C7+ Characterization of Heavy Oil Based on Crude Assay Data

SPE 165416

Phase Behavior and Viscosity Modeling of Athabasca Bitumen and Light Solvent Mixtures M.Ghasemi, SPE, NTNU, and C.H. Whitson, SPE, NTNU/PERA

Copyright 2013, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Heavy Oil Conference Canada held in Calgary, Alberta, Canada, 11–13 June 2013. 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 have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper 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 SPE copyright.

Abstract

This paper describes a systematic approach to model the phase behavior and viscosity of Athabasca bitumen and light-solvent mixtures for a wide range of temperature. A cubic equation of state (EOS) is first developed using Athabasca crude assay data for the bitumen. We use a modified Jacoby correlation to describe the relationship of specific gravity and molecular weight of the bitumen sample. A gamma molar distribution model is used to fit the Athabasca crude assay data, then single-carbon-number (SCN) fractions are defined out to C90+. The Twu correlation is used for estimating SCN critical properties, including C90+, resulting in an EOS with 89 components (EOSSCN).

Pure solvent-crude oil mixture PVT data were tuned to the EOSSCN model by adjusting a fixed set of BIPs (binary interaction parameters) between pure solvent components (N2, CO, CO2, C1, C2) and all C7+ components.

For viscosity modeling, the LBC (Lorenz-Bray-Clark) correlation is used, with SCN critical volumes modified individually to guarantee that the LBC correlation estimates SCN viscosities estimated from a modified Twu correlation based on specific gravity and normal boiling point.

The EOSSCN model was lumped into five pseudo-fractions (EOS5), the heaviest being C90+. The resulting model reproduces accurately all phase and volumetric behavior of pure-solvent-crude mixtures.

Initial viscosity prediction of the Athabasca crude by the EOSSCN/LBC and EOS5/LBC models is satisfactory for dead-bitumen with viscosity only affected by temperature. However, for viscosities of pure-solvent-saturated bitumen at varying temperatures, the EOS5/LBC model did not perform well. Our solution was to split the heaviest fraction C90+ into two sub-fractions, where only critical volumes differ, resulting in “lower-viscous” and “higher-viscous” C90+ fractions (C90+L into C90+H). The fraction of C90+L (fL) was found to correlate with pure solvent solubility and temperature, resulting in a quite-accurate overall viscosity fit. This final model has, in reality, six components, even though the two heaviest fractions are identical for EOS calculations – we call this final model EOS6/LBC.

The final EOS6/LBC model was checked against measured PVT and viscosity data for mixtures of the same Athabasca bitumen using synthetic combustion gas solvents made up of C1, CO2, and N2. Introduction The heavy-oil and bitumen phase behavior and thermodynamic properties are very important for reservoir production, pipe-line and surface processing. This paper presents the systematic approach for developing the equation of state (EOS) and viscosity modeling of N2, CO, CO2, C1, C2 with Athabasca bitumen. The result of this work is so vital for increasing the numerical modeling accuracy of thermal processes applied into heavy oil reservoir for increasing oil recovery. For example a thermal process with steam/solvent injection is significantly affected by the vapor-liquid equilibrium (VLE) prosperities at the gas-oil front which is mainly controlled by thermodynamic behavior of the system (Nasr et al. 2006, Yazdani et al. 2011). Moreover, Ghasemi and Whitson (2011) show that the performance of thermal process (e.g. SAGD) is mainly affected by the insitue fluid properties. Providing accurate phase behavior and precise viscosity model which covers vast range of temperatures is one of the key components to develop accurate numerical models for such type of processes.

Limited phase behavior and viscosity measurement data of solvent and bitumen are available in the literature. Fraudenfeld et al. (2002) measured the solubility and viscosity of methane, propane and carbon dioxide in L1oydminster Abderfedly oil at 19 oC and low pressures. Freitag et al. (2005) measured the solubility and viscosity of the propane in contact with the Winter L1oydminster oil at 15 oC and 28 oC. Badamchi-Zadeh et al. (2009) measured the saturation pressure, solubility, density and viscosity for the mixture of the propane and Athabasca bitumen from 10 to 50 oC. All of these experiments are taken at low

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https://www.researchgate.net/publication/266669310_A_New_Semi-Automatic_PVT_Apparatus_for_Characterizing_Vapex_Systems?el=1_x_8&enrichId=rgreq-7ce07e4bb0f422d0f6844fd51dc9c774-XXX&enrichSource=Y292ZXJQYWdlOzI0MTc5MDA4NjtBUzoxNTQwMTIwMTE3MzI5OTJAMTQxMzczMDczMzE3MQ==

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temperatures which are hardly used to develop an EOS/viscosity models for being valid for thermal operating condition. To our knowledge, there are very little published data which provide the complete datasets on the phase behavior and physical properties of solvent and bitumen mixture for high temperature ranges. Among them is the data reported by Svrcek and Mehrotra (1982), and Mehrotra and Svrcek (1985). They measured the gas solubility, density and viscosity of N2, CO, CO2, C1, C2 in Athabasca bitumen. The range of temperature used in their study was 25 to 118 oC and the pressure was varied up to 10 MPa. This foremost data available in the literature is used in our study. For our terminology; N2, CO, CO2, C1, C2 are classified as light-solvent based on the study by Shu and Hartman (1988). They performed as series of numerical simulation study to investigate the effect of solvent type and concentration on the oil recovery from heavy-oil reservoir. They grouped the solvents into light, medium and heavy solvents with respect to their volatility. Light solvents generally include the hydrocarbon and non- hydrocarbon gases i.e. CO2, C2, C3, and other gases. Hydrocarbon liquid in the range of about C15 to C20 is considered as heavy solvent. Medium solvent includes the hydrocarbon liquid in the range of C5 to about C14. The objectives of this study are to:

1. Developing a methodology to model the phase behavior of light-solvent in heavy oils and bitumen at desired

ranged of pressure and temperature. 2. Developing the viscosity model bases on available data for different mixture of heavy-oils/ bitumen and light-

solvent at wide temperature range. 3. Using developed phase behavior and viscosity model to predict the phase-behavior and viscosity for different

mixture of light-solvents with heavy-oil at different temperature and compare with published data (Mehrotra and Svrcek 1985).

4. Predict the viscosity and phase behavior of heavy and medium solvents using developed EOS/viscosity model. 5. Calculate thermal properties from developed EOS model.

Bitumen Samples Property The bitumen oil samples used in the Mehrotra and Svrcek (1982), Mehrotra and Svrcek (1985) study were obtained from an Athabasca oil batch sands by toluene extraction and then followed by volume distillation. Vorndran et al. (1980) describes the toluene procedure used to extract bitumen. Samples used in their study are categorize in three parts; maltene distillables, maltene un-distiallables and asphaltene. A common procedure on the fractioning scheme for bitumen was dissolving bitumen in n-pentane (Mehrotra and Svrcek 1988). The soluble portion in n-pentane is called meltenes and the insoluble part is asphaltene. The maltenes fraction is further divided into two cuts; distillable and un-distillable fractions.

Distillable fraction has lower boiling point lower than 600 oC and un-distillable fraction above 600 oC. Table 1 summarizes the analysis of maltene distillables, maltene undistillables and also asphaltene contents used for their study. All three samples have almost similar maltene and ashphaltene compositions.

Table 1—Athabasca Bitumen Analysis

Asphaltenes (%)

CO2 Expts. 19.2C1 & N2 Expts. 20.7

CO & C2 Expts. 21.4

Maltenes Distillables Maltenes Undistillables

39.6 41.242.4

36.5

36.9

42

Tb<600 oC Tb>600 oC

Bitumen Characterization Prediction the thermodynamic properties of bitumen using an equation of state is challenging since it needs the identifications of component presents in bitumen. Generally bitumen consists of thousands of individual components with un-known molecular structure which makes impossible to provide physical property data on these components. Therefore a bitumen characterization approach is required to:

1. Splitting the bitumen into single carbon number (SCN) or distillation cuts, with known (molar and mass) amounts and molecular weights.

2. Assign physical properties i.e. boiling point, molecular weight and specific gravity to each fraction. 3. Estimating critical properties of each fraction.

Gamma Model Distribution. Ghasemi et al. (2011) presents a systematic procedure for C7+ characterization of heavy oil based on crude assay data. This new approach is applied for characterizing Athabasca and Cold lake bitumen. Bitumen crude assay data (Alberta department of Energy, 1996) with ºAPI 9 for Athabasca are used to develop the physical properties of each distillation cuts. Table 2 gives the crude assay data for these samples. Six pseudo fractions with fixed normal boiling point range are defined for Athabasca. Lower boiling points with average specific gravities and mass fractions are reported in Table 2. The lower boiling point of the last cut for Athabasca bitumen is 524 oC and it almost covers 54 weight percent of the total crude sample. However the last fraction amount is significant, it may not be extend into more distillation fractions. The

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https://www.researchgate.net/publication/245548279_Effect_of_Solvent_on_Steam_Recovery_of_Heavy_Oil?el=1_x_8&enrichId=rgreq-7ce07e4bb0f422d0f6844fd51dc9c774-XXX&enrichSource=Y292ZXJQYWdlOzI0MTc5MDA4NjtBUzoxNTQwMTIwMTE3MzI5OTJAMTQxMzczMDczMzE3MQ==

SPE 165416 3

reason is that for ultra-heavy oil and bitumen, measuring the physical properties of the distillation cut for higher boiling points (e.g. more than 800 oC) may not be achieved due to thermal cracking and reaction that can occur below their boiling points. It is also important to notice that even if the physical properties of those fractions are measurable, the available correlations used for calculating the critical properties have significant errors since their boiling point is out of the correlation constraints.

Table 2—CRUDE ASSAY DATA FOR ATHABASCA BITUMEN (Ghasemi et al. 2011)

Fraction boiling point, ºC C5-160 160-204 204-343 343-371 371-524 524+ TOTAL

Yield of cut (w t% of crude) 0.4 1.16 10.38 4.61 29.29 54.2 100

Gravity,ºAPI 44.7 38.2 25.2 20.5 12.8 1.5 8.8

Specif ic gravity 0.8031 0.8338 0.903 0.9309 0.9806 1.06 1.0086

Athabasca Bitumen

In the proposed method, the Soreide (1989) correlation is used to define the specific gravity and molecular weight of the individual fractions. Twu (1984) and Soreide (1989) correlations are used to calculate the lower molecular weight for a given fraction lower-boiling point. The Gamma distribution model (Whitson 1983) is used to describe the molar distribution of the bitumen fractions. Gamma shape (α), bound (η) and average together with Soreide and Twu parameters are changed until the best fit for a measured amounts and specific gravity is obtained (i.e. minimizing RMS). Results give α = 2.05, η = 98 for Athabasca. Twu correlation factor, fTwu=1 for assay sample.

Gamma shape (α) and bound (η) found from Athabasca crude assay can be used to develop the Athabasca bitumen samples reported by Svrcek and Mehrotra (1982), Mehrotra and Svrcek (1985). Fig. 1 compares the cumulative weight vs. upper boiling point of the distillation fractions for the Athabasca crude assay from Table 2 and the bitumen sample reported by Mehrotra and Svrcek (1982). As shown in Fig. 1, the cumulative weight percent of the crude assay cuts (solid circle) is closed to the trend of the bitumen fraction reported by Mehrotra and Svrcek (1982) (open triangle in Fig. 1).

0

10

20

30

40

50

60

70

100 200 300 400 500 600 700

Cum

ulat

ive

Wei

ght,

%

Upper Boiling Point, oC

Mehrotra and Svrcek (1982)

Athabasca bitumen assay

Model: Athabasca bitumen assay

Model:Mehrotra and Svrcek (1982)

Fig. 1—Cumulative weight percent vs. upper boiling point.

Solid line in Fig. 1 represents the tuned gamma model (i.e. α = 2.05, η = 98) from Athabasca crude assay analysis. As

shown in Fig. 1, quality of match between the proposed gamma model and the bitumen are well fitted. The model follows similar trend and also gives closed match with the cumulative weight percent of the reported bitumen for upper boiling points up to 550 C. However, the model over predicts the amount of the distillation fractions more than 550 C. Dashed-line Fig. 1 represents different gamma model with α = 1.74, η = 98 which is used to fit the amount of reported bitumen sample. The amount of heavier fraction calculated by gamma model is slightly improved compared to gamma model used for tune crude assay data (i.e. α = 2.05, η = 98) but has less accuracy for the lower boiling point (less than 540 C). Gamma model based on crude assay data (i.e. α = 2.05, η = 98) is used for characterizing the bitumen sample which reported by Mehrotra and Svrcek (1982). The reason is that the model gives better performance for boiling point up to 550 C and overall fit is satisfactory (gamma RMS is 1.6%). Molecular Weight and Specific Gravity Relationship. Mehrotra and Svrcek (1985) report average molecular weight of 594.6 for the sample bitumen used for C2 and CO experiment. However specific gravity was not measured for this sample. Moreover, the average molecular weight and specific gravity of two other bitumen samples used for C1/N2 and also for CO2

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4 SPE 165416

experiments was not reported in their study (Svrcek and Mehrotra 1982). Peramanu et al. (1999) measured the average molecular weight of 557 and specific gravity of 1.014 (water =1) for Athabasca bitumen. Table 3 compares the C, H, N, O and S contents from their bitumen analysis with the one reported by Mehrotra and Svrcek (1985). Because both samples have similar properties, we use molecular weight of 557 and specific gravity of 1.014 for Athabasca bitumen sample. It is also important to notice that we use only one sample in our study as a representative sample for all three bitumen samples given in Table 1 due to similar bitumen properties (similarities also mentioned by Mehrotra and Svrcek 1985).

Table 3—Bitumen Samples Properties

Bitumen properties Peramanu et al.oAPI 8.05

Molecular weight 557Specific Gravity 1.014

Carbon(wt-%) 83.5

Hydrogen (wt-%) 10.21Sulfur (wt-%) 4.52

Oxygen (wt-%) 1.33

Nitrogen (wt-%) 0.44

-

83.34

10.264.64

1.08

0.53

Athabasca bitumen samples

-

594.6

Mehrotra & Svrcek (1985)

Fig. 2 shows the specific gravity versus molecular weight for the bitumen sample and also for the fractions from Athabasca crude assay data. A correlation (e.g. Soreide) that describes the relationship between specific gravity and molecular weight is needed. This correlation should honors both the specific gravity of crude assay data and also bitumen sample. However, the last cut of the crude assay data is neglected due to significant error that may exist for the last fraction. Instead average specific gravity of the sample is considered to be fitted with the correlation. As shown in Fig. 2, Jacoby equation has better performance than Soreide in matching the specific gravity of the sample and all five fraction of the crude assay. The resulted specific gravity using Jacoby is more flat as molecular weight increase whereas Soreide gives higher specific gravity for a given molecular weight. The Jacoby correlation is given as:

⎟⎟⎠

⎞⎜⎜⎝

⎛ ⋅−⋅+

⋅−=

ia

ii M

JM

771245608158468.0γ ............................................................................................................................. (1)

Jacoby can be expressed in Soreide form where Soreide correlation is given as: ( )D

ii CMBA −+=γ ............................................................................................................................................................... (2)

Using Eqs. 1and 2, we drive A, B, C and D for expressing Jacoby correlation in the form of Eq. 2:

2456.08468.0 ×+= aJA ....................................................................................................................................................... (4)

aJB 77.18.15 −−= ................................................................................................................................................................. (5) 0=C ....................................................................................................................................................................................... (6)

1−=D ..................................................................................................................................................................................... (7)

0.6

0.7

0.8

0.9

1

1.1

1.2

0 200 400 600 800

Spec

ific

Gra

vity

Molecular Weight

Crude Data Bitumen sample

Modified Jacoby Soreide

Last cut ‐ not included in regression

Fig. 2—Specific gravity vs. molecular weight.

SPE 165416 5

As shown in Fig. 2, modified Jacoby (solid line) as expressed in the form of Eq. 2 gives best match to crude assay data and bitumen samples. In modified Jacoby, A and B are defined as regression variable to fit crude assay data and crude sample. Initial values for A and B are calculated at Ja =0 results in 0.8468 for A and -15.8 for B (Eq. 4 and 5). The value of C and D are fixed to 0 and 1 during regression. The calculated RMS for modified Jacoby is 0.574% with final values of 1.0715 and -31.811 for A and B respectively. Fig. 2 also shows the Soreide correlation based on the final tuned parameters which is not able to give overall fit to crude assay data and bitumen sample. In Soreide correlation, B and D are used as regression variable whereas A and C are fixed to 0.286 and 66 during regression. The calculated RMS for Soreide correlation is 1.393% which is higher than 0.574% for modified Jacoby. Estimating Critical Properties of SCN. Based on the analysis of Athabasca crude assay data, the final value for Twu correlation factor, fTwu, is equal to one. fTwu=1 honors Twu correlation exactly which defines the chemical “makeup” of SCN fraction as less paraffinic and more napthenes and aromatics. Twu correlation uses fraction specific gravity to determine the relationship between molecular weight and boiling point. Table 4 summarizes the type of correlations with their final values used to calculate critical properties of SCN fractions.

Table 4—Summary of correlations used for bitumen characterization Correlation Used Parameters with final values

Gamma model α = 2.05, η = 98, average=557

Modified Jacoby A=1.0715, B=-15.8, C=0, D=-1

Twu correlation fTw u=1 (changes between 0 and 1) Experimental Procedure This section describes the experimental procedure that was performed to measure the solubility, density and viscosity of Athabasca bitumen saturated with the light solvents. This experimental procedure is based on the work done by Jacobs (1978) and later modified by Svrcek and Mehrotra (1982) and Mehrotra and Svrcek (1985). A schematic of the experimental setup is shown in Fig. 3. The apparatus consist of mixing cell, gear pump and viscometer. Prior to each experimental run, all of the apparatus parts was cleaned with toluene and dried with nitrogen. Bitumen sample was first charged into the mixing cell. The bitumen viscosity-temperature relationship is determined before to the solubility runs. The viscosity of the bitumen is linked to the bitumen bulk compositions at certain temperature.

Fig. 3—Schematic of apparatus for saturating bitumen with light-solvents. Redrawn after Mehrotra and Svrcek (1982).

The light solvents (N2, CO, CO2, C1, C2) are injected from top of the mixing cell at certain temperature and pressure. Gear

pump which located at the bottom of mixing cell draws bitumen from bottom of the mixing cells. The discharged bitumen from pump is divided into a recycle line and a circulating line. The bitumen in the recycle line passes sample cell and enter mixing cell from the top where mixing is enhanced due to large contact areas between dissolved gas and circulating bitumen. The circulation line takes bitumen to the viscometer for measuring viscosity before returning back to the mixing cell. In their experiment, the criteria for indicating equilibrium between injected light solvent and bitumen is determined by tracking the measured viscosity at the viscometer. Generally the viscosity of the bitumen represents the bitumen composition. When the light solvent is dissolved into bitumen, the live bitumen viscosity at constant pressure and temperature is reduced due to increasing the composition of the solvent into bitumen. Reduction in mixture viscosity continues until it reaches a certain constant viscosity. Therefore, the constant viscosity of the live bitumen indicates no additional dissolution of the light solvent into bitumen and hence reaching the equilibrium state. For each run, the constant viscosity condition lasted for at least 4

6 SPE 165416

hours to make sure that the equilibrium condition is fully established. Then, the sample cell is isolated and removed from the apparatus for measuring solvent solubility and saturated bitumen density. The sample cells were depressurized down to atmospheric pressure or slightly lower (0.5-2 atm). The volume of the released light-solvent is measured at 100 oC and the pressure range of 0.5-2 atm. The experimental run was repeated for different pressure and temperature. Gas solubility data is given as cm3 of gas at standard condition (SC) per cm3 of saturated bitumen. The experimental data (solubility, density and liquid viscosity) of the light solvents and bitumen mixtures at various pressures and temperature are reported by Svrcek and Mehrotra (1982) and Mehrotra and Svrcek (1985). Uncertainties and Error Sources Gas (light-solvent) solubility measurement performed at 100 oC. The reason for selecting high temperature(i.e. 100 oC) for calculating the volume of the dissolved gas is due to the fact that high temperature will accelerate the release of dissolved gas. However, depressurizing process at relatively high temperature (i.e. 100 oC) facilitates the vaporization of light ends from bitumen. It may affect the reported dissolved gas volume for gas-solubility measurement due to accompany of released gas with light bitumen-fractions. Moreover, each depressurizing experiment was performed in the pressure range of 0.5-2 atm instead of 1 atm which can be accounted as one of the source of error in measuring gas-volume.

Another uncertainty is the measurement of saturated bitumen mass, density and volume. The gamma-ray densitometer had failed to measure the density. For obtaining the density, the mass of the cell filled with saturated bitumen was weighed to ± 0.001g, and the mass of bitumen was determined by the difference. Hence, knowing the mass and volume of the bitumen sample determine its density. They noticed that the density measurements using this technique were found to be reliable by ± 0.003 g/cm3. It will result in ± 0.33 cm3 accuracy in the reported volume of the saturated bitumen. The volume of saturated sample was reported approximately by 6 cm3 (i.e. correct volume is between 6± 0.33 cm3). The uncertainty on the correct volume of saturated sample is significant and results more than ± 5 % error in the accuracy of the reported gas-solubility. Considering all source of errors, the EOS model accuracy of ± 10 % for calculating the gas solubility is reasonable. EOS Model Description The Peng-Robinson (1979) EOS with volume shift is used in this study. Using techniques for bitumen characterization described earlier in this chapter, EOS parameters were developed and extended up to C90+ fraction. The main reason for having SCN fractions up to C90+ is due to the fact that vaporization of light- to heavy- fractions may occur as temperature increases. Providing an EOS model with SCN fractions up to C90+ will always guarantee to account for vaporization effect of SCN fractions at higher temperature.

We name this EOS model as EOSSCN which contains SCN fraction up to C90+. The PVT software PhazeComp developed by Zick Technologies is used in this study. Appendix A provides the EOS parameters for all SCN fractions up to C90+. In the model, the first component presents in the bitumen sample is C7 for having gamma bound of 98. The composition of SCN fractions is obtained by splitting 100 mole-% of C7+ into SCN fractions from C7 up to C90+ using gamma parameters descried in Table 4. Matching Experimental Data In our work, measured properties of saturated bitumen with light solvents are matched. Svrcek and Mehrotra and (1982) and Mehrotra and Svrcek (1985) reported the solubility of the light-solvents in both volumetric (i.e. cm3 of solvent at SC per cm3 of saturated bitumen) and amounts (i.e. weight percent). The solubility of light-solvent in bitumen increases more or less linearly with increasing in pressure. However increasing the temperature will decrease the amount of light-solvent in soluble in the bitumen. We model the experimental work at different temperature. For each run at given temperature, the reported weight percent of solvent is input to the model. Then, the feed tank is filled with the mixture of dead-bitumen and measured amount of solvents. Having the composition of the mixture at a given temperature, the bubble-point pressure is calculated and compared with measured bubble point pressure. The model also calculates the saturated bitumen properties i.e. density and solubility at bubble-point pressure for comparing with measured data.

In this study, sum-of-squares (SSQ) function is used to define an objective target for minimizing the error of EOS model to the experimental data. The SSQ is expressed as:

2

1)(∑

=

=N

iiirwSSQ ...................................................................................................................................................................... (8)

where ri = residual = (dci-dmi)/drefi defined by EOS model-calculated data(dci), measured data dmi, and a reference data value, dref, which is usually defined as dref= max{dmi}. wi is weight factor defined for a given experiment data point.

It is important to mention that Svrcek and Mehrotra (1988) reported significant errors for their particular experimental data

points. The first run for N2 data at 32.8 C and 8.79 MPa was questioned by authors. For the saturated bitumen with C1, the run numbers 9, 16, 23 and 30 are flagged for being conducted at low pressure. For the C2 data, the run number 4 is omitted due to presenting two liquid regions in the mixture of bitumen and C2. All of these data points are not included in the regression. This can be done by wi=0 where i is referred to all six data points.

SPE 165416 7

First attempt to match reported saturation pressure is done with EOS model (EOSSCN) using zero binary interaction parameters (BIPs) between light-solvents and all C7+ fractions. Fig. 4a shows the deviation of bubble-point pressure (i.e. ri where d is bubblepoint pressure) versus the measured bubble-point pressure. As shown by Fig. 4a, EOS over-predicts the CO-saturated bitumen by the average of 40-% and under-predicts CO2-saturated bitumen by ~ 35%. The bubble-point pressure deviation for other light-solvents saturated bitumen is under-predicted by 10%. We also show the plot of deviation of saturation-pressure versus temperature to find out whether BIPs can be correlated with temperature. We found that the bubble-point pressure deviation is partly correlated versus temperature for C2-saturated bitumen but not for N2-, CO-, CO2- and C1- saturated bitumen (Fig. 4b).

-60

-40

-20

0

20

40

60

0 2000 4000 6000 8000 10000 12000

Dev

iatio

n in

Bub

blep

oint

Pre

ssur

e, %

Bubblepoint Pressure, kPa

C1 CO2C2 CON2

BIPs = 0

(a)

-50

-40

-30

-20

-10

0

10

20

0 50 100 150D

evia

tion

in P

b %

Temperature, oC

C2

C2‐SolventBIPs=0

(b) Fig. 4––EOSSNC prediction with BIPs = 0 for Pb deviation: (a) versus Pb for light-solvents and bitumen mixtures, and (b) versus temperature for C2 and bitumen mixtures.

It is indeed clear from Fig. 4a that using single variable for BIPs of light-solvent/ C7+ would not help to match the bubble-

point pressure data for that particular light-solvent saturated bitumen. For example, by changing the BIPs of CO2/C7+ will shift all solid triangles in Fig. 5 up to error bond between ~ -10% and +20% from which originally was between ~-50% and -20%. Best match is obtained by defining both BIPs and amount of light-solvent as regression variable. For example for having 29 data points of the bubblepoint pressure for CO2 saturated bitumen, amount of CO2 reported for each data point (total of 29) is changed together with the BIPs of CO2/C7+ in order to fit the reported bubble point pressure. We define ± 10% allowable change for weight-percent of light solvents amount in bitumen. The criteria for defining this constraint in the amounts of light-solvent is due to the expected error for the solubility data, and also similar translation between amount and volumetric solubility of light solvent in bitumen as shown by Fig. 5. As shown in Fig. 5, 6 cm3 (reported cell volume) of CO2-saturated bitumen with 2.77 weight-percent of CO2 amount is depleted from bubble-point pressure of 50 bara at 100 oC. Two other amounts of CO2 (i.e. 2.59 and 3.05 weight percent) are resulted from ± 10% changed in initial CO2 amount i.e. 2.77. The volume of gas released starts from zero at 50 bara and increases as pressure decreases down to atmospheric pressure. The error bar shown for gas volume is ± 10%. As it is clearly indicated by Fig. 5, ± 10% change in the amount of CO2 dissolved in the bitumen results in ± 10% change in volume of gas released at 100 oC and atmospheric pressure.

5.75

5.80

5.85

5.90

5.95

6.00

6.05

0

20

40

60

80

100

120

0 20 40 60

Oil

Volu

me,

cm

3

Rel

ease

d G

as V

olum

e, c

m3

Pressure, bara

CO2-wt% = 2.49CO2-wt% = 2.77CO2-wt% =3.05

CO2 + Bitumen

Fig. 5—Effect of different CO2 compositions in bitumen in the total volume of gas released and oil volume at atmospheric pressure.

8 SPE 165416

The final BIPs parameter between light- solvents and SCN up to C90+ is given in Table 5. The BIPs between SCN fractions is zero. Fig. 6 shows the final percent change in the amount of light-solvent dissolved in the bitumen which results in good fit for bubblepoint pressure. As shown in Fig. 6, the percent change in the final amounts of light-solvent is satisfactory (i.e. between ± 10%) except for CO-saturated bitumen which hits the boundary. The amount of CO in the bitumen needs to be changed more than 10% in order to fit the bubble-point pressure of CO-saturated bitumen. Since the solubility of CO in bitumen is very low from the minimum of 0.45 wt-% at 2.90 MPa and 78 oC to the maximum of 1.18 wt-% at 9.65 MPa and 26 oC, the error in the measured CO amount in the saturated bitumen can be significant (e.g. changing CO amount from 1.05 wt-% to 1.36 wt-% cause ~30% error).

Table 5—Final BIPs between light-solvents and all SCN up to C90+ CO CO2 N2 C1 C2 Cj(j=1 to 90+ , j≠i)

Ci (i=1 to 90+) ‐2.02E‐01 8.82E‐02 9.93E‐02 6.43E‐03 1.50E‐02 0

-20

-15

-10

-5

0

5

10

15

20

0 2000 4000 6000 8000 10000

Com

posi

tion

Chan

ge,

%

Bubblepoint Pressure, kpa

N2 CO2 CO C1 C2

Fig. 6—Change in light-solvent composition versus bubble-point pressure.

There are also some errors in the measured data of CO-saturated bitumen (Mehrotra and Svrcek 1985). For example,

reported CO amount at 2.80 MPa and 111 C (i.e. run number 14) should be lower than the CO amount at 2.90 MPa and 78.1 C (i.e. run 9) since both pressure and temperature of run 14 indicate lower solubility compared with run 9. It is also similar with runs 1 and 5, runs 2 and 6, and also with runs 7 and 18. We consider 30% change in the amount of CO in saturated bitumen. The reason is that the final amount of CO after regression (within ± 30% change) will not result in bias as shown in Fig. 7a. Moreover, calculated densities from final wt-% of CO (after regression) and reported wt-% are well fitted (Fig. 7b).

-0.4

-0.2

0.0

0.2

0.4

0.2 0.7 1.2 1.7

∆z/

z

Reported CO Amount (Z), wt-%

(a)

-0.01

0.01

0.03

0.05

0.97

0.98

0.99

1.00

1.01

0.97 0.98 0.99 1 1.01

∆ρ,

g/c

m3

Dens

ity U

sing

Fin

al C

O w

t-%,

g/cm

3

Density Using Reported CO wt-%, g/cm3

-

+0.001

‐0.0003

(b)

Fig. 7—(a) Change in final CO composition and (b) calculated saturated density using final and reported CO wt-%.

SPE 165416 9

Figs. 8a through 8i show the quality of fit for bubble-point pressure, saturated density of N2-, CO-, CO2-, C1-, and C2- saturated bitumen at four different temperatures. Calculated bubble point pressure by EOSSCN using modified BIPs in Table 5 is in good agreement to the reported bubble point pressure of light-solvents saturated bitumen. As it is also clearly shown by Figs. 8f through 8i, the density prediction by EOSSCN is mostly within 2% compared to reported saturated density of light solvent and bitumen mixtures at different pressure and temperature. Therefore, the modification in volume shift of C7+ is not required.

(a)

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Cal

cula

ted

Pb, k

Pa

Measured Pb, kPa

T=33 CT=52 CT=75 CT=100 C ‐5 %

+5 %

N2

(b)

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0 2000 4000 6000 8000 10000C

alcu

late

d Pb

, kPa

Measured Pb, kPa

T=27 C

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T=78 C

T=115 C ‐5 %

+5 %

CO

(c)

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cula

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Measured Pb, kPa

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‐5 %+5 %

CO2

(d)

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Pa

Measured Pb, kPa

T=27CT=45 CT=67 CT=100 C ‐5 %

+5 %

C1

(e)

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cula

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Pa

Measured Pb, kPa

T=23 CT=48 CT=80 CT=105 C

‐5 %

+5 %

C2

(f)

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-2

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0 2000 4000 6000 8000 10000

∆ρ/ρ

, %

Measured Pb, kPa

T=33 C T=52 CT=75 C T=100 CT=27 C T=50 CT=78 C T=115 C

N2CO

(g)

-4

-2

0

2

4

0 2000 4000 6000 8000

∆ρ/ρ

, %

Measured Pb, kPa

T=24 C T=42 C

T=63 C T=98 C

CO2

(h)

-4

-2

0

2

4

0 2000 4000 6000 8000 10000

∆ρ/ρ

, %

Measured Pb, kPa

T=27 C T=45 CT=67 C T=100 C

C1

(i)

-4

-2

0

2

4

0 2000 4000 6000 8000 10000

∆ρ/ρ

, %

Measured Pb, kPa

T=23 C T=48 CT=80 C T=105 C

C2

Fig. 8—Quality of fit for light solvents-saturated bitumen-Bubblepoint pressure (Pb): (a) N2 , (b) CO, (c) CO2 , (d) C1, (e) C2 and for saturated liquid density(ρb): (f) N2 (black) and CO (brown) , (g) CO2, (h) C1 and (i) C2. Figs. 9a through 9e show the quality of fit for solubility of light-solvents saturated bitumen. The quality of match for solubility at different temperature is satisfactory with more or less 10% error. Calculated solubility at lower temperature by EOSSCN is over predicted by more than 10% error. It can be explained by the fact that difficulties in the measuring of light solvent-saturated bitumen properties arises at low temperature due to low mobility (i.e. high viscosity) of bitumen (Mehrotra and Svrcek 1982).

Generally, quality of match for solubility at higher temperature is enhanced and with the error less than 10%. This is also mentioned by Svrcek and Mehrotra (1982) that carrying out measurement for bitumen at temperature greater than 70 oC is relatively easy (due to mobility improvement) compared to lower temperature which may have larger error in measurement. Figs. 9a through 9e also indicate that the solubility of C2 in bitumen is quite high and higher than that of CO2. Followed by CO2, C1 has higher solubility than CO and finally solubility of N2 is minimum (~ 2 times less than CO solubility).

10 SPE 165416

0

1

2

3

4

5

6

0 1 2 3 4 5 6

Solu

bilit

y of

N2

-C

alcu

late

d, c

m3 /c

m3

Solubility of N2 -Measured,cm3/cm3

T=33 CT=52 CT=75 CT=105 C

‐10 %

+10 %

(a)

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bilit

y of

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T=27 CT=50 CT=75 CT=105 C

‐10 %

+10 %

(b)

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bilit

y of

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cula

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Solubility of CO2 -Measured,cm3/cm3

T=24 C

T=42 C

T=63 C

T=98 C‐10 %

+10 %

(c)

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bilit

y of C

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ulat

ed,c

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Solubility of C1 -Measured,cm3/cm3

T=27 CT=45 CT=67 CT=100 C

‐10 %

+10 %

(d)

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20

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0 20 40 60 80 100 120So

lubi

lity

of C

2-

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cula

ted,

cm3 /c

m3

Solubility of C2 -Measured,cm3/cm3

T=23 CT=48 CT=80 CT=105 C ‐10 %

+10 %

(e)

Fig. 9—Quality of fit for solubility of light-solvents in bitumen: (a) CO2, (b) C1, (c) C2, (d) N2, (e) CO. Dashed lines shows ± 10% deviation.

Generally, solubility of light solvent is decreased when temperature increase. For example for all thermal processes applied for increasing oil recovery from bitumen deposition, the temperature at operating condition is much higher from the maximum reported temperature at these experiments(i.e. 118 oC). It is expected to have even less solubility of light solvents into bitumen at high range of temperature. Fig. 10 shows the solubility of light-solvents in bitumen at ~ 100 oC. The maximum calculated solubility is for C2 which is ~ 40 cm3/cm3 at 105 oC.

0

5

10

15

20

25

30

35

40

0 2000 4000 6000 8000 10000 12000

Sol

vent

Sol

ubili

ty, c

m3/

cm3


Data-C2 (T=105 C)Calculated-C2 (T=105 C)Data-C1 (T=100 C)Calculated-C1 (T=100 C)Data-CO2 (T=98 C)Calculated-CO2 (T=98 C)Data-CO (T=115 C)Calculated-CO (T=115 C)Data-N2 (T=100 C)Calculated-N2 (T=100 C)

Fig. 10—Solvent Solubility at ~ 100 oC. Dashed line with open symbol represents calculated solubility. Solid symbol shows solubility data.

EOS Model Prediction It is shown that EOSSCN is capable to match phase behavior and volumetric properties of pure-solvents and bitumen mixtures for a wide range of temperature. In this section, tuned EOSSCN is checked against measured PVT data for mixtures of the synthetic combustion gas (SCG) solvents and Athabasca bitumen. SCG is made up of N2, CO2, and C1. First experimental setup is explained and analyzed. Second, the results of SCG experiment are compared with EOSSCN prediction.

SPE 165416 11

SCG Experimental Setup. Experimental work for the phase behavior and volumetric properties SCG-solvents and bitumen was performed by Mehrotra and Svrcek (1982). A schematic of the experimental setup is shown in Fig. 11. The apparatus consist of sample cell, mixing cell, gas bottle, viscometer and gear pump. The SCG-solvents with desired composition comes into contact with the bitumen sample in the mixing cell.

The gas in contact with bitumen is continuously replaced with the fresh gas from the gas bottle and circulated through the circulation line. It is essential for having the circulation of the gas within the system since all three light-solvents N2, CO2 and C1 have significantly different solubility in bitumen. Otherwise, the equilibrium gas composition will be significantly different from the desired ratio of three gases. The gas circulation through the system was achieved by heating the gas in one side of the circulation loop and allowing the gas to cool in the other side. This technique would cause circulation of the gas by difference in the density.

Fig. 11––Schematic of apparatus for SCG experiment. Redrawn after Mehrotra and Svrcek (1982).

The target SCG composition was set for 82% N2, 17% CO2 and 1% C1 for all experimental runs. However it was difficult

to keep this target composition, instead equilibrium gas composition was attempted to maintain at the target SCG composition. Gas samples were analyzed by gas chromatograph. Recirculation gas samples were determined from a number of samplings at different locations of the loop to ensure nearly uniform gas composition. For each solubility run at certain pressure and temperature, SCG solvents-saturated bitumen properties (solubility and density) and also both dissolved and equilibrium gas are measured. The approach for solubility measurement is discussed earlier. Measured saturation pressure, saturated density and solubility of SCG-solvent saturated bitumen reported by Mehrotra and Svrcek (1982) is given in Appendix B. SCG Experimental Analysis and EOSSCN Prediction. We model SCG-experimental design by defining the reported equilibrium gas mixture as desired SCG-solvent feed composition. The target SCG feed is injected into stagnant bitumen at a given pressure and temperature. The injection gas is continuously injected until it reaches equilibrium with bitumen. At this state, the equilibrium gas will be similar with the SCG-solvent target composition. Then, the equilibrium oil (i.e. saturated bitumen) is collected at the equilibrium condition and its saturated properties such as dissolved gas composition, solubility and density are calculated.

The tuned EOSSCN with final BIPs is used for the prediction of the experimental result of SCG-solvent mixture. However in this experiment, the volume of the gas bottle, V4 (see Fig. 11) and the mixing cell,V2, were not given. It is also not clear whether the mixing cell was fully or partially filled with the bitumen sample. The equilibrium may not be achieved if the ratio of V4/V2 is small. The minimum ratio V4/V2 required for equilibrium state between SCG-solvent mixture and bitumen can be obtained by (Mg/Mo) × (ρo/ρg) × (ng/no) where we assumed that mixing cell is fully saturated with bitumen. Mg and ρg are the molecular weight and density of the SCG gas solvent in the gas bottle. Bitumen molecular weight and density at certain condition is given by Mo and ρo respectively. The ratio of ng/no is the critical mole ratio at specific pressure and temperature where equilibrium is achieved.

For example, we arbitrary choose run 15 (see Appendix B). For this case, Fig. 12 shows the profile of CO2 in the equilibrium gas versus the molar ratio of injected SCG-solvent to bitumen. The equilibrium is achieved after ng/no = 2.5 which results in V4/V2= 2.8. For the case where mixing cell, V2, is partially saturated with bitumen, this ratio will be slightly less than this critical value (i.e. 2.8-3.8×Vg΄/V2, Vg΄ is the volume of gas in the mixing cell).

12 SPE 165416

0

4

8

12

16

20

0.001 0.01 0.1 1 10y-

% E

quili

briu

m C

O2

Mole Injected, ng/no

ng/no = 2.5

Fig. 12––Profile of CO2 component in the equilibrium SCG-solvent.

Through having communication with Mehrotra (the main author), it was confirmed that the volume of gas in the gas bottle was much larger than the amount of dissolved gas in bitumen. However Mehrotra did not provide the volume of the oil and gas container. Here, we assumed that the ratio of V4/V2 was big enough to achieve equilibrium condition for the SCG-solvent and bitumen mixture (V4/V2> 2.8). Fig. 13 presents the effect of temperature on the equilibrium condition for the mixture of bitumen and SCG-solvents. Equilibrium profile for CO2, N2 and C1 are compared for run 15 and run 18 at similar pressure (~ 3990 kPa) and different temperature; 30.2 oC for run 15 and 97.6 oC for run 18. As shown in Fig. 13, the dissolution of SCG-solvents in bitumen at lower temperature is relatively slower-process compared to higher temperature

00.10.20.30.40.50.60.70.80.9

1

0.001 0.01 0.1 1 10

Equl

ilibr

ium

Com

posi

tion,

mol

e fr

ac.

SCG Mole Injected, moles

CO2 (Run 15)CO2 (Run 18)N2 (Run 15)N2(Run 18)

Basis: 25 cc of bitumen

P ≈ 3990 kPa

(a)

0.000

0.004

0.008

0.012

0.016

0.001 0.01 0.1 1 10

Equl

ilibr

ium

C

ompo

sitio

n, m

ole

frac

tion

SCG Mole Injected, moles

C1 (Run 15)C1(Run 18)

P≈ 3990 kPa

Basis: 25 cc of bitumen

(b)

Fig. 13––Effect of temperature on the profile of equilibrium SCG-solvents. Mehrotra and Svrcek (1982) proposed the generalized solubility correlation for pure- N2, CO2 and C1 in bitumen.

Correlation parameters b1, b2, b3, b4 were tuned to minimize the least-square-fit computation. Table 6 gives the pure-light solvents solubility correlation with its tuned parameters. Mehrotra and Svrcek (1982) applied this solubility correlation to predict the solubility and dissolved gas composition of SCG-solvents for comparing with experimental data. We compare the prediction of EOSSCN for solubility and dissolved gas composition of SCG-solvent in bitumen with data and also with provided correlation by Mehrotra and Svrcek (1982). Figs. 14a and 14b shows the solubility of SCG-solvent in bitumen at 29 and 70 oC. Solubility prediction by EOSSCN has better performance than the Mehrotra and Svrcek correlation for all temperature ranges (Ghasemi 2013). Figs. 14c and 14d compare the dissolved composition of SCG components in bitumen by EOSSCN at 70 oC. The prediction by EOS is well matched to SCG data. Prediction by Mehrotra and Svrcek correlation is also compared with data where gives lees accuracy than EOSSCN.

Table 6—Solubility correlation for pure-light solvents in bitumen (Mehrotra and Svrcek 1982)

sol = Light-solvent solubility in bitum en, cm 3/cm 3

T= Tem perature, Kp= Pressure, MPab1,b2,b3,b4= Correlation param ters

Light-solvent b1 b2 b3 b4CO 2 -0.0073508 -14.79400 6428.5 4971.39C1 -0.0189310 -0.850480 827.26 -635.26N2 -0.0008928 -0.112905 258.10 -2926.2

2

4321 ⎟⎠⎞

⎜⎝⎛×+×+×+=

Tpb

Tpbpbbsol

SPE 165416 13

0

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Sol

ubili

ty, c

m3 /c

m3


DataEOSSCNM&S Correlation

T=29 oC

(a)

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G S

olub

ility

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T=70 oC

(b)

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olve

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N2-data N2-EOSSCNN2-M&S Corr. CO2-data

T=70 oC

(c)

0.00

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Dis

solv

ed S

CG

-C1,

mol

efra

cBubblepoint Pressure, kPa

DataEOSSCNM&S Corr.

T=70 oC

(d)

Fig. 14—Solubility of SCG in Bitumen at: (a) 29 oC, (b) 70 oC, and dissolved SCG composition in bitumen at 70 oC: (c) CO2 and N2 component and (d) C1 component.

EOSSCN is also used to predict the saturated liquid density for the mixture of SCG-solvent and bitumen at four different

temperatures. Fig. 15a shows the deviation of density (∆ρ/ρ) versus bubble point pressure. The quality of fit from EOSSCN prediction is in good agreement with the data where error is within ±2 %. Fig. 15b compares the predicted and measured liquid density at high temperature i.e. 90 oC. It is clearly seen from Fig. 15b that measured liquid density does not follow a clear trend which indicates the possible error exists in the measured saturated bitumen density (Ghasemi 2013).

-4

-2

0

2

4

0 3000 6000 9000 12000

∆ρ/ρ

, %


T=29 C T=45 CT=70 C T=90 C

(a)

0.96

0.97

0.98

0.99

1.00

1.01

1.02

0 3000 6000 9000 12000

Liqu

id D

ensi

ty, g

/cm

3


DataEOSSCN

T=90 oC

(b)

Fig. 15––Quality of fit from EOSSCN for prediction the liquid density of SCG-saturated bitumen: (a) ∆ρ/ρ at four different temperatures and (b) calculated and measured liquid density at 90 oC.

EOS5 versus EOSSCN It is inefficient to conduct full-filed and large-sector thermal model simulation using the 89-component EOSSCN model due to CPU time limitation. We developed a “pseudoized” or reduced-component EOS model. The pseudo EOS has 5 pseudo components and is referred to EOS5. A stepwise pseudoization procedure is used to reduce the number of components from 89 while maintaining an accurate description of phase behavior and volumetric properties of bitumen and light solvent at wide range of temperature. The pseudoization procedure is summarized as:

1. Using the 89-component EOSSCN model to simulate a set of PVT experiments. 2. PVT experiment is simulated at different temperature to calculate the bubble-point pressure, solubility and liquid

density for the mixture of pure-light solvent and bitumen.

14 SPE 165416

3. The simulated PVT properties from EOSSCN is used as data for the ‘lumping’. 4. ‘Pseudo’ component is lumped from existing component as:

i. C7C20: C7 + C8+ … + C19+C20 ii. C21C31: C21+C22+…+C30+C31

iii. C32C55: C32+C33+…+C54+C55 iv. C56C89: C56+C57+…+C88+C89 v. C90+: C90+

5. The BIPs between light-solvents and C7+ is similar in EOSSCN and EOS5. EOS5 Prediction. Table 7 lists the EOS parameters for the pseudoized EOS (EOS5). The BIPs parameters between pseudo components and light-solvents are similar with EOSSCN and given in Table 5. Figs. 16a through 16c compare EOSSCN and EOS5 calculated properties such as bubblepoint pressure, saturated liquid density and light-solvent solubility in bitumen. The simulated PVT experiment is conducted at four different temperature between 20 oC and 118 oC similarly used in the Mehrotra and Svrcek experiment. As Figs. 16a through 16c present, the prediction by EOS5 in PVT properties has same accuracy as EOSSCN where exact-match is obtained for the temperature range of 20-118 oC. However at higher temperature, vaporization of C7+ fractions becomes significant and EOS5 predicts slightly less vaporization of C7+ fractions than EOSSCN (Ghasemi 2013). In general, EOS5 gives good prediction of both phase behavior and volumetric properties for a wide range of temperature from 10 to 350 oC.

Table 7—Fluid Properties for 5-pseudo components (EOS5) Component MW Tc, K Pc, bar ω s Tb, K γ Zc Parachor

C7C20 184.14 751.41 22.52 0.52654 0.12281 544.48 0.89774 0.2478 476.9C21C31 284.86 880.24 16.52 0.80964 0.18362 680.35 0.9597 0.2257 718.7C32C55 432.25 986.77 12.12 1.14698 0.20691 804.74 0.99778 0.1982 1072.4C56C89 658.87 1080.97 8.85 1.51438 0.20560 920.55 1.02314 0.1691 1616.3C90+ 1090.99 1185.75 5.82 1.91454 0.22045 1053.03 1.04235 0.1378 2653.4

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OS5

)

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C1

C2

CO

N2

(a)

0.9

0.94

0.98

1.02

0.9 0.94 0.98 1.02

ρb, g

/cm

3(E

OS5

)

ρb, g/cm3 (EOSSCN)

CO2C1C2CON2

(b)

0

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120

0 30 60 90 120Solv

ent S

olub

ility

, cm

3 /cm

3(E

OS5

)

Solvent Solubility, cm3/cm3 (EOSSCN)

CO2 C1C2 CON2

(c)

Fig. 16––EOS5 versus EOSSCN :(a) pb, (b) ρb, and (c) solubility of light-solvents. Viscosity Modeling Viscosity of Dead- and Live- Bitumen. This section describes the new approach to model the viscosity of dead Athabasca bitumen, and also light-solvent saturated bitumen. The detail of experimental set up is explained earlier. Svrcek and Mehrotra (1982), and Mehrotra and Svrcek 1985 report the viscosity data of light solvent saturated bitumen. Fig. 17 presents the viscosity of dead-Athabasca bitumen as strong function of temperature (Mehrotra and Svrcek 1982). For examples, the bitumen viscosity falls by four orders of magnitude after cold bitumen (~ 1,200,000 cp at 10 oC) is heated by 100 oC. It is also mention that an increase in both temperature and light-solvent solubility, significantly reduce the viscosity of saturated bitumen.

It is known that modeling the bitumen viscosity that covers all range of temperature and also accounts for the effect of solvent solubility is a big challenged. There are numerous studies available for the viscosity correlation of pure component and mixture crude oil (Lorenz-Bray-Clark (LBC) 1964, Orrick and Erbar 1973, Ely and Hanley 1981a, Pedersen et al. 1984, Twu 1985, Lawal 1986). However, most of these correlations are applied for low- and moderate- viscous crude oil. In our study, we use the LBC (Lorenz-Bray-Clark) correlation for calculating the viscosity of the mixture. The LBC is polynomial form (4th order) of reduced density. The correlation is not usually predictive for oil viscosity and the result are extremely sensitive to the input values of critical Z-factor (or critical volume). Therefore, SCN critical volumes need to be modified individually to enhance estimated viscosity by the LBC correlation. There are some available methods for estimating the viscosity of pure component at different temperature. The empirical viscosity correlation with temperature was first proposed by Guzman and it is expressed as ln(ν)= A+B/T (Mehrotra et al. 1996).

https://www.researchgate.net/publication/231294856_Internally_Consistent_Correlation_for_Predicting_Liquid_Viscosities_of_Petroleum_Fractions?el=1_x_8&enrichId=rgreq-7ce07e4bb0f422d0f6844fd51dc9c774-XXX&enrichSource=Y292ZXJQYWdlOzI0MTc5MDA4NjtBUzoxNTQwMTIwMTE3MzI5OTJAMTQxMzczMDczMzE3MQ==


https://www.researchgate.net/publication/223116525_Viscosity_of_Crude_Oils?el=1_x_8&enrichId=rgreq-7ce07e4bb0f422d0f6844fd51dc9c774-XXX&enrichSource=Y292ZXJQYWdlOzI0MTc5MDA4NjtBUzoxNTQwMTIwMTE3MzI5OTJAMTQxMzczMDczMzE3MQ==

SPE 165416 15

0

1

10

100

1000

10000

100000

1000000

10000000

0 100 200 300 400

Bitu

men

Vis

cosi

ty, c

p

Temperature,oC

Data

Fig. 17––Dead bitumen viscosity versus temperature. Solid and open circles show the measured and the extrapolated viscosity respectively (Mehrotra and Svrcek 1982).

Orrick and Erbar (1973) attempted to predict the constants A and B by group contribution as a function of average and

effective carbon number (CN). Their proposed methods can be successfully applied for light- to slightly heavy- crude oil to update the critical volume for LBC correlation. However for bitumen and highly viscous crude oil, LBC correlation with the modified critical volume from Orrik and Erbar (1973) method predicts orders of magnitude lower viscosity than the reported viscosity (Ghasemi et al. 2011).

Another viscosity correlation for estimating pure component (SCN) viscosity was developed by Ely and Hanley (1981). Their proposed viscosity correlation is based on corresponding states theory. According to this theory, a dimensionless property of one component is equal to that of another component (reference) at the same reduced condition. However their proposed method requires many properties (e.g. shape factors, critical pressure, acentric factor, molecular weight along with reference fluid viscosity and density correlations) for estimating liquid viscosity.

Later, Twu (1985) developed a method for estimating the liquid viscosity of petroleum fraction at all practical temperature. The method is based on perturbation model, in which normal paraffins are used as reference fluid. The correlation is most convenient and based on specific gravity and normal boiling point of each fraction. The range of average boiling point used in the regression vary from 810 to 1460 oR, and specific gravities from 0.78 to 0.94. The average error for calculating viscosity of pure petroleum fraction at 100 and 210 oF were 6.8% and 8.5%, respectively. Hence, we first modified Twu correlation at 100 and 210 oF based on dead-bitumen viscosity. Then, the ASTM viscosity-temperature (1981) is used to estimate viscosity at different temperature. Finally, critical volume is updated from estimated viscosity at different temperature and used in LBC for estimating bitumen viscosity. Modified Twu Correlation. The original form of Twu correlation for viscosities at 210 and 100 oF of real system are expressed as: Viscosity (ν2) at 210 oF:

2

2

222 )

2121)(/450ln()/450ln(

ffTT b

ob ×−

×++=+ νν ....................................................................................................................... (9)

2/122 /1141.21 bTxf γγ Δ×−Δ×= .......................................................................................................................................... (10)

2/1/7394.5699873.1 bTx −= .................................................................................................................................................. (11)

Viscosity (ν1) at 100 oF: 2

1

111 )

2121)(/450ln()/450ln(

ffTT b

ob ×−

×++=+ νν ....................................................................................................................... (12)

2/121 /1141.2133932.1 bTSGxf Δ×−Δ××= γ ........................................................................................................................ (13)

where ν2 and ν1 is kinematic viscosity at 210 and 100 oF respectively. Tb is normal boiling point and ∆γ=γ-γo. νo and γo are the viscosity and specific gravity of normal Alkanes and defined as follows:

422 4706.504491.490975.2773227.4)5.1ln( αααν −+−=+o .................................................................................................... (14)

)ln(37179.1801621.0)ln( 21oo νν += ........................................................................................................................................ (15)

and γo is given by Twu(1984): 123 5.1374936159.3128624.0843593.0 αααγ −−−=o ............................................................................................................ (16)

where

https://www.researchgate.net/publication/222985426_An_Internally_Consistent_Correlation_for_Predicting_Critical_Properties_and_Molecular_Weight_of_Petroleum_and_Coal_Tar_Liquid?el=1_x_8&enrichId=rgreq-7ce07e4bb0f422d0f6844fd51dc9c774-XXX&enrichSource=Y292ZXJQYWdlOzI0MTc5MDA4NjtBUzoxNTQwMTIwMTE3MzI5OTJAMTQxMzczMDczMzE3MQ==

16 SPE 165416

ocb TT /1−=α ......................................................................................................................................................................... (17)

273 10779681.010191017.0533272.0( bbo

c TTTbT ××+××+×= −− 11328310 )/10959468.010284376.0 −− ×+××− bb TT .................................................................................................................. (18)

We use Twu correlation (Eqs. 9 through 18) to calculated viscosity of SCN fractions at 100 and 210 oF. The only required properties are normal boiling point and specific gravity of C7 to C90+ (EOSSCN). Critical volume of each fraction is modified individually to guarantee that the LBC correlation estimates SCN viscosities estimated from a Twu correlation. Then, LBC correlation is used to predict the dead-bitumen mixture viscosity. Calculated bitumen viscosity at 100 and 210 oF is 1.1520e+08 and 24471 cp respectively which is extremely large compared to measured viscosity (i.e. µ=24471.1 cp at 100 oF and µ=203.8 cp at 210 oF). It indicates that Twu correlation significantly over predicts the SCN fractions viscosity. We modify Twu correlation for Tb by defining m2 and m1 multipliers in Eqs. 10 and 13 which express as:

2/1222 /1141.21 bTSGxmf Δ×−Δ××= γ ............................................................................................................................ (19)

2/1211 /1141.21 bTSGxmf Δ×−Δ××= γ ......................................................................................................................... (20)

m1 and m2 are used as tuned parameters for heavy SCN fractions with boiling point more than 1400 oR. It is important to notice that the original value of m1 and m2 (m1=1.33932 and m2=1) is used for the SCN fractions with Tb<1400 oR. Following stepwise procedure is used for tuning m1 and m2 for Tb>1400 oR:

1. Set temperature to 100 oF, and modify critical volume of SCN fractions of Tb<1400 oR so that estimated LBC viscosity of SCN fraction matches the estimated viscosity from the original Twu correlation.

2. Fix critical volume from step 1 for Tb<1400 oR , and change SCN fractions critical volume for Tb>1400 oR to guarantee that calculated viscosity by LBC match bitumen viscosity at 100 (and 210) oF.

3. Calculate SCN fractions viscosity using tuned critical volume from step 1 and 2. 4. Tune mi (i=1 for 100 oF and i=2 for 210 oF) from Eqs. 19 and 20 to match estimated fractions viscosity from step 3. 5. Repeat step 1 to step 4 for 210 oF.

For modifying critical volume (Vc) or Zc for Tb>1400 oR, we define following relation: **, ),,( CCbibic ZcTTAZ +−×= ................................................................................................................................................ (21)

where A is the slope of Zc,i versus Tb,i and is used as a regression variable in step 2. i starts from a first SCN carbon number (C*) with a corresponding boiling point (Tb,C*) that is larger than 1400 oR. Using EOSSCN characterization, C* is found as C48. The advantage of using Eq. 21 for modifying critical volume of SCN fractions is that it forces critical volume to change in consistent manner. The final value of A for 100 and 210 oF was found as 1.92424E-04 and 1.05343E-04 respectively. Fig. 18 shows the final modification of Zc after step 1 and 2. The slop, A (A1 is used for 100 oF, and A2 for 210 oF) is decreased for both 100 and 210 oF to match the estimated viscosity by LBC correlation with data.

0.1

0.2

0.3

0.4

0.5

400 600 800 1000 1200 1400 1600 1800 2000

Zc

Normal Boiling Point, oR

T=210 FT=100 F

A1

A2

Fig. 18––Modified Zc versus normal boiling point.

Fig. 19a shows the estimated viscosity using modified critical volume form step 2. The slope of LBC viscosity for SCN-

fraction is decreased after 1400 o. The final tuned m in Eq. 19 and 20 (modified Twu correlation) is found to be well correlated with α (see Eq. 17). Fig. 19b shows the relation between tune m and parameter α. Tuned parameter m is decreased as α decreases. For example for C90+ which has minimum value of α ~ 0.018, tuned m needs to be decreased from 1.3393 to 0.7427 at 100 oF and from 1 to 0.643 at 210 oF. As show in Fig. 3.27, one can find following correlation for m versus α:

5677.06407.5039.1831.211 231 ++−= αααm .................................................................................................................. (22)

6821.08569.426.11643.455 232 +−+−= αααm ............................................................................................................... (23)

ASTM viscosity-temperature is used for estimating viscosity at different temperatures. The generalized form is expressed as follows:

SPE 165416 17

TBAZ lnlnln += ................................................................................................................................................................ (24) where Z is ν+0.7. A and B can be found from known viscosity (ν) at two temperatures i.e. ν1 at T1=100 oF and ν2 at T2=210 oF. Fig. 20 shows good fit between the measured and LBC predicted viscosity of “dead”-bitumen for a wide range of temperature. Predicted viscosity by LBC correlation is obtained using updated critical volume from combination of modified Twu correlation and ASTM method at different temperatures. The EOSSCN with updated critical volume is referred as EOSSCN/LBC. Fig. 21 compares the bitumen viscosity with the SCN fractions viscosity for different range of temperatures (only few SCN fractions are shown).

0

1

10

100

1000

10000

100000

1000000

500 800 1100 1400 1700 2000

Frac

tion

Vis

cosi

ty, c

p

Normal Boiling Point, oR

T=210 FT=100 F

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0.00 0.05 0.10 0.15

m

α

m1

m2

Fig. 19—Change in fraction viscosity and parameter m for tuning bitumen viscosity: (a) fraction viscosity versus normal boiling point and (b) m1 and m2 multiplier versus α.

0.1

1

10

100

1000

10000

100000

1000000

10000000

0 100 200 300 400

Bitu

men

Vis

cosi

ty, c

p

Temperature,oC

Data

EOSSCN/LBC

0

1

10

100

1000

10000

100000

1000000

10000000

100000000

0 100 200 300 400

Com

pone

nt V

iscos

ity, c

p

Temperature, OC

C10C20C40C60C80C90+Bitumen

Fig. 20— Bitumen viscosity versus temperature. EOSSCN/LBC is the EOSSCN with modified critical volume.

Fig. 21––SCN fraction viscosity versus temperature. Red solid circle shows the viscosity of bitumen for comparison.

Initial viscosity prediction of the Athabasca crude by the EOSSCN/LBC model is satisfactory for dead-bitumen with

viscosity only affected by temperature. The model also predicts reasonable estimation of viscosity for solvent-saturated bitumen with low solubility (e.g. N2 and CO). The viscosity prediction error from EOSSCN/LBC for N2 is ~ 17% and for CO is ~ 23%. Generally, for viscosities of pure-solvent-saturated bitumen at varying temperatures, the EOSSCN/LBC model is not performing well. This is because the viscosity is affected by both temperature and solvent solubility. The new approach for modeling viscosity of pure-solvent saturated bitumen will be discussed later. EOS5/LBC Versus EOSSCN/LBC. Fig. 22a compares the predicted dead bitumen viscosity using EOSSCN/LBC and EOS5/LBC. EOS5/LBC model is the EOS5 with a modified critical volume (or Zc) from pseudoized EOSSCN/LBC (see Table 7 for EOS properties). Fig. 22b shows the Zc of pseudo-components in EOS5/LBC versus temperature. The calculated viscosities from both EOSSCN/LBC and EOS5/LBC models are in very good agreement (see Fig. 22a).

In addition, both models give close match for phase behavior and volumetric calculation for a wide range of temperature from 10 to 350 oC as shown in Fig. 16. Therefore instead of EOSSCN/LBC, the EOS5/LBC model can be used for all phase behavior, volumetric and also viscosity calculations. “Lower-viscous” and “Higher-viscous”(L&H) Splitting Approach. As discussed before, Initial viscosity prediction of the Athabasca crude by the EOSSCN/LBC and EOS5/LBC models is satisfactory for dead-bitumen with viscosity only affected by temperature. However, for viscosities of pure-solvent-saturated bitumen at varying temperatures, the EOS5/LBC model did not perform well. Our solution was to split the heaviest fraction C90+ from EOS5/LBC into two sub-fractions, “lower-

18 SPE 165416

viscous” and “higher-viscous” C90+ fractions (C90+L and C90+H). The C90+ properties used by the EOS5/LBC (MW, Tc, Pc, acentric factor, volume shift, BIPs) are identical for C90+L and C90+H.

(a)

0

1

10

100

1000

10000

100000

1000000

10000000

0 100 200 300 400

Bitu

men

Vis

cosi

ty, c

p

Temperature,oC

EOSSCN/LBC

EOS5/LBC

(b)

0.1

0.2

0.3

0.4

0.5

0.6

0 100 200 300 400

Zc

Temperature,oC

C90+C56C89C32C55C21C31C7C20

Fig. 22—(a) Bitumen viscosity versus temperature for EOSSCN/LBC and EOS5/LBC, and (b) Zc of pseudo-components versus temperature.

Only the critical Z-factors (Zc) of C90+L into C90+H are different. The Zc values affect viscosity predictions from the LBC model, but have no effect on phase behavior, volume or density predictions. In our approach, fL is defined as the mole fraction of C90+L and is used to calculate the critical Z factor of C90+ as given by:

HL CLCLC ZcfZcfZc+++

×−+×=909090

)1( .................................................................................................................................. (25) where ZcC90+L and ZcC90+H are the critical Z-factors for “lower-viscous” and “higher-viscous” respectively. For each measure viscosity point at specific bubblepoint pressure (or solvent solubility) and temperature, the “lower-viscous” fraction (fL) in the C90+ residue is determined to obtain a best fit of LBC viscosity to that measured saturated-bitumen viscosity. The regressed variable, fL is changed between zero and one. fL=1 for a fraction of the C90+ component that is pure “lower-viscous” fraction, and fL=0 if the C90+ component is pure “higher-viscous” fraction.

This final model has, in reality, six components, even though the two heaviest fractions are identical for EOS calculations we call this final model EOS6/LBC. It is important to notice that the final model EOS6/LBC is generated from EOS5/LBC with updated Zc’s from modified Twu correlation at 210 oF. In this approach, the Zc is not dependent to temperature and only fixed Zc values (i.e. Zc from modified Twu correlation at 210 oF) are used for a wide range of temperature (e.g. from 10 to 350 oC). The Zc of “lower-viscous” fraction (C90+L) is determined to match measured bitumen viscosity at 350 oC. Similarly, the “higher-viscous” fraction (C90+H) Zc is obtained to match LBC viscosity to measured bitumen viscosity at 10 oC. This selection of Zc for C90+L and C90+H will guarantee to cover viscosity range from ~1,300,000 cp at 10 oC to 1.4 cp at 350 oC. Default LBC coefficients are used for all viscosity calculations. Table 8 lists the EOS parameters for the pseudoized EOS6/LBC. Fig. 23 shows the Zc values for 6 pseudo-components in EOS6/LBC.

Table 8—Fluid Properties for pseudoized (EOS6/LBC)

Component MW Tc, K Pc, bar ω s Tb, K γ Zc Parachor

C7C20 184.14 751.41 22.52 0.52654 0.12281 544.48 0.89774 0.24767 476.9C21C31 284.86 880.24 16.52 0.80964 0.18362 680.35 0.9597 0.25034 718.7C32C55 432.25 986.77 12.12 1.14698 0.20691 804.74 0.99778 0.27018 1072.4C56C89 658.87 1080.97 8.85 1.51438 0.20560 920.55 1.02314 0.29195 1616.3C90+L 1090.99 1185.75 5.82 1.91454 0.22045 1053.03 1.04235 0.14922 2653.4C90+H 1090.99 1185.75 5.82 1.91454 0.22045 1053.03 1.04235 0.79366 2653.4

A global regression is run to obtain a best fit of the measured oil viscosity by adjusting fL values. Fig. 24 shows the quality of fit for all viscosity of light-solvents-saturated bitumen. Quite-accurate match is obtained for a wide viscosity range of pure-solvents saturated bitumen.

0.0

0.2

0.4

0.6

0.8

1.0

0 500 1000 1500

Zc

Molecular Weight

Zc C90+H

Zc C90+L

10

100

1000

10000

100000

10 100 1000 10000 100000Calc

ulat

ed V

isco

sity

, cp

Measured Viscosity, cp

CO2C1C2N2CO

Fig. 23––Zc of pseudo-components (EOS6/LBC) versus fraction molecular weight.

Fig. 24—Calculated viscosity versus measured viscosity.

SPE 165416 19

The fractions of C90+L (fL) for all solvents saturated are shown in Figs. 3.33a through 3.33e. It is found that the fL correlates with pure solvent solubility and temperature. At each temperature, the fL increases linearly as amount of solvents in bitumen increase. The fL is significantly affected by temperature and solvent solubility in orders for C2, CO2 and then C1. However for CO and N2 solvents, the fL is fairy constant with solvent solubility and is mainly affected by temperature. Table 9 lists the correlation of fL versus solvent solubility at different temperatures.

0

0.2

0.4

0.6

0.8

1

0 3 6 9 12

f L

Mole-% N2

T=100 C

T=75CT=52 C

(a) (b)

0

0.2

0.4

0.6

0.8

1

0 10 20 30

f L

Mole-% CO

T=115 CT=78 CT=50 C

(c)

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60

f L

Mole-% CO2

T=97 CT=63 CT=42 CT=25 C

(d)

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

f L

Mole- % C1

T=100 CT=67 CT=45 CT=27 C

(e)

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80

f L

Mole-% C2

T=105 CT=80 CT=50 CT=23 C

Fig. 25––The “lower-viscous” fraction, fL versus temperature for: (a) N2, (b) CO, (c) CO2, (d)C1 and (e)C2.

Table 9—fL is correlated with temperature and solvent solubility

T= 23 oC

T= 115 oC T= 100 oC

T= 75 oC

T= 52 oC

T= 78 oC

T= 50 oC

T= 105 oC

T= 63 oC T= 67 oC T= 80 oC

T= 42 oC T= 45 oC T= 50 oC

CO2

T= 97 oC T= 100 oC

T= 25 oC T= 27 oC

N2CO

C2C1

4210.0%005061.0 2 +×= COL xf

2745.0%005977.0 2 +×= COL xf

7157.0%003020.0 2 +×= COL xf

5773.0%003499.0 2 +×= COL xf

4733.0%003686.0 1 +×= CL xf

3353.0%002378.0 1 +×= CL xf

7576.0%001470.0 1 +×= CL xf

5234.0%002888.0 2 +×= CL xf

7576.0%001470.0 2 +×= CL xf

6424.0%002521.0 2 +×= CL xf

1778.0%005405.0 2 +×= CL xf

7581.0%001149.0 +×= COL xf

4311.0%001484.0 +×= COL xf

6134.0%003137.0 2 +×= NL xf

4955.0%001341.0 2 +×= NL xf

7386.0%0008425.0 2 +×= NL xf

6129.0%001110.0 +×= COL xf

6166.0%002983.0 1 +×= CL xf

For a new mixture of pure-solvents (i.e. CO2, C1, C2, N2 and CO) saturated bitumen, we recommend following stepwise procedure for calculating the mixture viscosity at desired pressure and temperature:

1. Set temperature, solvent type, and solvent composition. 2. Calculate mole fraction of “lower-viscous” C90+L (fL) from Table 9. 3. Calculate the mole fraction of “higher-viscous” (fH): fH=1-fL. 4. Calculate Zc of C90+ from Eq. 25—for indication only 5. Predict mixture viscosity of light-solvent saturated bitumen using EOS6/LBC described in Table 8.

The applicability of this method is discussed in proceeding section. EOS6/LBC Prediction. This section describes the applicability of the L&H splitting approach on the mixture viscosity of synthetic combustion gas (SCG). The experimental design for solubility, density and viscosity measurement of SCG and bitumen is briefly described earlier. Appendix B gives the viscosity of SCG-saturated bitumen at given temperature and SCG solubility (or bubblepoint pressure). For estimating the viscosity of saturated bitumen with mixture of solvents (e.g. SCG), following stepwise procedure is used based on generated fLs from pure solvents:

20 SPE 165416

1. Set temperature and pressure.

2. Use EOS6/LBC to calculate the solubility (mole-%) of SCG (i.e. CO2, N2 and C1) in the bitumen. 3. Calculate fL from Table 9 for CO2, N2 and C1solvents using SCG solubility from step 2. If fL correlation for a

desired temperature (step 1) is not given in Table 9, use linear interpolation for temperature. 4. calculate SCG mixture fL(fL,m ) using Kay’s mixing rule:

∑=

×=N

iiLimL fxf

1,,

............................................................................................................................................... (26)

where fL,m is the fL used for SCG mixture. xi is the dissolved SCG composition for a component i. N represents the total number of components in the SCG-solvent (for this case N = 3)

5. Estimate viscosity of SCG saturated bitumen using EOS6/LBC. Fig. 26 shows the quality of match for the estimated SCG-saturated viscosity (using step 1 through 5) versus measured data. The average error for a wide range of viscosity from 11600 cp at 45 oC to 148 cp at 99.6 oC is ~ 18%, indicating the successful application of L&H splitting approach with Kay’s mixing rule for fL. Modified form of Eq. 26 can be use as follows to enhance the SCG-saturated bitumen viscosity estimation:

∑=

×=N

iiLicmL fxFf

1,, ............................................................................................................................................................ (27)

where Fc is the correction factor used for modifying Kay’s mixing rule( Fc=1 is used for Eq. 3.26). It was found that using Fc= 1.0178 (small change from value of 1) gives better match of SCG-saturated bitumen viscosity with the average error of 9.8%. Fig. 3.34 also compares the quality of fit for Fc=1 and Fc=1.018. L&H splitting approach can also be used to estimate viscosity of light-solvent saturated bitumen at high temperature (i.e. thermal process operating condition) where experimental data is not available. This capability of the method is discussed in next section.

10

100

1000

10000

100000

10 100 1000 10000 100000

Estim

ated

Vis

cosi

ty, c

p

Measured Viscosity, cp

Fc=1Fc=1.018

‐20 %

44 oC

70 oC

98 oC

+20 %

Fig. 26––Estimated versus measured viscosity of SCG-saturated bitumen. Application of L&H Splitting Approach for Estimating Viscosity at High Temperature for Using in Thermal Simulators. Another application of L&H splitting approach is estimating viscosity of solvent and bitumen mixtures at high temperature (e.g. SAGD operating condition). EOS6/LBC is used to predict the viscosity of light-solvent saturated bitumen at high temperature (more than 100 oC). It can be achieved by extrapolating the “lower-viscous” C90+L (fL) for higher temperature. Fig. 27 shows the extrapolated fL versus temperature for different amounts of CO2 used as light-solvent (CO2 is used as an example). The extrapolated value of fL for different amount of CO2 is one at very high temperature (e.g. 350 oC). This assumption is due to the fact that the solubility of light-solvent at extreme temperature (i.e. 350 oC) is very low and at this state the oil viscosity is mainly affected by temperature rather than solvent solubility. Solid lines in Fig. 27 represent the best trend-line to the fLs found from fitting measured viscosities upto ~100 oC. The dashed lines for different amount of CO2 are extrapolated fLs at higher temperature. Extrapolation is bases on the fL values at zero amount of CO2 (i.e. dead bitumen sample).

However, LBC correlation for estimating the liquid viscosity of solvent-saturated bitumen is not used in thermal simulators. Instead, the common correlation for calculating the mixture oil phase viscosity is the logarithmic mixing rule which expressed as:

∑=

×=N

ioiio x

1)ln()ln( μμ .......................................................................................................................................................... (28)

SPE 165416 21

0.00.10.20.30.40.50.60.70.80.91.0

0 50 100 150 200 250 300 350

fL

Temperature,oC

40 % mole CO230 % mole CO220 % mole CO210 % mole CO20 % mole CO2

CO2

Fig. 27––fL versus temperature and solvent solubility for CO2-bitumen mixture.

Eq. 28 gives the mixture viscosity of light-solvents and bitumen at a particular temperature. It can be found from Figs. 28a and 28b that the predicted mixture viscosity by EOS6/LBC is well correlated with Eq. 28. At given temperature, the best-fit trend line is extrapolated to 100 mole-percent of CO2 to determine the viscosity of hypothetical-liquid CO2 which used as input to a thermal model.

Using Eq. 28, two viscosity points i.e. dead-bitumen viscosity at x%-CO2=0 and the viscosity of hypothetical-liquid CO2 at x%-CO2=100 are sufficient to calculate mixture viscosity at any CO2 solubility. Fig.28b shows the predicted viscosity at high temperature up to 350 oC. Again, lines represent the best-fit of Eq. 28 and are used to obtain the hypothetical liquid viscosity at different temperature.

(a)

0.1

1

10

100

1000

10000

100000

1000000

0 20 40 60 80 100

Oil

Visc

osity

, cp

CO2 Mole-%

Data(T=25 C) LBC (T=25 C)Date(T=42 C) LBC( T=42 C)Data (T= 63 C) LBC (T=63 C)Data (T=97 C) Data (T=97 C)

(b)

0.1

1

10

100

0 20 40 60 80 100

Oil

Visc

osity

, cp

CO2 Mole-%

T= 140 C T= 180 CT= 220 C T= 260 CT= 300 C T= 320 CT= 350 C

Fig. 28––Oil viscosity versus CO2 amount at different temperature: (a) T<100 oC where data are compared with LBC and (b) Extrapolated LBC viscosity for T>100 oC. Solid lines are best-fit trend lines to LBC viscosity using Eq. 28.

We use Mehrotra and Svrcek (1982) correlation to predict solvent saturate-viscosity at higher temperature. The viscosities are compared with the LBC viscosity from developed approach in this study. Appendix C gives the Mehrotra and Svrcek viscosity correlation for mixture of CO2 in Bitumen. Viscosity from Mehrotra and Svrcek correlation can be calculated at given temperature and bubblepoint pressure. Calculated solubility need to be converted in solvent amount (i.e. mole-%) to find out the hypothetical solvent viscosity from Eq. 28. Appendix C describes the equations used to translate volumetric solubility (Rs) into mole-fraction of CO2 dissolved into bitumen.

It was found that Mehrotra and Svrcek correlation is not reliable for predicting the viscosity of saturated bitumen. For example, Fig. 39 compares the predicted viscosity by Mehrotra and Svrcek correlation with the methodology described above. Error for predicting viscosity after 100 oC is increased for Mehrotra and Svrcek correlation. For example the hypothetical CO2 viscosity at 140 oC from the correlation is clearly not-consistent. It seems that the error is very significant for temperature more than 160 oC where the estimated hypothetical CO2 viscosity is negative. It is clear that the predicted viscosity by proposed model in this work is very consistent. Conclusion Based on analysis of experimental results for the light-solvent saturated bitumen and developed EOS/LBC model which describes accurately all key properties, following conclusions are made:

1. Systematic characterization technique which is based on Athabasca crude assay data was successfully applied for bitumen characterization where gives similar trend compared to measured distillation cuts for cumulative weight percent versus boiling point.

22 SPE 165416

0.1

1

10

100

1000

0 20 40 60 80 100

Oil

Visc

osity

, cp

CO2 Mole-%.

T=100 C(this work) T=140 C (this work)T=160 C (this work) T=100 C (M&H Corr.)T= 140 C (M&S Corr.) T= 160 C (M&H Corr.)

Fig. 29—Oil viscosity versus CO2 amount at 100, 140 and 160 oC. Red solid symbol indicates viscosity prediction in this work and black open symbol shows the estimated viscosity by Mehrotra and Svrcek correlation. Red solid and black dashed lines indicate best-fit (Eq. 28) to LBC viscosity from this work and M&H correlation respectively.

2. Proposed modified Jacoby in this study shows the best representative of specific gravity-molecular weight relationship for Athabasca bitumen.

3. Developed EOSSCN with 82 components was able to successfully match the bubble-point pressure, saturated liquid density and solubility of the bitumen and light-solvent mixtures for a wide temperature range from 20 to 100 oC.

4. Pure-solvent crude oil mixture PVT data were tuned to the EOSSCN model by adjusting a fix set of BIPs between pure solvents and all C7+ components and solvent amount.

5. Estimating well-match light-solvent saturated bitumen density without modification on volume shift indicates well-defined characterization approach (i.e. items 1 and 2).

6. EOSSCN prediction to the reported solubility and dissolved gas composition of SCG-saturated bitumen at different temperature was found to be successful. EOSSCN predicts better result than the best-fit correlation proposed by Mehrotra and Svrcek (1982).

7. “Pseudoized” EOS model, EOS5, predict accurate result compared to EOSSCN for a wide range of temperature from 10 to 350 oC.

8. Twu-viscosity correlation was modified and was used to update the critical z-factor used by LBC correlation. This proposed approach predicts well fit estimated viscosity to ‘dead’-bitumen viscosity data.

9. L&H splitting approach developed in this work was found to be efficient and successful technique for modeling the viscosity of light-solvent saturated bitumen. This approach is used by EOS6/LBC with only one set of modified critical volume at 210 oF to predicts the liquid viscosity for a wide range of temperature.

10. Estimating viscosity at higher temperature where experimental data are not available was achieved by using fL correlation. Predicted viscosity by proposed model in this work provides more consistence and reliable result compared to Mehrotra and Svrcek (1982) viscosity correlation.

Nomenclature Cf =Soreide coefficient fL =“lower-viscous” fraction M =molecular weight ng =mole amount of gas in gas bottol no = mole amount of oil in mixing cell pc =critical pressure, bara s =volume shift R =solvent solubility, cm3/cm3 Tb =boiling point temperature, ºK Tc =critical temperature, ºK Z =normalized mole fraction Zc =critical Z-factor for viscosity correlations α =gamma shape γ =specific gravity

SPE 165416 23

γci =calculated specific gravity of fraction i γmi =measured specific gravity of fraction i η =gamma bound ω =acentric factor Rs =solvent solubility, cm3/cm3 μo =oil viscosity, cp ρo =oil density, lb/ft3 γo =specific oil gravity Acknowledgment We would like to sincerely thank VISTA/ Statoil ASA and also PERA for financial support of this study as part of Ghasemi’s PhD research. Reference Alberta Department of Energy. http://www.fischertropsch.org/DOE/DOE_reports/96-03611/96-03611.pdf. American Society for Testing and Materlal (ASTM). 1981. 1981 Annual Book of ASTM Standards, Chap. 23,205. Philadelphia, PA. Badamchi-Zadeh, A., Yarranton, H.W., Svrcek, W.Y., Maini, B.B. 2009. Phase Behaviour and Physical Property Measurements for

VAPEX Solvents: Part I. Propane and Athabasca Bitumen. J. Cdn. Pet. Tech. 48(1):54-61. Frauenfeld, T.W.J., Kissel, G. and Zhou, S.W. 2002. PVT and Viscosity Measurements for Lloydmister-Aberfeldy and Cold Lake Blended

Oil Systems. Paper SPE 79018 presented at the SPE International Thermal Operations and Heavy Oil Symposium and International Horizontal Well Technology Conference, Calgary, AB, 4-7 November.

Freitag, N.P., Sayegh, S.G. and Exelby, R. 2005. A New Semiautomatic PVT Apparatus for Characterizing Vapex Systems. Paper SPE 97783 presented at the SPE/PS-CIM/CHOA International Thermal Operations and Heavy Oil Symposium, Calgary, AB, 1-3 November.

Ghasemi, M. and Whitson, C.H. 2011, Modeling SAGD with a Black-Oil Proxy. SPE 147072 presented at the SPE Annual Technical Conference and Exhibition held in Denver, Denver, Colorado, Oct. 30–Nov. 2.

Ghasemi, M., Alavian, S.A., Whitson, C.H. 2011. C7+ Characterization of Heavy Oil Based on Crude Assay Data. Paper SPE 148906 presented at the SPE Heavy Oil Conference and Exhibition, Kuwait, 12-14 December.

Ghasemi, M. 2013. Optimization of Thermal Processes in Heavy Oil Recovery, PhD dissertation, Norwegian University of Science and Technology, Trondheim, Norway.

Jacobs, F.A., Doonelly, J.K., Stanislav, J. and Svrcek, W.Y. 1980. Viscosity of Gas-Saturated Bitumen. J. Cdn. Pet. Tech. 19(4): 46-50. Jacoby, R.H. and Rzasa, M.J.1952. Equilibrium Vaporization Ratios for Nitrogen, Methane, Carbon Dioxide, Ethane, and Hydrogen

Sulfide in Absorber Oil/Natural Gas and Crude Oil/Natural Gas Systems. Trans. AIME 195:225-230. Lohrenz, J., Bray, B.G., and Clark, C.R. 1984. Calculation Viscosities of Reservoir Fluids from Their Compositions. J. Pet. Tech 16(10):

1171-1176; Trans., AIME, 231. SPE 915-PA. Mehrorta, A.K., Svrcek, W.Y., 1982. Correlation for Properties of Bitumen Saturated with CO2,CH4, and N2, and Experiments with

Combustion Gas Mixtures. J. Cdn. Pet. Tech. 95-104. Mehrorta, A.K., Svrcek, W.Y., 1985. Viscosity, Density and Gas Solubility Data for Oil Sand Bitumen. Part I: Athabasca Bitumen

Saturated with CO and C2H6. AOSTRA Journal of Research 1(4): 263-268. Mehrorta, A.K., Svrcek, W.Y., 1988. Characterization of Athabasca Bitumen for Gas Solubility Calculations. J. Cdn. Pet. Tech. 27(6):107-

110. Mehrorta, A.K., Monnery, W.D., and Svrcek, W.Y. 1996. A review of practical calculation methods for the viscosity of liquid

hydrocarbons and their mixtures. Fluid Phase Equilibria 117: 344-355. Nasr, T.N. and Ayodele, O.R. 2006. New Hybrid Steam-Solvent Process for the Recovery of Heavy Oil and Bitumen. Paper SPE 101717

presented at the Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, 5-8 November. Orrick, C. and Erbar, J.H. 1973. Estimation of Viscosity for Organic Liquids. Proposition Report, Oklahoma State University, Stillwater,

OK. Pedersen, K. S., Fredenslund, Aa., Christensen, P. L. and Thomassen, P. 1984. Viscosity of Crude Oils. Chem. Eng. Sci. 39(6):1011-1016. Peramanu, S., Pruden, B. B., and Rahimi, P. 1999. Molecular Weight and Specific Gravity Distributions for Athabasca and Cold Lake

Bitumen and Their Saturate, Aromatic, Resin, Asphaltene Fraction. Industrial Engineering and Chemistry Research 38(8): 3121-3130. Robinson, D.B., Peng, D.Y., and Ng, H.-Y. 1979. Capability of the Ping-Robinson Programs, Part 2: Three-Phase and Hydrate

Calculations. Hydrocarbon Proc. 58: 269-271. Shu, W.R., Hartman, K.J. 1988. Effect of Solvent on Steam Recovery of Heavy Oil. Paper SPE 14223 presented at the SPE Annual

Technical Conference and Exhibition, Las Vegas, 22-25 September. Soreide, I. 1989. Improved Phase Behavior Prediction of Petroleum Reservoir Fluids from a Cubic Equation of State. PhD dissertation,

Norwegian Inst. of Technology, Trondheim, Norway. Svrcek, W.Y. and Mehrorta, A.K. 1982. Gas Solubility, Viscosity and Density Measurements for Athabasca Bitumen. J. Cdn. Pet. Tech.

21(3):31-38. Twu, C.H. 1984. Internally Consistent Correlation for Prediction the Critical Properties and Molecular Weights of Petroleum and Coal-Tar

Liquids. Fluid Phase Equilibria 16:137-150. Twu, C.H. 1985. Internally Consistent Correlation for Predicting Liquid Viscosities of Petroleum Fractions. Ind. Eng. Chem. Process. Des.

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Chem. Eng. 58(5): 580-587. Whitson, C.H. 1983. Characterizing Hydrocarbon Plus Fractions. SPE J. 23(4): 683-694. SPE-12233-PA.



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24 SPE 165416

Yazdani, A., Alvestad, J., Kjønsvik, D., Gilje, E. and Kowalewski, E. 2011. A Parametric Simulation Study for Solvent Coinjection

Process in Bitumen Deposits. Paper SPE 30276 presented at the Canadian Unconventional Resources Conference, Calgary, 15-17 November.

Appendix-A—EOS Model (EOSSCN) Parameters Table A–1 gives the EOS model parameter for EOSSCN. This model is used for pseudoization which results in five phseudo fractions (EOS5 and EOS5/LBC).

TABLE A-1––EOS Model (EOSSCN) Parameters Component MW Tc, K Pc, bar ω s Tb, K γ Zc Pchor

CO 28.0 132.85 34.94 0.04500 ‐0.14587 81.3 0.2782 0.2945 61.7CO2 44.0 304.12 73.74 0.22500 0.00191 184.9 0.7619 0.2743 80.0N2 28.0 126.20 33.98 0.03700 ‐0.16758 77.2 0.2834 0.2918 59.1C1 16.0 190.56 45.99 0.01100 ‐0.14996 111.6 0.1461 0.2862 71.0C2 30.1 305.32 48.72 0.09900 ‐0.06280 184.4 0.3298 0.2792 111.0C7 99.6 562.28 31.22 0.28026 0.01612 375.8 0.7522 0.2649 274.1C8 107.6 584.68 30.51 0.29753 0.02130 393.4 0.7758 0.2628 293.2C9 117.9 613.01 29.33 0.32515 0.03714 416.7 0.8017 0.2596 318.0C10 128.4 639.79 28.13 0.35519 0.05279 439.6 0.8238 0.2564 343.2C11 138.9 664.45 26.97 0.38624 0.06760 461.4 0.8425 0.2534 368.3C12 149.2 687.11 25.88 0.41776 0.08139 482.0 0.8583 0.2507 393.1C13 159.5 707.97 24.86 0.44948 0.09410 501.4 0.8720 0.2481 417.7C14 169.6 727.24 23.90 0.48123 0.10575 519.8 0.8839 0.2457 442.0C15 179.6 745.09 23.01 0.50864 0.11637 537.2 0.8944 0.2435 466.1C16 189.5 761.68 22.19 0.53849 0.12603 553.7 0.9037 0.2413 489.9C17 199.4 777.13 21.43 0.56790 0.13479 569.4 0.9120 0.2393 513.5C18 209.1 791.57 20.72 0.59683 0.14273 584.2 0.9194 0.2373 537.0C19 218.8 805.10 20.06 0.62526 0.14991 598.3 0.9261 0.2355 560.2C20 228.4 817.81 19.45 0.65316 0.15640 611.8 0.9323 0.2336 583.2C21 238.0 829.77 18.87 0.68053 0.16227 624.6 0.9378 0.2319 606.1C22 247.4 841.06 18.34 0.70734 0.16757 636.8 0.9429 0.2301 628.8C23 256.8 851.73 17.84 0.73361 0.17235 648.5 0.9476 0.2284 651.3C24 266.1 861.84 17.38 0.75932 0.17667 659.6 0.9520 0.2268 673.7C25 275.4 871.44 16.94 0.78448 0.18055 670.3 0.9560 0.2252 696.0C26 284.6 880.57 16.53 0.80911 0.18405 680.5 0.9598 0.2236 718.1C27 293.8 889.26 16.15 0.83319 0.18719 690.3 0.9632 0.2220 740.1C28 302.9 897.55 15.78 0.85676 0.19001 699.8 0.9665 0.2205 761.9C29 311.9 905.47 15.44 0.87981 0.19254 708.8 0.9695 0.2190 783.7C30 321.0 913.05 15.11 0.90235 0.19481 717.5 0.9724 0.2175 805.3C31 329.9 920.31 14.81 0.92440 0.19683 725.9 0.9751 0.2160 826.8C32 338.8 927.28 14.51 0.94597 0.19863 734.0 0.9776 0.2146 848.2C33 347.7 933.97 14.24 0.96708 0.20023 741.8 0.9800 0.2132 869.5C34 356.6 940.40 13.97 0.98773 0.20164 749.4 0.9823 0.2118 890.7C35 365.3 946.59 13.72 1.00793 0.20289 756.7 0.9844 0.2104 911.8C36 374.1 952.56 13.48 1.02771 0.20398 763.7 0.9865 0.2091 932.9C37 382.8 958.31 13.25 1.04707 0.20494 770.5 0.9884 0.2078 953.8C38 391.5 963.87 13.03 1.06602 0.20577 777.1 0.9903 0.2065 974.7C39 400.2 969.24 12.82 1.08459 0.20648 783.5 0.9920 0.2053 995.4C40 408.8 974.44 12.62 1.10277 0.20709 789.8 0.9937 0.2040 1016.1C41 417.4 979.47 12.43 1.12057 0.20760 795.8 0.9953 0.2028 1036.7C42 426.0 984.34 12.24 1.13803 0.20803 801.6 0.9968 0.2016 1057.3C43 434.5 989.07 12.07 1.15513 0.20837 807.3 0.9983 0.2004 1077.8C44 443.0 993.66 11.89 1.17189 0.20865 812.9 0.9997 0.1992 1098.2C45 451.5 998.11 11.73 1.18833 0.20886 818.3 1.0011 0.1981 1118.6C46 459.9 1002.45 11.57 1.20446 0.20901 823.5 1.0024 0.1970 1138.8C47 468.4 1006.66 11.41 1.22027 0.20911 828.7 1.0036 0.1958 1159.1C48 476.8 1010.76 11.27 1.23579 0.20916 833.7 1.0048 0.1947 1179.2C49 485.1 1014.75 11.12 1.25101 0.20917 838.5 1.0059 0.1937 1199.4C50 493.5 1018.65 10.98 1.26596 0.20914 843.3 1.0071 0.1926 1219.4C51 501.8 1022.44 10.85 1.28063 0.20908 847.9 1.0081 0.1915 1239.4C52 510.2 1026.15 10.72 1.29504 0.20899 852.5 1.0092 0.1905 1259.4C53 518.4 1029.76 10.59 1.30919 0.20887 856.9 1.0102 0.1895 1279.3C54 526.7 1033.30 10.47 1.32309 0.20873 861.3 1.0111 0.1885 1299.1C55 535.0 1036.75 10.35 1.33675 0.20857 865.5 1.0121 0.1875 1318.9C56 543.2 1040.12 10.23 1.35018 0.20839 869.7 1.0130 0.1865 1338.7C57 551.4 1043.43 10.12 1.36337 0.20821 873.8 1.0138 0.1855 1358.4C58 559.6 1046.66 10.01 1.37634 0.20800 877.8 1.0147 0.1846 1378.1C59 567.8 1049.82 9.90 1.38910 0.20780 881.7 1.0155 0.1836 1397.7C60 576.0 1052.92 9.80 1.40164 0.20758 885.5 1.0163 0.1827 1417.3C61 584.1 1055.96 9.69 1.41398 0.20736 889.3 1.0171 0.1818 1436.8C62 592.2 1058.95 9.59 1.42611 0.20713 893.0 1.0178 0.1809 1456.3C63 600.3 1061.87 9.50 1.43805 0.20691 896.6 1.0185 0.1800 1475.8C64 608.4 1064.74 9.40 1.44980 0.20668 900.2 1.0192 0.1791 1495.2C65 616.5 1067.56 9.31 1.46137 0.20646 903.7 1.0199 0.1782 1514.6C66 624.6 1070.32 9.22 1.47275 0.20624 907.2 1.0206 0.1774 1534.0C67 632.6 1073.04 9.13 1.48395 0.20602 910.5 1.0212 0.1765 1553.3C68 640.6 1075.71 9.04 1.49498 0.20581 913.9 1.0219 0.1756 1572.6C69 648.7 1078.34 8.96 1.50584 0.20561 917.2 1.0225 0.1748 1591.8C70 656.7 1080.92 8.88 1.51654 0.20541 920.4 1.0231 0.1740 1611.0C71 664.7 1083.47 8.80 1.52707 0.20523 923.6 1.0237 0.1731 1630.2C72 672.6 1085.97 8.72 1.53744 0.20505 926.7 1.0242 0.1723 1649.3C73 680.6 1088.43 8.64 1.54766 0.20488 929.8 1.0248 0.1715 1668.4C74 688.5 1090.86 8.56 1.55773 0.20473 932.8 1.0253 0.1707 1687.5C75 696.5 1093.25 8.49 1.56764 0.20458 935.8 1.0258 0.1699 1706.6C76 704.4 1095.60 8.41 1.57741 0.20445 938.8 1.0264 0.1691 1725.6C77 712.3 1097.92 8.34 1.58703 0.20434 941.7 1.0269 0.1684 1744.6C78 720.2 1100.21 8.27 1.59652 0.20423 944.6 1.0273 0.1676 1763.5C79 728.1 1102.46 8.20 1.60586 0.20414 947.4 1.0278 0.1668 1782.5C80 736.0 1104.69 8.13 1.61507 0.20407 950.2 1.0283 0.1661 1801.4C81 743.8 1106.88 8.06 1.62414 0.20401 953.0 1.0287 0.1653 1820.2C82 751.7 1109.05 8.00 1.63308 0.20396 955.7 1.0292 0.1646 1839.1C83 759.5 1111.19 7.93 1.64189 0.20393 958.4 1.0296 0.1638 1857.9C84 767.4 1113.30 7.87 1.65057 0.20392 961.1 1.0301 0.1631 1876.7C85 775.2 1115.39 7.81 1.65912 0.20392 963.7 1.0305 0.1624 1895.5C86 783.0 1117.45 7.74 1.66755 0.20394 966.3 1.0309 0.1616 1914.2C87 790.8 1119.49 7.68 1.67585 0.20398 968.9 1.0313 0.1609 1932.9C88 798.6 1121.50 7.62 1.68404 0.20404 971.5 1.0317 0.1602 1951.6C89 806.4 1123.49 7.56 1.69210 0.20411 974.0 1.0321 0.1595 1970.3C90+ 1091.0 1185.75 5.82 1.91454 0.22045 1053.0 1.0424 0.1358 2653.4

SPE 165416 25

Appendix-B—PVT Data of SCG and Bitumen Mixtures Table B-1 gives the measured saturation pressure, saturated density, solubility and liquid viscosity of the SCG-solvent saturated bitumen. Equilibrium SCG mixtures and dissolved SCG composition in bitumen is also reported in Table B-1 (Mehrotra and Svrcek 1982).

TABLE B-1––PVT Data of SCG and Bitumen mixtures (Mehrotra and Svrcek 1982)

No. P, Mpa T,oC ρ ,g/cm3 cm3/cm3 wt% CO2 N2 C1 CO2 N2 C1 μo, cp

1 9.50 27.9 1.029 12.36 2.235 20.6 78.6 0.76 85.6 13.2 1.08 -2 9.70 45.7 1.016 10.44 1.769 21.7 77.6 0.75 67.0 31.9 1.12 44503 9.97 70.2 1.006 8.51 1.433 22.1 77.2 0.76 62.9 36.0 1.14 7304 10.01 96.9 0.985 7.00 1.091 22.5 77.1 0.77 54.1 44.7 1.20 1585 8.02 27.0 1.037 9.68 1.614 27.8 71.5 0.71 68.0 30.9 1.13 -6 8.06 39.4 1.021 7.58 1.282 28.4 70.9 0.72 68.0 30.9 1.16 83007 7.98 68.7 1.006 6.03 1.038 29.0 70.3 0.73 68.3 30.6 1.06 8208 8.18 99.6 0.981 5.57 0.957 27.5 71.8 0.75 61.8 37.1 1.11 1489 6.17 27.6 1.025 18.72 3.424 50.1 49.4 0.51 87.8 11.8 0.45 545010 6.15 44.1 1.014 15.59 2.454 47.4 52.1 0.54 80.5 18.8 0.69 166011 6.06 28.8 1.038 6.23 1.042 20.6 77.5 1.92 70.2 27.2 2.66 -12 5.96 43.0 1.032 5.36 0.888 18.8 79.6 1.65 66.0 31.7 2.37 825013 5.88 68.5 0.990 5.10 0.864 19.8 78.6 1.64 61.8 35.8 2.45 108514 6.04 97.2 0.999 3.56 0.578 18.8 79.8 1.47 54.0 43.7 2.34 19615 3.95 30.2 1.016 3.46 0.587 18.8 80.0 1.15 67.6 30.8 1.61 -16 3.99 44.5 1.022 3.13 0.521 18.3 80.6 1.15 64.5 33.9 1.64 20817 4.06 70.3 1.022 2.71 0.443 18.8 80.1 1.10 60.2 38.1 1.70 105018 3.99 97.6 0.977 1.98 0.330 19.1 79.8 1.10 55.0 43.3 1.67 910019 1.85 30.4 1.039 1.61 0.260 15.6 83.6 0.84 61.0 37.8 1.18 -20 1.94 45.1 1.017 1.30 0.215 16.2 82.9 0.88 61.9 36.9 1.16 1160021 1.98 71.7 1.016 1.08 0.177 16.7 82.4 0.87 58.3 40.5 1.20 116522 2.02 99.7 0.993 1.07 0.173 17.9 81.2 0.87 52.1 46.8 1.03 203

So lubility Equilibrium SC G, wt -% D isso lved SC G, wt-%

Appendix-C—Viscosity Correlation for Pure Light-Solvents in Bitumen. Table C-1 presents Mehrotra and Svrcek viscosity correlation obtained from best match with measured viscosity of solvent-saturated bitumen. Here only correlation parameters for CO2 saturated bitumen is given. TABLE C-1––Viscosity Correlation for Pure CO2 Solvents in Bitumen(Mehrotra and Svrcek 1982)

μ =viscosity of saturated bitumen, cpT= Temperature, oCp= Bubblepoint pressure, MPaa1,a2,a3,a4= Correlation paramters

Light-solvent a1 a2 a3 a4

CO2 0.8159910 -0.0044495 0.076639 -34.5133

⎟⎠⎞

⎜⎝⎛

+×+×+×+=

TpaTaTaa16.2 73

)(loglog 4321μ

Viscosity from Mehrotra and Svrcek correlation can be calculated at given temperature and bubblepoint pressure. Similarly, same pressure and temperature is used to calculate the solvent solubility from Table C-1. Calculated solubility need to be converted in solvent amount (i.e. mole-%) in order to find out the hypothetical solvent viscosity from Eq. 28. Measured solubility is defined as cm3 of light-solvent at SC per cm3 of saturated bitumen. The solubility (Rs) can be expressed as

o

g

oo

SCo

SCoo

SCg

bitsat

SCgs n

nMBVB

VVV

R ××=== ,

,

,

.

, 380ρ .............................................................................................................................. (C-1)

where Vg,SC is the solvent volume at SC and Vsat. bit. is the volume of saturated bitumen. Bo is shrinkage factor and Vo,SC is bitumen volume at SC. ρo,SC and Mo are bitumen density and molecular weight at SC. Here, we assumed that the amount of vaporized bitumen into gas-phase is negligible. Solving for no/ng, Eq. C-1 becomes:

26 SPE 165416

soo

SCo

g

o

RMBnn ,380

ρ×= ............................................................................................................................................................ (C-2)

Mole fraction of solvent into bitumen can be calculated as:

gogo

gg nnnn

nx

+=

+=

11 ...................................................................................................................................................... (C-3)

Thus substituting no/ng from Eq. C-2 into Eq. C-3, the mole fraction of light solvent (xg) can be found:

soo

SCog

RBM

x,236901

1γ

×+= ................................................................................................................................................... (C-4)

where γo,SC is specific gravity of bitumen at SC, solvent solubility Rs is cm3/cm3 and Bo, volume shrinkage factor is cm3 of bitumen at SC per cm3 of saturated bitumen. SI Metric Conversion Factors bbl × 1.589 873 E – 01 = m3

ft × 3.048* E – 01 = m ft0, 3 × 2.831 685 E – 01 = m3 oF (oF+459.67)/1.8 E – 01 = K in × 2.54 E – 02 = m lbm/ft3 × 2.831 685 E – 02 = m psi × 6.894 757 E + 03 = Pa oR oR/1.8 E – 01 = K

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C7+ Characterization of Heavy Oil Based on Crude Assay Data

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