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A correlation approach for prediction of crude oil viscosities
Journal of Petroleum Science and Engineering 47 (2005) 163 – 174 www.elsevier.com/locate/petrol
A correlation approach for prediction of crude oil viscosities A. Naseria,T, M. Nikazarb, S.A. Mousavi Dehghania b
a PVT Department, Research Institute of Petroleum Industry (RIPI), Tehran, Iran Chemical Engineering Department, Amirkabir University of Technology, Tehran, Iran
Received 29 June 2004; received in revised form 10 February 2005; accepted 14 March 2005
Abstract The role of reservoir fluid viscosity for reservoir evaluation in performance calculations, planning thermal methods of enhanced oil recovery, evaluation of hydrocarbon reserves and designing production equipment and pipelines makes its accurate determination necessary. Reservoir oil viscosity is usually measured isothermally at reservoir temperature. However, at temperature other than reservoir temperature these data are estimated by empirical correlations. High dependency of oil viscosity on fluid nature and fluid source causes the unique application of these correlations to special cases from which they have been derived. Here, based on Iranian oil reservoirs data; new correlations have been developed for prediction of dead, saturated and undersaturated oil viscosities. These correlations have been derived using so many oil viscosity data. Validity and accuracy of these correlations have been confirmed by comparing the obtained results of these correlations and other ones with experimental data for so many Iranian oil samples. In contrast to other correlations which need so many specific parameters for oil viscosity prediction, this type of correlations need only some field data which always are available. Checking the results of these correlations shows that the obtained results of Iranian oil viscosities in this work are in agreement with experimental data compared with other correlations. D 2005 Elsevier B.V. All rights reserved. Keywords: Correlation; Viscosity data; PVT; Oil reservoir
1. Introduction Reservoir fluid properties form the basis of many petroleum-engineering calculations. PVT data are used in field reserve calculation, EOR processes,
T Corresponding author. Tel.: +98 21 2221586; fax: +98 21 6154854. E-mail address: [email protected] (A. Naseri). 0920-4105/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.petrol.2005.03.008
surface facilities design and fluid flow in porous media and pipelines. Viscosity data in the petroleum industry are usually obtained at reservoir temperature, which is a constant value. However, viscosity data at temperatures other than reservoir temperature and in cases where laboratory data becomes unavailable are estimated from empirical correlations. Sampling and viscosity measurement costs are the main reasons for inaccessibility of these data at other temperatures.
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the first type. As it can be seen in the results section for Iranian crude oils, the results of these correlations were not in good agreement with experimental data. Some of them have high errors in viscosity prediction. It seems that these behaviors are expectable; this is due to high dependency of oil viscosity on oil nature (heavy component content and nature in crude oils) and source; as we know all of these correlations are based on specific regions/crude oils (Sutton and Farshad, 1990). Using Iranian crude oil data in this work, new correlations have been developed for prediction of dead, saturated and under-saturated oil viscosity. The final correlations have been applied for about 222 real samples of Iranian oils. Comparing with other correlations and experimental data has inspected the validity and accuracy of the proposed correlations.
Above Pb Below Pb
Oil Viscosity, c
2.24
2.08
1.92
1.76
1.60 0
1040
2080
3120
4160
5200
Pressure, psia Fig. 1. Oil viscosity as a function of pressure.
Generally it may be said that there are two main types of correlation for oil viscosity prediction. The first type is those that use oil field data that usually are available, such as reservoir temperature, oil API gravity, solution gas / oil ratio, saturation pressure and pressure. The second type are empirical and/or semiempirical correlations which use some parameters other than those used in the first type; such as reservoir fluid composition, pour point temperature, molar mass, normal boiling point, critical temperature, and acentric factor of components (Lohrenz et al., 1964; Little and Kennedy, 1968; Ahrabi et al., 1987). In this work at first the experimental data have been checked with so many viscosity correlations of
2. Viscosity correlations review A literature survey has indicated that empirical viscosity correlations developed by classical regression techniques are divided into three major sections. First, dead oil viscosity correlations, which are used to estimate crude oil viscosity at atmospheric condition (stock tank) as a function of stock tank API gravity and reservoir temperature. Second, saturated oil viscosity correlations that use usually solution gas–oil ratio and dead oil viscosity to estimate viscosity of oil reservoir at bubble point pressure. The third type is under-saturated oil viscosity correlations, which usually use saturated
Table 1 Statistical data for dead crude oil viscosity correlations Correlations
Beal (Beal, 1946)
Beggs and Robinson (Beggs and Robinson, 1975)
Glaso (Glaso, 1980)
Labedi (Labedi, 1992)
Schmidt and kartoatmodjo (Kartoatmodjo and Schmidt, 1994)
Elsharkawy and Alikhan (Elsharkawy and Alikhan, 1999)
This work
Source of the used oils API Temperature 8F Dead oil viscosity, Cp Average relative error % Average absolute error %
US 52–10 220–100 188–0.8 24.2 –
– 58–16 295–70 – 0.6 13.5
North Sea 48–20 300–50 39–0.6 15.5 22.1
Africa 48–32 306–100 0.6–4.8 2.6 –
Data Bank 59–14.4 320–80 586–0.5 13.2 39.6
Middle East 48–20 300–100 0.6–33.7 2.5 19.3
Iran 44–17 295–105 54–0.75 6.61 7.77
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Table 2 Statistical data for saturated oil viscosity correlations Correlations
Chew and Connaly (Chew and Connally, 1959)
Beggs and Labedi Robinson (Labedi, 1992) (Beggs and Robinson, 1975)
Schmidt and kartoatmodjo (Kartoatmodjo and Schmidt, 1994)
Elsharkawy and This work Alikhan (Elsharkawy and Alikhan, 1999)
Source of the used oils Gas oil ratio SCF / STB Saturation Pressure, Pisa Saturated oil viscosity, Cp Average relative error % Average absolute error %
US 51–3544 5645–132 0.37–50 – –
– 2070–20 5265–132 – 1.8 27.3
Data Bank 572–2.3 6054–14.7 0.1–6.3 0.1 16.1
Middle East 3600–10 100–3700 21–0.05 2.8 18.7
Africa 3533–13 6358–60 0.11–6.3 2.4 22.8
Iran 4116–255 5900–420 18.15– 0.11 1.2 16.4
and Schmidt correlation (Kartoatmodjo and Schmidt, 1994) is based on a given data bank. Recently, Elsharkawy and Alikhan (Elsharkawy and Alikhan, 1999) have presented other empirical correlations for estimating dead crude oil viscosity for Middle East crudes. All of these correlations have expressed dead oil viscosity (l od) as a function of both oil API gravity and reservoir temperature (see Appendix A). Usually, application of dead oil viscosity correlations to crude oil of different sources results in huge errors. This difference is attributed to the difference in asphaltic, paraffinic and/or mixed nature of the oils. Egbogah and Ng (Egbogah and Ng, 1990) improved Beggs and Robinson’s (Beggs and Robinson, 1975) correlation by adding a new parameter, pour point temperature. However, pour point temperature is neither reported in any usual PVT report nor measured in the field. Mehrotra and Svrcek (Mehrotra and Svrcek, 1988) presented a one-parameter viscosity equation for bitumen that was later extended by Mehrotra (Mehrotra, 1991) to predict the viscosity of light and medium
crude oil viscosity and pressure above the bubble point to estimate viscosity of under-saturated oil reservoirs. Fig. 1 shows a typical oil viscosity diagram as a function of pressure at constant reservoir temperature. 2.1. Dead oil viscosity correlations The most popular empirical correlations that are used for dead oil viscosity (stock tank) in petroleum engineering are those developed by Beal (Beal, 1946), Beggs and Robinson (Beggs and Robinson, 1975), Glaso (Glaso, 1980), Labedi (Labedi, 1992) and Kartoatmodjo and Schmidt (Kartoatmodjo and Schmidt, 1994). Beal’s correlation (Beal, 1946) was developed from crude oil data of California, Beggs and Robinson’s correlation (Beggs and Robinson, 1975) was developed based on the crude oils of an unknown location, Galso’s correlation was developed (Glaso, 1980) from the North Sea crude oils, Labedi correlation (Labedi, 1992) has been presented for African crudes and finally Kartoatmodjo
Table 3 Statistical data for under-saturated oil viscosity correlations Correlations
Beal (Beal, 1946)
Beggs and Vasquez (Vasquez and Beggs, 1980)
Labedi (Labedi, 1992)
Schmidt and kartoatmodjo (Kartoatmodjo and Schmidt, 1994)
Elsharkawy and Alikhan (Elsharkawy and Alikhan, 1999)
This work
Source of the used oils Pressure above bubble point, Pisa Under-saturated oil viscosity, Cp Average relative error % Average absolute error %
US 1515–5155 0.2–315 2.7 –
– 141–9515 0.2–1.4 7.5 –
Africa – – 3.1 6.9
Data Bank – 0.2–517 4.3 6.4
Middle East 1287–10,000 0.2–5.7 0.9 4.9
Iran 1400–7000 31–0.1 0.64 2.12
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100.00
viscosity, pressure and saturation pressure in their models.
T=100F T=200F
10.00
T=250F T=300F
3. Viscosity data
1.00
0.10
0.01 20
25
30
35
40
45
50
Oil API gravity Fig. 2. Dead oil viscosity.
hydrocarbons. This parameter is evaluated from molar mass, normal boiling point, critical temperature, and acentric factor of components; however these parameters are not available for most crudes. Several empirical or semi-empirical correlations have also been developed from corresponding state equations by Teja et al. (Teja and Rice, 1982), Johnson et al. (Johnson and Mehrotra, 1987), and Johnson and Svreck (Johnson and Svrcek, 1991). Although these corresponding state correlations involve numerous computations and use fluid composition as an input variable, their prediction of dead oil viscosity is poor (Elsharkawy and Alikhan, 1999).
In this study PVT experimental data of 472 series of Iranian oil reservoirs have been used. These data include oil API gravity, reservoir temperature, saturation pressure, solution gas–oil ratio and PVT measurements (oil characterization) at reservoir temperature. Using the Rolling Ball viscometer (Ruska, series 1602), reservoir oil viscosities have been measured at various pressures above and below the bubble point pressure. In this study about 250 series of PVT and viscosity data have been used in developing a new empirical
a 1000.0 This Work
Dead oil viscosity, Cp
Dead oil viscosity, Cp
T=150F
Beal
100.0
AliKhan
10.0
1.0
0.1 20
2.2. Live oil viscosity correlations
Beggs
25
30
35
40
45
50
Oil API gravity
b 1000.0 This Work
Dead oil viscosity, Cp
Viscosity data of saturated and under-saturated oils at temperatures other than reservoir temperature are predicted from live oil reservoir viscosity correlations. Most saturated oil viscosity correlations express saturated oil viscosity (l ob) as a function of both dead oil viscosity (l od) and solution gas–oil ratio (R s) (see Appendix B). These correlations are: Chew and Connally (Chew and Connally, 1959), Beggs and Robinson (Beggs and Robinson, 1975), Kartoatmodjo and Schmidt (Kartoatmodjo and Schmidt, 1994), Labedi (Labedi, 1992) and Elsharkawy and Alikhan (Elsharkawy and Alikhan, 1999). Also Appendix C shows some important correlations usually used in the prediction of under-saturated oil viscosity. All of these correlations use saturated oil
Glaso
100.0
Labedi Schmidt
10.0
1.0
0.1 20
25
30
35
40
45
50
Oil API gravity Fig. 3. (a) Dead oil viscosity from various correlations at 100 8F. (b) Dead oil viscosity from various correlations at 100 8F.
correlation. Validity and accuracy of the proposed correlations have been checked by their application to 222 samples, from which their PVT and viscosity data were available.
4. Development of the proposed correlations
Under-Saturated oil viscosity, cP
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167
0.9 Beal Beggs Schmidt Labedi Alikhan This Work
0.8 0.7 0.6 0.5 0.4 0.3 0.2
Proposed correlations are based on real data, which almost covers all Iranian oil types. Proposed correlations include dead oil viscosity, saturated and undersaturated viscosity correlations and Tables 1, 2, 3 show some statistical information data for all discussed correlations in this paper such as the source of the used oils, accuracy and the limitations of each correlation. Data in these tables have been presented by the authors who have developed the following correlations.
tional form is the best case for our dead oil viscosity data.
4.1. Dead oil viscosity correlation
lod ¼ antilog10 ð11:2699 4:2699log10 ðAPIÞ
0.1 0.0 0
500
1000 1500 2000 2500 3000 3500 4000
P-Pb , Psi Fig. 5. Under-saturated oil viscosity above P b.
2:052log10 ðT ÞÞ Table 1 shows different correlations for dead oil viscosity. This table also gives source of data that have been used for the correlations. In this table all limitations including API, temperature and dead oil viscosity ranges and error percentages have been considered. In this section, dead oil viscosity (l od) is considered to be a function of oil API gravity and reservoir temperature (T). Results of multiple regression analysis show that the following func-
Saturated oil viscosity, cP
100.00
10.00
Pb = 100 Psi Pb = 250 Psi Pb = 500 Psi Pb = 1000 Psi Pb = 1500 Psi Pb = 2500 Psi Pb = 3500 Psi Pb = 4500 Psi
1.00
0.10
0.01 0.1
Where l od is dead oil viscosity in cP, API is dead oil API gravity and T is temperature in 8F. 4.2. Saturated oil viscosity correlation As can be seen in Fig. 1, in single phase (undersaturated) oil viscosity decrease with pressure reduction. This trend continues to bubble point. Pressure reduction below the bubble point pressure causes gas release. This leads to increase in oil density and oil viscosity. It can be said that oil viscosity has its minimum value at bubble point. For oil viscosity at bubble point, one can use two distinct forms. At first form oil viscosity at bubble point is a function of dead oil viscosity and solution gas–oil ratio. At second form oil viscosity at bubble point is a function of dead oil viscosity and oil saturation pressure. Here both forms have been applied and the obtained results showed that the second form is better than the first. Proposed correlation in this section is: lob ¼ 101:1145 Pb0:4956 l0:9961 : od
1.0 10.0 Dead oil viscosity, cP
Fig. 4. Saturated oil viscosity.
ð1Þ
ð2Þ
100.0
Percentage errors, data range, and source of data that have been used for the correlations for some
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Table 4 Accuracy of dead crude oil correlations for estimating viscosity of Iranian oil reservoirs Correlations
Beal Beggs and Glaso Labedi Schmidt and (Beal, 1946) Robinson (Glaso, 1980) (Labedi, 1992) kartoatmodjo (Beggs and (Kartoatmodjo and Robinson, 1975) Schmidt, 1994)
Average relative error % 688 Average absolute error % 701 Standard deviation % 546.56
17.63 33.07 60.45
40.02 41.69 60.45
68.88 102.03 160.14
50.36 53.33 66.36
This work Elsharkawy and Alikhan (Elsharkawy and Alikhan, 1999) 14.44 54.55 74.78
8.9 15.3 30.3
Table 5 Accuracy of saturated oil correlations for estimating viscosity of Iranian oil reservoirs Correlations
Chew and Connaly (Chew and Connally, 1959)
Beggs and Robinson (Beggs and Robinson, 1975)
Labedi (Labedi, 1992)
Schmidt and kartoatmodjo (Kartoatmodjo and Schmidt, 1994)
Elsharkawy and Alikhan (Elsharkawy and Alikhan, 1999)
This work
Average relative error % Average absolute error % Standard deviation %
0.03 53.63 86.58
513.32 513.32 220.33
0.83 88.52 143.98
49.96 53.93 114.37
6.57 37.33 64.55
1.45 26.31 32.65
saturated crude oil viscosity correlations and the proposed correlation for the Iranian oil reservoirs are shown in Table 2. 4.3. Under-saturated oil viscosity correlation
for various oils. The slopes of these lines were found to be a function of dead oil viscosity (l od). Proposed correlation in this work (for under-saturated oil) is as follows: lop ¼ lob þ a ð P Pb Þ
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 under-saturated oil viscosity (l o) to saturated oil viscosity (l ob), and pressure increment above the bubble point ( P P b). It was found that plotting (l o l ob) versus ( P P b) results in a series of straight lines through the origin
ð3Þ
where a ¼ 1:5029 105 þ 1:602 105 lod þ 1:73695l2od 4:2347 106 l3 od :
ð4Þ
Similar to Tables 1 and 2, Table 3 shows the source of oil reservoirs, data range, and percentage errors for some under-saturated oil viscosity correlations; this table also contains these data for proposed correlation in this work.
Table 6 Accuracy of under-saturated oil correlations for estimating viscosity of Iranian oil reservoirs Correlations
Beal (Beal, 1946)
Beggs and Vasquez (Vasquez and Beggs, 1980)
Labedi (Labedi, 1992)
Schmidt and kartoatmodjo (Kartoatmodjo and Schmidt, 1994)
Elsharkawy and Alikhan (Elsharkawy and Alikhan, 1999)
This work
Average relative error % Average absolute error % Standard deviation %
3.98 6.69 9.72
4.00 4.75 12.10
11.99 11.99 12.10
7.22 7.22 10.27
0.29 5.94 11.43
1.24 3.68 5.49
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1000
100
500
50
0
0
Ei
Ei
Beggs Model
-500
-50 Beal Model
-1000 15
25
35
-100
45
15
25
35
Oil API gravity
Oil API gravity
Beal
Beggs
100
100
50
50
45
Ei
Ei
Labedi Model
0
0
-50
-50 Glaso Model
-100 15
25
35
-100 15
45
25
35
Oil API gravity
Oil API gravity
Glaso
Labedi
45
100
100
Elsharkawy and Alikhan
50
Ei
0
0
-50
-50 Schmidt and Kartoatmodjo
-100
-100 15
25
35
45
15
25
35
45
Oil API gravity
Oil API gravity
Schmidt and Kartoatmodjo
Elsharkawy and Alikhan
100 This Work
50
Ei
Ei
50
0
-50
-100
15
25
35
45
Oil API gravity
This Work
Fig. 6. Percent relative error distribution for dead oil viscosity correlations.
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correlation in this work. Fig. 3a and b, show that correlation in this work has the same trend as other correlations.
5. Validation of the proposed correlations In this section the validity of the proposed correlations, as well as other correlations, for estimating the viscosity of Iranian oils are checked.
5.2. Saturated oil viscosity correlation Fig. 4 shows saturation pressure and dead oil viscosity on saturated oil viscosity. As shown in this figure, the oils with higher saturation pressure have corresponding lower saturated oil viscosities; and the oils with higher dead oil viscosity have higher
5.1. Dead oil viscosity correlation Fig. 2 shows the general effects of temperature and oil API gravity on dead oil viscosity; as it can be seen these effects are correctly predicted by the proposed 100
1000
50 500
Ei
0
Ei
-50
0
-100 -500 -150
Beggs Model Chew Model
-1000
-200 0
1000
2000
3000
0
4000
Chew and Cannaly
2000
3000
Beggs and Robinson
Labedi Model
Schmidt and Kartoatmodjo
100
Ei
100
0
0
-100
-100
-200
-200
0
1000
2000
3000
4000
0
1000
2000
3000
4000
Solution Gas Oil Ratio (Rs)
Solution Gas Oil Ratio (Rs)
Labedi
Schmidt and kartoatmodjo
200
200 Elsharkawy and Alikhan
New
100
100
0
Ei
Ei
4000
200
200
Ei
1000
Solution Gas Oil Ratio (Rs)
Solution Gas Oil Ratio (Rs)
-100
0
-100
-200
-200 0
1000
2000
3000
4000
0
1000
2000
3000
4000
Solution Gas Oil Ratio (Rs)
Solution Gas Oil Ratio (Rs)
Elsharkawy and Alikhan
This Work
Fig. 7. Percent relative error distribution for saturated oil viscosity correlations.
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as Alikhan’s correlation (Elsharkawy and Alikhan, 1999) and Labedi’s correlation (Labedi, 1992).
saturated oil viscosities, which in live oils have the same trend as the one that was shown in this figure. 5.3. Under-saturated oil viscosity correlation
6. Accuracy of the proposed correlations Fig. 5 shows the trend of some correlations and also the proposed correlation in this work for predicting the viscosity of under-saturated oils. Increase in pressure gradient above the bubble point pressure results in increasing oil viscosity. It seems that under-saturated oil viscosity is very sensitive to pressure gradient above the bubble point pressure. This behavior is shown by the proposed model as well
Here, the accuracy of the proposed correlations in this work, as well as the correlations previously discussed, is checked. Using the 222 real cases data series of Iranian oils, the results of this work and other ones for estimating the oil viscosity are compared. Tables 4, 5, 6 and Figs. 6, 7, 8 show all of these comparisons. These tables give average
60
60 Beggs Model
Beal Model
40
20
20
Ei
Ei
40
0
0
-20
-20 -40
-40 1
2
3
4
5
6
7
8
1
2
3
P/Pb Beal
4
5
6
7
8
P/Pb Beggs
60
60 Schmidt Model
40
20
20
Ei
Ei
40
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-20
-20
-40
-40
Labedi Model
1
2
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1
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P/Pb
P/Pb
Schmidt and Kartoatmodjo
Labedi
6
7
8
60
60 Elsharkawy and AliKhan Model
This Work
40
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20
Ei
Ei
40
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-20
-20
-40
-40 1
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5
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7
8
1
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P/Pb
P/Pb
Elsharkawy and Alikhan
This Work
6
7
8
Fig. 8. Percent relative error distribution for under-saturated oil viscosity correlations.
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relative error, average absolute error, and standard deviation for all correlations and these figures show percent relative error distribution for all correlations. 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. 6.1. Dead oil viscosity correlations Table 4 gives the results of proposed correlations and also other ones for prediction of dead oil viscosity. This table shows that the suggested correlation for predicting of dead oil viscosity of Iranian oil reservoirs has the lowest average relative error, average absolute error, and standard deviations relative to the others. As it can be seen in Fig. 6, the new proposed model has the smallest relative error whereas Beal’s correlation, which was developed based on US crude oils, has biggest relative error than the other correlations. 6.2. Saturated oil viscosity correlations Table 5 and Fig. 7 reveal that the new correlation in estimating saturated oil viscosity for Iranian oil reservoirs has the smallest average relative error, absolute error, and standard deviation relative to other correlations. Against other correlations, which either underestimate (Schmidt and Kartoatmodjo (Kartoatmodjo and Schmidt, 1994) Correlation) or overestimate (Beggs (Beggs and Robinson, 1975) Correlation) viscosity, it can be seen the results of this work are in better agreement with experimental data. 6.3. Under-saturated oil viscosity correlations For under-saturated oil viscosity, Table 6 shows that the proposed correlation in this work has the smallest average relative error, average absolute error and standard deviations for predicting Iranian undersaturated oil viscosity. Fig. 8 shows that Kartoatmodjo and Schmidt (Kartoatmodjo and Schmidt, 1994) and Labedi (Labedi, 1992) correlations overestimate experimental data whereas Beggs and Robinson (Beggs and Robinson, 1975) correlation underestimate these data. This figure shows that the results of the proposed
model in this work are in better agreement with experimental data relative to the other ones.
7. Conclusions It seems that the most common method for getting viscosity data is viscosity correlations. Those correlations are very useful and effective in predicting oil viscosity at different environmental conditions such as temperature and pressure for different oil fluids. What are very important in the application of these correlations are their limitations on the parameters, which these correlations have derived from them. On the other hand one can say that these correlations are most bregional dependentQ. As may be seen in this paper for Iranian oil fluids these correlations have been applied, but almost all of them have a great error in estimating real viscosity. In this work a new set of correlations for estimation of dead, saturated and under-saturated Iranian oils has been proposed. These correlations are based on real data of the different types of Iranian oils. Input parameters for these correlations 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 correlations have a better accuracy and performance for predicting the viscosity of Iranian oils. It should be mentioned that, these proposed correlations might be used for the prediction of Iranian oil viscosity. Application of these correlations for other oil samples can result in errors.
Nomenclature cg gas specific gravity (air = 1.0) API Oil API gravity P Pressure, psi Pb Saturation pressure, psi Rs Solution gas–oil ratio, scf / stb lo Under-saturated oil viscosity, cp l ob Saturated oil viscosity, cp l od Dead oil viscosity, cp T Reservoir temperature, R Tf Reservoir temperature, F Ei Percent relative error E ave Average absolute percent relative error Ea Average percent relative error
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S Nd
Standard deviation Number of data points
173
Appendix B. Saturated oil viscosity correlations 1—Chew and Connally (Chew and Connally, 1959)
Appendix A. Dead oil viscosity correlations
lob ¼ ð10Þa ðlod Þb ;
1—Beal (Beal, 1946) 1:8 107 360 lob ¼ 0:32 þ a; T 460 API4:53
a ¼ Rs 2:2 107 Rs 7:4 104 ;
a ¼ 10ð0:43þ8:33=APIÞ : 2—Beggs and Robinson (Beggs and Robinson, 1975) lod ¼ 10x 1 y ¼ 10z x ¼ yðT 460Þ1:163 z ¼ 3:0324 0:02023API: 3—Glaso (Glaso, 1980) lod ¼ 3:141 1010 ðT 460Þ3:444 ½logðAPIÞa ; a ¼ 10:313½logðT 460Þ 36:447: 4—Labedi (Labedi, 1992) lob ¼
109:224 : API4:7013 Tf0:6739
5—Kartoatmodjo and Schmidt (Kartoatmodjo and Schmidt, 1994) lod ¼ 16 108 Tf2:8177 ðlogAPIÞx x ¼ 5:7526logðTf Þ 26:9718: 6—Elsharkawy and Alikhan (Elsharkawy and Alikhan, 1999) lod ¼ antilog10 ð xÞ 1:0 x ¼ antilog10 ð yÞ y ¼ 2:16924 0:02525API 0:68875log10 ðT Þ: 7—This work lod ¼ antilog10 ð11:2699 4:298log10 ðAPIÞ 2:052log10 ðTf ÞÞ:
b ¼ ð0:65=10c Þ þ 0:25=10d þ ð0:062=10e Þ; c ¼ 8:62 105 Rs ; e ¼ 3:74 103 Rs :
d ¼ 1:10 103 Rs ;
2—Beggs and Robinson (Beggs and Robinson, 1975) lob ¼ ð10Þa ðlod Þb a ¼ 10:715ðRs þ 100Þ0:515 b ¼ 5:440ðRs þ 150Þ0:338 3—Labedi (Labedi, 1992) 0:426 lob ¼ 102:3440:03542API l0:6447 = pb : od 4—Kartoatmodjo and Schmidt (Kartoatmodjo and Schmidt, 1994) lob ¼ 0:06821 þ 0:9824f þ 0:000403f 2 f ¼ 0:2001 þ 0:8428 100:000845 Rs ð xÞ ð0:43þ0:5165yÞ
x ¼ lod
y ¼ 100:00081Rs :
5—Elsharkawy and Alikhan (Elsharkawy and Alikhan, 1999) lod ¼ Aðlod ÞB A ¼ 1241:932ðRs þ 641:026Þ1:12410 B ¼ 1768:841ðRs þ 1180:335Þ1:06622 : 6—This work lob ¼ 101:1145 Pb0:4956 l0:9961 : od
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Appendix C. Under-saturated oil viscosity correlations
Average absolute percent relative error Eave ¼
1—Beal (Beal, 1946) 0:56 lo ¼ lob þ 0:001ð p pb Þ 0:024l1:6 ob þ 0:038lob : 2—Vasquez and Beggs (Vasquez and Beggs, 1980) lo ¼ lob ð p=pb Þm a ¼ 3:9 105 p 5
m ¼ 2:6 p1:187 ð10a Þ:
3—Labedi (Labedi, 1992) lo ¼ lob Mua ½1 ð p=pb Þ Mua ¼
102:488 l0:9036 Pb0:6151 od : 100:01976API
4—Kartoatmodjo and Schmidt (Kartoatmodjo and Schmidt, 1994) lo ¼ 1:00081lob þ 0:001127ð p pb Þ : þ 0:038l1:590 0:006517l1:8148 ob ob 5—Elsharkawy and Alikhan (Elsharkawy and Alikhan, 1999) lo ¼ lob : þ 102:0771 ð p pb Þ l1:19279 l0:40712 p0:7941 od ob b 6—This work lo ¼ lob þ a ð P Pb Þ a ¼ 1:5029 105 þ 1:602 105 lod þ 1:73695l2od 4:2347 106 l3 od :
Appendix D. Statistical analysis Percent relative error Xexp Xest Ei ¼ 100ði ¼ 1; 2 . . . ; nd Þ: Xexp Average percent relative error Ea ¼
nd 1 X Ei : nd 1
nd 1 X jEi j: nd 1
Standard deviation sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi nd X 1 ðEi Er Þ2 : S¼ nd 1 1 References Ahrabi, F., Ashcroft, S.J., Shearn, R.B., 1987. High pressure volumetric phase composition and viscosity data for a North Sea crude oil and NGL mixtures. Chem. Eng. Res. Des. 67, 329 – 334. Beal, C., 1946. Viscosity of air, water, natural gas, crude oil and its associated gases at oil field temperature and pressures. Trans. AIME 165, 114 – 127. Beggs, H.D., Robinson, J.R., 1975. Estimating the viscosity of crude oil systems. JPT 9, 1140 – 1141. Chew, J., Connally, C.A., 1959. Viscosity correlation for gassaturated crude oil. Trans. AIME 216, 23 – 25. Egbogah, E.O., Ng, J.T., 1990. An improved temperature viscosity correlation for crude oil systems. J. Pet. Sci. Eng. 5, 197 – 200. Elsharkawy, A.M., Alikhan, A.A., 1999. Models for predicting the viscosity of Middle East crude oils. Fuel 78, 891 – 903. Glaso, O., 1980. Generalized pressure–volume–temperature correlation for crude oil system. JPT 2, 785 – 795. Johnson, S.E., Mehrotra, A.K., 1987. Viscosity of Athabasca bitumen using the extended principle of corresponding states. Ind. Eng. Chem. Res. 26, 2290 – 2298. Johnson, S.E., Svrcek, W.Y., 1991. J. Can. Pet. Technol. 26 (5), 60. Kartoatmodjo, F., Schmidt, Z., 1994. Large data bank improves crude physical property correlation. Oil Gas J. 4, 51 – 55. Labedi, R., 1992. Improved correlations for predicting the viscosity of light crudes. J. Pet. Sci. Eng. 8, 221 – 234. Little, J.E., Kennedy, H.T., 1968. Calculating the viscosity of hydrocarbon systems with pressure temperature and composition. Soc. Pet. Eng. J. 6, 157 – 162. Lohrenz, J., Bray, B.C., Clark, C.R., 1964. Calculating viscosities of reservoir fluids from their composition. JPT 10, 1170 – 1176. Mehrotra, A.K., 1991. Generalized one parameter viscosity equation for light and medium hydrocarbon. Ind. Eng. Chem. Res. 30, 1367 – 1372. Mehrotra, A.K., Svrcek, Y., 1988. One parameter correlation for bitumen viscosity. Chem. Eng. Res. Des. 66, 323 – 327. Sutton, R.P., Farshad, F.F., 1990. Evaluation of empirically derived PVT properties for Gulf of Mexico crudes. Soc. Pet. Eng. Reservoir Eng. 79 – 86 (Feb.). Teja, A.S., Rice, P., 1982. Generalized corresponding state method for the viscosity of liquid mixtures. Ind. Engng. Chem. Fundam. 20, 77 – 79. Vasquez, M.E., Beggs, H.D., 1980. Correlations for fluid physical property predictions. JPT (June), 968 – 970.
A correlation approach for prediction of crude oil viscosities A. Naseria,T, M. Nikazarb, S.A. Mousavi Dehghania b
a PVT Department, Research Institute of Petroleum Industry (RIPI), Tehran, Iran Chemical Engineering Department, Amirkabir University of Technology, Tehran, Iran
Received 29 June 2004; received in revised form 10 February 2005; accepted 14 March 2005
Abstract The role of reservoir fluid viscosity for reservoir evaluation in performance calculations, planning thermal methods of enhanced oil recovery, evaluation of hydrocarbon reserves and designing production equipment and pipelines makes its accurate determination necessary. Reservoir oil viscosity is usually measured isothermally at reservoir temperature. However, at temperature other than reservoir temperature these data are estimated by empirical correlations. High dependency of oil viscosity on fluid nature and fluid source causes the unique application of these correlations to special cases from which they have been derived. Here, based on Iranian oil reservoirs data; new correlations have been developed for prediction of dead, saturated and undersaturated oil viscosities. These correlations have been derived using so many oil viscosity data. Validity and accuracy of these correlations have been confirmed by comparing the obtained results of these correlations and other ones with experimental data for so many Iranian oil samples. In contrast to other correlations which need so many specific parameters for oil viscosity prediction, this type of correlations need only some field data which always are available. Checking the results of these correlations shows that the obtained results of Iranian oil viscosities in this work are in agreement with experimental data compared with other correlations. D 2005 Elsevier B.V. All rights reserved. Keywords: Correlation; Viscosity data; PVT; Oil reservoir
1. Introduction Reservoir fluid properties form the basis of many petroleum-engineering calculations. PVT data are used in field reserve calculation, EOR processes,
T Corresponding author. Tel.: +98 21 2221586; fax: +98 21 6154854. E-mail address: [email protected] (A. Naseri). 0920-4105/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.petrol.2005.03.008
surface facilities design and fluid flow in porous media and pipelines. Viscosity data in the petroleum industry are usually obtained at reservoir temperature, which is a constant value. However, viscosity data at temperatures other than reservoir temperature and in cases where laboratory data becomes unavailable are estimated from empirical correlations. Sampling and viscosity measurement costs are the main reasons for inaccessibility of these data at other temperatures.
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the first type. As it can be seen in the results section for Iranian crude oils, the results of these correlations were not in good agreement with experimental data. Some of them have high errors in viscosity prediction. It seems that these behaviors are expectable; this is due to high dependency of oil viscosity on oil nature (heavy component content and nature in crude oils) and source; as we know all of these correlations are based on specific regions/crude oils (Sutton and Farshad, 1990). Using Iranian crude oil data in this work, new correlations have been developed for prediction of dead, saturated and under-saturated oil viscosity. The final correlations have been applied for about 222 real samples of Iranian oils. Comparing with other correlations and experimental data has inspected the validity and accuracy of the proposed correlations.
Above Pb Below Pb
Oil Viscosity, c
2.24
2.08
1.92
1.76
1.60 0
1040
2080
3120
4160
5200
Pressure, psia Fig. 1. Oil viscosity as a function of pressure.
Generally it may be said that there are two main types of correlation for oil viscosity prediction. The first type is those that use oil field data that usually are available, such as reservoir temperature, oil API gravity, solution gas / oil ratio, saturation pressure and pressure. The second type are empirical and/or semiempirical correlations which use some parameters other than those used in the first type; such as reservoir fluid composition, pour point temperature, molar mass, normal boiling point, critical temperature, and acentric factor of components (Lohrenz et al., 1964; Little and Kennedy, 1968; Ahrabi et al., 1987). In this work at first the experimental data have been checked with so many viscosity correlations of
2. Viscosity correlations review A literature survey has indicated that empirical viscosity correlations developed by classical regression techniques are divided into three major sections. First, dead oil viscosity correlations, which are used to estimate crude oil viscosity at atmospheric condition (stock tank) as a function of stock tank API gravity and reservoir temperature. Second, saturated oil viscosity correlations that use usually solution gas–oil ratio and dead oil viscosity to estimate viscosity of oil reservoir at bubble point pressure. The third type is under-saturated oil viscosity correlations, which usually use saturated
Table 1 Statistical data for dead crude oil viscosity correlations Correlations
Beal (Beal, 1946)
Beggs and Robinson (Beggs and Robinson, 1975)
Glaso (Glaso, 1980)
Labedi (Labedi, 1992)
Schmidt and kartoatmodjo (Kartoatmodjo and Schmidt, 1994)
Elsharkawy and Alikhan (Elsharkawy and Alikhan, 1999)
This work
Source of the used oils API Temperature 8F Dead oil viscosity, Cp Average relative error % Average absolute error %
US 52–10 220–100 188–0.8 24.2 –
– 58–16 295–70 – 0.6 13.5
North Sea 48–20 300–50 39–0.6 15.5 22.1
Africa 48–32 306–100 0.6–4.8 2.6 –
Data Bank 59–14.4 320–80 586–0.5 13.2 39.6
Middle East 48–20 300–100 0.6–33.7 2.5 19.3
Iran 44–17 295–105 54–0.75 6.61 7.77
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Table 2 Statistical data for saturated oil viscosity correlations Correlations
Chew and Connaly (Chew and Connally, 1959)
Beggs and Labedi Robinson (Labedi, 1992) (Beggs and Robinson, 1975)
Schmidt and kartoatmodjo (Kartoatmodjo and Schmidt, 1994)
Elsharkawy and This work Alikhan (Elsharkawy and Alikhan, 1999)
Source of the used oils Gas oil ratio SCF / STB Saturation Pressure, Pisa Saturated oil viscosity, Cp Average relative error % Average absolute error %
US 51–3544 5645–132 0.37–50 – –
– 2070–20 5265–132 – 1.8 27.3
Data Bank 572–2.3 6054–14.7 0.1–6.3 0.1 16.1
Middle East 3600–10 100–3700 21–0.05 2.8 18.7
Africa 3533–13 6358–60 0.11–6.3 2.4 22.8
Iran 4116–255 5900–420 18.15– 0.11 1.2 16.4
and Schmidt correlation (Kartoatmodjo and Schmidt, 1994) is based on a given data bank. Recently, Elsharkawy and Alikhan (Elsharkawy and Alikhan, 1999) have presented other empirical correlations for estimating dead crude oil viscosity for Middle East crudes. All of these correlations have expressed dead oil viscosity (l od) as a function of both oil API gravity and reservoir temperature (see Appendix A). Usually, application of dead oil viscosity correlations to crude oil of different sources results in huge errors. This difference is attributed to the difference in asphaltic, paraffinic and/or mixed nature of the oils. Egbogah and Ng (Egbogah and Ng, 1990) improved Beggs and Robinson’s (Beggs and Robinson, 1975) correlation by adding a new parameter, pour point temperature. However, pour point temperature is neither reported in any usual PVT report nor measured in the field. Mehrotra and Svrcek (Mehrotra and Svrcek, 1988) presented a one-parameter viscosity equation for bitumen that was later extended by Mehrotra (Mehrotra, 1991) to predict the viscosity of light and medium
crude oil viscosity and pressure above the bubble point to estimate viscosity of under-saturated oil reservoirs. Fig. 1 shows a typical oil viscosity diagram as a function of pressure at constant reservoir temperature. 2.1. Dead oil viscosity correlations The most popular empirical correlations that are used for dead oil viscosity (stock tank) in petroleum engineering are those developed by Beal (Beal, 1946), Beggs and Robinson (Beggs and Robinson, 1975), Glaso (Glaso, 1980), Labedi (Labedi, 1992) and Kartoatmodjo and Schmidt (Kartoatmodjo and Schmidt, 1994). Beal’s correlation (Beal, 1946) was developed from crude oil data of California, Beggs and Robinson’s correlation (Beggs and Robinson, 1975) was developed based on the crude oils of an unknown location, Galso’s correlation was developed (Glaso, 1980) from the North Sea crude oils, Labedi correlation (Labedi, 1992) has been presented for African crudes and finally Kartoatmodjo
Table 3 Statistical data for under-saturated oil viscosity correlations Correlations
Beal (Beal, 1946)
Beggs and Vasquez (Vasquez and Beggs, 1980)
Labedi (Labedi, 1992)
Schmidt and kartoatmodjo (Kartoatmodjo and Schmidt, 1994)
Elsharkawy and Alikhan (Elsharkawy and Alikhan, 1999)
This work
Source of the used oils Pressure above bubble point, Pisa Under-saturated oil viscosity, Cp Average relative error % Average absolute error %
US 1515–5155 0.2–315 2.7 –
– 141–9515 0.2–1.4 7.5 –
Africa – – 3.1 6.9
Data Bank – 0.2–517 4.3 6.4
Middle East 1287–10,000 0.2–5.7 0.9 4.9
Iran 1400–7000 31–0.1 0.64 2.12
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100.00
viscosity, pressure and saturation pressure in their models.
T=100F T=200F
10.00
T=250F T=300F
3. Viscosity data
1.00
0.10
0.01 20
25
30
35
40
45
50
Oil API gravity Fig. 2. Dead oil viscosity.
hydrocarbons. This parameter is evaluated from molar mass, normal boiling point, critical temperature, and acentric factor of components; however these parameters are not available for most crudes. Several empirical or semi-empirical correlations have also been developed from corresponding state equations by Teja et al. (Teja and Rice, 1982), Johnson et al. (Johnson and Mehrotra, 1987), and Johnson and Svreck (Johnson and Svrcek, 1991). Although these corresponding state correlations involve numerous computations and use fluid composition as an input variable, their prediction of dead oil viscosity is poor (Elsharkawy and Alikhan, 1999).
In this study PVT experimental data of 472 series of Iranian oil reservoirs have been used. These data include oil API gravity, reservoir temperature, saturation pressure, solution gas–oil ratio and PVT measurements (oil characterization) at reservoir temperature. Using the Rolling Ball viscometer (Ruska, series 1602), reservoir oil viscosities have been measured at various pressures above and below the bubble point pressure. In this study about 250 series of PVT and viscosity data have been used in developing a new empirical
a 1000.0 This Work
Dead oil viscosity, Cp
Dead oil viscosity, Cp
T=150F
Beal
100.0
AliKhan
10.0
1.0
0.1 20
2.2. Live oil viscosity correlations
Beggs
25
30
35
40
45
50
Oil API gravity
b 1000.0 This Work
Dead oil viscosity, Cp
Viscosity data of saturated and under-saturated oils at temperatures other than reservoir temperature are predicted from live oil reservoir viscosity correlations. Most saturated oil viscosity correlations express saturated oil viscosity (l ob) as a function of both dead oil viscosity (l od) and solution gas–oil ratio (R s) (see Appendix B). These correlations are: Chew and Connally (Chew and Connally, 1959), Beggs and Robinson (Beggs and Robinson, 1975), Kartoatmodjo and Schmidt (Kartoatmodjo and Schmidt, 1994), Labedi (Labedi, 1992) and Elsharkawy and Alikhan (Elsharkawy and Alikhan, 1999). Also Appendix C shows some important correlations usually used in the prediction of under-saturated oil viscosity. All of these correlations use saturated oil
Glaso
100.0
Labedi Schmidt
10.0
1.0
0.1 20
25
30
35
40
45
50
Oil API gravity Fig. 3. (a) Dead oil viscosity from various correlations at 100 8F. (b) Dead oil viscosity from various correlations at 100 8F.
correlation. Validity and accuracy of the proposed correlations have been checked by their application to 222 samples, from which their PVT and viscosity data were available.
4. Development of the proposed correlations
Under-Saturated oil viscosity, cP
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0.9 Beal Beggs Schmidt Labedi Alikhan This Work
0.8 0.7 0.6 0.5 0.4 0.3 0.2
Proposed correlations are based on real data, which almost covers all Iranian oil types. Proposed correlations include dead oil viscosity, saturated and undersaturated viscosity correlations and Tables 1, 2, 3 show some statistical information data for all discussed correlations in this paper such as the source of the used oils, accuracy and the limitations of each correlation. Data in these tables have been presented by the authors who have developed the following correlations.
tional form is the best case for our dead oil viscosity data.
4.1. Dead oil viscosity correlation
lod ¼ antilog10 ð11:2699 4:2699log10 ðAPIÞ
0.1 0.0 0
500
1000 1500 2000 2500 3000 3500 4000
P-Pb , Psi Fig. 5. Under-saturated oil viscosity above P b.
2:052log10 ðT ÞÞ Table 1 shows different correlations for dead oil viscosity. This table also gives source of data that have been used for the correlations. In this table all limitations including API, temperature and dead oil viscosity ranges and error percentages have been considered. In this section, dead oil viscosity (l od) is considered to be a function of oil API gravity and reservoir temperature (T). Results of multiple regression analysis show that the following func-
Saturated oil viscosity, cP
100.00
10.00
Pb = 100 Psi Pb = 250 Psi Pb = 500 Psi Pb = 1000 Psi Pb = 1500 Psi Pb = 2500 Psi Pb = 3500 Psi Pb = 4500 Psi
1.00
0.10
0.01 0.1
Where l od is dead oil viscosity in cP, API is dead oil API gravity and T is temperature in 8F. 4.2. Saturated oil viscosity correlation As can be seen in Fig. 1, in single phase (undersaturated) oil viscosity decrease with pressure reduction. This trend continues to bubble point. Pressure reduction below the bubble point pressure causes gas release. This leads to increase in oil density and oil viscosity. It can be said that oil viscosity has its minimum value at bubble point. For oil viscosity at bubble point, one can use two distinct forms. At first form oil viscosity at bubble point is a function of dead oil viscosity and solution gas–oil ratio. At second form oil viscosity at bubble point is a function of dead oil viscosity and oil saturation pressure. Here both forms have been applied and the obtained results showed that the second form is better than the first. Proposed correlation in this section is: lob ¼ 101:1145 Pb0:4956 l0:9961 : od
1.0 10.0 Dead oil viscosity, cP
Fig. 4. Saturated oil viscosity.
ð1Þ
ð2Þ
100.0
Percentage errors, data range, and source of data that have been used for the correlations for some
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Table 4 Accuracy of dead crude oil correlations for estimating viscosity of Iranian oil reservoirs Correlations
Beal Beggs and Glaso Labedi Schmidt and (Beal, 1946) Robinson (Glaso, 1980) (Labedi, 1992) kartoatmodjo (Beggs and (Kartoatmodjo and Robinson, 1975) Schmidt, 1994)
Average relative error % 688 Average absolute error % 701 Standard deviation % 546.56
17.63 33.07 60.45
40.02 41.69 60.45
68.88 102.03 160.14
50.36 53.33 66.36
This work Elsharkawy and Alikhan (Elsharkawy and Alikhan, 1999) 14.44 54.55 74.78
8.9 15.3 30.3
Table 5 Accuracy of saturated oil correlations for estimating viscosity of Iranian oil reservoirs Correlations
Chew and Connaly (Chew and Connally, 1959)
Beggs and Robinson (Beggs and Robinson, 1975)
Labedi (Labedi, 1992)
Schmidt and kartoatmodjo (Kartoatmodjo and Schmidt, 1994)
Elsharkawy and Alikhan (Elsharkawy and Alikhan, 1999)
This work
Average relative error % Average absolute error % Standard deviation %
0.03 53.63 86.58
513.32 513.32 220.33
0.83 88.52 143.98
49.96 53.93 114.37
6.57 37.33 64.55
1.45 26.31 32.65
saturated crude oil viscosity correlations and the proposed correlation for the Iranian oil reservoirs are shown in Table 2. 4.3. Under-saturated oil viscosity correlation
for various oils. The slopes of these lines were found to be a function of dead oil viscosity (l od). Proposed correlation in this work (for under-saturated oil) is as follows: lop ¼ lob þ a ð P Pb Þ
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 under-saturated oil viscosity (l o) to saturated oil viscosity (l ob), and pressure increment above the bubble point ( P P b). It was found that plotting (l o l ob) versus ( P P b) results in a series of straight lines through the origin
ð3Þ
where a ¼ 1:5029 105 þ 1:602 105 lod þ 1:73695l2od 4:2347 106 l3 od :
ð4Þ
Similar to Tables 1 and 2, Table 3 shows the source of oil reservoirs, data range, and percentage errors for some under-saturated oil viscosity correlations; this table also contains these data for proposed correlation in this work.
Table 6 Accuracy of under-saturated oil correlations for estimating viscosity of Iranian oil reservoirs Correlations
Beal (Beal, 1946)
Beggs and Vasquez (Vasquez and Beggs, 1980)
Labedi (Labedi, 1992)
Schmidt and kartoatmodjo (Kartoatmodjo and Schmidt, 1994)
Elsharkawy and Alikhan (Elsharkawy and Alikhan, 1999)
This work
Average relative error % Average absolute error % Standard deviation %
3.98 6.69 9.72
4.00 4.75 12.10
11.99 11.99 12.10
7.22 7.22 10.27
0.29 5.94 11.43
1.24 3.68 5.49
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100
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0
0
Ei
Ei
Beggs Model
-500
-50 Beal Model
-1000 15
25
35
-100
45
15
25
35
Oil API gravity
Oil API gravity
Beal
Beggs
100
100
50
50
45
Ei
Ei
Labedi Model
0
0
-50
-50 Glaso Model
-100 15
25
35
-100 15
45
25
35
Oil API gravity
Oil API gravity
Glaso
Labedi
45
100
100
Elsharkawy and Alikhan
50
Ei
0
0
-50
-50 Schmidt and Kartoatmodjo
-100
-100 15
25
35
45
15
25
35
45
Oil API gravity
Oil API gravity
Schmidt and Kartoatmodjo
Elsharkawy and Alikhan
100 This Work
50
Ei
Ei
50
0
-50
-100
15
25
35
45
Oil API gravity
This Work
Fig. 6. Percent relative error distribution for dead oil viscosity correlations.
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correlation in this work. Fig. 3a and b, show that correlation in this work has the same trend as other correlations.
5. Validation of the proposed correlations In this section the validity of the proposed correlations, as well as other correlations, for estimating the viscosity of Iranian oils are checked.
5.2. Saturated oil viscosity correlation Fig. 4 shows saturation pressure and dead oil viscosity on saturated oil viscosity. As shown in this figure, the oils with higher saturation pressure have corresponding lower saturated oil viscosities; and the oils with higher dead oil viscosity have higher
5.1. Dead oil viscosity correlation Fig. 2 shows the general effects of temperature and oil API gravity on dead oil viscosity; as it can be seen these effects are correctly predicted by the proposed 100
1000
50 500
Ei
0
Ei
-50
0
-100 -500 -150
Beggs Model Chew Model
-1000
-200 0
1000
2000
3000
0
4000
Chew and Cannaly
2000
3000
Beggs and Robinson
Labedi Model
Schmidt and Kartoatmodjo
100
Ei
100
0
0
-100
-100
-200
-200
0
1000
2000
3000
4000
0
1000
2000
3000
4000
Solution Gas Oil Ratio (Rs)
Solution Gas Oil Ratio (Rs)
Labedi
Schmidt and kartoatmodjo
200
200 Elsharkawy and Alikhan
New
100
100
0
Ei
Ei
4000
200
200
Ei
1000
Solution Gas Oil Ratio (Rs)
Solution Gas Oil Ratio (Rs)
-100
0
-100
-200
-200 0
1000
2000
3000
4000
0
1000
2000
3000
4000
Solution Gas Oil Ratio (Rs)
Solution Gas Oil Ratio (Rs)
Elsharkawy and Alikhan
This Work
Fig. 7. Percent relative error distribution for saturated oil viscosity correlations.
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171
as Alikhan’s correlation (Elsharkawy and Alikhan, 1999) and Labedi’s correlation (Labedi, 1992).
saturated oil viscosities, which in live oils have the same trend as the one that was shown in this figure. 5.3. Under-saturated oil viscosity correlation
6. Accuracy of the proposed correlations Fig. 5 shows the trend of some correlations and also the proposed correlation in this work for predicting the viscosity of under-saturated oils. Increase in pressure gradient above the bubble point pressure results in increasing oil viscosity. It seems that under-saturated oil viscosity is very sensitive to pressure gradient above the bubble point pressure. This behavior is shown by the proposed model as well
Here, the accuracy of the proposed correlations in this work, as well as the correlations previously discussed, is checked. Using the 222 real cases data series of Iranian oils, the results of this work and other ones for estimating the oil viscosity are compared. Tables 4, 5, 6 and Figs. 6, 7, 8 show all of these comparisons. These tables give average
60
60 Beggs Model
Beal Model
40
20
20
Ei
Ei
40
0
0
-20
-20 -40
-40 1
2
3
4
5
6
7
8
1
2
3
P/Pb Beal
4
5
6
7
8
P/Pb Beggs
60
60 Schmidt Model
40
20
20
Ei
Ei
40
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-20
-20
-40
-40
Labedi Model
1
2
3
4
5
6
7
8
1
2
3
4
5
P/Pb
P/Pb
Schmidt and Kartoatmodjo
Labedi
6
7
8
60
60 Elsharkawy and AliKhan Model
This Work
40
20
20
Ei
Ei
40
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-20
-20
-40
-40 1
2
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4
5
6
7
8
1
2
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5
P/Pb
P/Pb
Elsharkawy and Alikhan
This Work
6
7
8
Fig. 8. Percent relative error distribution for under-saturated oil viscosity correlations.
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relative error, average absolute error, and standard deviation for all correlations and these figures show percent relative error distribution for all correlations. 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. 6.1. Dead oil viscosity correlations Table 4 gives the results of proposed correlations and also other ones for prediction of dead oil viscosity. This table shows that the suggested correlation for predicting of dead oil viscosity of Iranian oil reservoirs has the lowest average relative error, average absolute error, and standard deviations relative to the others. As it can be seen in Fig. 6, the new proposed model has the smallest relative error whereas Beal’s correlation, which was developed based on US crude oils, has biggest relative error than the other correlations. 6.2. Saturated oil viscosity correlations Table 5 and Fig. 7 reveal that the new correlation in estimating saturated oil viscosity for Iranian oil reservoirs has the smallest average relative error, absolute error, and standard deviation relative to other correlations. Against other correlations, which either underestimate (Schmidt and Kartoatmodjo (Kartoatmodjo and Schmidt, 1994) Correlation) or overestimate (Beggs (Beggs and Robinson, 1975) Correlation) viscosity, it can be seen the results of this work are in better agreement with experimental data. 6.3. Under-saturated oil viscosity correlations For under-saturated oil viscosity, Table 6 shows that the proposed correlation in this work has the smallest average relative error, average absolute error and standard deviations for predicting Iranian undersaturated oil viscosity. Fig. 8 shows that Kartoatmodjo and Schmidt (Kartoatmodjo and Schmidt, 1994) and Labedi (Labedi, 1992) correlations overestimate experimental data whereas Beggs and Robinson (Beggs and Robinson, 1975) correlation underestimate these data. This figure shows that the results of the proposed
model in this work are in better agreement with experimental data relative to the other ones.
7. Conclusions It seems that the most common method for getting viscosity data is viscosity correlations. Those correlations are very useful and effective in predicting oil viscosity at different environmental conditions such as temperature and pressure for different oil fluids. What are very important in the application of these correlations are their limitations on the parameters, which these correlations have derived from them. On the other hand one can say that these correlations are most bregional dependentQ. As may be seen in this paper for Iranian oil fluids these correlations have been applied, but almost all of them have a great error in estimating real viscosity. In this work a new set of correlations for estimation of dead, saturated and under-saturated Iranian oils has been proposed. These correlations are based on real data of the different types of Iranian oils. Input parameters for these correlations 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 correlations have a better accuracy and performance for predicting the viscosity of Iranian oils. It should be mentioned that, these proposed correlations might be used for the prediction of Iranian oil viscosity. Application of these correlations for other oil samples can result in errors.
Nomenclature cg gas specific gravity (air = 1.0) API Oil API gravity P Pressure, psi Pb Saturation pressure, psi Rs Solution gas–oil ratio, scf / stb lo Under-saturated oil viscosity, cp l ob Saturated oil viscosity, cp l od Dead oil viscosity, cp T Reservoir temperature, R Tf Reservoir temperature, F Ei Percent relative error E ave Average absolute percent relative error Ea Average percent relative error
A. Naseri et al. / Journal of Petroleum Science and Engineering 47 (2005) 163–174
S Nd
Standard deviation Number of data points
173
Appendix B. Saturated oil viscosity correlations 1—Chew and Connally (Chew and Connally, 1959)
Appendix A. Dead oil viscosity correlations
lob ¼ ð10Þa ðlod Þb ;
1—Beal (Beal, 1946) 1:8 107 360 lob ¼ 0:32 þ a; T 460 API4:53
a ¼ Rs 2:2 107 Rs 7:4 104 ;
a ¼ 10ð0:43þ8:33=APIÞ : 2—Beggs and Robinson (Beggs and Robinson, 1975) lod ¼ 10x 1 y ¼ 10z x ¼ yðT 460Þ1:163 z ¼ 3:0324 0:02023API: 3—Glaso (Glaso, 1980) lod ¼ 3:141 1010 ðT 460Þ3:444 ½logðAPIÞa ; a ¼ 10:313½logðT 460Þ 36:447: 4—Labedi (Labedi, 1992) lob ¼
109:224 : API4:7013 Tf0:6739
5—Kartoatmodjo and Schmidt (Kartoatmodjo and Schmidt, 1994) lod ¼ 16 108 Tf2:8177 ðlogAPIÞx x ¼ 5:7526logðTf Þ 26:9718: 6—Elsharkawy and Alikhan (Elsharkawy and Alikhan, 1999) lod ¼ antilog10 ð xÞ 1:0 x ¼ antilog10 ð yÞ y ¼ 2:16924 0:02525API 0:68875log10 ðT Þ: 7—This work lod ¼ antilog10 ð11:2699 4:298log10 ðAPIÞ 2:052log10 ðTf ÞÞ:
b ¼ ð0:65=10c Þ þ 0:25=10d þ ð0:062=10e Þ; c ¼ 8:62 105 Rs ; e ¼ 3:74 103 Rs :
d ¼ 1:10 103 Rs ;
2—Beggs and Robinson (Beggs and Robinson, 1975) lob ¼ ð10Þa ðlod Þb a ¼ 10:715ðRs þ 100Þ0:515 b ¼ 5:440ðRs þ 150Þ0:338 3—Labedi (Labedi, 1992) 0:426 lob ¼ 102:3440:03542API l0:6447 = pb : od 4—Kartoatmodjo and Schmidt (Kartoatmodjo and Schmidt, 1994) lob ¼ 0:06821 þ 0:9824f þ 0:000403f 2 f ¼ 0:2001 þ 0:8428 100:000845 Rs ð xÞ ð0:43þ0:5165yÞ
x ¼ lod
y ¼ 100:00081Rs :
5—Elsharkawy and Alikhan (Elsharkawy and Alikhan, 1999) lod ¼ Aðlod ÞB A ¼ 1241:932ðRs þ 641:026Þ1:12410 B ¼ 1768:841ðRs þ 1180:335Þ1:06622 : 6—This work lob ¼ 101:1145 Pb0:4956 l0:9961 : od
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Appendix C. Under-saturated oil viscosity correlations
Average absolute percent relative error Eave ¼
1—Beal (Beal, 1946) 0:56 lo ¼ lob þ 0:001ð p pb Þ 0:024l1:6 ob þ 0:038lob : 2—Vasquez and Beggs (Vasquez and Beggs, 1980) lo ¼ lob ð p=pb Þm a ¼ 3:9 105 p 5
m ¼ 2:6 p1:187 ð10a Þ:
3—Labedi (Labedi, 1992) lo ¼ lob Mua ½1 ð p=pb Þ Mua ¼
102:488 l0:9036 Pb0:6151 od : 100:01976API
4—Kartoatmodjo and Schmidt (Kartoatmodjo and Schmidt, 1994) lo ¼ 1:00081lob þ 0:001127ð p pb Þ : þ 0:038l1:590 0:006517l1:8148 ob ob 5—Elsharkawy and Alikhan (Elsharkawy and Alikhan, 1999) lo ¼ lob : þ 102:0771 ð p pb Þ l1:19279 l0:40712 p0:7941 od ob b 6—This work lo ¼ lob þ a ð P Pb Þ a ¼ 1:5029 105 þ 1:602 105 lod þ 1:73695l2od 4:2347 106 l3 od :
Appendix D. Statistical analysis Percent relative error Xexp Xest Ei ¼ 100ði ¼ 1; 2 . . . ; nd Þ: Xexp Average percent relative error Ea ¼
nd 1 X Ei : nd 1
nd 1 X jEi j: nd 1
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