Vapor–Liquid Phase Equilibria and Physical Properties

Article pubs.acs.org/jced

Vapor−Liquid Phase Equilibria and Physical Properties Measurements for Ternary Systems (Methane + Decane + Hexadecane) Mohammad Kariznovi, Hossein Nourozieh, and Jalal Abedi* Department of Chemical & Petroleum Engineering, University of Calgary, Calgary, Canada ABSTRACT: The vapor−liquid equilibrium (VLE) data for ternary systems (methane + decane + hexadecane) have been determined using a designed pressure−volume−temperature (PVT) apparatus. Three different (decane + hexadecane) binary mixtures were prepared, and the solubility and phase equilibria of three prepared mixtures with methane at ambient temperature and different pressures from (1 to 8) MPa were studied. The phase composition and saturated liquid density and viscosity were reported for each pressure. The VLE data of the ternary mixtures were correlated using Soave−Redlich− Kwong and Peng−Robinson equations of state. The equations of state models with their best-fitted parameters of the binary systems, (methane + decane and methane + hexadecane), were used to predict the VLE data of ternary systems. Both equations of state were found to be capable of describing the phase equilibria of binary pairs and ternary systems over the range of studied conditions. The Peng−Robinson equation of state gave better predictions of saturated liquid densities than those of the Soave− Redlich−Kwong equation of state.

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INTRODUCTION The phase behavior and thermodynamic properties of hydrocarbon systems are of crucial importance in the oil industry and in petrochemical processes. The phase equilibrium information is also applicable for the design of in situ recovery techniques, pipeline transportation, and surface upgrading methods. From a reservoir production point of view, vapor−liquid equilibrium (VLE) properties of hydrocarbon mixtures at in situ conditions are important for the production of crude oil from the reservoirs. In addition, phase behavior experimental data are essential in the development of numerical simulators and the application of various flooding processes in enhanced oil recovery. However, only limited experimental data for hydrocarbon mixtures have been reported in the literature, and most of the data are confined to simple binary systems for particular temperature and pressure conditions. Although some data1,2 for the VLE equilibrium of binary systems (methane + decane) and (methane + hexadecane) have been reported in the literature, there is a lack of experimental phase equilibrium data for ternary hydrocarbon systems (methane + decane+ hexadecane). In the next few paragraphs, the available literature experimental data for binary and ternary systems containing methane, decane, and/or hexadecane are summarized. In 1947, Reamer et al.3 measured the phase equilibrium for ternary systems of methane + butane + decane. The authors prepared five mixtures and evaluated their volumetric behavior for seven temperatures from 311 K to 511 K (100 °F to 460 °F) and pressures up to 69 MPa. Reamer et al.4 also measured the composition of equilibrium phases for ternary systems © 2012 American Chemical Society

(methane + butane + decane) at a temperature of 344 K. Experimental measurements were conducted in the pressure range of 6.9 MPa to 27.6 MPa. In a subsequent study, Reamer et al.5 reported the volumetric behavior of a ternary systems (methane + butane + decane) for a temperature range of 311 K to 511 K and pressures up to 69 MPa .The authors also presented the phase behavior measurements for the ternary system (methane + butane + decane) at the low temperature condition of 278 K.6 Koonce and Kobayashi7 measured the k-values of methane and propane in two ternary systems (methane + propane + decane) and (methane + propane + heptane). The measurements for (methane + propane + decane) system were reported in a temperature range of 244 K to 294 K over a pressure range of 0.14 MPa to 6.9 MPa. In 1967, Beaudion and Kohan1 conducted VLE measurements for a binary system (methane + decane) at seven temperatures between 248 K and 423 K and pressures up to 10 MPa. Wiese et al.8 conducted the compositional measurements for the VLE of a ternary system (methane + propane + decane) for a temperature range of 278 K to 511 K. In 1984, Glaser et al.2 presented the experimental results for the two-phase boundary in a binary system (methane + hexadecane) at temperatures and pressures up to 360 K and 85 MPa, respectively. Weiguo et al.9 reported the vapor pressures of ternary mixtures (hexane + octane + hexadecane) at a temperature of 298.15 K. Recently, Received: May 28, 2012 Accepted: July 20, 2012 Published: August 3, 2012 2535

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within a predetermined distance. The fluid sample surrounded the piston, and depending on the viscosity, the piston’s round trip travel time was measured at a constant force exerted. The time required to complete a two-way cycle was an accurate measure of viscosity. The viscometer was equipped with sensor SPC-372, and it is factory calibrated. Materials. The methane was supplied by Praxair with a purity of 0.9997 mole fraction, and decane and hexadecane were obtained from Alfa Aesar Company. All of the chemicals were used without any further purification. Table 1 summarizes the chemical sample specifications.

Khasanshin et al.10 measured the density of a binary mixture (decane+ hexadecane) in a temperature range of 298 K to 433 K and a pressure range of 0.1 MPa to 100 MPa. Despite the limited data available for the VLE of ternary systems, no experimental information for the ternary system (methane + decane+ hexadecane) has been reported in the literature. In addition, phase density and viscosity measurements at equilibrium conditions, as important fluid flow properties, have received even less attention in the measurements. Thus, it has become essential to carry out experimental phase equilibrium studies, including the density and viscosity of the saturated phase, for a ternary system (methane + decane + hexadecane). The objectives of this research were the study of the VLE for a ternary system of (methane + decane + hexadecane) and the measurements of the saturated phase properties: composition, density, and viscosity of equilibrium phases. Thus, new VLE data for the ternary system (methane + decane + hexadecane) have been measured at ambient temperature over a pressure range of 1 MPa to 8 MPa. Three different binary mixtures of decane and hexadecane were prepared to cover the entire composition range (0.25, 0.50, and 0.75 mole fractions). The solubility of methane in three prepared binary mixtures were then measured over a pressure range of 1 MPa to 8 MPa. The data of the composition and the saturated liquid density and viscosity are reported for each pressure. To gain a better understanding of the impact of dissolved methane on the liquid phase density, the densities of the prepared binary mixtures were also measured in the pressure range of 1 MPa to 10 MPa. Finally, the generated experimental data (compositions and densities) were correlated using the Soave−Redlich−Kwong (SRK)11 and Peng−Robinson (PR)12 equations of state (EoS's). The binary interaction parameters and the volume translation values from the experimental information on the binary pairs, (methane + decane) and (methane + hexadecane), were used to predict the VLE data of the ternary system of methane + decane+ hexadecane.

Table 1. Chemical Sample Specifications chemical name methane

source

initial purity

decane

Praxair (3.7 ultra high purity) Alfa Aesar

hexadecane

Alfa Aesar

0.9997 mole fraction 0.99 mass fraction 0.99 mass fraction

purification method none none none

Binary Mixture Preparation. Three different binary mixtures of (decane + hexadecane) were prepared by mass, using a Sartorius balance (model: LP4200S) with a measurement uncertainty of ± 0.01 g. The prepared mixture had a weight of at least 1000 g; therefore, the uncertainty introduced by sample preparation for molar composition was less than ± 0.0001 for all compositions. The mixtures were prepared in mole fractions from 0.25 to 0.75 in increments of 0.25, to cover the entire composition range. The densities of the three prepared binary mixtures were measured at ambient temperature using the vibrating tube density measuring cell and are given in Table 2. The Table 2. Densities, ρm, of {Decane (1) + Hexadecane (2)} Binary Mixtures at Constant Temperature and Different Pressures Pa

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ρm/(kg·m−3)

EXPERIMENTAL SECTION Apparatus. In the previous studies,13,14 a designed PVT apparatus for phase behavior study and measurements of physical properties was described in detail. This equipment was also used for the measurements in this present work. The apparatus consisted of feeding cells, an equilibration cell, four sampling cells, a density measuring cell, a viscometer, and two Quizix automated pressure-activated pumps. The equilibration and sampling cells, density measuring cell, and viscometer were placed in a temperature-controlled Blue M oven. The oven was equipped with a temperature controller capable of maintaining the temperature within ± 0.1 K. An Anton Paar vibrating tube density measuring cell equipped with a DMA HPM external high-pressure unit was calibrated using nitrogen and water. The data for the densities of nitrogen and water at specific temperatures and pressures were taken from the database of National Institute of Standards and Technology (NIST).15 The Cambridge viscometer (ViscoPro 2000), which is a flowthrough viscosity sensor, was capable of measuring the viscosity in the range of 0.25 mPa·s to 20 000 mPa·s and pressure up to 14 MPa. The piston-style viscometer used two magnetic coils within a stainless steel sensor and a magnetic piston inside the pipe line. The piston was forced magnetically back and forth

P/MPa

x1 = 0.75 at 295.0 K

x1 = 0.50 at 295.3 K

x1 = 0.25 at 295.0 K

1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00

741.6 742.4 743.1 743.8 744.5 745.3 746.0 746.7 747.4 748.2

753.0 753.7 754.4 755.1 755.8 756.5 757.1 757.8 758.5 759.2

762.6 763.3 764.0 764.6 765.3 766.0 766.6 767.3 767.9 768.6

a u(T) = 0.1 K, u(P) = 0.01 MPa, and the combined expanded uncertainty of uc is uc(ρ) = 0.1 kg·m−3.

uncertainty of the density measurements was ± 0.1 kg·m−3. To compare the binary mixtures, their densities and that of pure decane are plotted in Figure 1. The data for densities of decane were taken from the NIST15 Chemistry WebBook. No experimental data for the density of hexadecane at 295 K over a pressure range of 1 MPa to 10 MPa have been reported in the literature. As depicted in Figure 1, the binary mixture became heavier when the decane concentration was reduced from 1 to 0.25 mole fraction. 2536

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of the gas phase was also measured with gas chromatography (GC). The equilibrium vapor phases for all experiments were virtually pure methane; the decane and hexadecane compositions were too low in gas phase for accurate measurement. The composition of decane was less than 0.001 mole fraction for all experiments, and due to low volatility of the hexadecane, no hexadecane was detected by GC. This result was confirmed by the modeling study and the density measurement of the vapor phase. The density of the vapor phase was close to the density of pure methane at the same temperature and pressure conditions.

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RESULTS AND DISCUSSION Experimental Results. The VLE data of the ternary systems (methane + decane + hexadecane) were measured at ambient temperature (295 K). Experiments were performed for eight different pressures, ranging from 1 MPa to 8 MPa. The saturated liquid composition, density, and viscosity were measured and summarized in Table 3. The equilibrium vapor phases for all experiments were virtually pure methane. As the results in Table 3 indicate, the methane composition in the saturated liquid phase increased with the pressure for all three considered mixtures. Thus, the saturated liquid density and viscosity decreased with the pressure due to higher

Figure 1. Densities ρm of {decane (1) + hexadecane (2)} binary mixtures at 295 K and different pressures P. Experimental data of this study: ■, x1 = 0.25; ⧫, x1 = 0.5; ▲, x1 = 0.75. ○, NIST data for pure decane (x1 = 1).

Procedure. The experimental procedure used in this study was similar to our previous studies,13,14,16,17 and it is briefly discussed here again. Prior to each experiment, the entire system was thoroughly cleaned to remove any contaminant, and the cells and lines were then successively evacuated and flushed with helium and methane. After cleaning, the prepared mixture of (decane + hexadecane) was supplied into the equilibration cell using the two Quizix pumps. The methane was then charged into the cell. To measure the solubility at a specific temperature and pressure, the experimental pressure and temperature were fixed. The pressure in the equilibrium cell was kept constant using the Quizix pump. The equilibration cell was rocked to achieve effective mixing and to reach the equilibrium condition for the ternary system. During the mixing period, the volume of mixture that kept a constant pressure in the equilibration cell was recorded. When there was no change in the volume, equilibrium was achieved. Prior to the discharge of the equilibrium fluids, the equilibration cell was first kept in an upright position (vertical position) for a few hours to obtain a single bulk volume of each phase vertically segregated in the order of phase density. The equilibrium fluids were then discharged through the density measuring cell and viscometer, while maintaining a constant temperature and pressure. The phase samples were collected with steady readings of the density measuring cell and viscometer; any change in density and viscosity indicated a passage of a phase boundary through the measuring instruments. Vapor and liquid phases were transferred into sampling cells 1 to 3, and the last sampling cell was used to purge the phase boundary portion and clean the transition between the phases. Saturated samples could be collected through the sampling port for compositional analysis or further studies. To measure the solubility of the saturated liquid, the collected samples were flashed at atmospheric pressure. The volume of the evolved gas was measured by the Chandler Engineering gasometer (model 2331) with a 0.2 % accuracy of the reading. The solubility was then calculated with the density and volume of the evolved gas at atmospheric conditions. An uncertainty of ± 0.002 in the measurements of the mole fractions for the liquid phase was estimated. The composition

Table 3. Experimental Equilibrium Data of the Systems {Methane (1) + Decane (2) + Hexadecane (3)} for Temperature T, Pressure P, Saturated Liquid Density ρs, Saturated Liquid Viscosity μs, and Mole Fraction of Component in Saturated Liquid Phase xa T/K

P/MPa

102 x1

294.5 294.6 294.9 295.0 295.1 295.0 294.4 294.5

0.93 1.99 2.90 3.87 4.98 5.92 6.90 7.92

5.2 10.0 14.4 17.9 22.3 25.5 29.2 32.0

294.9 294.9 295.1 295.2 294.5 294.8 294.6 294.7

1.01 2.04 3.15 4.00 5.02 6.02 6.86 7.88

5.9 11.2 16.0 19.5 23.3 26.8 29.3 32.3

294.4 294.1 294.5 294.7 295.0 295.1 294.5 294.8

1.05 2.02 3.01 4.06 5.09 6.02 6.94 8.01

6.4 10.9 15.7 20.1 23.8 26.7 29.6 33.4

102 x2

(x2/x3) = 3 71.1 67.5 64.2 61.6 58.2 55.9 53.1 51.0 (x2/x3) = 1 47.0 44.4 42.0 40.2 38.4 36.6 35.3 33.8 (x2/x3) = 1/3 23.4 22.3 21.1 20.0 19.1 18.3 17.6 16.7

ρs/(kg·m−3)

μs/(mPa·s)

735 730 725 721 716 712 707 702

1.22 1.18 1.11 1.04 0.97 0.93 0.86 0.80

746 742 737 733 729 724 721 717

1.88 1.69 1.60 0.50 1.40 1.25 1.18 1.05

756 752 748 744 739 735 732 728

2.34 2.14 2.04 1.93 1.78 1.63 1.44 1.30

a

u(T) = 0.1 K, u(P) = 0.01 MPa, u(x) = 0.002 and the combined expanded uncertainties uc are u(ρs) = 1 kg·m−3, and u(μs) = 0.05 μ. 2537

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simplicity and high degree of accuracy in VLE predictions. The general form for these two cubic equations of state is,

solubility of methane. This effect was more pronounced in the case of saturated liquid viscosities in which the liquid viscosity was reduced to almost 50% of initial values at the highest pressure (Figure 2).

P=

a α(T ) RT − 2 v−b v + ubv + wb2

(1)

with a = Ωa

R2Tc2 Pc

(2)

b = Ωb

RTc Pc

(3)

⎛ ⎡ α(T ) = ⎜⎜1 + κ ⎢1 − ⎢⎣ ⎝

T Tc

⎤⎞ ⎥⎟⎟ ⎥⎦⎠

2

(4)

κ = d1 + d 2ω − d3ω 2 + d4ω3

(5)

where parameters a and b are constant. P is the pressure, Pc is the critical pressure, T is the absolute temperature, Tc is the critical temperature, v is the molar volume of the mixture, κ is a constant characteristic of each substance, and ω is the acentric factor. The modified version of the PR EoS18 for hydrocarbons heavier than decane was used in this study. The coefficients in eqs 1 to 4 are summarized in Table 4. The properties of the pure compounds used in this work are summarized in Table 5. To determine the EoS parameters for the mixture, the van der Waals mixing rules were used,

Figure 2. Saturated liquid viscosities μs for ternary systems {methane (1) + decane (2) + hexadecane (3)} at 295 K; P, pressure; x, mole fraction. Experimental data: ■, (x2/x3) = 1/3; ⧫, (x2/x3) = 1; ▲, (x2/ x3) = 3.

The comparison of the methane in the three different mixtures revealed that the methane composition in the saturated liquid phase was almost the same for the three binary systems considering isobaric data. This behavior was observed when the methane composition was reported in mole fraction. It can be further investigated by converting the methane composition into weight fraction instead of mole fraction. In this case, the methane composition in the saturated liquid phase decreased at a constant pressure as the mixture became heavier (i.e., x2/x3 decreased from 3 to 1/3). Thus for this study, the composition is reported in weight fractions in all figures to distinguish the methane composition in the three ternary systems. Equation of State (EoS) Modeling. Phase behavior modeling of hydrocarbon mixtures is a complex physical phenomenon which cannot be described well with simple generalizations and modeling approaches. Hydrocarbon mixtures are complex mixtures of organic compounds that have different molecule sizes and structures. Even normal hydrocarbons with straight chains and a simple structure, but different chain sizes, can lead to a departure from ideality. This nonideality can significantly affect the thermodynamic properties of a system and make it more complex for modeling. For the phase behavior modeling study, the EoS approach was selected because it is one of the most popular methods in the oil industry with practical applications. Among the EoS models, two cubic EoS's, SRK and PR, were tested to describe the phase equilibrium and the volumetric behavior of the considered binary and ternary systems due to their relative

am =

∑ xiDi

(6)

i

bm =

∑ xibi

(7)

i

where Di =

ai

∑ xj(1 − δij)

aj (8)

j

The so-called interaction parameters, δij, for binary pairs within the mixture were optimized for each EoS. To improve the volumetric results, a volume translation according to Peneloux et al.19 was considered in both EoS's. Based on this technique, the details of which are described in Peneloux et al.,19 we could perform translation along the volume axis, while keeping the other equilibrium properties unchanged. Therefore, the density prediction improved, but the other properties prediction was not affected. The corrected volume was obtained with eq 9: v cor = v − c

(9)

where vcor is the corrected molar volume, and c is the matching parameter, which is obtained from experimental data. For multicomponent systems, c can be obtained by eq 10:

Table 4. Coefficients for PR EoS and SRK EoS coefficients equation of state

u

w

Ωa

Ωb

d1

d2

d3

d4

PR (1978) SRK

2 1

−1 0

0.45724 0.42747

0.07780 0.08664

0.379642 0.480

1.48503 1.574

0.164423 0.176

0.016666 0

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Table 5. Thermodynamic Properties (Molecular Weight, MW, Boiling Point, Tb, Critical Temperature, Tc, Critical Pressure, Pc, Critical Volume, Vc, and Acentric Factor, ω) of Components20 Vc

MW component

g·mol−1

Tb/K

Tc/K

Pc/MPa

cm3·mol−1

ω

methane decane hexadecane

16.043 142.285 226.446

111.66 447.30 560.01

190.58 618.45 720.60

4.604 2.123 1.419

99.3 603.1 930

0.011 0.484 0.747

N

c=

∑ xici

(10)

i=1

where xi is the mole fraction of component i in the mixture ci = Ω bvsi

RTc Pc

(11)

where Pc is the critical pressure, Tc is the critical temperature, and vis is the volume translation which is tuning parameter and obtained by matching experimental data. For a binary mixture, a binary interaction parameter can be adjusted to fit the EoS to the VLE data. However, in the ternary systems, three binary interaction coefficients are needed for evaluating the VLE data. Thus, in the present study, the binary interaction parameters for the binary pairs (methane + decane), (methane + hexadecane), and (decane + hexadecane) were required. The interaction parameters between two components were usually investigated on the basis of the experimental VLE data of binary pairs. For the binary system of methane + decane, the experimental VLE data (composition and density) of Beaudoin and Kohn1 at 298.15 K were used to determine the binary interaction parameter as well as the decane volume translation value for both the SRK and the PR EoS's. As no volumetric phase equilibrium experimental data has been reported for a methane + hexadecane system in the literature, the binary interaction parameter for this system was evaluated from the VLE data reported by Glaser et al.2 The average absolute deviations (AADs) for composition and density were minimized to determine the adjustable parameters. The AADs were calculated as, %AAD(x) =

%AAD(ρ) =

xcalcd − xexptl ⎛ 100 ⎞ ⎜ ⎟ ∑ ⎝ N ⎠ xexptl

(12)

ρcalcd − ρexptl ⎛ 100 ⎞ ⎜ ⎟ ∑ ⎝ N ⎠ ρ

(13)

exptl

Figure 3. The calculated deviations of experimental saturated liquid compositions xexp and experimental saturated liquid densities ρexp from values xcal and ρcal obtained with SRK EoS and PR EoS. Open symbols, SRK EoS; solid symbols, PR EoS. ●,▲,○,△, saturated liquid compositions; ■, □, saturated liquid densities. ▲, △, (methane + hexadecane) system2 at 293.3 K; ●, ■, □, ○, (methane + n-decane) system1 at 298.15 K.

hexadecane, the binary interaction parameter was also investigated and fixed from the reported binary VLE composition data.2 The binary interaction parameters and volume translation values for both EoSs are listed in Table 6. The modeling results for the ternary system of the methane + decane + hexadecane using the SRK and PR EoS's and the adjusted parameters listed in Table 6 are shown in Figures 4 to 7. In these plots, the solid lines denote the calculation results by an EoS, and the dots show the experimental data. Figures 4 and 6 show the methane compositions in the saturated liquid Table 6. Volume Translation Values,a Vs, and Binary Interaction Parameters, δij, of Various Systems; Methane (1), Decane (2), Hexadecane (3) δij

Vs SRK EoS8

PR EoS9

SRK EoS8

PR EoS9

0.1981

0.0748

δ12 = 0.0486

δ12 = 0.0528

0.2805b

0.1789b

δ13 = 0.0403

δ13 = 0.0409

c

c

δ23 = 0.0459d

δ23 = 0.0431d

system

Figure 3 illustrates the deviation between the reported experimental VLE data in the literature1,2 and the modeling results obtained with the EoS's for two binary systems. The best results for the correlations of the experimental data were achieved with the PR EoS. The remaining unknown parameters for the ternary system (methane + decane + hexadecane) were the interaction parameter between decane and hexadecane and the volume translation value for the hexadecane component. These parameters were adjusted using the generated experimental phase equilibrium composition and density data in this study. The binary interaction parameter and volume translation value for the methane + decane binary pair were fixed from the reported binary VLE data.1 For the binary system of methane +

methane + decane methane + hexadecane methane + decane+ hexadecane a

The volume translation values were applied to decane and hexadecane components. bThe volume translation values of the binary system (methane + hexadecane) were investigated from the VLE data of the ternary system (methane + decane + hexadecane). cThe volume translation values of binary systems were applied for ternary systems. d The binary interaction parameters, δ12 and δ13, were fixed at the values obtained from binary systems for each equation of state. 2539

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Figure 4. Phase equilibria for ternary systems {methane (1) + decane (2) + hexadecane (3)}; P, pressure; w1, weight fraction of methane in saturated liquid phase; x, mole fraction. Solid symbols, experimental data of this study at 295 K; , − − −, SRK EOS; ■, (x2/x3) = 1/3; ⧫, (x2/x3) = 1; ▲, (x2/x3) = 3; △, literature experimental data2 for the methane + hexadecane system (x2 = 0) at 293.3 K; ○, literature experimental data1 for the methane + decane system (x3 = 0) at 298.15 K.

Figure 6. Phase equilibria for ternary systems {methane (1) + decane (2) + hexadecane (3)}; P, pressure; w1, weight fraction of methane in saturated liquid phase; x, mole fraction. Solid symbols, experimental data of this study at 295 K; , − − −, PR (1978) EOS; ■, (x2/x3) = 1/3; ⧫, (x2/x3) = 1; ▲, (x2/x3) = 3; △, literature experimental data2 for the methane + hexadecane system (x2 = 0) at 293.3 K; ○, literature experimental data1 for the methane + decane system (x3 = 0) at 298.15 K.

Figure 5. Saturated liquid densities ρs for ternary systems {methane (1) + decane (2) + hexadecane (3)}; P, pressure; x, mole fraction. Solid symbols, experimental data of this study at 295 K; , − − −, SRK EOS; ■, (x2/x3) = 1/3; ⧫, (x2/x3) = 1; ▲, (x2/x3) = 3; ○, literature experimental data1 for the methane + decane system (x3 = 0) at 298.15 K.

Figure 7. Saturated liquid densities ρs for ternary systems {methane (1) + decane (2) + hexadecane (3)}; P, pressure; x, mole fraction. Solid symbols, experimental data of this study at 295 K; , − − −, PR (1978) EOS; ■, (x2/x3) = 1/3; ⧫, (x2/x3) = 1; ▲, (x2/x3) = 3; ○, literature experimental data1 for the methane + decane system (x3 = 0) at 298.15 K.

phases, and Figures 5 and 7 demonstrate the saturated phase densities. The experimental data in the literature for the binary methane + decane and methane + hexadecane systems at a similar temperature and pressures are also shown in Figures 4 to 7. A comparison of the experimental data from this study for ternary systems and the literature data1,2 for methane + decane and methane + hexadecane binary systems (Figures 4 and 6) indicates that the solubility data were consistent: the methane composition in the saturated liquid phase decreased from the methane + decane system to the methane + hexadecane system, considering isobaric data at ambient temperature. The saturated liquid density data also confirmed the consistency of the data

from this study for ternary systems with the data of Beaudoin and Kohn1 for the binary system. From the experimental data presented in Figure 4 and 6, one can conclude that the solubility of methane (in weight fractions) in any prepared mixture of decane + hexadecane would be a value between the solubility of methane in decane and the solubility of methane in hexadecane at the same temperature and pressure. This statement can be generalized into the saturated liquid densities (Figures 5 and 7). As one can observe from Figures 4 to 7, both EoSs' predicted the composition of methane in liquid phase well over the studied pressure range. For the saturated liquid densities, the PR EoS had better predictions than the SRK EoS. For a better comparison of the generated data and modeling results, the 2540

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revealed that the PR EoS gave better predictions for composition than did the SRK EoS. Although the predicted results for compositions by two EoS's seem to be same (Figure 8), a comparison based on AADs demonstrates that the PR EOS provided lower average deviations of compositions. From Figure 9, which presents deviations for the saturated liquid densities and the average deviations of densities, we can conclude that the calculated values of the densities with the PR EoS were much better than those of the SRK EoS.

deviations between the experimental and the modeling results as well as the AADs for the composition and density of saturated liquid phase were also calculated and are presented in Table 7 and Figures 8 and 9. A closer examination of the AADs Table 7. Average Absolute Deviation, AAD, in Saturated Liquid Composition, x, and Saturated Liquid Density, ρ, Data of Methane Containing Systems Calculated from SRK EoS and PR EoS SRK EoS

PR EoS

system

AAD-x

AAD-ρ

AAD-x

AAD-ρ

methane + decane methane + hexadecane methane + decane + hexadecane

2.12 2.53 3.52

0.420

1.80 2.21 3.29

0.039

0.487

■

CONCLUSIONS

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AUTHOR INFORMATION

The VLE data of ternary systems of methane, decane, and hexadecane at ambient temperature and a wide range of pressures, from 1 MPa to 8 MPa, were measured. The generated experimental data indicated that the methane composition in the saturated liquid phase increased with the pressure in all three prepared (decane + hexadecane) binary mixtures considered here. A comparison of the solubility of methane in the three different mixtures revealed that the methane composition when reported in mole fractions was almost the same for the three binary systems considering isobaric data. However, when converted to the weight fractions, the methane composition in the saturated liquid phase decreased at constant pressure as the mixture became heavier (x2/x3 decreased from 3 to 1/3). From the experimental data, it was concluded that the solubility of methane in weight fractions in any prepared binary mixture of decane + hexadecane would be a value between the solubility of methane in decane and the solubility of methane in hexadecane at the same temperature and pressure. Finally, the saturated liquid compositions and densities were correlated with two cubic EoSs, PR and SRK. The modeling results revealed that both EoSs could reasonably describe the phase equilibria of the ternary system over the range of studied conditions using the binary interaction parameters and the volume translation values obtained from the experimental information on the binary pairs. The PR EoS gave better predictions of the saturated liquid densities than did the SRK EoS

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Figure 8. Calculated deviations of generated experimental saturated liquid compositions xexp from values xcal obtained with SRK EoS and PR EoS for the ternary system (methane + decane + hexadecane) at 295 K. Open symbols, SRK EoS; solid symbols, PR EoS; □, ■, (x2/x3) = 1/3; ◊, ⧫, (x2/x3) = 1; △, ▲, (x2/x3) = 3.

Corresponding Author

*Address: 2500 University Dr., NW, Calgary, Alberta, T2N 1N4 Canada. E-mail: [email protected]. Tel.: 403-220-5594. Funding

This work was carried out as part of the SHARP (Solvent/ Heat-Assisted Recovery Processes) consortium. The authors wish to express their appreciation for the financial support of all member companies of the SHARP consortium: Alberta Innovates Energy and Environment Solutions, Chevron Energy Technology Co., Computer Modeling Group Limited, ConocoPhillips Canada, Devon Canada Co., Foundation CMG, Husky Energy, Japan Canada Oil Sands Limited, MacKay Operating Co, Nexen Inc., Laricina Energy Ltd., National Sciences and Engineering Research Council of Canada (NSERC-CRD), OSUM Oil Sands Co., Penn West Energy, Statoil Canada Ltd., Suncor Energy, and Total E&P Canada.

Figure 9. Calculated deviations of generated experimental saturated liquid densities ρexp from values ρcal obtained with SRK EoS and PR EoS for the ternary system (methane + decane + hexadecane) at 295 K. Open symbols, SRK EoS; solid symbols, PR EoS; □, ■, (x2/x3) = 1/3; ◊, ⧫, (x2/x3) = 1; △, ▲, (x2/x3) = 3.

Notes

The authors declare no competing financial interest. 2541

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Article

REFERENCES

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