a new correlation for prediction of undersaturated crude oil viscosity

Petroleum & CoalISSN 1337-7027Available online at www.vurup.sk/pcPetroleum & Coal 52 (1) 50-55, 2010A NEW CORRELATION FOR PREDICTION OF UNDERSATURATEDCRUDE OIL VISCOSITYR. Abedini 1, *, A. Abedini 2 , N. Eslami Yakhfrouzan 11Department of Chemical Engineering, Ferdowsi University of Mashhad,Mashhad, Iran, 2 Department of Petroleum Engineering,Petroleum University ofTechnology, Ahwaz, IranReceived November 13, 2009, Accepted February 1, 2010AbstractViscosity is one of the most important governing parameters of the fluid flow, either in the porous media or inpipelines. So it is of great importance to use an accurate correlation to calculate the oil viscosity at variousoperating conditions. Whenever laboratory data are obtained, efforts are made to find a best-fit correlation,because demand for mathematical equation of fluid flow for reservoir simulation, pressure traverse calculationand so on compel the person to use empirical and semi-empirical correlations to find viscosity at variouspoints of the flow path (along which T, P, R s and other parameters may vary). In the literature, severalempirical correlations have been proposed for predicting undersaturated oil viscosity. Here, based on Iranianoil reservoirs data; new correlation has been developed for prediction of undersaturated oil viscosity. Validityand accuracy of this correlation has been confirmed by comparing the obtained results of this correlation andother ones with experimental data for Iranian oil samples. Checking the results of this correlation shows thatthe obtained results of Iranian oil viscosities in this work are in agreement with experimental data comparedwith other correlations.Keywords: Oil Viscosity, Correlation, Undersaturated, Saturated, Dead, API gravity.1. IntroductionCrude oil viscosity is an important physical property that controls and influences the flow of oilthrough porous media and pipes. The viscosity, in general, is defined as the internal resistance ofthe fluid to flow. Oil viscosity is a strong function of many thermodynamic and physical propertiessuch as pressure, temperature, solution gas-oil ratio, bubble point pressure, gas gravity and oilgravity. Usually oil viscosity is determined by laboratory measurements at reservoir temperature.Viscosity is usually reported in standard PVT analyses. Increasing pressure always causes increasein viscosity above the bubble point. However below the bubble point, increasing pressure causesan increase in solution gas, which in turn decreases the oil viscosity. Thus, oil viscosity correlationsall belong to three categories: dead oil, saturated oil and undersaturated oil viscosity correlation.Numerous correlations have been proposed to calculate the oil viscosity. These correlationsare categorized into two types. The first type which refers to black oil type correlations predictviscosities from available field-measured variables include reservoir temperature, oil API gravity,solution gas- oil ratio, saturation pressure and pressure [1-9] . The second type which refers tocompositional models derives mostly from the principle of corresponding states and its extensions.In these correlations beside previous properties, other properties such as reservoir fluidcomposition, pour point temperature, molar mass, normal boiling point, critical temperature andacentric factor of components are used [ 9, 10] .2. Undersaturated oil viscosity correlationsUndersaturated oil viscosity correlations, which usually use saturated crude oil viscosity andpressure above the bubble point to predict viscosity of undersaturated oil reservoirs. Thesecorrelations are Beal [1] , Vasquez and Beggs [2] , Khan [4 ], and Kartoatmodjo and Schmidt [7] .

R. Abedini et al./Petroleum& Coal 52(1) 46-51, 2010 512.1. Beal correlation [1]This correlation proposes that for any specified oil, when only pressure is the variable, viscosityvaries linearly with the pressure.2.2. Vasquez-Beggs Correlation [2]This correlation ignores the effect of μ ob on the coefficient which is multiplied by μ ob to predict μ o .m⎛ p ⎞μo= μob⎜ ⎟⎝pb⎠Where:−5a = ⎡−3.9 ( 10 ) P⎤−5⎣⎦a( ) ( )m= 2.6 P 1.187 102.3. Khan Correlation [4]Like the previous case, this correlation ignores the effect of μ ob on the coefficient which ismultiplied by μ ob to predict μ o .μο= μ exp(9.6 × 10 ( P − P ))(5)ob−52.4. Kartoatmodjo and Schmidt Correlation [7]bLike beal one, this correlation proposes that for any specified oil, when only pressure is thevariable, viscosity varies linearly with the pressure.1.8148 1.59(6)μ = 1.00081μ + 0.001127 P − P − 0.006517μ + 0.038μ3. Experimental Data1.6 0.56( P P )( )μ = μ + 0.001 − 0.024μ + 0.038μo ob b ob ob( )( )o ob b ob obIn this study, PVT experimental data of five sample oils from Iranian oil reservoirs have beenused. These data include oil reservoir temperature, saturation pressure, API gravity and solutiongas-oil ratio at reservoir temperature. Reservoir oil viscosities have been measured at variouspressures above and below the bubble point pressure for different temperatures. Statisticalexperimental data are shown in Table 1.Table 1. Statistical experimental data of sample oils.Oil properties Oil 1 Oil 2 Oil 3 Oil 4 Oil 5API 15.4 24.2 30.3 36.7 41.6Temperature (ºF) 134-272 134-272 134-272 134-272 134-272Solution gas-oil ratio (SCF/STB) 647 823 954 1167 1542Saturation pressure (psia) 2490-35002520-33281340-20401585-29141638-4513Undersaturated viscosity (cp) 0.394-2.2110.374-0.7260.683-18.4350.316-8.2530.341-1.146The accuracy and ability of each mentioned correlation for predicting oil viscosity was checkedwith experimental data and Figs. 1, 2, 3 and 4 show this comparison. These figures confirm thedisability of correlations for accurate prediction of oil viscosities.(1)(2)(3)(4)

R. Abedini et al./Petroleum& Coal 52(1) 46-51, 2010 52Fig. 1. Oil viscosity as a function ofpressure.Fig. 2. Experimental values compared with calculated valuescalculated by Beal correlationFig. 3. Experimental values compared with calculatedvalues calculated based on the Vasquez-Beggscorrelation4. Development of the proposed correlationsFig. 4. Experimental values compared with calculatedvalues calculated based on the khan correlationProposed correlation is based on real data, which almost covers Iranian oil types. At pressuresabove bubble point pressure, oil is at single-phase state, while its solution gas–oil is constant andit seems that pressure will be the most effective in oil viscosity. By increasing pressure above thebubble point, oil density and oil viscosity will be increased (Fig. 1). Several function forms havebeen tested to correlate undersaturated oil viscosity (μ o ) to saturated oil viscosity (μ ob ), and pressureincrement above the bubble point (P-P b ). Proposed correlation in this work (for under-saturatedoil) is as follows:b1 b2 b3 b4 b5 b6 b7( ) ( )μ = μ + 0.001 P − P a μ + a μ + a μ + a P + a P + a P + a P (7)o ob b 1 ob 2 ob 3 ob 4 b 5 b 6 b 7 bWhere:a 1 =0.05601 a 2 =0.47557 a 3 =-0.2257 a 4 =-0.29598 a 5 =-0.07734 a 6 =-0.42436 a 7 =-1.64149b 1 =1.45198 b 2 =0.35997 b 3 =0.86389 b 4 =-0.41866 b 5 =-0.29981 b 6 =-0.1946 b 7 =-0.313395. Results and Discussion5.1. Validation of the proposed correlationThe accuracy and ability of each mentioned correlation for predicting oil viscosity was checkedwith experimental data and Figs. 2, 3, 4 and 5 show this comparison. These figures confirm thedisability of correlations for accurate prediction of oil viscosities.Fig. 6 depicts the comparison of experimental values of viscosity with predicted ones by twodimensions plot for undersaturated oil respectively. It is obvious from the figure that the newcorrelation provides results in good agreement with experimental values.Table 2 reveals average relative error (ARE), absolute average relative error (AARE) andstandard deviation (SD) for undersaturated oil viscosity correlations respectively. ARE, AARE andSD are defined as below.

R. Abedini et al./Petroleum& Coal 52(1) 46-51, 2010 53Fig. 5. Experimental values compared withcalculated values calculated based on theKartoatmodjo and Schmidt correlationFig. 6. Experimental values compared withcalculated values calculated based on the NewModelTable 2. Accuracy of viscosity correlations for prediction of undersaturated oil viscosities.Correlation ARE (%) AARE (%) SD (%)Undersaturated oil Beal, 1946 1.33 4.21 5.92Vasquez and Beggs, 1980 7.83 9.12 13.83Khan,1987 -2.44 4.64 6.48Kartoatmodjo and Schmidt, 1994 4.13 6.43 9.94New Model 0.85 2.58 4.27AREN1 ⎛ Xexp erimental( i) − Xcalculated( i)⎞=N∑⎜ X⎟i = 1 ⎝exp erimental( i)⎠(8)N1 ⎛ X∑⎟ ⎟ ⎞⎜exp erimental ( i)− Xcalculated ( i)AARE =N ⎜i= 1⎝Xexp erimental(i)⎠SD =N1 ⎛ X∑⎟ ⎟ ⎞⎜exp erimental− Xcalculated− AAREN −1⎜i= 1⎝Xexp erimental ( i)⎠2(9)(10)New viscosity correlation derived based on Iranian field data which does not requirecompositional information and can be used for black oil type fluids. The correlation can be used inblack oil reservoir simulators, it can be easily tuned, and it provides better estimates of oilviscosity than the previous existing correlations. This is shown in the figure 7.Fig. 7. Comparison between all introduced correlations

R. Abedini et al./Petroleum& Coal 52(1) 46-51, 2010 545.2. Accuracy of the proposed correlationHere, the accuracy of the proposed correlations in this work, as well as the correlations previouslydiscussed, is checked. Using the 86 real cases data series of Iranian oils, the results of this workand other ones for estimating the oil viscosity are compared. Table 2and Fig.8 shows all of thesecomparisons.Fig. 8. Percent relative error distribution for undersaturated oil viscosity correlationsFig. 8 shows percent relative error distribution for all correlations.⎛ Xexp erimental(i)− Xcalculated(i)⎞Where: Ei = ⎜⎟ × 100 (i= 1, 2, 3…,n d ) (11)⎝ Xexp erimental(i)⎠At this point, it should be mentioned the proposed correlations are only applicable to Iranianoils and their applicability to other regions should be checked.6. ConclusionGenerally the most common method for calculating viscosity of crude oils is viscositycorrelations. However these correlations fail to predict oil viscosities at wide range of operatingconditions such as pressure and temperature. In this work a new correlation for estimation ofundersaturated Iranian oils has been proposed. This correlation is based on real data of thedifferent types of Iranian oils. Input parameters for this correlation are oil API gravity, saturationpressure, reservoir temperature and pressure, which are easily measured in oil fields. Incomparison with correlations previously published in the literature, new correlation has a betteraccuracy and performance for predicting the viscosity of Iranian oils. It should be mentioned that,

R. Abedini et al./Petroleum& Coal 52(1) 46-51, 2010 55this proposed correlation might be used for the prediction of Iranian oil viscosity. Application ofthis correlation for other oil samples can result in errors.NomenclatureSymbolsGreeksAPI Oil API gravity μ ob Saturated oil viscosity (cp)R s Solution gas-oil ratio (SCF/STB) μ o Undersaturated oil viscosity (cp)T Temperature (R, F)AbbreviationsP Pressure (psia) ARE Average relative errorP b Saturation pressure oil bubble point AARE Average absolute relative errorpressure (psia)Ei Percent relative error SD Standard deviationn d Number of data pointsReferences[1] Beal, C., 1946. Viscosity of air, water, natural gas, crude oil and its associated gases at oilfield temperature and pressures. Trans. AIME 165, 114– 127.[2] Beggs, H.D., Robinson, J.R., 1975. Estimating the viscosity of crude oil systems. JPT 9,1140– 1141.[3] Chew, J., Connally, C.A., 1959. Viscosity correlation for gassaturated crude oil. Trans.AIME 216, 23–25.[4] Khan, S. A., et al., “Viscosity Correlations for Saudi Arabian Crude Oils,” SPE Paper 15720,Presented at the Fifth SPE Middle East Conference held in Manama, Bahrain, March 7-10,1987.[5] Elsharkawy, A.M., Alikhan, A.A., 1999. Models for predicting the viscosity of Middle Eastcrude oils. Fuel 78, 891– 903.[6] Glaso, O., 1980. Generalized pressure–volume–temperature correlation for crude oilsystem. JPT 2, 785– 795.[7] Kartoatmodjo, F., Schmidt, Z., 1994. Large data bank improves crude physical propertycorrelation. Oil Gas J. 4, 51–55.[8] Labedi, R., 1992. Improved correlations for predicting the viscosity of light crudes. J. Pet.Sci. Eng. 8, 221– 234.[9] Little, J.E., Kennedy, H.T., 1968. Calculating the viscosity of hydrocarbon systems withpressure temperature and composition. Soc. Pet. Eng. J. 6, 157– 162.[10] Lohrenz, J., Bray, B.C., Clark, C.R., 1964. Calculating viscosities of reservoir fluids fromtheir composition. JPT 10, 1170– 1176.