A viscosity prediction model for Kuwaiti heavycrude oils at elevated temperatures

Osamah Alomair n, Adel Elsharkawy, Hassan AlkandariPetroleum Engineering Department, College of Engineering and Petroleum, Kuwait University, P.O. Box # 5969, Safat 13060, Kuwait

a r t i c l e i n f o

Article history:Received 7 September 2013Accepted 31 May 2014Available online 11 June 2014

Keywords:correlationsdead oil viscosityheavy oil viscosityKuwait

a b s t r a c t

Viscosity is a key uid property for characterization, evaluation, management and development ofpetroleum reservoirs. The accurate prediction of dynamic viscosity will be helpful for heavy oil recoverymethods including primary production, thermal production, and enhanced oil recovery (EOR). Reservoiroil viscosity is usually measured isothermally at reservoir temperature. However, at temperatures otherthan reservoir, dynamic viscosity is estimated by empirical correlations. Most of the publishedcorrelations have been performing well at the reservoir temperature, especially for conventional crudes.However, the published literature has lack of reliable methods for viscosity estimation due to an acuteshortage of dead oil data at elevated temperatures. These methods are essential and employed inplanning thermal recovery methods (Kuwait as well as worldwide). In this study, the API gravity andviscosity of 50 dead crude oil samples collected from various areas of Kuwaiti oil elds were measured.These oil samples have API gravity ranging from 101 to 201. The viscosities were determined attemperatures ranging from 20 1C to 160 1C. Consequently the results of the heavy oil viscosity data wereused to develop a reliable model and to compare the proposed model with the published models. Bothquantitative and qualitative analytical methods were implemented using statistical parameters andperformance plot, respectively. From the general evaluation it has been shown that the proposed modelhas the lowest average absolute error of 11.04% and highest coefcients of correlation of 92% for trainingand 96% for the testing data. The performance of the proposed correlation has also been tested usingdead heavy crude oil data from the region as well as various parts of the world. Compositional data ofheavy oil viscosity has been used to compare predicted viscosity from the proposed correlation with thatfrom LorenzBrayClark (LBC) and Pederson models. These comparisons show that the proposedcorrelation performed better than the other correlations, corresponding state and EOS-based methodsfor the dead heavy crude oils considered.

& 2014 Elsevier B.V. All rights reserved.

1. Introduction

The properties of petroleum reservoir uids are essential foroptimizing their production and transportation. Viscosity plays animportant role in the calculations of uid ow through reservoirrock, pressure loss (with implications for the designs of tubing andpipelines), and the design of surface facilities, reservoir simula-tions, and predictions of oil recovery. The thermal oil recovery ofheavy crude oils is designed to meet the industry demand forimproving oil production. Because it is necessary to consider thevariation of viscosity with temperature in engineering activities,including piping and pipeline construction for enhanced transpor-tation, thermal expansion is the key property for increasing theproductivity of heavy oils. Modern reservoir engineering practicesrequire accurate information concerning the thermodynamic and

transport uid properties, in addition to the reservoir rock proper-ties, to perform material balance calculations. Viscosity is often thelimiting factor in heavy oil production.

The viscosity of oils has been studied for many years. Although theviscosity is affected by pressure and gas content, it is primarily afunction of oil gravity and temperature (Batzle et al., 2004). Accurateprediction of the physical properties of oil is required to designappropriate recovery, storage, transportation, and processing systemsfor crude oil handling (Quail et al., 1987). Heavy oils are characterizedby high viscosities, ranging from 100 CP to 10,000 CP at the reservoirtemperature, as dened by the World Petroleum Congress, and havelow API gravity, ranging from 101 to 221, as dened by the U.S.Department of Energy (Nehring et al., 1983). Heavy oils have a low APIgravity compared with conventional oil and are particularly known forthe difculty associated with achieving accurate measurements oftheir uid properties.

The uncertainty of heavy oil uid property measurementsaffects the quality of the data, which in turn affects the accuracy

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Journal of Petroleum Science and Engineering

http://dx.doi.org/10.1016/j.petrol.2014.05.0270920-4105/& 2014 Elsevier B.V. All rights reserved.

n Corresponding author.E-mail address: osamah@dr-alomair.com (O. Alomair).

Journal of Petroleum Science and Engineering 120 (2014) 102110

of the production forecast (Zabel et al., 2008) and the recoveryprocesses, such as the steam-assisted gravity drainage (SAGD)process. An optimal recovery process must be a function of oilmobility (permeability/viscosity ratio). Therefore, a comprehen-sive and well-dened mapping of the reservoir oil mobility basedon viscosity is essential for the effective exploration and designoptimization of production strategies, particularly in biodegradedheavy oil and bitumen reservoirs (Adams et al., 2008, 2009).For live oils, the variation in dynamic viscosity with changesin temperature and pressure is typically predicted empirically(Sattarina et al., 2007).

The reservoir oil viscosity is typically measured isothermally atthe reservoir temperature. However, at temperatures other thanthe reservoir condition, these data are estimated using empiricalcorrelations (Naseri et al., 2005). The viscosity of crude oil variesdepending on its origin and type, as well as the nature of itschemical composition, particularly the polar components, forwhich intermolecular interactions can occur. For this reason,developing a comprehensive model of viscosity to include differ-ent regions of the world appears to be a difcult task. The variousapproaches to addressing this issue have been the topic ofnumerous studies, as reported in the following section.

2. An overview of published oil viscosity correlations

This study conducted a detailed literature review of variouscorrelations to estimate the viscosity of crude oil. These correla-tions can be divided into three categories, including dead, satu-rated, and under saturated. For the purpose of this research, onlydead, heavy od (oil with no gas in the solution) correlations willbe discussed.

Table 1 explains the different published correlations that can beconsidered for the purpose of comparing Kuwait dead-heavy oils.These correlations were divided into three groups based on theirrange of API and/or temperature values. Group A comprises thecorrelations that are outside the range of the viscositytempera-tureAPI gravity data described in this study and includes theGlaso (1980), Labedi (1992), Petrosky and Farshad (1995) and

Elsharkawy and Alikhan (1999) correlations. Group B comprisesthe correlations that fully cover the range of the viscositytemperatureAPI gravity data and includes the Beal (modiedform as Standing, 1981), Egbogah and Ng (1990), De Ghetto et al.(1995), Bennison (1998) and Hossain et al. (2005) correlations.Group C includes the correlations that partially cover the range ofthese parameters from the entire databank and includes the Beggsand Robinson (1975), Al-Khafaji et al. (1987), Kartoatmodjo (1990)and Naseri et al. (2005) correlations.

Many correlations utilize the oil API gravity and temperature todetermine dead oil viscosity. Beal (1946) presented a dead oildynamic viscosity correlation as a function of API gravity andtemperature using 655 viscosity data points collected from 492 oilelds in the United States at a temperature of 38 1C and 98 datapoints at temperatures above 38 1C.

Using the same input variables, Beggs and Robinson (1975)published a similar correlation that was developed with 460 datapoints from 93 different oil samples.

Glaso (1980) realized that parafnic crudes and naphtheniccrudes have the same API gravity but not the same viscosity at agiven temperature. For the same reason, the author published adead oil viscosity correlation with the suggestion of an adjustmentto the API gravity.

Al-Khafaji et al. (1987) presented a modied form of Beal'scorrelation for predicting the viscosity of dead crude oil fromthe Middle East. Egbogah and Ng (1990) presented two diffe-rent correlations for predicting the viscosity of dead oil. The rstcorrelation was a modied form of the Beggs and Robinson (1975)correlation using 394 data points, and in the second correlation,Egbogah and Ng introduced the pour point (Tp) as a new para-meter for estimating the dead oil viscosity (Egbogah and Ng, 1990;De Ghetto et al., 1995). Additionally, Svrcek and Mehrotra (1988)presented a one-parameter viscosity equation for bitumen.

The application of dead oil viscosity correlations to crude oilsfrom different sources results in signicant errors. These devia-tions are attributed to the difference in asphaltic and parafnic oilsand/or the mixed nature of the oils (Sattarina et al., 2007). Using alarge databank of crude oils from different parts of the world,Kartoatmodjo presented a modied form of Glaso's correlation(Kartoatmodjo 1990). Labedi (1992) presented a correlation forAfrican dead oils, in particular, from Libya. Puttagunta et al. (1988)published a viscosity correlation for Athabasca and Cold Lakeheavy oil and bitumen that depends on a single-point viscositymeasurement at a temperature of 30 1C and atmospheric pressure.Another correlation was later developed for heavy oil viscositywith dissolved gas (Puttagunta et al., 1993). Petrosky and Farshad(1995) presented a correlation for estimating the viscosity of deadoil recovered from the Gulf of Mexico. De Ghetto et al. (1995)published a set of two modied correlations for dead oil (extraheavy oil and heavy oil) viscosity predictions, and Bennison (1998)presented a new correlation for the viscosity of heavy dead oilfrom the North Sea. Elsharkawy and Alikhan (1999) presentedcrude oil viscosity correlations for Middle East crudes. Argillieret al. (2001) analyzed the rheology of heavy oil with contents ofasphaltene and resin by dividing heavy oil crudes into two groupsas a non-colloidal liquid (the maltene) and a dark brown powder(the asphaltene); their rheological experiment with the mixture of

Nomenclature

API specic gravity @ 15.56 1C (deg)T temperature, (1C)MRE mean relative error (%)

AARE absolute average relative error (%)SD standard deviationRMSE root mean square errorm dynamic viscosity (CP)

Table 1Comparison of the range of application of the dead-heavy oil correlations.

Developer API range Temperature range(deg) (1C)

Group A Glaso (1980) 20.148.1 10149Labedi (1992) 32.248 38152Petrosky and Farshad ( 1995) 25.446.1 46142Elsharkawy and Alikhan (1999) 19.948 38149

Group B Standing (1981) 10.152.5 38149Egbogah and Ng (1990) 558 1580De Ghetto et al. (1995) 1022.3 24146Bennison (1998) 1022 10121Hossain et al. (2005) 7.121.8 093

Group C Beggs-Robinson (1975) 1658 24146Al-Khafaji et al. (1987) 1551 16149Kartoatmodjo (1990) 14.458.9 24160Naseri et al. (2005) 1744 41246

O. Alomair et al. / Journal of Petroleum Science and Engineering 120 (2014) 102110 103

maltene and asphaltene demonstrated that the viscosity of heavyoil increased signicantly above a critical asphaltene concentra-tion. Dindoruk and Christman (2001) developed an empirical newdead oil viscosity correlation using data from the Gulf of Mexico.Naseri et al. (2005) published a correlation for the prediction ofthe viscosity of Iranian dead oil viscosity. Hossain et al. (2005)established a heavy oil databank based on three heavy oil datasetsto assess and develop correlations for each set. The datasetprovided by Chevron also included the composition, shear rate,and saturates, aromatics, resins, and asphaltenes (SARA) analysisof the oils. Bergman and Sutton (2007) developed a new correla-tion using a large database from conventional PVT reports, crudeoil assays, and the literature. Additionally, these authors improvedtheir proposal by introducing the Watson characterization factor(Kw), together with the oil API gravity and temperature, in theviscosity correlation.

It is apparent from the aforementioned survey that the literaturecontains an abundance of information and a database for viscositymeasurements, although mainly for saturated oils. However, thereare still several methods, such as corresponding state (CS) models(Little and Kennedy, 1968; Ely and Hanley, 1981) and equation-of-state-based (EOS) models (Lohrenz et al., 1964; Pedersen et al., 1984)that are used to calculate the viscosity of heavy oil. However, theprediction of heavy oil viscosity is limited at elevated temperatures.The viscosity of heavy oil is rarely measured at a temperature higherthan the formation temperature.

In this study, the dynamic viscosity data for several dead heavyoil samples are measured at the original formation temperatureand at elevated temperatures, that is, the temperatures that aretypically anticipated in hot water, cyclic-steam stimulation (CSS),SAGD, and steam ooding. Considering the conguration ofpublished dead-heavy-oil correlations, the main objective of thiswork is to develop a dead-heavy-oil viscosity correlation forKuwaiti crude oils as a function of API gravity and temperature.Further, this research aims to develop a correlation that can beemployed with condence by engineers (design, production, andreservoir) for the design of good ow and surface facility, with aspecial emphasis on application at elevated temperature.

3. Experimental methods

3.1. Materials and preparation

Fifty heavy Kuwaiti crude oil samples of different API gravityvalues were collected in specially designed glass-stoppered bottlesof 0.0025 m3 in capacity and stored at 20 1C. Before analysis, eachsample was degassed, and the bottles were shaken vigorouslyusing open-air platform shakers to achieve homogeneity. Thehomogenized samples were transferred into a separating funneland stored for 24 h while waiting for gravity settling. The com-mercial demulsier Nalco product (USA) was mixed with eachcrude oil sample in centrifuge tubes with a volume of 0.0001 m3;the samples were spun at 400650 rpm for 30 min at 40 1C in aK60002 automatic oil test centrifuge (Koehler Instrument, USA) toremove any traces of basic sediments and water. The watercontent of each sample was veried using a GD-2122 petroleumoil water content tester (Karl Fischer Titrator), and the results weresatisfactory, with an average range of 0.010.03%. These puriedcrude oil samples were transferred to clean dry bottles, each witha unique identication tag.

3.2. Viscosity and density measurements

The viscosity of each crude oil sample was measured usingviscosity monitoring and control electronics (VISCO lab 3000,

Cambridge Viscosity, Inc., USA). The main purpose of this state-of-the-art equipment is to measure the strength of an electro-magnetic eld generated from two magnetic coils inside a stain-less steel body. This structure allows the stainless steel pistoninside the measurement chamber to move by magnetic force backand forth in the uid. The time required for the piston to move axed distance (approximately 0.508 cm) is then very accuratelyrelated to the dynamic shear viscosity of the uid in the chamber.Instrument calibration was performed by a triplicate measurementof the two reference samples supplied by the manufacturerin the temperature range of interest, that is, up to 160 1C, with areproducibility of 0.92% of the measuring range, and theestimated uncertainty in the dynamic viscosity measurementswas observed to be no larger than 9103 mPa s, with a con-dence interval of 95% for all measurements. The densities weremeasured at temperature intervals between 20 and 160 1C using adensimeter (mPDS 2000, Anton paar, GmbH), which functionsaccording to the oscillating U-tube techniques. The calibration wasperformed using dry air and ultra-pure water (S. No. 78169, S.H.Kalibrier, GmbH products) at the temperature of interest. Themeasurement cell is thermostatic with a solid-state thermostatand two integrated Pt 100 measuring sensors, with a temperaturereproducibility of 102 K. Triplicate density measurementswere performed for all samples. The results were averaged,and the estimated uncertainty of the measurements was within0.5 kg m3. After verication, only 41 heavy crude oil sampleswith a calculated API gravity ranging from 101 to 201 were used forthe study. Each sample was tested for approximately 12 tempera-ture steps from 20 to 160 1C, and a total of 492 data points werecollected in the viscosity range from 1.784 to 4867 CP.

4. Proposed model

Fig. 1 illustrates the general trend of the experimental viscositymeasurement data at different temperatures, with the API of thesamples ranging from 11.81 to 20.51, corresponding to the entireviscosity databank. Experimentally, it is observed that most ofthe viscosity measurement population is approximately 1000 CP,which is in agreement with published studies (Oskui and Al Naqi,2009; Tirtharenu and Al-Sammak, 2011).

The viscosity measurements at different temperatures for thecrude oil samples in this study were used to develop a heavy oilviscosity correlation. The entire dataset was divided into a trainingset composed of 374 viscosity measurements and a testing setcontaining 118 measurements. The training and testing sets were

Fig. 1. Experimental viscosity measurements (API from 101 to 201, Kuwaitiheavy oils).

O. Alomair et al. / Journal of Petroleum Science and Engineering 120 (2014) 102110104

selected randomly. Note that the 118 data points were not used todevelop the proposed models or the correlations considered inthis paper.

Multiple non-linear regressions (the least-squares minimiza-tion technique) were employed in a surface tting (3D-type curve)software to obtain an optimum viscosity model. The followingproposed model is able to simulate the viscositytemperatureAPIrelationship for heavy Kuwaiti crude oil with a correlation coef-cient of 95%. The new proposed viscosity model has the followingform:

lnln 0:075475:76588lnAPI 0:001011:8T32

ln1:8T32 1Where is the dynamic viscosity in cp, API is the crude oil APIgravity, and T is the formation temperature in 1C. The model coversa reasonable API gravity range, from 101 to 201, and is quitesuitable for the anticipated temperatures of Kuwaiti reservoirsbecause it covers a wide range, from 4 1C to 177 1C.

5. Results and discussion

In this section, the accuracy of the proposed model used tosimulate the experimentally measured viscosity data of the heavycrude oil was studied. The viscosity data predictions using thenewly proposed model, in addition to many of the publishedcorrelations, were compared with experimentally measured visc-osity data. Quantitative and qualitative analyses were performedas a part of the comparison. The quantitative analyses includecalculations of relative and absolute errors, standard deviations,and correlation coefcients. The qualitative analysis includesviscosity temperature plots and cross plots. The viscosity tem-perature plots were used to determine whether the modelcaptured the physical trend of the viscosity change as a functionof both temperature and API gravity. For comparison purposes,many of the correlations considered in this study (Table 1) haveseveral limitations in terms of both the API gravity and tempera-ture ranges.

A comprehensive assessment of all of the correlation groups (A,B, and C) revealed that none of the existing correlations are able toproperly match the Kuwaiti dead-heavy oil viscosity measure-ments over the entire range of temperatures with a reasonabledegree of accuracy. Therefore, it was necessary to propose a newcorrelation capable of predicting the viscosity behavior of heavy oilat the formation and elevated temperatures with an appropriatedegree of accuracy.

5.1. Assessment of the proposed model

Fig. 2 presents a cross-plot of the measured viscosity data ofthe training set versus the corresponding predictions. This gureindicates that the data points are uniformly distributed along theunit slope line.

Fig. 3 presents the performance of the proposed model on the118 data points of the testing set. This gure indicates that most ofthe predicted data are signicantly closer to the unit slope line.

5.2. Statistical performance

As mentioned above, many of the correlations considered inthis study have limitations, either for the associated API gravityrange or the temperature range, or were not developed for heavycrudes. A detailed descriptive statistical analysis was performedto evaluate the performance of each correlation. The statisticalanalysis tools employed for this purpose were the percentage

means relative error (MRE), absolute average relative error (AARE),standard deviation (SD), coefcient of correlation (r), coefcient ofdetermination (r2), and relative mean square error (RMSE). Table 2presents a comparison of the error analysis obtained for thetraining data described in this study for the proposed correlationversus the published existing correlations.

Table 2 demonstrates that the proposed empirical model hasthe smallest average absolute error (25%) and mean relative error(11%) and the highest correlation coefcient (0.96), followed bythe Bennison correlation. Some of the well-known correlationsthat have been frequently used in the petroleum industry topredict dead oil viscosity, such as the Standing (modied form ofBeals) and Kartoatmodjo correlations, yield exceptionally higherrors and low correlation coefcients. The same error analyseswere applied to the testing dataset.

Table 3 demonstrates that the proposed model produces thelowest errors and standard deviations and the highest correlationcoefcients of all of the correlations considered in this study. Thisresult indicates that the proposed model performed signicantlybetter than the other models.

5.3. Graphical performance

To further investigate the performance of our proposed corre-lation, detailed graphical comparisons between the differentpublished correlations (Groups AC) and the proposed correlationhere were prepared and are discussed in the following sections.

Fig. 2. Cross plot of the Kuwaiti heavy crude oil viscosity data of the training set.

Fig. 3. Validation viscosity cross-plot of the proposed model (testing data).

O. Alomair et al. / Journal of Petroleum Science and Engineering 120 (2014) 102110 105

5.3.1. Comparison with Group A correlationsThe performance of the proposed model is compared with that

of the Group A correlations in Fig. 4a, b, and c for low, medium,and high APIs, respectively. The proposed model performs verywell compared with the Group A correlations, with the measuredviscosities being in good agreement with the proposed modelpredictions. The performance curves for the Group A correlationsare plotted for three different APIs (low, medium, and high). Forthe low API in Fig. 4a, the Labedi viscosity predictions are mostlikely the largest outliers, whereas the remaining Group A correla-tions, comparatively, overestimate the viscosity of heavy Kuwaiticrude oils. However, for both the medium and high APIs in Fig. 4band c, respectively, the Glaso and PetroskyFarshad predictions arerelatively close to the experimental measurements for somehigher temperatures. This result is not surprising, as these correla-tions are applied to light crudes. Overall, no single correlation wasable to completely capture the viscosity measurements for theentire temperature range.

5.3.2. Comparison with Group B correlationsThe performance of the proposed model is compared with the

Group B correlations in Fig. 5a, b, and c for low, medium, and high

APIs, respectively. The proposed model clearly outperforms thecommonly published Group B correlations. Fig. 5a demonstratesthat the Bennison and Hossain correlations overestimate theviscosity predictions because both the Bennison and Hossain aredened for the same API gravity range as that of the current study,but if we observe Table 1, these API gravity ranges are notsufciently compatible with the temperature range. The Standingcorrelation exhibits insensitive behavior for the majority of thetemperature range for this particular low-API crude oil. The GroupB correlations are in good agreement with the measured data,mainly at elevated temperatures. The Egbogah and Ghetto correla-tions underestimate the viscosity.

Fig. 5b presents the viscosity predictions for medium APIs forthe same group; however, the predictions are poorly dened atrelatively low temperatures. However, after a certain high tem-perature value, all of the predictions exhibit similar behavior. Boththe Bennison and Hossain models overestimate the viscosity attemperatures below 66 1C with a similar trend. The Standing andGhetto models also overestimate the viscosity, whereas theEgbogah model underestimates the viscosity. The same behaviorcan be observed in Fig. 5c, even for temperatures greater than82 1C. However, below this temperature, both the Ghetto andHossain models yield overestimated predictions. The Egbogah

Table 2Statistical analysis of the training data.

Model AARE MRE SD r r2 RMSE(%) (%) (Correlation) (Determination)

Group A Proposed 25.29 11.04 129.97 0.96 0.92 16.80Glaso 103.86 90.22 121.29 0.87 0.76 53.51Labedi 649.00 628.82 121.33 0.20 0.04 118.34PetroskyFarshad 139.36 103.92 59.20 0.67 0.45 40.80ElsharkawyAlikhan 93.91 86.24 238.09 0.93 0.86 84.50

Group B Standing 217.25 180.19 53.38 0.46 0.21 47.33Bennison 62.90 53.87 387.90 0.92 0.84 156.09Hossain 111.11 107.15 448.17 0.92 0.85 175.82Ghetto 72.75 63.24 203.80 0.94 0.88 70.78EgbogahNg 85.55 57.86 84.59 0.95 0.91 26.05

Group C BeggsRobinson 68.30 16.23 811.62 0.83 0.68 457.85Khafaji 85.28 68.74 306.61 0.75 0.56 203.03Kartoatmodjo 145.55 131.55 116.73 0.84 0.70 63.84Naseri et al. 77.87 30.00 47.04 0.87 0.76 22.94

Table 3Statistical analysis of the testing data.

Model AARE MRE SD r (correlation) r2 (determination) RMSE(%) (%)

Proposed 28.08 11.81 124.42 0.96 0.92 15.70Group A Glaso 113.54 101.46 124.89 0.87 0.76 61.29

Labedi 783.45 765.64 143.58 0.20 0.04 140.54PetroskyFarshad 157.21 126.72 65.01 0.67 0.45 48.11ElsharkawyAlikhan 97.18 89.98 227.02 0.93 0.86 84.98

Group B Standing 238.75 208.08 60.82 0.44 0.20 54.52Bennison 60.17 48.90 380.48 0.92 0.84 166.35Hossain 105.86 102.51 440.01 0.93 0.86 175.82Ghetto 75.59 64.87 190.06 0.91 0.84 77.05EgbogahNg 90.78 64.54 82.08 0.95 0.89 26.76

Group C Beggs-Robinson 66.41 9.87 683.06 0.80 0.64 408.88Khafaji 98.62 83.68 373.03 0.63 0.40 290.01Kartoatmodjo 167.01 154.20 124.64 0.79 0.62 76.55Naseri et al. 87.41 42.24 47.97 0.84 0.71 25.99

O. Alomair et al. / Journal of Petroleum Science and Engineering 120 (2014) 102110106

model underestimates the viscosity at relatively low referencetemperatures. A comparison between the proposed model perfor-mance and the other correlations for medium crude is presented

in Fig. 5b. The Group B correlations fail to predict the actualviscosity at low temperature but predict almost the same viscosityat temperatures greater than 71 1C. However, the correlation

Fig. 4. (a). Comparison of the performance of the Group A correlations for low-API(13.01) crude oils. (b). Comparison of the performance of the Group A correlationsfor medium-API (16.51) crude oils. (c). Comparison of the performance of the GroupA correlations for high-API (19.81) crude oils.

Fig. 5. (a). Comparison of the performance of the Group B correlations for low API(13.01) crude oils. (b). Comparison of the performance of the Group B correlationsfor medium-API (16.51) crude oils. (c). Comparison of the performance of the GroupB correlations for high-API (19.81) crude oils.

O. Alomair et al. / Journal of Petroleum Science and Engineering 120 (2014) 102110 107

proposed in this paper performs better and is in good agreementwith the measured viscosity for the entire temperature range.

The same comparison is considered for high-API crude oils inFig. 5c. This gure demonstrates that the proposed model, as wellas the Ghetto and Bennison correlations, was able to match themeasured viscosity for the entire temperature range. However, theStanding and Egbogah correlations do not match the experimentaldata well at low temperatures, which is typical of heavy oilreservoirs.

5.3.3. Comparison with Group BThe performance of the proposed model is compared with the

Group C correlations in Fig. 6a, b, and c for low, medium, and highAPIs, respectively. The proposed model again exhibits an excellentt with the measured data. For low API, the Group C correlationseither over- or underestimate the viscosities, whereas the pro-posed model performs well over the entire temperature range.However, the Beggs model is in good agreement over the majorityof the temperature range. Fig. 6a demonstrates that for low API,only the Beggs correlation exhibits a good match with themeasured heavy oil viscosity for the entire temperature range,whereas both the Khafaji and Kartoatmodjo models display pooragreement with the measured data. This anomaly can be under-stood by reviewing Table 1 for the parameter ranges. The viscosityprediction based on the Naseri correlation is similar to theexperimental measurements over the entire temperature range.For a medium API, Fig. 6b demonstrates that only the Kartoat-modjo correlation is a good match with the pertinent data range,whereas both the Beggs and Khafaji correlations overestimate theexperimental viscosity data. The Naseri model is in good agree-ment only at higher temperatures.

Most of the time, the proposed model performs well comparedwith the Group C correlations. Additionally, the Group C correla-tions are in good agreement for a portion of the elevatedtemperature range. Fig. 6c presents the performance of the GroupC correlations for the high API range. The Kartoatmodjo andKhafaji correlations are in good agreement for temperatures above54 1C and exhibit the same viscosity prediction trend. The Beggsand Naseri correlations overestimate and underestimate the visc-osity predictions, respectively. The proposed correlation displaysgood agreement with the experimentally measured viscosities.All of the Group C correlations are in an underestimating locus.However, in a portion of the elevated temperature range, thisgroup agrees well with the proposed model. In summary, thereservations and concerns that were raised in the rst qualitativephase of this study (Alomair et al., 2011) have now beenaddressed. An overall assessment of the correlation proposed inthe current study reveals that although the correlation is notgeneralized, it still performs relatively better for the group ofKuwaiti dead-heavy oils. The robustness of the current model canbe visualized from Figs. 2 and 3 for the training and testingdatasets, respectively. Both datasets indicate that the model per-forms well at elevated temperatures.

5.4. Accuracy using regional and crude oils from different regions

Table 4 shows the experimental dead crude oil viscosity for sixsets of crudes from various parts of the world. The rst set isregional oil from the Middle East. This oil is with 13.9 API degreesgravity. The proposed correlation was able to predict the deadoil viscosity for this set with an average absolute error (AAE) inthe order of 32%, and the second accurate correlation wasBeggsRobinson with an AAE in the order of 68%. The next set isMaya Mexico-2004 that has API gravity of 20.21. The proposed

correlation was able to predict the dead oil viscosity for this crudewith AAE of 29% followed by Beal's correlation (58%).

The third oils set are extremely heavy crudes from Venezuelawith API gravity of 8.31. None of the dead oil viscosity correlations

Fig. 6. (a) Comparison of the performance of the Group C correlations for low-API(13.01) crude oils; (b) Comparison of the performance of the Group C correlationsfor medium-API (16.51) crude oils; (c) Comparison of the performance of the GroupC correlations for high-API (19.81) crude oils.

O. Alomair et al. / Journal of Petroleum Science and Engineering 120 (2014) 102110108

Table 4Testing accuracy of proposed and other correlations using regional and world heavy crudes.

Crude sample Tested parameter Correlation

API T Measured viscosity Beal's BeggsRobinson Glaso Labedi Kartoatmodjo ElsharkawyAlikhan Proposed(1F) (cp)

Middle East 13.9 85 575 1458.5 1642.6 778.9 354.9 701.6 1217.6 724.413.9 150 58.53 162 44.8 154.7 242 171.2 121.1 91.313.9 250 17.02 11 7.3 36.2 171.5 48.1 28.4 10.913.9 350 3.02 1.3 3.2 13.9 136.7 20.9 13.6 3.4

Maya Mexico-2004 21.8 32 1112 275 8,562,624 462 82.6 441 6613 523.721.8 59 229 134 2529 125 54.7 123 320 242.821.8 77 205 87 313 71 45.7 70 121 147.7

Venezuela Orimulsin-100 8.2 32 789 2.77E08 2.612E08 1,356,311 8195.3 478,539 265,455,745 3063861.98.2 59 623 12,819,495 2,583,980 128,832 5426.4 74,375 336,769 489839.18.2 68 548 4,940,100 273,107 74,609 4931.3 48,285 102,906 269036.38.2 86 515 804,696 13,710 30,225 4209.5 23,631 18,359 84590.4

California Gail-Ca 20.6 32 1393 411 21,436,699 680 107.8 619 12,489 654.620.6 59 406 194 3969 175 71.4 168 486 295.320.6 77 196 122 436 97 59.7 95 172 176.5

Boscan Crude 10.5 77 61,080 34,131 16,851 7003 1418.3 5518 10,598 7580.110.5 104 11,052 7205 953 2558 1158.3 2403 1872 2183.610.5 149 1202 716 90 767 909 889 358 364.210.5 212 204.4 45 19 235 716.7 335 100 53.4

Alberta crudes 18 73.6 2152 319 1383 234 116 219 483 317.118 124 321.3 86 51 66 81.7 68 74 76.818 151 163.4 46 22 41 71.6 44 43 40.318 160 132 38 18 36 68.9 38 37 33.118 177 58.43 26 13 28 64.2 30 28 23.118 196 39.33 18 9 22 60 24 22 16.318 213 30.86 13 7 18 56.7 20 19 12.218 232 18.89 9 6 15 53.6 17 16 9.218 259 10.66 6 4 11 49.7 13 12 6.418 290 7.92 3 3 8 46.1 10 10 4.518 311 6.94 2 3 7 43.9 9 9 3.718 332 5.54 2 3 6 42.1 7 8 3.118 348 4.4 1 2 5 40.8 7 7 2.8

Table 5Comparison between measured and calculated viscosity from the proposed correlation, corresponding state and EOS methods.

Sample 1 (API17.51) Sample 2 (API19.844)

Comp mol% wt% MW SG Comp mol% wt% MW SG

C1 0.00 0.00 16.04 0.300 C1 0.00 0.00 16.04 0.300C2 0.00 0.00 30.07 0.356 C2 0.00 0.00 30.07 0.356C3 0.00 0.00 44.10 0.506 C3 0.00 0.00 44.10 0.506i-C4 0.17 0.03 58.12 0.562 i-C4 0.13 0.02 58.12 0.562n-C4 0.29 0.05 58.12 0.583 n-C4 0.12 0.02 58.12 0.583C5 0.00 0.00 72.15 0.624 C5 0.07 0.02 72.15 0.624i-C5 0.14 0.03 72.15 0.630 i-C5 0.11 0.02 72.15 0.630n C5 0.35 0.07 72.15 0.685 n C5 1.39 0.31 72.15 0.685C6 1.95 0.47 86.18 0.668 C6 3.94 1.03 85.73 0.666C7 97.10 99.36 367.35 0.951 C7 94.24 98.58 343.10 0.940T, 1F Measured m, cp Proposed LBC Pedersen T, 1F Measured m, cp Proposed LBC Pedersen176 23.51 25.4 3.39 47.2 104 96.460 96.420 3.550 150.290

Sample 3 (API13.504) Sample 4 (API15.069)

Comp mol% wt% MW SG Comp mol% wt% MW SG

C1 0.00 0.00 16.04 0.300 C1 0.00 0.00 16.04 0.300C2 0.00 0.00 30.07 0.356 C2 0.00 0.00 30.07 0.356C3 0.00 0.00 44.10 0.506 C3 0.00 0.00 44.10 0.506i-C4 0.01 0.00 58.12 0.562 i-C4 0.00 0.00 58.12 0.562n-C4 0.04 0.01 58.12 0.583 n-C4 0.15 0.02 58.12 0.583C5 0.00 0.00 72.15 0.624 C5 0.00 0.00 72.15 0.624i-C5 0.01 0.00 72.15 0.630 i-C5 0.04 0.01 72.15 0.630n C5 0.04 0.01 72.15 0.685 n C5 0.28 0.06 72.15 0.685C6 0.39 0.09 86.18 0.671 C6 1.37 0.32 86.18 0.668C7 99.52 99.90 384.46 0.975 C7 98.16 99.59 369.29 0.966T, 1F Measured m, cp Proposed LBC Pedersen T, 1F Measured m, cp Proposed LBC Pedersen194 28.3 34.35 4.06 66.52 176 29.95 37.19 3.84 63

O. Alomair et al. / Journal of Petroleum Science and Engineering 120 (2014) 102110 109

were able to estimate the dead oil viscosity for this extra heavycrude. The fourth group is from California that has API gravity of20.61. Again the proposed correlation has the smallest error (30%)followed by Glaso's correlation (AAE53%). The fth oil is Boscancrude which has API gravity 10.51. The API gravity of this oil isbelow the practical limit of most of the correlation. Therefore, onlyBeal's and Glaso's correlations were able to predict its dead oilviscosity with AAE in the order of 49% and 54% respectively. Thelast crude oil is from Alberta that has an API gravity of 181.Kartomtodjo's correlation was able to predict its dead oil viscositywith AAE of 34% followed by the proposed correlation (42%).

Compositional data as well as measured viscosity for fourheavy crude oil samples are shown in Table 5. This table alsoshows a comparison between the predicted viscosities from theproposed model, corresponding state and EOS based model. Thecorresponding state model by Lohrenz, BrayClark method (LBC)and the EOS model by Pederson are considered in this study. TheLBC model severely underestimated the dead heavy oil viscosity ofall the four samples as shown in Table 5. Therefore, it is suggestednot to use the LBC model to predict dead heavy oil viscosity. Theproposed model shows a better accuracy than the Pederson modelfor all the four compositional data considered.

The correlation proposed in this study should be carefully usedoutside the range of data. It should not be used to predict dead oilviscosity for extra heavy crudes having API gravity below 101 orlight crudes having API gravity above 221. It should not also beused at extremely low temperature of 20 1C (68 1F). For predictingthe effect of gas injection upon viscosity of heavy crudes or topredict the saturated or undersaturated oil viscosity the designengineers should consider other correlations, corresponding statesmethods, or equation of state based methods.

6. Conclusions

This study considered 492 viscosity measurements of heavyKuwaiti crude oil samples at both the formation and elevatedtemperatures. The data were also used to develop a new heavy oilviscosity model for Kuwait crudes. These data were used toevaluate the performance of published correlations in addition tothe well-known correlations that have been considered bench-marks for the petroleum industry. Using regional as well as worldheavy crude oil data, the performance of the proposed model wascompared with various correlations as well as CorrespondingState, and EOS-based methods. The comparison revealed that theproposed model has better accuracy and acceptable performancerelative to the other published methods with respect to theviscosity prediction of heavy Kuwait crude oils. This correlationshould be used in case experimental data is unavailable orunreliable. It should be carefully used outside the range of data.It should not also be used to predict dead oil viscosity for extraheavy crudes having API gravity below 101 or light crudes havingAPI gravity above 221, or at extremely low temperature of 20 1C(68 1F).

Acknowledgments

This work was supported by Kuwait University, Research Grantno. [EP 02/08]. The authors also acknowledge the support receivedfrom the General Facility Research Grant [GE 01/07]. The authorsextend their appreciation to the Research and Technology (R&T)Group at the Kuwait Oil Company (KOC) for assistance with thecrude oil samples.

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O. Alomair et al. / Journal of Petroleum Science and Engineering 120 (2014) 102110110

A viscosity prediction model for Kuwaiti heavy crude oils at elevated temperaturesIntroductionAn overview of published oil viscosity correlationsExperimental methodsMaterials and preparationViscosity and density measurements

Proposed modelResults and discussionAssessment of the proposed modelStatistical performanceGraphical performanceComparison with Group A correlationsComparison with Group B correlationsComparison with Group B

Accuracy using regional and crude oils from different regions

ConclusionsAcknowledgmentsReferences