Vapor–liquid equilibrium measurement and thermodynamic modeling of binary systems (methane + n-tetradecane)

Fluid Phase Equilibria 318 (2012) 96–101

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Vapor–liquid equilibrium measurement and thermodynamic modeling of binary systems (methane + n-tetradecane) Hossein Nourozieh, Mohammad Kariznovi, Jalal Abedi ∗ Department of Chemical & Petroleum Engineering, University of Calgary, Calgary, Canada

a r t i c l e

i n f o

Article history: Received 5 November 2011 Received in revised form 18 January 2012 Accepted 20 January 2012 Available online 28 January 2012 Keywords: Vapor–liquid Methane n-Tetradecane Equation of state

a b s t r a c t The vapor–liquid equilibrium (VLE) data for binary system of methane + n-tetradecane at four temperatures T = 295, 324, 373, and 448 K were measured using a designed pressure–volume–temperature (PVT) apparatus. The phase composition and density and viscosity of saturated liquid phase were measured for pressures up to 10 MPa. The experimental VLE data were compared with the modeling results obtained using the Peng–Robinson and Soave–Redlich–Kwong equations of state. Two approaches, a single temperature-independent interaction parameter and temperature-dependent interaction parameter, were considered to fit the generated experimental data. © 2012 Elsevier B.V. All rights reserved.

1. Introduction The thermodynamic behavior of binary and multi-components systems, including hydrocarbons, is of considerable interest in the design and development of many industrial processes, such as enhanced oil recovery methods and the processing of petroleum products. Moreover, the knowledge of the phase behavior of the fluids becomes important at certain stages of the many industrial processes, especially in the cases that the operational conditions change. This would be certainly of vital importance when the mixtures of volatile components and heavy normal hydrocarbons have been considered. The non-ideal behavior in binary systems containing hydrocarbons with greatly different molecular sizes has gained less attention while these systems provide the information for the description of the phase behavior of multi-component systems. The present study was attempted to measure the phase equilibrium properties (solubility, density, and viscosity) of hydrocarbon mixtures that contain components of greatly different volatilities. From reservoir and production prospective, the density and viscosity are of especial importance because they determine the fluid flow properties as well as estimation about the total mass of reserves. In the past, some experimental studies on the phase behavior of binary systems containing methane and heavy normal hydrocarbons have been reported. Ng et al. [1] reported low pressure

∗ Corresponding author at: 2500 University Dr., NW, Calgary, Alberta T2N 1N4, Canada. Tel.: +1 403 220 5594. E-mail address: [email protected] (J. Abedi). 0378-3812/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2012.01.023

solubilities of light hydrocarbons, methane, ethane, propane, ethylene, and propylene, in octadecane, eicosane, and docosane in the temperature region 30–200 ◦ C (303–473 K). Cukor and Prausnitz [2] measured Henry’s constants for methane, ethane, and hydrogen in n-hexadecane, bicyclohexyl and diphenylmethane for the temperature range 25–200 ◦ C (298–473 K) using a new gas solubility apparatus. Cordeiro et al. [3] performed the VL isotherm measurements for the methane + n-dotriacontane system at 70 ◦ C (343 K) and pressures up to 70 atm (7.09 MPa). Chappelow and Prausnitz [4] reported the low-pressure solubilities of methane, ethane, propane, n-butane, isobutane, and hydrogen in n-hexadecane, n-eicosane, squalane, bicyclohexyl, octamethylcyclotetrasiloxane, diphenylmethane, and 1-methylnaphthalene over the temperature range 25–200 ◦ C (298–473 K). D’Avila et al. [5] reported vapor-phase solubilities of n-decane, 2,2,5- trimethylhexane, tert-butylbenzene, and n-dodecane in compressed methane and compressed nitrogen in the range 30–100 atm (3.04–10.13 MPa) and 25–125 ◦ C (298–398 K). Kaul and Prausnitz [6] also measured the solubilities of heavy hydrocarbons in compressed gases, methane, ethane, and ethylene, at temperatures 50–170 ◦ C (323–443 K) for hexadecane, bicyclohexyl, diphenylmethane, and 1-methyl naphthalene, and in the region 165–272 ◦ C (438–545 K) for eicosane and squalane. Measurements were made in the pressure region 9–80 atm (0.91–8.11 MPa). Lin et al. [7] presented experimental results for gas–liquid phase equilibria in binary mixtures of n-hexadecane with methane at four temperatures from 190 to 430 ◦ C (463 to 703 K) and pressures from 20 to 250 atm (2.03 to 25.33 MPa). Glaser et al. [8] performed the experimental measurements for several kinds of two-phase

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boundary in methane + n-hexadecane binary systems in the temperature region from about 285 up to 360 K and pressures up to 85 MPa. Huang et al. [9,10] have measured the solubility of carbon dioxide, methane, ethane in n-octacosane and n-eicosane at temperatures up to 300 ◦ C (573 K) and pressures to 50 atm (5.07 MPa). de Leeuw et al. [11] measured VLE of the binary systems nitrogen + tetradecane, methane + tetradecane, and butane + tetradecane at 320–440 K. Rijkers et al. [12] reported experimental measurements on the solubility of hexadecane in methane at temperatures between 285 and 315 K and at pressures up to 25 MPa. van der Kooi et al. [13] reported the experimental results for the various phase equilibria of methane + eicosane at temperatures varied between 303 K and 370 K and pressures up to 100 MPa. Flöter et al. [14] have measured the experimental vapor–liquid, solid–fluid, and solid–liquid–vapor equilibrium data of the binary system (methane + tetracosane) in the temperature range 315–450 K and for pressures up to 200 MPa. In a subsequent study, Flöter et al. [15] reported the experimental results on vapor–liquid and solid–fluid phase equilibria for three types of ternary mixtures, methane + water + hexadecane, ethane + propane + tetracosane, and methane + docosane + tetracosane at temperatures up to 350 K and at pressures up to 200 MPa. Machado and de Loos [16] measured the experimental vapor–liquid and solid–fluid equilibrium data for the system methane + triacontane over the temperature range of 315–450 K, and pressures up to 200 MPa. In subsequent study, Machado and de Loos [17] experimentally determined bubble-point curves, dew-point curves, and solid + fluid/fluid boundary curves of methane + tetracosane + triacontane in the temperature range 320–475 K and at pressures up to 200 MPa. Recently, Campos et al. [18] conducted the experimental measurement of methane solubility in water and hexadecane at temperature range from 303.2 to 323.2 K and a low pressure range from 60.8 to 638.5 kPa. Although only a few data [11] for vapor–liquid equilibrium of binary systems of methane + ntetradecane has been reported, there is also a lack of experimental data for density and viscosity of saturated liquid phase. We have already reported the binary pair ethane + n-tetradecane [19], ethane + n-octadecane [20], methane + n-octadecane [21], and in the current text, the experimental results of the VLE properties for binary system of methane + n-tetradecane were measured. The solubility, density, and viscosity of methane-saturated ntetradecane were reported at four temperatures 295, 324, 373, and 448 K and pressures up to 10 MPa. Finally, the phase compositions and densities were modeled using Peng–Robinson (PR) and Soave–Redlich–Kwong (SRK) equations of state.

2. Experimental 2.1. Apparatus In previous studies [19–21], a designed PVT apparatus for gas solubility measurement was described in detail. In the present work, this equipment was used for the measurements, where Fig. 1 represents its schematic diagram. The apparatus consists of two 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 are placed in a temperature-controlled Blue M oven. The oven is equipped with a temperature controller capable of maintaining the temperature within ±0.1 K. The uncertainty of temperature measurements is estimated to be ±0.1 K. An Anton

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Table 1 Chemical sample specifications. Chemical name

Source

Initial purity

Purification method

Methane n-tetradecane

Praxair Spectrum Chemical Mfg. Corp.

0.9997 mole fraction 0.99 mass fraction

None None

Paar density measuring cell equipped with a DMA HPM external high-pressure unit was used to measure the density of the fluids. The fluid is transferred into a U-shaped Hastelloy tube. The tube is electronically vibrated at its characteristic frequency and depending on the density of the fluid, the characteristic frequency changes. By precise determination of the characteristic frequency and a mathematical conversion, the density of the fluid will be calculated. The external unit was calibrated using nitrogen and water and the density measurements are precise to ±0.5 kg m−3 with an uncertainty of ±1 kg m−3 . The density of saturated liquid phase during each experiment was measured several times which resulted in the above mentioned precision. The uncertainty was investigated by repeating the experiment at constant temperature and pressure to get a good estimate of deviation of the density values. The Cambridge viscometer (ViscoPro 2000) was factory calibrated, and the accuracy of measurements was tested with pure hydrocarbons and some standard fluids. The average error for the measurements was less than 5%. The piston-style viscometer uses two magnetic coils within a stainless steel sensor and a magnetic piston inside the pipeline. The piston is forced magnetically back and forth within a predetermined distance. The fluid sample surrounds the piston and depending on the viscosity, the piston’s round trip travel time measured at constant force exerted. The time required to complete a two way cycle is an accurate measure of viscosity. 2.2. Chemicals The methane (3.7 ultra high purity) used in these measurements was supplied by Praxair and n-tetradecane was obtained from Spectrum Chemical Mfg. Corp. All materials were found to be within acceptable purity specifications and were used without further purifications. Table 1 summarizes the chemical sample specifications. 2.3. Procedure The same experimental procedure adopted by Kariznovi et al. [19] was used in this work, and it is briefly discussed. Prior to each experiment, the entire system was thoroughly cleaned to remove any contaminant. To ensure no contaminants were left inside the system, cells and lines were successively evacuated and flushed with helium and methane. After cleaning, n-tetradecane was charged 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 Quizix pumps kept a constant pressure with an error of less than ±5 kPa. The equilibration cell was rocked to achieve effective mixing and to reach the equilibrium condition for the methane + n-tetradecane systems. During the mixing period, the volume of mixture to keep a constant pressure in the equilibration cell was recorded. When there was no change in the volume, equilibrium was achieved. Thus, the volume change in the mixing of binary systems was the criteria for equilibrium condition. Prior to the discharge of the equilibrium fluids, the equilibration cell was first kept in an upright position

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Fig. 1. Schematic diagram of experimental apparatus.

(vertical position) for a few hours to obtain single bulk volumes of each phase vertically segregated in the order of phase density. Then, the equilibrium fluids were discharged through the density measuring cell and viscometer, while maintaining a constant temperature and pressure. The pressure was measured by both the in-line and Quizix pump pressure transducers. The uncertainty of pressure measurements was ±10 kPa. The phase samples were collected with steady readings of the viscometer and the density measuring cell; any change in density and viscosity indicated a passage of a phase boundary through the measuring instruments. Vapor and liquids were transferred into sampling cells 1–3, 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(s), 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 composition of gas phase was also measured with gas chromatography (GC).

3. Results and discussion Isothermal VLE data for the methane + n-tetradecane system were measured at T = 294.7, 324.1, 373.4, and 447.6 K, and are presented in Table 2. Experiments were performed for six different pressures from 2 to 10 MPa. The saturated liquid density and viscosity were also measured and summarized in Table 2. The uncertainty of the measurements for compositions was 0.001. The equilibrium gases for all experiments were virtually pure methane due to low volatility of n-tetradecane and the n-tetradecane composition was too low in gas phase for accurate measurement. From the results, one can observe that the methane solubilities decrease in liquid with increasing the temperature.

The VLE data obtained in this work were correlated with the SRK [22] equation of state and PR [23] equation of state. The critical temperature and pressure and the acentric factor were obtained from Yaws [24]. The binary interaction parameters for the PR and SRK equations of state were considered as tuning parameters. First, we have considered a single binary interaction parameter (ıij )

Table 2 Experimental VL equilibrium properties for methane + n-tetradecane systems at T = 295, 324, 373, and 448 K: P, pressure; , densities; , saturated liquid viscosity; x, mole fraction of methane in saturated liquid phase. T (K)

P (MPa)

294.8 294.8 294.4 294.8 294.6 294.6 324.1 324.0 324.0 324.0 324.1 324.1 373.5 373.5 373.3 373.3 373.5 373.5 447.6 447.6 447.5 447.5 447.6 447.6

2.05 3.54 5.03 6.50 8.00 9.49 2.07 3.54 5.05 6.56 8.07 9.54 2.10 3.56 5.06 6.56 8.03 9.50 1.99 3.59 4.92 6.45 7.96 9.47

 (kg m−3 ) n-tetradecane

Saturated

760 762 764 765 766 767 742 743 744 746 747 748 708 709 711 712 713 715 655 658 660 662 665 667

752 746 740 734 728 723 732 726 722 716 711 706 699 694 689 683 678 674 646 640 636 631 625 620

 (mPa s)

102 x

1.74 1.64 1.48 1.33 1.16 1.05 1.07 0.97 0.91 0.82 0.75 0.70 0.57 0.54 0.51 0.49 0.46 0.44 0.31 0.29 0.28 0.27 0.25 0.24

11.2 17.6 23.2 28.2 33.1 36.4 10.0 15.9 21.3 26.4 30.6 34.2 9.0 14.3 19.3 23.9 27.9 31.7 7.8 13.7 17.6 22.3 26.6 30.3

u(T) = 0.1 K, u(p) = 0.01 MPa, u() = 1 kg m−3 , u() = 0.05 , and u(x) = 0.001.

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8000

8000

6000

6000 P/kPa

10000

P/kPa

10000

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0

99

4000

2000

0

10

20

30

0

40

500

600

2

10 x CH4

700

800

-3 ρ /(kg . m )

Fig. 2. Phase equilibria for methane + n-tetradecane system: P, pressure; xCH4 , mole fraction of methane in saturated liquid phase; , , , , experimental data; —, SRK EOS with ıij = 0.0129; , T = 294.7 K; , T = 324.1 K; , T = 373.4 K; , T = 447.6 K.

Fig. 4. Saturated densities  for methane + n-tetradecane system: P, pressure; , , , , experimental data; —, SRK EOS with ıij = 0.0129; – – –, SRK EOS with ıij = f(T); , T = 294.7 K; , T = 324.1 K; , T = 373.4 K; , T = 447.6 K.

for each equation of state capable of representing all isotherms. This universal ıij value was then adjusted to predict isothermal VLE experimental data. The composition and density of methanesaturated n-tetradecane were applied to investigate the single binary interaction parameter at all temperatures and pressures. This parameter was found to be 0.0157 and 0.0129 for PR and SRK equations of state, respectively. The modeling results with the equations of state and universal ıij are shown in Figs. 2–5 as solid lines. In these plots, the lines denote the calculation results by the equations of state for the four temperatures of 294.7, 324.1, 373.4, and 447.6 K. For comparison, the experimental data are also shown by dots. Figs. 2–3 show the methane compositions in saturated liquid phases predicted with the equations of state and Figs. 4–5 demonstrate the saturated phase densities. To improve the predictions for the saturated liquid densities, the volume translation technique of Peneloux et al. [25] was applied. The PR equation of state resulted in the best agreement with volume shift of 0.1280 while this value is 0.2412 for SRK equation of state. As previously mentioned, de Leeuw et al. [11] measured VLE of the binary system methane + tetradecane at 320–440 K. To compare the experimental results generated in this study with those of de Leeuw et al., the saturated liquid phase compositions at similar temperatures and pressures were used to tune both equations of state. The direct comparison of experimental data was not possible because the isotherms were not the same in two studies. Thus, the binary interaction parameters and average absolute deviations

(x = [1/N] |xcalcd − xexptl |) for PR and SRK equations of state were compared. The experimental data for the pressure range of 2–9 MPa and temperatures 324, 373, and 447 K were considered for modeling. The binary interaction parameters were found to be 0.0016 and 0.00156 for PR and SRK equations of state using experimental data in this study while these parameters were 0.0577 and 0.0621 for PR and SRK equations of state using experimental data of de Leeuw et al. [11]. The average absolute deviations for PR and SRK equations of state were 0.007 and 0.006 in this study while these values were 0.003 and 0.002 for de Leeuw et al. study. As depicted in Figs. 2–5, the large deviation between the modeling results (solid lines) and experimental data (dots) indicates that an universal ıij , representative of all four isotherms, would be unlikely. We validated this further by adjusting the binary interaction parameter for each temperature. Thus, interaction parameters for each isothermal VLE data were different. The adjusted interaction parameters for the equations of state were plotted in Fig. 6 by dots. The interaction parameters exhibit a non-linear behavior, with a change in sign. The need to readjust interaction parameters at each temperature suggests that the temperature dependency terms of the equations of state coupled with van der Waals mixing rule alone were not sufficient in describing the temperature influence [26]. As a result, we took into account the temperature dependency by considering the binary interaction parameters for both equations of state to be a function of temperature. The temperature dependency of interaction parameters was selected due to



10000

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8000

8000

6000 P /kPa

P /kPa

6000

4000

2000

0

4000

2000

0

10

20

30

40

2

10 x CH4

Fig. 3. Phase equilibria for methane + n-tetradecane system: P, pressure; xCH4 , mole fraction of methane in saturated liquid phase; , , , , experimental data; —, , T = 324.1 K; , T = 373.4 K; , PR EOS (1978) with ıij = 0.0157; , T = 294.7 K; T = 447.6 K.

0 500

600

700

800

-3 ρ /(kg . m )

Fig. 5. Saturated densities  for methane + n-tetradecane system: P, pressure; , , , , experimental data; —, PR EOS (1978) with ıij = 0.0157; – – –, PR EOS (1978) with ıij = f(T); , T = 294.7 K; , T = 324.1 K; , T = 373.4 K; , T = 447.6 K.

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0.04

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0.02

P /kPa

δ C1-C14

6000 0.00

4000

-0.02

2000 -0.04 250

300

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450

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500

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T /K

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the non-ideal behavior in binary hydrocarbon systems containing hydrocarbons with greatly different molecular sizes. The correlated equations for ıij over the studied pressure and temperature ranges were as follows: ıij = 0.3418 − 0.001504T + 1.53 × 10−6 T 2 for PR

(1)

ıij = 0.249 − 0.00106T + 1.04 × 10−6 T 2 for SRK

(2)

where T is the temperature in Kelvin. Figs. 4 and 5 and Figs. 7 and 8 show the comparison of VLE data on the methane + n-tetradecane systems with values predicted using the ıij values calculated from Eqs. (1) and (2). The modeling results with the temperature dependent ıij were shown as dashed line. As one can observe, both equations of state predicted the composition of methane much better than those with a universal ıij at four temperatures over the studied pressure range. As before, to improve the predictions for the saturated liquid densities, the volume translation technique was applied. The adjusted values for each temperature and equation of state were summarized in Table 3. The modeling results for both equations of state with temperature dependent ıij were also confirmed the improvement in the predictions. Finally, the saturated liquid phase viscosities were plotted in Fig. 9. As shown in the figure, the viscosity reduction with pressure would be less at higher temperatures. This is caused by the decrease in the solubility with temperature. Worthy mentioned that the saturated liquid viscosity exhibits almost a linear trend at higher temperatures.

Fig. 8. Phase equilibria for methane + n-tetradecane system: P, pressure; xCH4 , mole , , , experimental data; fraction of methane in saturated liquid phase; , , T = 324.1 K; , T = 373.4 K; – – –, PR EOS (1978) with ıij = f(T); , T = 294.7 K; , T = 447.6 K.

Table 3 Binary interaction parameters, ıij , and volume shift, Vs , for SRK and PR equations of state at four different temperatures. Equation of state

T (K)

Vs

ıij

SRK [16]

294.7 324.1 373.4 447.6 294.7 324.1 373.4 447.6

0.2485 0.2429 0.2364 0.2380 0.1392 0.1303 0.1173 0.1071

0.0279 0.0130 −0.0007 −0.0175 0.0311 0.0157 −0.0070 −0.0249

PR [17]

2.0

1.6

1.2

μ / mPa.s

Fig. 6. Binary interaction parameter ıij for methane + n-tetradecane system; T, tem, PR EOS; , SRK EOS. perature; , , adjusted parameters;

0.8

0.4

0.0

0

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2000

4000

6000

8000

10000

P/kPa

Fig. 9. Saturated liquid viscosities  for methane + n-tetradecane system: P, pressure; , , , , experimental data; , T = 294.7 K; , T = 324.1 K; , T = 373.4 K; , T = 447.6 K.

8000

P /kPa

6000

4. Conclusion 4000

2000

0

0

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20

30

40

102 x CH4

Fig. 7. Phase equilibria for methane + n-tetradecane system: P, pressure; xCH4 , mole fraction of methane in saturated liquid phase; , , , , experimental data; – – –, SRK EOS with ıij = f(T); , T = 294.7 K; , T = 324.1 K; , T = 373.4 K; , T = 447.6 K.

The experimental VLE data, composition and saturated liquid density and viscosity for binary system of methane + n-tetradecane were measured at four different temperatures. Measurements were performed using a designed PVT apparatus. The experimental data obtained were modeled using the PR and SRK equations of state. Two different approaches, universal binary interaction parameter and temperature dependent parameter, were considered for the equations of state. The modeling results with the universal binary interaction parameter demonstrated large deviation compared to the experimental data. However, both equations of state considered

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here closely modeled the VLE data using temperature dependent parameters. Acknowledgements This work was carried out as part of the SHARP (Solvent/HeatAssisted Recovery Processes) research 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. References [1] S. Ng, H.G. Harries, J.M. Prausnitz, J. Chem. Eng. Data 14 (1969) 482–483. [2] P.M. Cukor, J.M. Prausnitz, J. Phys. Chem. 76 (1972) 598–601. [3] D.J. Cordeiro, K.D. Luks, J.P. Kohn, Ind. Eng. Chem. Proc. Des. Dev. 12 (1973) 47–51. [4] C.C. Chappelow, J.M. Prausnitz, AIChE J. 20 (1974) 1097–1104. [5] S.G. D’Avila, B.K. Kaul, J.M. Prausnitz, J. Chem. Eng. Data 21 (1976) 488–491.

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