Abstract
In this study, the prediction issue of oil viscosity, on oil samples taken from Guneshli oil field of Azerbaijan has been viewed applying empirical correlations as Beggs-Robinson, Labedi, modified Kartoatmodjo, Elsharkawy and Alikhan, Al-Khafaji. The correlation models used in the evaluation of viscosity of Azerbaijan oil have been implemented in the Python software environment. The obtained values on empirical correlations have been compared to experimental data obtained from Guneshli oil field. The result of prediction has been evaluated using statistic functions as absolute average deviation (AAD), mean absolute error (MAE), correlation coefficient, root mean square error (RMSE). According to statistical analysis, it has been known that the Beggs-Robinson model has shown the lowest value on AAD (10.5614%), MAE (12.4427 %), RMSE (20.0853 %). The Labedi model has presented the worst result on every four criterions. Even though the Elsharkawy-Alikhan model has presented the highest result (99.9272%) on correlation coefficient, in the evaluation of viscosity of Azerbaijan crude oil, the Beggs-Robinson model can be considered more acceptable.
Keywords: Correlation, Pressure, Volume, Temperature, Oil viscosity, Dead oil, Solution gas oil ratio, Bubble pressure point.
Received: 24 October 2018 / Revised: 30 November 2018 / Accepted: 4 January 2019/ Published: 11 February 2019
1. INTRODUCTION
In oil fields, the accurate knowledge about pressure-volume-temperature (PVT) properties of reservoir fluid are considered primary data for engineer-oilmen in the projection of oil fields, development and exploitation, calculation of well debit, projection of surface devices, as well as, calculation of hydrocarbon reserves. Viscosity is one of the most important parameters of PVT properties. Especially, viscosity is important in the modeling of oil gas fields, projection of pipelines or compressor stations, increasing oil extraction and storing natural gas [1-13]. It plays a major role in the management of oil in porous environment and pipes, and determines the internal resistance of the liquid flow. Oil viscosity is a function of physical properties of saturated oil-gas as pressure, temperature, the specific gravity of oil, the specific gravity of gas, bubble point pressure: [8, 10, 11, 14].
The oil viscosity directly affects to the flow of oil into the bottom of the well during the operation of the oil reservoirs. How much oil viscosity is little, its flow rate increases so much. In atmosphere, the viscosity of gas free oil (dead oil) can range from 0.1 to 1000 cp. The viscosity of the oil in the laying conditions varies depending on the pressure and temperature of the layer and the amount of gas that solved in oil. That’s why with the increase of temperature the viscosity of the oil decreases, and when gas solves in oil, the oil viscosity is significantly reduced. Therefore, the viscosity of the oil in the atmosphere and laying conditions is different. In one of Azerbaijan oilfields the oil viscosity is 1,23 cp in layer condition (Pl=119 atm, tl=24°C və Qf=100 m3/T), but its viscosity in atmosphere condition is 5. However, experiments show that the oil's viscosity increases poorly with pressure increasing starts from saturation pressure. The smallest value of oil viscosity exists in the saturation pressure when oil and gas create touch surface [14-16].
Bubble point pressure Pb– is the maximum pressure that gas begins to separate from the oil during the isothermal expansion of the oil under the thermodynamic balance condition. Saturation pressure is high when the temperature is high.
Solution Gas Oil Ratio ( GOR), Rs– is the ratio of the volume of measured gas under normal condition (on the surface) to the volume of the remaining oil.
Generally, in the standard PVT analyses increased pressure to cause increase in viscosity when increased pressure is higher than saturation pressure. Ideally, viscosity is defined by laboratory experiments using samples taken from bottom of well at reservoir pressure and temperature conditions. When laboratory information are not satisfactory, engineers use empiric correlations, which usually differ by the complexity and accuracy, according to exist information of crude oil. Correlation means regression equations based on experimental data acquired in laboratory studies. The accuracy of these correlations largely depends on primary data used in the calculations and composition of fluids of various geographic places.
Over the last 70 years, in the prediction of oil viscosity, numerous correlation equations, which characterize these or other oils of the world have been proposed by authors as Beal [1]; Chew and Connally [5]; Vazquez and Beggs [6]; Beggs and Robinson [2]; Khan, et al. [8]; Labedi [3]; Glaso [7]; Kartoatmodjo and Schmidt [4]; Al-Marhoun [11]; Abdulmajeed [17]. The summary of used correlations in this study has been given in appendix-1.
The purpose of the study is to explore the possibility of applying the widely spread correlations in scientific literature in the evaluation of the Azerbaijani oils’ viscosity for prediction of viscosity, which is one of the main parameters of PVT properties of reservoir fluid.
2. VISCOSITY DATA
Oil samples published in Huseynov, et al. [14] of Azerbaijan Guneshli oil field have been used to conduct experiment (table 1). For Azerbaijan oil, the relative density (specific gravity) of gas has been taken 0.8, the relative density (specific gravity) of oil has been taken 0.8644, API gravity has been taken 32.1974 [14].
Table-1. Data of Guneshli oil field
Source: Huseynov, et al. [14]
For Azerbaijan oil, the relative density (specific gravity) of gas has been taken 0.8, the relative density (specific gravity) of oil has been taken 0.8644, API gravity has been taken 32.1974 [14].
Beggs-Robinson, Labedi, modified Kartoatmodjo, Al-Khafiji and Elsharkawy-Alikhan correlations have been used which are come across mainly in the literature, for calculating oil viscosity [2-4, 9, 10].
Experiments were conducted using Python programming language (jupyter notebook) on Linux OS (Ubuntu Desktop 16.04) with 1.7GB RAM, Intel(R) Core(TM) i5-2400, 64bit prosessor, 3.10GHz CPU properties. And Matlab are used for visualize of results.
3. RESULTS AND DISCUSSIONS
The viscosity of crude oil has been calculated by Beggs-Robinson, modified Kartoatmodjo, Labedi, Elsharkawy-Alikhan and Al-Khafiji correlations. The comparison of calculated results to viscosty of oil samples taken from Guneshli oil field has been shown in Table 2. One sample of pseudo code of program is presented in appendix 2.
Table-2. The calculated values of viscosity with Beggs-Robinson, Modified Kartoatmodjo, Labedi, Elsharkawy-Alikhan and Al-Khafiji
Oils samples |
Experimental correlation |
Calculated correlations |
||||
Beggs-Robinson |
Labedi |
Modified Kartoatmodjo |
Elsharkawy - Alikhan |
Al-Khafaji |
||
1 |
0.57 |
0.7039 |
1.5402 |
0.7252 |
0.6836 |
0.8764 |
2 |
0.63 |
0.7819 |
1.6177 |
0.8359 |
0.8034 |
1.0049 |
3 |
0.717 |
0.8498 |
1.6385 |
0.9558 |
0.9224 |
1.1225 |
4 |
0.762 |
0.8714 |
1.6193 |
1.0065 |
0.9678 |
1.1621 |
5 |
0.869 |
0.9563 |
1.6625 |
1.1657 |
1.1083 |
1.3043 |
6 |
0.932 |
0.9964 |
1.6672 |
1.25 |
1.1769 |
1.3706 |
7 |
1.004 |
1.0429 |
1.6795 |
1.3449 |
1.2522 |
1.445 |
8 |
1.084 |
1.1002 |
1.7027 |
1.4568 |
1.3396 |
1.5335 |
9 |
1.277 |
1.2836 |
1.8294 |
1.775 |
1.5909 |
1.8026 |
10 |
1.391 |
1.391 |
1.8949 |
1.9501 |
1.7234 |
1.9476 |
11 |
1.52 |
1.5319 |
1.9892 |
2.1588 |
1.8816 |
2.127 |
12 |
1.663 |
1.7138 |
2.1197 |
2.3978 |
2.0632 |
2.3422 |
13 |
1.82 |
1.9635 |
2.3137 |
2.6798 |
2.2794 |
2.6116 |
14 |
1.99 |
2.2553 |
2.5205 |
2.9252 |
2.462 |
2.8596 |
15 |
2.174 |
2.8277 |
3.2115 |
3.3294 |
2.7818 |
3.2632 |
Saturated oil viscosity is predicted by Beggs-Robinson, Modified Kartoatmodjo, Labedi, Elsharkawy-Alikhan and Al-Khafiji correlations. The accuracy has been checked with experimental data for calculation of saturated oil viscosity.
Figure-1. The comparison of experimental viscosity with calculated viscosity by Elsharkawy and Alikhan correlation.
Labedi correlation [3] has been applied to calculate oil viscosities of obtained Azerbaijan oil samples. The comparison of calculated values with predicted values has been shown in figure 2. In this correlation model, AAD is 73.4591%, is 91.4944%, MAE is 70.6893%, RMSE is 73.4825%.
Figure-2. The comparison of experimental viscosity with calculated viscosity by Labedi correlation
The modified Kartoatmodjo correlation [4] is has been checked over Azerbaijan crude oil samples, and obtained result has been presented graphically in figure 3. AAD is 38.3125%, is 99.8744%, MAE is 50.3589%, RMSE is 58.2237%.
Figure-3. The comparison of experimental viscosity with calculated viscosity by modified Kartoatmodjo correlation
Beggs-Robinson correlation [2] has been tested with viscosity of oil samples taken from Guneshli oil reservoir and comparative result has been shown in figure 4. For this model, AAD is 10.5614%, is 97.2405%, MAE is 12.4427%, RMSE is 20.0853%.
Fig-4. The comparison of experimental viscosity with calculated viscosity by Beggs-Robinson correlation
Al-Khafiji correlation [9] has been applied to calculate viscosity of Azerbaijan oil samples. The comparison predicted value with experimental value has been shown in figure 5. AAD is 46.9403%, is 99.6687%, MAE is 55.7998%, and RMSE is 59.5658%.
Figure-5. The comparison of experimental viscosity with calculated viscosity by Al-Khafiji correlation
4. STATISTICAL ANALYSIS
The accuracy of applied correlations – expressed by (1)-(5) formulas – has been calculated based on statistical parameters [18, 19] as absolute average deviation, mean absolute error, correlation coefficient.
Where, n is the number of experimental points, is experimental viscosity, is calculated viscosity. AAD% shows how to be near the calculated values are to experimental values.
The results of calculations have been presented in table 3, and graphically in figure 6.
Table-3. The results of statistical analysis
Correlations |
Statistical analysis |
|||
AAD(%) |
R2 (%) |
MAE (%) |
RMSE (% ) |
|
Beggs - Robinson |
10.5614 |
97.2405 |
12.4427 |
20.0853 |
Labedi |
73.4591 |
91.4944 |
70.6893 |
73.4825 |
Modified Kartoatmodjo |
38.3125 |
99.8744 |
50.3589 |
58.2237 |
Elsharkawy - Alikhan |
25.2323 |
99.9272 |
30.8906 |
33.4159 |
Al-Khafaji |
46.9403 |
99.6687 |
55.7998 |
59.5658 |
As seen from Figure 6, the %AAD value is respectively 10.5614, 73.4591, 38.3125, 25.2323, and 46.9403%, and % is 97.2405, 91.4944, 99.8744, 99.9272 and 99.6687 for Beggs-Robinson, Labedi, modified Kartoatmodjo, Elsharkawy-Alikhan and Al-Khafaji corrections.
Figure-6. The result of statistical analysis
5. CONCLUSION
Five empiric models have been applied to evaluate viscosity of crude oil on the basis of Azerbaijan Guneshli oil field. At the end of the analysis, it was became clear that the Beggs and Robinson model had the lowest %AAD (10.5614%) value and the Labedi model had the highest %AAD value (73.4591 %) for Azerbaijani oil compared to other correlation models. Elsharkawy-Alikhan model have showed the highest result for correlation coefficient (99.9272%). According to the results of statistical analysis, we can say that Beggs-Robinson model compared to other used correlation models can be considered more acceptable in the evaluation of viscosity of Azerbaijan crude oil. Experiments show that, in the prediction of viscosity, partial compline is observed to offer traditional empiric correlations according to different regions for oil which differ sharply each other by PVT properties between predicted and experimental values. That’s why none of these correlations can be considered universal correlation. More compatible empiric correlations must be applied to calculate and to predict accurately viscosity of Azerbaijan crude oil. In future studies, it is planned to develop more accurate correlation models for the evaluation of the viscosity of Azerbaijan crude oil. The development of model based on machine learning methods is also intended to evaluate more accurately viscosity.
| Funding: This work was supported by the SOCAR Science Foundation of Azerbaijan (Grant 16LR - AMEA) |
| Competing Interests: The authors declare that they have no competing interests. |
| Contributors/Acknowledgement: All authors contributed equally to the conception and design of the study. |
REFERENCES
[1] C. Beal, "The viscosity of air, water, natural gas, crude oil and its associated gases at oil field temperatures and pressures," Transactions of the AIME, vol. 165, pp. 94-115, 1946.
[2] H. D. Beggs and J. Robinson, "Estimating the viscosity of crude oil systems," Journal of Petroleum Technology, vol. 27, pp. 1,140-1,141, 1975.Available at: https://doi.org/10.2118/5434-pa.
[3] R. Labedi, "Improved correlations for predicting the viscosity of light crudes," Journal of Petroleum Science and Engineering, vol. 8, pp. 221-234, 1992.Available at: https://doi.org/10.1016/0920-4105(92)90035-y.
[4] T. Kartoatmodjo and Z. Schmidt, "Large data bank improves crude physical property correlations," Oil and Gas Journal, vol. 92, pp. 51-55, 1994.
[5] J. Chew and C. H. Connally, "Viscosity correlations for gas saturated crude oils," Jr Trans AIME, vol. 216, pp. 23-25, 1959.
[6] M. Vazquez and H. D. Beggs, "Correlations for fluid physical property prediction," Journal of Petroleum Technology, vol. 32, pp. 968-970, 1980.Available at: https://doi.org/10.2118/6719-pa.
[7] O. Glaso, "Generalized pressure-volume-temperature correlations," Journal of Petroleum Technology, vol. 32, pp. 785-795, 1980.Available at: https://doi.org/10.2118/8016-pa.
[8] S. Khan, M. Al-Marhoun, S. Duffuaa, and S. Abu-Khamsin, "Viscosity correlations for Saudi Arabian crude oils," in SPE Paper 15720 Presented at the Fifth SPE Middle East Conference held in Manama, Bahrain, 1987, pp. 7-10.
[9] A. H. Al-Khafaji, G. H. Abdul-Majeed, and S. F. Hassoon, "Viscosity correlation for dead, live and undersaturated crude oils," Journal of Petres's Research, vol. 6, pp. 1-16, 1987.
[10] A. Elsharkawy and A. Alikhan, "Models for predicting the viscosity of Middle East crude oils," Fuel, vol. 78, pp. 891-903, 1999.Available at: https://doi.org/10.1016/s0016-2361(99)00019-8.
[11] M. A. Al-Marhoun, "Preasure-volume-temperature standsrd deviation correlations for Saudi crude oils," in Paper SPE, 13718 Presented at the SPE 1985 Middle East Technical Conference, Bahrain, 1985, pp. 11-14.
[12] R. Abedini, A. Abedini, and N. E. Yakhfrouzan, "A new correlation for prediction of undersaturated crude oil viscosity," Petroleum & Coal, vol. 52, pp. 50-55, 2010.
[13] M. Sattarin, H. Modarresi, M. Bayat, and M. Teymori, "New viscosity correlations for dead crude oils," Petroleum & Coal, vol. 49, pp. 33-39, 2007.
[14] M. A. Huseynov, V. J. Abdullayev, and N. N. Hamidov, "The prediction of horizontal well performance on the basis of reservoir and well model," Azerbaijan Oil Industry, vol. 5, pp. 13-18, 2014.
[15] A. Mirzajanzadeh and M. A. Iskandarov, "The theoretical bases of the development and exploitation of oil and gas fields," Baku, p. 395, 2010.
[16] A. M. Salmanov, A. S. Eminov, and L. A. Abdullayeva, "Current status of oil development deposits of Azerbaijan and their geological field indicators," Baku, p. 74, 2015.
[17] R. K. Abdulmajeed, "New viscosity correlation for different Iraqi oil fields," Iraqi Journal of Chemical and Petroleum Engineering, vol. 15, pp. 71–76, 2014.
[18] F. Borns, Statistics for Petroleum Engineers. Dallas: SPE, 1969.
[19] W. J. Dixon and F. J. Massey, Introduction to statistical analysis. Tokyo: Jr.,Kogakusha Co., Ltd., 1969.
Appendix-1. Summary of used viscosity correlation
Appendix-2. Pseudo code of the Beggs-Robinson correlation
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
#input data
P=np.array(#value of pressure)
Rs=np.array(#value of solution gas-oil ratio)
exp_vis=np.array(#value of experimental viscosity)
T=np.array(#value of oil reservoir temperature)
Pb=np.array(#value of bubble point pressure)
sg_o=0.8644
sg_g=0.8
API=141.5/sg_o-131.5
x=pow(T,(-1.163))*pow(10,(3.0324-0.02023*API))
do_vis=pow(10,x)-1
a=10.715*pow((Rs+100),(-0.515))
b=5.44*pow((Rs+150),(-0.338))
cal_vis=a*pow(do_vis,b)
#visualization
plt.plot(exp_vis,color='blue',marker=".")
plt.plot(cal_vis,color='red',marker=".")
plt.legend(('Experimental viscosity', 'Calculated viscosity'), loc='upper left')
plt.xlabel('Experimental')
plt.ylabel('Calculated')
plt.title('The Beggs-Robinson correlation ')
plt.show()
Views and opinions expressed in this article are the views and opinions of the author(s), Review of Information Engineering and Applications shall not be responsible or answerable for any loss, damage or liability etc. caused in relation to/arising out of the use of the content. |