Improvement on the Viscosity Models for the Effects of Temperature

Article pubs.acs.org/jced

Improvement on the Viscosity Models for the Effects of Temperature and Pressure on the Viscosity of Heavy Crude Oils Brittany A. MacDonald* and Adango Miadonye Department of Chemistry, Cape Breton University, Sydney, Nova Scotia B1P 6L2, Canada ABSTRACT: With the industrial need for oil creating a growing scarcity of light, transport-efficient oil, a need for more readily transportable heavy crude is being developed. The processes of production and pipeline transportation of heavy crude oil require an understanding of material composition and physical and rheological characteristics, and the changes which occur at different process parameters. Typically this would require a series of expensive and wasteful experiments, done by exposing various crudes to varied processing conditions, such as pressure and temperature, which through exposure produce changes in the oil properties but are overall inefficient. Modeling eliminates these needs as a simple equation can predict heavy crude oil characteristics given parameters of use. This study comparatively examines a new simplistic, semiempirical equation against current empirical models for the viscosity of Tangleflags and Athabasca bitumen. The equation gave values of relatively low percent errors for the effect of temperature and pressure on viscosity based on one viscosity measurement.

1. INTRODUCTION The in-depth understanding of crude oil viscosity and the modeling of such can improve industrial operations through less harm to the environment, ease of transportation, cost efficiency increase, and overall production efficiency.1 Viscosity as an essential flow property of crude oil is required in many industrial production processes and would prove problematic if moved through a pipe of small diameter. To date, much research has occurred in this field on both pure oils as well as mixtures with additives such as alcohols.2−7 Industrial application requires the transport of heavy crudes on a regular basis and with current practices, lengthy and uneconomical testing must occur prior to defining feasible rheological properties which can be mitigated through the use of a predefined equation. Pure crudes are the most available source for industrial use and allow for precise modeling due to the unaltered form of the asphaltenes. The alteration of crude oil properties for ease of use can be done by modification of the process parameters such as temperature and pressure. Bitumen, being an example of a heavy crude oil with a known flow resistance boasts difficulty which can be overcome through heat addition as even the slightest change in temperature to a highly viscous oil can produce vastly modified flow abilities, but this is only a temporary fix as if transport speed decreases and occurs over an expansive distance, then the viscosity will rise due to a lack of change to the physical oil structure.4 Pressure, conversely has been shown by several studies to increase viscosity.7−10 The experimental measurement of viscosity at high pressure is cumbersome and expensive. Although several equations, either empirical and/or semiempirical in nature, have been developed for the viscosity−pressure relationship, comparatively © 2017 American Chemical Society

less attention has been directed to this area of research. Mehrotra and Svrcek8 have used a three-parameter empirical correlation to model the effect of temperature and pressure on viscosity of bitumen. They illustrated that pressure has a significant effect on bitumen viscosity. Puttagunta et al.9 developed Table 1. Coefficient Values for eqs 2 and 35 equation

b1

b2

b3

2 3

23.95318 23.55379

−3.76743 −3.69839

0.049118 0.005766

Table 2. Derived Temperature Coefficients temp (K)

Bo

∼308 ∼319 ∼330 ∼342 all temperatures

0.290 0.653 1.369 2.770 0.028

a viscosity correlation that predicts the effects of both temperature and pressure of bitumen with absolute error of less than 5%. A study done using three middle-East oils also showed that the viscosity of crude oil increases with increase in pressure7. Thus, both temperature and pressure have opposite but strong influence on the viscosity characteristics of heavy oils. Received: July 11, 2016 Accepted: February 10, 2017 Published: February 27, 2017 924

DOI: 10.1021/acs.jced.6b00619 J. Chem. Eng. Data 2017, 62, 924−930

Journal of Chemical & Engineering Data

Article

Athabasca heavy oils. The in-house viscosity data for Tangleflags heavy oil were obtained at different temperatures from 20 to 60 °C with the use of Cannon-Fenske transparent reversible viscometers in accordance with ASTM D445 Standard methods,11 During the experiment the oil bath was regulated to the desired temperatures and allowed to sit for at least 30 min to ensure equilibrium was reached. The accuracy of temperature was approximately ±0.02 °C. The literature data on the effects of temperature and pressure on Athabasca oil were obtained from Guan et al.,5 running between approximate temperatures of 35 and 70 °C and pressures from 0.124 to 9.994 MPa. 2.2. Development of Correlation. Several viscosity models based on the cubic equation of state or free-volume concept12,13 have been used in modeling the effects of temperature and pressure collectively or independently on viscosity of heavy oils. Such equations, in simplistic forms include the use of the cubic-plus-association equation of state15 which produces respectable data values but requires the input of many variables as seen in eq 1.

This study focuses on improving upon previously defined empirical equations through variations in crude oil data as well as decreasing error percentage and discovery of limiting parameters. By expanding upon the article of Puttagunta et al.9 further experimental data have been modeled as well as improvements being completed upon this empirical formula. Complete modeling is difficult at this time due to experimental data being required in the capacity of all crudes, diluents, and mixtures. Conception of a simplistic and accurate model would create an immensely easier and more financially and environmentally sustainable route for the global oil industry sector and would increase competitiveness with other energy users and sources. The main objective of this study is to develop a correlation for the effect of both temperature and pressure on the viscosity of heavy oils that fits into this concept of a simplistic and accurate model.

2. EXPERIMENTAL AND COMPUTATIONAL METHODS 2.1. Data Acquisition. Data used for this study were obtained in-house for Tangleflags and from Guan et al.5 for

Table 3. Values Obtained for Athabasca Bitumen Assuming μ@30 °C = 77.090 Pa·s (77090 mPa·s)a

a

T/K (±0.02 °C)

P (MPa)

μexp/(mPa·s)5

μ multiple Bo values (mPa·s)

μ single Bo values (mPa·s)

342.2 341.1 342.0 342.2 341.8 342.6 342.3 342.6 342.7 342.8 330.0 331.3 330.3 331.5 331.6 331.6 331.6 331.6 331.7 331.7 331.7 319.5 319.8 319.9 319.9 319.9 319.9 319.9 319.8 319.9 319.9 319.9 308.7 308.8 308.9 309.0

0.124 1.002 2.002 4.000 4.999 5.998 6.997 7.996 8.995 9.994 0.124 1.002 2.002 3.001 4.000 4.999 5.998 6.997 7.996 8.995 9.994 0.124 1.002 2.002 3.001 4.000 4.999 5.998 6.997 7.996 8.995 9.994 0.124 1.002 2.002 3.001

1236 1465 1499 1561 1708 1643 1765 1789 1859 1944 3619 3519 3945 3728 3876 4053 4246 4433 4621 4848 5061 10499 11135 11882 12446 12869 13342 13843 14590 15184 16119 17048 36164 38371 40237 41420

1265 1442 1411 1533 1663 1640 1765 1811 1887 1967 3593 3337 3858 3640 3801 4005 4221 4448 4645 4895 5159 10344 10528 11026 11672 12357 13082 13849 14822 15521 16431 17394 36974 38295 39926 41624

1266 1146 1419 1551 1687 1668 1800 1852 1937 2024 3594 3343 3870 3657 3825 4038 4262 4498 4704 4966 5241 10343 10517 11004 11637 12307 13016 13765 14718 15396 16282 17220 36990 38426 40200 42053

Uncertainties u: u(T) = 0.1 K, u(P) = 0.007 MPa, and u(μ) = 0.02 μ.5 925



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where μB is viscosity in mPa·s, T is temperature in K, P is the pressure in MPa, and relevant constants b1−b3 can be seen in Table 1.5

Table 4. Validation of Data with eqs 2 and 3 % error for correlationsb

P/MPa 0.124 1.002 2.002 4.000 4.999 5.998 6.997 7.996 8.995 9.994 0.124 1.002 2.002 3.001 4.000 4.999 5.998 6.997 7.996 8.995 9.994 0.124 1.002 2.002 3.001 4.000 4.999 5.998 6.997 7.996 8.995 9.994 0.124 1.002 2.002 3.001

a

T/K μexp/ (±0.02 °C)a (mPa*s)a eq 25 342.2 341.1 342.0 342.2 341.8 342.6 342.3 342.6 342.7 342.8 330.0 331.3 330.3 331.5 331.6 331.6 331.6 331.6 331.7 331.7 331.7 319.5 319.8 319.9 319.9 319.9 319.9 319.9 319.8 319.9 319.9 319.9 308.7 308.8 308.9 309.0

1236 1465 1499 1561 1708 1643 1765 1789 1859 1944 3619 3519 3945 3728 3876 4053 4246 4433 4621 4848 5061 10499 11135 11882 12446 12869 13342 13843 14590 15184 16119 17048 36164 38371 40237 41420

4.5 0.4 4.0 0.1 0.9 1.6 1.7 3.0 3.2 2.9 1.9 3.0 0.3 0.8 0.7 0.3 0.1 0.5 0.4 0.5 1.1 1.8 3.0 5.6 5.3 3.8 2.6 1.4 0.7 0.8 1.9 2.6 6.6 3.5 2.4 3.1

eq 3

this work (multiple Bo values)

this work (single Bo value)

7.1 2.2 3.0 0.3 1.8 0.1 0.5 0.0 0.3 1.3 2.7 2.2 0.2 0.4 0.5 0.2 0.0 0.5 0.2 0.3 0.9 0.6 3.7 5.8 5.1 3.1 1.3 0.5 1.8 2.3 1.9 1.9 2.6 0.8 0.8 2.8

−2.4 1.6 5.9 1.8 2.6 0.2 0.0 −1.2 −1.5 −1.2 0.7 5.2 2.2 2.4 1.9 1.2 0.6 −0.4 −0.5 −1.0 −1.9 1.5 5.5 7.2 6.2 4.0 2.0 0.0 −1.6 −2.2 −1.9 −2.0 −2.2 0.2 0.8 −0.5

−2.4 1.3 5.3 0.6 1.2 0.6 −2.0 −3.5 −4.2 −4.1 0.7 5.0 1.9 1.9 1.3 0.4 −0.4 1.5 −1.8 −2.4 −3.6 1.5 5.5 7.4 6.5 4.4 2.4 0.6 −0.9 −1.4 −1.0 −1.0 −2.3 −0.1 0.1 −1.5

5

ln(ln(μB )) = [b1 + b2 ln(T )] + b3(P − 0.090)

(3)

where μB is viscosity in mPa·s, T is temperature in K, and relevant constants b1−b3 can be seen in Table 1.5 Guan et al. reported that both eqs 2 and 3 estimated the combined effects of temperature and pressure on viscosity of Athabasca bitumen with high accuracy. The model of Puttagunta et al.9 has also been shown to correlate the relationship between temperature, pressure, and viscosity very well, and is based on one experimental data point. It is given as follows: ⎡ b ⎢ ln μ = 2.30259⎢ T − 30 ⎢⎣ 1 + 303.15

(

s

)

⎤ ⎥ + C ⎥ + BoP exp(dT ) ⎥⎦

(4)

where μ represents viscosity in Pa·s, b is the characterization parameter, Bo, s, and d are parameters dependent upon b, C is a constant, P is guage pressure in MPa, and T is temperature in °C.9 In this study, we will model the viscosity of the heavy oils (Tangleflags and Athabasca) using a modified Puttagunta et al. model, and compare the results with those obtained with eqs 2 and 3. The model differs from eqs 2 and 3 because only one experimental piece of viscosity data must be measured by the user at one chosen temperature and 1 atm pressure. Once one point is defined any other parameter can be easily calculated. The viscosity data at different temperatures obtained from in-house measurement of Tangleflags oil and from Guan et al.7 on Athabasca bitumen were used to derive new parameters by constrained linear regression technique. The regression analysis gave an r2 of 0.998 at optimal condition after several hundreds of regression steps. The values for the new parameters are as given in the new model (eq 5). μ=

b + c + BoP exp(dT ) q

(5)

where; μ = viscos ity in Pa·s

Uncertainties u: u(T) = 0.1 K, u(P) = 0.007 MPa, and u(μ) = 0.02 μ. b ARD (%) = 100·|μcorr − μexp|/μexp.5 a

b = (log μ@30 ° C ) − c

c = −3.002

ex ⎛ ⎛ A assoc 1 − xR ⎞ 1 − XA ⎞ ⎟ + N X ⎜ln x + ⎟ = NAxA ⎜ln xA + R R ⎝ ⎝ R nRT 2 ⎠ 2 ⎠

Bo = 0.028 (1)

d = −0.003

where subscripts A and R representation aromatics and/or resins, XA and XR are mole fractions of each and NR and NA are association sites along with a universal gas constant, R, and absolute temperature, T. This equation is only a portion of an overall discovery and hence would be unusable on a daily basis. It works specifically to predict asphaltene precipitation. Mehrotra and Svrcek8 developed two empirical equations for the dynamic viscosity of solvent-free bitumen. Both equations have been modified by Guan et al.5 for estimation of the combined effects of temperature and pressure on viscosity for Athabasca bitumen as follows: ln(μB ) = exp[b1 + b2 ln(T )] + b3(P − 0.090)

s = (0.362b) + 1.986 s ⎛ ⎛ T − 30 ⎞⎞ ⎟⎟ q = ⎜1 + ⎜ ⎝ 303.15 ⎠⎠ ⎝

and T = temperature in Celsius

P = pressure in MPa

To provide more accurate results as seen in Table 3, pressure correction coefficients were derived for each temperature corresponding to the pressure range, which while increasing

(2) 926



Article

Figure 1. Viscosity of Athabasca bitumen vs temperature at atmospheric pressure.

Table 5. Correlated Viscosity Data for Tangleflags Bitumen at 0.120 MPa Assuming μ@30 °C = 5.105 Pa·s (5105 mPa·s)

a b

T/K (±0.02 °C)a

μexp/(mPa·s)a

μpredicted/(mPa·s)

% errorb

293.570 298.280 313.050 332.050

13447 8139 2153 1000

13384 8196 2147 1001

0.47 −0.70 0.30 −0.07

Uncertainties u: u(T) = 0.1 K, u(P) = 0.007 MPa, and u(μ) = 0.02 μ. ARD (%) = 100·|μcorr − μexp|/μexp.5

Figure 2. Comparison of percentage error at different temperatures.

Figure 4. Comparison of predicted and experimental viscosity− temperature data for different heavy oils.

3. RESULTS AND DISCUSSION Equations 2 and 3 were used to reproduce the data by Guan et al. to check for validity of the equation; producing values from those in the study with little or no error. Table 4 illustrates the results from the Guan et al. study in comparison with the validation Replication of the data was step one in the experimental process, with the next step being the development of a new equation that is equally accurate but simpler to use in predicting the actual viscosity values. Effect of Increasing Temperature. The relationship between heavy oil viscosity and temperature is illustrated in

Figure 3. Viscosity of Athabasca bitumen vs pressure at different temperatures using eq 5.

accuracy, user-ease, and efficiency decreases. The derived values for the parameter, Bo, at each temperature are found in Table 2. The values obtained from the proposed equation, eq 5 are found in Table 3. It is already known that asphaltene content directly affects viscosity through an exponential relationship.6 It would be reasonable to assume that is the case of this pure oil, and is shown in the original data.5 927



Article

Figure 5. Comparison of predicted and experimental viscosity− pressure data for different models. Figure 8. Comparison of % error at different pressures for various viscosity models at ∼319 °C.

Figure 9. Comparison of % error at different pressures for various viscosity models at ∼331 °C.

Figure 6. Lower viscosity range. Comparison of predicted and experimental viscosity−pressure data for different models.


Figures 1 and 2, it indicates that the viscosity reduction trend with increasing temperature is increasingly negligible at higher temperature. The equation predicted this trend accurately for both Tangleflags heavy oil and Athabasca bitumen as shown in Figure 1. Also from the plots in Figures 1 and 2 the new equation values show little deviation from literature values. The average absolute deviations obtained with the equations are 0.39% and 1.71% for Tangleflags heavy oil and Athabasca bitumen, respectively. The equation predicts viscosity values at different temperatures from one viscosity value either measured or as in this case correlated at 30 °C and 1 atm. The same viscosity value at 30 °C is used to predict the combined effects of temperature and pressure of viscosity of heavy oils.


Effect of Increasing Pressure. The new values obtained for the parameter, Bo, by constrained linear regression of the data at different temperatures, are shown in Table 2. In Figure 3, the viscosity data of the bitumen sample studied and the calculated ones using the new eq 5 are compared. As can be observed, the new model fits fairly well the experimental data in the whole range of pressure for each given temperature. There is no significant difference in the results of eqs 2 and 3 observed, and the new model (eq 5) predicted the viscosity 928



Article

Table 6. Average Absolute Deviation Valuesa

a

pressure (MPa)

AAD (%) eq 2

AAD (%) eq 3

AAD (%) eq 5 (multiple Bo)

AAD (%) eq 5 (single Bo)

0.124 1.002 2.002 3.001 4.000 4.999 5.998 6.997 7.996 8.995 9.994

3.68 2.50 3.08 3.10 1.55 1.25 1.02 0.97 1.40 1.87 2.18

3.27 2.22 2.47 2.79 1.29 1.10 0.19 0.95 0.84 0.84 1.36

1.70 2.23 2.53 2.33 0.96 0.49 0.22 0.62 0.60 0.31 0.33

1.71 3.00 3.68 3.31 2.11 1.35 0.83 1.45 2.25 2.54 2.90

values based upon approximate pressures. The parameters for the equations are given in Table 1, and the viscosity results and errors are summarized in Table 7. To have a better representation of data and comparison with the models, the viscosity data at various temperatures are plotted in Figures 7−10. Error is greatest at lower temperatures; the reason is arguably that at lower temperature conditions it is difficult to obtain more accurate experimental viscosity values. The three models seem to show a low error percentage at ∼6 MPa, and lower pressures, like lower temperatures, yield again more error.

4. CONCLUSIONS Percentages of error from this design when examining pure samples of Athabasca crude oil are on average below 2%. This experiment provides improvement upon previously designed equations for the pure Athabasca crude. The greatest improvement apart from a decrease in error is the inclusion of another oil type, Tangleflags. From here further data sets must be tested apart from those presented previously (ref5). Lab tests will be run on more various crude oils in their pure forms as well as mixtures containing various diluents or combination with lighter crude (ref14). This will prove the validity of the designed model and its ability to predict all ranges of composition. While the use of multiple coefficients may produce a smaller error percentage, the goal of this proposed equation, eq 5, is to provide an easy to use, simple equation. Percent error can always be increased, but this adds numerous variables, which will deter a user from implementing this into daily operations. A core correction to the current equation that must be made is the inclusion of a more vast array of data. Innovation in this case is an in depth-process which in this article has progressed due to the inclusion of Tangleflags crude oil; a large database will allow for accurate changes to be made to better reflect all mixtures and crudes. This data in the model of an equation is valuable as it can be used to provide a graph of composition, versus viscosity, and shape factor. The use for such correlations will be next defined as well as their limitations,10 one of which has been previously identified; changing temperature is only efficient if the oil is being transported over a small distance. With a large enough data collection and variety, any mixture composition could be related to both shape factor and viscosity values. This is done in hopes that with a known composition one could retrieve the other two missing values, fill them into our equation, and be provided with a related viscosity value. Also the additive diluents are necessary as with today’s industrial process requirements (distance, etc.), light oils are required for ease of use and hence slight composition changes must be made.

Uncertainties u: u(P) = 0.007 MPa.5

data with similar accuracy. An examination of Figure 3 demonstrates that the petroleum viscosity shows a linear trend with increasing pressure irrespective of temperature of the viscosity, particularly at higher viscosity temperatures. Figures 1 and 2 utilize data from Tables 4, 5, and 3 to compare the literature values for Athabasca bitumen and Tangleflags with the new predicted values (from eq 5) as well as the values predicted by eqs 2 and 3. An examination of Figures 1 and 2 demonstrates that pressure creates an opposing effect to temperature: with increased pressure the viscosity actually becomes greater, which is in agreement with Newton’s law of viscosity that when pressure decreases, viscosity will decrease as well.6 Figures 4−6 illustrate the predicted viscosity using different models compared to the experimental viscosity data. The predicted viscosity matched the measured viscosity extremely well for all three equations but more so for the new eq 5. Figure 6 highlights the predictions at lower pressures, with all equations showing deviations from the measured values between 12000 and 16000 MPa pressure, which can arguably be attributed as errors in the measured values. As depicted in Figures 7−10, eqs 2 and 3 predict the viscosity data over wide range of pressure with higher errors; the new model provides better predictions. Specifically in Figure 8, there is a clear distinction of error across pressures; once 4 MPa has been surpassed a decrease in error is seen, which allows for a range of best use to be identified as occurring after this pressure. It is acknowledged that after this point a continued decrease is not seen; however, there is a significant difference in error percentages, boasting success in the definition of parameters. The viscosity predictions using eqs 2 and 3 lead to almost similar results. A comparison on the basis of percent average absolute deviations (AADs) shows that for approximate temperatures of 309, 319, 331, and 342 K eqs 2 and 3 gave 1.35, 2.03, 0.89, 1.90% (eq 2) and 0.95, 2.64, 0.94, 1.78% (eq 3), respectively, and the new eq 5 gave 0.90, 2.97, 1.32, 1.54%. See Table 6 for resulting AAD

Table 7. Correlated Viscosity Data Constant Pressure vs Varied Temperature for Athabasca Bitumen at 0.124 MPa Assuming μ@30 °C = 77.090 Pa·s (77090 mPa·s) T/K (±0.02 °C)a μexp/(mPa·s)a μpredicted/(mPa·s) % error, this work eq 5b 308.70 319.50 330.00 342.20 a

36164.000 10499.000 3619.000 1236.000

36742 10280 3573 1259

−1.60 2.09 1.26 −1.87

μcorr/ (mPa*s) eq 25

μcorr/ (mPa*s) eq 35

38547 10686 3688 1291

37116 10564 3718 1324

% error eq 25 b % error eq 3 5 b 6.6 1.8 1.9 4.5

2.6 0.6 2.7 7.1

Uncertainties u: u(T) = 0.1 K, u(P) = 0.007 MPa, and u(μ) = 0.02 μ. bARD (%) = 100·|μcorr − μexp|/μexp .5 929



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Article

AUTHOR INFORMATION

Corresponding Author

*taff[email protected]. ORCID

Brittany A. MacDonald: 0000-0002-2351-6865 Funding

We would like to gratefully acknowledge the financial support of Cape Breton University through the University’s Research Grant. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Ali Mansoori, G. Modeling of asphaltene and other heavy organic depositions. J. Pet. Sci. Eng. 1997, 17, 101−111. (2) Hemmati-Sarapardeh, A.; Khishvand, M.; Naseri, A.; Mohammadi, A. Toward reservoir oil viscosity correlation. Chem. Eng. Sci. 2013, 90, 53−68. (3) Hemmati-Sarapardeh, A.; Majidi, S.; Mahmoudi, B.; Ramazani, S.; A, A.; Mohammadi, A. Experimental measurement and modeling of saturated reservoir oil viscosity. Korean J. Chem. Eng. 2014, 31, 1253− 1264. (4) Sánchez-Minero, F.; Sánchez-Reyna, G.; Ancheyta, J.; Marroquin, G. Comparison of correlations based on API gravity for predicting viscosity of crude oils. Fuel 2014, 138, 193−199. (5) Guan, J.; Kariznovi, M.; Nourozieh, H.; Abedi, J. Density and Viscosity for Mixtures of Athabasca Bitumen and Aromatic Solvents. J. Chem. Eng. Data 2013, 58, 611−624. (6) Ghanavati, M.; Shojaei, M.; S. A., A. Effects of Asphaltene Content and Temperature on Viscosity of Iranian Heavy Crude Oil: Experimental and Modeling Study. Energy Fuels 2013, 27, 7217−7232. (7) Mehrotra, A. Modeling the effects of temperature, pressure, and composition on theviscosity of crude oil mixtures. Ind. Eng. Chem. Res. 1990, 29, 1574−1578. (8) Mehrotra, A. K.; Svrcek, W. Y. Viscosity of compressed Athabasca bitumen. Can. J. Chem. Eng. 1986, 68, 844−847. (9) Puttagunata, V. R.; Singh, B.; Miadonye, A. Correlation of bitumen viscosity with temperature and pressure. Can. J. Chem. Eng. 1993, 71, 447−450. (10) Miadonye, A.; Singh, B.; Puttagunta, V. R. Modelling the Viscosity-Temperature Relationship of Alberta Bitumens. Fuel Sci. Technol. Int. 1994, 12, 335−350. (11) ASTM International. (2016). ASTM D445.15a Standard Test Method for Kinematic Viscosity of Transparent and Opaque Liquids (and Calculation of Dynamic Viscosity). http://www.astm.org/Standards/ D445.htm (accessed January 4, 2016). (12) Cheung, C. Y. Mechanical behaviour of bitumens and bituminous mixes. Master Thesis. Cambridge University, 1995. Engineering Department. (13) Miadonye, A., Singh, B., Puttagunta, V. R. Viscosity of Bitumen, Effect of Pressure and Temperature. In Encyclopedia of Chemical Processing and Design; McKetta, John J., Ed.; CRC press Taylor and Francis, 1998; Vol. 62, pp 455−464. (14) Naseri, A.; Nikazar, M.; Mousavi Dehghani, S. A correlation approach for prediction of crude oil viscosities. J. Pet. Sci. Eng. 2005, 47, 163−174. (15) Li, Z.; Firoozabadi, A. Modeling Asphaltene Precipitation by n -Alkanes from Heavy Oils and Bitumens Using Cubic-PlusAssociation Equation of State. Energy Fuels 2010, 24, 1106−1113.

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Improvement on the Viscosity Models for the Effects of Temperature

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