A NEW CORRELATION FOR PREDICTION OF UNDERSATURATED CRUDE OIL VISCOSITY

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1 Petroleum & Coal ISSN Available online at Petroleum & Coal 52 (1) 50-55, 2010 A NEW CORRELATION FOR PREDICTION OF UNDERSATURATED CRUDE OIL VISCOSITY R. Abedini 1, *, A. Abedini 2, N. Eslami Yakhfrouzan 1 1 Department of Chemical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran, 2 Department of Petroleum Engineering,Petroleum University of Technology, Ahwaz, Iran Received November 13, 2009, Accepted February 1, 2010 Abstract Viscosity is one of the most important governing parameters of the fluid flow, either in the porous media or in pipelines. So it is of great importance to use an accurate correlation to calculate the oil viscosity at various operating 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 calculation and so on compel the person to use empirical and semi-empirical correlations to find viscosity at various points of the flow path (along which T, P, R s and other parameters may vary). In the literature, several empirical correlations have been proposed for predicting undersaturated oil viscosity. Here, based on Iranian oil reservoirs data; new correlation has been developed for prediction of undersaturated oil viscosity. Validity and accuracy of this correlation has been confirmed by comparing the obtained results of this correlation and other ones with experimental data for Iranian oil samples. Checking the results of this correlation shows that the obtained results of Iranian oil viscosities in this work are in agreement with experimental data compared with other correlations. Keywords: Oil Viscosity, Correlation, Undersaturated, Saturated, Dead, API gravity. 1. Introduction Crude oil viscosity is an important physical property that controls and influences the flow of oil through porous media and pipes. The viscosity, in general, is defined as the internal resistance of the fluid to flow. Oil viscosity is a strong function of many thermodynamic and physical properties such as pressure, temperature, solution gas-oil ratio, bubble point pressure, gas gravity and oil gravity. Usually oil viscosity is determined by laboratory measurements at reservoir temperature. Viscosity is usually reported in standard PVT analyses. Increasing pressure always causes increase in viscosity above the bubble point. However below the bubble point, increasing pressure causes an increase in solution gas, which in turn decreases the oil viscosity. Thus, oil viscosity correlations all belong to three categories: dead oil, saturated oil and undersaturated oil viscosity correlation. Numerous correlations have been proposed to calculate the oil viscosity. These correlations are categorized into two types. The first type which refers to black oil type correlations predict viscosities 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 to compositional models derives mostly from the principle of corresponding states and its extensions. In these correlations beside previous properties, other properties such as reservoir fluid composition, pour point temperature, molar mass, normal boiling point, critical temperature and acentric factor of components are used [ 9, 10]. 2. Undersaturated oil viscosity correlations Undersaturated oil viscosity correlations, which usually use saturated crude oil viscosity and pressure above the bubble point to predict viscosity of undersaturated oil reservoirs. These correlations are Beal [1], Vasquez and Beggs [2], Khan [4 ], and Kartoatmodjo and Schmidt [7].

2 R. Abedini et al./petroleum& Coal 52(1) 46-51, Beal correlation [1] This correlation proposes that for any specified oil, when only pressure is the variable, viscosity varies linearly with the pressure 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: 5 a = 3.9 ( 10 ) P 5 a ( ) ( ) m= 2.6 P Khan Correlation [4] Like the previous case, this correlation ignores the effect of μ ob on the coefficient which is multiplied by μ ob to predict μ o. μο = μ exp( ( P P )) (5) ob Kartoatmodjo and Schmidt Correlation [7] b Like beal one, this correlation proposes that for any specified oil, when only pressure is the variable, viscosity varies linearly with the pressure (6) μ = μ P P μ μ 3. Experimental Data ( P P )( ) μ = μ μ μ o ob b ob ob ( )( ) o ob b ob ob In this study, PVT experimental data of five sample oils from Iranian oil reservoirs have been used. These data include oil reservoir temperature, saturation pressure, API gravity and solution gas-oil ratio at reservoir temperature. Reservoir oil viscosities have been measured at various pressures above and below the bubble point pressure for different temperatures. Statistical experimental 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 5 API Temperature (ºF) Solution gas-oil ratio (SCF/STB) Saturation pressure (psia) Undersaturated viscosity (cp) The accuracy and ability of each mentioned correlation for predicting oil viscosity was checked with experimental data and Figs. 1, 2, 3 and 4 show this comparison. These figures confirm the disability of correlations for accurate prediction of oil viscosities. (1) (2) (3) (4)

3 R. Abedini et al./petroleum& Coal 52(1) 46-51, Fig. 1. Oil viscosity as a function of pressure. Fig. 2. Experimental values compared with calculated values calculated by Beal correlation Fig. 3. Experimental values compared with calculated values calculated based on the Vasquez-Beggs correlation 4. Development of the proposed correlations Fig. 4. Experimental values compared with calculated values calculated based on the khan correlation Proposed correlation is based on real data, which almost covers Iranian oil types. At pressures above bubble point pressure, oil is at single-phase state, while its solution gas oil is constant and it seems that pressure will be the most effective in oil viscosity. By increasing pressure above the bubble point, oil density and oil viscosity will be increased (Fig. 1). Several function forms have been tested to correlate undersaturated oil viscosity (μ o ) to saturated oil viscosity (μ ob ), and pressure increment above the bubble point (P-P b ). Proposed correlation in this work (for under-saturated oil) is as follows: b1 b2 b3 b4 b5 b6 b7 ( ) ( ) μ = μ 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 b Where: a 1 = a 2 = a 3 = a 4 = a 5 = a 6 = a 7 = b 1 = b 2 = b 3 = b 4 = b 5 = b 6 = b 7 = Results and Discussion 5.1. Validation of the proposed correlation The accuracy and ability of each mentioned correlation for predicting oil viscosity was checked with experimental data and Figs. 2, 3, 4 and 5 show this comparison. These figures confirm the disability of correlations for accurate prediction of oil viscosities. Fig. 6 depicts the comparison of experimental values of viscosity with predicted ones by two dimensions plot for undersaturated oil respectively. It is obvious from the figure that the new correlation provides results in good agreement with experimental values. Table 2 reveals average relative error (ARE), absolute average relative error (AARE) and standard deviation (SD) for undersaturated oil viscosity correlations respectively. ARE, AARE and SD are defined as below.

4 R. Abedini et al./petroleum& Coal 52(1) 46-51, Fig. 5. Experimental values compared with calculated values calculated based on the Kartoatmodjo and Schmidt correlation Fig. 6. Experimental values compared with calculated values calculated based on the New Model Table 2. Accuracy of viscosity correlations for prediction of undersaturated oil viscosities. Correlation ARE (%) AARE (%) SD (%) Undersaturated oil Beal, Vasquez and Beggs, Khan, Kartoatmodjo and Schmidt, New Model ARE N 1 Xexp erimental( Xcalculated( = N X i = 1 exp erimental( (8) N 1 X exp erimental ( X calculated ( AARE = N i= 1 X exp erimental( SD = N 1 X exp erimental X calculated AARE N 1 i= 1 X exp erimental ( 2 (9) (10) New viscosity correlation derived based on Iranian field data which does not require compositional information and can be used for black oil type fluids. The correlation can be used in black oil reservoir simulators, it can be easily tuned, and it provides better estimates of oil viscosity than the previous existing correlations. This is shown in the figure 7. Fig. 7. Comparison between all introduced correlations

5 R. Abedini et al./petroleum& Coal 52(1) 46-51, Accuracy of the proposed correlation Here, the accuracy of the proposed correlations in this work, as well as the correlations previously discussed, is checked. Using the 86 real cases data series of Iranian oils, the results of this work and other ones for estimating the oil viscosity are compared. Table 2and Fig.8 shows all of these comparisons. Fig. 8. Percent relative error distribution for undersaturated oil viscosity correlations Fig. 8 shows percent relative error distribution for all correlations. X exp erimental( X calculated( Where: Ei = 100 (i= 1, 2, 3,n d ) (11) X exp erimental( At this point, it should be mentioned the proposed correlations are only applicable to Iranian oils and their applicability to other regions should be checked. 6. Conclusion Generally the most common method for calculating viscosity of crude oils is viscosity correlations. However these correlations fail to predict oil viscosities at wide range of operating conditions such as pressure and temperature. In this work a new correlation for estimation of undersaturated Iranian oils has been proposed. This correlation is based on real data of the different types of Iranian oils. Input parameters for this correlation are oil API gravity, saturation pressure, reservoir temperature and pressure, which are easily measured in oil fields. In comparison with correlations previously published in the literature, new correlation has a better accuracy and performance for predicting the viscosity of Iranian oils. It should be mentioned that,

6 R. Abedini et al./petroleum& Coal 52(1) 46-51, this proposed correlation might be used for the prediction of Iranian oil viscosity. Application of this correlation for other oil samples can result in errors. Nomenclature Symbols Greeks API 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) Abbreviations P Pressure (psia) ARE Average relative error P b Saturation pressure oil bubble point AARE Average absolute relative error pressure (psia) Ei Percent relative error SD Standard deviation n d Number of data points References [1] Beal, C., Viscosity of air, water, natural gas, crude oil and its associated gases at oil field temperature and pressures. Trans. AIME 165, [2] Beggs, H.D., Robinson, J.R., Estimating the viscosity of crude oil systems. JPT 9, [3] Chew, J., Connally, C.A., Viscosity correlation for gassaturated crude oil. Trans. AIME 216, [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, [5] Elsharkawy, A.M., Alikhan, A.A., Models for predicting the viscosity of Middle East crude oils. Fuel 78, [6] Glaso, O., Generalized pressure volume temperature correlation for crude oil system. JPT 2, [7] Kartoatmodjo, F., Schmidt, Z., Large data bank improves crude physical property correlation. Oil Gas J. 4, [8] Labedi, R., Improved correlations for predicting the viscosity of light crudes. J. Pet. Sci. Eng. 8, [9] Little, J.E., Kennedy, H.T., Calculating the viscosity of hydrocarbon systems with pressure temperature and composition. Soc. Pet. Eng. J. 6, [10] Lohrenz, J., Bray, B.C., Clark, C.R., Calculating viscosities of reservoir fluids from their composition. JPT 10,

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