Copyright 2006, Society of Petroleum Engineers This paper was prepared for presentation at the 2006 SPE Annual Technical Conference and Exhibition held in San Antonio, Texas, U.S.A., 24–27 September 2006. This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435. Abstract The determination of viscosity is required for evaluation of the pressure drop resulting from flow through porous media, tubing or pipelines. Viscosity is a necessary property to ascertain well productivity or to properly size tubing, pipelines and pumps. Numerous methods exist to estimate viscosity for computer calculations. Oils encountered in deep water environments are often highly undersaturated – in some cases in excess of 15,000 psi. For transport, the dead oil must be pumped in an environment with temperatures as low as 35°F. At this temperature, the dead oil atmospheric viscosity can be in excess of 500 cp. The pressure required to pump oil through pipelines from deep water can exceed 3000 psi at the pump on the platform and over 5000 psi at the sea floor. The pressure effect on viscosity results in a significant additional increase in this property which can adversely affect pipeline performance. The existing methods for estimating undersaturated viscosity were not developed using data that encompasses the pressure or viscosity range that are currently encountered by the industry. A large database comprised of 1,399 oils and 10,248 data points was constructed to evaluate the accuracy of existing correlation methods. Pressure differentials up to 25,000 psi and viscosity in excess of 1000 cp are included in the database to ensure that viscosity at both typical conditions and the extreme conditions encountered in deep water are represented. The existing methods are shown to be inadequate over this wide range of conditions. A new method was developed that offers improved accuracy and consistency over the expanded range of viscosity and pressure differential. Introduction Viscosity is an important parameter necessary for the determination of the pressure drop associated with fluid flow. For radial flow through porous media, the relationship between flow rate and pressure drop is described by Darcy’s law 8 . h k s r r B q p p w e o o o wfs r 3 10 0815 . 7 75 . 0 ln − × ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = − μ ........................ (1) For situations above bubblepoint in a reservoir, the fluid composition and temperature remain constant and properties vary only with pressure. Viscosity changes range from 5- 35%/1000 psi as shown in Fig. 1. On the other hand, density or formation volume factor above bubblepoint changes range from 0.5-2.8%/1000 psi. An examination of Eqn. 1 shows pressure drop is directly proportional to change in viscosity and formation volume factor. Clearly viscosity changes are the most significant property and must be accurately quantified. Fluid flow in pipes 8 is characterized by ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ Δ Δ + + = Δ Δ L g v v d g v f L p o o o ρ ρ θ ρ 2 cos 144 1 2 ......................... (2) where the three parts of the equation describe the hydrostatic, frictional and kinetic energy losses in the system, respectively. The friction factor, f, is defined by the Moody Friction factor chart as a function of Reynolds Number and pipe roughness. The Reynolds Number is calculated μ ρ v d R e 1488 = ................................................................. (3) For laminar flow at Reynolds Numbers less than 2000, the friction factor is defined e R f 64 = .............................................................................. (4) Therefore for situations of single phase laminar oil flow in pipelines, the pressure drop is directly proportional to changes in viscosity and density. As viscosity is most sensitive to changing pressure, it is the most important term to accurately quantify with changing pressure. Numerous correlations have appeared in the literature for estimating the viscosity of undersaturated oil. These methods are reviewed by Lake 30 ; however, a more complete summary table is provided in the Appendix because of updates due to recently published correlations. SPE 103144 Undersaturated Oil Viscosity Correlation for Adverse Conditions D.F. Bergman, BP America, and R.P. Sutton, Marathon Oil Co.
Transcript
Copyright 2006, Society of Petroleum Engineers This paper was prepared for presentation at the 2006 SPE Annual Technical Conference and Exhibition held in San Antonio, Texas, U.S.A., 24–27 September 2006. This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.
Abstract The determination of viscosity is required for evaluation of the pressure drop resulting from flow through porous media, tubing or pipelines. Viscosity is a necessary property to ascertain well productivity or to properly size tubing, pipelines and pumps. Numerous methods exist to estimate viscosity for computer calculations. Oils encountered in deep water environments are often highly undersaturated – in some cases in excess of 15,000 psi. For transport, the dead oil must be pumped in an environment with temperatures as low as 35°F. At this temperature, the dead oil atmospheric viscosity can be in excess of 500 cp. The pressure required to pump oil through pipelines from deep water can exceed 3000 psi at the pump on the platform and over 5000 psi at the sea floor. The pressure effect on viscosity results in a significant additional increase in this property which can adversely affect pipeline performance. The existing methods for estimating undersaturated viscosity were not developed using data that encompasses the pressure or viscosity range that are currently encountered by the industry. A large database comprised of 1,399 oils and 10,248 data points was constructed to evaluate the accuracy of existing correlation methods. Pressure differentials up to 25,000 psi and viscosity in excess of 1000 cp are included in the database to ensure that viscosity at both typical conditions and the extreme conditions encountered in deep water are represented. The existing methods are shown to be inadequate over this wide range of conditions. A new method was developed that offers improved accuracy and consistency over the expanded range of viscosity and pressure differential. Introduction Viscosity is an important parameter necessary for the determination of the pressure drop associated with fluid flow. For radial flow through porous media, the relationship between flow rate and pressure drop is described by Darcy’s law8.
hk
srrBq
pp we
ooo
wfsr 3100815.7
75.0ln
−×
⎥⎦⎤
⎢⎣⎡ +−⎟
⎠⎞⎜
⎝⎛
=−μ
........................ (1)
For situations above bubblepoint in a reservoir, the fluid composition and temperature remain constant and properties vary only with pressure. Viscosity changes range from 5-35%/1000 psi as shown in Fig. 1. On the other hand, density or formation volume factor above bubblepoint changes range from 0.5-2.8%/1000 psi. An examination of Eqn. 1 shows pressure drop is directly proportional to change in viscosity and formation volume factor. Clearly viscosity changes are the most significant property and must be accurately quantified. Fluid flow in pipes8 is characterized by
⎥⎥⎦
⎤
⎢⎢⎣
⎡
ΔΔ
++=ΔΔ
Lgvv
dgvf
Lp oo
oρρθρ
2cos
1441 2
......................... (2)
where the three parts of the equation describe the hydrostatic, frictional and kinetic energy losses in the system, respectively. The friction factor, f, is defined by the Moody Friction factor chart as a function of Reynolds Number and pipe roughness. The Reynolds Number is calculated
Therefore for situations of single phase laminar oil flow in pipelines, the pressure drop is directly proportional to changes in viscosity and density. As viscosity is most sensitive to changing pressure, it is the most important term to accurately quantify with changing pressure. Numerous correlations have appeared in the literature for estimating the viscosity of undersaturated oil. These methods are reviewed by Lake30; however, a more complete summary table is provided in the Appendix because of updates due to recently published correlations.
SPE 103144
Undersaturated Oil Viscosity Correlation for Adverse Conditions D.F. Bergman, BP America, and R.P. Sutton, Marathon Oil Co.
2 SPE 103144
A large database comprised of 1,399 oils and 10,248 data points was constructed to evaluate existing correlation methods. Pressure differentials up to 25,000 psi and viscosity in excess of 1000 cp are included in the database to ensure viscosity at both typical conditions and the extreme conditions such as those encountered in deep water is represented. The data was obtained from both public sources5,7,9,10,12,14,17,22,23,25,29,31 and internal reports26. This data is summarized in the table below.
In some instances, the data obtained from public sources was incomplete so the table above is reflective of the information available. In addition to crude oil data, lubricant oils, Canadian bitumen, n-decane, n-undecane, n-dodecane, n-tetradecane, n-pentadecane, n-hexadecane, n-octadecane, n-butylbenzene, n-hexylbenzene, and n-octylbenzene are represented in the database. The data is plotted as a function of pressure in Fig. 2. In general, the data is linear with log of viscosity; however, some downward curvature is noted at pressure differentials above 5000 psi. Furthermore, the slope of the lines increases as bubblepoint viscosity increases. Correlation Development A total of 18 methods have appeared in the literature. Methods fall into a category that either use pressure ratio (pressure divided by bubblepoint pressure) or pressure differential (pressure minus bubblepoint pressure) as the primary correlating parameter. In addition, bubblepoint viscosity is a common correlating parameter. Some methods also use solution gas-oil ratio, oil API gravity and dead oil viscosity as correlating parameters. One of the more widely used equation forms for correlating undersaturated oil viscosity was proposed by Barus6 in 1893. The equation describes a linear relationship resulting from a semilog plot (Fig. 2) of undersaturated oil viscosity with pressure.
( )bppobo e −= αμμ ..............................................................(5)
This equation can be rearranged as follows where the term, α, is the viscosity-pressure coefficient which is simply the slope of the viscosity ratio – pressure differential relationship.
Use of this equation typically involves the determination of the viscosity-pressure coefficient for a given oil. Kouzel20
made use of this equation form and correlated α with bubblepoint viscosity. Khan19 and Orbey-Sandler24 also utilized the Barus form of equation but instead determined constants for the viscosity-pressure coefficient. The API4 found results similar to Kouzel and provided an update to that method. Various correlation forms suggested by Hershey and Hopkins15 and Roelands27 as well as other formulations in Table A-1 were tested against the database and it was concluded that the Barus form equation showed the most promise. Data from the database was plotted using the functional equation form offered by Eqn. 6, as shown in Fig. 3. The data actually represents several slopes representing different ranges of bubblepoint viscosity. Fig. 4 illustrates this for three coarse data groupings. If a more detailed examination is made of the slopes, a definite relationship with bubble point oil viscosity is observed, as shown in Fig. 5. The relationships proposed by Kouzel, the API, Khan and Orbey-Sandler are provided for reference in this plot. The results would indicate that a method such as Orbey-Sandler might provide accurate results for oil with a bubblepoint viscosity less than 1 cp, but would be increasingly inaccurate as bubblepoint viscosity increased. The Barus equation was originally limited in applicability to lower pressure differentials. Kouzel suggested a limit of 5000 psi while the API update to his equation contradicted the recommendation and specified a limit of 20,000 psi. Orbey-Sandler determined a limit of 5800 psi which is closer in agreement to Kouzel. Examination of the equation shows that it can be linearized by adding an exponent, β, to the pressure term to account for the slight downward curvature observed at higher pressure differentials.
( )βαμμ bppobo e −= ............................................................ (7)
Values of β averaged approximately 0.9 for the entire database. However, if only high pressure differential data is used, a trend is observed as shown in Fig. 6, even though there is still significant scatter present. A nonlinear regression routine was used to determine the final form of the Bergman-Sutton method based on Eqn. 7. The coefficient, α, and exponent, β, are defined as
( )( ) 45
27
1027877.2ln1048211.1
ln105698.6−−
−
×+×
−×=
ob
ob
μ
μα......................... (8)
( ) 873204.0ln1024623.2 2 +×= −
obμβ ................................ (9) Comparison of the statistical accuracy of the proposed Bergman-Sutton method along with existing published methods is summarized in Tables 1-10. The database contained a total of 10,248 measurements. Most of the correlations require only pressure, bubblepoint pressure and bubblepoint viscosity to determine the undersaturated
SPE 103144 3
viscosity. Methods with a data point count of less than 10,248 require additional data such as dead oil viscosity, API gravity or solution gas-oil ratio. Unfortunately, this data was not always available from published sources so these methods could not be tested against the full database. Furthermore, results from the Abdul-Majeed1 method were found to be severely degraded below a gas-oil ratio of 50 scf/STB (see note Table 3). The results below this value were excluded to provide a meaningful comparison of statistics. Additionally, methods proposed by Kartoatmodjo17,18 and De Ghetto10 resulted in negative viscosity values for cases involving high bubblepoint viscosity and high pressure differentials. Errors for methods that use pressure ratio as a correlating parameter tend to show higher errors than methods that use pressure differential as a correlating parameter. Tables 2 and 3 provide a summary of correlation evaluations for bubblepoint pressures greater than and less than 50 psia respectively. In the latter case, a significant portion of the data is comprised of gas free oils with a bubblepoint pressure set to atmospheric pressure. The Bergman-Sutton method performs well in both environments. Tables 4 and 5 examine the effect of temperature on correlation accuracy. This was actually more of a test of data quality. Many of the oils found in the Gulf of Mexico exhibit a cloud point of approximately 100 °F. Below this temperature wax crystals appear which can disrupt viscosity measurements and result in non-Newtonian behavior in the oil. The average absolute error for the Bergman-Sutton method in these cases was found to increase from 3.64% (for data above 100°F) to 5.56% (for cooler temperatures). It is felt that this change is not significantly impacted by measurement issues below cloud point. Tables 6-9 provide correlation statistics for various ranges of bubblepoint viscosity. The Bergman-Sutton method is found to be more accurate for all of the viscosity ranges investigated. Table 10 examines the effect of high pressure differential on correlations accuracy. Figs. 7-25 graphically depict correlation error as a function of pressure differential. The Bergman-Sutton method shows increased error at high pressure differentials mainly due to the scatter in the pressure exponent correlation (Fig. 6). Results show an average absolute error of 7.71% with only 25% of the data exhibiting absolute errors greater than 10%. At pressure differentials in excess of 20,000 psi, the average absolute error increases to 13.2% with a standard deviation of 10.7%. None the less, the Bergman-Sutton method still out-performs all of the available published methods. Correlation error is visually displayed in Fig. 26-44. The plots were constrained to values up to 1000 cp so that visual comparisons could be made. A further comparison of the various methods is shown in Figs. 45-46 for reservoir fluids only and for the entire database. The consistency of the Bergman-Sutton method is clearly evident over the range of pressure differential and bubblepoint viscosity depicted in the graphs.
Conclusions 1. A comprehensive database of undersaturated crude oil
viscosity has been created for evaluating the accuracy of existing methods and developing improved viscosity estimation methods.
2. Methods using pressure ratio as a correlating parameter were found to be not as accurate for determining the pressure effect on the viscosity of undersaturated crude oils. This is most apparent for undersaturated crude oils that are gas free or have low saturation pressure.
3. Methods developed by Kartoatmodjo and De Ghetto can evaluate a negative viscosity under situations of high bubblepoint viscosity and high pressure differential. Extreme caution should be exercised if these methods are used for general application in computer programs.
4. A new method has been proposed which provides more accurate results over a wider range of bubblepoint viscosity and pressure differentials than existing methods. The new method derives undersaturated viscosity using only bubblepoint viscosity and pressure differential. The correlation can be satisfactorily used on oils that contain solution gas or are gas free. The data used to derive the correlation included samples with bubblepoint viscosity from less than 0.1 cp to in excess of 14,000 cp. Accuracy is maintained over this wide range of values.
5. As a practical limit, a maximum pressure differential of 20,000 psi is recommended. Although there is an increased error at higher differentials, the Bergman-Sutton method still offers superior results than those obtained from all of the currently available published correlations.
Acknowledgment The authors would like to thank the management of Marathon Oil Company and BP America for permission to publish this paper. Finally, the primary author would like to thank his wife, Nancy. Without her patience and understanding, this would have never been written. Statistical Quantities AE = average error, %
∑=
−=
N
i i
ii
meas
meascalc
XXX
NAE
1
100
AAE = average absolute error, %
∑=
−=
N
i i
ii
meas
meascalc
XXX
NAAE
1
100
S = standard deviation
( )1
1
2
−
−
=∑=
N
XX
S
N
ii
X = generic dependent variable N = number of observations Nomenclature d = pipe diameter, ft f = friction factor
4 SPE 103144
g = acceleration due to gravity, ft/sec2 h = net reservoir thickness, ft k = effective permeability, md L = length, ft p = pressure, psia pb = bubblepoint pressure, psia pr = average reservoir pressure, psia p wfs = flowing sandface pressure, psia qo = oil flow rate, STBPD re = drainage radius, ft Re = Reynolds Number Rs = solution gas-oil ratio, scf/STB rw = wellbore radius, ft s = skin factor T = temperature, ˚F v = velocity, ft/sec α = Barus equation viscosity-pressure coefficient β = pressure exponent γAPI = oil API gravity ρo = oil density, lbm/ft3 μod = dead oil viscosity, cp μob = bubblepoint oil viscosity, cp μo = oil viscosity, cp θ = angle, degrees from vertical References 1. Abdul-Majeed, G.H., Kattan, R.R. and Salman, N.H.:
“New Correlation for Estimating the Viscosity of Undersaturated Crude Oils,” J. Cdn. Pet. Tech. (May-June, 1990) 80-85.
2. Al-Khafaji, A.H., Abdul-Majeed, G.H. and Hassoon, S.F.: “Viscosity Correlation For Dead, Live and Undersaturated Crude Oils,” J. Pet. Res. (Dec., 1987) 1-16.
3. Almehaideb, R.A.: “Improved PVT Correlations for UAE Crude Oils,” paper SPE 37691 presented at the 1997 Middle East Oil Conference and Exhibition in Manama, Bahrain (Mar. 17-20, 1997).
4. API Technical Data Book – Petroleum Refining: API, Washington DC 6th ed, (April, 1997) Chap 11.
5. ASME Pressure-Viscosity Report: Viscosity and Density of Over 40 Lubricating Fluids of Known Composition at Pressures to 150,000 psi and Temperatures to 435 F, Vol. I and II, ASME, New York, NY (1953).
6. Barus, C.: “Isothermals, Isopiestics and Isometrics Relative To Viscosity,” The American Journal of Science, Vol. XLV, No. 266 (1893) 87-96.
7. Beal, C.: “The Viscosity of Air, Water, Natural Gas, Crude Oil and Its Associated Gases at Oil Field Temperatures and Pressures,” SPE Reprint Series No. 3 Oil and Gas Property Evaluation and Reserve Estimates, SPE, Richardson, TX (1970) 114-127.
8. Brill, J.P. and Mukherjee, H.: Multiphase Flow in Wells, Monograph 17, SPE, Richardson, TX (1999).
9. Caudwell, D.R., Trusler, J.P.M., Vesovic, V., and Wakeham, W.A.: “The Viscosity and Density of n-Dodecane and n-Octadecane at Pressures up to 200 MPa
and Temperatures up to 473 K,” Int. J. of Thermophysics, Vol. 25 (2004) 1339-1352.
10. De Ghetto, G., Paone, F. and Villa, M.: “Reliability Analysis on PVT Correlations,” paper SPE 28904 presented at the European Petroleum Conference in London U.K. (Oct. 25-27, 1994).
11. Dindoruk, B. and Christman, P.G.: “PVT Properties and Viscosity Correlations for Gulf of Mexico Oils,” paper SPE 71633 presented at the 2001 SPE ATCE in New Orleans, LA (Sept 30-Oct 3, 2001).
12. Ducoulombier, D., Zhou, H., Boned, C., Peyrelasse, J. Saint-Guirons, H., and Xans, P.: “Pressure and Temperature Dependence of the Viscosity of Liquid Hydrocarbons,” J. Phys. Chem., Vol. 90, No. 8 (1986) 1692-1700.
13. Elsharkawy, A.M. and Alikhan, A.A.: “Models For Predicting The Viscosity of Middle East Crude Oils,” Fuel (June, 1999) 891-903.
14. Farshad, F.F., Leblanc, J.L., Garber, J.D. and Osorio, J.G.: “Empirical PVT Correlations For Colombian Crude Oils,” unsolicited paper SPE 24538 (June, 1992).
15. Hershey, M.D. and Hopkins, R.F.: Viscosity of Lubricants Under Pressure, ASME, New York, NY (1954).
16. Hossain, M.S., Sarica, C., Zhang, H.Q., Rhyne, L., and Greenhill, K.L.: “Assessment and Development of Heavy-Oil Viscosity Correlations,” SPE/PS-CIM/CHOA 97907 PS2005-407 presented at the 2005 SPE International Thermal Operations and Heavy Oil Symposium, Calgary, Canada (Nov. 103, 2005).
17. Kartoatmodjo, R.S.T.: “New Correlations for Estimating Hydrocarbon Liquid Properties,” MS Thesis, University of Tulsa (1990).
18. Kartoatmodjo, R.S.T. and Schmidt, Z.: “New Correlations For Crude Oil Physical Properties,” Unsolicited Paper SPE 23556 (Sept, 1991).
19. Khan, S.A., Al-Marhoun, M.A., Duffuaa, S.O., and Abu-Khamsin. S.A.: “Viscosity Correlations for Saudi Arabian Crude Oils,” paper SPE 15720 presented at the 5th SPE Middle East Oil Show in Manama, Bahrain (Mar 7-10, 1987).
21. Labedi, R.M.: “PVT Correlations of the African Crudes,” PhD Thesis, Colorado School of Mines (May, 1982).
22. Mehrotra, A.K. and Svrcek, W.Y.: “Viscosity of Compressed Athabasca Bitumen,” The Cdn. J. of Chem. Eng. (Oct., 1986) 844-847.
23. Mehrotra, A.K. and Svrcek, W.Y.: “Viscosity of Compressed Cold Lake Bitumen,” The Cdn. J. of Chem. Eng. (Aug., 1987) 672-675.
24. Orbey, H. and Sandler, S.I.: “The Prediction of the Viscosity of Liquid Hydrocarbons and Their Mixtures as a Function of Temperature and Pressure,” The Cdn. J. of Chem. Eng. (June, 1993) 437-446.
25. Petrosky, G.E., Jr.: “PVT Correlations for Gulf of Mexico Crude Oils,” M.S. Thesis, University of Southwestern Louisiana (1990).
27. Roelands, C.J.A.: “Correlational Aspects of the Viscosity-Temperature-Pressure Relationship of Lubricating Oils,” PhD Thesis, University of Delft, The Netherlands (1963).
28. Standing, M.B,: Volumetric and Phase Behavior of Oil Hydrocarbon Systems, 9th Printing, Society of Petroleum Engineers of AIME, Dallas, TX (1981).
29. Stephan, K. and Lucas, K.: Viscosity of Dense Fluids, Plenham Press, New York, NY (1979).
30. Sutton, R.P..: Petroleum Engineering Handbook, General Engineering, Vol. 1, J. Fanchi and L.W. Lake (eds.) Society of Petroleum Engineers, Richardson, TX (2006) 257-331.
31. Vazquez, M.E.: “Correlations for Fluid Physical Property Prediction,” M.S. Thesis, The University of Tulsa (1976).
32. Vazquez, M.E. and Beggs, H.D.: “Correlations for Fluid Physical Property Prediction,” J. Pet. Tech. (June, 1980) 968-970.
SI Metric Conversion Factors
141.4/(131.5+°API) = g/cm3
bbl × 0.1589873 = m3 ft3 × 0.02831685 = m3
cp × 1.0E−03* = Pa•s (°F–32)/1.8* = °C
psi × 6.894757E+00 = kPa °R × 5/9* = °K
*Conversion factor is exact
Fig. 1 – Change in undersaturated oil viscosity with pressure
Fig. 2 – Measured undersaturated oil viscosity
6 SPE 103144
Author Correlation Origin No. of Data
Points
μo Range
(cp)
μob Range
(cp)
p Range
(psia)
pb Range
(psia)
ARE (%)
SD (%)
AARE
(%)
Beal7,28 (1946)
USA 26 0.16 to 315
0.142 to 127 na na 2.7 na na
Kouzel20 (1965)
(exponential form of equation) na 95 1.78 to
202 1.22 to
134 423 to 6,015 14.7 -4.8 12.4 10.7
Vazquez and Beggs31,32
(1976)
Worldwide 3,593 0.117 to 148 Na 126 to
9,500 na -7.541 na na
Labedi21 (1982)
Libya 91 na 0.115 to 3.72 na 60 to 6,358 -3.1 27.19 na
Labedi21 (1982)
Nigeria and Angola 31 na 0.098 to 10.9 na 715 to
4,794 -6.8 41.07 na
Khan19 (1987)
Saudi Arabia 1,503 0.13 to 71.0
0.13 to 77.4 na 107 to
4,315 0.094 2.999 1.915
Al-Khafaji2 (1987)
na 210 0.093
to 7.139
na na na 0.0578 0.713 0.44
Abdul-Majeed1 (1990)
North America and Middle East
253 0.096 to 28.5
0.093 to 20.5 na 498 to
4,864 -0.0193 1.978 1.188
Petrosky25 (1990)
Gulf of Mexico 404 0.22 to 4.09
0.211 to
3.546
1,600 to 10,250
1,574 to 9,552 -0.19 4.22 2.91
Kartoatmodjo and Schmidt17,18
(1991)
Indonesia, N. America, Middle East, and Latin
America
3,588 0.168
to 517.03
0.168 to
184.86
25 to 6,015 25 to 4,775 -4.29 na 6.88
Orbey and Sandler24
(1993)
Pure component data nC6-nC18,
Alkylbenzenes and Cyclic
Hydrocarbons
377 0.225 to 7.3
0.217 to 3.1
740 to 14,504 14.5 na na 4.8
Table A-1 – Summary of published undersaturated oil viscosity methods
Table 3 – Statistical accuracy of viscosity methods for bubblepoint pressure < 50 psia (Note: Abdul-Majeed was not evaluated as all data had a GOR < 50 scf/STB.
Including this data, the method has an average error of 33,445%.)
Method # Pts % AE Std Dev % AAE Std Dev Min % Error
Table 10 - Statistical accuracy of viscosity methods for pressure differential 10,000-25,000 psi
13 SPE 103144
Fig. 3 – Barus viscosity relationship Fig. 5 – Comparison of “Barus-type” methods with measured viscosity data Fig. 7 – Error in calculated viscosity from Beal method
Fig. 4 – Bubblepoint viscosity effect on Barus viscosity relationship Fig. 6 – Pressure exponent to linearize viscosity equation (data from experiments with pressure differential in excess of 12,000 psi) Fig. 8 – Error in calculated viscosity from Kouzel method
14 SPE 103144
Fig. 9 – Error in calculated viscosity from Vazquez & Beggs method Fig. 11 – Error in calculated viscosity from Labedi (Nigeria/Angola) method Fig. 13 – Error in calculated viscosity from Al-Khafaji method
Fig. 10 – Error in calculated viscosity from Labedi (Libya) method Fig. 12 – Error in calculated viscosity from Khan method Fig. 14 – Error in calculated viscosity from Abdul-Majeed method
SPE 103144 15
Fig. 15 – Error in calculated viscosity from Petrosky method Fig. 17 – Error in calculated viscosity from Orbey & Sandler method Fig. 19 – Error in calculated viscosity from De Ghetto - Agip method
Fig. 16 – Error in calculated viscosity from Kartoatmodjo & Schmidt method Fig. 18 – Error in calculated viscosity from De Ghetto method Fig. 20 – Error in calculated viscosity from Almehaideb method
16 SPE 103144
Fig. 21 – Error in calculated viscosity from method Kouzel API method Fig. 23 – Error in calculated viscosity from Dindoruk & Christman method Fig. 25 – Error in calculated viscosity from Bergman & Sutton method
Fig. 22 – Error in calculated viscosity from Elsharkawy method Fig. 24 – Error in calculated viscosity from Hossain method Fig. 26 – Accuracy of Beal method
SPE 103144 17
Fig. 27 – Accuracy of Kouzel method Fig. 29 – Accuracy of Labedi (Libya) method Fig. 31 – Accuracy of Khan method
Fig. 28 – Accuracy of Vazquez & Beggs method Fig. 30 – Accuracy of Labedi (Nigeria/Angola) method Fig. 32 – Accuracy of Al-Khafaji method
18 SPE 103144
Fig. 33 – Accuracy of Abdul-Majeed method Fig. 35 – Accuracy of Kartoatmodjo & Schmidt method Fig. 37 – Accuracy of De Ghetto method
Fig. 34 – Accuracy of Petrosky method Fig. 36 – Accuracy of Orbey & Sandler method Fig. 38 – Accuracy of De Ghetto – Agip method
SPE 103144 19
Fig. 39 – Accuracy of Almehaideb method Fig. 41 – Accuracy of Elsharkawy method Fig. 43 – Accuracy of Hossain method
Fig. 40 – Accuracy of Kouzel – API method Fig. 42 – Accuracy of Dindoruk & Christman method Fig. 44 – Accuracy of Bergman & Sutton method
20 SPE 103144
Fig. 45 – Summary of undersaturated oil viscosity methods for reservoir fluid systems only Fig. 46 – Summary of undersaturated oil viscosity methods for entire database
