Improved Density Prediction for Mixtures of Native and Refined Heavy

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IMPROVED DENSITY PREDICTION FOR MIXTURES OF NATIVE AND REFINED HEAVY OIL WITH SOLVENTS Maria Catalina Sanchez Lemus, Jane C. Okafor, Diana P Ortiz, Florian F Schoeggl, Shawn David Taylor, Frans G.A. van den Berg, and Harvey William Yarranton Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.5b00528 • Publication Date (Web): 22 Apr 2015 Downloaded from http://pubs.acs.org on April 26, 2015

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IMPROVED DENSITY PREDICTION FOR MIXTURES OF NATIVE AND REFINED HEAVY OIL WITH SOLVENTS M.C. Sánchez1, J.C. Okafor1, D.P. Ortiz1, F.F. Schoeggl1, S. D. Taylor2, F.G.A. van den Berg3, H.W. Yarranton1 1

2

3

Department of Chemical and Petroleum Engineering, University of Calgary, 2500 University Dr. NW, Calgary, Alberta, T2N 1N4, Canada DBR Technology Center, Schlumberger Canada Limited, 9450 17th Avenue NW, Edmonton, Alberta, Canada T6N 1M9

Shell Technology Centre Amsterdam, Shell Global Solutions International BV, PO Box 38000, 1030 BN Amsterdam, The Netherlands

A correlation was developed to predict the density of mixtures of heavy oil (and other petroleum liquids) and hydrocarbon solvents when the densities of each fluid in the mixture are available. Densities at atmospheric pressure and 293 K were measured for: saturates and aromatics (SA) fractions from ten native, thermo-cracked, and hydrocracked heavy oils all mixed with toluene and n-heptane; distillation cuts from 6 heavy oils mixed with toluene; mixtures of de-asphalted heavy oils with naphtha, diesel, and condensate. Density of mixtures of hydrocarbons and solvents at higher pressures (0.1 to 10 MPa) and temperatures (298 to 353 K) were also measured or obtained from the literature. Symmetry versus mass fraction was observed for all of the mixtures and their densities were fitted with a mixing rule where excess volumes are quantified with a binary interaction parameter and the density of each mixture component. The excess volume mixing rule fit the data for each mixture with average absolute deviations (AAD) less than 1.1 kg/m³ and the overall average AAD was 0.39 kg/m³. The binary interaction parameter was correlated to the density of the components in the mixture and to temperature. Pressure was found to have no consistent effect in the interaction parameter and was neglected. The overall AAD for the density determined with the correlated β12 for binary mixtures was 1.1 kg/m³ compared with 3.0 kg/m³ if regular solution behaviour was assumed and 3.6 kg/m³ when the standard API correlation was used to predict the density of the mixtures. The API correlation and correlated excess volume mixing rule performed similarly for hydrocarbons with carbon numbers above five. The proposed correlation was also tested on ternary data from the literature with comparable results.

KEYWORDS: density, heavy oil, excess volume, binary interaction parameter, ternary mixtures

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Introduction Heavy oil has become a significant contributor to the North American energy supply with over 1.9 million bbl/d produced in Alberta alone1. Since heavy oils have viscosities ranging from 1000 mPa.s to over 106 mPa.s at ambient conditions, they usually require heating or dilution to reduce the viscosity for recovery, transportation, and processing. For oil recovery processes, a solvent (usually an n-alkane) can be used directly, as in the VAPEX process2, or together with steam as in the ES-SAGD3, N-SOLV4, SAP5, LASER6 and SAS7 processes. For transportation, condensates and naphthas are frequently used as diluents8,9. In refineries, heavy oil and its fractions may be blended with other crude oil fractions to obtain the desired feed and product specifications10. For all of these processes, the density of the mixture is an important operational parameter. For example, solvent assisted processes are usually gravity drainage recovery processes that depend on the density difference between the diluted heavy oil and the vapour phase. Density is also critical for volume calculations in pipelines and refineries where product values are calculated from volumes. Volume expansion is an important driver in the current refinery environment. Some refinery blends involve reacted fluids with altered properties that may not follow the density prediction methods used for unreacted petroleum fluids. It is not always practical to measure mixture densities; for example, mixtures are inaccessible for in situ applications and production planning for refinery blend compositions can be accomplished faster with reliable predictions of blend properties. Therefore, there is a need for a method to accurately predict the density of these mixtures.

Densities of hydrocarbon mixtures can be determined by two different methods: equations of state (EoS) and correlations. Equations of state, such as the Soave-Redlich-Kwong (SRK) EoS and the Peng-Robinson (PR) EoS, are designed for phase behaviour and volumetric property calculations. However, these equations fail to accurately predict the molar volume of liquid hydrocarbons particularly in the compressed liquid state11. Equations of state based on the statistical associating fluid theory (SAFT), particularly a modification using the perturbed chain theory (PC-SAFT EoS), give better predictions for liquid densities of hydrocarbons. However, due to the numerical complexity of these models, phase predictions sometimes fail and inaccuracies in volumetric property predictions can still arise11.


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To overcome cubic EoS limitations for liquid densities, Peneloux et al 12 proposed a componentdependent volume correction constant and applied the volume translation to the SRK EoS. Other authors13-16 have proposed enhanced volume translation corrections by introducing the effect of temperature in the constant developed by Peneloux. These modifications considerably improved the prediction of saturated liquid densities. However, one drawback of EoS, even with volume translation, is that the critical properties and acentric factors must be available for the components in the mixture of interest. These data are limited for heavy oil and bitumens and the critical properties of heavy oil pseudo-components are usually determined from correlations originally developed for pure hydrocarbons or conventional oils. These correlations do not necessarily extrapolate accurately to heavy oil components, introducing uncertainty into the volumetric predictions. For example, EoS are almost always tuned to fit densities of mixtures of heavy oil with a solvent such as carbon dioxide 17, 18.

The second option to calculate mixture density is to use a correlation. The most common correlations for crude oils, such as the Rackett 19 and COSTALD 20 correlations, are based on the corresponding states principle. The COSTALD equation provides better predictions for the densities of saturated liquids compared to EoS. Spencer et al. 21 improved the Rackett correlation to further reduce the error in the predicted densities of saturated liquids from the triple to the critical point. The inputs for these density correlations are the critical properties and, in some cases, the acentric factor as well

20

. However, it is challenging to apply these correlations to

mixtures because the pseudo-critical properties of the mixture are usually not known but must be estimated using established conventional oil correlations 22 leading to uncertainty in the predicted density. The predicted density is also sensitive to the choice of mixing rule used in the critical property correlations. For heavy oils, the critical properties must be extrapolated beyond the range for which the correlations were developed, leading to further inaccuracies in the predicted mixture densities.

A simpler way to deal with the density for mixtures of heavy oils and solvents is to use mixing rules based on the component densities. Mixtures of hydrocarbons form nearly regular solutions; that is, solutions where the volumes of the components are additive. Nonetheless, these mixtures usually have non-zero excess volumes and these small excess volumes must be accounted for Page 3 of 31 ACS Paragon Plus Environment

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when accurate volumes calculations are required. The value of the excess volume term depends on the size, shape, and interaction forces between the molecules of each component and can be positive or negative. The API Bulletin 2509C

23

reported that blends of light and heavy

petroleum components have negative excess volumes indicating a reduction in the final volume of the mixture. While mixtures of light hydrocarbons and crude oil have negative excess volumes (shrinkage), mixtures of toluene and high boiling point paraffinic products with crude oil have positive excess volumes (expansion)

24-26

. Since crude oils are ill-defined multicomponent

mixtures, developing a generalized correlation to predict excess volumes of crude oils with any solvent is challenging.

The objective of this study is to develop a correlation to predict the density of mixtures of heavy petroleum liquids and hydrocarbon solvents when the densities of each fluid in the mixture are available. The correlation is to be applicable to both native and reacted oils over a broad range of temperatures and pressures. It must also be in a form suitable for multicomponent mixtures for use in simulation where multiple phases may form and fluids are characterized into several components.

The correlation was developed using density data collected at atmospheric pressure and 293 K from binary mixtures of solvents with crude oils, de-asphalted crude oils, distillation fractions from crude oils, and saturate and aromatic fractions from several native, thermo-cracked, and hydrocracked heavy oils. The solvent consisted of pure compounds, namely toluene or nheptane, as well as common commercial diluents such as naphtha, diesel and condensate. The measured densities were fitted with a mixing rule where excess volumes are quantified with a binary interaction parameter. A generalized correlation for the binary interaction parameter was constructed based on the binary interaction parameters calculated from the density dataset. Densities of binary mixtures at higher temperatures and pressures were used to determine the dependence of temperature and pressure on the binary interaction parameter correlation. The binary interaction parameter correlation was then tested on density data for mixtures of bitumen with pure solvents, including propane and butane, and on ternary mixtures. For comparison the results for binary mixtures were compared with the API correlation.


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Experimental Methods Materials In addition to data available in the literature, this study utilizes density data compiled from two projects conducted at the University of Calgary. The first project, referred to here as the SA Fractions Project, was focused on generation and property measurement of saturate and aromatic (SA) fractions from native and reacted bitumen mostly from Western Canadian (WC) feedstocks. The second project, referred to as the Distilled Cuts Project, focused on the generation and property measurement of distillation cuts from de-asphalted heavy oils from different sources. In each project, the choice of samples was dictated by availability of the samples and their fractions, but altogether the dataset encompasses a range of sources and reaction history.

For the SA Fractions Project, the samples, the whole oil density, and their saturate, aromatic, resin and asphaltene compositions (SARA) are listed in Table 1. The Native samples include a heavy oil (HO), a bitumen (B), a diluted bitumen product (DB), and a bitumen derived vacuum bottoms (VB). The In Situ Thermocracked (B-IS79 and 98) samples were obtained from a thermal process and were partially cracked. The VISB Thermocracked (VR-TC31) sample was the product after vacuum distillation of a visbreaker pilot plant. The Hydrocracked set of samples includes the bottoms product from a heavy oil stripper in a hydrocracking process (SRHC77C) and two hydrocracked samples (SR-HC56 and 80) from a pilot plant. Finally, the last sample (XX-CO-A1) in the dataset is a sample of unknown origin and reaction history.

The sample set for the Distilled Cuts Project is listed in Table 2. The WC-B-B1 sample was provided by Shell. The samples denoted as CO-HO-A1 and MX-HO-A1 were received from Schlumberger. These oils were de-asphalted prior to distillation and the density of the deasphalted oils are provided in Table 2.

The diesel used in this work was a commercial grade fuel sold in Alberta. The condensate and naphtha, both from Western Canada, were provided by CNOOC-Nexen and Shell, respectively. Densities of these fuels are presented in Table 3. Technical grade (EMD) n-heptane, n-pentane, Page 5 of 31 ACS Paragon Plus Environment

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toluene and acetone were purchased from VWR International, LLC. These solvents were used for asphaltene precipitation, solids removal, and SARA fractionation.

Table 1. SARA assays and densities for the ten oils from the SARA project. Oil Sample

Sample Density* kg/m³

Saturates

Aromatics

Resins

Asphaltenes

wt%

wt%

wt%

wt%

41.2 44.0 44.9 37.4

15.6 19.4 23.4 20.1

7.8 19.4 10.6 37.2

46.5 52.2

20.7 15.2

15.2 11.5

31.4

13.4

51.2

47.3 49.3 45.1

17.3 15.1 14.5

15.7 2.8 25.1

31.5

17.2

4.8

Native ME-HO-A1 870 35.3 WC-B-B2 1105 17.1 WC-DB-A2 904 21.1 5.3 WC-VR-B2 In Situ Thermocracked WC-B-IS79 878 17.6 WC-B-IS98 870 21.1 VISB Thermocracked WC-VR-TC31 4.0 Hydrocracked WC-SR-HC77C 980 19.7 954 32.8 WC-SR-HC56 WC-SR-HC80 15.3 Unknown Origin XX-CO-A1 846 46.4 * Density at 293K and atmospheric pressure

Table 2. Distillation summary and density of the three deasphalted oils from the distillation project. Oil Sample

C5 Asphaltene Cumulative Mass Content Distilled† wt% wt% WC-B-B1 17.4 51.7 CO-HO-A1 25.8 42.8 MX-HO-A1 21.2 41.4 †Cumulative mass distilled based on the whole oil mass *Density at 293K and atmospheric pressure


Deasphalted Oil Density* kg/m³ 998.4 959.5 958.4

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Table 3. Densities of the fuels used in the mixtures with deasphalted heavy oils. Oil Sample

Density* kg/m³ WC Diesel A 866.1 WC Naphtha A 730.1 WC Condensate A 682.2 *Density at 293K and atmospheric pressure

SARA Analysis and Deasphalting The procedure to de-asphalt samples involved mixing a known amount of bitumen with npentane at a ratio of 40 mL of solvent per 1 g of bitumen. The mixture was sonicated for 60 minutes and left to settle for 24 hours. Then, the supernatant was decanted and filtered through a Whitman #2 filter. Solvent was added to the sediment at an amount equivalent to 10 vol% of the initial solvent added. The mixture was sonicated for 45 minutes and left to settle. After 16 hours of settling, the solution was filtered through the same filter. For the samples used in distillation, all of the filtrate was placed in a rotovap and the solvent was evaporated to recover the maltenes.

To determine the asphaltene content, the filter cake was washed with n-pentane until the liquid leaving the filter was colorless and then dried in a closed fume hood until the total mass of the filter did not change. The filter cake contains both asphaltenes and toluene insolubles (inorganic solids, carbenes, and carboids which co-precipitate with the asphaltenes). To determine the toluene insolubles content, a sample of precipitate was dissolved in toluene and sonicated for one hour, and settled for 45 minutes. The asphaltene-toluene solution was then centrifuged at 3500 rpm for six minutes and the supernatant was decanted. The thermo- and hydrocracked samples contained more fine toluene insoluble particles than the native samples and an extra step was required. The supernatant from these solutions was filtered after centrifugation to remove the remaining fine toluene insoluble. The filter was washed with toluene and dried. The recovered toluene insolubles (centrifuged and recovered in the filter) were dried and weighed. C5asphaltene contents were then calculated as the mass of precipitate less the mass of toluene Page 7 of 31 ACS Paragon Plus Environment

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insolubles all divided by the initial mass of bitumen; that is, the asphaltene yields were all determined on a toluene insolubles-free basis.

The saturate, aromatic, and resins fractions were prepared following the procedure in ASTM D2007. The de-asphalted oil (maltenes) is mixed with n-pentane and introduced into a liquid chromatography apparatus consisting of an upper column containing Attapulgus clay and a lower column containing silica gel. The resins adsorb on the clay, the aromatics adsorb on the silica gel, and the saturates pass through. The columns are then separated and the resins are desorbed with a mixture of toluene and acetone while the aromatics are desorbed with a mixture of npentane and toluene. The SARA analysis and solids-free C5 asphaltene content of the seven oils in the SA Fractions Project are reported in Table 1.

Deep Vacuum Distillation Distillation cuts were obtained on a recently developed Deep Vacuum Fractionation apparatus following a standardized procedure presented in detail elsewhere27, 28. Briefly, the apparatus is a batch distillation unit with no reflux but capable of reaching pressures as low as 1x10-7 Pa. The apparatus can distill up to ~50 wt% of a bitumen and provides repeatable boiling point cuts and repeatable cut properties. To perform a distillation, the oil is first de-asphalted as described above. Then, the maltenes are distilled into eight fractions plus a non-distillable fraction or residue. A previously developed inter-conversion method28 was used to convert the raw data into atmospheric equivalent temperatures (AET). The relevant properties of three crude oils evaluated in the Distillated Cuts Project are summarized in Table 2.

Density Measurement All density measurements were completed using an Anton Paar DMA 4500M density meter. The instrument precision was ±0.01 kg/m³ with a repeatability of ±0.05 kg/m³ for unmixed components such as pure solvents, distillation cuts, or saturate and aromatic fractions. The repeatability of mixture densities was ±0.09 kg/m³ based on a 95% confidence interval.


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For the SA Fractions Project, density data was collected for the saturate and aromatic fractions from all of the oil samples listed in Table 1. Mixture densities of saturates and aromatics in heptane or toluene were also measured. For the Distillated Cuts Project, densities of the individual distillation cuts and mixtures of the distillation cuts with toluene were measured for each oil in the dataset.

The density of low viscosity fractions (saturates, aromatic and light distillation fractions) and all mixture densities were measured directly at standard conditions of 293K and atmospheric pressure. However, the densities at 293 K of the more viscous fractions (i.e. samples with densities higher that 990 kg/m³) were obtained by linearly extrapolating the density of the sample at higher temperatures down to 293 K. To validate the linear extrapolation, the same procedure was used on some light fractions. The extrapolated densities at 293 K were within the experimental error of the densities measured directly at 293K. Note, distillation residues, resins and asphaltene mixing densities were not included in this study since there was either insufficient sample to complete the density measurements on the mixtures or the liquid density of the ‘pure’ component (e.g. asphaltenes) could not be measured.

Mixing Rules and Data Fitting Excess Volume Mixing Rules Most of the systems examined in this study are mixtures of a solvent with a petroleum cut (e.g. distillation cut, saturate, or aromatic) consisting of hundreds of thousands of components. These mixtures are treated as a pseudo-binary system consisting of the solvent and the petroleum cut. Figure 1a and 1b shows the specific volumes of mixtures of a) heptane and aromatics from WCB-B2 oil and b) toluene and a distillation cut from MX-HO-A1 oil, respectively. The data clearly indicate that the solvent-petroleum cut mixtures deviate from regular solution behavior. The deviation for these hydrocarbon mixtures was found to be symmetric with respect to the weight percent of either component

29

. The data for all of the hydrocarbon mixtures examined in this

study were consistent with this observation.


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1.166

1.550

MX-HO-A1

WC-B-B2 aro

Regular Solution

1.164

Regular Solution

1.450

Excess Mixing Rule

Excess Mixing Rule

Specific Volume, cm3/g

Specific Volume, cm3/g

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1.350

1.250

1.150

1.050

1.162 1.160 1.158 1.156 1.154

(a)

(b)

1.152

0.950 0

0.2

0.4

0.6

0.8

0

1

0.2

0.4

0.6

0.8

1

Cut Mass Fraction

Aromatic Mass Fraction

Figure 1. Specific volume at 293 K and atmospheric pressure of mixtures of: a) aromatics from WC-B-B2 in heptane; b) a distillation fraction from MX-HO-A1in toluene. Note, the error bars are smaller than the symbols.

To develop an appropriate mixing rule for the specific volume or density of these mixtures, consider the mixing rule for a two component mixture that forms a regular solution: = +

(1)

where wi and vi are the mass fraction and specific volume of component i. For mixtures that do not form regular solutions, that is have an excess volume of mixing, the specific volume of the mixture is given by, = + +

(2)

where vE is the excess volume of mixing which depends on the composition of the mixture. For symmetric mixtures, Equation 2 can be modified to express the excess volume in terms of a binary interaction parameter as follows, = + + ( + )

(3)

or, in terms of density,

= + − +

(4)

where ρ is density and β12 is the binary interaction parameter between the two components in the mixture. A positive binary interaction parameter indicates shrinkage and a negative value indicates expansion. Equations 3 and 4 apply to all compositions. Since the mixtures are


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symmetric, the maximum excess volume in a binary mixture occurs when the mass fraction of both components are equal (50 wt%).

The excess volume mixing rule can be extended to ternary mixtures as follows:

= + + − + − + − +

(5)

In this case, the density of the three components and their binary interaction parameters are required. If a regular solution is assumed, then βij = 0 and only the densities of each component are required.

A least squares regression was performed to find the binary interaction parameter using Equations 4 and 5. To determine how errors in direct densities and mixture densities affected the value of the binary interaction parameter, an error analysis was performed by varying the measured density values within their experimental error (±0.09 kg/m3) and obtaining a new fitting following the same regression procedure. Based on this sensitivity analysis, the βij has an uncertainty of ±0.00025.

API Method API developed two empirical equations for the density of blends of petroleum components with solvents. The original equation

23

was based on 460 data points and the highest accuracy of the

correlation corresponded to data where the concentration of the lighter components was at least 21 vol%. This correlation was later updated for the whole compositional range of heavy and light components with densities between 644 and 979 kg/m³ and 581 and 889 kg/m³, respectively 29. This latest version of the API equation in SI units is given by:

= 26900 ! (100 − !)#.%& ( − ) . % '

(

(6)

where S is the volumetric shrinkage as a percentage of the total mixture ideal volume; C is the concentration in liquid volume percent of the lighter component in the mixture; ρL and ρH correspond to the densities of the light and heavy component in the mixture in kg/m³, respectively.


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Datasets The data collected in this study include i) pure component and mixture densities for saturate and aromatic fractions for the samples from the SA Fractions Project, ii) pure component and mixture densities for distillation cuts from the Distilled Cuts Project, iii) pure component and mixture densities of heavy oils with typical petroleum solvents (diesel, naphtha, and condensate), and iv) pure component and mixture density data found in the literature for heavy oils and solvents. The literature data included binary mixtures at ambient conditions, binary mixtures at elevated temperatures and pressures, and ternary data.

For each mixture, the pure component and mixture densities were fit using Equation 4 or 5 to determine the value of βij (Fitted) and the maximum value of the excess volume for the mixture (Maximum vE). The pure component densities, Maximum νE, and βij (Fitted) for each dataset is summarized below.

Binary Mixtures at Ambient Conditions The binary mixture dataset included data from saturates, aromatics and distillation fractions, mixtures of de-asphalted oils with diesel, naphtha and condensate, and literature data. The densities, excess volumes, and binary interaction parameters for the saturate, aromatic, and three distillation fractions are reported in Tables 4 through 8, respectively. The same data are reported in Table 9 for the binary mixtures of two de-asphalted oils with naphtha, diesel and condensate as well as the data found in literature. The excess volumes and binary interaction parameters are discussed later. The component densities and either the maximum excess volume or binary interaction parameter are sufficient to determine the mixture density at any composition to within the experimental error of the measurements.


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Table 4. Densities, maximum excess volumes, and binary interaction parameters of saturates mixed with toluene or n-heptane at 293 K and atmospheric pressure. Source Oil Native ME-HO-A1 WC-B-B2 WC-B-B2 WC-DB-A2 In Situ Thermocracked WC-B-IS79 WC-B-IS79 WC-B-IS98 Hydrocracked WC-SR-HC77C Unknown Origin XX-CO-A1 XX-CO-A1

Saturate Density

Maximum νE

β12

β12

kg/m³

cm³/g

Fitted

Corr.

Toluene Toluene Heptane Toluene

826.7 887.1 887.1 888.2

+0.0033 +0.0056 -0.0077 +0.0020

-0.0057 -0.0098 +0.0120 -0.0036

-0.0049 -0.0051 +0.0131 -0.0051

Toluene Heptane Toluene

860.6 860.6 847.8

+0.0022 -0.0080 +0.0045

-0.0039 +0.0121 -0.0076

-0.0052 +0.0107 -0.0051

Toluene

876.9

+0.0022

-0.0038

-0.0052

Toluene Heptane

844.8 844.8

+0.0027 -0.0078

-0.0046 +0.0118

-0.0051 +0.0087

Solvent

Table 5. Densities, maximum excess volumes, and binary interaction parameters of aromatics mixed with toluene or n-heptane at 293 K and atmospheric pressure. Source Oil Native ME-HO-A1 WC-B-B2 WC-DB-A2 In Situ Thermocracked WC-B-IS79 WC-B-IS79 WC-B-IS98 Hydrocracked WC-SR-HC77C Unknown Origin XX-CO-A1 XX-CO-A1

Aromatic Density

Maximum vE

β12

β12

kg/m³

cm³/g

Fitted

Corr.

Toluene Toluene Toluene

978.5 1005.9 1002.9

+0.0008 -0.0018 -0.0011

-0.0015 +0.0034 +0.0020

-0.0020 +0.0006 +0.0002

Toluene Heptane Toluene

1008.7 1008.3 1028.1

-0.0021 -0.0080 -0.0004

+0.0039 +0.0131 +0.0007

+0.0009 +0.0155 +0.0033

Toluene

1033.8

-0.0009

+0.0017

+0.0040

Toluene Heptane

969.7 970.6

-0.0007 -0.0089

+0.0014 +0.0142

-0.0027 +0.0154

Solvent


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Table 6. Densities, maximum excess volumes, and binary interaction parameters for the distillation cuts (DC) of WC-BIT-B1 mixed with toluene at 293 K and atmospheric pressure. Cut 1 2 3 4 5 6 7

Cumulative Oil Distilled

AET

Cut Density

Maximum vE

β12

β12

wt% Bitumen

K

kg/m³

cm³/g

Fitted

Corr.

16.3 21.4 28.8 35.0 40.5 45.9 51.8

333 377 415 425 427 470 483

920.4 954.8 970.9 977.9 987.5 998.5 1001.1

+0.0023 +0.0006 +0.0004 -0.0003 +0.0008 +0.0001 +0.0001

-0.0041 -0.0011 -0.0007 +0.0005 -0.0015 -0.0002 -0.0002

-0.0047 -0.0035 -0.0026 -0.0021 -0.0013 -0.0002 +0.0000

Table 7. Densities, maximum excess volumes, and binary interaction parameters for the distillation cuts (DC) of CO-HO-A1 mixed with toluene at 293 K and atmospheric pressure. Cut 0 1 2 3 4 5 6 7


AET

Cut Density

Maximum vE

β12

β12

wt% Bitumen

K

kg/m³

cm³/g

Fitted

Corr.

10.9 15.7 19.7 23.0 26.9 33.0 37.6 42.8

306 330 368 390 424 435 477 496

897.7 921.2 941.9 958.1 967.6 976.5 984.6 988.2

+0.0029 +0.0026 +0.0032 +0.0030 +0.0032 +0.0033 +0.0021 +0.0013

-0.0052 -0.0047 -0.0057 -0.0055 -0.0059 -0.0060 -0.0039 -0.0024

-0.0050 -0.0046 -0.0040 -0.0033 -0.0028 -0.0022 -0.0016 -0.0012

Table 8. Densities, maximum excess volumes, and binary interaction parameters for the distillation cuts (DC) of MX_HO_A1 mixed with toluene at 293 K and atmospheric pressure. Cut 0 1 2 3 4 5 6 7


AET

Cut Density

Maximum vE

β12

β12

wt% Bitumen

K

kg/m³

cm³/g

Fitted

Corr.

12.7 17.0 19.9 25.1 28.5 33.3 37.5 41.5

270 333 352 385 400 441 457 480

858.2 899.2 916.7 928.5 940.4 950.5 963.8 967.1

+0.0019 +0.0019 +0.0019 +0.0019 +0.0043 +0.0018 +0.0024 +0.0012

-0.0033 -0.0034 -0.0034 -0.0034 -0.0077 -0.0032 -0.0044 -0.0022

-0.0052 -0.0050 -0.0047 -0.0045 -0.0041 -0.0037 -0.0030 -0.0028


Page 15 of 31

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Table 9. Densities, maximum excess volumes, and binary interaction parameters for bitumen and de-asphalted oils (DAO) samples mixed with solvents at 293 K and atmospheric pressure. Mixture Label Literature Bit/C7 26 Bit/C5 26 This Work Bit/Tol DAO1/diesel DAO1/naphtha DAO1/cond DAO2/diesel DAO2/naphtha DAO2/cond

Component 2

Oil Density kg/m³

Solvent Density kg/m³

Maximum vE cm³/g

n-heptane n-pentane

1014.1 1014.1

679.7 626.5

WC-B-B3 MX-DAO-A1 MX-DAO-A1

toluene diesel naphtha

1013.5 958.4 958.4

MX-DAO-A1 SK-DAO-A1 SK-DAO-A1 SK-DAO-A1

condensate

958.4 972.1 972.1 972.1

Component 1

WC-B-B2 WC-B-B2

diesel naphtha condensate

β12

β12

Fitted

Corr.

-0.0109 -0.0118

+0.0177 +0.0183

+0.0156 +0.0156

866.8 866.1 730.2

+0.0009 +0.0027 -0.0060

-0.0016 -0.0047 +0.0100

+0.0014 -0.0033 +0.0137

682.7 866.1 730.2 682.7

-0.0120 -0.0006 -0.0096 -0.0161

+0.0192 +0.0011 +0.0161 +0.0258

+0.0153 -0.0025 +0.0143 -0.0053

Binary Mixtures at Higher Temperatures and Pressures Table 10 provides a dataset for elevated temperature and pressure conditions that was compiled from seven binary mixtures. The densities for the Bit/Tol mixture (this study) were measured using a capillary viscometer equipped with an in-line Anton Paar density-meter following the procedure presented by Saryazdi et al.

30

. The pure component densities for n-heptane, n-

pentane, n-butane, and n-propane in Table 10 are the calculated effective density (the density of the gas when dissolved in a liquid) as presented by Saryazdi et al.

30

. The use of effective

densities will be discussed in more detail later.

Table 10. Binary mixture components and their densities at higher temperatures and pressures. Mixture Label (Ref)

Component 1

Component 2

CH/Dec 31

methylcyclohexane

cis-decalin

(31)

Bit/Tol (this work)

WC-B-B3

toluene

Temp

Pressure

Density1

Density2

β12

β12

K

MPa

kg/m³

kg/m³

Fitted

Corr.

293

0.1

769.2

896.8

+0.0037

+0.0011

323

0.1

742.9

873.9

+0.0047

+0.0041

353

0.1

715.9

851.1

+0.0067

+0.0075

293

40

797.6

917.9

+0.0027

-0.0003

323

40

776.3

898.1

+0.0033

+0.0022

353

40

755.6

878.8

+0.0030

+0.0047

298 323

0.1 0.1

1010.0 992.9

862.1 838.6

-0.0014 +0.0001

+0.0020 +0.0050


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Page 16 of 31

348 323 348 323 348

0.1 2.5 2.5 7.5 10

975.7 994.4 977.6 997.2 981.7

814.9 841.1 817.4 845.4 824.9

+0.0020 -0.0001 -0.0019 +0.0001 -0.0009

+0.0081 +0.0048 +0.0080 +0.0045 +0.0073

Bit/C14 32

Athabasca

n-tetradecane

293 298 323 348

0.1 0.1 0.1 0.1

1008.2 1005.0 989.3 973.6

762.9 759.4 742.0 724.5

+0.0025 +0.0018 +0.0029 +0.0040

+0.0140 +0.0144 +0.0163 +0.0181

Bit/C7 30

WC-B-B2

n-heptane

293 323 348 373 398

0.1 0.1 0.1 0.1 0.1

1013.9 994.2 978.3 962.9 945.7

686.6 662.9 643.1 623.3 603.5

+0.0175 +0.0202 +0.0235 +0.0236 +0.0254

+0.0155 +0.0175 +0.0192 +0.0208 +0.0224

Bit/C5 30

WC-B-B3

n-pentane*

293 323 348 373 398

0.1 0.1 0.1 0.1 0.1

1015.3 995.9 979.9 964.0 947.6

625.6 594.1 566.6 537.9 508.1

+0.0171 +0.0212 +0.0217 +0.0218 +0.0233

+0.0156 +0.0176 +0.0192 +0.0208 +0.0225

Bit/C4 30

WC-B-B3

n-butane*

293 323 348 373 398

0.1 0.1 0.1 0.1 0.1

1015.3 995.9 979.9 964.0 947.6

597.7 571.8 550.5 529.3 508.0

+0.0043 +0.0089 +0.0083 +0.0101 +0.0125

+0.0156 +0.0176 +0.0192 +0.0208 +0.0225

Bit/C3 30

WC-B-B2

n-propane*

293 323 348 373 398

0.1 0.1 0.1 0.1 0.1

1014.4 994.6 978.3 962.1 945.8

453.6 517.7 496.3 474.9 453.6

+0.0123 +0.0137 +0.0140 -

+0.0156 +0.0176 +0.0192 +0.0208 +0.0225

*Densities reported at 0.1 MPa, β12 calculated at 2.5 MPa (no mixture data available at 0.1 MPa)

Ternary Mixtures A dataset was compiled from three ternary hydrocarbon mixtures found in the literature, Table 11. The binary interaction parameters in Table 11 were determined by fitting the experimental binary mixture density data from the same sources when the data was available. All the pairs showed symmetry and the average absolute deviation (AAD) and average absolute relative deviation (AARD) were less than 0.3 kg/m³ and 0.04% for all of the binary mixtures when Equation 5 was used.


Page 17 of 31

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Energy & Fuels

Table 11. Densities, maximum excess volumes, and binary interaction parameters for the ternary mixtures at 293 K and atmospheric pressure (mCH is methylcyclohexane, mN is 1-methyl naphthalene).

133

pentane hexane heptane

hexane heptane pentane

621.5 655.2 679.7

655.2 679.7 621.5

Maximum vE g/cm³ +0.0037 +0.0037 +0.0029

234

o-xylene o-xylene p-xylene

p xylene m-xylene m-xylene

875.6 875.6 856.7

856.7 860.1 860.1

+0.0004 +0.0002 -0.0006

-0.0006 -0.0003 +0.0010

-0.0051 -0.0052 -0.0052

335*

heptane mCH mN

mCH mN heptane

676.0 760.4 1015.4

760.4 1015.4 676.0

+0.0016 -0.0083 -0.0096

-

-0.0023 +0.0144 +0.0156

Mixture

Component Pairs 1

2

Density 1 kg/m³

Density 2 kg/m³

β12

β12

Fitted

Corr. 1

+0.0011 +0.0006 +0.0031

-0.0048 -0.0050 -0.0038

*Temperature of the binary and ternary mixtures was 303.15 K

Results and Discussion Correlation for the Binary Interaction Parameter at 293K Saryazdi et al. 30 demonstrated that the binary interaction parameters of families of hydrocarbons appeared to correlate to the normalized specific volume difference, vN, defined as, ) =

|+ + | + ,+

(7)

Figure 2 shows that the binary interaction parameters of mixtures hydrocarbons from the same family follow one trend versus vN while the parameters of mixtures hydrocarbons from different families follow another trend. Each of these trends includes mixtures with positive excess volumes and mixtures with negative excess volumes. Mixtures of different sized molecules from similar chemical families (i.e., larger vN) have a negative excess volume indicating efficient packing. Mixtures between molecules of different chemical families are shifted towards positive excess volumes consistent with larger repulsion forces and less efficient packing.

Figure 2 also indicates that the data for mixtures of the saturate and aromatic fractions and distillation cuts generally follow a trend in-between the “same family” and “different family” lines described above. It is not surprising that these mixtures fall between the two trends. Not only are crude oils mixtures of millions of different chemical species but most of these species Page 17 of 31 ACS Paragon Plus Environment

Energy & Fuels

consist of a combination of paraffinic, naphthenic, and aromatic groups

36

. Therefore, mixtures

involving crude oil components are neither of the same family nor of different families. The SA Fractions Project and Distilled Cut Project data are shown in more detail in Figure 3a.

Figure 2. Binary interaction parameter of mixtures of pure hydrocarbons with each other (same family and different family) and with SARA fractions and distillation cuts of WC_BIT_B1 all versus the normalized specific volume difference.

0.03

0.03

(b)

(a) 0.02

0.02

0.01

Sat-Tol Aro-Tol Sat-Hept Aro-Hept DC/tol DAO/D-N-C Bit/Tol Bit/C7 b12 Corr.

0.00

-0.01

-0.02 0

0.1 0.2 0.3 0.4 0.5 Normalized Specific Volume Difference

Fitted β12

Binary Interaction Parameter, β12

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 18 of 31

0.01 Sat-Tol Aro-Tol Sat-Hept Aro-Hept DC/Tol DAO/D-N-C Bit/Tol Bit/C7 b12 Corr.

0

-0.01

-0.02 -0.02

-0.01

0 0.01 0.02 Calculated β12

0.03

Figure 3. a) β12 of the excess volume of mixing for the ambient binary mixture dataset and b) dispersion plot obtained using correlation for β12 as a function of vN.


Page 19 of 31

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The saturates consist of paraffins and naphthenes and when mixed with n-heptane lies close to the “same family” trend. These mixtures shrink, consistent with effective packing of different sized molecules. Mixtures of saturates and toluene expand, consistent with the different chemical families trend. Aromatic molecules, while predominantly aromatic in structure, include paraffinic and naphthenic groups and fall between the “same family” and “different family” trends as expected. The largest shrinkage is observed for aromatics mixed with n-heptane suggesting that n-alkanes are able to pack efficiently with aromatics.

For the distillation fractions mixed with toluene, the β12 generally increases from low boiling point (negative β12) to high boiling point fractions (less negative or near positive β12), consistent with a size and aromaticity progression along the distillation curve. The low boiling point fractions have relatively low molecular weight and aromaticity. They have small positive excess volumes when mixed with toluene probably due to inefficient packing and lower chemical compatibility. The higher boiling point fractions have higher molecular weight, are more aromatic, and less positive excess volume values are observed. This consistency between distillation and solubility fractions suggests that a generalized correlation for the β12 of heavy oil and bitumen samples is feasible.

Several attempts were made to improve the correlation of β12 by introducing additional properties of the individual components including combinations of the normalized molecular weight, H/C ratio, and density. Additional properties such as acentric factors and boiling points were also included in the analysis although these properties were not available for all of the samples examined in this study. Equations with same form as the Watson characterization factor and correlation index were also investigated including multiplicative, additive and fractional forms for combinations of molecular weight, density and elemental analysis. No improvement in the correlation of β12 was found compared with correlating to the normalized specific volume difference. The best correlation found for the binary interaction parameter at 293 K, β12293, as a function of vN is given by:

& = −0.00542 +

#.# #/

,012 ( /.&33∗+5 ,6.%6/&)


(8)

Energy & Fuels

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Page 20 of 31

Figure 3a shows the fit of the β12 Correlation (Equation 8) to the binary interaction parameters from the ambient binary mixture dataset. Note, the correlation reaches a maximum β12 for normalized specific volume differences higher than 0.35. There are no data to confirm that β12 decreases after this point and therefore the correlation is limited to mixtures with vN < 0.35 (β12 < 0.017). Also note that the binary mixture between SK_HO_A1 and condensate shows the highest error. The condensate contained some relatively volatile components and the high error can be attributed to compositional changes caused by rapid evaporation of the condensate during sample preparation.

A dispersion plot of the binary interaction parameters from the β12 Correlation is provided in Figure 3b. The density average deviations with the regular solution mixing rules (Equation 1), fitted excess volume mixing rule (Equation 4), API standard (Equation 6), and excess volume mixing rules with interaction parameters from the correlation (Equation 8) are summarized in Table 12 and the maximum deviations are provided in Table 13. The average deviation for the whole ambient binary mixture dataset using the β12 Correlation is 0.8 kg/m³ (0.18 %), compared with 2.7 kg/m³ (0.38%) with the regular mixing rule and 1.5 kg/m³ (0.18%) with the API standard. The errors using the correlation are greatest for nearly ideal solutions given a relative high average percent error although the average absolute error is relatively low. To aid in visualizing the dispersion of error, the error in the predicted maximum excess volume is shown in Figure 4. The error was calculated as the difference between the correlated excess volume and the fitted excess volume at a mass fraction of 0.5 for each component.

It is hardly surprising that the proposed correlation does not give a perfect match to the data. Recall that the petroleum cuts in these pseudo-binary mixtures are a multicomponent mixture themselves. The many interactions between all of these components are averaged when we represent the cut as a single component. This implicit averaging likely introduces errors into any correlation for the binary interaction parameters. In addition, normalized specific volume is not sufficient to account for the large variety of sizes, shapes, and interaction forces in these mixtures. Nonetheless, the β12 Correlation is a significant improvement over the regular solution mixing rule. In most of the cases, it performs better than the API method but the comparison is unfair because the β12 Correlation was tuned to this dataset. Page 20 of 31 ACS Paragon Plus Environment

Page 21 of 31

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Energy & Fuels

Table 12. AAD and ARD for the density of the ambient binary mixture dataset using regular solution, excess volume mixing rule, β12 Correlation, and API standard. Reg. Soln. Rule

Excess Vol. Rule

β12 Correlation

AAD kg/m³ 0.07

ARD % 0.01

AAD kg/m³ 0.01

ARD % 0.00

AAD kg/m³ 0.03

ARD % 0.00

AAD kg/m³ 0.03

ARD % 0.00

Sat-C7(n-heptane)

0.13

0.02

0.03

0.00

0.04

0.01

0.14

0.02

Aro-Tol

0.03

0.00

0.02

0.00

0.03

0.00

0.03

0.00

Aro/C7

0.15

0.02

0.04

0.01

0.04

0.01

0.14

0.02

DC/Tol

0.91

0.10

0.16

0.02

0.36

0.04

0.88

0.10

DAO/diesel

1.20

0.13

0.33

0.04

1.10

0.12

2.31

0.25

DAO/naphtha

5.07

0.61

0.39

0.05

1.05

0.12

4.01

0.48

DAO/condensate

8.30

1.03

0.42

0.05

2.68

0.33

6.27

0.78

Bit/Tol

0.10

0.63

0.07

0.47

0.05

1.09

1.14

0.12

Bit-C7

6.29

0.68

1.04

0.11

1.46

0.16

0.97

0.10

Bit-C5(n-Pentane)

7.60

0.90

0.90

0.11

1.36

0.14

0.77

0.09

Mixture Sat-Tol

API Correlation

Table 13. MAAD and MARD for the density of the ambient binary mixture dataset using regular solution, excess volume mixing rule, β12 Correlation, and API standard. Reg. Soln. Rule

Excess Vol. Rule

β12 Correlation

API Correlation

MAD kg/m³ 0.15

MRD % 0.02

MAD kg/m³ 0.01

MRD % 0.00

MAD kg/m³ 0.07

MRD % 0.01

MAD kg/m³ 0.00

MRD % 0.00

Sat-C7(n-heptane)

0.19

0.03

0.05

0.01

0.06

0.01

0.33

0.05

Aro-Tol

0.09

0.01

0.03

0.00

0.07

0.01

0.09

0.01

Aro/C7

0.16

0.02

0.05

0.01

0.05

0.01

0.23

0.03

DC/Tol

3.62

0.40

2.82

0.31

3.77

0.40

12.19

1.32

DAO/diesel

2.69

0.29

0.69

0.08

1.60

0.17

2.96

0.32

DAO/naphtha

6.73

0.78

0.67

0.08

2.11

0.25

3.23

0.37

DAO/condensate

10.90

1.29

0.80

0.10

4.50

0.53

4.90

0.58

Bit/Tol

1.07

0.11

0.57

0.06

1.74

0.19

1.83

0.20

Bit-C7

6.37

0.71

1.23

0.13

2.27

0.24

1.28

0.13

Bit-C5(n-Pentane)

8.50

0.90

1.00

0.06

1.98

0.23

1.27

0.15

Sample Sat-Tol


Energy & Fuels

8

Error in Predicted Max. Excess Volume, cm³/g x 1000

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 22 of 31

6 4 2 0 -2 -4 -6

Sat-Tol

Aro-Tol

Sat-Hept

Aro-Hept

DC/Tol

DAO/D-N-C

Bit/Tol

Bit/C7

-8 0

0.1 0.2 0.3 0.4 0.5 Normalized Specific Volume Difference

Figure 4. Error in the predicted excess volume of mixing for the ambient binary mixture dataset.

Extending the β12 Correlation to Higher Temperatures and Pressures A second requirement of the excess mixing rule is to predict mixture densities at temperatures and pressures other than the ambient conditions. One issue at these conditions is the appropriate choice of density for a component that is near its critical point or a vapour in its native state but part of a liquid after mixing. One option is to use the effective density; that is, the density of the component if it were in a liquid state at the given conditions. Saryazdi et al.

23

developed

correlations for the effective densities of light n-alkanes and they were used for the solvent densities in mixtures Bit/C7, Bit/C5, Bit/C4, and Bit/C3 for all of the mixing rules and the API method. Note that the effective densities are only valid when the mixture is in the liquid region (reduced temperature < 0.52); all of the mixtures in this study are far from their critical point.

All of the data from Table 10 were found to exhibit the same symmetric excess volumes as at ambient conditions. The data for these mixtures were fitted with the excess volume mixing rule (Equation 4) to determine the β12. As indicated by Figure 5a, the binary interaction parameter was found to be linearly related to temperature, as proposed by Saryazdi et al.

23

Figure 5b

indicates that the effect of pressure on the binary interaction parameter was of relatively small magnitude (at least up to 10 MPa) and therefore, can be neglected. With the additional data available in this study, the linear correlation to temperature was updated as follows: Page 22 of 31 ACS Paragon Plus Environment

Page 23 of 31

7 = 7 & + 0.000065(8 − 293)

(9)

where T is the absolute temperature in K and βij is calculated by Equation 8. The density average deviations with regular solution mixing rules, fitted excess volume mixing rule, API standard, and excess volume mixing rules with interaction parameters from Equation 9 are summarized in Table 14 and the maximum deviations are provided in Table 15. The average deviation for the high temperature and pressure binary mixture dataset using the β12 Correlation is 1.6 kg/m³ (0.19%), compared with 3.5 kg/m³ (0.41%) with the regular mixing rule and 6.8 kg/m³ (0.79%) with the API standard. The API method outperforms the β12 Correlation for the heavier solvents (n-heptane and up) but has much higher deviations for the lighter solvents. The error in the maximum excess volume predicted with the β12 Correlation is shown in Figure 6.

0.03

0.03

(a)

Adjusted Binary Interaction Parameter

Adjusted Binary Interaction Parameter

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

0.025 0.02 0.015 CH/Dec Bit/Tol Bit/C14 Bit/C7 Bit/C5 Bit/C4 fit

0.01 0.005 0

(b)

CH/dec

0.025

Bit/Tol Bit/C7

0.02

Bit/C5 Bit/C4

0.015 0.01 0.005 0 -0.005

-0.005 0

50

100 150 Temperature, °C

200

0

10

20 30 Pressure, MPa

40

Figure 5. Effect of a) temperature and b) pressure on the binary interaction parameter.


50

Energy & Fuels

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Page 24 of 31

Table 14. AAD and ARD for the density of the high temperature and pressure binary mixture dataset using regular solution, excess volume mixing rule, β12 Correlation, and API standard.

β12

Reg. Soln. Rule

Excess Vol. Rule

CH/Dec

AAD kg/m³ 1.3

ARD % 0.2

AAD kg/m³ 0.4

ARD % 0.0

Bit/Tol

0.7

0.1

0.7

0.1

1.6

Bit/C14

0.9

0.1

0.2

0.0

Bit/C7

7.2

0.8

0.7

Bit/C5

7.5

0.9

Bit/C4

2.7

Bit/C3

4.0

Mixture

Correlation AAD ARD kg/m³ % 0.7 0.1

API Correlation AAD kg/m³ 0.8

ARD % 0.1

0.2

0.8

0.1

4.3

0.5

1.4

0.2

0.1

1.0

0.1

1.1

0.1

0.3

0.0

1.1

0.1

7.3

0.9

0.3

0.9

0.1

1.7

0.2

13.4

1.5

0.5

0.4

0.0

0.7

0.1

22.7

2.6

Table 15. MAAD and MARD for the density of the high temperature and pressure binary mixture dataset using regular solution, excess volume mixing rule, β12 Correlation, and API standard.

β12

Reg. Soln. Rule

Excess Vol. Rule

CH/Dec

MAD kg/m³ 2.8

MRD % 0.4

MAD kg/m³ 2.2

MRD % 0.3

Bit/Tol

1.9

0.2

1.3

0.1

5.5

Bit/C14

1.8

0.2

0.6

0.1

Bit/C7

10.0

1.2

1.3

Bit/C5

10.8

1.4

Bit/C4

7.6

Bit/C3

6.3

Mixture

Correlation MAD MRD kg/m³ % 2.0 0.3

API MAD kg/m³ 1.6

MRD % 0.2

0.6

1.8

0.2

7.6

0.9

2.5

0.3

0.1

1.5

0.2

3.6

0.4

1.1

0.1

2.7

0.3

16.7

2.2

0.9

1.5

0.2

2.1

0.2

27.2

3.3

0.8

1.6

0.2

2.0

0.2

48.1

6.0


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15

Error in Maximum Excess Volume cm³/g x 1000

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CH/Dec Bit/C14 Bit/C5 Bit/C3

10

Bit/Tol Bit/C7 Bit/C4

5 0 -5 -10 -15 0

0.2 0.4 0.6 Normalized Specific Volume

0.8

Figure 6. Error in the predicted excess volume of mixing for the high temperature and pressure binary mixture dataset.

Application to Ternary Mixtures The third requirement of the mixing rule is that the density of a multi-component mixture can be predicted from known binary interaction parameters. The excess volume mixing rule was tested on the density data from three ternary mixtures found in the literature, Table 11. The density of the ternary mixture was predicted with the excess volume mixing rule, Equation 5 (using both fitted and correlated β12), and with the regular solution mixing rule. Tables 16 and 17 present the AAD and ARD, and MAD and MRD, respectively, for each ternary mixture for both mixing rules. Note, the excess volume with fitted binary interaction parameters could not be evaluated for Mixture 3 because binary data were not found for each pair of components in this mixture.

The excess volume mixing rule with fitted β12 provided a slightly better prediction of the density of the ternary mixture than the regular solution mixing rule. The average deviations with the fitted binaries was less than 0.3 kg/m³ (0.04%) compared with AAD of less than 0.53 kg/m³ (0.09%) with the regular solution mixing rule. The limited improvement is not surprising because Mixtures 1 and 2 each consist of similar components where near regular solution behavior is to be expected.


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The excess volume mixing rule with correlated β12 provided mixed results but in all cases the average and maximum deviations were less than 2.2 kg/m³ (0.04%) and 4.7 kg/m³ (0.55%), respectively. The deviation was larger than for the regular solution mixing rules for Mixtures 1 and 2 where the excess volumes are small. The deviation was lower than for the regular solution mixing rules for Mixture 3 which consisted of chemical different components where the excess volumes are larger.

In general, the excess volume mixing rules with fitted binary interaction parameters is the most accurate of the three approaches. The excess volume mixing rules with correlated binary interaction parameters is more accurate than the regular solution mixing rules only when the components are from different chemical families or significantly different in size.

Table 16. Deviations from measured densities using regular and excess volume mixing rules (fitted and with the β12 Correlation). Regular Solution Excess Volume β12 Correlation Mixture AAD ARD AAD ARD AAD ARD kg/m³ % kg/m³ % kg/m³ % 1 2 3

0.54 0.27 2.44

0.08 0.03 0.29

0.24 0.28

0.04 0.03

-

-

2.20 0.90 1.66

0.34 0.01 0.20

Table 17. Deviations from measured densities using regular and excess volume mixing rules (fitted and with the β12 Correlation). Regular Solution Excess Volume β12 Correlation Mixture MAD MRD MAD MRD MAD MRD kg/m³ % kg/m³ % kg/m³ % 1 2 3

1.24 0.34 6.06

0.19 0.04 0.69

0.59 0.35

0.09 0.04

-

-


3.21 2.98 4.73

0.49 0.35 0.55

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CONCLUSIONS The density of mixtures of hydrocarbons with other hydrocarbons including heavy oil, bitumen, and their fractions was shown to follow a symmetric excess volume mixing rule where the excess volume is quantified via a binary interaction parameter. Expansion was observed for mixtures of components of similar density particularly with different chemical families because molecular interaction forces are more significant. Shrinkage was observed for mixtures of components with different densities probably because the molecules were of different size and could pack more efficiently.

A new correlation was developed for the binary interaction parameter (β12 Correlation) to improve the prediction of the density of mixtures of heavy oil, bitumen, and their fractions with solvents. The input to the correlation is the normalized specific volume difference calculated from the component properties. The specific volume is able to partially capture the effect of differences in size, shape and chemical family on the mixture density. It was observed that a linear relation exits between the binary interaction parameter and temperature. Using this proportionality, a correlation to estimate the change of the binary interaction parameter with temperature was developed. The effect of pressure was neglected because it was inconsistent and less significant than that of temperature over the pressure range of the study (0.1 MPa to 40 MPa).

At ambient conditions, the excess volume mixing rule fit the data for each binary mixture in the study with average and maximum absolute deviations less than 1.1 kg/m³ (0.11%) and 2.8 kg/m³ (0.31). When the β12 Correlation was used, the average and maximum deviations were less than 3.8 kg/m³ (0.33%) and 3.8 kg/m³ (0.40%), respectively. At higher temperatures and pressures, the AAD (ARD) for the whole ambient binary mixture dataset using the β12 Correlation was 1.6 kg/m³ (0.2%), compared with 3.5 kg/m³ (0.4%) with the regular mixing rule. The average deviation for the ternary mixtures when using the β12 Correlation was 2.1 kg/m³ (0.28%) compared with 1.1 kg/m³ (0.14%) when regular solution mixing rule was used. Two of the three ternaries consisted of similar components. Overall, the mixing rule with correlated β12


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outperformed the regular solution mixing rule for mixtures with components from different chemical families or different size but was less accurate for mixtures of similar components.

The excess volume mixing rule with the β12 Correlation performed comparably to the API method for mixtures involving solvents heavier than n-heptane; however, the β12 Correlation provided better results for mixtures with lighter solvents. The correlation can be easily applied to determine the density of multi-components mixtures. Note that the correlation applies only to symmetric mixtures. All of the mixtures considered in this study involved relatively non-polar components and were symmetric. The correlation is expected to apply to most petroleum related applications but caution is advised for polar solvents.

ACKNOWLEDGEMENTS The authors are grateful for financial support from the sponsors of the NSERC Industrial Research Chair in Heavy Oil Properties and Processing, including NSERC, CNOOC Nexen, Petrobras, Schlumberger, Shell Canada Energy Ltd., Suncor, and Virtual Materials Group. The authors also thank Shell Global Solutions for financial support for the SA Fractions Project and are grateful to Zhongxin Huo for his input.

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Improved Density Prediction for Mixtures of Native and Refined Heavy

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