VaporâLiquid Equilibrium Measurements and Thermodynamic

Article pubs.acs.org/jced

Vapor−Liquid Equilibrium Measurements and Thermodynamic Modeling of the System (Methane + Cyclohexane + Ethanol) Junqing Cai,* Junkai Zhang, and Wensheng Song Chemical Engineering and Pharmaceutics College, Henan University of Science and Technology, Kaiyuan Road No. 263, Luoyang, 471023, China

ABSTRACT: The work reports vapor−liquid equilibrium measurements for the binary systems (methane + cyclohexane) and (methane + ethanol) and the ternary system (methane + cyclohexane + ethanol) at high pressures. Experiments were carried out in a variable-volume cell with operating temperatures ranging from (280 to 333) K and pressures up to 12 MPa. The phase equilibrium data obtained for the systems were modeled using The Peng−Robinson equation of state with the classical van der Waals (PR-vdW2) and Wong−Sandler (PR-WS) mixing rules. The PR-WS model showed good performance in the prediction of the phase behavior for the ternary system based on the binary systems data.

1. INTRODUCTION Gas hydrates are nonstoichiometric, ice-like crystals formed by low molecular weight hydrocarbons confined in a framework of water molecules. Depending on the pressure and the composition of the hydrocarbon fluid, hydrates may be stable at temperatures up to 30 °C. Under conditions typical for oil and gas production and transport in colder climates, hydrates can easily form in pipelines and production equipment. This has long been a problem for the oil and gas industry. Traditionally, this problem was addressed using hydrate inhibitors such as methanol, ethanol, or glycols, which shift the hydrate equilibrium phase boundary away from the operating condition.1,2 Knowledge of compositions of the hydrocarbon phase is important for optimal operation of pipeline and process equipment. So, measurement and prediction of the phase behavior of water, methanol/ethanol/ glycols, and hydrocarbon fluid mixtures is helpful for the oil and gas industry to ensure reliable production and processing, to minimize losses, and to reduce the impact on the environment.3 Experimental data are the basis of all fundamental development of thermodynamic models and industrial processes, and there is therefore an urgent and constant need to be able to obtain them rapidly and reliably. Phase equilibrium data of (methane + cyclohexane) and (methane + ethanol) systems have been studied by different reseachers.4−9 The data are sometimes scarce in particular ranges of pressure and temperature. Therefore, some new data of the binary systems were determined in this work. © 2015 American Chemical Society

In general, computational models, molecular simulations, and correlation methods are necessary to reduce the number of experimental data points that have to be measured. Cubic equations of state (EoS) are used widely for phase equilibrium calculations. To use such equations to model fluid behavior of highly nonideal mixtures, mixing rules are required. Various mixing rules have been reported in the literature.10−15 In this work, measurements were made in the ternary system (methane + cyclohexane + ethanol) at temperatures from 291 K to 318 K and pressures to 12 MPa. Also, for the thermodynamic modeling of the system, the Peng−Robinson16 equation of state with quadratic van der Waals and Wong−Sandler15 mixing rules were used to correlate and model the data obtained experimentally.

2. EXPERIMENTAL SECTION 2.1. Materials. Purities and suppliers of chemicals are presented in Table 1. No further purifications were made. Two different binary mixtures of cyclohexane + ethanol were prepared. For the preparation of samples, an electronic balance (JY2000, Keshi Technologies, Inc., China) with the measurement uncertainty of 0.01 g was used. The binary mixtures were prepared in two ethanol mass fractions 0.1 and 0.2. The prepared Received: June 6, 2014 Accepted: February 16, 2015 Published: February 25, 2015 976

DOI: 10.1021/je5010388 J. Chem. Eng. Data 2015, 60, 976−982

Journal of Chemical & Engineering Data

Article

as a consequence of its thermal inertia. The analytical work was carried out using a Param 7800 gas chromatography (GC) system, equipped with an automatic injector, a HP-PLOT Q capillary column, and a flame ionization detector (FID). The detector was calibrated using chromatographic syringes with maximum mole numbers uncertainties of 1 %. Prior to each experiment, the cell and lines were evacuated and flushed with methane to remove any contaminant. After cleaning, the liquid solvent (about 400 cm3) was fed into the equilibrium cell. Methane was then charged into the cell. The mixer was started and kept in operation for 4 h to 6 h until the temperature and pressure remained the same for more than 30 min. The vapor and liquid samples from the equilibrium cell were introduced to the samplers which had previously been evacuated. The operation should be done slowly and carefully to allow samples to be taken from each of the phases without disturbing the phases in equilibrium. The samplers were heated to 473 K, for immediate vaporization of samples, and then the composition of the vapor was measured by GC. Ultra high-purity helium (99.999 %) was used as the carrier gas. Each result presented in this paper is the mean value of the data obtained in at least three equivalent experiments.

Table 1. List of Compounds Used with Mass Purity and Suppliers chemical name

supplier

mass fraction purity

methane ethanol cyclohexane

Beijing Analysis Instrument, China Tianjin Chemical Agents Corp., China Tianjin Chemical Agents Corp., China

≥ 0.9997 ≥ 0.99 ≥ 0.99

mixtures had a weight of at least 1000 g. Therefore, the uncertainty introduced by sample preparation for mass composition was less than 0.0001. 2.2. Apparatus and Operation. In the previous studies,17−20 a similar equilibrium system for phase behavior study was described in detail. In the present work, the experimental apparatus was modified for the study of high pressure vapor− liquid equilibrium, at temperatures ranging from 273 K to 473 K and at pressures up to 20 MPa. The core of the apparatus is a variable-volume high-pressure equilibrium cell of stainless steel equipped with a magnetic stirrer and a Teflon-coated stirring bar to provide an excellent mixing of gas and liquid. The cell has a maximum volume of about 900 cm3, which provides enough phase volumes for further analyses. Inside the upper segment of the cell there is a piston. It serves the purpose of compensating for any pressure drops that might result from the sampling process, although it can also be used to set a specific value of pressure in the cell. The pressure inside the cell is monitored with a temperature compensated pressure sensor Tange PTX7517 (Tange sensor and apparatus Co., Ltd., China), for measurements up to 20 MPa with an accuracy of 0.1 % of full scale (0.02 MPa), connected to an AIJ-3 data acquisition unit (Yudian Technologies, Inc., China). The temperature of the cell is measured with a precision of 0.01 K, through two calibrated thermal resistance thermometer (Pt100) connected to the same AIJ-3 data acquisition unit. The setup is presented with schematics in Figure 1, where the cell is shown inside an air thermostat Hengtai HT/GDW-408

3. RESULTS AND DISCUSSION The objective of this work was to provide experimental vapor−liquid equilibrium (VLE) data of hydrocarbons with polar chemicals. Several of new VLE data of binary systems of (methane + cyclohexane) and (methane + ethanol) were first given in this work. It helps close gaps in published data in the open literature. The VLE data have been obtained for the (methane + cyclohexane) system at three different temperatures (293, 313 and 323) K, and at pressures varying from (2 to 12) MPa and for the (methane + ethanol) system at (280, 313 and 333) K, and at pressures varying from (2 to 12) MPa. The results were collected in Tables 2 and 3 and shown in Figures 2 to 5. Table 2. Experimental Vapor−Liquid Equilibrium Data for the System {Methane (1) + Cyclohexane (2)}a

Figure 1. Schematic representation of the experimental system for the measurement of vapor liquid equilibrium: (A) high pressure equilibrium cell; (B) stirring motor; (C) pressure sensor; (D) thermal resistance thermometer; (E) thermostat; (F) gas sampler; (G) liquid sampler; (H) vacuum pump; (I) valve for loading of cell; (J) manual oil pump; (K) data acquisition unit.

T/K

P/MPa

x1

y2

293.15 293.15 293.15 293.15 293.15 293.15 313.15 313.15 313.15 313.15 313.15 313.15 323.20 323.20 323.20 323.20 323.20 323.20

2.12 4.09 6.23 8.03 10.07 12.15 2.02 4.09 6.06 8.01 10.03 12.08 2.06 4.08 6.03 8.01 9.97 12.09

0.075 0.131 0.191 0.240 0.295 0.350 0.059 0.120 0.176 0.230 0.283 0.335 0.061 0.119 0.172 0.223 0.271 0.319

0.009 0.007 0.006 0.007 0.009 0.010 0.017 0.013 0.012 0.013 0.015 0.017 0.024 0.023 0.021 0.021 0.022 0.025

a x1 and y2 correspond to the molar fraction of methane in the liquid phase and of cyclohexane in the vapor phase. Standard uncertainties u for temperature T and pressure P are u(T) = 0.01 K and u(P) = 0.02 MPa. Standard uncertainties u for the compositions are u(x1) = u(y2) = 0.002.

(Hengtai Co., Ltd., China). The thermostat is designed to promote a stable temperature in the range from 273 K to 423 K with temperature constancy better than ± 0.5 K over time. Tests showed that the temperature stability of cell is better than 0.01 K, 977



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Table 3. Experimental Vapor−Liquid Equilibrium Data for the System {Methane (1) + Ethanol (3)}a T/K

P/MPa

x1

y3

280.15 280.15 280.15 280.15 280.15 280.15 313.40 313.40 313.40 313.40 313.40 313.40 313.40 333.40 333.40 333.40 333.40 333.40 333.40

2.54 3.61 5.09 6.12 8.47 10.03 2.39 4.02 5.48 6.51 8.43 10.31 11.89 2.10 4.09 6.04 8.89 10.08 12.10

0.031 0.045 0.063 0.075 0.100 0.114 0.027 0.046 0.061 0.072 0.092 0.109 0.124 0.023 0.044 0.063 0.091 0.102 0.120

0.005 0.005 0.005 0.004 0.004 0.004 0.009 0.007 0.006 0.005 0.005 0.005 0.005 0.027 0.018 0.015 0.011 0.011 0.011

Figure 3. Cyclohexane molar fraction in gas phase of methane + cyclohexane system: ▲, this work (T = 293.15 K); △, ref 9 (T = 294.25); ■, this work (T = 313.15 K); □, ref 9 (T = 310.91 K); ●, this work (T = 323.20).

a

x1 and y3 correspond to the molar fraction of methane in the liquid phase and of ethanol in the vapor phase. Standard uncertainties u for temperature T and pressure P are u(T) = 0.01 K and u(P) = 0.02 MPa. Standard uncertainties u for the compositions are u(x1) = u(y3) = 0.002.

Figure 4. Methane molar fraction in liquid phase of methane + ethanol system: ▲, this work (T = 280.15 K); △, ref 4 (T = 280.15); ■, this work (T = 313.40 K); □, ref 6 (T = 313.40 K); ●, this work (T = 333.40); ○, ref 6 (T = 333.40).

the methane composition in the liquid phase decreased at constant temperature and pressure as the ethanol to cyclohexane mass ratio increased. However, the methane composition in the vapor phase had no significant regular change in the range of experimental conditions. The study of Reamer9 for methane + cyclohexane system was consistent with this work.

Figure 2. Methane molar fraction in liquid phase of methane + cyclohexane system: ▲, this work (T = 293.15 K); △, ref 9 (T = 294.25); ■, this work (T = 313.15 K); □, ref 9 (T = 310.91 K); ●, this work (T = 323.20); ○, ref 8 (T = 323.20).

The values are compared against literature data. A good overall agreement between the results obtained in this work and the literature data can be observed. The VLE data for the system (methane + cyclohexane + ethanol) were then measured. Experiments were performed with the two prepared binary mixtures over a range of temperatures (291 to 318) K and pressures (3 to 12) MPa. The experimental ternary data are collected in Table 4 and shown in Figures 6 and 7. As the results in Table 4 indicate, the solubility of methane in the liquid phase increased with the pressure and decreased with the temperature for all two prepared binary mixtures. Comparing the solubility of methane in two different mixtures revealed that

4. THERMODYNAMIC MODELING To represent the experimental phase equilibrium data, thermodynamic modeling was performed for the system investigated with Peng−Robinson equation of state (PR-EoS) using the conventional quadratic van der Waals mixing rule (vdW2) and the Wong-Sandler mixing rule (WS). The PR-EoS is given by P=

a(T ) RT − 2 V−b V + 2bV − b2

(1)

To apply this equation to mixtures, the equation of state parameters a and b are made functions of compositions using 978



Article

bm =

∑ ∑ 0.5xixj(bi + bj)(1 − lij) i

(3)

j

where ai and bi are parameters of pure compounds calculated by the equation of state and lij and kij are adjustable parameters. The Wong−Sandler15 mixing rule is expressed as am D =Q (4) RT 1−D Q 1−D

bm =

(5)

with Q and D defined as Q=

⎛

∑ ∑ xixj⎜⎝b − i

j

a ⎞⎟ RT ⎠ij

(6)

and Figure 5. Ethanol molar fraction in gas phase of methane + ethanol system: ▲, this work (T = 280.15 K); ■, this work (T = 313.40 K); □, ref 6 (T = 313.40 K); ●, this work (T = 333.40); ○, ref 6 (T = 333.40).

D=

i

C=

T/K

P/MPa

x1

x2

y1

y2

291.15 291.15 291.15 291.15 291.15 303.15 303.15 303.15 303.15 303.15 318.15 318.15 318.15 318.15 318.15 291.15 291.15 291.15 291.15 291.15 303.15 303.15 303.15 303.15 303.15 318.15 318.15 318.15 318.15 318.15

2.97 5.02 7.06 9.08 12.03 2.99 5.00 6.98 9.03 12.12 3.04 5.18 7.06 8.99 11.96 3.02 5.05 7.01 9.15 11.99 2.91 5.11 6.92 9.04 12.03 2.99 5.01 7.09 9.04 12.06

0.089 0.144 0.205 0.254 0.340 0.086 0.141 0.190 0.241 0.325 0.074 0.136 0.188 0.232 0.319 0.076 0.132 0.187 0.245 0.316 0.074 0.127 0.172 0.224 0.299 0.067 0.112 0.16 0.200 0.279

0.753 0.703 0.655 0.609 0.539 0.754 0.706 0.659 0.612 0.544 0.764 0.71 0.668 0.629 0.556 0.628 0.588 0.551 0.511 0.460 0.631 0.589 0.556 0.518 0.468 0.635 0.603 0.571 0.542 0.487

0.993 0.995 0.995 0.995 0.994 0.987 0.990 0.991 0.991 0.989 0.978 0.981 0.983 0.984 0.984 0.993 0.996 0.996 0.996 0.995 0.988 0.992 0.993 0.993 0.992 0.976 0.984 0.986 0.987 0.987

0.005 0.004 0.004 0.004 0.005 0.010 0.008 0.007 0.008 0.009 0.014 0.014 0.013 0.012 0.013 0.004 0.003 0.003 0.003 0.004 0.008 0.006 0.005 0.006 0.007 0.011 0.010 0.009 0.009 0.010

(

ai RT

(8) aj

) + (bj − RT ) (1 − K ) ij

2

(9)

where AE∞ is the excess Helmholtz free energy at infinite pressure,

Kij is a second virial coefficient binary interaction parameter. If the nonrandom two liquids (NRTL)21 activity coefficient model is used here for AE∞, the equation is E A∞ = RT

⎛ ∑ xjτjig ⎞ j ji ⎟ x ∑ i⎜⎜ ⎟ ∑ x g ⎝ k k ki ⎠ i

(10)

with gij = exp( −αijτij)

(αij = αji)

where gij, τij, and αij are NRTL model parameters. Thus, considering the two mixing rule used with PR-EoS, the following binary interaction parameters were fitted to the experimental data: kij and lij for PR-vdW2 and τij, τji, αij, and Kij for PR-WS. Binary interaction parameters were optimized by minimizing the following objective function using the Nelder− Mead simplex method.22 i=1

OF =

∑ (fî

v

l − fi ̂ )2

(11)

N

v

l

where N is the number of data points, fi ̂ and fi ̂ are, respectively, the fugacity in vapor and liquid phase. To evaluate the correlation of the thermodynamic models with the experimental data, the average absolute deviation (AADx) was calculated according to eqs 12.

Standard uncertainties u for temperature T and pressure P are u(T) = 0.01 K and u(P) = 0.02 MPa. Standard uncertainties u for compositions are u(x1) = u(x2) = u(y1) = u(y2) = 0.002.

mixing rules. The mixture parameter for vdW2 can be summarized as

AADx =

∑ ∑ xixj(aiaj)0.5 (1 − kij) j

(7)

1 ln( 2 − 1) 2

bi − ⎛ a ⎟⎞ ⎜b − = ⎝ RT ⎠ij

a

i

ai AE + ∞ biRT CRT

with

Table 4. Experimental Vapor−Liquid Equilibrium Data for the System {Methane (1) + Cyclohexane (2) + Ethanol (3)}a

am =

∑ xi

1 N

i=1

∑ N

x cal − x exp x exp

(12)

where the superscripts cal and exp denotes the calculated and experimental values, respectively.

(2) 979



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Figure 6. Prediction of methane molar fraction in the vapor and liquid phase for (methane + cyclohexane + ethanol) system (ethanol/cyclohexane = 1/9 wt) at (a) 291.15 K, (b) 303.15 K, and (c) 318.15 K: ▽, in the vapor phase; △, in the liquid phase. Symbols are experimental data from this work, continuous lines denote calculated values using the PR-WS model and dashed lines denote calculated values using PR-vdW2 model.

systems (methane + cyclohexane) and (methane + ethanol) were fitted using experimental data presented in Tables 2 and 3. The binary parameters for the systems (cyclohexane + ethanol) were fitted using experimental data of VLE presented in the literature.23 The results of fitting are presented in Tables 5 and 6. These binary parameters were fixed during the ternary system modeling. The AADx values obtained in this case were 8.1 % and 3.2 %, for the PR-vdW2 and PR-WS models, respectively. Figures 6 and 7 show the composition-pressure diagrams for the ternary system for the two ethanol-to-cyclohexane mass ratios (1:9 and 2:8), and afford a comparison between the experimental data and PR-vdW2 and PR-WS modeling. From these results, both models showed a good capability in predicting the phase behavior of the ternary system. However, a slightly better performance was obtained using the PR-WS model

Table 5. Fitted Interaction Parameters of the PR-vdW2 Model Used in This Work system

kij

lij

methane (1) + cyclohexane (2) methane (1) + ethanol (3) cyclohexane (2) + ethanol (3)

0.0284 0.0911 0.0791

0.0071 −0.1653 0.0825

AADx 2.1 %a 1.9 %a 2.6 %b

8.1 %c

a

AADx1. bAADx2. cAADx1 for the ternary system {methane (1) + cyclohexane(2) + ethanol(3)}.

The two models were used to predict the phase behavior for the ternary system (methane + cyclohexane + ethanol), at two ethanol to cyclohexane mass ratio (1:9 and 2:8). In this work, the thermodynamic modeling was performed by fitting the binary interaction parameters using all isothermal data for obtaining a unique set of parameters. The binary parameters for

Table 6. Fitted Interaction Parameters of the PR-WS Model Used in This Work

a

system

Kij

αij

τij

τji

methane (1) + cyclohexane (2) methane (1) + ethanol (3) cyclohexane (2) + ethanol (3)

0.1637 0.4474 0.3511

0.30 0.20 0.45

−1.0127 6.7431 2.3472

8.1429 −1.5621 1.3805

AADx 2.4 %a 1.9 %a 2.7 %b

3.2 %c

AADx1. bAADx2. cAADx1 for the ternary system {methane (1)+ cyclohexane(2) + ethanol(3)}. 980



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Figure 7. Prediction of methane molar fraction in the vapor and liquid phase for (methane + cyclohexane + ethanol) system (ethanol/cyclohexane = 2/8 wt) at (a) 291.15 K, (b) 303.15 K, and (c) 318.15 K: ▽, in the vapor phase; △, in the liquid phase. Symbols are experimental data from this work, continuous lines denote calculated values using PR-WS model and dashed lines denote calculated values using PR-vdW2 model.

when compared its AADx value with that obtained using the PRvdW2 model.

Funding

5. CONCLUSIONS

Notes

This work was supported by the Natural Science Foundation of Henan University of Science and Technology (2011QN001). The authors declare no competing financial interest.

■

This work reported vapor−liquid equilibrium data for the binary systems (methane + ethanol) and (methane + cyclohexane), over a temperature range of (280 to 333) K. Good agreement is observed between these values and data available in the literature. Also, the (methane + ethanol + cyclohexane) ternary system was measured experimentally, and the methane solubility in the liquid phase decreased at constant temperature and pressure as the ethanol to cyclohexane mass ratio increased. For the ternary system modeling, using parameters taken from the binary system, the Peng−Robinson equation of state with Wong−Sandler mixing rules worked better than the use of Peng−Robinson equation of state with van der Waals mixing rules.

■

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VaporâLiquid Equilibrium Measurements and Thermodynamic

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