosity has been categorized based on its pressureinto:

– Undersaturated oil viscosity: Crude oil viscosity above bubblepoint pressure.

– Bubble point oil viscosity: Crude oil viscosity at the bubblepoint pressure.

– Saturated oil viscosity: Crude oil viscosity below bubble pointpressure.

– Dead oil viscosity: Crude oil viscosity at the atmospheric pres-sure for a given temperature.

Many studies have been conducted for different regions todevelop specific correlations to predict oil viscosities at differentconditions based on the data collected for those specific locations.Due to their merit, empirical correlations best predict the oils withsimilar composition (i.e. paraffinic, naphthenic, and/or aromatic),which depends on the oils geochemical origins. Hence, some corre-lations can satisfactorily predict some oils but fail to predict others.

Table 2The published bubble point oil viscosity correlations.

Authors Samples origin No. of da

Khan et al. [10] Saudi Arabia 75 Sampl

Labedi [14] Libya 91

Hanafy et al. [23] Egypt 324 Samp

Naseri et al. [24] Iran 250

Isehunwa et al. [22] Niger Delta More tha

Table 3The published bubble point pressure correlations.

Authors Samples origin No. of data points

Standing [2] California 105

Glaso [25] North Sea 41

Al-Marhoun [26] Middle East 160

Petrosky and Frashad [27] Gulf of Mexico 81 PVT Reports

Al-Shammasi [3] Worldwide 1243

Bolon-darzadeh et al. [28] Iran 166

Ikiensiki-mama and Ogboja [29] Niger Delta 250

This study focuses on predicting the undersaturated oil viscosity ofOmani crude oil. Table 1 shows a summary of the correlationsavailable in the literature. It is obvious that these correlations arefunctions of bubble point oil viscosity and bubble point pressure.Correlations that predict the bubble point oil viscosity and bubblepoint pressure are also available in the literature and can be usedinstead of the measured ones as input parameters. This is very vitalespecially when these data are not available. Tables 2 and 3 pro-vide a summary of the correlations developed to predict the bubblepoint oil viscosity and bubble point pressure respectively.

In this work, a parametric study is conducted to assess theperformance of the undersaturated oil viscosity, bubble point oilviscosity and bubble point pressure correlations in predicting theoil properties of Omani crude oil. The results of this parametricstudy are used to suggest a robust methodology which predictsthe viscosity of Omani crude oil based on the minimum measuredinput parameters.

2. Reservoir fluid property database

In this study the data were collected from the PVT reports pro-vided by PDO (Petroleum Development Oman). A total of 118 PVTreports with 1093 data points have been used in this study. Amongthese, 92 PVT reports with ranges of different properties presentedin Table 4 were used to evaluate the existing correlations and de-velop new correlations if necessary. The remaining 26 reports withsimilar ranges for different properties were used to validate thesecorrelations.

ta points used Correlation

es lob ¼0:09

ffiffiffifficgp

ffiffiffiffiffiRsb

3p

Tþ459:67459:67ð Þ4:5ð1�coÞ

3

lob ¼ 102:344�0:03542API� �

l0:6447od

p0:426b

les lob ¼ eð7:296q3ob�3:095Þ

lob ¼ 101:1145 :p�0:4956b :l0:9961

od

n 400 Oil Reservoirs lob ¼ eBR�0:38sb T þ 459:7ð Þ�4:34

B ¼ 27:07� 17:51 � co þ 8:56:ec2o

used Correlation

pb ¼ 18:2 Rsbcg

� �0:8310ð0:00091:T�0:0125:APIÞ

� �

pb ¼ 101:7669þ1:7447: log X�0:30218:ðlog XÞ2

X ¼ Rsbcg

� �0:816T0:172

API0:989

� �

pb ¼5:38088x10�3 :R0:715082

sb c3:1437o ðTþ459:67Þ1:32657

c1:87784g

pb ¼ 112:727 R0:577421sbc0:8439

g:10X � 12:34

� �

Rsb ¼ pb112:727þ 12:34

c0:8439g :10�X

h i1:73184

X ¼ 4:561� 10�5:T1:3911 � 7:916� 10�4API1:541

pb ¼c5:527215

o ½cg RsbðTþ459:67Þ�0:783716

eð1:841408:co :cg Þ

pb ¼ 27:16 3:4394:R0:57102sb

0:56807:c0:922092g

� �3:7387:T0:2304

6:27605:API0:42469

� �� 30:28

� �

S ¼ 47:57094772� 0:677706662:API½ �1:530935619

Q ¼Rsb

336:0064009

ð Rsb336:0064009Þþð6:7063984:co

S Þ

p�b ¼ 0:243181338� 2:316548789:Q þ 10:60657909:Q1:518030465

pb ¼p�

b:ðTþ635:4152349Þ

cg

Table 4Range of data used for evaluation of the existing correlations and predicting a new correlation for bubble point oil viscosity (92 PVT reports, 936 data points).

Reservoir parameters Symbol Minimum Median Mean Maximum

Reservoir pressure (psia) p 115 4515 4693 16,684Undersaturated oil viscosity (cP) lo 0.16 1.23 81.39 6200.00Bubble point pressure (psia) pb 75 2016 2468 6577Bubble point oil viscosity (cP) lob 0.16 1.04 51.15 2380.00Dead oil viscosity (cP) lod 0.56 4.08 90.28 4800.00Bubble point solution gas-oil ratio (scf/STB) Rsb 5 522 770 2964Reservoir temperature (�F) T 106 174 170 275Reservoir oil density (Ib/ft3) qo 29.8 47.5 47.0 59.6Bubble point oil density (Ib/ft3) qob 29.5 46.8 45.9 58.6Stock-tank oil gravity (�API) API 14.9 33.2 33.0 49.8Oil specific gravity co 0.780 0.859 0.863 0.967Gas specific gravity cg 0.593 0.854 0.866 1.274Relative volume (Vt/Vb)F 0.852 0.985 0.975 1.000

Table 5Statistical analysis of the published undersaturated oil viscosity correlations based on the range of data used in this study.

Published correlations Predicted undersaturated oil viscosity

ARE% AARE% SD% t-test p-value

Bergman and Sutton [1] �0.91 5.10 8.42 0.32Kouzel [7] 3.32 6.50 12.57 0.29Hossain et al. [4] 4.37 7.02 10.61 0.38Almehaideb [17] �1.78 7.31 11.54 0.18Standing [8] 2.26 8.39 26.07 0.07De Ghetto et al. [15] �0.01 8.92 14.73 0.07Kartoatmodjo and Schmidt [13] �6.76 8.97 12.15 0.28Elsharkawy and Alikhan [18] �2.74 9.00 14.38 0.06Khan et al. [10] 1.69 9.24 16.71 0.09Labedi [14] 2.48 9.58 16.17 0.16Isehunwa et al. [22] 3.19 10.17 18.37 0.10Vasquez and Beggs [9] 7.71 11.11 18.63 0.45Abdul Majeed et al. [12] �17.56 17.56 22.36 0.02Kulchanyavivat [21] �17.56 17.56 22.36 0.02Al-Khafaji et al. [11] 155.98 164.85 293.95 0.04Petrosky and Farshad [16] 426.11 443.99 1105.85 0.03Elsharkawy and Gharbi [19] 32517.83 32519.73 389008.07 0.02Dindoruk and Christman [20] 5.46 � 1028 5.46 � 1028 7.45 � 1029 0.02

Table 6Statistical Analysis of the published undersaturated oil viscosity correlations based on author defined oil viscosity ranges.

Published correlations Predicted undersaturated oil viscosity Range of oil viscosity

ARE% AARE% SD% t-test p-value (cP)

Bergman and Sutton [1] �0.91 5.10 8.42 0.32 0.067–24,180Kouzel [7] 3.58 5.91 11.00 0.41 1.78–202Hossain et al. [4] 4.86 6.88 10.39 0.37 3–517Almehaideb [17] NA NA NA NA NAStanding [8] �0.69 5.71 9.28 0.22 0.16–315De Ghetto et al. [15] 1.16 8.13 13.55 0.09 0.13–354.6Kartoatmodjo and Schmidt [13] �6.61 8.49 11.78 0.38 0.168–517.03Elsharkawy and Alikhan [18] 2.69 5.85 9.65 0.46 0.2–5.7Khan et al. [10] 5.54 7.53 15.38 0.36 0.13–71.0Labedi [14] NA NA NA NA NAIsehunwa et al. [22] 7.70 8.75 17.80 0.49 0.08–43.00Vasquez and Beggs [9] 8.62 10.69 18.13 0.42 0.117–148Abdul Majeed et al. [12] �15.62 15.62 19.63 0.01 0.096–28.5Kulchanyavivat [21] �17.06 17.06 21.33 0.01 0.167–279.83Al-Khafaji et al. [11] 241.29 214.29 352.39 0.00 0.096–7.139Petrosky and Farshad [16] 606.85 612.33 1308.19 0.00 0.22–4.09Elsharkawy and Gharbi [19] NA NA NA NA NADindoruk and Christman [20] 2.44 4.36 6.15 0.30 0.211–10.6

114 M. Al-Balushi et al. / Fuel 119 (2014) 111–119

3. Evaluation of the existing correlations with the field-measured data

The accuracy of the available correlations in the literature forundersaturated oil viscosity was evaluated using both statistical

and graphical methods. The statistical method involved the follow-ing four statistical indicators:

The average relative error, which determines how incorrect a cal-culated quantity is in comparison to a measured data, it representsthe bias of the calculated results and it is calculated by the followingequation:

Fig. 1. Graphical interpretation of calculated versus measured undersaturated oil viscosity data.

M. Al-Balushi et al. / Fuel 119 (2014) 111–119 115

116 M. Al-Balushi et al. / Fuel 119 (2014) 111–119

ARE ¼ 100N

XN

i¼1

xcalc � xmeas

xmeasð1Þ

The average absolute relative error, which determines the dif-ferences in the magnitude between the measured and the calcu-lated data. The lower the value of the average absolute relativeerror is the better the results are. It is calculated by the followingequation:

AARE ¼ 100N

XN

i¼1

xcalc � xmeas

xmeas

�������� ð2Þ

The standard deviation, which represents the deviation of thecalculated values from the average value and it is calculated bythe following equation:

Table 7Performance of the published bubble point oil viscosity correlations based on therange of bubble point oil viscosity data covered in this study.

Bubble point oil viscositycorrelations

Predicted bubble point oil viscosity

ARE% AARE% SD% t-testp-value

Naseri et al. [24] 13.04 26.53 35.72 0.05Hanafy et al. [23] �32.08 36.99 48.11 0.00Khan et al. [10] �20.71 41.07 54.98 0.00Labedi [14] 17.52 42.49 63.76 0.13Isehunwa et al. [22] �43.57 48.15 54.70 0.00

Table 8Performance of the published bubble point oil viscosity correlations based on therange of data used by different authors.

Publishedcorrelations

Predicted bubble point oil viscosity Range of bubblepoint oil viscosity

ARE% AARE% SD% t-test p-value (cP)

Naseri et al. [24] 7.61 24.52 34.09 0.35 0.11–18.15Hanafy et al. [23] �18.69 24.69 30.45 0.00 0.119–34.9Khan et al. [10] �7.50 33.01 48.90 0.46 0.13–17.9Isehunwa et al. [22] �30.28 36.30 39.56 0.01 0.03–9.1Labedi [14] 21.46 49.55 72.18 0.01 0.11–3.7

Table 9Performance of the published bubble point pressure correlations based on the range of bu

Published correlations Predicted bubble point press

ARE%

Standing [2] �4.21Al-Shammasi [3] �2.11Glaso [25] 0.40Al-Marhoun [26] 1.96Bolondarzadeh et al. [28] �55.19Pertosky and Farshad [27] 96.73Ikiensikimama and Ogboja [29] 547.93

Table 10Performance of the published bubble point pressure correlations based on the range of da

Published correlations Predicted bubble point pressure

ARE% AARE%

Standing [2] �4.08 13.59Al-Shammasi [3] �2.11 13.69Glaso [25] 5.74 16.17Al-Marhoun [26] 1.29 20.00Bolondarzadeh et al. [28] �40.62 48.63Pertosky and Farshad [27] 45.52 45.52Ikiensikimama and Ogboja [29] 547.93 547.93

SD ¼ 100

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

N � 1

XN

i¼1

xcalc � xmeas

xmeas

� �2vuut ð3Þ

where xcalc and xmeas are the calculated and measured reservoirparameters respectively, and N is the total number of data pointsin the database.

The significance t-test of null hypothesis is also performed forthe studied predicted data as compared to the experimental ones.The calculated p-value, represents the probability of obtaining thetest statistics at least as extreme as the one actually observed.When the p-value is smaller than the significance level (0.05 in thiscase) we reject the null hypothesis as being false and accept ouralternative hypothesis. In other words, a p-value of less than 0.05indicates significant difference between the reference experimen-tal measurements and the correlation predicted ones.

In addition to these statistical indicators, graphical interpreta-tions were used which display the results in visual format in a scat-ter plot form. In graphical error analysis procedure the calculateddata were plotted against the measured data. Then the 45� trendline was imposed on the figure to determine the accuracy betweenthe measured and the calculated data. In this case, the closer thepoints are to the 45� line the better the results are.

The results of the statistical evaluation tests are presented inTable 5 using the range of undersaturated oil viscosity covered inthis study and in Table 6 using the database created for Omanicrude oil with author defined range for oil viscosity. In addition,Fig. 1 represents the graphical interpretation for the publishedcorrelations.

The results of the statistical evaluation tests indicate thatalthough all of the literature available correlations for predictingundersaturated oil viscosity have been developed for data from dif-ferent regions with different ranges, most of them can predict theundersaturated Omani crude oil viscosity with an AARE of less than10% and a t-test p-value greater than 0.05. The best three of theseavailable correlations are those published by Bergman and Sutton[1], Kouzel [7] and Hossain et al. [4]. Also the graphical interpreta-tions show that most of the correlations are applicable for Omanicrude oil except the lower four correlations [11,19,20,16] which

bble point pressure data covered in this study.

ure

AARE% SD% t-test p-value

13.58 17.19 0.2413.69 17.23 0.0819.85 26.50 0.0322.02 31.99 0.0162.36 156.69 0.0596.73 130.95 0.00

547.93 888.20 0.00

ta defined by different authors.

Range of bubble point pressure

SD% t-test p-value Psia

17.18 0.24 130–700017.22 0.08 31.7–712719.91 0.03 150–664129.36 0.09 130–3573

117.30 0.12 100–530050.16 0.00 1574–6523

888.20 0.00 67–6560

Table 11Performance of the best undersaturated oil viscosity correlations with the calculatedbubble point pressure data.

Undersaturated oil viscosity Bubble point pressure (AARE%)

Standing [2] Al-Shammasi [3]

Kouzel [7] 8.08 8.12Hossain et al. [4]] 8.98 8.98Bergman and Sutton [1] – –

Table 12Performance of the best undersaturated oil viscosity correlations with the calculatedbubble point oil viscosity.

Undersaturated oilviscosity

Bubble point oil viscosity (AARE%)

Naseriet al. [24]

Hanafyet al. [23]

Khanet al. [10]

Labedi[14]

Isehunwaet al. [22]

Bergman and Sutton [1] 25.44 36.98 41.71 45.02 48.09Hossain et al. [4] 28.12 35.80 41.70 48.56 46.46Kouzel [7] 29.07 36.25 41.56 47.04 47.02

Table 13Performance of the undersaturated oil viscosity correlations with the calculatedbubble point oil viscosity by the proposed correlation.

Undersaturated oil viscosity Proposed bubble point oil viscosity correlation

ARE% AARE% SD% t-test p-value

Bergman and Sutton [1] �1.13 15.62 22.58 0.42Hossain et al. [4] 4.02 16.46 23.99 0.46Kouzel [7] 2.95 16.67 25.53 0.24

Table 14Validation test of bubble point oil viscosity correlations.

Bubble point oilviscosity correlations

Predicted bubble point oil viscosity

ARE% AARE% SD% t-test p-value

This work �5.54 16.00 20.83 0.44Labedi [14] 0.01 26.35 33.54 0.10Naseri et al. [24] 16.47 34.77 46.58 0.16Khan et al. [10] �39.61 41.11 48.53 0.00Isehunwa et al. [22] �46.27 48.04 63.34 0.00Hanafy et al. [23] �46.27 48.04 59.56 0.00

M. Al-Balushi et al. / Fuel 119 (2014) 111–119 117

cannot predict high viscosity data since they were developed forlow viscous oils (see Tables 5 and 6).

Due to that, it was concluded that the available correlations asstated above can give good predictions for undersaturated Omanicrude oil viscosity. Hence, there was no need to develop a new cor-relation for this property. However, it was found that all of the cor-relations depend on bubble point pressure and bubble point oilviscosity. Therefore, the next step in this study was to evaluatethe published correlations for these two parameters using thesame database. This is a very important step to investigate theeffect of these two calculated parameters on the prediction of

Table 15Validation test of undersaturated oil viscosity correlations with calculated bubble point o

Undersaturated oil viscosity Bubble point oil viscosity (AARE%)

This work Labedi [14] Naseri et al.

Bergman and Sutton [1] 16.96 27.12 33.28Hossain et al. [4] 16.90 29.04 34.68Kouzel [7] 19.22 27.28 39.35

undersaturated oil viscosity. The results of this evaluation testare presented in Tables 7–10.

The previous tables indicate that the errors from the publishedcorrelations for bubble point oil viscosity are quite high since theywere developed based on low ranges of oil viscosity as shown inTable 8 and it can be seen that the best correlation available inthe literature for bubble point oil viscosity is that predicted byNaseri et al. [24]. On the other hand, for bubble point pressurethe best correlations are those predicted by Standing [2] andAl-Shammasi [3] and it can be recognized that these twocorrelations have similar errors for different ranges of bubble pointpressure. Consequently, it can be concluded that using thepublished correlations for ranges other than those used by theauthors (to develop their correlations specially those for bubblepoint oil viscosity) affect the AARE values resulted from differentcorrelations which in turn affect the calculated undersaturatedoil viscosity values as shown in the next section.

4. Evaluation of the existing undersaturated oil viscositycorrelations with the calculated data

The published correlations for undersaturated oil viscosity wereevaluated using the calculated bubble point pressure and bubblepoint oil viscosity to verify the accuracy of the available correla-tions in the absence of these data. The evaluation results will alsobe used to determine the best correlation which predicts the miss-ing oil property as well as to determine the most effective param-eter for predicting undersaturated oil viscosity.

4.1. Using the calculated bubble point pressure

First, the evaluation test was carried out with the calculatedbubble point pressure using the two best correlations for bubblepoint pressure on the three best correlations for undersaturatedoil viscosity. The results of the performance test provided in Ta-ble 11 (in terms of the AARE values) indicate that the calculatedbubble point pressure data have insignificant effect on the calcu-lated undersaturated oil viscosity data. In addition, it can be no-ticed that Bergman and Sutton [1] correlation although was thebest when used with the measured data, does not work with calcu-lated bubble point pressure which resulted in negative pressuredifferentials (pressure minus bubble point pressure).

It can be concluded from Table 11 that in the absence of bubblepoint pressure data, Standing [2] and Al-Shammasi [3] correlationsgave the best prediction when used with the undersaturated oilviscosity correlations of Hossain et al. [4] and Kouzel [7].

4.2. Using the calculated bubble point oil viscosity

The accuracy of the published undersaturated oil viscositycorrelations was then evaluated using the calculated bubble pointoil viscosity. The results for this performance test are presented inTable 12 from which the high dependency of undersaturated oilviscosity on the bubble point oil viscosity is clear from the highAARE values.

il viscosity.

[24] Khan et al. [10] Hanafy et al. [23] Isehunwa et al. [22]

39.94 47.98 57.1638.49 47.23 55.7939.21 47.84 56.76

Table 16Validation test of undersaturated oil viscosity correlations with calculated bubblepoint pressure.

Undersaturated oil viscosity Bubble point pressure (AARE%)

Standing [2] Al-Shammasi [3]

Bergman and Sutton [1] – –Hossain et al. [4] 6.57 6.94Kouzel [7] 7.12 7.41

Table 17Validation test of undersaturated oil viscosity correlations with calculated bubblepoint oil viscosity and bubble point pressure.

Undersaturated oil viscosity Bubble point pressure and oil viscosity(AARE%)

This work (lob) Labedi (lob) [14]Standing (pb) [2] Standing (pb) [2]

Bergman and Sutton [1] – –Hossain et al. [4] 17.55 29.30Kouzel [7] 19.29 27.16

118 M. Al-Balushi et al. / Fuel 119 (2014) 111–119

Since all of the available correlations for predicting bubble pointoil viscosity give high errors when used to predict the undersatu-rated oil viscosity data. Therefore it is vital to develop a new corre-lation for predicting bubble point oil viscosity with higheraccuracy. The development of the new bubble point oil viscositycorrelation for Omani crude oil is discussed in the next section.

5. Development of the new correlation for bubble point oilviscosity

In order to develop a new correlation for bubble point oil viscos-ity the genetic optimization algorithm (GA) was used. It is one ofthe best optimization algorithms used for modeling multivariatedata due to its independency on the initial conditions and its abil-ity of avoiding local optima. The details of this algorithm can befound in specialized optimization literature [30–32]. Using thisalgorithm, the following correlation was developed for this studyin terms of the field-measured properties with AARE of 14.06%,ARE of (�0.30%), SD of 21.25% and t-test p-value of 0.39:

lob ¼ e T0:12417ð Þ � R�0:35965sb

� �� lðqob=62:43Þ2:40826

od

� �� 0:27217 ð4Þ

The calculated bubble point oil viscosity data by the proposedcorrelation given by Eq. (4) reduced the AARE values of the calcu-lated undersaturated oil viscosity data as shown in Table 13.

It is clear from the Table 13 that the correlation developed inthis study outperforms all the published correlations for bubblepoint oil viscosity and it improves the performance of all the pub-lished correlations for undersaturated oil viscosity.

6. Validation tests of the correlations

The accuracy of the published correlations as well as the corre-lation proposed in this study for bubble point oil viscosity was val-idated using another set of data. The results of the validation testare presented in Table 14.

It is clear from Table 14 that the correlation proposed in thisstudy for bubble point oil viscosity outperforms all the publishedcorrelations in the literature. In addition, out of the compared pub-lished correlations, it can be observed that for this set of data thebest correlation is that provided by Labedi [14] where the best cor-relation with the previous set of data was that of Naseri et al. [24].Whereas in both cases the correlation developed in this study hasbetter performance compared to all published correlations which

proves the effectiveness of the developed correlation over theavailable ones.

Finally, the calculated data using different correlations for bub-ble point oil viscosity and bubble point pressure have been used todetermine the accuracy of the published correlations for undersat-urated oil viscosity as shown in Tables 15–17.

These tables indicate that the best correlation to be used todetermine undersaturated oil viscosity using the calculated bubblepoint oil viscosity and bubble point pressure is that provided byHossain et al. [4]. Whereas, the Standing [2] correlation is the bestto be used for calculating bubble point pressure and to predict bub-ble point oil viscosity the proposed correlation in this study is thebest.

7. Conclusions

The published correlations for undersaturated oil viscosity wereevaluated for Omani crude oil. The correlation by Bergman andSutton [1] provided the best viscosity predictions among all otherstested with measured data.

Since the best tested correlations were functions of bubblepoint oil viscosity and bubble point pressure, therefore; the pub-lished correlations for these two parameters were evaluated forOmani crude oil and the undersaturated oil viscosity correlationswere evaluated based on these calculated data. It was observedthat the calculated bubble point pressure using the published cor-relations have insignificant effects on the calculated undersatu-rated oil viscosity, whereas, the calculated bubble point oilviscosity is effective. Hence, a new correlation was developed forbubble point oil viscosity and it was found to outperform all theavailable correlations in the literature.

Consequently, it was concluded that the proposed bubble pointoil viscosity correlation improves the performance of all the avail-able correlations for undersaturated oil viscosity. Overall, it wasconcluded that the best correlation for predicting the undersatu-rated Omani crude oil viscosity with calculated data was that ofHossain et al. [4]. Whereas, the Standing [2] correlation was thebest for predicting the bubble point pressure and the newlyproposed correlation in this study was superior in predicting thebubble point oil viscosity.

Acknowledgement

The authors appreciate the financial support of College ofEngineering, Sultan Qaboos University, Muscat, Oman.

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