Characterization of Heavy Oils and Bitumens. 1. Vapor Pressure and

Energy & Fuels 2008, 22, 455–462

455

Characterization of Heavy Oils and Bitumens. 1. Vapor Pressure and Critical Constant Prediction Method for Heavy Hydrocarbons G. N. Nji, W. Y. Svrcek, H. W. Yarranton, and M. A. Satyro* Department of Chemical and Petroleum Engineering, UniVersity of Calgary, AB, Canada ReceiVed August 9, 2007. ReVised Manuscript ReceiVed October 3, 2007

Vapor pressures, critical constants, and the acentric factor are generally used in thermodynamic correlations based on corresponding states to perform phase equilibrium and physical property calculations. These thermophysical properties cannot be measured for heavy hydrocarbons due to thermal decomposition at temperatures far below the critical point. An integrated method is described for predicting the critical constants as well as the vapor pressures over a broad range of temperatures, and it is the first step for the development of a comprehensive methodology for the characterization and simulation of heavy oil and bitumen systems. The method applies perturbation theory using n-paraffins as a reference system and correlates departures of the heavy hydrocarbons from paraffinic behavior. The critical constants and vapor pressures of heavy hydrocarbons were correlated as a function of only their molecular weight and specific gravity at 15.6 °C. The molecular weights ranged from 28.05 to 695.30 g/gmol, while the specific gravities ranged from 0.4327 to 1.4154. For the hydrocarbons used in this study, the predicted critical constants and vapor pressures showed a significant improvement over previously published correlations. The experimental critical temperatures and critical pressures were reproduced closely with an average absolute percentage deviation of 2 and 8%, respectively. The resultant vapor pressure equation fit the available vapor pressure data with an average absolute deviation of 17% between reduced temperatures of 0.37 and 0.95.

1. Introduction With the current rapid depletion of conventional oil resources, the recovery and refining of heavier oil stocks as well as bitumens are now major economic activities. Good predictions of the thermophysical properties for reservoir simulation and surface facility design are therefore required. The most important pure component physical property from a simulation point of view is the vapor pressure, as it is the backbone for thermodynamic equilibrium calculations, ranging from vacuum distillation to vapor–liquid–liquid and vapor–liquid–solid equilibrium. These calculations in turn are used to determine the number of phases in equilibrium for a given system as well as estimate physical properties such as enthalpies, entropies, and heat capacities. Cubic equations of state (CEOSs) are commonly used in reservoir simulation to predict the phase behavior of petroleum fluids. The CEOS must predict component vapor pressures accurately if it is to provide a useful thermodynamic model. In order to do so, the attractive parameter of the CEOS is usually designed to incorporate vapor pressure data either from experimental vapor pressures or estimated vapor pressures from an estimation method. In this work, we describe the necessary first step for the creation of a self-consistent model for the description of heavy-oil- and bitumen-containing materials by defining a vapor pressure estimation method and the related methods for the estimation of critical pressures and temperatures. The complete equation of state method will be presented in a future paper. A conventional oil is usually characterized on the basis of a GC analysis or a distillation curve. The oil can be divided into known components such as butanes and lighter alkanes and * Author to whom correspondence should be addressed.

pseudocomponents. The pseudocomponents are usually subdivisions of the distillation curve such that each pseudocomponent represents an average boiling point range. In this case, the vapor pressure of each pseudocomponent at its average boiling point is simply the distillation pressure. If only a GC analysis is available, there are well-established methods to estimate the vapor pressures of the pseudocomponents.1 This approach works well for conventional oils because the nondistillable fraction is small, typically less than 5 wt % of the oil. The same approach does not work well for heavy oils and bitumens where approximately 60% of the oil is nondistillable. For these fluids, the nondistillable part is often characterized using extraction techniques like SARA (saturates, aromatics, resins, and asphaltenes) fractionation.2 This type of extraction analysis provides estimates for the average molecular weight and average density of the fractions, and therefore, one could estimate the remaining average boiling points of the distillation curve if these boiling points could be estimated on the basis of molecular weight and liquid density. This is shown in a conceptual form in Figure 1. We point out that Figure 1 depicts a simplification of the actual problem, since there is some overlap between the different fraction boundaries. With such a correlation at hand, the mathematical machinery developed for the characterization of conventional oils can be reused and pseudocomponents necessary for simulation generated in a consistent manner. The literature abounds with generalized vapor pressure correlation equations for light pure hydrocarbons and narrow (1) Riazi, M. R. Characterization and Properties of Petroleum fractions, 1st ed.; ASTM Manual Series; American Society of Testing and Materials: Philadelphia, PA, 2005; p 58. (2) Yarranton, H. W.; et al. Estimation of SARA fraction properties with the SRK EOS. J. Can. Pet. Technol. 2004, 43 (9), 31–39.

10.1021/ef700488b CCC: $40.75  2008 American Chemical Society Published on Web 11/21/2007

456 Energy & Fuels, Vol. 22, No. 1, 2008

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Figure 1. Distillation curve of heavy oil and/or bitumen. Note that the overlap of boiling ranges for different SARA fractions is not shown in this simplified representation.

Figure 2. Limits of Tsonopoulos’ critical temperature correlation. Table 1. Constants for the Boiling Point Equation at Reference Pressures pressure (mmHg)

a

b

c

d

760 100 10 1

477.63 586.28 968.85 2871.80

88.51 128.97 195.32 276.55

1007.00 724.65 492.45 368.25

1214.40 1062.30 941.77 862.03

boiling range petroleum fractions. Models such as the Lee-Kesler3 and the Ambrose-Walton4 vapor pressure equations, widely used in the industry, are not applicable to high molecular weight compounds due to limitations of the original experimental database used for the development of the models. Such data are not available experimentally for heavy hydrocarbons, and the estimated values are usually uncertain. Abrams et al.5 used the kinetic theory of polyatomic fluids as first suggested by Moelwyn-Hughes6 to determine the constants of the vapor pressure equation recommended by Miller.7 In their approach, they expressed the vapor pressure equation parameters as functions of kinetic parameters: s, the (3) Lee, B. I.; Kesler, M. G. A generalized thermodynamic correlation based on three-parameter corresponding states. AIChE J. 1975, 22, 510– 527. (4) Ambrose, D.; Walton, J. Vapor pressures up to their critical temperatures of normal alkanes and 1-alkanols. Pure Appl. Chem. 1989, 61 (8), 1395–1403.

Figure 3. Correlated and experimental boiling point temperatures of n-paraffins.

number of equivalent harmonic oscillators per molecule; E0, the energy of vaporization of a hypothetical liquid at T ) 0; and Vw, the hard-core van der Waals volume. According to the authors, these parameters could be calculated from a nonlinear fit of experimental vapor pressure data. If no data are available, they recommended the group contribution method by Bondi8 to calculate the hard-core van der Waals volume while the other two can be predicted by the group contribution method published by Macknick and Prausnitz.9 The Abrams-Macknick-Prausnitz (AMP) method9 is of limited utility for heavy hydrocarbons because it requires prior knowledge of either the chemical structure or experimental vapor pressure data to determine the constants of the equation. (5) Abrams, D. S.; et al. Vapor Pressures of Liquids as a function of temperature. Two-parameter equation based on kinetic theory of fluids. Ind. Eng. Chem. Fundam. 1974, 13 (3), 259–262. (6) Moelwyn-Hughes, E. A. Physical Chemistry, 2nd ed.; Pergamon Press: Oxford, U.K., 1961; p 709. (7) Miller, D. G. J. Phys. Chem. 1964, 68, 1399. (8) Bondi, A. Physical Properties of Molecular Crystals, Liquids, and Glasses; Reinhold Publishing Corporation: New York, 1951, p 453. (9) Macknick, A. B.; Prausnitz, J. M. Vapor pressures of heavy liquid hydrocarbons by a Group-Contribution method. Ind. Eng. Chem. Fundam. 1979, 18 (4), 348. (10) Twu, C. H.; Coon, J. E.; Cunningham, J. R. A generalized vapor pressure equation for heavy hydrocarbons. Fluid Phase Equilib. 1994, 96, 19–31.

Characterization of HeaVy Oils and Bitumens

Energy & Fuels, Vol. 22, No. 1, 2008 457

Table 2. Average and Maximum Absolute Percentage Deviations for n-Paraffin Boiling Points at Different Pressures pressure (mmHg)

% MAD

% AAD

760 100 10 1

0.99 1.54 2.11 2.90

0.20 0.28 0.36 0.41

Table 3. Constants of the Critical Temperature and Pressure Correlations property

a

b

c

d

Tc (K) Pc (kPa)

226.50 141.20

6.78 45.66e-02

1.282e-06 16.59e-03

2668 2.19

Twu10 maintained the form of the Lee-Kesler3 vapor pressure equation in order to predict the vapor pressure of heavy hydrocarbons. In his work, he proposed an internally consistent method for predicting the critical temperature and pressure using an estimated normal boiling point (NBP) and the specific gravity. The normal boiling point is initially estimated assuming a Watson characterization factor of 12. Then, the critical temperature, critical pressure, and normal boiling point are obtained iteratively using a perturbation expansion. However, this method requires at least a single vapor pressure data point, and convergence can be problematic. The Maxwell and Bonnell11 correlation is probably the most easily applied method for estimating the vapor pressure of heavy hydrocarbons because it does not require critical constants for its computation. Maxwell and Bonnell chose the vapor pressure curve of n-hexane as a reference. They predicted the vapor pressure curve of all other n-paraffins from the reference using two constants, which are characteristic of each component. For hydrocarbons other than n-paraffins, they proposed a correction on the basis of the Watson characterization factor, eq 1. Kw )

NBP1⁄3 SG

(1)

NBP is the normal boiling point in degrees Rankine, while SG is the specific gravity at 15.6 °C and 1 atm. In order to use the Maxwell-Bonnell11 vapor pressure equation, either the normal boiling point or the Watson characterization factor is required. Experimental NBPs are not available for heavy hydrocarbons due to thermal decomposition. Therefore, correlations based on NBP as a characterization parameter are of limited value for heavy hydrocarbons. The objective of this study is to develop a simple, reliable, and internally consistent method for predicting the vapor pressure of heavy hydrocarbons and heavy hydrocarbon fractions, when no experimental vapor pressure data are available. The proposed vapor pressure prediction method for heavy hydrocarbons begins with a well-defined vapor pressure prediction method for a reference system. The family of n-paraffins, rather than spherical molecules or a single n-paraffin, was chosen as the reference system for correlating the vapor pressure because they are closest to the systems of interest and, as pointed out by Twu,12 the expansion is expected to converge more rapidly. An additional motivating factor for choosing the n-paraffins as the reference system is the availability of experimental data. (11) Maxwell, J. B.; Bonnell, L. S. Ind. Eng. Chem 1957, 49, 1187. (12) Twu, C. H. An Internally Consistent Correlation for Predicting the Critical Properties and Molecular Weights of Petroleum and Coal-Tar Liquids. Fluid Phase Equilib. 1984, 16, 137–150.

Figure 4. Correlated and experimental critical temperatures of nparaffins.

Figure 5. Correlated and experimental critical pressures of n-paraffins.

Given a well-defined reference system, the characteristics of any other system can be estimated on the basis of a perturbation expansion, a correction to the original base system. A perturbation expression based on molecular weight and specific gravity was developed and tested on 276 components with molecular weights ranging from 28.05 to 695.30 g/gmol and specific gravities ranging from 0.4327 to 1.4154. Boiling temperatures at different pressures as well as the critical constants were correlated to develop a generalized correlation for vapor pressure that can be used for subatmospheric and superatmospheric applications. 2. Methodology 2.1. Vapor Pressure Equation. The constants of a vapor pressure equation are generally determined by regressing pure component vapor pressure data. In this study, “quasi-experimental” or empirically derived boiling point temperatures at different pressures as well as critical constants are predicted from the perturbation equation. The predicted boiling temperatures are then fitted with the following truncated form of the Riedel vapor pressure correlation:13 ln pv ) A +

B + C ln T T

(2)

where T is the boiling point temperature or critical temperature in degrees Kelvin, Pv is the vapor pressure or critical pressure (13) Riedel, L. Chem. Ing. Tech. 1954, 26, 679.


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Table 4. Newly Regressed Rackett Compressibilities n-paraffin

ZRA

methane ethane propane n-butane n-pentane n-hexane n-heptane n-octane n-nonane n-decane n-undecane n-dodecane n-tridecane n-tetradecane n-pentadecane n-hexadecane n-heptadecane n-octadecane n-nonadecane icosane n-heneicosane n-docosane n-tricosane n-tetracosane n-pentacosane n-hexacosane n-heptacosane n-octacosane n-nonacosane n-triacontane n-hentriacontane n-dotriacontane n-tritriacontane n-tetratriacontane n-pentatriacontane n-hexatriacontane n-heptatriacontane n-octatriacontane n-nonatriacontane n-tetracontane n-hentetracontane n-dotetracontane n-tetratetracontane n-pentacontane

0.2895 0.2737 0.2768 0.2730 0.2690 0.2649 0.2610 0.2573 0.2546 0.2506 0.2476 0.2446 0.2422 0.2393 0.2374 0.2351 0.2331 0.2310 0.2293 0.2275 0.2257 0.2242 0.2223 0.2212 0.2196 0.2186 0.2171 0.2160 0.2146 0.2132 0.2123 0.2115 0.2106 0.2086 0.2082 0.2073 0.2069 0.2060 0.2050 0.2041 0.2034 0.2024 0.2010 0.1949

property

a

b

c

d

e

SG

0.83

89.9513

139.6612

3.2033

1.0564

which is not possible for any equation with less than four constants.14 Most vapor pressure equations use either the critical point or a vapor pressure point or both points to determine the constants of the vapor pressure equation. In this study, we use four boiling points calculated at pressures equal to 760, 100, 10, and 1 mmHg, and the critical point enabled us to determine more reliable constants for the vapor pressure equation. Usually, correlations based on normal boiling point and critical points alone do not provide good estimates for boiling temperatures under vacuum conditions. For example, the table below shows the experimental and calculated vapor pressures for dodecane. T (K)

Pva (mmHg)

323.12

0.90 ( 0.01

a

Clapeyronb (mmHg)

percent errorc

2.30

153.82

Experimental data from Equation 7-2.4 of ref 16. c Percent error ) [(calcd - exptl)/exptl] × 100.

NIST.15 b

2.2. Perturbation Expansion. For heavy hydrocarbons, the four boiling points and the critical point are predicted from a correlation on the basis of the perturbation of these boiling points and the critical constants around a reference system. Perturbation theory is based on the idea that if we use a reasonable model for a reference system based on well-defined data, one can create a better model by adding a correction (or perturbation) to the simpler model. Twu12 recommended Stell et al.’s17,18 form of the Padé approximation, because it was found to account for the physical effects, such as the limiting behavior of critical properties, that are present in a real fluid in a convenient manner (Gubbins and Twu19). The form of the perturbation expansion is given by g ) g°

Table 5. Hydrocarbon Liquid and Solid Densities

hydrocarbon

density at freezing point (kg/m3)

liquid density (kg/m3)

o-xylene naphthacene chrysene

1017.80 1330 1289

915.44 1190 1190

Table 6. Liquid Densities of Selected Compounds

compound

liquid density at 15.6 °C and 1 atm (kg/m3)

source

methane ethane propane butane water polyethylene

299.71 355.85 506.50 583.43 999.022 828

24 24 24 24 24 25

in mmHg, and A, B, and C are pure component constants. The Riedel equation13 is a semiempirical equation that generally fits vapor pressure data well. It also reproduces the correct curvatures of log Pr versus 1/Tr plots (where Pr and Tr are the reduced vapor pressures and boiling temperatures, respectively) (14) Waring, W. Ind. Eng. Chem 1954, 46, 762.

Table 7. Constants for the Boiling Point Equation at Reference Pressures

2f) [ (1(1 -+ 2f) ]

2

(3)

where g° is the boiling point or critical constant of the reference system, g is the value of the real system, and f is the perturbation factor, constrained as follows: lim g f g° f f0

(4)

The form of the perturbation expansion also ensures that all correlated boiling points and critical constants will be positive under extreme conditions, provides rapid convergence, and ensures that the reference system is reproduced when the perturbation term is zero.12 To create the correlation, it is necessary to determine the boiling temperatures and critical constants of the reference system (g°) and the perturbation factor for heavy hydrocarbons (f). The perturbation factor (f) is to be fitted to all hydrocarbon (15) NIST ThermoData Engine. Standard Reference Database #103, version 2.0; National Institute of Standards and Technology, Gaithersburg, MD, 2005. http://www.nist.gov. (16) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P. The Properties of Gases and Liquids, 5th ed.; Mc-Graw-Hill: New York, 2001. (17) Stell, G.; Rasaiah, J. C.; Narang, H. Thermodynamic perturbation theory for simple polar fluids. I. Mol. Phys. 1972, 23, 393–406. (18) Stell, G.; Rasaiah, J. C.; Narang, H. Thermodynamic perturbation theory for simple polar fluids. II. Mol. Phys. 1974, 27, 1393–1414. (19) Twu, C. H.; Gubbins, K. E. Thermodynamics of polyatomic fluid mixtures. II. Polar, quadrupolar, and octopolar molecules. Chem. Eng. Sci. 1978, 33, 879–887.



correlation by weighting the data, thus anchoring the results to a rigorous statistical framework. 3.1. Boiling Point Temperatures. The experimental boiling point temperatures at 760, 100, 10, and 1 mmHg as well as the critical pressure and critical temperature for n-paraffins were obtained from the NIST Standard Reference Database #103.15 Although PE was chosen as the limiting n-paraffin, boiling point data were only available for n-paraffins up to C50 while predicted boiling point data based on group contribution theory were available up to C100. These boiling points were therefore a good practical upper limit allowing one to establish a reasonable physical picture beyond what can be actually measured. The boiling points at each pressure were fitted with the following equation: Figure 6. Experimental and correlated specific gravity versus molecular weight.

data available in the literature including all different major chemical families (paraffin, aromatic, naphthene, napthalenic, and polycyclic aromatic). 3. Reference System The family of n-paraffins from methane (C1) to polyethylene (PE) is chosen as the reference system. PE represents the limiting n-paraffin as the molecular weight goes to infinity. The main idea for selecting PE as the limiting n-paraffin is to preserve the data on the limiting behavior of n-paraffin properties, such as the boiling point, critical temperature, and critical pressure, as the molecular weight goes to infinity. An earlier paraffin-based reference system for hydrocarbons was created by Tsonopoulos.20 He developed correlations for the normal boiling point, critical temperature, critical pressure, and critical density of n-paraffins as a function of the carbon number. Although Tsonopoulos’ correlations have been extensively used, the fact the critical temperature curve crosses the normal boiling point curve around 1054 g/gmol and then begins to decrease, as shown in Figure 2 indicates that the slope of the curves as well as the limiting values for these properties are not well-correlated at high carbon numbers. A correlation for specific gravity is also required for the perturbation expansion. Recent studies show that the molecular weight is presently the most accurately measured property, especially with the current advancements in measuring techniques such as Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS).21 Therefore, the correlation was chosen to be a function of molecular weight. The correlation for the reference system as well as the perturbation term is based on data from the National Institute of Standards and Technology (NIST) Standard Reference Database #103.15 NIST has developed a new data collection process and has reported that about 10% of all the data published in the literature over the last century are poor.22 The proposed correlation incorporates the benefits of this data screening. One major advantage of the NIST data used in these correlations is that they were reported together with an uncertainty attributed to each value. This uncertainty was incorporated in creating the (20) Tsonopoulos, C. Critical constants of n-alkanes from methane to polyethylene. AIChE J. 1987, 33 (2), 2080–2083. (21) Alan, G. M.; Rodgers, P. R. Petroleomics: The Next Grand Challenge for Chemical Analysis. Acc. Chem. Res. 2004, 37, 53–59. (22) Frenkel, M.; et al. New Global Communication Process in Thermodynamics: Impact on Quality of Published Experimental Data. J. Chem. Inf. Model. 2006, 46, 2487.

[

Tbi° ) ai ln

MW° + bi MW° + ci

]

2

+ di

(5)

where Tb° is the boiling temperature of the reference component, MW° is the molecular weight of the reference component, a, b, c, and d are the fitting parameters, and the subscript i represents the pressure of interest. The parameter d is the limiting boiling point as the molecular weight goes to infinity for a given pressure. The fitted values of a, b, c, and d for each boiling point pressure are listed in Table 1. Figure 3 shows the plots of the experimental and calculated boiling points as a function of the molecular weight. Table 2 presents the percentage average absolute deviation (% AAD) and the percentage maximum absolute deviation (% MAD) in the experimental and calculated boiling points at each pressure. Equation 5 fits the normal boiling points of the reference system to within a % AAD of 0.20 and a % MAD of 0.99, compared to 0.41 and 1.18 for Tsonopoulos’ correlations, respectively. 3.2. Critical Temperature. A similar equation was fitted to the critical temperatures of n-paraffins from C1 to C26:

[

Tc° ) aTc ln

MW° + bTc MW° + cTc

]

+ dTc

(6)

where Tc° is the critical temperature of the reference component. The constants of eq 6 are listed in Table 3, and the fitted equations are plotted against the data in Figure 4. The % AAD as well as the % MAD from experimental data were 0.58 and 2.12, respectively. Tsonopoulos20 reported 0.94 and 16.38, respectively. The critical temperature correlation has the same form as the boiling point correlation, and the limiting critical temperature is higher than the limiting boiling temperature. Therefore, the boiling temperature curve does not cross the critical temperature curve. 3.3. Critical Pressure. The critical pressures (Pc°) for C1-C26 were correlated as a function of the molecular weight, as follows: Pc° )

aPcMW (bPc + cPcMW)dPc

(7)

The constants of eq 7 are listed in Table 3. Figure 5 is a plot of the correlated and experimental data as well as the correlation of Tsonopoulos20 for comparison. The % AAD in the proposed correlation developed is 2.24 with a % MAD of 8.56 compared


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Table 8. Average Absolute and Maximum Absolute Percentage Deviations for n-Paraffin NBP, Critical Temperature, Critical Pressure, and Specific Gravity Riazi-Daubert

Twu

Tsonopoulos

this study

physical property

% MAD

% AAD

% MAD

% AAD

% MAD

% AAD

% MAD

% AAD

NBP Tc Pc SG

9.56

2.17

2.07 2.25 21.32

0.35 0.43 3.79

1.18 16.38 24.20

0.41 0.94 6.15

0.99 2.12 9.79 5.90

0.20 0.58 2.87 0.67

Table 9. Constants in the Perturbation Expansion physical property

a

b

c

d

e

Tb, 760 mmHg (K) Tb, 100 mmHg (K) Tb, 10 mmHg (K) Tb, 1 mmHg (K) Tc (K) Pc (kPa)

-7.4120 × 10-2 -6.2094 × 10-2 -5.9488 × 10-2 -5.5895 × 10-2 -6.1294 × 10-2 1.8270 × 10-1

-7.5041 × 10-3 -5.2571 × 10-3 -5.3983 × 10-4 3.4874 × 10-3 -7.0862 × 10-2 -2.4864 × 10-1

-2.6031 -2.0601 -1.5677 -1.0391 6.1976 × 10-1 8.3611

9.0180 × 10-2 7.6749 × 10-2 4.9410 × 10-2 2.8620 × 10-2 -5.7090 × 10-2 -2.2389 × 10-1

-1.0482 -8.9956 × 10-1 -8.5746 × 10-1 -7.9294 × 10-1 -8.4583 × 10-2 -2.6984

with values of 5.70 and 24.20 for the Tsonopoulos20 correlation, respectively. 3.4. Specific Gravity. The specific gravity of each reference n-paraffin is required for the perturbation expansion. However, liquid densities are not usually reported at 15.6 °C and 1 atm. In order to consistently calculate liquid densities for compounds that have density data but no data reported at 15.6 °C and 1 atm, the modified form of the Rackett equation,

Figure 7. Dispersion plot of the calculated and experimental NBP.

Figure 8. Dispersion plot of the calculated and experimental critical temperature.

eq 8, by Spencer and Danner23 was used to estimate the saturated volumes. Vs° )

RTc° [1+(1-Tr)2⁄7] Z Pc° RA

(8)

where Vs° is the saturated molar volume of the reference component, R is the universal gas constant, Tr is the reduced temperature, and ZRA is the Rackett compressibility. The Rackett compressibility represents the slope of the variation of density with temperature. Therefore, the liquid density at 15.6 °C and 1 atm can be calculated from a single density value and the Rackett compressibility. The Rackett compressibilities (ZRA) were regressed from liquid density data from the NIST Standard Reference Database #103.15 The newly regressed values of ZRA for some of the n-paraffins are shown in Table 4. The values reported here are in the same range as those reported by Spencer and Danner in Poling et al.23 but are expected to be more accurate because they are based on better quality density data. PE, the limiting n-paraffin as the molecular weight goes to infinity, is a solid at 15.6 °C and 1 atm, with a solid density of 0.92 g/cc. Since liquids are usually 10% less dense than solids (water excluded), Table 5, the liquid density of PE was assumed to be approximately equal to 0.83 g/cc. The standard liquid densities of some other compounds used for the specific gravity correlation are given in Table 6. For the other hydrocarbons, the ZRA-based density data were used. The density of water was used to convert to specific gravity.

Figure 9. Dispersion plot of the calculated and experimental critical pressure.



Table 10. Average Absolute and Maximum Absolute Percentage Deviations for Critical Temperature and Pressure Cavett

Lee-Kesler

Riazi-Daubert

Twu

this study

physical property

% AAD

% MAD

% AAD

% MAD

% AAD

MAD%

% AAD

% MAD

% AAD

% MAD

Tc Pc

2.89 21.72

61.67 126.82

2.66 10.94

48.71 83.22

2.78 10.53

57.12 80.17

2.39 13.35

22.26 80.30

1.95 6.47

19.48 53.88

The experimental and calculated specific gravities at 15.6 °C and 1 atm were correlated as a function of molecular weight as follows: SG° ) a +

c b MW° (MW° + d)e

(9)

The constants of eq 9 are listed in Table 7. A comparison of the calculated and experimental specific gravities as a function of molecular weight is shown in Figure 6. The plot shows that the limiting value of the specific gravity for the molecular weight at infinity is 0.83, the specific gravity of PE. The % AAD and % MAD are 0.67 and 5.9, respectively. Table 8 compares the normal boiling point, critical temperature, and critical pressure of n-paraffins predicted in this study to those predicted by Riazi-Daubert,26 Twu,27 and Tsonopoulos.20 The % AAD values for the prediction of n-paraffin NBPs by Twu27 and Tsonopoulos20 are of the same order of magnitude as those predicted in this study. However, the percentage absolute deviation (% AD) decreases significantly with an increase in molecular weight corresponding to heavy hydrocarbons, which are the focus of this study. At this point, the boiling point, critical temperature, critical pressure, and specific gravity correlations for the reference system are internally consistent and are functions only of the molecular weight. Therefore, if the molecular weight of any n-paraffin is known, any of these properties can be calculated. 4. Heavy Hydrocarbons 4.1. Perturbation Function. The form of the perturbation function (f) is arbitrary, provided it goes to zero as the perturbations go to zero, eq 4. A perturbation based on molecular weight and specific gravity was selected. Molecular weight captures the size of the component, while specific gravity captures some of the chemistry of the different hydrocarbons. Both properties are also readily measured and available. In this study, a quadratic bivariate polynomial approximation was chosen as the form for the perturbation correlation, eq 10 f ) af ∆SG2 + bf ∆MW2 + cf ∆SG + df ∆MW + ef ∆SG∆MW (10) ∆SG ) ln

SG° SG

(11)

MW° (12) MW where SG is the specific gravity of the liquid hydrocarbon at 15.6 °C and 1 atm and MW is the molecular weight. The degree ∆MW ) ln

(23) Spencer, C. F.; Danner, R. P. J. Chem. Eng. Data 1972, 17, 236. (24) The Technical Data Book - Petroleum Refining, American Petroleum Institute, 6th ed., May 1992. (25) Wilson, G. M.; Johnston, R. H.; Hwang, S.; Tsonopoulos, C. Volatility of Coal Liquids at High Temperatures and Pressures. Ing. Eng. Chem. Process Des. DeV. 1981, 20, 94–104. (26) Riazi, M. R.; Daubert, T. E. Ind. Eng. Chem. Res. 1987, 26, 755– 759 (Corrections, p 1268). (27) Twu, C. H. Predict thermodynamic properties of normal paraffins using only normal boiling point. Fluid Phase Equilib. 1983, 11, 65–81.

sign denotes the n-paraffin reference components, that is, hypothetical n-paraffins having the same number of carbon atoms or the same molecular weight as the heavy hydrocarbon of interest. The constants af through ef are fitting parameters. The subscript f represents the different pressures. All of the constants in the perturbation expansion were regressed using a least-squares fit with the objective function defined as n

OF )

∑ i

[

(Pexptl - Pcalcd ) i i σp

]

2

(13)

where P is the regressed property, σ is the standard deviation, i represents each hydrocarbon, and n is the total number of hydrocarbons used in the perturbation correlation fit. The standard deviation is the uncertainty in the experimental value from NIST.15 Regressed properties included the critical properties and boiling points. The constants of eqs 10-12 for all of the regressed properties are provided in Table 9. 4.2. Critical Properties and Boiling Points. Boiling point data as well as specific gravity data for many other hydrocarbons, with special emphasis on data related to polycyclic aromatic types such as pyrenes and anthracenes, were used in determining the constants of the perturbation correlation. The ThermoData Engine from NIST15 as well as the Advanced Chemistry Development (ACD) Inc. software28 were used to estimate properties for some compounds which had no experimental data reported in the NIST Standard Reference Database #10315 but whose chemical structure was known. The ACD software28 was used to estimate the boiling point temperatures as well as the liquid density at 20 °C of these compounds. The ThermoData Engine,15 which uses Joback’s group contribution method,29 was used to estimate the critical constants of these compounds. Both types of software attribute an uncertainty to each property estimated. A volume-translated version of the Peng–Robinson EOS31 by Virtual Materials Group32 was used to calculate the necessary liquid density at 15.6 °C on the basis of the liquid density value at 20 °C as estimated by the ACD software28 when necessary. It is worth noting that although all of the data used in the regression are not experimental, the “quasi-experimental data”, generated using molecular simulation software, was included in the regression to give a general shape to the correlation.12 This was not a rigorous procedure but rather a consistent way to estimate boiling points, critical constants, and specific gravities, which were used in the correlation of the perturbation term and determination of numerical constants. (28) ACD/Labs 8.00, version 8.17; Advanced Chemistry Development Inc.: 2005. http://www.acdlabs.com. (29) Joback, K. G. A Unified Approach to Physical Property Estimation Using Multivariate Statistical Techniques. S.M. Thesis, Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Elsevier, 1984. (30) Soreide, I. Improved Phase Behavior Predictions of Petroleum Reservoir Fluids from a Cubic Equation of State. Doctor of Engineering Dissertation, Norwegian Institute of Technology, Trondheim, Norway, 1989. (31) Peng, D. Y.; Robinson, D. B. Ind. Eng. Chem. Fundam. 1976, 15, 59. (32) Virtual Materials Group Inc., Canada.


Nji et al Table 11. Average Absolute Percentage Deviations for Vapor Pressures

Figure 11. Predicted vapor pressure curve.

Figures 7, 8, and 9 are dispersion plots of the normal boiling point, critical temperature, and critical pressure, respectively. These plots illustrate the accuracy of the correlation over a broad range of data. Table 10 contains the percentage average absolute deviation and percentage maximum absolute deviation for each property. Most of the high percentage errors observed were for quasiexperimental data. A dispersion plot for the normal boiling point computed in this work as well as those from correlations by Riazi-Daubert26 and Soreide30 is shown in Figure 10. Table 10 also shows that the proposed correlation provides a better prediction of the critical properties. The other correlations are generally biased toward lighter hydrocarbons.33 The RiaziDaubert,26 Lee-Kesler,34 Cavett,35 and Twu12 methods for the critical temperature and critical pressure are functions of the normal boiling point and specific gravity. Given that there are no experimental normal boiling points for heavy hydrocarbons, the equations are of limited applicability for high molecular weight hydrocarbons. Also, Twu’s critical properties data bank12 was back calculated from vapor pressure data which are not available for heavy hydrocarbons. 4.3. Vapor Pressure. Equation 3 was used to generate four boiling point temperatures at 760, 100, 10, and 1 mmHg as well as the critical temperature and critical pressure of the hydrocarbon of interest. These five points are then used to determine the constants of the vapor pressure equation as given in eq 2. Equation 13 was again used as the objective function. A typical predicted vapor pressure curve is shown in Figure 11. The percentage average absolute deviation in this study for the proposed vapor pressure correlation is 16.9. Table 11 (33) Satyro, M. A.; Li, Y.-K.; Svrcek, W. Y.; Virtual Materials Group Inc., Canada. Creating better refinery simulation through molecular weight estimation, Hydrocarbon Engineering, January 2006. (34) Kesler, M. G.; Lee, B. I. Improve Prediction of Enthalpy of Fractions. Hydrocarbon Process. 1976, 55, 153–158. (35) Cavett, R. H. Physical Data for Distillation Calculations, VaporLiquid Equilibria, Proceedings of the 27th API Meeting, API Division of Refining; 1962; Vol. 42 (No. 3), pp 351-366.

method

% AAD

Ambrose-Walton Lee-Kesler Maxwell-Bonnell Twu this study

74.10 74.60 30.60 38.60 16.90

compares the vapor pressures predicted in this study to those predicted by Maxwell-Bonnell,11 Twu,10 Lee-Kesler,3 and Ambrose-Walton4 for the same database. The MaxwellBonnell11 method reproduces experimental data for pure heavy hydrocarbons to within an average error of 8% for vapor pressures greater than 1 mmHg and 30% for vapor pressures between 10-6 and 1 mmHg. The Lee-Kesler3 equation reproduces experimental data to within an average error of 75% below the critical point. This is because the uncertainty in the critical properties on which the correlation is based is very large and, typically, heavy hydrocarbons would begin to crack at temperatures above 250 °C. The AMP9 correlation was also very poor to within an average error of 70%, since the group contribution parameters were developed using relatively lighter hydrocarbons. Twu’s method,10 despite the low average percentage error, is not very useful because it requires an experimental vapor pressure point in order to proceed with the calculations. 5. Conclusions A truncated form of the Riedel equation was used to predict the temperature-dependent vapor pressures of 276 hydrocarbons. The constants of the equation were determined from the molecular weights and specific gravities of the hydrocarbons using a perturbation expansion. The predicted vapor pressures especially at vacuum pressures were within (1.0% of reported data, but at pressures below 1 mmHg, the average percentage error increases to within 10%. The reason for this high average deviation is because even small absolute deviations for low vapor pressure values (i.e., less than 0.1 mmHg) for heavy hydrocarbons show a large value in terms of average percentage deviation when compared to the uncertainty values. Although the difference in the chemical nature of individual components was approximated only by variations in liquid density and molecular weights, the use of a large data set of different hydrocarbons to determine the perturbation term constants provides robustness to the correlation and predictions of acceptable quality for engineering work. The vapor pressure prediction method developed here can be used to extrapolate the distillation curve, the first step toward oil characterization. Acknowledgment. Financial support from Shell Canada Ltd through its Shell Experiential Energy Learning Program is gratefully acknowledged. Virtual Materials Group Inc. provided their thermodynamic simulation software package (VMGSim) to test the correlation in thermodynamic calculations. EF700488B

Characterization of Heavy Oils and Bitumens. 1. Vapor Pressure and

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