Fuel Processing Technology, 26 (1990) 25-37 25 Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands

Viscosi ty Data and Correlation for Mixtures of Bi tumen Fract ions

ROBERT R. EASTICK and ANIL K. MEHROTRA*

Department of Chemical and Petroleum Engineering, The University of Calgary, Calgary, Alberta, T2N 1N4 (Canada)

(Received June 30th, 1989; accepted in revised form March 30th, 1990)

ABSTRACT

A Cold Lake bitumen sample was distilled under vacuum into five fractions or "cuts". The viscosities of these bitumen fractions differ considerably by several orders of magnitude. The viscosity data over a 60-100°C temperature span are presented for several reconstituted binary blends of these fractions. The effect of temperature on the viscosity of the blends is correlated very well by use of a two-parameter correlation, with average deviations between predicted and experimental values of less than 3%. The validity of a recently proposed viscosity mixing formula, which does not involve any viscous interaction term, is investigated with the new binary blends viscosity data. Also proposed are generalized correlations in terms of the molar mass fractions, for the two parameters in the viscosity-temperature correlation.

INTRODUCTION

In many aspects of oil-sands industry, such as reservoir simulation and pipe- line or surface facilities design, the viscosity of the bitumen under considera- tion is an extremely important property. Due to the diverse nature of bitumens from the vast reservoirs in Alberta, the bitumen viscosity can vary consider- ably at any given temperature (and pressure). This diversity in bitumen vis- cosity may be attributed to differences in the bulk composition of the bitu- mens. Typically, however, bitumens are very viscous at reservoir conditions. Bitumen viscosity decreases dramatically with temperature [1-6] but in- creases significantly with pressure due to compression effects [7,8]. The ad- dition of gaseous and liquid diluents also has a marked effect on bitumen viscosity.

Several calculation methods for the viscosity of bitumens have been pre- sentedein literature [2,7-13]. Recently [14], a two-parameter correlation found suitable for a number of Alberta bitumens [2,7-9,11 ] was shown to cor-

*To whom correspondence about this paper should be addressed.

0378-3820/90/$03.50 @) 1990 Elsevier Science Publishers B.V.

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TABLE1

Measured data and properties of Cold Lake bitumen and its fractions

Sample Mass fraction M Density Asphaltenes of whole (gmo1-1 ) (gcm -a ) (mass%) bitumen

Maltenes (mass%)

Distillable a Undistillable bp<550°C bp> 550°C

whole bitumen 1.000 582 0.995 16.7 47.8 35.5

Cut 1 0.103 209 0.879 0.0 100.0 0.0 Cut 2 0.283 310 0.941 0.0 100.0 0.0 Cut 3 0.168 667 0.990 2.2 67.1 30.7 Cut 4 0.065 800 0.999 1.7 20.3 78.0 Cut 5 0.381 2500 1.072 49.5 0.0 50.5

aSIMDIST analyses were provided in Ref. (14).

relate the viscosities of the five fractions (or cuts) of Cold Lake bitumen with average deviations from 0.9 to 6.6%. Of the five bi tumen fractions that were obtained by vacuum distillation [ 14 ], Cuts 1 and 2 were clear liquids whereas Cuts 3 and 4 resembled the whole bitumen. Cut 5, however, was a glass-like solid at room temperature with a softening point around 100 ° C. Table 1 sum- marizes some of the properties of these five fractions. Cuts 1 to 4 contain little or no asphaltenes while approximately 50 mass% of Cut 5 is asphaltenes.

In this paper, new viscosity data for a number of reconstituted binary blends (mixtures) of the Cold Lake bitumen fractions are reported. These binary blend viscosity data are found to be correlated well with the two-parameter viscosity correlation. In addition, a viscosity mixing formula presented previously [ 14 ] is used to predict viscosities of blends. It should be noted that this viscosity mixing formula does not involve any viscous interaction terms. Based on these results, a liquid-mixture viscosity calculation procedure is developed, which requires only the proportions of the bi tumen fractions and their molar mass to be known. Furthermore, generalized correlations are proposed for the two pa- rameters in the viscosity-temperature correlation in terms of the fraction mo- lar mass. Finally, this generalized approach is evaluated for predicting the vis- cosity of the blends, as well as of the whole bitumen.

Viscosity-temperature correlation for bitumen fractions

The following two-parameter correlation was shown to represent the viscos- i ty-temperature variation for a number of Alberta bitumens with average de- viation below 10% [13]. The viscosity-temperature data for the five bitumen fractions, as mentioned previously, have also been correlated successfully with this correlation [ 14 ].

27

log[log (H+0.7)] =b, +b~ log (T) (1)

The empirical constants bl and b2 in eqn. (1) may be viewed as viscosity char- acterization parameters. The parameter b2 in eqn. (1) was found to vary within a narrow range of values, from -3 .74 to -3.50, for several bitumens. Based on this finding, a single constant value of b2 = -3.6303 for 7 bitumens over wide ranges of viscosity and temperature was proposed [ 13 ]. The value of pa- rameter b2 is noted to vary considerably for the five bitumen fractions. Hence, the one-parameter viscosity correlation may not be suitable for bitumen fractions.

It should be pointed out that each of the five bitumen fractions consists of a multitude of hydrocarbon compounds. In modeling the liquid-mixture viscos- ity, each bitumen fraction is treated as one pseudocomponent. In other words, the Cold Lake bitumen is approximated as a mixture comprising five pseudo- components. The viscosity characterization parameters bl and b2 for each bi- tumen fraction and the whole Cold Lake bitumen are given in Table 2. Figure I compares the viscosity data and the correlated values for each bitumen frac- tion. Clearly, eqn. (1) is capable of fitting the viscosity-temperature data in every case. A closer examination of the parameter values in Table 2 reveals that bl decreases as the bitumen fractions become heavier. The values of b2 are higher (i.e. less negative) for the heavier fractions.

Viscosity of mixtures of bitumen fractions

For calculating mixture viscosity from component viscosities, several liquid- mixture viscosity correlations are available. Most simple (additive) liquid- mixture viscosity correlations can be generalized as [ 15 ]:

106

105 f]} " , ~ ' "

(D 13_ 10 4 E >~I0 3

"~0 102 i !!i!. bitumen ._~

101 100 , ~ -- Eq~otlon (1)

1 O0 200 300 TernperGture, °C

Fig. l. Effect of temperature on the viscosity of Cold Lake bitumen and its fractions.

28

n f(fi) = ~ Xi[(#i) (2)

i ~ l

where, f(#) may be #, 1/#, #_+1/3, In (#), log (#), etc., and xi may be either of the liquid volume, mass or mole fraction [ 15]. Other liquid-mixture viscosity correlations are also available in the literature but a majority of those involve some form of binary, and occasionally ternary, viscous interaction terms. Ob- viously, eqn. (2) assumes no viscous interaction between the various constit- uents of a liquid-mixture.

After screening several choices for [(#) and xi in eqn. (2), the following viscosity mixing formula was proposed for the bitumen fractions [14]:

log (/2+0.7)= ~ x , x / - M ~ log (#, +0.7) (3) i = 1

where, xi is the mole fraction of Cut i, Mi is the molar mass of Cut i, and l~ is the average mixture molar mass. The term x i ~ in eqn. (3) represents the geometric mean of mass and mole fractions of component i in an n-com- ponent mixture. The bitumen viscosity predictions from eqn. (3) compared satisfactorily with the experimental data, with an average deviation of 38% [14]. Equation (3) in the anti-logarithmic form is:

(/2+0.7) = I~I (#i +0.7) x' M~/$~'-~'/~ (4) i = 1

VISCOSITY MEASUREMENT FOR RECONSTITUTED BINARY BLENDS

A total of twelve binary blends of the Cold Lake bitumen fractions were prepared by mixing different proportions of the individual constituents. Two different proportions were selected for each pair of bitumen fractions. These blends were composed of either Cut 1 or Cut 2 mixed with either Cut 3, 4 or 5. Table 2 provides the details of the blend constituents and the molar composi- tion. The composition data indicate that most of the blends had substantially high mole fractions of the two lighter bitumen fractions. The viscosity of each blend was measured at several temperatures, over a 60-100 °C temperature span, using a Model RV8 viscometer from Viscometers (UK) Ltd. The tem- perature range and the number of viscosity data points for each binary blend are also given in Table 2.

RESULTS AND DISCUSSION

Correlation of binary blend viscosities

The viscosity-temperature data for the twelve reconstituted binary blends were correlated using the two-parameter correlation, eqn. (1). The results of

29

TABLE 2

Viscosity-temperature data for Cold Lake bitumen fractions and blends and their correlation with eqn. (1)

Sample No. of Temperature x a b, b2 A A D b

points range ( % )

Whole Bitumen 20 24-121°C - 9.1451 - 3.4281 4.3

Cut 1 29 22- 94°C - 11.6244 -4 .7535 0.9 Cut 2 23 30- 90°C - 11.2120 -4 .4068 1.2 Cut 3 22 26= 100 ° C - 10.4535 - 3.9527 2.3 Cut 4 20 30-106°C - 10.1941 -3 .8061 3.1 Cut 5 18 120-210°C - 8.9592 -3 .1573 6.6

Blend 1 (Cut 1 /Cu t 3) 23 30- 95°C 0.381 10.3078 -3 .9575 1.4 Blend 2 (Cut 1 /Cu t 3) 21 30- 95°C 0.585 10.3065 -3 .9914 1.5 Blend 3 (Cut 1 /Cu t 4) 21 22- 90°C 0.678 9.9007 -3 .8220 1.3 Blend 4 (Cut 1 /Cu t 4) 11 21- 65°C 0.900 9.8916 -3 .9338 1.6 Blend 5 (Cut 1 /Cu t 5) 14 60- 95°C 0.902 8.8943 -3 .3338 1.8 Blend 6 (Cut 1 /Cu t 5) 23 30- 95°C 0.937 8.9679 -3 .4209 1.7 Blend 7 (Cut 2 / C u t 3) 21 38- 90°C 0.603 10.6535 -4 .0932 2.1 Blend 8 (Cut 2 / C u t 3) 24 21- 95°C 0.792 10.8638 -4 .2127 1.6 Blend 9 (Cut 2 / C u t 4) 26 23- 95°C 0.683 10.3647 -3 .9617 1.4 Blend 10 (Cut 2 / C u t 4) 24 30- 95°C 0.841 10.4476 -4 .0358 2.5 Blend 11 (Cut 2 / C u t 5) 14 80-130°C 0.669 9.0623 -3 .2690 2.8 Blend 12 (Cut 2 / C u t 5) 23 23- 90°C 0.974 10.0422 -3 .8770 2.9

ax: Mole fraction of lighter fraction. N

b A A D = ( 1 / N ) ~ [ [~exp-- Pcorrl/]lexp].

these regression calculations are given in Table 2. The fit for each blend using eqn. (1) is remarkable, with average deviation consistently under 3%. Hence, the two-parameter viscosity correlation can be used to describe the effect of temperature on the viscosity of whole bitumens, bitumen fractions and the blends of the bitumen fractions.

Figure 2 shows the viscosity data for Cuts 1 and 4 and their two blends (Blends 3 and 4 in Table 2). The solid curves in Fig. 2 represent the viscosities corre- lated by using eqn. (1). The broken curves for the two blends represent the viscosity predictions by use of generalized parameters which will be discussed later.

Liquid-mixture viscosity predictions for binary blends

When a lighter fraction of bitumen, such as Cut 1 or 2, is added incremen- tally to a heavier fraction, such as Cut 3, 4 or 5, a gradual reduction in the viscosity of the heavier fraction will take place. The viscosity change during

30

106 ' ' 0 Cu'st '

[] Blends ~ _ - - Equation (1)

10 5 ~ t i o n s ' ( 5 ) and (6)

10 4 n

E 103

~ 10 2

101 --

100 ~ , 20 40 60 80 1 O0 120

T e m p e r e t u r e , °C

Fig. 2. Viscosities of Cuts I and 4, and their two reconstituted binary blends.

such "dilution" experiments with bi tumen fractions may span several orders of magnitude. At 25 ° C, for example, the viscosities of Cuts 4 and 1 are 937,000 mPa s and 4.6 mPa s, respectively; a ratio of approximately 200,000. When Cut 4 is diluted with Cut 1 in a "dilution" experiment at 25 ° C, the viscosity of Cut 4 will decrease from 937,000 mPa s to approach 4.6 mPa s ultimately.

To study such simulated "dilution" experiments by using eqn. (3), several sets of viscosity calculations were made at an arbitrarily selected temperature of 100 ° C. In these calculations, Cut 1 was mixed with each of the four heavier bi tumen fractions, and the results are shown in Fig. 3. The logarithm of mix- ture viscosity decreases rapidly once the mole fraction of Cut 1 is greater than about 0.5-0.7. This is more pronounced for the results with the heavier bitu- men fractions, especially Cut 5.

Parameters bl and b2 for binary mixtures Any binary mixture of bi tumen fractions would have a unique set of the

viscosity characterization parameters bl and b2 for describing the effect of tem- perature on its viscosity. However, the bl and b2 values for a liquid-mixture cannot be determined explicitly from eqn. (3). The liquid-mixture viscosity results presented below were obtained from a large number of calculations in- volving the viscosity mixing formula, eqn. (3). This was accomplished by cal- culating viscosity values from eqn. (3), over a range of temperatures, for sev- eral binary mixtures followed by regressing the parameters b~ and b2 for each mixture from eqn. (1).

31

03

E) o_ E

4_a

(O

b3

>

107

10 6

105

104

103

102

101

100

i i i i

mixtures

Oil 1/Cut4mixtures ~ e s

.Cut 1/Cut 2 mixtures __

I I I I

0.0 0.2 0.4 0.6 0.8 Mole Fraction of Cut 1

.0

Fig. 3. Influence of Cut 1 on the predicted viscosity of binary mixtures at 100 ° C.

The effect of mixture composition on the values of bl and b2 is shown in Fig. 4 for binary mixtures of Cut 1 and each of the other four bi tumen fractions. Here, an increasing influence of the lighter fraction (Cut 1 ) at its higher con- centrations is more clearly evident. The trends for bl of the heavier bi tumen fractions are very interesting. As the mole fraction of Cut 1 is increased, the bt curves pass through a minimum before increasing sharply to the bl value for Cut 1.

The results in Fig. 5 give a "phase space" representation of the viscosity characterization parameters bl and b2. The filled circles in Fig. 5 correspond to the parameter values for the five bitumen fractions, and these appear to fall on a straight line. The parameters for the twelve binary blends, Table 2, are shown as hollow symbols in Fig. 5. These experimental data for the reconsti- tuted blends lie below and to the left of the points for the individual fractions. This implies that the viscosity characterization parameters for binary mix- tures cannot be obtained by a simple interpolation procedure. The predicted loci for the parameters of binary mixtures of bi tumen fractions are shown by the curves connecting the filled circles. Note that these curves do deviate con- siderably from the straight lines that would connect the filled circles denoting the bitumen fractions.

Blend viscosity predictions using empirical parameters The results for the twelve binary blends, with viscosities calculated from

eqn. (3), are summarized in Table 3. The average deviations are generally

32

12

b l lo

9

8 -3.0

-3.5

b2 -,.o

-4.5

- 5 . 0 0.0

Cut 1/Cut 2

Cut 1/Cut 3

Cut 1/Cut ,

Cut 1/Cut 5 J I I I

Cut 1/Cut 5

Cut 1/Cut ,

Cut 1/Cut 3

Cut 1/Cut 2

i i i

0.2 0., 0.6

Mole F rac t i on o f Cut 1

I

i

0.8 1.0

Fig. 4. Effect of Cut 1 on the parameters b~ and b 2 for binary mixtures.

- 3

\X,t c°,, b2_4 -~~3

• c,,ts \\\'% [] Cut 1/Cut 3 blends " ~ , o co~ l~/Cut ~ ~i~n~s \ \ ' ~ Cut Z z~ Cut 1/Cut 5 blends v Cut 2/Cut 3 blends ~ . o Cut 2 / C u t , blends Cut 1 "%- ® Cut 2/Cut 5 blends

--Predicted; Equation (3) - - 5 I I

8 9 10 11 12

bl Fig. 5. Data and "phase space" representation for the parameters b~ and b2 of binary blends.

33

TABLE3

Prediction of viscosity-temperature data for blends of Cold Lake bitumen fractions using eqn. (3) -- Empirically determined parameters vs. generalized parameters

Sample Empirically determined parameters (Table 2)

AVR"

Parameters from eqns. (5) and (6)

bl b2 A VR

Whole Bitumen 0.62 9.2307 - 3.4581 1.10

Cut 1 - 11.6426 -4.6972 1.85 Cut 2 - 11.2194 -4.4476 0.52 Cut 3 - 10.3968 -3.9624 0.31 Cut 4 - 10.2014 -3.8473 0.20

Cut 5 - 8 .9783 -3.1258 18.53

Blend 1 (Cut 1/Cut 3) 1.54 10.4452 -4.0215 0.76 Blend 2 (Cut 1/Cut3) 1.22 10.5230 -4.0858 0.72 Blend 3 (Cut 1/Cut 4) 1.65 10.3471 -4.0075 0.83 Blend 4 (Cut 1/Cut 4) 1.42 10.8048 -4.2720 1.55 Blend 5 (Cut 1/Cut5) 0.42 8.8619 -3.3118 1.64 Blend 6 (Cut 1/Cut 5) 0.61 9.0293 -3.4239 1.20 Blend 7 (Cut 2/Cut 3) 0.98 10.5992 -4.1054 0.39 Blend 8 (Cut 2/Cut 3) 0.91 10.7839 -4.2124 0.44 Blend 9 (Cut 2/Cut 4) 0.94 10.4450 -4.0309 0.33 Blend 10 (Cut 2/Cut 4) 0.96 10.6683 -4.1592 0.59 Blend 11 (Cut 2/Cut 5) 0.22 8.8636 -3.1911 1.48 Blend 12 (Cut 2/Cut 5) 0.98 9.9381 -3.8447 0.86

N

aAVR= ( I /N) ~. (/~o,/~,p).

large. As mentioned previously, almost all of the twelve blends had contained relatively large mole fraction of the lighter fractions (i.e. Cuts i and 2). In Fig. 4, the parameter values were shown to undergo significant changes in the re- gion where the concentration of the lighter fraction is high. In other words, the predicted parameters in this region of high mole fraction of the lighter cuts would be quite sensitive to the composition. A small experimental error in preparing the reconstituted blends would correspond to a large change in the predicted parameters. The match between the viscosity data and predictions, Table 3, is generally better for the blends containing lower concentration of the lighter fractions. Most blend viscosity predictions, nevertheless, are within an order of magnitude of the viscosity data.

Generalization of viscosity characterization parameters

The bitumen fraction molar mass, given in Table 1, and the two parameters, listed in Table 2, are plotted in Fig. 6. Obviously, there is a strong evidence of

34

12

11

bl lo

9

8 -

10 2

. . . . . . . . i . . . . . . . .

Cut ~,/~ / >

Cut 5 ~ ' ~ u t 4

i i i i i i i l l i i i i i i i i

10 3 1 Molar Moss, g / m o l

-5

-4 b 2

- 5 ~4

Fig. 6. Relationship between molar mass and parameters b] and b2 for bitumen fractions.

a correlation between molar mass and the two parameters. A first order regres- sion gave the following generalized correlations.

bl =17.378-2.472 log (M) (5)

b2 = - 8 . 0 8 0 + 1.458 log (M) (6)

Equations 5 and 6 are plotted as the solid lines in Fig. 6. Although the sta- tistical correlation between the parameters and the fraction molar mass is quite good with r 2 > 0.99, the use of eqns. (5) and (6) for calculating the viscosity of bi tumen fractions did not produce very satisfactory results. The results in Ta- ble 3 show that the average viscosity ratio (AVR) for bi tumen fractions ranges between 0.20 (predictions within one order of magnitude) and a phenomenal 18.53 (over one order of magnitude deviation). Apparently, a variation in even the fourth significant figure of the parameter values can cause an appreciable change in the calculated viscosities. Hence, similar data on more bitumen frac- tions are needed to provide further confidence in the generalized correlations.

Blend viscosity predictions using generalized parameters The predicted values of the parameters for the twelve binary blends along

with the AVR values are also provided in Table 3. The average viscosity ratios are no worse than those obtained with the empirically determined parameters in Table 2. For Blends 3 and 4, the viscosity predictions using the generalized parameters are plotted as broken curves in Fig. 2.

35

105

o 104 O_

E

~ 03 o 1 0 ffJ

5~ c

E 02

O3

101

e. • Experimental data -- Equations (I) & (3) ~ '., " ..... Equations (5)/(6) & (3)

~.,,

"b'"b,."

I i I i i

0 50 100 150

Temperature, °C

Fig. 7. Comparison of the whole bitumen viscosity data with predictions.

Whole bitumen viscosity predictions using generalized parameters Calculations were undertaken for the viscosity of whole Cold Lake bitumen

for comparing the predictions with the data shown in Fig. 1. The calculation procedure involved evaluation of the parameters bl and b2 for each bitumen fraction, from eqns. ( 5 ) and (6), based on the molar mass data in Table 1. The bitumen viscosities were calculated from the viscosity mixing formula (eqn. 3 ) in conjunction with the mole fraction data (Table 1 ) and the two-parameter viscosity correlation (eqn. 1 ).

The average deviation between model and experimental values for the vis- cosity of whole Cold Lake bitumen was calculated as 17% (AVR= 1.10). This compares favourably with an average absolute deviation (AAD) of 38% (A VR = 0.62 ) that was obtained using the empirical parameters, listed in Table 2, for bitumen fractions. Figure 7 compares the whole bitumen viscosity data with the predictions using the empirical and generalized values of bl and b2.

CONCLUSIONS

The two-parameter viscosity correlation has been shown to be generally ap- plicable for the viscosity of Cold lake bitumen, its fractions and the reconsti- tuted binary blends of the bitumen fractions. The average deviation in the viscosity values for the bitumen fractions, which span several orders of mag- nitude from 1 mPa s to 10 6 mPa s, was typically less than 5%. The validity of a proposed viscosity mixing formula was demonstrated with the new viscosity-

36

temperature data for twelve reconstituted binary blends of the bitumen fractions.

Generalized correlations were proposed for the two parameters (bl and b2) in the viscosity-temperature correlation in terms of the fraction molar mass. The predicted blend viscosities were well within an order of magnitude of the viscosity data. The whole bitumen viscosity predictions using the generalized parameters and the viscosity mixing formula were within 17% of the data.

ACKNOWLEDGEMENTS

The authors thank Mr. Rod Rundle for his assistance in data collection. The bitumen fractions were supplied by Esso Resources Canada Ltd, Calgary. Fi- nancial support was provided by the Natural Sciences and Engineering Re- search Council of Canada (NSERC) and the Alberta Oil Sands Technology and Research Authority (AOSTRA).

NOTATION

AAD

AVR

bx,b2 M

n N r 2

T x

/1

( N ) average absolute deviation = ( l / N ) ~ I / ~ p - #¢o~1//~p

average viscosity ratio ( = (1/N) ~ ([~co~/[~exp) )

parameters in viscosity-temperature correlation molar mass, g mol- 1 mean molar mass of blend, g tool- number of bitumen fractions in blend number of viscosity data points correlation coefficient temperature, K mole fraction dynamic viscosity, mPa s liquid-mixture viscosity, mPa s

Subscripts

corr exp i

correlated/calculated value experimental value fraction (cut) of bitumen

37

REFERENCES

1 Jacobs, F.A., Donnelly, J.K., Stanislav, J. and Svrcek, W.Y., 1980. Viscosity of gas-saturated bitumen. J. Can. Pet. Technol., 19(4): 46.

2 Mehrotra, A.K. and Svrcek, W.Y., 1984. Measurement and correlation of viscosity, density and gas solubility for Marguerite Lake bitumen saturated with carbon dioxide. AOSTRA J. Res., 1: 51.

3 Mehrotra, A.K. and Svrcek, W.Y., 1985. Viscosity, density and gas solubility data for oil sand bitumens. Part I: Athabasca bitumen saturated with CO and C2Hs. AOSTRA J. Res., 1: 263.

4 Mehrotra, A.K. and Svrcek, W.Y., 1985. Viscosity, density and gas solubility data for oil sand bitumens. Part II: Peace River bitumen saturated with N2, CO, CH4, C02 and C2Hs. AOS- TRA J. Res., 1: 269.

5 Mehrotra, A.K. and Svrcek, W.Y., 1985. Viscosity, density and gas solubility data for oil sand bitumens. Part III: Wabasca bitumen saturated with N2, CO, CH4, C02 and C2Hs. AOSTRA J. Res., 2: 83.

6 Mehrotra, A.K. and Svrcek, W.Y., 1988. Properties of Cold Lake bitumen saturated with pure gases and gas mixtures. Can. J. Chem. Eng., 66: 656.

7 Mehrotra, A.K. and Svrcek, W.Y., 1986. Viscosity of compressed Athabasca bitumen. Can. J. Chem. Eng., 64: 844.

8 Mehrotra, A.K. and Svrcek, W.Y., 1987. Viscosity of compressed Cold Lake bitumen. Can. J. Chem. Eng., 65: 672.

9 Mehrotra, A.K. and Svrcek, W.Y., 1982. Correlations for properties of bitumen saturated with C02, CH4 and N2, and experiments with combustion gas mixture. J. Can. Pet. Technol., 21(6): 95.

10 Johnson, S.E., Svrcek, W.Y. and Mehrotra, A.K., 1987. Viscosity prediction of Athabasca bitumen using the extended principle of corresponding states. Ind. Eng. Chem. Res., 26: 2290.

11 Khan, M.A.B., Mehrotra, A.K. and Svrcek, W.Y., 1984. Viscosity models for gas-free Atha- basca bitumen. J. Can. Pet. Technol., 23 (3): 47.

12 Mehrotra, A.K. and Svrcek, W.Y., 1987. Corresponding states method for calculating bitu- men viscosity. J. Can. Pet. Technol., 26(5): 60.

13 Svrcek, W.Y. and Mehrotra, A.K., 1988. One parameter correlation for bitumen viscosity. Chem. Eng. Res. Des., 66: 323.

14 Mehrotra, A.K., Eastick, R.R. and Svrcek, W.Y., 1989. Viscosity of Cold Lake bitumen and its fractions. Can. J. Chem. Eng., 67" 1004.

15 Reid, R.C., Prausnitz, J.M. and Sherwood, T.K., 1977. The properties of gases and liquids, 3rd edn., McGraw-Hill, New York, NY, p. 457.