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Prediction of Viscosity for Characterized Oils and Their Fractions Using the Expanded Fluid Model Francisco Ramos-Pallares, Shawn David Taylor, Marco Aurelio Satyro, Robert A Marriott, and Harvey William Yarranton Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.6b01419 • Publication Date (Web): 09 Aug 2016 Downloaded from http://pubs.acs.org on August 10, 2016

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Prediction of Viscosity for Characterized Oils and Their Fractions Using the Expanded Fluid Model F. Ramos-Pallares1, S.D. Taylor2, M.A. Satyro3, R. A. Marriott4, H.W Yarranton1* 1. Department of Chemical and Petroleum Engineering, University of Calgary, 2500 University Dr. NW, Calgary, Alberta, Canada, T2N 1N4 2. Schlumberger-Doll Research, 1 Hampshire St., Cambridge, Massachusetts, USA, 02139 3. Department of Chemical and Biomolecular Engineering, Clarkson University, 8 Clarkson Ave., Potsdam, New York, United States, 13699. 4. Department of Chemistry, University of Calgary, 2500 University Dr. NW, Calgary, Alberta, Canada, T2N 1N4 *Corresponding author; Telephone: (403) 220-6529; Email: [email protected] Abstract A methodology was developed to predict the viscosity of crude oils and their fractions from a distillation based oil characterization. The maltenes were characterized as a set of pseudo-components with properties determined from established generalized correlations. The asphaltene fraction was characterized as a single component and its properties were measured. The viscosities of the pseudocomponents, asphaltenes, whole oils and their fractions were determined with the Expanded Fluid (EF) viscosity model. The inputs for the model are the pressure, the density of the fluid at a given pressure and temperature, the dilute gas viscosity calculated from established generalized correlations, and three fluidspecific parameters, c2, ρso, and c3. Densities were calculated using the modified Rackett correlation with the Tait-COSTALD compressibility correction. The c3 parameter was determined from a previously developed correlation. New correlations were developed for the c2 and ρso parameters of the maltene pseudo-components as a function of their boiling point and specific gravity. The parameters for the asphaltene fraction were estimated based on the measured viscosity of molten asphaltenes. The EF parameters for the whole oil, or any oil fraction, were determined with mass-based mixing rules and binary interaction parameters, calculated from a previously developed correlation. To develop and test the proposed approach, density and viscosity data were collected for 40 distillation cuts from 6 oils, 7 maltenes, 2 asphaltenes, 3 partially deasphalted oils, and 14 dead oils. Using this model to predict crude oil viscosity at any condition requires the distillation assay data, the asphaltene mass content, and the specific gravity and molecular weight of the oil. The approach was tested on a development and test dataset of 4 crude oils (this study) and an independent test dataset of 4 oils from the literature with overall AARD of 41 and 43%, respectively. Single multiplier tuning of the c2 parameter to one viscosity data point halved the error. Tuning both the c2 and ρso parameters using two viscosity data points reduced the AARD to less than 8% in both cases.

KEYWORDS: viscosity, distillation cuts, crude oil, petroleum, boiling point, specific gravity, oil characterization, expanded fluid model, correlations

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1. Introduction Heavy oil and oil sands are significant petroleum reserves and could potentially extend the world’s energy supply by 15 years1. However, the high viscosity of these fluids must be reduced by heating or dilution for their recovery, transport, and processing. For example, steam and solvent assisted processes are commonly implemented in Western Canada to recover heavy oil2. Heavy oil and bitumen are diluted with condensates or other solvents for transport by rail or pipeline. Mined bitumen is heated and diluted with either naphtha or a paraffinic solvent in the froth treatment stage of the bitumen extraction process3. In many of these processes, such as solvent-assisted recovery and deasphalting processes, multiple phases can be formed. The composition and viscosity of these phases depend on the temperature, pressure, and type of solvent, and must be determined for design and operational purposes. Since it is less practical, or often impossible, to measure the viscosity at all conditions, a method is required to accurately predict the viscosity of each phase as a function of its composition at any temperature and pressure.

For phase behavior modeling, the heavy oil composition is normally represented as a mixture of defined components and pseudo-components that represent boiling point intervals4. The mass fraction for each boiling point interval (i.e. pseudo-component) is assigned based on a distillation assay obtained from true boiling point distillation5, spinning band distillation6, simulated distillation7, or Deep-Vacuum fractionation8. Since less than 50 wt% of a heavy oil is distillable, the distillable fraction data must be extrapolated to define the heavy fractions and complete the oil characterization9. Once the pseudo-components are defined, the normal boiling point, specific gravity, and molecular weight of each pseudo-component must be measured or determined from correlations. Critical properties and acentric factor, can be calculated using another set of correlations. Finally, the physical properties of the crude oil are calculated by combining the properties of the pseudo-components. This approach can also be extended to viscosity modeling.

Several viscosity models have incorporated the compositional approach into their calculation schemes and can be classified into two groups. In the first group, the viscosity of each component is determined and then mixing rules are applied to determine the whole fluid viscosity. In the second group, the fluid-specific parameters of each component are determined 2 ACS Paragon Plus Environment

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and the parameters for the whole fluid are determined from mixing rules. The fluid viscosity is then determined from the mixture parameters.

The first group includes empirical models that were developed to predict the viscosity of distillation cuts only at specific temperatures at atmospheric pressure. Watson and coworkers10 developed two charts to predict the kinematic viscosity of distillation cuts at 37.7°C (100°F) and 98.8°C (210°F), respectively, based on their API gravity and the Watson characterization factor. The API Technical Data Book11 replotted the Watson charts as a nomograph. Abbot et al.12 developed analytical expressions of the API nomograph suitable for computer applications; however, singularities in the expressions have been reported13. Twu13 developed analytical expressions to predict the kinematic viscosity of distillation cuts at two temperatures, 37.7°C and 98.8°C, from their normal boiling point and specific gravity using a departure function from nalkane reference fluids. Once the cut viscosities are determined, the viscosity of the whole oil is calculated through molar-based or mass-based mixing rules14. Since the correlations are only applicable to atmospheric pressure, another procedure would be required to determine the viscosity at higher pressures.

The second group includes the Corresponding States (CS), Friction Theory (f-Theory), Walther, and Expanded Fluid (EF) approaches. •

The Corresponding States (CS) model relates the reduced viscosity of a fluid to the reduced viscosity of a reference fluid at the same reduced temperature and density15. Shape factors have been included into the model in order to correct the noncorrespondence of most fluids to the reference fluid. This model has been successfully applied to conventional oils16 but extension to heavy oils and bitumens can lead to considerable deviations17.

•

Friction Theory (f-Theory)18 relates the viscosity of a fluid to the friction forces between the fluid layers that arise from the attractive and repulsive contributions to the thermodynamic pressure. Repulsive and attractive pressure terms are calculated with cubic equations of state (EoS) and some adjustable parameters have been introduced to improve the accuracy of the predictions for hydrocarbons19. This version of the model was extended to crude oils characterized as pseudo-components20. The critical viscosity 3 ACS Paragon Plus Environment

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of the pseudo-components was related to their molecular weight and critical pressure and temperature through one common proportionality factor which can be tuned to fit experimental viscosity data. The model requires an additional parameter for characterized oils with molecular weights higher than 200 g/mol. The additional parameter is used to correct the estimation of the repulsive and attractive pressure terms calculated with the EoS. Zuo et al.21 introduced temperature dependence into these two parameters to improve the accuracy of predictions. The model has also been extended to predict the viscosity of oils characterized based on a GC assay with a chi-square probability distribution applied to the C7+ heavy fraction22. This approach has been used to predict the viscosity of dead and live oil at reservoir conditions. Additionally, Kumar et al.23 proposed a tuning method to improve the accuracy of the model for heavy oils at pressures below the saturation pressure. •

The Walther correlation24 relates the viscosity of a fluid to two empirical parameters. Yarranton et al.25 extended the correlation to characterized oils by developing expressions for the two empirical parameters as a function of the molecular weight of the pseudo-component. The Walther correlation is simple to apply but is limited to the liquid region and will deviate near the critical point.

•

The EF model26 calculates the viscosity of a fluid as a departure from the dilute gas viscosity using density and pressure as inputs. Like the Corresponding States and Friction Theory models, the EF model describes the viscosities for the entire phase diagram. Motahhari et al.27, 28 proposed mass based mixing rules and later on a methodology to calculate the EF fluid specific parameters for pseudo-components based on GC assays as a function of their molecular weight (MW) and specific gravity (SG). The EF model has also been and extended to natural gas applications29 and applied to non-hydrocarbon fluids encountered in petroleum processes such as water, carbon dioxide, hydrogen sulfide, methanol, and glycols. A version of the model has been implemented in a commercial simulator using densities calculated using the Peng Robinson equation of state30.

The above methodologies were developed based on experimental data collected from conventional oil distillation cuts and have been tested on whole heavy oils but not their fractions. 4 ACS Paragon Plus Environment

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Heavy oils and bitumens have a greater proportion of high boiling point components than conventional oils because they have a higher content of polycyclic aromatic and naphthenic compounds31. Hence, there is significant uncertainty in attempting to predict heavy oil fraction properties using correlations based on conventional oil cuts. Recently, a deep vacuum fractionation apparatus was developed and used to obtain physical samples of heavy oil distillation cuts representing approximately 50 wt% of the heavy oil32,33. This dataset provides an opportunity to develop and test viscosity characterization methodologies for heavy oils.

The objectives of this study were to: 1) measure the viscosities of these heavy boiling cuts as well as lighter boiling cuts, and asphaltenes; 2) develop a pseudo-component based method for heavy oil viscosity prediction based on these measurements. This study focuses on the EF model but, unlike Motahhari et al.’s27 approach, the characterization will be based on distillation assays rather than GC analysis because boiling points are more representative of the molecular interactions that define the physical properties of a fraction31. In addition, a reliable methodology for the boiling point curve extrapolation and characterization of heavy oils has been developed9 but the development of a reliable extrapolation methodology for GC data is challenging due to the imprecision of the mass of the residue fraction (e.g. C30+). The proposed oil characterization and viscosity modeling methodology is tested on measured viscosities of heavy oils and on similar data obtained from the literature. A simple tuning procedure is proposed for cases where at least one viscosity measurement is available. Note, the proposed model does not apply to fluids containing solid phases, such as waxes and hydrates.

2. Experimental Methods 2.1 Materials The following dead oil samples were used in this study: WC-B-B1, WC-B-B3, WC-B-A1, WCB-A2, WC-B-A3, US-HO-A1, MX-HO-A1, CO-B-B1, CO-B-A1, EU-HO-A1 and ME-CV-A1. WC, US, MX, CO, EU and ME correspond to the oil producing regions of Western Canada (WC), United States (US), Mexico (MX), Colombia (CO), Europe (EU) and Middle East (ME), respectively. B, HO and CV indicate bitumen, heavy oil or conventional oil respectively; and the third term indicates the source reservoir and sample number. Deep vacuum distillation cuts from the oils WC-B-B1, WC-B-A1, US-HO-A1, MX-HO-A1, CO-B-B1 and CO-B-A1 were provided 5 ACS Paragon Plus Environment

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by Sanchez-Lemus et al.33 and details of the procedures used to obtain these cuts are provided in the same reference. Asphaltene samples were prepared in this study as described later.

Spinning band distillation assays were performed on all the above oils except WC-B-B3. The sample WC-B-B3 was recovered from the same reservoir as WC-B-B1 but had different density and viscosity. The distillation curve and other properties such as atomic hydrogen-to-carbon (H/C) ratio and molecular weight were assumed to be the same as the WC-B-B1 sample. Some selected physical properties of the crude oil samples are summarized in Table 1.

Table 1. Specific gravity (SG), atomic hydrogen-to-carbon (H/C) ratio, molecular weight (MW), viscosity at 20°C and atmospheric pressure, asphaltene content, and toluene insoluble (TI) content of samples measured in this study. Sample WC-B-B1 WC-B-B3 WC-B-A1 WC-B-A2 WC-B-A3 US-HO-A1 MX-HO-A1 CO-B-B1 CO-B-A1 EU-HO-A1 ME-CV-A1

SG

H/C

MW

Viscosity at 20°C, mPa.s

C5-Asph. wt%

TI wt%

1.012 1.020 0.996 1.026 1.101 0.961 0.976 0.992 1.106 0.968 0.872

1.473 1.473 1.577 1.476 1.453 1.587 1.624 1.473 1.440 1.596 1.756

558 558 585 598 550 548 652 577 603 475 475

89,200 150000 33,737 7,500,000 33,737 5,627 831,600 106,500 2,800,000 5,036 18.1

17 22 16 22 18 14 21 22 27 7 3.8

0.63 0.68 0.51 0.72 0.55 0.62 0.81 0.74 1.00 0.31 0.03

2.2 Deasphalting Bitumen and Determination of Asphaltene and Solids Content Asphaltenes were precipitated from bitumen using a 40:1 ratio (mL/g) of n-pentane/bitumen. The mixture was sonicated in an ultrasonic bath for 60 min at room temperature and left to settle for 24 h. The supernatant was filtered through a 24 cm Whatman #2 filter paper (pore size 8µm) until approximately 20% of the solution remained in the beaker. A total of 10% of the original volume of solvent was added to the remaining asphaltenes in the beaker, and then the mixture was sonicated for 60 min and left to settle overnight for 18 h. The remaining mixture was filtered through the same filter paper. The filter cake was washed using 25 mL aliquots of n-pentane at least three times a day until the effluent from the filter was almost colorless and then dried for 8 6 ACS Paragon Plus Environment

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days. All the filtrate was place in a rotary evaporator and the solvent was evaporated to recover the residual oil. The evaporation process was performed until the mass of the residue no longer changed with time. The final product of this process is termed maltenes. Note, if only some of the C5-asphaltenes were removed in the first step, the product is termed a (partially) deasphalted oil (DAO). The filter cake contains the asphaltenes and any co-precipitated material and is here termed asphaltene-solids. The asphaltene-solids content is the mass of the filter cake divided by the mass of the bitumen.

Material referred to as solids corresponds to mineral material, such as sand, clay, ash, and adsorbed organics that precipitates along with the asphaltenes34. Solids were removed from the asphaltenes by dissolving the asphaltene-solids in toluene and centrifuging the mixture to separate out the solids. A solution of asphaltenes-solids in toluene was prepared at 10 kg/m³ at room temperature. The mixture was sonicated in an ultrasonic bath for 20 minutes or until all material was dispersed. After 1 hour, the mixture was divided into centrifuge tubes and centrifuged at 4000 rpm for 6 minutes. The supernatant (solid-free asphaltene solution) was decanted into a beaker and allowed to evaporate until the mass no longer changed. The nonasphaltenic solids, corresponding to remaining material in the centrifuge tubes, were dried and weighted to calculate the solid content as the mass of solids divided by the original asphaltenesolid mass and is called here toluene insoluble. The asphaltenes extracted with n-pentane and treated with toluene are termed here C5-asphaltenes. The C5-asphaltene and toluene insoluble (TI) content of the samples used in this study are summarized in Table 1.

2.3 Viscosity and Density Measurements Viscosity was measured in two apparatus: 1) a cone and plate rheometer 2) a capillary viscometer with an in-line density meter. A second density meter was used to determine the density of the samples tested with the cone and plate apparatus.

Cone and Plate Rheometer and Density Meter An Anton Paar MCR-52 cone and plate rheometer equipped with an Anton Paar Peltier P-PTD 200 mechanism for temperature control was used in this study. The viscosity was 7 ACS Paragon Plus Environment

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determined from the slope of the shear stress versus the shear rate. The data were linear above 25°C for all samples considered in this study, indicating Newtonian behavior. The instrument was calibrated using Cannon Instruments certified viscosity standards with viscosities from 5 mPa.s to 70000 mPa.s at temperatures up to 150°C and at atmospheric pressure. After calibration, the measured viscosities were within ± 2% of the reported viscosity of the standards. The repeatabilities of the distillation cuts and bitumen viscosities were found to be ± 3% and ± 5%, respectively.

The densities of the samples tested in the cone and plate rheometer were determined using an Anton Paar DMA 4500M oscillating U-tube density meter at atmospheric pressure and temperatures up to 90°C. The temperature of the sample cell was controlled to within ±0.01°C by a Peltier mechanism enabling measurements from 0°C to 90°C. The samples were injected directly into the apparatus and their density was measured once thermal equilibrium was reached at a set temperature. The instrument was calibrated using reverse-osmosis water and nitrogen. The precision and repeatability of the density measurements were ±0.01 kg/m³ and ± 0.05 kg/m³, respectively.

The density of C5-asphaltenes was indirectly calculated from the densities of asphaltene/toluene mixtures at temperatures up to 90°C and at atmospheric pressure. The densities of a series of mixtures with different asphaltene concentrations were measured at each temperature using the Anton Paar DMA 4500M density meter described above. It was assumed that the asphaltenes formed regular solutions with toluene35 as follows:

= ∑

(1)

where ρ is density and subscripts mix and i denote the mixture and component i, respectively. The densities were determined at each temperature from a least squares fit of the mixing rule to the mixture data. The repeatability of the indirectly determined densities was found to be ± 0.9 kg/m³.

Capillary Viscometer This device consists of two transfer vessels and two capillary tubes in a temperature controlled oven, Figure 1. The apparatus is also equipped with an Anton Paar DMA HPM density meter 8 ACS Paragon Plus Environment

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with an external Anton Paar mPDS 2000V3 evaluation unit. Hydraulic oil is used as the displacement fluid and pressure in the apparatus is controlled using a back pressure regulator (BPR) on the return line of the hydraulic oil. The set pressure of the regulator is maintained using compressed air and is monitored with a Bourdon pressure gauge with a precision of 0.05 MPa. The temperature of the air bath is controlled within ±0.05°C of the intended measurement temperature, except for the room temperature experiments. The room temperature varied within a range of ±0.25°C. The capillary tubes were calibrated at temperature range of 20 to 175°C using Cannon Instruments certified viscosity standards. The density meter was calibrated using pure nitrogen and distilled water at temperature range of 20 to 175°C and pressures up to 10 MPa. The measured viscosity and density reproduced the calibration data, as well as some other test fluids such as n-heptane and toluene, to within ±3% and ±0.5 kg/m³, respectively. Density and viscosity measurements were measured simultaneously for each fluid at the test pressure and temperature. Prior to the measurements, the fluid was flowed back and forth through the apparatus to ensure homogeneity, which was confirmed when the density and pressure drop through capillary tubes were consistent for the entire displacement. To collect the required data for the viscosity measurement, the fluid flowed from one vessel to other through one of the installed capillary tubes at 5 different fixed flow rates. Once each flow reached a steady state, the pressure difference between its inlet and outlet was recorded. The viscosity of the fluid was then calculated from the slope of the differential pressures versus flow rate and the calibration constant for the capillary tube. To measure density, the flow rate through the capillary tube was set at 0.001 cm³/min to maintain the test pressure set by the BPR throughout the apparatus. Once the flow reached a steady state condition, the density was measured. Measurements for the diluted bitumen samples were collected from room temperature up to 175°C in increments of 25°C. At each temperature, the data were collected at pressures well above the bubble point pressure of the fluid up to 10 MPa in increments of 2.5 MPa.


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Figure 1. Schematic of the capillary viscometer and in-line density-meter.

Quality Check of Viscosity Data Walther24 demonstrated that for many liquids well below their critical point, the double log of viscosity is linearly related to the log of the absolute temperature. Others25,36 have confirmed that heavy oils and bitumens also follow this relationship. Hence, one check on the quality of any sub-critical liquid viscosity data is to confirm its linearity when plotted in these coordinates. This condition was satisfied for all the data measured in this study or obtained from the literature. Walther plots for the whole and deasphalted crude oil samples as well as their distillation cuts used in this study are shown in the supporting information.

In addition, the viscosities of WC-B-B1 bitumen were measured in both the capillary viscometer and the cone and plate rheometer. The measured viscosities were compared where the data ranges overlapped; that is, at atmospheric pressure and temperatures from 21 to 100°C. The average deviation between the viscosities from the two methods was within 2%.


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3. Oil Characterization Methodology A schematic of the characterization procedure is provided in Figure 2. The maltene and C5asphaltene fractions of each oil were characterized separately as recommended by CastellanosDiaz et al.9 The asphaltenes are characterized separately because they self-associate and their properties do not follow the same trends as the maltenes versus cumulative wt% distilled. The asphaltene fraction was treated as a single component for viscosity modeling purposes.

Boiling Temperature

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maltene pseudo-component

C5-asphaltenes

Maltene pseudo-components Existing correlations for: SGi, MWi, H/Ci, Tci, Pci, ωi ,c3i Proposed correlations, f(Tb, SG), for:

extrapolation w, SG, MW, H/C

w, Tb

c2i, ρsio C5 asphaltenes Defined properties:

c2, ρso

maltenes

SGi, H/Ci

c2i, ρsio, c3i

Cumulative Mass Fraction Distilled

Characterization Data

αij

Mixing Rules

Density (Rackett or measured) c2, ρso, c3

EF Model

tuning multiplier(s)

µ

Figure 2. Schematic of characterization procedure for predicting crude oil viscosity.

Maltene Characterization Unless otherwise stated, the maltene fraction was characterized from its distillation assay. Since the maltenes are not fully distillable, a Gaussian extrapolation was performed to extend the distillation curve over the entire concentration range of maltenes, as indicated in Figure 2. The distillation curve was divided into pseudo-components, each representing a boiling point interval of the same width (delta TBP) as recommended by Castellanos-Diaz et al.9 The pseudocomponent properties required for the viscosity parameter correlations (to be developed later) are the boiling point from the characterization as well as the specific gravity, molecular weight, and H/C ratio. The critical properties and acentric factor are also required to determine pseudo-


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component densities at different temperatures and pressures for input into the viscosity model.

The molecular weight and initial estimate of the specific gravity of each maltene pseudocomponent were calculated using the Lee-Kesler37 and the Katz-Firoozabadi38 correlations, respectively. The H/C ratio for each pseudo-component in the maltene fraction was calculated using the correlation developed by Sanchez-Lemus39:

H / C = 3.4388− 1.9327SG

(2)

where H/C is the atomic hydrogen/carbon ratio and SG is the specific gravity. The critical temperature, critical pressure, and acentric factor of each pseudo-component in the maltene fraction were calculated from the Lee-Kesler correlations37,40 as suggested by Castellanos-Diaz et al.9

The initial specific gravities of the cuts were tuned to match the density of the whole maltenes with a single constant multiplier and therefore, the predicted density of the whole maltenes was also required. The following empirical relation is proposed for cases where the experimental specific gravity of the maltenes is not available: SGmal = 0.8254SGoil + 0.1496

(3)

where SGmal and SGoil are the specific gravity of the maltenes and crude oil respectively. Eq. 3 was found to correlate to the measured SGmal with an average absolute deviation of 0.5%. The maltenes were obtained from crude oils with specific gravities between 0.87 and 1.1.

C5-Asphaltene Characterization The asphaltene fraction was represented by a single pseudo-component for viscosity modeling purposes and its EF model parameters, specific gravity, molecular weight, and H/C are the only required input properties for the viscosity model. The EF model parameters are discussed later. The H/C ratio was determined from Eq. 2. The specific gravity and molecular weight were determined indirectly from the measured oil properties, the characterized maltene properties, and the measured mass fraction of C5-asphaltenes in the oil. First, the maltenes were characterized as described above and their bulk molecular weight and specific gravity determined. Then, the


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asphaltene molecular weight was calculated from a molar mixing rule and the specific gravity was determined from Eq. 1.

4. Viscosity Model 4.1 Expanded Fluid Viscosity Model Details of this model and its development are given elsewhere26. Briefly, the model is based on the empirical observation that the viscosity of the fluid decreases as it expands from a compressed state of infinite viscosity. The viscosity of the fluid, µ, in mPa.s, is formulated as a departure from dilute gas viscosity, µo: − = 0.165 − 1

(4)

where c2 is a parameter specific for each fluid which determines the response of the viscosity of the fluid to the expansion from the compressed state. β is the correlating parameter between the density and viscosity and is related to the expansion of the fluid as follows: β =

1

(5)

  ρ *  0.65  exp   s  − 1 − 1   ρ  

where ρs* is pressure dependent compressed state density of the fluid given by:

ρ s* =

ρ so

exp (− c3 P − Po

(6)

)

where ρso is the compressed state density of the fluid in vacuum, c3 is the fluid-specific pressure dependency constant in kPa-1, P is the pressure of the fluid in kPa, and Po is the atmospheric pressure in kPa. The parameter c3 is calculated as a function of molecular weight according to27:

c3 =

2.8 × 10 −7 1 + 3.23 exp − 1.54 × 10 − 2 MW

(

)

(7)

The inputs to the EF model are the pressure, density, and dilute gas viscosity of the fluid. The dilute gas viscosity of the components was estimated using the following empirical correlation41:

µ o = Ao + BoT + C oT 2 + DoT 3

(8)

where Ao, Bo, Co and Do are fitting parameters specific for each pure component and usually defined at 1 atm. The value of these parameters are obtained from Yaws’ handbook41. For distillation cuts, the coefficients of the n-alkane with the same molecular weight as the cut were


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used as recommended by Motahhari42. The fluid-specific parameters: c2, c3 and ρso are fitted using the available viscosity data.

Mixing Rules The EF model treats a mixture as one single fluid with fluid-specific parameters calculated from those of the components of the mixture with following mixing rules28: ,

=

*,,

" !,

)* ∑)* ∑'

)* = ∑)* ∑'

c3,mix

" !,

+

" !,

+

$ %1 − &' ($

*,,

*

,, " + " $ %1 − &' ( !,

 nc w =  ∑ i =1 i  c3,i 

!,

  

(9) (10)

−1

(11)

where nc is the number of components in the mixture and wi is the mass fraction of the component “i” in the mixture. αij is the viscosity binary interaction parameter. The viscosity binary interaction parameter can be calculated using the following expressions43: α ij = α ijo − ∆ α ij

(12)

ΔSGnorm ≤ 0.165

α ijo = 0 .021

(13)

ΔSGnorm > 0.165

α ijo = 0 . 038304 − 0 .10478 ∆ SG norm

(14)

where ΔSGnorm is the normalized difference of specific gravity defined as follows:

∆SGnorm =

2 SGi − SG j SGi + SG j

(15)

and SGi and SGj are the specific gravities of components “i” and “j” respectively. The perturbation term, Δαij, in Eq. 12 is calculated according to:

Δ(H/C)norm ≤ 0.25 ∆ α ij = 0.02756 − 0.1103 ∆ (H C )norm Δ(H/C)norm > 0.25

∆α ij = 0

(16) (17)

where Δ(H/C)norm is the normalized difference of atomic hydrogen-to-carbon ratio between components “i” and “j” : ∆ (H C )norm =

2 (H C )i − (H C ) j

(H C )i + (H C ) j

(18)


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When no experimental value is available, H/C can be estimated as a function of the specific gravity using Eq. 2. The dilute gas viscosity of the mixture (µo,mix) is calculated using Wilke’s method44 as follows:

µo,mix = ∑ i

xi µo,i

(19)

∑ x jϕij j

where:

(

) (

1 + µ / µ 0.5 MW / MW o ,i o, j j i  ϕij =  0.5 8 1 + MWi / MW j   

(

)

0.25 



)

2

(20)

and where xi, µo,i and MWi are the mole fraction, dilute gas viscosity and molecular weight of the component “i” of the mixture.

4.2 Application to Pseudo-Components To apply the EF model to pseudo-components, the fluid specific parameters (c2 c3, and ρso) and the density of each pseudo-component at the specified temperature and pressure are required. Correlations for the c2 and ρso parameters as a function of normal boiling point and specific gravity are developed later. The c2 and ρso parameters for the single component asphaltenes are also discussed later. The pressure dependency parameter c3 was calculated using Eq. 7. When predicting crude oil viscosities, the binary interaction parameters between the pseudocomponents were determined with Eqs. 12 to 18 and the required H/C ratio of each pseudocomponent was determined with Eq. 2.

The density of the whole crude oil at a given temperature and pressure was predicted from those of the maltenes and asphaltenes at the same conditions using Eq. 1. The density of the maltenes was determined from the pseudo-component densities using Eq. 1 as described previously. The methods used to determine the density of the maltene pseudo-components and the asphaltenes at any given temperature and pressure are described below.


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Maltene Pseudo-Components For the maltenes produced from the precipitation of C5-asphaltenes, the density of a pseudocomponent at a given temperature and pressure was determined using the Tait-COSTALD correlation45:

ρT ,P

  B+P = ρ T , Po 1 − C ln  B + Po 

  

−1

(21)

where ρT,P is the density of the fluid at a temperature, T, and pressure, P, and ρT,Po is the density at T and atmospheric pressure, Po. The parameters C and B are given by:

C = 0 . 0861488 + 0 . 0344483 ω

(22)

B 1/ 3 2/ 3 4/ 3 = −1− 9.0702(1 − Tr ) + 62.45326(1 − Tr ) −135.1102(1− Tr ) + e(1− Tr ) Pc

(23)

e = exp( 4.79594 + 0.250047ω + 1.14188ω 2 )

(24)

where ω, Pc and Tr are the acentric factor, critical pressure, and reduced temperature, respectively.

The density of the pseudo-components at atmospheric pressure, ρT,Po, was assumed equal to that of the saturated liquid and was calculated from the modified Rackett correlation given by46:

vs =

RTc Z RA Pc

 1+  1− T Tc   

2   7    

(25)

where vs is the molar volume of the saturated liquid at temperature T, Tc is the critical temperature, Pc is the critical pressure, and ZRA is the Rackett compressibility factor. The density is simply the component molecular weight divided by the calculated saturated molar volume. The density of the pseudo-component at atmospheric pressure was assumed equal to that of the saturated liquid at the same temperature because the compression correction between saturation pressure and atmospheric pressure is very small27. The Rackett compressibility factor was determined by tuning Eq. 25 applied at 15.6°C to fit the previously determined specific gravity. Eq. 21 predicts the density of the maltenes of bitumen WC-B-B1 with an average and maximum deviation of 0.2% and 0.5% respectively at temperatures and pressures up to 175°C and 10 MPa.


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C5-Asphaltenes Due to the lack of data, it was assumed that the C5-asphaltenes were incompressible and only the temperature dependence of their density was considered. The following empirical relation was found to fit the density data calculated from the asphaltene/toluene solutions with the regular solution assumption (Eq. 1):

ρ asph = 1000 SG asph − (6 .7424 − 5 .098 SG asph )(T − 15 .6 )

(26)

where ρasph and SGasph are the density at temperature, T, in °C and the specific gravity of the asphaltenes at 15.6°C respectively. Eq. 26 fitted the estimated C5-asphaltene density from the WC-B-B1, WC-B-A1, CO-B-A1, and EU-HO-A1 oils with average and maximum absolute deviations of 2 and 5 kg/m3, respectively at temperatures up to 90°C at atmospheric pressure.

5. Data Collected and Organization of Datasets In order to develop correlations for the maltene pseudo-components, the density and viscosity of the distillation cuts from six heavy oils were measured. Similarly, the density and viscosity of molten asphaltenes were measured to determine the EF model parameters for the asphaltenes. Density and viscosity data for maltenes, partially deasphalted oils, and whole oils were also measured to validate the proposed approach for EF model parameters and model mixing rules. The data collected in this study are summarized below. Note, the capillary viscometer apparatus covered a broader range of temperatures and pressures than the cone and plate apparatus but required more sample and time. Therefore, most samples were run with the cone and plate apparatus with a small subset run with the capillary viscometer when sample size permitted. The data collected in this study were supplemented from the literature where applicable and organized into development and test datasets as described below.

5.1 Data Collected in This Study Whole Oils The density and viscosity of the WC-B-B1, CO-B-A1 and ME-CV-A1 oils were reported previously43. The density and viscosity of the WC-B-B1, WC-B-A2 and WC-B-A3 whole oils were measured at temperatures and pressures up to 175°C and 10 MPa using the capillary viscometer. The viscosities of the WC-B-B1, WC-B-A1, US-HO-A1, MX-HO-A1, CO-B-B1, 17 ACS Paragon Plus Environment

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Page 18 of 65

and EU-HO-A1 whole oils were measured in the cone and plate rheometer at atmospheric pressure and temperatures up to 125°C. The viscosities of the CO-B-A1 and ME-CV-A1 whole oils were measured in the same apparatus at atmospheric pressure at temperatures up to 75°C and at 25°C, respectively. For the cone and plate measurements, fresh sample (around 2 mL) was used every time the temperature was changed to minimize the potential for light end losses. Testing at higher temperatures was avoided in the cone and plate apparatus in order to minimize the evaporation of light components. The density of the samples from the cone and plate measurement set was measured in the Anton Paar density meter at atmospheric pressure at temperatures up to 90°C. The molecular weight and H/C ratio of the crude oils (and of the distillation cuts and maltenes discussed below) were measured by Sanchez-Lemus39. The whole oil properties are summarized in Appendix A.

Distillation Cuts The viscosities of the WC-B-B1, WC-B-A1, US-HO-A1, MX-HO-A1, CO-B-B1, and CO-B-A1 distillation cuts (40 in total) were measured in the cone and plate rheometer at atmospheric pressure and temperatures up to 150°C. For these measurements, the sample was not replaced when the temperature was ramped because there was a limited amount of sample. The viscosity of the distillation cuts was found to be stable as long as the temperature was kept below their boiling point.

The density of the distillation cuts of sample CO-B-A1 were measured in the Anton Paar density meter at temperatures up to 70°C at atmospheric pressure. The same apparatus was employed to measure a single density data point at 15.6°C for the other distillation cuts in order to determine their specific gravity. Densities at different temperatures were not measured due to the limited amount of sample available. The cut properties are summarized in Appendix B.

Maltenes The viscosity and density of maltenes obtained from sample WC-B-B1 were measured at temperatures and pressures up to 175°C and 10 MPa using the capillary viscometer apparatus. The viscosities of the C5-maltenes obtained from samples WC-B-A1, WC-B-A2, US-HO-A1, MX-HO-A1, CO-B-B1, and CO-B-A1 were measured in the cone and plate rheometer at 18 ACS Paragon Plus Environment

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atmospheric pressure at temperatures up to 120°C. The densities of these maltenes were measured in the Anton Paar density meter at atmospheric pressure at temperatures up to 90°C. The maltene properties are summarized in Appendix C.

Partially De-Asphalted Oils WC-B-B3 bitumen was diluted with n-pentane at three conditions (50, 60, and 67 wt% npentane) to obtain three partially deasphalted oils with residual asphaltene contents of 16, 4, and 3 wt%, respectively. The viscosity and density of these samples were measured at atmospheric pressure and temperatures up to 75°C using the cone and plate rheometer and Anton Paar density meter, respectively. The density and viscosity data of the deasphalted oils are provided in Appendix D.

C5-Asphaltenes The viscosities of WC-B-B1 and CO-B-A1 C5-asphaltenes were measured in the cone and plate rheometer at temperatures between 175°C to 200°C at atmospheric pressure and at shear rates between 0.01 s-1 and 10 s-1. The data was collected at these temperatures to ensure that the asphaltenes were completely molten47. The shear rate range was chosen to obtain Newtonian behavior; shear thinning was observed at shear rates higher than 10 s-1.

The density of the WC-B-B1 C5-asphaltenes was determined indirectly from the density of asphaltene/toluene solutions measured in the Anton Paar density meter at atmospheric pressure and temperatures between 25°C and 90°C as described previously. The densities could not be measured at higher temperatures because 90°C is the upper temperature of the apparatus. Instead, the asphaltene densities were linearly extrapolated to the temperatures at which the viscosities were measured. The measured asphaltene densities and viscosities are provided in Appendix D.

In order to validate the density extrapolation, data were collected in the capillary viscometer for one asphaltene/toluene mixture (5 wt% WC-B-B1 C5-asphaltenes) at temperatures from 21 to 175°C (for density) and from 21 to 100°C (for viscosity) all at pressures up to 9 MPa. Note, viscosity data were not collected at higher temperatures because the viscosity was too low for an accurate measurement. The mixture densities were then predicted using the previously 19 ACS Paragon Plus Environment

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extrapolated WC-B-B1 C5-asphaltene densities. Regular solution behaviour was assumed and the asphaltenes were assumed to be incompressible. The density of toluene was obtained from the NIST database48. Figure 3 shows experimental and predicted density of the mixture asphaltenes/toluene. The average and maximum absolute relative deviations are 0.3% and 0.5%, respectively. Hence, the extrapolated asphaltene densities are sufficiently accurate for predicting mixture densities. These data were also used to evaluate the viscosity correlations and are provided in Appendix D.

880 860 840

Density, kg/m3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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820 800 780 50°C 100°C 150°C 175°C predicted

760 740 720 0

2

4 6 Pressure, MPa

8

10

Figure 3. Measured and predicted density of a mixture of 5 wt% C5-asphaltenes in toluene.

5.2 Datasets Development Dataset 1: Distillation Cuts (this Study) and Pure Hydrocarbons (from Literature) This dataset was used to develop correlations for the maltene pseudo-component EF model parameters. It includes the EF model parameters, normal boiling point, specific gravity and molecular weight of the distillation cuts from this study and pure hydrocarbons. The normal boiling point and specific gravity are required for the EF model parameter correlations. The molecular weight is required to calculate the density of the distillation cuts from Eq. 25 and is also used to determine the c3 parameter for the EF model for high pressure applications (Eq. 7). The atomic hydrogen-to-carbon ratio was not included in this dataset because it is only used to calculate the viscosity binary interaction parameter in the mass-based mixing rules (Eqs. 9 to 11) 20 ACS Paragon Plus Environment

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and is not required for modeling single pseudo-components. The EF parameters, c2 and ρso, for the distillation cuts were calculated by fitting the correlation to the experimental viscosity data using the calculated density as input. The cut density was determined at any temperature using Eq. 25 with a Rackett compressibility factor fitted to the density at 15.6°C. The EF model parameters for each cut are provided in Table B1 in Appendix B. The EF model parameters for each pure hydrocarbon were determined by fitting the model to measured viscosity data using the measured density as input. The density and viscosity of pure hydrocarbons: normal alkanes (C5 to C36) and assorted pure hydrocarbons were gathered from the literature48,49. The assorted pure hydrocarbon group includes aromatics and alkylbenzenes (17components), fused aromatics (10 components), non-fused aromatics (11 components) alkyl cycloalkanes (33 components), branched alkanes (16 components), fused naphthenics (18 components), and non-fused naphthenics (13 components). The EF model parameters for the pure hydrocarbons are provided in the Supporting Information.

Development Dataset 2: C5-Asphaltenes (this Study) This dataset was used to determine the EF model parameters of C5-asphaltenes. It includes density and viscosity data for C5-asphaltenes from the WC-B-B1 and CO-B-A1 oils. The fitting of the EF model parameters is discussed later.

Test Dataset 1: Distillation Cuts (from Literature) This dataset was used to test the proposed correlations for the EF model parameters for maltene pseudo-components. It includes literature data for over 120 distillation cuts collected from the 19 crude oils listed in Table 2. In most cases, the data reported for each distillation cut were the kinematic viscosity versus temperature at atmospheric pressure, and physical properties such as normal boiling point and specific gravity. Critical temperature, critical pressure, and molecular weight were calculated from the Lee-Kesler correlations37. The density of the cuts was calculated from Eq. 25 using calculated critical properties and molecular weight, as described for Development Dataset 1. The calculated density was also used to convert the reported kinematic


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viscosities to dynamic viscosities. Each distillation cut were modeled as a single pseudocomponent with EF model parameters determined from proposed correlations (presented later).

Table 2. Summary of range of selected physical properties of the distillation cuts in Test Dataset 1. Crude Oil Alaska North Slope Altamont Arab Berry Arabian Light Boscan California Iranian Export Kern River Light Valley Maya Midway Special Minas Sumatra Oklahoma Pennsylvania Safania Sahara San Joaquin Valley Stabilized Arabian Waxy Crude Oil Wyoming Cracked Residue

Number of Cuts 11 11 3 8 3 3 4 3 3 3 3 4 3 3 2 1 9 3 3 3 3

SG Range 0.80-0.98 0.76-0.88 0.75-0.84 0.77-0.99 0.81-0.88 0.78-0.81 0.71-0.80 0.95-1.01 0.79-0.86 0.82-0.95 0.74-0.87 0.69-0.81 0.75-0.82 0.74-0.70 0.74-0.78 0.83 0.85-1.00 0.73-0.78 0.76-0.82 0.76-0.82 0.99-1.02

Tb Range, °C 196-593 196-649 149-301 156-411 182-290 137-187 90-223 393-621 159-252 232-387 100-245 83-266 137-237 137-237 144-201 289 196-537 118-196 124-217 137-237 404-411

Viscosity Range, mPa.s 57-0.4 13-0.5 0.4-14 0.4-3.0 0.7-4 0.3-0.9 0.3-1.2 44-1x106 0.6-2.1 1-14 0.4-1.9 0.3-1.1 0.3-4 0.3-1.5 0.5-1 1.7-5 0.9-1700 0.4-0.9 0.4-1.2 0.3-1.6 205-1920

Reference 50 50 51 53 51 51 51 52 51 52 51 51 51 51 51 54 50 51 51 51 10

Test Dataset 2: Maltenes (this Study) This dataset was used to assess the proposed viscosity modeling methodology for maltenes, and includes viscosity and density data of C5-maltenes obtained from the WC-B-B1, WC-B-A1, USHO-A1, MX-HO-A1, CO-B-B1, CO-B-A1 oils (the oils from which the distillation cuts were obtained) and from the WC-B-A2 oil. The maltenes were characterized as a set of pseudocomponents as described previously. The EF model parameters of each pseudo-component were determined from the proposed correlations. 22 ACS Paragon Plus Environment

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Test Dataset 3: Whole and Partially De-Asphalted Oil, and Asphaltenes in Toluene (This Study) This dataset was used to assess if crude oil viscosity could be predicted from the known maltene and asphaltene contents and the EF model parameters determined for the maltenes and the asphaltenes. It includes density and viscosity data collected in this study for: 1) a whole heavy oil WC-B-B1; 2) a partially deasphalted heavy oil WC-B-B3, and: 3) an asphaltene/toluene mixture. In this case, the oils were characterized as a pseudo-binary mixture of maltenes and C5asphaltenes. The EF parameters of the maltenes were determined by fitting their measured density and viscosity. The EF parameters for the asphaltenes are discussed later. The dataset also included the measured H/C ratios of the maltenes and the asphaltenes which were required to determine the binary interaction parameter.

Test Dataset 4: Heavy Oils and Bitumens (this Study) This dataset was used to assess the proposed viscosity modeling methodology for whole oils. It includes the density and viscosity of the oil samples used to provide the distillation cuts for the Development Dataset 1 (WC-B-B1, WC-B-A1, US-HO-A1, MX-HO-A1, CO-B-B1 and CO-BB1). The same type of data are also included for the EU-HO-A1, WC-B-A2, WC-B-A3 and MECV-A1 oils. The maltenes were characterized as a set of pseudo-components and the asphaltenes as single component. The EF model parameters of the pseudo-components were determined from the proposed correlations. The parameters for the asphaltenes are presented later. The H/C ratios required to determine the binary interaction parameter between the asphaltenes and maltenes were determined from a correlation (Eq. 2) and therefore H/C data were not required for this dataset.

Test Dataset 5: Crude Oils (From Literature) This dataset provided an independent test of the viscosity modeling methodology. Viscosity and density of four crude oils at atmospheric pressure was collected from the literature. The selected crude oils were chosen because a distillation essay was also reported. For these fluids, the distillation assays were performed on the entire oil, not just the maltenes, and the asphaltene content was not always reported with the data. When the asphaltene content was not reported, it was obtained from other publications on the same oil. The distillation assay was extrapolated to 23 ACS Paragon Plus Environment

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Page 24 of 65

characterize the maltenes and the asphaltenes were treated as a single pseudo-component, as described for Test Dataset 4.

Table 3 presents a summary of some physical properties of the crude oils grouped in the independent dataset. The asphaltene contents of crude oils Alaska North Slope and San Joaquin Valley were not reported in the work from which distillation assay, viscosity and density were taken but rather by McLean and co-workers

55

who used samples from the same regions. These

samples have similar specific gravity and viscosity at 37.7°C as those reported in the original source. Similarly, Castellanos-Diaz et al.9 reported distillation data for the Athabasca bitumen sample while Badamchi-Zadeh et al.56 reported density and viscosity for the same bitumen sample.

Table 3. Selected physical properties of the crude oils in the Test Dataset 5. Crude Oil Alaska North Slope Athabasca Boscan San Joaquin Valley

SG

C5-Asph. wt%

Viscosity mPa.s

Source

0.891 1.007 0.993 0.977

3.35 22.7 18 4.57

28.1 (15.6°C) 30,090 (35.5°C) 485,500 (15.6°C) 1,376 (40°C)

50, 55 9, 56 57 50, 55

6. Results and Discussion 6.1 Development of Correlations for Maltene Pseudo-Component EF Model Parameters As discussed previously, the heavy oils are each characterized as a set of maltene fractions plus a single asphaltene fraction. The objective is to find correlations for the EF model parameters of the maltene cuts and to determine the model parameters for the asphaltene fraction. This section focuses on the maltenes; the asphaltenes are discussed later. There are three EF model parameters (c2, c3, ρso) to be determined. The parameter c3 was calculated from Eq. 7 and was found to provide satisfactory predictions for the higher pressure viscosity data and therefore was not modified. The following steps were taken to develop correlations for the c2 and ρso parameters: 24 ACS Paragon Plus Environment

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1. Validate the accuracy of input density. Since the accuracy of the EF model depends on the accuracy of the input density, the accuracy of the Rackett correlation for the maltene cut densities was evaluated before proceeding to the correlations. 2. Develop a correlation for the c2 parameter. Since the maltene characterization is based on a distillation assay, the boiling point was selected as the main input parameter. However, boiling point alone was insufficient to obtain a good correlation and specific gravity was added as a second input parameter. Note, these two physical properties roughly characterize molecular energy and size respectively, and have been widely used as inputs to crude oil property correlations31. 3. Develop a correlation for the ρso parameter. The EF model is very sensitive to the ρso parameter and a sufficiently accurate correlation of ρso to the known physical properties was not found. Instead, a separate correlation was developed for a synthetic viscosity data point at a single temperature and atmospheric pressure. The EF model equation (Eq. 4) was then rearranged to obtain an expression for ρso which incorporated the synthetic data point. Each step is discussed in detail below. The combined correlations are then evaluated on the Development Dataset 1 and Test Dataset 1 viscosities. Note, the following metrics are used to assess the model errors: 00

2,3456 +2.57!

∑) 1

Average absolute relative deviation (%)

--./ =

Maximum absolute relative deviation (%)

8-./ = 100max 1

Bias (%)

=>?@ =

)

2,3456

1

2,3456 +2.57!

00 )

∑)

2,3456

1

2,3456 +2.57! 2,3456

where subscripts i, n, pred, and meas denote one data point, the total number of data points, a predicted value, and the measured value.

Validation of Rackett Correlation Densities for Maltene Cuts Ideally, the density of each cut would be measured at the conditions of each viscosity measurement. However, the sample volumes were limited and the experimental density data for most of the cuts in this study were only collected at 15.6°C. As discussed previously, the cut densities at any temperature were determined from the Rackett correlation tuned to match the 25 ACS Paragon Plus Environment

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one measured density. In order to validate this approach, the density of the six distillation cuts from the bitumen CO-B-A1 were measured from 20 to 70°C at atmospheric pressure. The correlated densities are compared to the measured values in Figure 4. The average absolute relative deviation (AARD) and maximum absolute relative deviation (MARD) are 0.1% and 0.3% respectively.

The EF model using the calculated densities fits the distillation cut viscosity data with an AARD and MARD of 2% and 22%, respectively, compared with an AARD and MARD of 1.8 and 20% using the measured densities. Therefore, we conclude that the densities from the tuned Rackett correlation are sufficiently accurate for the viscosity modeling at atmospheric pressure. 1000 980 960

Density, kg/m3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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940 920 900 880 Tb=311°C, SG=0.900 Tb=358°C, SG=0.924 Tb=389°C, SG=0.944 Tb=404°C, SG=0.961 Tb=441°C, SG=0.971 Tb=487°C, SG=0.979 predicted

860 840 820 800 20

30

40 50 Temperature, °C

60

70

Figure 4. Measured and calculated densities of the distillation cuts from CO-B-A1 bitumen.

Correlation of EF Model Parameter c2 The symbols in Figure 5 shows the c2 parameters of Development Dataset 1 versus normal boiling point (Tb). Both distillation cut and hydrocarbon parameters are shown and the parameters for the distillation cuts are similar to the majority of the aromatic compounds, in agreement with the high aromatic content that have been reported for heavy oil distillation cuts52. In general, the c2 parameter increases monotonically for each well-defined chemical family but decreases with aromaticity when moving along a constant boiling point line. Hence boiling point alone is insufficient for correlating this parameter. One approach to improve the correlation is to 26 ACS Paragon Plus Environment

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choose a reference family for a correlation of c2 to Tb, and then determine a departure function based on a second property such as specific gravity. The c2 parameter is then given by: c 2 = c2o − ∆c 2

(27)

where c2o is the reference value and Δc2 is a departure value which captures the difference of c2 values between a component and the reference substance with the same normal boiling point.

Normal alkanes have been used as a reference system to predict viscosity, critical properties of distillation cuts13,58, and EF fluid-specific parameters for pseudo-components27. However, as the normal boiling point and molecular weight increase, the properties of the normal alkanes highly deviate from those of the pseudo-components and the prediction of their properties becomes challenging. We found that better results were obtained when the distillation cuts were used as the reference system rather than pure hydrocarbons. This system is not a true chemical family but represents the mono-to polycyclic aromatic progression typical of heavy petroleum fluids.

The reference function was obtained by fitting the distillation cut data from Development Dataset 1. Note that the viscosity and specific gravity of light distillation cuts (and hence their EF model parameters) are similar to those of n-alkanes and; therefore, the reference function was constrained to approach n-alkane values at low boiling points (c2 0.199 as the boiling point goes to 0°C). The proposed reference function is given by: c 2o = 1 .882 × 10 −3 exp (0.0058855 Tb ) + 0.3674 Tb−0.1177

(28)

where Tb is the normal boiling point temperature in K. The line in Figure 5 shows the reference function. While this correlation alone may be sufficient for these heavy, highly aromatic distillation cuts, it will likely deviate for lighter, more paraffinic cuts. Light paraffinic cuts have properties similar to mixtures of alkanes with relatively small amounts of cyclic and aromatic compounds. Figure 5a shows that the correlation does not accurately represent the alkanes and cyclics. Therefore, a departure function was developed based on specific gravity in order to account for differences in cut chemistries.


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0.6

0.6

cuts alkanes branched alkanes alkyl cycloalkanes alkylbenzenes reference

0.5

cuts non-fused aromatics fused aromatics non-fused naphthenics fused naphthenics reference

0.5

0.4

0.4

0.3

c2

c2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.3

0.2

0.2

0.1

0.1

(a)

(b)

0

0 0

200 400 600 Normal Boiling Point, °C

800

0


800

Figure 5. Parameter c2 versus normal boiling point for Development Dataset 1: (a) alkanes, branched alkanes, alkyl cycloalkanes and alkylbenzenes; (b) non-fused aromatics, fused aromatics, non-fused naphthenics and fused naphthenics. Distillation cuts are included in (a) and (b).

The first step in developing the departure function is to find an expression for the specific gravity of the reference distillation cuts. The measured specific gravities of the distillation cuts were correlated to their normal boiling point with the following two constraints. First, the reference specific gravity must tend to that of normal alkanes at low boiling point because the reference function for c2 tends to the n-alkanes at low boiling points. Hence, the specific gravity of the reference family must also tend to that of n-alkanes to ensure that the value of the departure function is zero. Second, at high boiling points, the specific gravity approaches an asymptote. This maximum value was set equal to the average measured specific gravity of the C5asphaltenes from the WC-B-B1 bitumen (SGmax=1.098). This specific gravity is comparable to those reported elsewhere35,59. The constrained fitted equation for the reference specific gravity is given by:

[

(

SG o = 1.098 1 − exp − 0.00148 Tb1.1128

)]

(29)

where SGo is the specific gravity of the reference distillation cut. As indicated by the line in Figure 6a, the proposed correlation fits the specific gravity data of the reference distillation cuts with an AARD and MARD of 0.8% and 2%, respectively.


Page 29 of 65

1.2

0.15

1.1

0.10

1.0

pure hydrocarbons cuts fitted

0.05

∆c2

0.9

SG

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.8

alkanes branched alkanes non-fused aromatics fused aromatics non-fused naphthenics fused naphthenics alkyl cycloalkanes alkylbenzenes cuts reference

0.7 0.6

(a) 0.5 0

200 400 600 800 Normal Boiling Point, °C

1000

0.00 -0.05 -0.10

(b) -0.15 -0.3

-0.2

-0.1

0 ∆SG

0.1

0.2

0.3

Figure 6. The two parts of the correlation for the c2 parameter: a) the reference function shown with the specific gravity of the cuts and pure hydrocarbons in Development Dataset 1; b) Δc2 versus ΔSG.

The final step is to determine the departure values, (∆c2 = c2o-c2 and ∆SG = SGo-SG) and find a correlation between them. The following equation was found to fit the data to within ±30%, Figure 6b: ∆c 2 = −2.01417∆SG 2 − 0.1324∆SG

(30)

The complete correlation for c2 is then given by Eqs. 28 to 30. The deviation between fitted and correlated c2 parameters for Development Dataset 1 is shown in Figure 7. Although the deviations in the calculation of Δc2 seem to be high, the actual difference between fitted and calculated c2 is not enough to cause large deviations in the viscosity. The AARD and MARD in the predicted c2 values were 10 and 30%, respectively for pure hydrocarbons, including nalkanes, and 5 and 20% respectively for the heavy oil distillation cuts. Note the correlation was developed using the data presented in Figure 5 and its validity for boiling points lower than 0°C was not investigated.


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0.10

c2 Deviation = fitted-predicted

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.05

0.00

-0.05

-0.10 pure hydrocarbons cuts

-0.15 -0.2

-0.1

0 ∆SG

0.1

0.2

Figure 7. Relative deviation of predicted c2 parameter versus ΔSG for Development Dataset 1.

Correlation of EF Model Parameter: ρso As mentioned, the EF model is highly sensitive to the ρso value; therefore, the uncertainty in ρso must be kept to a minimum to produce accurate modeling results. Various forms of direct correlations were attempted for this parameter but all gave unacceptably high errors. Instead, an indirect approach was developed where ρso is calculated with the EF model (using the correlated c2 parameter) from a single viscosity data point at a reference temperature and atmospheric pressure, as follows:

      c  o 2   ρ s = ρT 1 + ln 1 +   µT − µ o     ln 1 +    0.165     

1

0.65

(31)

where ρT and µT are the density and viscosity in kg/m3 and mPa.s, respectively, at a reference temperature T and µo is the dilute gas viscosity. The atmospheric pressure viscosity data point, µT, can be measured or predicted using a correlation. Note that Eq. 31 is the EF model written explicitly in terms of ρso. The Twu13, Abbott12 and API60 correlations were assessed for the prediction of µT. The output of the correlations is the kinematic viscosity and the density is required to determine the dynamic 30 ACS Paragon Plus Environment

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Energy & Fuels

viscosity. The inputs in all cases are the normal boiling point and specific gravity, and the correlations only predict the viscosity at two temperatures, 37.7°C and 98.8°C, at atmospheric pressure. The temperature of 37.7°C was selected as the reference temperature. To test the accuracy of these correlations, the predicted viscosity data point at 37.7°C was compared to the measured value for the heavy oil distillation cuts of this study. In general, the viscosity of the heavy oil distillation cuts at 37.7°C was predicted with average deviations of 60%, 100% and 70% with the Twu, Abbott, and API correlations, respectively. The high deviations are not surprising considering that the correlations were developed based on conventional oil distillation cuts.

The Twu correlation was modified in order to improve the accuracy of the viscosity prediction at 37.7°C for heavy cuts. In the original correlation, the viscosity of a cut is calculated as a departure from the viscosity of n-alkanes. Here, the viscosity at 37.7°C of a cut or pure hydrocarbon is calculated as a departure from the viscosity of the cuts in the Development Dataset 1 at the same temperature at atmospheric pressure. Hence the experimental viscosity of the heavy oil cuts at 37.7°C was used to develop the reference function defined as:

[ (

)]

log log ν 37o .7 + 1 = ( 0 .0036 Tb − 2 .0942 ) 0 .95

Tb

200

(32)

where ν37.7 o and Tb are the reference kinematic viscosity in cSt at 37.7°C and the normal boiling point in K respectively. Note that the form of Eq. 32 is different from the original reference function proposed by Twu at 37.7°C. Figure 8 shows that the new reference function is consistent with the original correlation for light cuts but follows the trend of the heavy cut viscosities.

The departure function was retuned against the data collected in this study for pure components to obtain the following equations:

  250  250  1 + 2 f  = lnν 37o .7 +  lnν 37.7 + Tb  Tb  1 − 2 f   f = − x ∆SG + 53.2315

  

∆SG 2 Tb0.5

2

(33)

(34)


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x = 3.7012 −

73.02779 Tb0.5

(35)

where ν37.7 is the kinematic viscosity in cSt of the distillation cut at 37.7°C and atmospheric pressure. ΔSG (∆SG = SGo-SG) is determined as described in the previous section with reference specific gravity, SGo, calculated from Eq. 29. The AARD and MARD of modified correlation for the viscosity at 37.7°C are 29% and 90%, respectively, for the pure hydrocarbons and 35% and 95%, respectively, for the distillation cuts in Development Dataset 1. Note that the correlation presented here is applicable to cuts and pure hydrocarbons. The original correlation by Twu has an extra set of equations for pure hydrocarbons. 100000

Kinematic Viscosity @ 37.7°C, cSt

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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10000

1000

100

10 pure hydrocarbons cuts reference Twu reference this work

1

0.1 0


800

Figure 8. Kinematic viscosity at 37.7°C of heavy oil distillation cuts and pure hydrocarbons from Development Dataset 1 versus normal boiling point. The new reference kinematic viscosity function (this study) as well as original reference kinematic viscosity developed by Twu13 are also shown.

Testing on Distillation Cuts The proposed correlations were used to calculate the EF model parameters and predict the viscosity of the distillation cuts in Development Dataset 1 and in Test Dataset 1. Note that the densities of the distillation cuts were calculated from the modified Rackett correlation after tuning to match the specific gravity of the cut, as described previously. The viscosities of the distillation cuts from Development Dataset 1 were “predicted” with an overall AARD, MARD 32 ACS Paragon Plus Environment

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and bias of 49, 106 and 28%, respectively. The viscosities for the distillation cuts from Test Dataset 1 were predicted with an overall AARD, MARD and bias of 24, 130, and -10%, respectively, Table 4. A typical example of the predicted cut data is provided in Figure 9.

The deviations are comparable to the errors in estimating the viscosity at 37.7°C indicating that the single point viscosity prediction (Eq. 33 to 35) is the main source of error in the overall correlation. In general, the EF model with correlated parameters tends to under-predict the viscosity of heavy cuts with higher deviations for high boiling point cuts, as indicated in Figure 10a. Although the correlation was developed from heavy oil distillation cut data, it provided better AARD for the lighter cuts that made up the test dataset. It appears that the departure function based on pure hydrocarbon data is able to compensate for the different chemistry of the lighter cuts compared with the heavier cuts, as indicated in Figure 10b.

Table 4. Summary of the deviations and bias in the predicted viscosity of the distillation cuts from Test Dataset 1. Crude Oil Alaska North Slope Altamont Arab Berry Arabian Light Boscan California Iranian Export Kern River Light Valley Maya Midway Special Minas Sumatra Oklahoma Pennsylvania Safania Sahara San Joaquin Valley Stabilized Arabian Waxy Crude Oil Wyoming Cracked Residue

AARD % 33 31 8 10 22 14 28 62 32 16 20 25 28 24 20 8 16 28 33 16 22

MARD % 130 100 31 47 38 29 44 83 46 29 51 36 58 50 35 12 63 40 41 28 35

Bias % -21 -27 -3 -4 -22 -13 -23 62 -32 -7 16 -25 -28 -24 -20 8 5 -28 -33 -16 20


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10000

SG=0.915, Tb=313°C SG=0.936, Tb=350°C SG=0.960, Tb=400°C SG=0.967, Tb=430°C predicted

Viscosity, mPa.s

1000

100

10

1 0


150

Figure 9. Measured and predicted viscosities for the cuts obtained from WC-B-A1 bitumen at atmospheric pressure.

1.E+7

100

Predicted Viscosity, mPa.s

80 60

Relative Deviation, %

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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40 20 0 -20 -40 -60 -80 -100 300

1.E+3

1.E+1

(b)

(a) 250

1.E+5

350 400 450 500 550 Normal Boiling Point, °C

600

1.E-1 1.E-1

1.E+1 1.E+3 1.E+5 Measured. Viscosity, mPa.s

1.E+7

Figure 10. Illustration of errors in the predicted viscosities of distillation cuts: a) relative deviation (100x(Measured – Predicted)/Measured) versus normal boiling point for the cuts in Development Dataset 1; b) predicted versus measured viscosities for Test Dataset 1.


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Testing on C5-Maltenes Another test for the proposed methodology is the ability to predict the viscosity of the maltenes from a pseudo-component characterization. This prediction depends on both the correlations for the pseudo-component EF model parameters and the EF model mixing rules. The proposed methodology was tested on the maltenes in Test Dataset 2. The measured and predicted viscosities for maltenes are shown in Figure 10 as an example. Overall, when experimental density was the input to the viscosity model, the viscosity of the maltenes was predicted with an overall AARD, MARD, and bias of 62, 90, and 62%, respectively. When predicted density was the input, the overall AARD, MARD, and bias were 59, 91, and 55%, respectively, Table 5. In contrast, when the EF model was fitted directly to the measured viscosity, the overall AARD, MARD and bias were 2, 11, and 1%, Table 6.

The predictions are significantly less accurate than directly fitting the data and, in general, the viscosity of the maltenes is under-predicted. The density prediction is not the main source of error because the results with measured and predicted densities are similar. The magnitude of the error is similar to the errors observed when predicting the cut viscosities. Hence, much of the error can be attributed to the EF parameter correlations. It is also possible that binary interaction parameters used to predict the maltene viscosity were incorrect; however, the values required to fit the maltene viscosity were unrealistically large compared to the binary interaction parameters for all other similar materials43. The maltene tests indicate that the errors in predicting the viscosity of a whole oil without any tuning could be in the order of 60%. While this potential error is significant, the untuned model captures the correct trends with pressure and temperature, suggesting that tuning to a single data point should be sufficient to produce an accurate viscosity model.


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100000 Data input: Exp. Dens. input: Rackett dens.

50°C 100°C 175°C input: Exp. Dens. input: COSTALD dens.

1000

Viscosity, mPa.s

10000

Viscosity, mPa.s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1000

100

100

10

10

(b)

(a)

1

1 20

40


100

0

120

2

4 6 Pressure, MPa

8

10

Figure 10. Measured and predicted viscosity of C5-maltenes: a) WC-B-A2-DAO at atmospheric pressure; b) WC-B-B1-DAO. The solid line is the EF with the measured density (Exp. Dens.) as input and the dashed line is the EF with predicted density as input. DAO stands for deasphalted oil. Recall that COSTALD becomes Rackett correlation at atmospheric pressure.

Table 5. Calculated EF model parameters for C5-maltenes, and the average and maximum relative deviation and bias of the predicted viscosity with experimental and predicted density as input. DAO stands for deasphalted sample according to procedure described previously.

C5-Maltenes

c2

Used for correlations WC-B-B1-DAO 0.3115 WC-B-A1-DAO 0.3809 US-HO-A1-DAO 0.2835 MX-HO-A1-DAO 0.3065 CO-B-B1-DAO 0.2697 CO-B-A1-DAO 0.3809 Not used for correlations WC-B-A2-DAO 0.3653

ρso kg/m³

EF with Experimental Density AARD MARD Bias % % %

EF with Predicted Density AARD MARD Bias % % %

1037.7 1032.1 1010.9 1019.6 1013.9 1032.1

50 51 83 73 63 51

55 63 90 79 65 63

50 51 83 74 63 51

47 42 83 72 83 42

56 61 90 79 91 61

22 42 83 72 83 42

1045.1

44

48

44

14

30

12


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Energy & Fuels

Table 6. Fitted EF model parameters for C5-maltenes, and the average and maximum relative deviation and bias of the fitted viscosity. The measured density was used to fit the EF to viscosity data. DAO stands for deasphalted sample according to procedure described previously. C5-Maltenes Used for correlations WC-B-B1-DAO WC-B-A1-DAO US-HO-A1-DAO MX-HO-A1-DAO CO-B-B1-DAO CO-B-A1-DAO Not used for correlations WC-B-A2-DAO

c2

ρso kg/m³

AARD %

MARD %

Bias %

0.3964 0.4042 0.4017 0.4214 0.4338 0.4042

1047.3 1030.7 1013.3 1027.5 1033.1 1030.7

2 3 1 3 2 3

4 11 4 5 3 11

0 3 1 0 2 3

0.4114

1048.3

2

7

0

6.2 EF Model Parameters of C5-Asphaltenes The EF fluid-specific parameters for C5-asphaltenes were estimated by fitting the correlation to the viscosity data (and density data as the input) for the C5-asphaltenes in Development Dataset 2, Figure 11. Although the two asphaltene samples were obtained from heavy oils from different geographical locations, they both have similar viscosity values. Therefore, it was assumed that all C5-asphaltenes have the same EF fluid-specific parameters when they are modeled as a single component. The EF model fitted the experimental viscosity data with an AARD and MARD of 5% and 24%, respectively. The fitted parameters c2 and ρso were 0.9057 and 1113.7 kg/m³, respectively.


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1.E+6

WC-B-B1 CO-B-A1 fitted

Viscosity, mPa.s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 65

1.E+5 170

180 190 Temperature, oC

200

Figure 11. Viscosity versus temperature of molten C5-asphaltenes from the WC-B-B1 and COB-A1 bitumens. The viscosity was measured in a shear rate range of 0.01 s-1 to 10 s-1. Note this is a Cartesian plot.

Testing the Asphaltene EF Model Parameters To test the asphaltene EF model parameters, the accuracy of the model was evaluated when asphaltenes were part of the mixture to be modeled. Any errors in the asphaltene parameters would be expected to propagate to the viscosity prediction for the mixture. The parameters were first tested on the simplest possible mixture: a 5 wt% solution of asphaltenes in toluene from Test Dataset 3. The measured density was used as the input. The EF model parameters for toluene were taken from Ramos-Pallares et al.43 The EF model parameters for the mixture were calculated using the mass-based mixing rules with an interaction parameter calculated from Eq. 12 to 18 using the H/C ratio of 1.192 measured for the WC-B-B1 C5-asphaltenes. The molecular weight of the asphaltenes for the calculation of c3 from Eq. 7 was estimated from the known mass fractions of maltenes and asphaltenes and the known molecular weight of the whole oil and the maltenes (MWoil = 558 g/mol, MWmaltenes = 483 g/mol). To date, Eq. 7 has only been used to estimate c3 parameters for pure hydrocarbons and distillation cuts. However, the results shown here suggest that the calculated value is suitable for the modeling of asphaltenes represented as a single component.


Page 39 of 65

The EF model predictions are compared with the experimental data at 9 MPa in Figure 12. The viscosity of toluene is also shown for comparison purposes. The viscosity of the mixture was predicted with an AARD, MARD and bias of 4, 9 and 0.6%, respectively. The accuracy of the prediction demonstrates that the asphaltene EF model parameters determined from molten asphaltenes can be applied to simple mixtures.

1.1

Data toluene fitted predicted

0.9

Viscosity, mPa.s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.7

0.5

0.3

0.1 0

20

40 60 80 Temperature, °C

100

120

Figure 12. Viscosity versus temperature for a mixture of 5 wt% C5-asphaltenes in toluene at 9 MPa. The toluene data are from NIST database48.

The EF model parameters for the asphaltenes were next tested on viscosity data for whole WCB-B1 bitumen from Test Dataset 3. In this case, the bitumen was modeled as a two component mixture of maltenes and asphaltenes and the measured density was used as the input to the EF model. The maltenes were treated as a single component to avoid introducing error from the characterization procedure. The EF fluid-specific parameters for the maltenes were determined from experimental viscosity and density data at atmospheric pressure (c2=0.3959, ρso=1047.2 kg/m3). The EF fluid-specific parameters for the heavy oil were calculated using the mass-based mixing rules. The binary interaction parameter was calculated from Eq. 12 to 18 using the measured specific gravities (SGmal=0.986, SGasph=1.098) and H/C ratios for maltenes and asphaltenes (H/Cmal =1.533, H/Casph=1.192). Note, the asphaltenes from this oil were part of the dataset used to determine the asphaltene EF model parameters.


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Figure 13a shows that the model predicts the viscosity of the whole bitumen with an AARD, MARD and bias of 20, 80 and -20%, respectively. In comparison, the EF model directly fitted to bitumen viscosity data at atmospheric pressure has an AARD, MARD and bias of 8, 16 and 1%, respectively. Note that the maximum deviation was found at room temperature for which large uncertainties in the density measurement have been noted. The small loss in accuracy with the model predictions may be caused by inaccuracy in the predicted binary interaction parameters. The satisfactory accuracy of the prediction indicates that the EF model parameters determined for the asphaltenes can be applied as part of a petroleum mixture without modification. The results also demonstrate that, for viscosity modeling purposes, asphaltenes in a crude oil and asphaltenes dissolved in a hydrocarbon solvent can be treated in the same way, even though they may self-associate differently.

10000000

1000000

Bitumen Maltenes Asphaltenes fitted predicted

1000000

16 wt% 4 wt% 3 wt% Maltenes fitted predicted

100000

100000

Viscosity, mPa.s

Viscosity, mPa.s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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10000 1000 100

10000

1000

10

(a)

(b)

100

1 0

50


250

20


80

Figure 13. Measured and predicted viscosity of: a) bitumen and its C5-maltenes and C5asphaltenes at 0.1 MPa; b) partially deasphalted WC-B-B3 bitumen. Mass percentage in the label corresponds to asphaltene content.

Recall that the asphaltenes were treated as a single component even though they are a complex multi-component mixture. Therefore, partially deasphalted oils from the WC-B-B3 bitumen (Test Dataset 3) were examined to determine the sensitivity of the model predictions when the asphaltenes are fractionated. The partially deasphalted samples were modeled as a two pseudocomponent mixture of maltenes and asphaltenes, as described for the whole bitumen test. The EF 40 ACS Paragon Plus Environment

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model parameters for the asphaltenes were not altered. Figure 13b shows that the model predicts the viscosity of the partially deasphalted bitumens with an AARD, MARD, and bias of 12, 33%, and 4%, respectively. In comparison, the data were fitted directly with the EF model and the AARD, MARD, and bias were 3, 5% and 0.5%, respectively. Hence, using a single set of EF model parameters for the asphaltenes provides satisfactory viscosity predictions even when the asphaltenes are fractionated. It appears that the effect of asphaltenes on the viscosity does not significantly depend on small differences in their molecular weight, self-association, or structural configuration in the crude oil.

6.3 Predicting and Tuning the Viscosity of Crude Oils Viscosity Prediction The proposed correlations and modeling approach were tested on the whole oils from Test Dataset 4. Note, four of the 10 oils in this dataset (WC-B-A2, WC-B-A3, EU-HO-A1, and MECV-A1) were not used to develop the EF model parameter correlations. To predict the viscosity of any crude oil using the EF model only the distillation curve, the asphaltene content, and the specific gravity and molecular weight of the whole oil are required. Either experimental or predicted whole oil density can be used as input and here both are evaluated. The density of the whole oil was predicted as described previously.

The oils were characterized as described previously and as shown in the supporting information. The boiling point curve was extended over the entire maltene fraction following a Gaussian extrapolation. The maltene fraction was split into pseudo-components and their properties calculated from existing correlations. The EF parameters, c2 and ρso, for each pseudo-component were calculated using the proposed correlations (Eq. 27 to 35). The EF parameters of the single component asphaltene fraction were set to c2 = 0.9057 and ρso = 1113.7 kg/m³. The c3 parameter was calculated for each pseudo-component and the asphaltene fraction using Eq. 7. The H/C ratio was calculated for each pseudo-component and asphaltene fraction using Eq. 2. Finally, the EF parameters for the whole crude oil were calculated by combining those of the pseudocomponents and the asphaltene fraction using the mass-based mixing rules (Eq. 9 to 11) with binary interaction parameters determined from Eq. 12 to 18.


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Figure 14 shows the viscosity predictions for the WC-B-A2 bitumen using predicted densities as the input (solid line). Note, bitumen WC-B-A2 was not used to develop the EF parameter correlations or to tune the asphaltene density correlation (Eq. 26). The maltene fraction was modeled using 12 pseudo-components. The AARD and MARD were 31 and 38%, respectively, when experimental densities were used as input and 37 and 49%, respectively, when predicted densities were used as input. In comparison, the AARD and MARD for the model directly fitted to the whole oil data are 2 and 7%, respectively. The untuned predictions are not as accurate as the directly fitted model but follow the correct trends with pressure and temperature. The same behavior was observed for all the oils. For example, Figure 15 shows the measured and predicted viscosity versus temperature for EU-HO-A1 heavy oil, a sample from a different geographical region. Note, that high pressure viscosities were not measured for this oil.

To determine the sensitivity of the viscosity model to the number of pseudo-components in the maltene fraction, the viscosity of the heavy oil EU-HO-A1 at atmospheric pressure was predicted for 1, 3, 4, 6, and 12 pseudo-components using experimental density as input, Figure 15. The EU-HO-A1 heavy oil was not used for any of the model development. The AARD for 1, 3, 4, 6 and 12 pseudo-components were 60, 53, 52, 52, 52 and 52% respectively. 4 pseudo-components are sufficient to minimize the error and significant deviations are only observed for 3 or fewer pseudo-components.


Page 43 of 65

100000

Viscosity, mPa.s

10000 1000 100 10

50°C 100°C 175°C predicted 1-P tuned model 2-P tuned model

1 0.1 0

2

4 6 Pressure, MPa

8

10

Figure 14. Measured and predicted viscosities of WC-B-A2 bitumen. Dashed and dotted lines corresponds to EF predictions after tuning one parameter, c2, and both model parameters, c2 and ρso, respectively. data 1 PC 3 PC 4 PC 6 PC 12 PC 1-P tuned model 2-P tuned model

1000

Viscosity, mPa.s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

100

10 30

40

50

60 70 80 90 Temperature, °C

100 110

Figure 15. The effect of the number of pseudo-components (PC) on the predicted viscosities of EU-HO-A1 bitumen at atmospheric pressure.

The calculated EF model parameters, the deviations, and the bias are provided for all of the oils in Test Dataset 4 in Table 7. The maltene fractions were modeled with 12 pseudo-components. When measured density was used as the input, the overall AARD, MARD, and bias of the crude oil samples in the Test Dataset 4 were 40, 98, and 27%, respectively. When predicted density


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was used as the input, the overall AARD, MARD, and bias were 43, 99, and 29%, respectively. Note that the deviations presented in Table 7 (and all following error tables in this section) were calculated over the entire dataset including data at high pressure. There was no significant difference in the errors between the oils whose cuts were used in the development datasets and those which were not. The deviations with the measured or predicted density as the input are similar, indicating that the proposed method for the prediction of crude oil density is not contributing significantly to the error in the viscosity predictions.

The viscosities were fitted directly with the EF model (using measured density as the input) and the fitted parameters and errors are provided in Table 8. The overall AARD, MARD, and bias of the fitted viscosities were 3.2%, 35%, and +0.5%, respectively. As found for the maltenes, the predictions are significantly less accurate than the fitted model. In addition, the predicted EF parameters, c2 and ρso, are, in general, lower than the fitted values. The deviation in the predicted viscosities are similar to those obtained for the distillation cuts (with no asphaltene content) and it appears that the main source of error is the prediction of the single viscosity data point at 37.7°C for the pseudo-components in the maltene fraction. Nevertheless, the results demonstrate that the characterization approach using maltene pseudo-components and a single asphaltene component can provide crude oil viscosity predictions with an accuracy within ±40%.


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Table 7. Calculated EF model parameters for whole crude oils, and the average and maximum relative deviation and bias of the predicted viscosity.

Oil

c2

Used for correlations WC-B-B1 0.4077 WC-B-A1 0.4002 US-HO-A1 0.3618 MX-HO-A1 0.4241 CO-B-B1 0.4027 CO-B-A1 0.4657 Not used for correlations WC-B-A2 0.4721 WC-B-A3 0.3959 EU-HO-A1 0.3376 ME-CV-A1 0.3335

ρso kg/m³

EF with Measured Density AARD MARD Bias % % %

EF with Predicted Density AARD MARD Bias % % %

1056.3 1041.3 1011.3 1043.9 1038.3 1050.9

20 32 22 98 32 42

30 47 35 98 45 50

12 27 7 98 32 77

29 37 36 99 35 44

85 54 61 99 51 67

24 32 29 99 35 44

1064.4 1046.3 1014.1 956.1

31 26 52 46

38 33 54 62

2 21 42 -46

37 19 53 47

49 35 55 57

37 8 33 -46

Table 8. Fitted EF model parameters for whole crude oils, and the average and maximum relative deviation and bias of the fitted viscosity. The measured density was used to fit the EF to viscosity data. Oil Used for correlations WC-B-B1 WC-B-A1 US-HO-A1 MX-HO-A1 CO-B-B1 CO-B-A1 Not used for correlations WC-B-A2 WC-B-A3 EU-HO-A1 ME-CV-A1

c2

ρso kg/m³

AARD %

MARD %

Bias %

0.5050 0.5091 0.4472 0.6923 0.5143 0.5895

1072.1 1055.1 1026.2 1041.8 1054.1 1064.3

7 2 3 0.7 1 3

20 7 10 1 2 6

4 -0.1 0.1 0 0 -0.1

0.5281 0.4845 0.4214 0.3959

1069.5 1057.2 1024.8 979.3

3 8 1 3

6 32 3 7

-0.2 1 0 -0.1


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Model Tuning If data are available the EF model parameters can be tuned with single multipliers applied to c2 alone or to both c2 and ρso. The parameter c2 was chosen for the single multiplier adjustment because the tuning process converges faster and the outcome is similar for either parameter. In this study, the model was tuned to dead oil atmospheric pressure data. A single viscosity data point was chosen when c2 was adjusted and two data points when c2 and ρso were adjusted. As an example, the single and two parameter tuned viscosities (with measured density used as input) for the bitumen WC-B-A2 and the heavy oil EU-HO-A1 are compared with the predicted viscosities in Figure 14 and 15, respectively. The tuning reduced the overall AARD of both samples to 14% (single parameter) and 6% (two parameter) compared with 42% without tuning.

The model, tuned with a single multiplier for c2 and using measured density as the input, matched the viscosity of the crude oils in Test Dataset 4 with an AARD, MARD, and bias of 17, 56, and 7%, respectively, Table 9. The deviations after tuning are approximately half those obtained for with no tuning. The model, tuned with single multipliers to both c2 and ρso and using measured density as the input, reduced the AARD, MARD, and bias to 4, 21, and -1%, respectively, Table 10. These errors are comparable to errors obtained when directly fitting the data, Table 8.

Table 9. The average and maximum relative deviation and bias of the tuned (single multiplier to c2 parameter only; measured density input) viscosities for Test Dataset 4. NP stands for number of experimental data points in the dataset. Oil

NP

Used for correlations WC-B-B1 25 WC-B-A1 22 US-HO-A1 22 MX-HO-A1 12 CO-B-B1 16 CO-B-A1 13 Not used for correlations WC-B-A2 27 WC-B-A3 27 EU-HO-A1 16 ME-CV-A1 16

c2 multiplier

AARD %

MARD %

Bias %

0.9605 1.0157 0.9560 1.6738 1.0080 1.0542

21 31 25 2 28 21

35 47 56 5 43 39

19 15 -4 -2 28 0.2

1.0410 1.0025 1.0753 0.9462

14 17 14 11

22 32 23 20

12 11 4 -10


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Table 10. The average and maximum relative deviation and bias of the tuned (single multipliers to both c2 and ρso; measured density input) viscosities for Test Dataset 4. NP stands for number of experimental data points in the dataset. Oil

NP

Used for correlations WC-B-B1 25 WC-B-A1 22 US-HO-A1 22 MX-HO-A1 12 CO-B-B1 16 CO-B-A1 13 Not used for correlations WC-B-A2 27 WC-B-A3 27 EU-HO-A1 16 ME-CV-A1 16

c2 multiplier

ρso multiplier

AARD %

MARD %

Bias %

1.1893 1.3036 1.3094 1.6493 1.3026 1.5771

1.0166 1.0148 1.0156 0.9988 1.0167 1.0240

3 4 2 1 2 8

9 9 13 3 6 21

0 -3 2 -0.6 -2 -0.8

1.1643 1.2489 1.2398 1.8028

1.0067 1.0144 1.0100 1.0829

6 7 1 7

18 17 4 17

-9 -6 0.5 5

Testing the Model on an Independent Dataset Finally, the proposed characterization and modeling approach was also evaluated on the four crude oils from the literature in Test Dataset 5. The oils were characterized as described above. Note, the crude oil density at the temperature of the viscosity measurements was not always reported (only the specific gravity of the whole crude oil); therefore, the densities of all the crude oils in this dataset were predicted as described previously.

Figure 16 compares the predicted and tuned viscosities with measured data for the best prediction (Athabasca bitumen) and the worst prediction (Alaska North Slope crude oil). The EF model predicted the viscosity of the Athabasca bitumen with an AARD 8%, almost within the accuracy of the tuned model. The non-tuned predictions for the Alaska North Slope oil have an AARD of 64%. However, tuning substantially improves the model (AARD 5% with single parameter tuning and 0.1% with two parameter tuning). The deviations for all four oils are provided in Table 11. The overall AARD, MARD, and bias were 43, 100, and -19% without tuning, 16, 66, and 5% when c2 was adjusted, and 7, 26, and -0.6% when both c2 and ρso were adjusted.


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100000

100

Data predicted 1-P tuned model 2-P tuned model

Viscosity, mPa.s

10000

Viscosity, mPa.s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1000

100

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Data predicted 1-P tuned model 2-P tuned model

10

10

(a)

(b)

1

1 30

50


130

150

10

20


50

Figure 16. Measured and modeled viscosity versus temperature at atmospheric pressure for Athabasca bitumen (a) and Alaska North Slope crude oil (b). Dashed and dotted lines corresponds to EF predictions after tuning one parameter, c2, and both model parameters, c2 and ρso, respectively.

Table 11. Average and maximum relative deviations and bias of predicted and tuned viscosities for Test Dataset 5. Predicted densities were used as input. Predicted Crude Oil

Tuned c2, ρso

Tuned c2

AARD

MARD

Bias

AARD

MARD

Bias

AARD

MARD

Bias

%

%

%

%

%

%

%

%

%

Alaska North Slope

64

75

-64

5

9

-5

0

0

0

Athabasca

8

43

-8

3

11

-1

3

9

1

Boscan

55

100

-47

19

44

9

22

26

2

San Joaquin Valley

44

61

44

30

60

18

4

10

-4

Conclusions Density and viscosity data were collected for distillation cuts from heavy oils, maltenes, C5asphaltenes, partially deasphalted heavy oils, and whole oils. The data were used to develop and test correlations for the EF viscosity model parameters (c2 and ρs°) of distillation cuts (equivalent to distillation based pseudo-components).


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A methodology was proposed to predict viscosity from a distillation assay with maltenes characterized as a set of pseudo-components and C5-asphaltenes treated as a single component. Densities were predicted using the modified Rackett correlation. The EF model predictions with predicted density as an input were of similar accuracy as those with measured densities as the input. The proposed methodology predicted the viscosity of the oils in the development and test datasets with overall AARDs of 40 and 42%, respectively. Single multiplier tuning of the c2 parameter to a single atmospheric pressure data point reduced the AARDs to 21 and 14%, respectively. Single multiplier tuning of each of the c2 and ρs° parameters (using two atmospheric pressure data points) reduced the AARDs to 4 and 7%, respectively. The latter deviations were almost the same as the deviations from directly fitting the EF model to the data.

The proposed methodology only requires a distillation assay, the asphaltene mass content, specific gravity and molecular weight of the oil to provide a reasonable viscosity prediction. Two atmospheric viscosity data point are sufficient for predictions within experimental error. As few as four maltene pseudo-components are sufficient for a consistent viscosity prediction.

Acknowledgements The authors are grateful to the sponsors of the NSERC Industrial Research Chair in Heavy Oil Properties and Processing: NSERC, Nexen Energy ULC, Petrobras, Shell, Schlumberger, Suncor Energy, and Virtual Materials Group. We also want to thank Mr. Florian Schoeggl from the University of Calgary who helped in the collection of viscosity data from the capillary viscometer.

References (1) World Energy Council: 2010 Survey of Energy Resources. World Energy Council. London, UK, 2010. (2) AEUB, Alberta Energy Reserves 2005 and Supply/Demand Outlook for 2006-2015, ST982006, Alberta Energy and Utilities Board, Calgary, 2006. (3) Masliyah, J.; Czarnecki, J. and Z. Xu, 2011, Handbook on Theory and Practice of Bitumen Recovery from Athabasca Oil Sands, Vol. 1: Theoretical Basis, Kingsley, Calgary. Alberta, Canada. (4) Whitson, C. H.; Brule, M. R. Phase Behavior. Society of Petroleum Engineers, Richardson, Texas, 2000. 49 ACS Paragon Plus Environment

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(5) ASTM D2892, 2009. Standard Test Method for Distillation of Crude Petroleum (15Theoretical Plate Column). (6) Powers, D. P. Characterization and Asphaltene Precipitation Modeling of Native and Reacted Crude Oils. Ph.D Thesis, University of Calgary. Calgary, Alberta, Canada, September 2014. (7) ASTM D2887, 2015. Standard Test Method for Boiling Range Distribution of Petroleum Fractions by Gas Chromatography. (8) Castellanos-Diaz, O. Measurement and Modeling Methodology for Heavy Oil and Bitumen Vapor Pressure. Ph.D Thesis. University of Calgary, Calgary, Alberta, Canada. April, 2012. (9) Castellanos-Diaz, O.; Modaresghazani, J.; Satyro, M. A.; Yarranton, H. W. Modeling the Phase Behavior of Heavy Oil and Solvent Mixtures. Fluid Phase Equilib. 2011, 304, 74-85. (10) Watson, K. M.; Nelson, E. F.; Murphy, G. B. Characterization of Petroleum Fractions. Ind. Eng. Chem.1935, 27, 1460-1464. (11) American Petroleum Institute (API). Technical Data Book – Petroleum Refining. American Petroleum Institute, New York, 1978. (12) Abbott, M. M.; Kaufmann, T. G.; Domash, L. A Correlation for Predicting Liquid Viscosities of Petroleum Fractions. Can. J. Chem. Eng. 1971, 49, 379-384. (13) Twu, C. H. Internally Consistent Correlation for Predicting Liquid Viscosities of Petroleum Fractions. Ind. Eng. Chem. Process Des. Dev. 1985, 24, 1287-1293. (14) Centeno, G.; Sanchez-Reyna, G.; Ancheyta, J.; Munoz J. A. D.; Cardona, N. Testing various Mixing Rules for Calculation of Viscosity of Petroleum Blends. Fuel, 2011, 90, 3561-3570. (15) Hanley, H. J. M. Prediction of the Viscosity and Thermal Conductivity Coefficients of Mixtures. Cryogenics, 1976, 16, 643-651. (16) Pedersen, K. S.; Fredenslund, A.; Christensen, P. L. Viscosity of Crude Oils. Che. Eng. Sci. 1984, 39, 1011-1016. (17) Mehrotra, A. K.; Svrcek, W. Y. Corresponding States Method for Calculating Bitumen Viscosity. J. Can. Pet. Technol. 1987, 26, 60-66. (18) Quinones-Cisneros, S.E.; Zeberg-Mikkelsen, C.K.; Stenby, E. H. The Friction Theory (fTheory) for Viscosity Modeling. Fluid Phase Equilib. 2000, 169, 249-276. (19) Quinonez-Cisneros, S.E.; Zeberg-Mikkelsen, C.K.; Stenby, E.H. One Parameter Friction Theory Models for Viscosity. Fluid Phase Equilib. 2001, 178, 1-16. (20) Quinonez-Cisneros, S.E.; Zeberg-Mikkelsen, C.K.; Stenby, E.H. The Friction Theory for Viscosity Modeling: Extension to Crude Oil Systems. Chem. Eng. Sci. 2001, 56, 7007-7015. (21) Zuo, J. Y.; Zhang, D. D.; Creek, J. Modeling of Phase Equilibria and Viscosity of Heavy Oils. Proceedings of the World Heavy Oil Congress, Edmonton, Alberta, Canada, March 10-12, 2008; Paper 2008-392. (22) Quinonez-Cisneros, S.E.; Dalberg, A.; Stenby, E. H. PVT Characterization and Viscosity Modeling and Prediction of Crude Oils. Pet. Sci. Technol. 2004, 22, 1309-1325. (23) Kumar, A.; Henni, A.; Shirif, E. Heavy Oil Viscosity Modeling with Friction Theory. Energy and Fuels, 2011, 25, 493-498. 50 ACS Paragon Plus Environment

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(24) Walther, C. The Evaluation of Viscosity Data. Erdol und Teer. 1931, 7, 382-384. (25) Yarranton, H. W.; van Dorp, J.; Verlaan, M.; Lastovka, V. Wanted Dead or Live: Crude Cocktail Viscosity-A Pseudo-Component Method to Predict the Viscosity of Dead Oils, Live Oils and Mixtures. J. Can. Pet. Technol. 2013, 52, 176-191. (26) Yarranton, H. W.; Satyro, M. A. Expanded Fluid-Based Viscosity Correlation for Hydrocarbons Ind. Eng. Chem. Res. 2009, 48, 3640-3648. (27) Motahhari, H.; Satyro, M. A.; Taylor, S. D.,; Yarranton, H. W. Extension of the Expanded Fluid Viscosity Model to Characterized Oils. Energy and Fuels, 2013, 27, 1881-1898. (28)Motahhari, H.; Satyro, M. A.; Yarranton, H. W. Predicting the Viscosity of Asymmetric Mixtures with the Expanded Fluid Correlation. Ind. Eng. Chem. Res. 2011, 50, 12831-12843. (29)Motahhari, H.; Satyro, M.A.; Yarranton, H.W. Viscosity Prediction for Natural Gas Processing Applications. Fluid Phase Equilib., 2012, 322-323, 56-65. (30) Satyro, M.A.; Yarranton, H.W. Expanded Fluid-Based Viscosity Correlation for Hydrocarbons Using an Equation of State. Fluid Phase Equilib., 2010, 298, 1-11. (31) Riazi, M. R. Characterization and Properties of Petroleum Fractions. ASTM International; West Conshohocken, PA, 2005. (32) Castellanos-Diaz, O.; Sanchez, M. C.; Schoeggl, F. F.; Satyro, M. A.; Taylor, S. D.; Yarranton, H. W. Deep-Vacuum Fractionation of Heavy Oil and Bitumen, Part I: Apparatus and Standardized Procedure. Energy and Fuels, 2014, 28, 2857-2865. (33) Sanchez-Lemus, M. C.; Schoeggl, F. F.; Taylor, S. D.; Ruzicka, K.; Fulem, M.; Yarranton, H. W. Deep Vacuum Fractionation of Heavy Oil and Bitumen, Part II: Interconversion Method. Energy and Fuels, 2014, 28, 2866-2873. (34) Mitchell, D.L.; Speight, J.G. The Solubility of Asphaltenes in Hydrocarbon Solvents. Fuels, 1973, 52, 149-152. (35) Barrera, D. M.; Ortiz, D. P.; Yarranton, H. W. Molecular Weight Distributions of Asphaltenes from Crude Oils. Energy and Fuels, 2013, 27, 2474-2487. (36) Butler, R. M. Thermal Recovery of Oil and Bitumen, 1st ed.; GravDrain Inc, Calgary, 1997. (37)Kesler, M. G.; Lee, B. I. Improve Predictions of Enthalpy of Fractions. Hydro. Proc., 1976, 55, 153-158. (38) Katz, D. L.; Firoozabadi, A. Predicting Phase Behavior of Condensate/Crude-Oil Systems Using Methane Interaction Coefficients. SPE paper 6727-PA, 1978. (39) Sanchez-Lemus, M. C. University of Calgary, Calgary, Alberta, Canada. Personal Communication, March 2015. (40) Lee, B. I.; Kesler, M. G. A Generalized Thermodynamic Correlation Based on ThreeParameter Corresponding States. AIChE J. 1975, 21, 510-527. (41) Yaws, C.L. Transport Properties of Hydrocarbons. William Andrew Inc. Norwich, NY, 2008. (42) Motahhari, H. Development of the Expanded Fluid Viscosity Model. Ph.D Thesis, University of Calgary, Calgary, Canada, 2013. 51 ACS Paragon Plus Environment

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(43) Ramos-Pallares, F.; Schoeggl, F.F.; Taylor, S.D.; Satyro, M.A.; Yarranton, H.W. Predicting the Viscosity of Hydrocarbon Mixtures and Diluted Heavy Oils Using the Expanded Fluid Model, Energy Fuels, 2016, 30, 3575-3595. (44) Wilke, C. R. A Viscosity Equation for Gas Mixtures. J. Chem. Phys. 1950, 18, 517-519. (45) Thomson, G. H.; Brobst, K. R.; Hankinson, R. W. An Improved Correlation for Densities of Compressed Liquids and Liquid Mixtures. AIChE J. 1982, 28, 671-676. (46) Spencer, C. F.; Danner, R. P. Improved Equation for Prediction of Saturated Liquid Density. J. Chem. Eng. Data, 1972, 17, 236-241. (47) Lastovka, V.; Fulem, M.; Becerra, M.; Shaw, J. M. A similarity Variable for Estimating the Heat Capacity of Solid Organic Compounds Part II. Application: Heat Capacity Calculation for ill-Defined Organic Solids. Fluid Phase Equilib. 2008, 268, 134-141. (48) National Institute of Standards and Technology (NIST). Standard Reference Database; WinSource, Version 2008. (49) American Petroleum Institute (API). Properties of Hydrocarbons of High Molecular Weight. API, Washington, D. C. 1966, Research Project 42. (50) American Petroleum Institute (API). Comprehensive Report of API Crude Oil Characterization Measurements. Washington, D.C. 2000, API Technical Report 997. (51) Beg, S. A.; Amin, M. B.; Hussain, I. Generalized Kinematic Viscosity-Temperature Correlation for Undefined Petroleum Fractions. Chem. Eng. J. 1988, 38, 123-136. (52) Altgelt, K. H.; Boduszynski, M. M. Composition and Analysis of Heavy Petroleum Fractions. Marcel Dekker, Inc., New York, 1994. (53) Kanti, M.; Zhou, H.; Ye, S.; Boned, C., Lagourette, H., Saint-Guirons, P., Xans, P., Montel, F. Viscosity of Liquid Hydrocarbon, Mixtures and Petroleum Cuts, as a Function of Pressure and Temperature. J. Phys. Chem. 1989, 93, 3860-3864. (54) Queimada, A. J.; Rolo, L. I.; Caço, A. I.; Marrucho, I. M.; Stenby, E. H.; Coutinho, J. A. P. Prediction of Viscosities and Surface Tensions of Fuels Using a New Corresponding States Model. Fuel, 2006, 85, 874-877. (55) McLean, J. D.; Kilpatrick, P. K. Effects of Asphaltene Solvency on Stability of Water-inCrude-Oil Emulsions. J. Colloid Interface Sci. 1997, 189, 242-253. (56) Badamchi-Zadeh, A.; Yarranton, H. W.; Svrcek, W. Y.; Maini, B. B. Phase Behavior and Physical Property Measurements for VAPEX solvents: Part I. Propane and Athabasca Bitumen. J. Can. Pet. Technol. 2009, 48, 54-61. (57) EST: Emergency Science and Technology Division Environment Canada. Oil Properties Database. Environment Canada, Otawa, Canada, 2001. (58) Twu, C. H. An Internally Consistent Correlation for Predicting the Critical Properties and Molecular Weights of Petroleum and Coal-Tar Liquids. Fluid Phase Equilib. 1984, 16, 137-150. (59) Rogel, E.; Carbognani, L. Density Estimation of Asphaltenes Using Molecular Dynamics Simulations. Energy and Fuels, 2003, 17, 378-386.


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Appendix A: Density and Viscosity Data from Whole Oils Collected in this Study

Table A1. Density and viscosity of WC-B-A2 bitumen measured in the capillary viscometer apparatus. Temp. °C 49.9 49.9 49.9 49.9 49.9 74.6 74.6 74.6 74.6 74.6 99.7 99.7 99.7 99.7 99.7 124.6 124.6 124.6 124.6 149.8 149.8 149.8 149.8 174.8 174.8 174.8 174.8

Pressure Density Viscosity MPa kg/m³ mPa.s 0.1 1004.3 38200 2.5 1005.6 43400 5.0 1006.9 48400 7.5 1008.3 54000 10.0 1009.6 60700 0.1 988.6 3140 2.5 990.1 3470 5.0 991.6 3800 7.5 992.9 4140 10.0 994.3 4560 0.1 972.6 532 2.5 974.4 561 5.0 975.9 608 7.5 977.6 656 10.0 979.0 707 2.5 958.3 152 5.0 959.9 161 7.5 961.6 172 10.0 963.5 183 2.5 941.5 54.7 5.0 943.5 57.7 7.5 945.4 60.9 10.0 947.3 64.5 2.5 924.6 25.0 5.0 926.8 26.2 7.5 929.1 27.4 10.0 931.1 28.6


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Table A2. Density and viscosity of WC-B-A3 bitumen measured in the capillary viscometer apparatus. Temp. °C 49.9 49.9 49.9 49.9 49.9 75.2 75.2 75.2 75.2 75.2 100.0 100.0 100.0 100.0 100.0 125.0 125.0 125.0 125.0 150.0 150.0 150.0 150.0 175.0 175.0 175.0 175.0

Pressure Density Viscosity MPa kg/m³ mPa.s 0.1 989.9 5500 2.5 990.9 5960 5.0 992.3 6500 7.5 993.7 7240 10 995.0 7990 0.1 973.6 699 2.5 974.9 746 5.0 976.4 798 7.5 977.9 852 10 979.3 919 0.1 957.5 161 2.5 959.0 172 5.0 960.6 183 7.5 962.3 195 10 963.9 209 2.5 936.3 38.3 5.0 938.2 40.1 7.5 940.0 42.1 10 941.9 44.1 2.5 919.6 18.5 5.0 921.8 19.2 7.5 923.8 20.0 10 925.8 20.8 2.5 903.1 10.5 5.0 905.4 10.8 7.5 907.8 11.2 10 909.8 11.6


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Table A3. Density and viscosity of WC-B-B1 bitumen measured in a cone and plate rheometer and density meter at atmospheric pressure. Temp. °C 39.3 40.0 50.0 51.1 54.7 55.0 60.0 68.5 87.7 90.0

Density Viscosity kg/m3 mPa.s 7720 1000.7 994.3 2520 1900 991.1 987.9 634 192 968.6 -

Table A4. Density and viscosity of the WC-B-A1, US-HO-A1 and MX-HO-A1 oils measured in a cone and plate rheometer and density meter at atmospheric pressure. Temp. °C 25 35 40 45 50 60 75 80 90 100 125

WC-B-A1 US-HO-A1 MX-HO-A1 Density Viscosity Density Viscosity Density Viscosity kg/m3 mPa.s kg/m3 mPa.s kg/m3 mPa.s 992.5 35200 957.3 2160 972.9 10800 871 983.1 959.1 31693 2620 941.4 297 970.4 934.6 948.6 7183 433 925.1 77.8 938.2 2147 957.8 915.6 927.7 122 31.1 47.1 16.0 -


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Table A5. Density and viscosity of the CO-B-B1 and EU-HO-A1 oils measured in a cone and plate rheometer and density meter at atmospheric pressure. Temp. °C 25 35 40 50 60 75 80 90 100 125

CO-B-B1 EU-HO-A1 Density Viscosity Density Viscosity kg/m3 mPa.s kg/m3 mPa.s 994.2 1240 984.7 953.0 978.3 4023 946.6 383 972.0 940.4 612 930.9 91.5 927.8 953.0 154 34.0 59 -


Energy & Fuels

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Page 58 of 65

Appendix B: Density and Viscosity Data from Distillation Cuts Collected in this Study Table B1. Normal boiling point (Tb), specific gravity (SG), molecular weight (MW), and fitted EF parameters (c2 and ρso) of distillation cuts from the WC-B-B1, WC-B-A1, CO-B-A1, CO-BB1, US-HO-A1, and MX-HO-A1 oils. Cut WC-B-B1 1 2 3 4 5 6 WC-B-A1 1 2 3 4 5 6 7 CO-B-A1 1 2 3 4 5 6 7 CO-B-B1 1 2 3 4 5 6 7 US-HO-A1 1 2 3 4 5 6 7 MX-HO-A1 1 2 3 4 5 6

Tb °C

SG

MW g/mol

c2

ρ so kg/m³

335 346 414 425 427 470

0.921 0.962 0.973 0.982 0.992 0.999

247 272 327 351 424 479

0.1889 0.1416 0.2583 0.2555 0.2640 0.2919

975.8 996.3 1022.5 1019.9 1025.1 1033.9

285 313 349 376 396 412 429

0.891 0.915 0.936 0.952 0.961 0.965 0.968

225 259 287 323 372 451 463

0.2266 0.2486 0.2574 0.2641 0.2643 0.2849

979.6 995.8 1002.6 1005.9 1005.0 1007.0

311 358 389 404 441 487 537

0.900 0.924 0.944 0.961 0.971 0.979 0.988

236 257 301 328 380 397 475

0.2424 0.2116 0.2650 0.2577 0.2663 0.2927 0.3155

978.4 979.1 1003.9 1005.1 1008.4 1014.7 1022.6

289 321 338 365 378 395 405

0.886 0.923 0.937 0.947 0.958 0.964 0.975

234 281 306 350 388 432 447

0.2405 0.2271 0.2422 0.2416 0.2718 0.2787 0.3005

970.6 980.7 987.8 988.5 998.2 998.9 1008.1

290 315 342 357 377 406 424

0.868 0.900 0.918 0.926 0.936 0.948 0.958

227 261 295 337 372 411 485

0.2369 0.2461 0.2558 0.2721 0.2895 0.2915

967.5 976.6 978.8 984.3 991.1 996.3

298 319 353 372 398 475

0.901 0.918 0.930 0.942 0.952 0.968

265 285 325 345 408 468

0.2431 0.2397 0.2231 0.2789 0.2569 0.3069

971.4 986.0 978.0 994.2 993.8 1011.7


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Table B2. Viscosity (cone and plate) of distillation cuts from the WC-B-B1 and WC-B-A1 bitumens. Cut 1

2

3

4

5

6

WC-B-B1 T °C 10.6 15.5 20.0 10.6 20.1 24.6 34.3 25.9 41.3 60.9 73.4 90.9 26.0 46.9 75.2 82.2 29.0 44.3 60.2 89.0 110.5 29.1 44.5 62.3 85.6 120.9 -

Viscosity mPa.s 27.1 19.8 15.6 125 47.3 29.4 13.7 160 56.4 20.4 12.3 7.8 923 167 23.9 18.5 2910 581 155 28.1 12.5 6290 1310 285 57.0 12.9 -

Cut 1 2

3

4

5

6

7

WC-B-A1 T Viscosity °C mPa.s 0.0 14.5 0.0 56.8 15.0 23.2 25.0 14.5 35.0 9.8 15.0 66.9 25.0 36.0 35.0 21.8 50.0 12.3 15.0 266 25.0 118 35.0 60.4 50.0 27.1 70.0 12.5 25.0 342 35.0 152 50.0 57.4 75.0 18.0 25.0 934 35.0 369 50.0 120 75.0 30.7 100.0 12.6 25.0 2110 35.0 767 50.0 223 75.0 49.7 100.0 17.9 110.0 13.2


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Page 60 of 65

Table B3. Viscosity (cone and plate) of distillation cuts from the US-HO-A1 and MX-HO-A1 heavy oils. Cut 1 2

3

4

5

6

7

US-HO-A1 T Viscosity °C mPa.s 0.0 7.6 0.0 49.1 5 36.0 15 21.2 30 11.2 5 117 15 57.9 25 32.4 35 20.0 50 11.0 25 75.6 35 41.7 50 20.5 65 11.7 25 214 35 104 50 43.5 75 15.5 25 895 35 362.4 50 120.5 75 32.0 100 13.2 25 2920 35 984 50 281 75 60.2 100 21.0 120 11.6

Cut 1

2

3

4

5

6

MX-HO-A1 T Viscosity °C mPa.s 15 18.9 17 17.3 20 14.9 22 14.1 25 12.5 15 23.8 20 18.9 25 15.2 30 12.6 35 10.5 25 57.3 35 33.1 45 19.1 55 13.1 25 170 35 76.5 50 34.6 75 12.9 25 433 35 188 50 75.6 75 21.3 90 13.0 25 2070 50 205 75 52.4 100 19.8 110 14.6 -


Page 61 of 65

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Table B4. Viscosity (cone and plate) of distillation cuts from the CO-B-A1 and CO-B-B1 bitumens. Cut 1

2

3

4

5

6

7

CO-B-A1 T °C 15 17 20 10 13 20 25 35 42 24 37 50 20 25 52 75 20 25 52 80 98 20 25 53 78 105 20 25 50 76 105 130

Viscosity mPa.s 11.7 11.0 10.0 58.5 47.7 31.4 24.6 15.5 12.7 59.8 28.7 16.1 557 340 49.9 17.9 3280 1780 148 32.0 15.5 17600 8450 411 73.2 22.0 87000 46900 1340 192 38.7 15.9

Cut 1

2

3

4

5

6

7

CO-B-B1 T Viscosity °C mPa.s 5 10.8 10 9.1 15 7.6 5 89.0 10 62.0 20 33.4 30 20.0 40 12.6 20 105 35 40.0 50 19.0 65 10.6 20 506 35 116 50 46.1 75 15.0 20 3630 35 411 50 130 75 32.5 100 12.5 35 1350 50 308 75 61.8 100 20.8 115 12.7 35 4620 50 867 75 134 100 37.4 125 15.2 -


Energy & Fuels

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Page 62 of 65

Appendix C: Density and Viscosity Data from C5-Maltenes Collected in this Study Table C1. Density and viscosity of WC-B-B1-DAO C5-maltenes measured in the capillary viscometer apparatus. Temp. °C 20.1 20.1 20.1 20.1 20.1 50.0 50.0 50.0 50.0 50.0 75.0 75.0 75.0 75.0 75.0 100.0 100.0 100.0 100.0 100.0 125.0 125.0 125.0 125.0 125.0 150.0 150.0 150.0 150.0 175.0 175.0 175.0 175.0

Pressure Density Viscosity MPa kg/m³ mPa.s 0.1 2.5 5.0 7.5 10 0.1 2.5 5.0 7.5 10 0.1 2.5 5.0 7.5 10 0.1 2.5 5.0 7.5 10 0.1 2.5 5.0 7.5 10 2.5 5.0 7.5 10 2.5 5.0 7.5 10

981.3 982.5 983.7 984.9 986.6 961.4 962.8 964.4 965.9 967.3 945.1 946.9 948.5 950.0 951.6 928.2 930.2 931.9 933.6 935.4 911.5 913.9 915.7 917.6 919.6 897.2 899.5 901.5 903.5 880.3 882.8 885.3 887.5

1280 1390 1540 1650 1810 145 157 167 177 187 41.8 44.5 47.2 49.8 52.6 16.8 17.5 18.3 19.2 20.1 8.7 9.1 9.4 9.8 10.2 5.4 5.6 5.8 6.0 3.5 3.7 3.8 3.9


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Energy & Fuels

Table C2. Density and viscosity of WC-B-A1-DAO, WC-B-A2-DAO and US-HO-A1-DAO C5maltenes measured in a cone and plate rheometer and density meter at atmospheric pressure. Temp. °C 20 25 30 35 40 47 50 60 70 71 75 100

WC-B-A1-DAO WC-B-A2-DAO US-HO-A1-DAO Density Viscosity Density Viscosity Density Viscosity kg/m3 972.4 966.0 959.7 953.3 947.0 940.7 -

mPa.s 3670 1420 449 103 36.4

kg/m3 998.1 982.5 976.2 969.9

mPa.s 43600 2610 358

966.8 67.9

kg/m3 948.9 942.2 935.7 929.3 922.8 916.4 -

mPa.s 819 365 138 41.5 17.8

Table C3. Density and viscosity of MX-HO-A1-DAO, CO-B-A1-DAO and CO-B-B1-DAO maltenes measured in a cone and plate rheometer and density meter at atmospheric pressure. Temp. °C 20 25 30 35 40 48 50 60 70 75 90 100 104

MX-HO-A1-DAO CO-B-A1-DAO CO-B-B1-DAO Density Viscosity Density Viscosity Density Viscosity kg/m3 959.3 952.4 945.6 939.1 932.7 926.2 -

mPa.s 856 142 45.6 19.4 -

kg/m3 981.1 965.6 950.1 940.8 -

mPa.s 32300 1970 283 52.2

kg/m3 958.1 951.6 945.1 938.7 932.3 925.9 -

mPa.s 1400 577 177 52.8 21.3 -


Energy & Fuels

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Page 64 of 65

Appendix D: Density and Viscosity Data from Partially Deasphalted Bitumen, C5Aphaltenes and 5 wt% C5-Aphaltenes in Toluene Collected in this Study

Table D1. Density and viscosity of partially deasphalted bitumen WC-B-B3 measured in a cone and plate rheometer and density meter at atmospheric pressure. Original asphaltene content of the bitumen is of 22 wt%. Temp.

0 wt% Asphaltenes

3 wt% Asphaltenes

4 wt% Asphaltenes

16 wt% Asphaltenes

Density

Density

Density

Density

°C

3

kg/m

25 35

Viscosity mPa.s

3

kg/m

992.7

10700

986.4

3740

50

976.9

75

961.1

Viscosity

Viscosity

3

Viscosity

mPa.s

3

kg/m

mPa.s

kg/m

mPa.s

999.1

22300

1000.9

26700

1010.8

161500

992.8

7010

994.7

8970

1005.4

40800

990

983.5

1730

985.4

2150

997.1

7800

188

967.8

295

969.9

354

983.4

1020

Table D2. Density and viscosity of C5-asphaltenes from samples WC-B-B1 and CO-B-A1. The viscosity was measured at atmospheric pressure using a cone and plate rheometer and the density was indirectly calculated from asphaltene/toluene mixtures assuming regular solution behavior. C5-Asphaltenes WC-B-B1 Temp.

Density 3

Viscosity

C5-Asphaltenes CO-B-A1 Density

Viscosity

3

°C

kg/m

mPa.s

kg/m

mPa.s

25

1094.5

-

1095.6

-

50

1082.7

-

1083.7

-

75

1070.8

-

1071.9

-

90

1063.7

-

1064.8

-

175

-

1000000

-

979000

178

-

-

-

773000

185

-

454000

-

371000

190

-

271000

-

-

200

-

132000

-

137000


Page 65 of 65

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Energy & Fuels

Table D3. Density and viscosity of 5 wt% WC-B-B1 C5-asphaltenes in toluene measured in the capillary viscometer apparatus. Temp. °C

Pressure MPa

Density kg/m³

Viscosity mPa.s

20.1 20.1 20.1 20.1 20.1 50.1 50.1 50.1 50.1 74.7 74.7 74.7 74.7 100.0 100.0 100.0 100.0 124.7 124.7 124.7 124.7 124.7 124.7 150.4 150.4 150.4 150.4 175.1 175.1 175.1 175.1 175.1

0.1 2.5 5.0 7.5 9.0 2.5 5.0 7.5 9.0 2.5 5.0 7.5 9.0 2.5 5.0 7.5 9.0 5.0 6.0 6.5 7.5 8.5 9.0 5.0 6.5 7.5 9.0 5.0 6.0 7.5 8.5 9.0

879.4 881.2 883.1 884.9 886.2 853.7 855.9 857.9 859.3 830.2 832.8 835.1 836.6 806.0 808.8 811.6 813.3 785.4 786.7 787.4 788.7 790.2 790.9 759.8 762.1 763.8 766.1 733.8 735.8 738.9 740.7 741.5

0.80 0.82 0.84 0.85 0.86 0.59 0.60 0.61 0.62 0.48 0.48 0.49 0.50 0.39 0.40 0.40 0.41 -


Prediction of Viscosity for Characterized Oils and ... - ACS Publications

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