Density of Hydrocarbon Mixtures and Bitumen Diluted with Solvents

Jun 3, 2013 - DBR Technology Center, Schlumberger, 9450-17th Avenue NW, Edmonton, AB T6N 1M6, Canada. Energy Fuels , 2013, 27 (7), pp 3666–3678...
0 downloads 0 Views 3MB Size
Download PDF
Article pubs.acs.org/EF

Density of Hydrocarbon Mixtures and Bitumen Diluted with Solvents and Dissolved Gases F. Saryazdi,† H. Motahhari,† F. F. Schoeggl, S. D. Taylor,‡ and H. W. Yarranton*,† †

Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada ‡ DBR Technology Center, Schlumberger, 9450-17th Avenue NW, Edmonton, AB T6N 1M6, Canada S Supporting Information *

ABSTRACT: Density data are reported for the following mixtures at temperatures from 20 to 175 °C and pressures up to 40 MPa: ethane + n-decane, propane + n-decane, butane + n-decane, propane + toluene, and propane + cyclooctane, as well as bitumen diluted with ethane, propane, n-butane, n-pentane, n-heptane, and carbon dioxide. A straightforward excess volume based mixing rule is proposed to determine the density of liquid mixtures of hydrocarbons. Excess volumes are accounted for with a binary interaction parameter, and a correlation is proposed to estimate the interaction parameter when mixture data are unavailable. For dissolved gaseous solvents and liquid solvents near their critical point, the input to the mixing rule is their effective liquid density. Effective density correlations were developed for n-alkanes from methane to n-heptane and carbon dioxide. The method is only valid for mixtures in the liquid region with a reduced temperature below approximately 0.52 (or higher at higher pressure). The mixing rule with no excess volume predicted the density of over 60 binary mixtures of liquid hydrocarbons at 25 °C and hydrocarbon mixtures with dissolved gas components over a broad range of pressures and temperatures with an average deviation of less than 1% when the criterion for validity was met. The density of diluted bitumen mixtures was also predicted with the same accuracy. All of the data were fitted to within experimental error when using binary interaction parameters.

1. INTRODUCTION Most heavy oils and bitumens are too viscous to produce and transport unaided, and either heat or dilution is employed to reduce their viscosity and density. For example, heavy oils are commonly diluted with natural gas liquid condensates for pipeline transport and blended with lighter streams in refineries. Historically, thermal recovery methods1 have been applied to recover heavier oils including steam flooding, cyclic steam stimulation (CSS), and steam-assisted gravity drainage (SAGD). Recently, solvent based or solvent assisted processes, such as the vapor extraction process (VAPEX),2 expanding solvent steam assisted gravity drainage (ES-SAGD),3 solvent aided process (SAP),4,5 liquid addition to steam for enhanced recovery (LASER),6 and steam alternating solvent process (SAS)7 have been considered because they are less energy and water intensive than the thermal methods8 and emit considerably less greenhouse gases.9 In these methods, gaseous solvents such as light n-alkanes are used to dilute the in situ heavy crude and reduce its viscosity. The density of these heavy oil and solvent mixtures is an important property in all of these applications. Most of the solvent based recovery methods for heavy crudes rely on the drainage of the diluted crude toward the producing well due to the gravity. Thus, accurate densities of the diluted crude as a function of temperature, pressure, and composition are required to model the process. The density under process conditions is also required to calculate the volumes of the diluted crudes in pipelines based on the measured volumes of the crudes and the solvent. In addition, density is a critical parameter in the separation of heavy oil and water. © XXXX American Chemical Society

The volumes of hydrocarbons in a mixture are not additive; that is, there is a nonzero excess volume of mixing. The excess volumes for mixtures of liquids are relatively small, and therefore additive mixing rules can be used when an approximate density is adequate for the application. However, a different approach is required to determine the density of liquid mixtures accurately or to determine the density of a liquid with a dissolved gas. Alternative methods are partial molar volumes, excess volumes, density correlations, and equations of state. Equations of state (EoS), commonly in cubic form, are widely used in commercial software to model the phase behavior of hydrocarbons and conventional crude oils. However, cubic EoS do not correctly predict the molar volumes of liquid hydrocarbons. Peneloux et al.10 introduced volume translation to improve the volumetric predictions of the Soave−Redlich−Kwong equation of state, without affecting the phase behavior predictions. Others have implemented volume translation for several different cubic equations of state.11−15 Although volume translation improved the predictions for saturated liquid density, the predictions remained poor for compressed liquids at high pressures.16 Also, for mixtures, the volume translation parameter is taken as the molar average of the component parameters,10 which does not always correspond to the molar volume of the mixture. Despite these deficiencies, EoS are the most commonly applied method to Received: February 25, 2013 Revised: June 2, 2013

A

dx.doi.org/10.1021/ef400330j | Energy Fuels XXXX, XXX, XXX−XXX

Energy & Fuels

Article

determine the density of petroleum fluids although there are only a few studies17−20 on the application of cubic equations of state to predict the density of heavy crudes. In general, to obtain accurate density predictions with the EoS approach, the model must be modified or tuned to fit density data for the fluid mixtures of interest. An alternative approach to calculate mixture density is to use the general density correlations developed for saturated liquids, such as the Rackett compressibility equation21,22 and the COSTALD equation.23 These correlations are based on the corresponding states principle and were originally developed for pure components. The inputs are the critical constants of the fluid, but the COSTALD requires the acentric factor as well. At least one density data point is required to tune the value of the adjustable parameter of each correlation. Mixing rules applied to the critical properties of the components are used to determine the mixture density under the saturation conditions.22,23 A modification of the Tait equation is used to calculate the compressed liquid densities of the pure components and mixtures.24 Although these correlations are recommended25 by the American Petroleum Institute (API) for pure hydrocarbons, petroleum fractions, and mixtures with defined compositions, their application to diluted heavy oils and bitumen has not been studied. Robinson26 adapted the COSTALD equation for conventional crude oils diluted with a solvent. He developed correlations for characteristic volume, molecular weight, critical constants, and acentric factor of the crudes as functions of the crude density. These correlations were developed by matching the predictions of COSTALD with several guidelines of API for the calculation of the density of the crudes. The accuracy and general application of this correlation particularly for heavy oils has not been tested. Heavy oils have very high critical temperatures, and even heavy oils diluted with dissolved gases are usually subcritical. Therefore, partial molar volumes or excess volume based mixing rules are a relatively straightforward alternative to determine the density of these mixtures. The molar volume of a mixture is simply the molar average of the partial molar volumes of its components. However, the partial molar volumes are composition dependent, and few data are available. Therefore, the excess volume approach is more convenient to use. The excess molar volume of mixing is the difference between the actual molar volume of the mixture and calculated molar volume by assumption of the regular solution. These volumes are either positive or negative depending on the expansion or shrinkage that occurs upon mixing, respectively. Excess molar volumes have been studied extensively for the mixtures of liquid hydrocarbons. The excess molar volumes depend on (1) differences in the size (or chain length) of the components and (2) differences in their chemical family. The absolute value of excess molar volumes increases as the molecular size of the blended components increases. Also, unlike components tend to form positive excess molar volumes, whereas negative excess molar volumes are observed for the chemically similar hydrocarbons. Excess molar volumes were determined for a number of binary hydrocarbon mixtures27−30 and can be used to determine the actual molar volumes of these mixture at any given pressure and temperature. Thiele and Kay31 observed shrinkage (negative excess volumes) for conventional crude oils diluted with light liquid hydrocarbons and condensates. The American Petroleum Institute provided correlations32,33 to calculate the shrinkage

factor of diluted crudes as function of the volume fraction of the diluent and the API gravity difference of the diluent and the crude oil (API 2509C, later revised to API 12.3 guidelines). Erno et al.34 found that the shrinkage of heavy oil mixtures with condensate solvents was, in most cases, greater than the values predicted by the API guidelines. They proposed new formulations to estimate the shrinkage factors. Ashcroft et al.35 found that expansion can occur in the case of crudes diluted with toluene, cyclohexane, and some high-boiling point paraffinic petroleum cuts. Hence, the API and related methods may not be valid for some solvents. Few data are available for the excess molar volumes of liquid hydrocarbons with dissolved gases. The partial molar volume of dissolved gases in low pressure dilute mixtures can be significantly lower than the actual molar volume of the free gas.36,37 For example, Arnaud et al.38 observed negative excess volumes as high as 18% for mixtures of methane and ntetradecane at 374 K and pressures between 20 and 110 MPa. It appears that dissolved gases occupy liquid-like volumes in the mixture. Standing and Katz39 assumed that hydrocarbon mixtures with dissolved gases form regular solutions and calculated apparent liquid densities of methane and ethane from mixture density data. Katz40 used similar logic to develop empirical correlations for live conventional oil densities using the API gravity of the crude, the gas gravity, and the solution gas/oil ratio. Marra et al.41 followed the same approach and developed correlations to calculate the density of the crude oils saturated with CO2. Recently, Tharanivasan et al.42 adapted the idea of the liquid-like molar volumes for dissolved gases to predict the density of a live oil sample as a regular solution. They developed empirical correlations for the effective density of light n-alkanes at any given pressure and temperature by extrapolating the density of heavier liquid n-alkanes. The objective of this study is to update the effective density correlations and excess volumes used to predict the density of hydrocarbon mixtures with dissolved gases, particularly diluted heavy oils. The diluents considered are light n-alkanes from methane to n-heptane and carbon dioxide. The density model was updated on the basis of literature data as well as new density data collected for mixtures of the light n-alkanes and decane (20−175 °C, 10−40 MPa) as well as bitumen diluted with light n-alkanes and carbon dioxide (20 to 175 °C, 0.1 to 10 MPa).

2. EXPERIMENTAL METHODS 2.1. Materials. Ethane, 99% purity; propane, 99.5% purity; and nbutane, 99.5% purity, were purchased from PraxAir Canada Inc. nDecane, 99.7% purity; cyclooctane, purity ≥99%; and toluene, 99.99% purity, were purchased from Fischer Scientific, Sigma-Aldrich, and VWR, respectively. Technical grade acetone and toluene were applied for cleaning the apparatus and were supplied by VWR. Reverse osmosis water supplied by the University of Calgary water plant and nitrogen, 99.9% purity, from PraxAir was used for apparatus calibration. Two samples of bitumen from the same Western Canadian source were received from Shell Energy Canada and are denoted WC_BIT_B1 and WC_BIT_B2. This bitumen was recovered from a steam assisted gravity process and was distilled by ARC (Alberta Research Council) to remove water and solids. 2.2. Apparatus. The apparatus used for density measurements is a capillary viscometer equipped with an in-line Anton Paar DMA HPM density-meter. Two transfer vessels were connected on either side of the capillary tubes and density-meter and were used to flow the fluid through the apparatus. The capillary tubes were isolated when taking a B

dx.doi.org/10.1021/ef400330j | Energy Fuels XXXX, XXX, XXX−XXX

Energy & Fuels

Article

density measurement. An air bath enclosed the apparatus and maintained a fixed temperature to within ±0.05 °C, except for the room temperature experiments. The room temperature varied within a range of ±0.25 °C. The pressure was maintained and controlled by a Quizix Pump model Q5200 to within ±0.05 MPa of the test pressure for the measurements done on pure hydrocarbon mixtures. For the diluted bitumen mixtures, pressure in the apparatus was controlled using a back pressure regulator on the return line of the hydraulic oil. The set pressure of the regulator was maintained using compressed air pressure monitored with a Bourdon pressure gauge with a precision of 0.05 MPa. Only density measurements were performed for a pure hydrocarbon mixture. Both the density and viscosity of diluted bitumen mixtures were measured, but only density data are reported here. The density meter cell has a built-in temperature sensor which was used to measure the equilibrium temperature and to confirm it was within ±0.05 °C of the test temperature. The cell is connected by an interface module to an evaluation unit displaying the meter oscillation period and the temperature. The oscillation period was measured with a precision of ±0.001 μs and the temperature measured with a precision of 0.01 °C. The density is determined as follows:

ρ = DA . Λ2 − DB

approximately 1 week before displacement to the measurement apparatus. The mixing apparatus is a simple contactor with a perforated middle disk to agitate the mixture at a controlled temperature and pressure. The mass of each component was determined gravimetrically. All displacements were performed at a pressure sufficient to ensure the light component was in a liquid or compressed fluid state. The equilibrated bitumen or nonequilibrated hydrocarbon mixture were then displaced to the measurement apparatus. Both types of mixtures were flowed back and forth (5 cycles per hour) through the apparatus to ensure homogeneity. Since the dead volume (∼5−10 cm3) in the apparatus is small compared to the total sample volume (∼250 cm3), this procedure was able to ensure thorough mixing of the sample. The mixture was considered to be homogeneous when the density measurements were constant throughout the displacement. Then, the flow was stopped and the oscillation period of the fluid was measured. Densities were measured for the mixtures and conditions listed in Table 1. Note, there are two main sources of error:

Table 1. Summary of the Mixture Density Measurements for This Study

(1)

where ρ is density (kg/m3), Λ is the period of the oscillations, and DA and DB are constants determined by calibration. Note that the density of the high viscosity fluids calculated from eq 1 can be higher than the actual values due to damping effects,43 which will be discussed in the next section. 2.3. Calibration. The density meter was calibrated to nitrogen and degassed reverse osmosis water for the temperatures 50, 75, 100, 125, 150, and 175 °C and pressures 0.1, 2.5, 5, 7.5, 10, 12.5, 15, 17.5, 20, 25, 30, 35, and 40 MPa. The densities of the calibration fluids were taken from the Anton Paar DMA HPM instructional manual.44 The calibration constants were determined at each temperature and pressure and linearly interpolated for any intermediate pressure and temperature conditions. Note, the accuracy of the temperature control at 25 °C was not sufficient for calibration purposes. Therefore, a linear extrapolation (corrected based on measured n-decane densities at 18 °C) was used to estimate the density meter constants for any measurements at or near room temperature (18 to 25 °C). The ndecane densities were compared with data from the NIST database44 for the correction. The accuracy of the density measurements with the calibrated density-meter was evaluated against the known density of the pure hydrocarbons and the viscosity standards. The measured densities for propane, n-decane, and toluene were compared with the experimental values of other authors from the NIST database45 over the range of temperatures and pressures indicated above (excluding data below 50 °C for n-decane). The average absolute deviations were less than 0.5 kg/m3 in all cases. The accuracies of the density measurements for high viscosity fluids were assessed using the viscosity standards provided by Cannon Instruments (viscosity ranging from 3 to 30 000 mPa s). The densities of these fluids were measured (using eq 1) at temperatures of 40, 50, 80, and 100 °C and were within 0.5 kg/m3 of the reported values. Although viscous damping is expected to cause deviations that increase with viscosity and reach a plateau above approximately 300 mPa s,43 no clear correlation was observed between deviations and viscosity of the fluids. It appears that inaccuracies in the calibration and the precision of temperature control to within 0.05 °C of the test temperature obscure the expected trend. Therefore, no viscous damping correction was applied, and the accuracy of density measurements using the calibrated density-meter in this study is assessed to be ±0.5 kg/m3 over a viscosity range of 0.5 to 105 mPa s. 2.4. Density Measurements for Mixtures. To prepare a hydrocarbon mixture for measurement, mixtures of a specified composition were prepared in a transfer vessel. The volumes of each phase were determined from the pump displacement verified with the amount of displaced hydraulic oil. Diluted bitumen mixtures were prepared using an in-house mixing apparatus and were equilibrated for

component 1

component 2

n-decane n-decane n-decane cyclooctane toluene WC_BIT_B2 WC_BIT_B2 WC_BIT_B2 WC_BIT_B2 WC_BIT_B1 WC_BIT_B2

ethane propane n-butane propane propane ethane propane n-butane n-pentane n-heptane carbon dioxide

composition (wt % comp 2)

temperature (°C)

pressure (MPa)

6, 12.5 6, 12.5, 25 6, 12.5, 25 6, 12.5, 25 6, 12.5, 25 5.2 7.6, 16 7.3, 14.5 15, 30 15, 30 5.1

20−175 20−175 20−175 20−175 20−175 20−150 20−175 20−175 20−175 20−175 20−150

10−40 10−40 10−40 10−40 10−40 2.5−10 2.5−10 1.2−10 0.1−10 0.1−10 3.5−10

composition and temperature. A composition error will manifest as a systematic error in the density, while errors in temperature will cause random variation in density from one temperature to another.

3. MODELING For mixtures of liquids which form regular solutions, the density of the mixture is given by ρmix

−1 ⎡ wi ⎤ = ⎢∑ ⎥ ⎢⎣ ρi ⎥⎦

(2)

where ρmix is the density of the mixture and ρi and wi are the density and mass fraction, respectively, of component i. For mixtures which do not form regular solutions, the excess volume of mixing must be accounted for. In this study, the density of such a mixture is calculated as follows: ρmix

⎡ ⎤−1 ⎛ ⎞ ww 1 i j 1 ⎢ ⎜ + ⎟(1 − β )⎥ = ∑∑ ij ⎥ ⎜ρ ⎢ ρj ⎟⎠ 2 ⎝ i ⎣ i j ⎦

(3)

where βij is the binary interaction parameter between components i an j. For a binary mixture, eq 3 simplifies to ρmix

⎡w ⎤−1 ⎛1 w2 1⎞ ⎥ 1 ⎢ ⎜ ⎟ = + − w1w2⎜ + ⎟β12 ρ2 ρ2 ⎠ ⎥⎦ ⎢⎣ ρ1 ⎝ ρ1

(4)

where subscripts 1 and 2 denote the two components. The last term on the right-hand side of the expression is the excess C

dx.doi.org/10.1021/ef400330j | Energy Fuels XXXX, XXX, XXX−XXX

Energy & Fuels

Article

volume of mixing. The values of the binary interaction parameters must be determined from data fitting or from a correlation. For liquids containing a dissolved gas, the above mixing rules cannot be applied using the pure component gas density. Instead, the effective liquid density of the dissolved gas, ρe, is required. Tharanivasan et al.42 estimated the effective liquid density of light n-alkanes based on the extrapolated molar volumes of higher carbon number n-alkanes against their molecular weight. However, the effective liquid densities calculated from these molar volumes were only valid for pressure above 10 MPa. Figure 1 illustrates why the correlations

Figure 2. Effective liquid densities of several n-alkanes at 60 °C.

ρe0 = a1 + a 2T

(6)

B = b1 + b2T

(7)

where a1, a2, b1, and b2 are constants specific to each n-alkane. The correlation parameters are provided in Table 2. Validation of the proposed correlation is discussed later. The correlation for the effective density of carbon dioxide was developed on the basis of measured densities from NIST,45 Padua et al.,46 and Van der Gulik.47 On the basis of the comparison between the measured densities of the propane and the effective densities, the following assumptions were made about the effective density of carbon dioxide: (1) For temperatures well below the critical temperature (T < 240 K, Tc = 304 K), the effective density and liquid density of the carbon dioxide are the same. (2) For temperatures between 240 and 308 K, the effective density of carbon dioxide approaches its density at high pressures (P > 200 MPa). The effective density of the carbon dioxide was then correlated using the form suggested by Tharanivasan et al.:42

Figure 1. Molar volumes of liquid n-alkanes at 60 °C and 10 MPa (dotted line, extrapolation including all liquid n-alkanes; solid line, extrapolation including only n-alkanes with carbon numbers above six).

failed at lower pressure. When the molar volumes of n-alkanes near their critical point are included, the molar volumes deviate upward from a linear trend at lower carbon numbers, Figure 1. However, when only the molar volumes of n-alkanes well into the liquid region are included, the molar volumes follow a linear trend, Figure 1. The molar volumes determined from the linear extrapolation are in better agreement with experimental data for liquid mixtures, as will be shown later. For example, the effective molar volume of methane as part of a liquid mixture is lower (more liquid like) than that of pure methane. The linear based correlation is only valid for mixtures in the liquid region, not near the critical point, and only densities from the liquid region should be used to develop the correlation. The correlations of Tharanivasan et al.42 were revised based on linear extrapolations of the n-alkanes with carbon numbers from 7 to 16. Densities were obtained for all of the n-alkanes from the NIST standard reference database.44 The molar volumes of n-alkanes from methane through n-heptane were calculated at temperatures of 20, 40, 60, 80, 100, and 120 °C and pressures up to 100 MPa. The effective liquid density at each temperature and pressure was calculated from the extrapolated molar volumes and the molecular weight of the n-alkane. At each temperature, the effective liquid densities increase approximately linearly with pressure, Figure 2. Therefore, the effective liquid densities were fit with the following expression: ρe = ρe0 + B × P (5)

ρe = ρeo exp[4.12 × 10−4P + α2 (1 − exp( −1.37 × 10−2P))]

(8)

where P is the pressure in MPa. The parameters ρeo and α2 are functions of temperature (T in K) as follows: ρeo = 2334.9 exp( −0.003157T )

α2 = −0.3233 + 0.001897T

(9) (10)

The numerical values of the parameters in eqs 8, 9, and 10 were determined by fitting to the measured density of the carbon dioxide that satisfied the two assumptions.

4. RESULTS 4.1. Liquid−Liquid Mixtures of Pure Hydrocarbons. Mixtures of liquid hydrocarbons generally have small excess volumes, and their density can usually be modeled with regular solution based mixing rules (eq 2) with less than 1% error based on a data set of 67 hydrocarbon mixtures collected by Chevalier et al.48 The data can be fitted to within experimental error when using the excess volume based mixing rule. Figure 3 shows two examples of the regular solution mixing rule predictions and excess volume mixing rule fits for binary hydrocarbon mixtures. Recall that the specific volume is simply the reciprocal of the density and for a regular solution will be linear versus the mass fraction of a component.

where ρe0 is the effective liquid density at zero pressure, B is a constant specific to each n-alkane, and P is pressure. ρe0 and B were correlated to the temperature as follows: D

dx.doi.org/10.1021/ef400330j | Energy Fuels XXXX, XXX, XXX−XXX

Energy & Fuels

Article

Table 2. Parameters for the Effective Liquid Density Correlation for n-Alkanes from Methane to n-Heptane component

a1 (kg/m3)

a2 (kg/m3 K)

b1 (kg/m3 MPa)

b2 (kg/m3 MPa K)

AARD (%)

MARD (%)

methane ethane propane n-butane n-pentane n-hexane n-heptane

532.157 704.900 793.847 846.443 878.006 901.512 918.603

−0.69737 −0.82749 −0.85489 −0.85024 −0.82817 −0.80985 −0.79155

0.42606 0.21442 0.05309 −0.05448 −0.09229 −0.14176 −0.17738

0.001143 0.002012 0.002440 0.002648 0.002648 0.002685 0.002692

0.7 0.6 0.5 0.4 0.4 0.4 0.3

2.9 2.2 1.8 1.5 1.2 1.1 0.9

Figure 3. Specific volumes of mixtures of liquid hydrocarbons at 25 °C and 0.1 MPa modeled with regular solution mixing rules and excess volume mixing rules: (a) n-hexane and n-tetradecane; (b) benzene and n-decane. Data from Chevalier et al.48

Figure 4. Binary interaction parameters fitted to specific volume data from Chevalier et al.48 for mixtures of liquid hydrocarbons at 25 °C and 0.1 MPa: (a) versus normalized molecular weight difference; (b) versus normalized specific volume difference.

Figure 5. Measured and predicted densities for mixtures of propane and n-decane: (a) 6.0 wt % propane; (b) 25 wt % propane.

E

dx.doi.org/10.1021/ef400330j | Energy Fuels XXXX, XXX, XXX−XXX

Energy & Fuels

Article

For mixtures of molecules from the same chemical family such as n-alkanes, the excess volumes tend to become more negative as the size difference of the molecules increases, probably reflecting more efficient packing, Figure 3a. For mixtures of molecules from different chemical families, the excess volumes tend to be positive, reflecting the larger repulsion forces, Figure 3b. Hence, there is no clear trend when interaction parameters for binary pairs are plotted versus the normalized molecular weight difference (ΔMW/MWavg), Figure 4a. However, clear trends for similar components and dissimilar components emerge when the interaction parameters are plotted versus the normalized difference in specific volume (Δv/vavg), Figure 4b. It appears that the specific volume difference approximately captures both the packing and repulsion effects. The trends in Figure 4 may provide a basis for a generalized correlation of the binary interaction parameters as will be discussed later. 4.2. Hydrocarbon Mixtures with Dissolved Gas. The density of mixtures of propane and n-decane are presented as an example and are shown at different temperatures and pressures at compositions of 6.0 and 25 wt % in Figure 5. The mixture densities were predicted using the regular solution mixing rule and the effective densities from the new correlation (dashed lines on all figures). The predicted densities are generally within 1% of the measured values except at conditions where the mixture is approaching its critical point; that is, at high temperature, low pressure, and high dissolved gas content. The good agreement with the data indicates that mixtures of propane and n-decane do form regular or nearly regular solutions and that the effective densities are accurate at least for mixtures of n-alkanes. However, it is necessary to develop a criterion related to the proximity to the critical point to identify where the correlation breaks down. To develop a criterion to define the range of validity of the correlation, the limiting pressure and temperature were identified at which the error in the calculated mixture density exceeded 1%. The critical point of the mixture was determined using the Advanced Peng−Robinson equation of state in VMGSim software49 with the default interaction parameters. The limiting temperature and pressure were converted to reduced coordinates, and then the reduced limiting temperatures and pressures for all the binary mixtures measured in this work were plotted, Figure 6. Each symbol represents the boundary between accuracy less than 1% (to the right) or greater than 1% (to the left). Most of the boundary points cluster along a line, and therefore the following criterion was defined for the valid range of the correlation: Tr < 0.52 + 0.021Pr

Figure 6. Errors in mixture density based on effective densities plotted at reduced temperature and pressure. The solid line is the criterion for less than 1% error.

The criterion, eq 11, was used to screen the hydrocarbon mixture data listed in Table 1 as well as additional data from the literature for the following mixtures: methane/n-decane45 and methane/toluene,45 ethane/n-decane,50 methane/n-tetradecane,51 and ethane/n-tetradecane.52 The accuracy of the correlation was then assessed against all of the screened data. Dispersion plots of the predicted density versus measured density for mixtures of butane/n-decane, propane/n-decane, ethane/n-decane, ethane/n-tetradecane, methane/n-decane, and methane/n-tetradecane are shown in Figures 7 and 8. The average absolute deviation (AAD), average absolute relative deviation (AARD), maximum absolute deviation (MAD), and maximum absolute relative deviation (MARD) for each case are summarized in Table 3. The predicted densities are generally in very good agreement with data with the highest deviations occurring when the fluid approaches the critical region and reaches the boundary where the correlation is no longer valid. In several cases, the maximum relative error exceeded 1%. For example, the largest deviations were observed for the methane/decane data set. In this case, data from different sources reported different values under the same conditions. We therefore attribute the deviations to compositional errors. The same argument applies to the other data sets with high maximum errors. There is no clear evidence of a systematic deviation at higher solvent contents that would be expected if there were excess volumes of mixing. This observation appears to contradict the observed trend in βij for n-alkane mixtures, Figure 4. However, the maximum expected excess volumes for these mixtures (at 50 wt % solvent) are on the order 2 kg/m3, and it was not possible to distinguish this effect from scatter in the data, particularly at low solvent contents. For example, changing the βij value from −0.01 to +0.01 altered the absolute deviation by less than 0.5 kg/m3 in all cases. (Note, there was less scatter in the data for liquid−liquid mixtures from which the βij in Figure 4 were obtained.) Hence, based on the data available, it is concluded that mixtures of n-alkanes involving a dissolved gas can be modeled as regular solutions within the error of the measurements when effective densities are employed. Dispersion plots for the densities of mixtures of propane/ toluene, propane/cyclooctane, and methane/toluene are also shown in Figures 9a,b and 10, respectively. The AAD, AARD, MAD, and MARD for the predicted densities of these mixtures

(11)

Only the data for 12.5 wt % ethane in n-decane violated the criterion. Possible explanations are as follows: there is a composition error in the data; the criterion does not apply to more extreme differences in component properties; the critical point of the mixture is calculated incorrectly; or excess volumes must be accounted for. Note that the critical temperatures of diluted bitumens are expected to be high except at very high dilutions, and therefore the effective density correlation is expected to be valid for all conditions of interest to this study. Note, the error for the predicted densities of mixtures of ethane from different sources is sometimes positive and sometimes negative, suggesting that compositional errors are likely the main source of error. F

dx.doi.org/10.1021/ef400330j | Energy Fuels XXXX, XXX, XXX−XXX

Energy & Fuels

Article

Figure 7. Predicted versus measured density for mixtures of (a) n-butane and n-decane; (b) propane and n-decane (data from this work).

Figure 8. Predicted versus measured density for mixtures of (a) ethane and n-decane (this work and data from 2−16 wt % ethane from Bufkin et al.50) and ethane and n-tetradecane (data from 1.7−5 wt % ethane from Kariznovi et al.52); (b) methane and n-decane (data from 1.2 to 26 wt % methane from NIST45) and methane and n-tetradecane (data from 0.7 to 4.4 wt % methane from Nourizadeh et al.51).

carbon dioxide were compiled from the literature and screened according to the criterion of eq 11: squalane,53 n-hexadecane,54 n-decane,55,56 n-hexane,57 and toluene.58 These mixture were assumed to form regular solutions, and their densities were predicted using eq 3 with βij = 0 and the proposed effective density correlation for carbon dioxide. The summary of the deviations of the model predictions for each mixture are given in Table 4. The predictions are generally in good agreement with the measured values with a maximum relative deviation of 1.5%. Nonetheless, most of the predictions are higher than measurements, indicating that these mixtures expand upon mixing (relative to the mixture density based on the effective densities for carbon dioxide). The modeling of the density of these mixtures can be improved using the excess volume mixing rule, Table 4. The values of βij for the mixtures were determined by regression using a least-squares fit to all available data regardless of pressure and temperature. The most significant improvement occurred for the n-decane + carbon dioxide mixtures where the maximum deviation was reduced from 10.7 kg/m3 to 5.8 kg/m3, Figure 11a and b. It was not practical to generalize the βij for mixtures of hydrocarbons and carbon dioxide due the limited available data. 4.4. Diluted Bitumens. Before considering the density of diluted bitumen, it is necessary to determine the density of the bitumen itself. The measured densities are shown for Bitumen WC_BIT_B2 in Figure 12. The density of Bitumen WC_BIT_B2 was approximately 2 kg/m3 greater than that of

Table 3. Summary of Deviations of the Calculated Densities of the Liquid Mixtures of Pure Hydrocarbon Compounds with Gaseous n-Alkanes mixture ethane/n-decane propane/n-decane n-butane/n-decane propane/toluene propane/ cyclooctane methane/n-decane methane/ntetradecane methane/toluene ethane/ntetradecane

# points

AAD (kg/ m3 )

AARD (%)

MAD (kg/ m3)

MARD (%)

24 38 43 28 42

6.0 2.0 1.5 2.2 2.2

0.9 0.3 0.2 0.3 0.3

9.4 6.9 5.3 4.4 6.5

1.4 1.0 0.7 0.6 0.8

230 18

6.2 2.8

0.9 0.4

21.6 4.1

3.2 0.6

60 6

4.4 3.2

0.6 0.5

13.7 5.2

1.9 0.8

are provided in Table 3. The results are similar to those obtained for mixtures of n-alkanes. The largest errors were observed for mixtures of methane/toluene and are likely caused by compositional errors, Figure 10. Hence, the effective densities appear to be valid for any hydrocarbon mixtures. Again, there is little evidence for significant excess mixing volumes. The larger MARD for toluene appears to be more related to data scatter than excess mixing volumes, Figure 10. 4.3. Hydrocarbon Mixtures with Dissolved Carbon Dioxide. Data for mixtures of the following hydrocarbons with G

dx.doi.org/10.1021/ef400330j | Energy Fuels XXXX, XXX, XXX−XXX

Energy & Fuels

Article

Figure 9. Predicted versus measured density for mixtures of (a) propane and toluene; (b) propane and cyclooctane.

where T is the temperature in K, and A, B, C, and D are fitting parameters. The fitted parameters for Bitumens WC_BIT_B1 and WC_BIT_B2 are provided in Table 5. The correlations fit the density data with an AAD of 0.4 kg/m3 and an AARD of 0.03%, Figure 12. Figures 13 and 14 are dispersion plots of the calculated versus measured density for bitumens and heavy oil diluted with hydrocarbon solvents and carbon dioxide, respectively. The density was calculated with the regular solution mixing rule (a) and the excess volume mixing rule (b). For the mixtures of diluted bitumen with heptane, pentane, butane, and propane, the density values measured in this study were higher than the density calculated from the regular solution mixing rule. In other words, the mixtures shrank upon mixing (negative excess volumes). The shrinkages observed for the dissolved gaseous propane and n-butane were similar to that observed for the diluted mixtures with liquid heptane and pentane. Even with the regular solution mixing rule, the average absolute deviations did not exceed 8 kg/m3, Table 6, only slightly outside the accuracy of the measured mixture densities (±3 kg/m3 based on ±0.5 wt % accuracy in the composition measurement). Mixtures of ethane and bitumen as well as carbon dioxide and bitumen appeared to form nearly regular solutions. The density data were also fitted with the excess volume mixing rule and a single binary interaction parameter, independent of pressure, temperature, and composition, for each diluted bitumen mixture. The binary interaction parameters used to fit the data are provided in Table 6 along with the deviations for the regular solution mixing rule and excess volume mixing rule. The excess volume mixing rule fit the data almost within the precision of the individual density measurements (±0.5 kg/m3). As a further test, experimental density data were compiled from the literature for the following diluted bitumen mixtures:

Figure 10. Predicted versus measured density for mixtures of methane (C1) and toluene (data from 5.5 to 14.8 wt % from NIST45).

WC_BIT_B1 at any given temperature and pressure. The small difference in density may arise from small differences in the amount of light ends in each sample after their treatment to remove water and solids. The bitumen density data were fit with the following expression: ρ = ρo exp[co(P − 0.1)]

(12)

where ρo is the density in kg/m3 at atmospheric pressure, P is the pressure in MPa, and co is the oil compressibility in MPa−1. The atmospheric density and oil compressibility were related to temperature as follows: ρo = A − BT

(13)

co = C exp(DT )

(14)

Table 4. Summary of Deviations of the Calculated Densities of the Mixtures of Pure Hydrocarbon Compounds with Carbon Dioxidea regular solution mixing rule

a

mixture

NP

AAD kg/m

squalane n-hexadecane n-decane toluene

112 8 378 6

4.2 0.9 2.5 1.5

3

AARD %

MAD kg/m

0.51 0.11 0.34 0.17

12.5 2.5 10.7 3.4

3

excess volume mixing rule MARD %

βij

AARD kg/m3

MAD %

MARD kg/m3

MARD %

1.50 0.32 1.40 0.39

−0.015 −0.006 −0.028 0.003

3.7 0.4 0.5 1.7

0.46 0.05 0.07 0.19

10.2 1.0 5.8 2.8

1.43 0.12 0.76 0.32

NP is number of points. H

dx.doi.org/10.1021/ef400330j | Energy Fuels XXXX, XXX, XXX−XXX

Energy & Fuels

Article

Figure 11. Predicted versus measured density for mixtures of carbon dioxide and n-decane: (a) regular solution mixing rule; (b) excess volume mixing rule with βij = −0.028.

example, the reported shrinkage of Athabasca bitumen with propane was significantly greater in magnitude than the shrinkage observed for mixtures of WC_BIT_B2 with propane. The shrinkage for both Cold Lake and Wabasca bitumens with carbon dioxide was significantly greater than the shrinkage for both WC_BIT_B2 and HO with carbon dioxide. The ternary mixture of Athabasca bitumen with propane and carbon dioxide appeared to expand upon mixing relative to its binary mixture with propane. It is possible that these differences relate to different properties of the bitumens. However, these bitumens are from the same region, and it is not apparent why their interaction with a given solvent would differ. The uncertainties on the reported density and compositions of the mixtures from literature can be considerable due to the measurement methodologies. Nonetheless, the effective liquid density correlations provide satisfactory results for the mixture densities, and experimental error is likely the largest contribution to the higher deviations. 4.5. Generalization of Binary Interaction Parameters. Figure 15a shows the best fit values of the binary interaction parameters (βij) at 25 °C for chemically dissimilar pure hydrocarbons (from Figure 4) as well as the diluted bitumens plotted versus normalized specific volume difference. For the diluted bitumens, the binary interaction parameters were determined by interpolation from regressed βij values at different temperatures, Figure 15b. Note that only the βij values for mixtures with data collected in this study were plotted because the βij values for the literature data were significantly scattered and did not follow a clear trend. Additional data were available for an n-decane diluted heavy oil (HO X+C10)64 and toluene diluted maltenes from another bitumen (DA Bit+Tol).65 The fitted βij’s for the respective mixtures were −0.002 and 0.008. While there is some scatter, the βij298 for mixtures of liquid components increases as the normalized specific volume difference increases. The trend is consistent for mixtures of pure hydrocarbon liquids as well as bitumen and heavy oil diluted with liquid solvents. The βij298 value for carbon dioxide diluted bitumen also falls on the observed trend for pure hydrocarbon mixtures. The trend reverses at a normalized

Figure 12. Measured and correlated density of Bitumen WC_BIT_B2.

Cold Lake (CL)59 and Wabasca (WB)60 bitumens with methane, ethane, and carbon dioxide; Athabasca (AT) bitumen61,62 with propane and propane + carbon dioxide; and Bartlett heavy oil (HO)63 with carbon dioxide. The density data for the base dead Cold Lake, Wabasca, and Athabasca bitumens were only available at atmospheric pressure conditions versus temperature and were fitted with eq 13. The density values of these bitumens at higher pressure conditions were calculated using eq 12 with the same compressibility values as the WC_BIT_B2. The deviations in the density predictions for the literature data were greater than for the data collected in this study but still within an ARD of 1.5%, Table 6. Part of the resulting higher deviations for the mixtures from the literature can be attributed to the assumption made about their compressibility to calculate the dead density values at elevated pressures. However, there are some issues with the data as well. First, some of the data are not self-consistent. For instance, mixtures of methane and ethane with Cold Lake bitumen were reported to expand and shrink, respectively, relative to the density from the regular solution mixing rule. However, the opposite trends were observed for Wabasca bitumen. Second, significantly different shrinkages were reported for similar bitumens. For

Table 5. Fitted Parameters of the Density Correlations for Bitumen Samples bitumen

A (kg/m3)

B (kg/m3K)

C × 104 (MPa−1)

D (1/K)

AARD (%)

MARD (%)

WC_BIT_B1 WC_BIT_B2

1202.7 1203.9

−0.6451 −0.6433

1.296 1.488

0.0045 0.0041

0.03 0.02

0.10 0.04

I

dx.doi.org/10.1021/ef400330j | Energy Fuels XXXX, XXX, XXX−XXX

Energy & Fuels

Article

Figure 13. Calculated versus measured density for diluted bitumen mixtures with hydrocarbon solvents: (a) regular solution mixing rule; (b) excess volume mixing rule with fitted βij values given in Table 6.

Figure 14. Calculated versus measured density for diluted bitumen mixtures with carbon dioxide: (a) regular solution mixing rule; (b) excess volume mixing rule with fitted βij values given in Table 6.

Table 6. Summary of the Deviation of the Calculated Densities of the Diluted Bitumen Mixturesa regular solution mixing rule (βij = 0) mixture this study B2 + C2 B2 + C3 B2 + n-C4 B2 + n-C5 B1 + n-C7 B2 + CO2 literature CL+C1 CL+C2 CL+CO2 WB+C1 WB+C2 WB+CO2 AT+C3 AT+C3+CO2 HO+CO2

excess volume mixing rule with fitted βij

ex. vol. mix. rule with generalized βij

NP

AAD (kg/m )

ARD (%)

βij

AAD (kg/m )

ARD (%)

AAD (kg/m3)

ARD (%)

19 41 62 54 53 15

0.4 4.2 2.9 7.6 7.2 1.9

0.04 0.48 0.34 0.90 0.82 0.20

−0.001 +0.017 +0.015 +0.023 +0.022 +0.008

0.4 0.9 1.0 0.9 1.3 1.8

0.04 0.10 0.12 0.11 0.15 0.18

0.3 1.6 1.5 0.7 0.7 1.9

0.03 0.18 0.17 0.09 0.08 0.19

16 19 23 12 19 18 21 22 56

4.8 10.6 12.3 6.9 6.2 7.2 12.9 10.6 5.33

0.49 1.18 1.2 0.72 0.69 0.74 1.40 1.21 0.61

−0.066 +0.048 +0.069 +0.156 −0.030 +0.066 +0.042 −0.008b +0.014

3.8 5.8 6.3 2.0 4.7 3.1 7.8 1.1 5.2

0.39 0.64 0.64 0.21 0.52 0.32 0.85 0.13 0.56

4.1 11.5 13.2 8.1 5.7 7.7 11.4 10.9 6.4

0.42 1.28 1.33 0.84 0.63 0.78 1.24 1.25 0.69

3

3

a Note Bitumen WC_BIT_B1 and B2 (B1 and B2 in table) are from the same source reservoir; NP is number of points. bBinary interaction parameters between Athabasca bitumen and carbon dioxide; the interaction parameter for bitumen and propane is assumed to be the same as regressed for AT+C3 data.

specific volume difference of ∼0.45, at the approximate transition from liquid solvents to dissolved gases (except

CO2). Two possible explanations are as follows: (1) The predicted effective densities for the dissolved gases are too J

dx.doi.org/10.1021/ef400330j | Energy Fuels XXXX, XXX, XXX−XXX

Energy & Fuels

Article

Figure 15. (a) Binary interaction parameters for diluted bitumens and pure hydrocarbon mixtures at 298 K. Symbols are fitted values; line is eq 15. (b) Binary interaction parameters for diluted bitumens versus temperature. Symbols are fitted values, lines are from eq 16.

Figure 16. Density of bitumens WC_BIT_B1 and WC_BIT_B2 diluted with n-alkanes and carbon dioxide at (a) 50 °C and 2.5 MPa; (b) 100 °C and 10 MPa. Equations 15 and 16 were used to determine the βij for the excess volume mixing rule.

Figure 15b shows that the regressed values of the βij for diluted bitumen mixtures with solvents increase linearly versus temperature. The observed slopes for hydrocarbon solvents are similar (solid lines), but the slope for carbon dioxide is considerably greater (dashed line). The deviation can be attributed to the inaccuracy of the effective density correlation for carbon dioxide at higher temperatures. Recall that the correlation was developed from extrapolations at temperatures above 308 K. The βij’s for the hydrocarbon solvents were regressed versus temperature to obtain the following correlation (solid lines in Figure 15b):

large, causing an overprediction of the mixture density that partially compensates for the expected negative excess volume of the mixture (the increasing trend gives larger positive binary interaction parameters corresponding to larger negative excess volumes). (2) There is a maximum in βij that reflects a shifting balance between efficient packing and increased repulsion forces as the size difference between the molecules changes. For example, mixtures of an n-alkane with a nonhydrocarbon do show30 a maximum in the excess mixing volumes when plotted against the carbon number of the n-alkane. Since there is not an obvious alternative method to evaluate the effective densities, we assume for convenience that there is a maximum in the 25 °C binary interaction parameters. The following correlation provides an optimized but still imperfect fit (solid line in Figure 15a) for all binaries:

βij = βij 298 + 8.74 × 10−5(T − 298)

(16)

where T is the temperature in K. The proposed correlations for βij values were used to calculate the density of the diluted bitumen mixtures, Table 6. Figure 16a and b show the measured and calculated densities of the diluted bitumens at 50 and 100 °C, respectively. The AAD and AARD are less than 1.9 kg/m3 and 0.19%, respectively, at all temperatures, pressures, and compositions for the data collected in this study. The predictions are more deviated for the mixtures from the literature, with AAD and AARD less than 13.2 kg/m3 and 1.33%, respectively.

⎛ |vi298 − vj298| ⎞ ⎟⎟ + 0.022 βij 298 = −0.092 0.435 − 2⎜⎜ ⎝ (vi298 + vj298) ⎠ (15)

where βij298 is the binary interaction parameter and vi298 is the specific volume (in m3/kg) of the component “i” at 298 K (25 °C). Note that eq 15 only applies to dissimilar hydrocarbons and for use with effective densities. It has not been tested for liquid−liquid mixtures where the normalized specific volume difference values are higher than 0.4 and is only recommended when data are not available to fit a binary interaction parameter.

5. CONCLUSIONS The densities of hydrocarbon mixtures and diluted heavy bitumen were modeled, generally within experimental error, K

dx.doi.org/10.1021/ef400330j | Energy Fuels XXXX, XXX, XXX−XXX

Energy & Fuels

■

ACKNOWLEDGMENTS We thank the NSERC Industrial Research Chair in Heavy Oil Properties and Processing sponsors for financial support and to Shell Chemical Americas for supplying samples.

using a symmetric excess volume based mixing rule. The mixing rule includes a binary interaction parameter, βij, which can be determined by fitting experimental data. The mixing rule reduces to the ideal mixing rule for regular solutions when βij = 0. It was shown that the binary interaction parameters for liquid−liquid mixtures of pure hydrocarbon compounds correlate to the normalized molar volume difference. The concept of the effective density42 was utilized to use the proposed mixing rule for liquid mixtures containing dissolved gas components. The effective density correlations of Tharnivasan et al.42 were updated for light n-alkanes from methane to n-heptane in the temperature and pressure ranges of 20−120 °C and 0.1−100 MPa. The new set of the correlations was developed based on linear extrapolation of molar volumes of higher carbon number n-alkanes against their molecular weight at temperatures well below critical temperature. In addition, the effective densities of carbon dioxide were also correlated to temperature and pressure based on the actual liquid density data of carbon dioxide at lower temperatures and/or higher pressures and extrapolation under other conditions. A criterion based on the critical temperature and pressure of the mixture was proposed to define the range of validity of the mixing rule and the effective density correlation. The criterion was developed based on the density data, collected in this study, for binary mixtures of n-decane with ethane, propane, and n-butane; toluene and propane; and cylooctane and propane at pressures from 10 to 40 MPa and temperatures from room temperature up to 175 °C. The densities of the diluted bitumen mixtures with solvents were also predicted generally within 1% of the measured values using the proposed mixing rule (with βij = 0) and the effective density correlations at temperature and pressure ranges of 20− 175 °C and 0.1−10 MPa. The studied solvents included ethane, propane, n-butane, n-pentane, n-heptane, and carbon dioxide. For all diluted bitumens, shrinkage was observed; i.e., there are negative excess volumes for these mixtures. The existence of negative excess mixing volumes is not surprising for the mixtures of hydrocarbons with different sizes and indicates a more efficient packing at the molecular level. Binary interaction parameters were also adjusted to nonzero values, independent of pressure, temperature, and composition, to fit the density of diluted bitumen mixtures with average absolute deviations less than 1.6 kg/m3. A general correlation was developed relating the βij values to the normalized difference in molar volumes. The densities of the diluted bitumen mixtures were then predicted by the proposed mixing rule and generalized βij to within 5.0 kg/m3 of the measured values and the overall average absolute deviations of 2.0 kg/m3.

■

■

REFERENCES

(1) Butler, R. M. GravDrain’s Blackbook: Thermal Recovery of oil and bitumen; GravDrain Inc.: Calgary, Alberta, Canada, 1997; ISBN09682563-0-9. (2) Butler, R. M.; Mokrys, I. J. Solvent Analog Model of SteamAssisted Gravity Drainage. AOSTRA J. Res. 1989, 5, 17. (3) Nasr, T. N.; Ayodele, O. R. New Hybrid Steam-Solvent Processes for the Recovery of Heavy Oil and Bitumen; Paper SPE 101717 presented at the 2006 Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, U.A.E., November 5−8, 2006. DOI: 10.2118/101717-MS. (4) Gupta, S.; Gittins, S.; Picherack, P. Field Implementation of Solvent Aided Process; Paper 2002−299 presented at the 53rd Canadian International Petroleum Conference, Calgary, Alberta, June 11−13, 2002. (5) Gupta, S.; Gittins, S.; Picherack, P. J. Can. Pet. Technol. 2003, 43 (2), 54−61. (6) Leaute, R. P. Liquid addition to steam for enhancing recovery of bitumen with CSS: evolution of technology from research concept to a field pilot at Cold lake; SPE/Petroleum Society of CIM/CHOA Paper 79011 presented at the SPE International Thermal Operations and Heavy Oil Symposium and International Horizontal Well Technology Conference, Calgary, Alberta, Canada, November 4−7, 2002. (7) Zhao, L. Steam Alternating Solvent Process; Paper SPE 86957 presented at the SPE International Thermal Operations and Heavy Oil Symposium and Western Regional Meeting, Bakersfield, California, U. S. A., March 16−18, 2004. (8) Singhal, A. K.; Das, S. K.; Leggitt, S. M.; Kasraiem M.; Ito, Y. Screening of Reservoirs for Exploitation by Application of Steam Assisted Gravity Drainage/VAPEX Processes; Paper SPE 37144 presented at the International Confernce on Horizontal Well Technology, Calgary, Alberta, Canada, 18−20 November, 1996. (9) Luhning, R. W.; Das, S. K.; Fisher, L. J.; Bakker, J.; Grabowski, J.; Engeleman, J. R.; Wong, S.; Sullivan, L. A.; Boyle, H. A. J. Can. Pet. Technol. 2003, 42, 29−33. (10) Peneloux, A.; Rauzy, E.; Freze, R. Fluid Phase Equilib. 1982, 8, 7−23. (11) Mathias, P. M.; Naheiri, T.; Oh, E. M. Fluid Phase Equilib. 1989, 47, 77−87. (12) Jhaveri, B.; Youngren, G. SPE Reservoir Eng. 1988, 3 (3), 1033− 1040. (13) Sǿreide, I. Improved Phase Behavior Predictions of Petroleum Reservoir Fluids From a Cubic Equation of State; Dr. Ing. Dissertation, Norwegian Institute of Technology: Trondheim, Norway, 1989. (14) Magoulas, K.; Tassios, D. Fluid Phase Equilib. 1990, 119−140. (15) Ungerer, P.; Batut, C. Oil Gas Sci. Technol. 1997, 52 (6), 609− 623. (16) de Sant’Anaa, H.; Ungerer, P.; de Hemptinne, J. Fluid Phase Equilib. 1999, 193−204. (17) Mehrotra, A. K.; Sarkar, M.; Svrcek, W. Y. AOSTRA J. Res. 1985, 1 (4), 215−229. (18) Kokal, S.; Sayegh, S. J. Can. Pet. Technol. 1990, 29 (5) DOI: 10.2118/90-05-07. (19) Jamaluddin, A. K. M.; Kalogerakis, N. E.; Chakma, A. Fluid Phase Equilib. 1991, 64, 33−48. (20) McFarlane, R. A.; Gray, M. R.; Shaw, J. M. Fluid Phase Equilib. 2010, 293 (1), 87−100. (21) Rackett, H. G. J. Chem. Eng. Data 1970, 15, 514−527. (22) Spencer, C. F.; Danner, R. P. J. Chem. Eng. Data 1972, 17, 236− 241. (23) Hankinson, R. W.; Thomson, G. H. AIChE J. 1979, 25 (4), 653−663.

ASSOCIATED CONTENT

S Supporting Information *

The density data collected for pure hydrocarbon and diluted bitumen mixtures as well as calculated values from the proposed model are provided. This information is available free of charge via the Internet at http://pubs.acs.org/.

■

Article

AUTHOR INFORMATION

Corresponding Author

*Telephone: (403) 220-6529. Fax: (403) 282-3945. E-mail: [email protected]. Notes

The authors declare no competing financial interest. L

dx.doi.org/10.1021/ef400330j | Energy Fuels XXXX, XXX, XXX−XXX

Energy & Fuels

Article

(24) Thomson, G. H.; Brobst, K. R.; Hankinson, R. W. AIChE J. 1982, 28 (4), 671−676. (25) API Technical Data Book-Petroleum Refining, 6th ed.; Daubert, T. E., Danner, R. P., Eds.; American Petroleum Institute (API): Washington, DC, 1997. (26) Robinson, E. R. Hydrocarbon Process. 1983, 115−120. (27) Goates, J. R.; Ott, J. B.; Moellmer, J. F. Chem. Thermodyn. 1977, 9 (3), 249−257. (28) Goates, J. R.; Ott, J. B.; Grigg, R. B. Chem. Thermodyn. 1979, 497−506. (29) Goates, J. R.; Ott, J. B.; Grigg, R. B. Chem. Thermodyn. 1981, 11 (5), 497−506. (30) Witek, M.; Goldon, A.; Hofman, T.; Domanska, U. Chem. Eng. Data 1997, 60−63. (31) Thiele, E. W.; Kay, W. B. Ind. Eng. Chem. 1933, 25 (8), 894− 898. (32) API 2509 C. Volumetric Shrinkage Resulting from Blending Volatile Hydrocarbons and Crude Oils; American Petroleum Institute: Washington, DC, 1967. (33) Manual of Petroleum Measurement Standards (MPMS); American Petroleum Institute: Washington, DC, 1996; chapter 12, section 3. (34) Erno, B. P.; Chriest, J.; Given, R. Oil Gas J. 1994, 92, 49. (35) Ashcroft, S. J.; Booker, D. R.; Turner, J. C.R. J. Inst. Energy 1992, 65, 131−136. (36) Handa, Y. P.; D’Arcy, P. J.; Benson, G. C. Fluid Phase Equilib. 1982, 8 (2), 181−196. (37) Ashcroft, S. J.; Isa, M. B. J. Chem. Eng. Data 1997, 42 (6), 1244− 1248. (38) Arnaud, J. F.; Ungerer, P.; Behar, E.; Moracchini, G.; Sanchez, J. Fluid Phase Equilib. 1996, 124 (1), 177−207. (39) Standing, M. B.; Katz, D. L. Trans. AIME 1994, 146, 159−65. (40) Katz, D. L. Drilling and Production Practice; American Petroleum Institute: Washington, DC, 1942; pp 137−147. (41) Marra, R.; Poettmann, F.; Thompson, R. SPE Reservoir Eng. 1988, 3 (3), 815−821. (42) Tharanivasan, A. K.; Yarranton, H. W.; Taylor, S. D. Energy Fuels 2010, 25 (2), 528−538. (43) Fitzgerald, H.; Fitzgerald, D.; Jones, G. Pet. Rev. 1992, 46 (550), 544−9. (44) DMA HPM Instructional Manual; Anton Paar: Ashland, VA. (45) Standard Reference Database; NIST/TRC Source Database; WinSource, version 2008; National Institute of Standards and Technology (NIST); Gaithersburg, MD, 2008. (46) Padua, A.; Wakeham, W. A; Wilhelm. J. Int. Thermophys. 1994, 15, 767−777. (47) Van der Gulik, P. S. Physica A 1997, 238, 81−112. (48) Chevalier, J. L.; Petrlno, P. J.; Gaston-Bonhomme, Y. H. Chem. Eng. Data 1990, 206−212. (49) VMGSim Process Simulator, version 6.5; Virtual Materials Group, Inc.: Calgary, Alberta, Canada, 2011. (50) Bufkin, B. A.; Robinson, R. L., Jr.; Estera, S. S.; Luks, K. D. J. Chem. Eng. Data 1986, 31, 421−423. (51) Nourizadeh, H.; Kariznovi, M.; Abedi, J. Fluid Phase Equilib. 2012, 318, 96−101. (52) Kariznovi, M.; Nourizadeh, H.; Abedi, J. Chem. Eng. Data 2011, 56 (9), 3669−3672. (53) Ciotta, F.; Maitland, G.; Smietana, M.; Martin Trusler, J. P.; Vesovic, V. J. Chem. Eng. Data 2009, 54, 2436−2443. (54) Tanaka, H.; Yamaki, Y.; Kato, M. J. Chem. Eng. Data 1993, 38 (3), 386−388. (55) Bessières, D.; Saint-Guirons, H.; Daridon, J. L. J. Chem. Eng. Data 2001, 46 (5), 1136−1139. (56) Zúñiga-Moreno, A.; Galicia-Luna, L. A.; Camacho-Camacho, L. E. J. Chem. Eng. Data 2005, 50 (3), 1030−1037. (57) Tolley, W. K.; Izatt, R. M.; Oscarson, J. L. Thermochim. Acta 1991, 181, 127−141. (58) Chang, C. J.; Chen, C. Y.; Lin, H. C. J. Chem. Eng. Data 1995, 40 (4), 850−855.

(59) Mehrotra, A. K.; Svrcek, W. Y. Can. J. Chem. Eng. 1988, 66 (4), 656−665. (60) Mehrotra, A. K.; Svrcek, W. Y. AOSTRA J. Res. 1985, 2 (2), 83− 93. (61) Badamchi-Zadeh, A.; Yarranton, H.; Svrcek, W.; Maini, B. J. Can. Pet. Technol. 2009, 48 (1), 54−61. (62) Badamchi-Zadeh, A.; Yarranton, H.; Maini, B.; Satyro, M. A. J. Can. Pet. Technol. 2009, 48 (3), 57−65. (63) Chung, F.; Jones, R.; Nguyen, H. SPE Reservoir Eng. 1988, 3 (3), 822−828. (64) Kumar, K. Effect of Salinity on the Interfacial Tension of Model and Crude Oil Systems, M.Sc. Thesis, University of Calgary, Calgary, 2012. (65) Sanchez, M. C. Personal communication, University of Calgary, Calgary, 2013.

M

dx.doi.org/10.1021/ef400330j | Energy Fuels XXXX, XXX, XXX−XXX