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Estimation of gas–oil surface tension
Journal of Petroleum Science and Engineering 27 Ž2000. 197–200 www.elsevier.nlrlocaterjpetscieng
Short communication
Estimation of gas–oil surface tension Ghassan H. Abdul-Majeed a,) , Nimat B. Abu Al-Soof a
b
Computer Center, UniÕersity of Baghdad, P.O. Box 47101, Jadiriyah, Baghdad, Iraq b Petroleum Research Center, Baghdad, Iraq Received 16 November 1998; accepted 10 April 2000
Abstract A method for estimating gas–oil surface tension has been presented in this study. This method consists of two empirical equations. The first equation relates dead oil surface tension with API gravity and temperature, while the second relates the ratio of live to dead oil surface tension with solution gas–oil ratio. The proposed method shows excellent results compared to the experimental data, and clearly outperforms the empirical work of Baker and Swerdloff. q 2000 Elsevier Science B.V. All rights reserved. Keywords: physical fluid properties; gas–oil surface tension; solution GOR
1. Introduction Surface tension is an important property where wetting, penetrating, foaming or droplet formation of a liquid is considered. Values of gas–liquid surface tension are used in the design of fractionators, absorbers, separators, two-phase pipelines and in reservoir calculations. It has been shown in the literature that the surface tension of a mixture Žlike crude oil. is a function of temperature, pressure and composition. Unfortunately, in most cases, the composition is not available and then the composition model for estimating surface tension becomes inapplicable. Many attempts ŽBaker and Swerdloff, 1956; Katz et al., 1959. have been made to develop correlations that are based on other properties rather than composition. Baker and Swedloff’s method has found wide
)
Corresponding author. E-mail address: [email protected] ŽG.H. Abdul-Majeed..
application ŽBrill and Beggs, 1991. in the industry despite its empirical origin. A brief description of this method follows.
2. Baker–Swerdloff method This method consists of two relationships: Ž1. the first ŽFig. 8 of their work. relates the dead oil surface tension Žsurface tension of gas-free oil. with temperature and API gravity; only two temperature values are considered in this relation, and Ž2. the second represents the effect of solution gas on surface tension. To estimate this effect, the authors relate the ratio of live to dead oil surface tension with saturation pressure ŽFig. 9 of their work.. They suggested that the data could be represented by a single curve for all oil samples, regardless of the API gravity. Analysis of Fig. 9 of the Baker–Swerdloff paper indicates a considerable scatter of data for pressures
0920-4105r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 0 - 4 1 0 5 Ž 0 0 . 0 0 0 5 8 - 9
198
G.H. Abdul-Majeed, N.B. Abu Al-Soofr Journal of Petroleum Science and Engineering 27 (2000) 197–200
Table 1 Experimental data of dead oil surface tension API gravity
sdo Ždynrcm. T s 54.448C
T s 37.788C
T s15.568C
15 20 30 35 40 50
32.8 31.5 29.0 28.0 26.2 23.1
34.0 33.0 30.2 29.4 27.8 24.9
36.0 35.0 32.2 31.4 30.0 26.9
greater than 2758 kPa Ž400 psi.. This scatter is due to the fact that for any pressure in the intermediate to high-pressure range, the gas dissolved in light oils is much greater than that dissolved in heavy oils. Therefore, at any pressure the surface tension for light oils is lower than for heavy oils. The purpose of this study is to develop a general and accurate method for estimating gas–oil surface tension.
chemistry texts. A complete list of the data obtained is presented in Tables 1 and 2. It is clear from these tables that wide ranges of the important parameters are covered by the data bank.
4. New correlations 4.1. Dead oil surface tension The values of dead oil surface tension are plotted against API gravity for three different temperatures. A straight line can represent the data for each temperature ŽFig. 1.. This plot shows that dead oil surface tension is inversely related to temperature and API gravity. Since the lines of Fig. 1 are parallel, it is possible to make them coincident by multiplying each line by a constant, A, which is a function of temperature. The line of 37.788C is arbitrarily chosen as the base line, with A defined as 1.0. The values of A necessary to shift each of the other lines until they coincide with the base line are then approximated as a function of temperature as follows: A s 1.11591 y 0.00305T
3. Data acquisition The analyses of six selected bottom-hole oil samples are made available for this investigation. The data bank consists of 18 PVT tests for dead oil surface tension, sdo and 42 PVT tests for live oil surface tension s lo taken at a temperature of to 37.788C. The measured values are obtained using two standard means, the tensiometer and the drop method. The procedures can be found in physical
Ž 1.
where T is the temperature in 8C. The data of the baseline for T s 37.788C can be reproduced by:
sdo s 38.085 y 0.259API
Ž 2.
Therefore, the dead oil surface tension at any temperature and API gravity can be calculated using:
sdo s A Ž 38.085 y 0.259API .
Ž 3.
Table 2 Experimental data of live oil surface tension at T s 37.788C API gravity
15.0 20.0 30.0 35.0 40.0 50.0
s lo Ždynrcm. Pressure ŽkPa. 1378.95
2757.9
5515.8
9652.7
13,789.5
17,236.9
20,684.3
30.6 29.04 25.972 24.820 23.352 20.418
27.2 25.74 22.65 21.32 19.74 16.93
22.1 20.13 16.01 15.18 13.07 10.96
15.64 14.19 11.17 9.636 8.062 6.747
11.22 9.9 6.644 5.840 5.004 3.735
8.5 7.59 5.436 4.380 3.614 2.739
6.46 5.445 3.926 3.066 2.641 2.117
G.H. Abdul-Majeed, N.B. Abu Al-Soofr Journal of Petroleum Science and Engineering 27 (2000) 197–200
199
ing equations are suggested to reproduce the data:For Rs - 50 m3rm 3 :
s lo sdo
1 s
1 q 0.02549Rs1.0157
For Rs G 50 m3rm 3 : s lo s 32.0436Rsy1.1367 sdo
Ž 4.
Ž 5.
Since the solution gas–oil ratio depends on temperature, pressure, gas specific gravity and API gravity, the inclusion of Rs makes proposed equations account for the effects of these variables. Fig. 1. Surface tension of crude oils at atmospheric pressure.
5. Validity 4.2. LiÕe oil surface tension As previously noted, the use of pressure as a correlating variable for estimating live oil surface tension does not seem practical. Therefore, the solution gas–oil ratio, Rs, was selected as a correlating variable. For each data point, the ratio Ž s lo rsdo . is calculated and plotted as a function of Rs as shown in Fig. 2. The Lasater Ž1958. correlation is used to calculate Rs; a very satisfactory correlation exists between the plotted parameters ŽFig. 2.. The follow-
Fig. 2. Effect of solution gas on surface tension of crude oils Žthis study..
To check their validity, the developed equations and the work of Baker and Swerdloff are tested against the present experimental data. Fig. 3 shows the comparison between the measured and predicted live oil surface tension values. As shown, excellent agreement is obtained between observations and those given by the new equations. The performance of the Baker–Swerdloff method is also shown in Fig. 3. A larger spread of the predicted values is observed for their method. Table 3 gives a summary of the statistical results. Comparison of the results reveals that the newly developed equations are more accurate than the method of Baker and Swerdloff.
Fig. 3. Comparison between the proposed and Baker–Swerdloff methods using present data.
200
G.H. Abdul-Majeed, N.B. Abu Al-Soofr Journal of Petroleum Science and Engineering 27 (2000) 197–200
Table 3 Prediction of methods using present data Method
Average percentage error
Absolute average percentage error
Standard deviation
Baker–Swerdloff This study
1.12 0.64
16.25 7.280
21.7 9.77
Table 4 Prediction of methods using Baker–Swerdloff data Method
Average percentage error
Absolute average percentage error
Standard deviation
Baker–Swerdloff This study
18.32 y1.18
23.43 10.91
36.8 19.6
For further checking, the proposed method is tested against the Baker and Swerdloff Ž1956. data. This data was used by Baker and Swerdloff to develop their method. The statistical results are listed in Table 4. It is clear that the proposed equations give results much better than those given by the Baker and Swerdloff method.
Notation API Rs T sdo s lo
6. Conclusions
References
1. Based on 60 experimentally measured data points, a new method for estimating gas–oil surface tension as a function of temperature, API gravity and solution GOR is proposed. 2. The new method is more accurate than the widely used Baker and Swerdloff method when tested against the present data and data from other sources.
Baker, O., Swerdloff, W., 1956. Finding surface tension of hydrocarbon liquids. Oil Gas J. 2 Ž3., 125–128. Brill, J.P., Beggs, H.D., 1991. Two-Phase Flow in Pipes. Univ. of Tulsa. Katz, D.L. et al., 1959. Handbook of Natural Gas Engineering. McGraw-Hill, New York. Lasater, J.A., 1958. Bubble point pressure correlation. Trans. AIME, 379.
API gravity solution GOR, m3rm 3 temperature, 8C dead oil surface tension, dynrcm live oil surface tension, dynrcm
Short communication
Estimation of gas–oil surface tension Ghassan H. Abdul-Majeed a,) , Nimat B. Abu Al-Soof a
b
Computer Center, UniÕersity of Baghdad, P.O. Box 47101, Jadiriyah, Baghdad, Iraq b Petroleum Research Center, Baghdad, Iraq Received 16 November 1998; accepted 10 April 2000
Abstract A method for estimating gas–oil surface tension has been presented in this study. This method consists of two empirical equations. The first equation relates dead oil surface tension with API gravity and temperature, while the second relates the ratio of live to dead oil surface tension with solution gas–oil ratio. The proposed method shows excellent results compared to the experimental data, and clearly outperforms the empirical work of Baker and Swerdloff. q 2000 Elsevier Science B.V. All rights reserved. Keywords: physical fluid properties; gas–oil surface tension; solution GOR
1. Introduction Surface tension is an important property where wetting, penetrating, foaming or droplet formation of a liquid is considered. Values of gas–liquid surface tension are used in the design of fractionators, absorbers, separators, two-phase pipelines and in reservoir calculations. It has been shown in the literature that the surface tension of a mixture Žlike crude oil. is a function of temperature, pressure and composition. Unfortunately, in most cases, the composition is not available and then the composition model for estimating surface tension becomes inapplicable. Many attempts ŽBaker and Swerdloff, 1956; Katz et al., 1959. have been made to develop correlations that are based on other properties rather than composition. Baker and Swedloff’s method has found wide
)
Corresponding author. E-mail address: [email protected] ŽG.H. Abdul-Majeed..
application ŽBrill and Beggs, 1991. in the industry despite its empirical origin. A brief description of this method follows.
2. Baker–Swerdloff method This method consists of two relationships: Ž1. the first ŽFig. 8 of their work. relates the dead oil surface tension Žsurface tension of gas-free oil. with temperature and API gravity; only two temperature values are considered in this relation, and Ž2. the second represents the effect of solution gas on surface tension. To estimate this effect, the authors relate the ratio of live to dead oil surface tension with saturation pressure ŽFig. 9 of their work.. They suggested that the data could be represented by a single curve for all oil samples, regardless of the API gravity. Analysis of Fig. 9 of the Baker–Swerdloff paper indicates a considerable scatter of data for pressures
0920-4105r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 0 - 4 1 0 5 Ž 0 0 . 0 0 0 5 8 - 9
198
G.H. Abdul-Majeed, N.B. Abu Al-Soofr Journal of Petroleum Science and Engineering 27 (2000) 197–200
Table 1 Experimental data of dead oil surface tension API gravity
sdo Ždynrcm. T s 54.448C
T s 37.788C
T s15.568C
15 20 30 35 40 50
32.8 31.5 29.0 28.0 26.2 23.1
34.0 33.0 30.2 29.4 27.8 24.9
36.0 35.0 32.2 31.4 30.0 26.9
greater than 2758 kPa Ž400 psi.. This scatter is due to the fact that for any pressure in the intermediate to high-pressure range, the gas dissolved in light oils is much greater than that dissolved in heavy oils. Therefore, at any pressure the surface tension for light oils is lower than for heavy oils. The purpose of this study is to develop a general and accurate method for estimating gas–oil surface tension.
chemistry texts. A complete list of the data obtained is presented in Tables 1 and 2. It is clear from these tables that wide ranges of the important parameters are covered by the data bank.
4. New correlations 4.1. Dead oil surface tension The values of dead oil surface tension are plotted against API gravity for three different temperatures. A straight line can represent the data for each temperature ŽFig. 1.. This plot shows that dead oil surface tension is inversely related to temperature and API gravity. Since the lines of Fig. 1 are parallel, it is possible to make them coincident by multiplying each line by a constant, A, which is a function of temperature. The line of 37.788C is arbitrarily chosen as the base line, with A defined as 1.0. The values of A necessary to shift each of the other lines until they coincide with the base line are then approximated as a function of temperature as follows: A s 1.11591 y 0.00305T
3. Data acquisition The analyses of six selected bottom-hole oil samples are made available for this investigation. The data bank consists of 18 PVT tests for dead oil surface tension, sdo and 42 PVT tests for live oil surface tension s lo taken at a temperature of to 37.788C. The measured values are obtained using two standard means, the tensiometer and the drop method. The procedures can be found in physical
Ž 1.
where T is the temperature in 8C. The data of the baseline for T s 37.788C can be reproduced by:
sdo s 38.085 y 0.259API
Ž 2.
Therefore, the dead oil surface tension at any temperature and API gravity can be calculated using:
sdo s A Ž 38.085 y 0.259API .
Ž 3.
Table 2 Experimental data of live oil surface tension at T s 37.788C API gravity
15.0 20.0 30.0 35.0 40.0 50.0
s lo Ždynrcm. Pressure ŽkPa. 1378.95
2757.9
5515.8
9652.7
13,789.5
17,236.9
20,684.3
30.6 29.04 25.972 24.820 23.352 20.418
27.2 25.74 22.65 21.32 19.74 16.93
22.1 20.13 16.01 15.18 13.07 10.96
15.64 14.19 11.17 9.636 8.062 6.747
11.22 9.9 6.644 5.840 5.004 3.735
8.5 7.59 5.436 4.380 3.614 2.739
6.46 5.445 3.926 3.066 2.641 2.117
G.H. Abdul-Majeed, N.B. Abu Al-Soofr Journal of Petroleum Science and Engineering 27 (2000) 197–200
199
ing equations are suggested to reproduce the data:For Rs - 50 m3rm 3 :
s lo sdo
1 s
1 q 0.02549Rs1.0157
For Rs G 50 m3rm 3 : s lo s 32.0436Rsy1.1367 sdo
Ž 4.
Ž 5.
Since the solution gas–oil ratio depends on temperature, pressure, gas specific gravity and API gravity, the inclusion of Rs makes proposed equations account for the effects of these variables. Fig. 1. Surface tension of crude oils at atmospheric pressure.
5. Validity 4.2. LiÕe oil surface tension As previously noted, the use of pressure as a correlating variable for estimating live oil surface tension does not seem practical. Therefore, the solution gas–oil ratio, Rs, was selected as a correlating variable. For each data point, the ratio Ž s lo rsdo . is calculated and plotted as a function of Rs as shown in Fig. 2. The Lasater Ž1958. correlation is used to calculate Rs; a very satisfactory correlation exists between the plotted parameters ŽFig. 2.. The follow-
Fig. 2. Effect of solution gas on surface tension of crude oils Žthis study..
To check their validity, the developed equations and the work of Baker and Swerdloff are tested against the present experimental data. Fig. 3 shows the comparison between the measured and predicted live oil surface tension values. As shown, excellent agreement is obtained between observations and those given by the new equations. The performance of the Baker–Swerdloff method is also shown in Fig. 3. A larger spread of the predicted values is observed for their method. Table 3 gives a summary of the statistical results. Comparison of the results reveals that the newly developed equations are more accurate than the method of Baker and Swerdloff.
Fig. 3. Comparison between the proposed and Baker–Swerdloff methods using present data.
200
G.H. Abdul-Majeed, N.B. Abu Al-Soofr Journal of Petroleum Science and Engineering 27 (2000) 197–200
Table 3 Prediction of methods using present data Method
Average percentage error
Absolute average percentage error
Standard deviation
Baker–Swerdloff This study
1.12 0.64
16.25 7.280
21.7 9.77
Table 4 Prediction of methods using Baker–Swerdloff data Method
Average percentage error
Absolute average percentage error
Standard deviation
Baker–Swerdloff This study
18.32 y1.18
23.43 10.91
36.8 19.6
For further checking, the proposed method is tested against the Baker and Swerdloff Ž1956. data. This data was used by Baker and Swerdloff to develop their method. The statistical results are listed in Table 4. It is clear that the proposed equations give results much better than those given by the Baker and Swerdloff method.
Notation API Rs T sdo s lo
6. Conclusions
References
1. Based on 60 experimentally measured data points, a new method for estimating gas–oil surface tension as a function of temperature, API gravity and solution GOR is proposed. 2. The new method is more accurate than the widely used Baker and Swerdloff method when tested against the present data and data from other sources.
Baker, O., Swerdloff, W., 1956. Finding surface tension of hydrocarbon liquids. Oil Gas J. 2 Ž3., 125–128. Brill, J.P., Beggs, H.D., 1991. Two-Phase Flow in Pipes. Univ. of Tulsa. Katz, D.L. et al., 1959. Handbook of Natural Gas Engineering. McGraw-Hill, New York. Lasater, J.A., 1958. Bubble point pressure correlation. Trans. AIME, 379.
API gravity solution GOR, m3rm 3 temperature, 8C dead oil surface tension, dynrcm live oil surface tension, dynrcm