(p, Ï, T) Behavior of CO2 + Tetradecane Systems: Experiments and

Article pubs.acs.org/jced

(p, ρ, T) Behavior of CO2 + Tetradecane Systems: Experiments and Thermodynamic Modeling Yi Zhang, Weiwei Jian,* Yongchen Song,* Weiguo Liu, Mingjun Yang, Jiafei Zhao, Yu Liu, and Yuechao Zhao Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, P. R. China ABSTRACT: The injection of CO2 into oil reservoirs (CO2 enhanced oil recovery, CO2-EOR) can result in higher production, and the use of CO2 as a mining resource can thus be an economic driver for oil production. The thermodynamic properties of CO2 mixtures are essential for the design and operation of CO2-EOR systems. This paper addresses the (p, ρ, T) properties of a CO2 + tetradecane solution. Experimental densities were measured on a magnetic suspension balance, and experiments were performed at pressures from 10 MPa to 19 MPa, temperatures from 313.15 K to 353.15 K, and CO2 mole fractions of x1 = 0, 0.2469, 0.5241, 0.7534, and 0.8773. Solution densities increased with pressure and decreased with temperature over the experimental range. Density versus the CO2 mole fraction increased at first and then decreased at higher temperatures and higher CO2 concentrations. The compositions intersect when plotted, and the pressure intersection increased with temperature. The excess molar volumes of the binary mixtures were negative over the entire range of composition, which increased with increasing pressure and became more negative with increasing temperature. The PCSAFT and tPC-PSAFT equations of state were used to calculate the densities of the binary mixtures. New PC-SAFT parameters for tetradecane were obtained by fitting to experimental densities directly. In both PC-SAFT and tPC-PSAFT, the binary interaction parameter kij was fitted as a function of the CO2 mole fraction. The tPC-PSAFT combined with the correlation of kij gave the best predictions of the CO2 + tetradecane mixture densities. al.5 obtained compositional and density data of the liquid− liquid−vapor equilibria of CO2 + tetradecane systems from 279.26 K to 303.13 K and 3.95 MPa to 6.92 MPa. Laugier et al.6 reported vapor−liquid equilibrium data for CO2 + tetradecane systems at three temperatures (290 K, 295 K, and 300 K) and pressures from 5.18 MPa to 6.49 MPa. Ashcroft and Isa7 studied the effect of dissolved air on the densities of liquid hydrocarbons at 298.15 K and a total pressure of 0.1 MPa, and they found that liquid saturated with carbon dioxide increased the densities by a maximum of almost 0.1 %. Recently, Kariznovi et al.8 and Nourozieh et al.9 examined the solubility of CO2 in tetradecane and the liquid saturation properties (i.e., density and viscosity) when tetradecane was saturated with CO2 over a pressure range of 1 MPa to 6 MPa at 323.2 K and 373.2 K, respectively. A literature survey indicated that measurements are primarily limited to the solubility of CO2 in tetradecane, the saturated density and the phase equilibrium composition of CO2 + tetradecane binary mixtures. Moreover, most of the existing experimental data have been obtained at low pressures (P < 10 MPa). There are no experimental density data for binary

1. INTRODUCTION The capture and storage of CO2, the dominant greenhouse gas, has attracted significant attention from scientists and engineers. CO2-EOR (CO2-enhanced oil recovery), injection of CO2 into an oil reservoir to increase the recovery of oil, is an alternative location for storage CO2 under the oil reservoir.1 When CO2 is injected into the oil reservoir at high pressures, it displaces the oil, reduces its viscosity, and thus increases its mobility.2 Thermodynamic characterization involving phase compositions, densities, viscosities, and interfacial intensions of the CO2 + hydrocarbon mixtures must be known for accurate simulation of the CO2 displacement process.3 The (p, ρ, T) characteristic of CO2 + hydrocarbon mixtures is one of the important properties determining the fluid flow in petroleum reservoirs. Thus, accurate evaluation of the CO2-EOR technique requires understanding of the density properties of the CO2 + hydrocarbon system. In addition, the development of the equation of state for the CO2 + oil system requires support from reasonable data. The phase behavior data of binary mixtures of CO2 and nalkanes has been extensively investigated in the literature. Measurements of binary mixtures of CO2 + n-tetradecane have also been reported. Gasem et al.4 presented experimental vapor−liquid phase compositions, phase densities, and interfacial tensions for CO2 + n-tetradecane at 344.3 K and pressures from 6.89 MPa to the critical point. Van Der Steen et © 2015 American Chemical Society

Received: January 14, 2015 Accepted: April 22, 2015 Published: May 1, 2015 1476

DOI: 10.1021/acs.jced.5b00049 J. Chem. Eng. Data 2015, 60, 1476−1486

Journal of Chemical & Engineering Data

Article

Table 1. Chemical Sample Specifications chemical name

source

purification method

mole fraction purity

analysis method

nitrogen carbon dioxide tetradecane

Dalian Da-te Gas Co., Ltd. Dalian Da-te Gas Co., Ltd. TCI Development Co., Ltd.

none none none

0.99999 0.9999 0.991a

gas chromatography and dew point method gas chromatography and dew point method gas chromatography

a

The purity of tetradecane (0.991) was different from the mole or mass fraction; the purity depended on the sensitivity of the FID detector in GC (gas chromatography).

Figure 1. Schematic diagram of the experimental apparatus.

environments with the balance remaining in ambient conditions. The MSB was designed to operate at temperatures from 253.15 K to 423.15 K and in an UHV (ultra high vacuum) up to 20 MPa. A schematic diagram of the apparatus is shown in Figure 1. The temperature was controlled by a JULABO FP50-ME refrigerated/heating circulator with a double-walled thermostatic jacket that fit exactly around the measuring cell to reduce heat transfer between the balance and the laboratory atmosphere. The temperature of the MSB was detected by a resistance thermometer (pt100), with a controlling accuracy of 0.01 K. The pressures during the measurement were regulated by a piston pump (pump b in Figure 1). The pressure was measured with a reproducibility of 0.08 % at 20 MPa. The resolution and reproducibility of the mass were 10−5 g and ± 3· 10−5 g, respectively. Principle of Operation. In MSB, the Archimedes principle was used to determine the density, which involves weighing a “sinker” of known volume V while it is suspended in the fluid that will be measured. The balance reading W is the difference between the sinker mass and the buoyancy of the fluid:

systems (CO2 + tetradecane) with different CO2 concentration at pressures from 10 MPa to 19 MPa. Thus, this study provides density behavior data for binary systems containing CO2 and tetradecane to investigate the impact of different CO2 concentrations on the density of liquid tetradecane. Measurements were performed using a magnetic suspension balance (MSB), and the mixtures were measured at different CO2 mole fractions (x1 = 0, 0.2469, 0.5241, 0.7534, and 0.8773) at temperatures from 313.15 K to 353.15 K and pressures from 10 MPa to 19 MPa. The mixture density data were modeled using PC-SAFT and tPC-PSAFT in four different cases, and the constant kij value and the correlation of kij with the CO2 mole fraction were introduced to calculate densities of the CO2 + tetradecane solution.

2. EXPERIMENTAL SECTION Materials. Table 1 summarizes the chemical sample specifications. CO2 and N2 were supplied by Dalian Da-te Gas Co., Ltd. with nominal purities of 99.99 mol % and 99.999 mol %, respectively. Tetradecane was supplied by the TCI (Shanghai) Development Co., Ltd. with a nominal purity of 99 %. All materials were used as received without any further purification. Apparatus. Density measurements were made on a magnetic suspension balance (MSB) with a high-pressure measuring cell, and the details of this apparatus have been described previously.10,11 The apparatus essentially contains an electromagnet and a so-called suspension magnet. The suspension magnet consists of a permanent magnet, a sensor core, and a measuring load decoupling cage. The MSB makes it possible to weigh samples with no contact in almost all

W = m − ρV

(1)

Equation 1 is rearranged to the fluid density as

ρ=

m−W V

(2)

where W is the apparent mass reader from the MSB, and m is the true mass (vacuum) of the sinker, which is calibrated by measuring densities of N2. During calibration, the density data of N2 at specific temperatures and pressures were obtained 1477



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from the National Institute of Standards and Technology (NIST) database. ρ is the density measured, and V is the volume of the sinker at the measured T and P, which can be corrected from its known volume V0 in reference state (T0, P0) given as ⎤ ⎡ 1 V (T , P) = V (T0 , P0)⎢1 + αp(T − T0) − (P − P0)⎥ κT ⎦ ⎣ (3)

where αp and κT are the isobaric thermal expansion coefficient and isothermal compressibility, respectively, which can be obtained as a function of temperature as stated in the MSB specifications. Procedure. The detailed experimental procedure can be found in Song et al.10 and is only briefly discussed here. Prior to each measurement, the measuring cell and pipes must be cleaned and evacuated with a vacuum pump. A specific amount of CO2 was injected, and the density ρCO2 was measured. The amount of CO 2 injected was controlled by the CO 2 concentration of the mixtures that were to be measured. Tetradecane was then charged into the measuring cell, and the circulation pump began to operate, which accelerated the dissolution of CO2 in tetradecane. It typically took 1 to 2 days for the CO2 to dissolve completely. Then, the density of the mixture ρmix was measured, and the mass fraction of CO2 could be calculated from eq 4, in which the volume of the measuring cell changed only slightly after injection of tetradecane.10 After the CO2 dissolved completely, the temperature was fixed at a specific value, and the pressure was adjusted from 10 MPa to 19 MPa. The mass fraction of CO2 yi (0 ≤ yi ≤ 1) was calculated from

yi =

Figure 2. Density of tetradecane in this work and the literature. ☆, ○, ●, This work at 313.15 K, 323.15 K, and 333.15 K; ■, the reproducibility of this work at 323.15 K; ▲, Kariznovi et al.,8 323.15 K; ◊, Gawronska et al.,12 323.5 K; ▷, ◆, Khasanshin et al.,13 313.15 K and 333.15 K; ▼, Kariznoviet al.,14 323.15 K; □, Kariznoviet al.,15 323.15 K.

Experimental Densities. The isothermal density data for tetradecane and the CO2 + tetradecane binary mixtures were obtained at temperatures from 313.15 K to 353.15 K and at six different pressures from 10 MPa to 19 MPa. Four different CO2 concentrations were measured for the binary mixtures at x1 = 0.2469, 0.5241, 0.7534, and 0.8773. All experiments were performed above the bubble point of the CO2 + tetradecane mixtures.

ρCO

2

ρmix

Table 2. Experimental Densities of Pure Tetradecanea

(4)

The mole fraction of CO2 can be calculated from eq 5: yi

x1 =

M1 yi M1

+

yi M2

(5)

where M1 and M2 are the molar mass of CO2 and tetradecane, respectively.

3. EXPERIMENTAL RESULTS Data Validation. To verify the reliability and reproducibility of the measurements, densities of tetradecane were measured from 1 MPa to 19 MPa at 323.15 K. The generated data are presented in Figure 2, which were also compared to the densities reported in Gawronska et al.,12 Khasanshin et al.,13 and Kariznovi et al.8,14,15 As depicted in Figure 2, the reproducibility in our experiment is very good, and the data are in good agreement with those of Gawronska et al.12 and Khasanshin et al.13 Densities reported by Kariznovi et al.8,15 were slightly lower than those measured in this work, but the density variation versus pressure was the same. However, there is discrepancy between the data of Kariznovi et al.14 and that in other literature. The slope of density versus pressure in Kariznovi et al.14 was slightly different from that of this work and Kariznovi et al.,8,15 and the tetradecane densities in Kariznovi et al.14 were the same at 5 and 6 MPa as in Figure 2, which is inconsistent with the thermodynamic behavior.

T/K

P/MPa

ρ/kg·m−3

T/K

P/MPa

ρ/kg·m−3

313.19 313.23 313.15 313.13 313.15 313.17 323.26 323.18 323.14 323.18 323.23 323.25 333.14 333.16 333.28

10.02 12.04 14.05 16.04 18.06 19.04 10.00 12.04 14.05 16.07 18.06 19.08 10.05 12.04 14.06

756.25 757.62 759.03 760.35 761.65 762.28 749.44 750.93 752.38 753.74 755.07 755.76 742.64 744.14 745.66

333.16 333.13 333.13 343.32 343.32 343.35 343.31 343.34 343.31 353.63 353.58 353.66 353.48 353.50 353.51

16.06 18.05 19.06 10.04 12.05 14.07 16.03 18.02 19.04 10.02 12.05 14.04 16.03 18.01 19.05

747.18 748.61 749.31 736.00 737.59 739.16 740.68 742.16 742.92 729.05 730.83 732.42 734.17 735.70 736.41

a

Standard uncertainties were u(T) = 0.01 K and u(P) = 0.002 MPa. The combined expanded uncertainty was Uc(ρ) = 0.17 kg·m−3 at a 0.95 level of confidence (k ≈ 2).

Tables 2 and 3 summarize the densities of pure tetradecane and the CO2 + tetradecane binary systems. The uncertainties for the measured temperature, pressure, and liquid density were 0.01 K, 0.002 MPa, and 0.17 kg·m−3 (with 0.95 level of confidence k ≈ 2), respectively. The uncertainty of the CO2 mole fraction for the binary mixtures was 0.0005 mol·mol−1. The method for fluid density uncertainty was presented in 1478



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Table 3. Experimental Densities for the CO2 + Tetradecane Mixtures at Different CO2 Mole Fractionsa T/K

P/MPa

313.07 313.08 313.08 313.08 313.09 313.11 323.14 323.14 323.11 323.12 323.19 323.14 333.13 333.15 333.13

10.01 12.05 13.99 16.02 18.00 19.00 10.12 12.06 14.02 16.02 17.96 18.98 10.01 12.06 13.97

313.19 313.16 313.17 313.35 313.21 313.16 323.23 323.23 323.23 323.21 323.22 323.22 333.09 333.15 333.20

10.11 11.93 13.93 16.05 18.06 19.06 10.03 12.04 13.98 16.08 18.05 19.04 10.10 11.93 13.97

313.05 313.05 313.14 313.12 313.00 313.13

10.04 11.94 13.04 13.94 15.04 16.01

ρ/kg·m−3

T/K

x1 = 0.2469 761.87 333.11 763.39 333.15 764.87 333.16 766.36 343.25 767.75 343.25 768.47 343.34 754.69 343.27 756.22 343.24 757.81 343.27 759.35 353.48 760.81 353.43 761.61 353.48 747.30 353.52 749.05 353.40 750.65 353.47 x1 = 0.5241 776.82 333.15 778.74 333.11 780.74 333.13 782.84 343.22 784.76 343.26 785.72 343.25 767.22 343.37 769.42 343.36 771.51 343.39 773.72 353.36 775.72 353.39 776.70 353.43 757.94 353.43 760.02 353.39 762.35 353.44 x1 = 0.7534 799.71 333.12 804.49 333.12 806.93 333.07 809.04 333.07 811.66 333.17 813.59 343.29

P/MPa

ρ/kg·m−3

T/K

P/MPa

16.04 17.98 18.98 10.08 12.00 14.06 16.01 18.02 19.05 9.97 11.99 14.00 16.03 18.07 19.02

752.33 753.84 754.70 739.80 741.71 743.54 745.25 746.97 747.79 733.10 735.13 737.01 738.93 741.03 741.82

313.01 313.01 312.99 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 333.07 333.17 333.11 333.07

17.01 18.06 19.07 10.07 12.03 13.00 14.02 15.06 16.04 17.01 18.07 19.02 10.05 12.05 13.04 14.03

15.99 18.06 19.08 10.08 11.93 13.97 15.99 18.04 19.08 9.98 11.96 14.02 16.06 18.06 19.06

764.66 766.90 767.96 748.36 750.66 753.12 755.45 757.81 758.96 738.86 741.42 744.02 746.56 748.96 750.06

15.02 16.04 17.06 18.06 19.05 11.99

777.38 779.31 782.56 784.44 786.81 755.90

313.19 313.20 313.17 313.17 313.23 313.18 313.18 313.19 313.12 323.11 323.15 323.14 323.14 323.16 323.14 323.14 323.14

9.97 11.99 12.99 14.05 15.01 16.02 17.01 18.04 19.06 10.98 12.05 13.02 14.05 15.05 16.04 17.04 18.06

Ux1 =

2

T/K

x1 = 0.7534 815.79 343.18 817.99 343.20 819.95 343.37 782.23 343.32 787.20 343.34 789.82 343.28 791.84 343.37 794.75 353.36 796.67 353.41 799.28 353.47 801.50 353.46 803.65 353.46 764.82 353.39 769.75 353.46 771.85 353.54 774.55 x1 = 0.8773 799.39 323.11 806.52 333.19 810.26 333.18 813.95 333.22 818.70 333.14 822.71 333.14 826.33 333.11 829.70 333.13 833.41 343.29 783.24 343.28 786.07 343.26 788.73 343.30 791.99 343.32 795.16 353.48 799.20 353.46 801.18 353.47 805.90

P/MPa

ρ/kg·m−3

13.03 14.07 15.00 15.97 16.93 18.03 19.03 12.05 13.00 14.01 15.04 15.99 17.03 18.04 18.99

757.60 759.71 761.76 764.11 766.37 768.86 770.90 743.36 744.77 746.82 748.68 750.82 753.15 755.21 756.97

19.02 13.02 14.03 15.04 16.05 17.04 18.06 19.05 15.01 16.05 17.07 18.04 19.05 17.02 18.01 19.04

809.81 771.46 774.07 776.33 779.75 782.59 785.49 788.14 756.06 759.70 763.58 766.93 770.12 747.37 751.14 754.52

Standard uncertainties were u(x1) = 5·10−4 mol/mol, u(T) = 0.01 K, u(P) = 0.002 MPa. The combined expanded uncertainty was Uc(ρ) = 0.17 kg·m−3 at a 0.95 level of confidence (k ≈ 2). a

detail in Song et al.10 The uncertainty for the CO2 mole fraction Ux1 was calculated using the partial differential equation in eq 6, as follows: ⎛ ⎞2 ⎛ ⎞2 ⎜ ∂x ⎟ Uρ 2 + ⎜⎜ ∂x ⎟⎟ Uρ 2 mix ⎜ ∂ρ ⎟ CO2 ⎝ ∂ρsol ⎠ ⎝ CO2 ⎠

ρ/kg·m−3

pressure) became larger with increasing CO2 concentration at a constant temperature, which led to an intersection point between the composition density lines and CO2 concentrations at x1 = 0.7534 and 0.8773. This intersection was also observed for binary mixtures of CO2 + decane in our previous work10 and is caused by the density variations of pure fluids: carbon dioxide has a lower density than tetradecane at low pressures and high temperatures, and the density character of the CO2 + tetradecane systems is inclined to CO2 when the CO2 concentration is much higher. Thus, when the CO2 mole fraction reaches a certain value, higher CO2 concentrations lower the density of the binary mixtures. In Figure 3, the crossing points shift to higher pressures with increasing temperature. The accurate pressures of the intersections occurred at 10.35 MPa, 14.35 MPa, and 15.65 MPa at temperatures from 313.15 K to 333.15 K. Behind the intersection point in Figure 3 (i.e., at higher pressures than the intersection pressure), the densities of the CO2 + tetradecane mixtures increased with the CO2 mole fraction, but below the crossing point, the mixture densities

(6)

where UρCO2 and Uρmix are the density uncertainties of CO2 and the binary mixtures, respectively. Experimental densities were plotted as functions of pressures, temperatures, and CO2 mole fractions for different compositions in Figures 3, 4, and 5. The densities of the binary mixtures, as presented in Figures 3 and 4, increased proportionally when the pressure increased and diminished when the temperature increased. As revealed in Figure 3, the dissolution of CO2 increased the densities of tetradecane, and for pure tetradecane and mixtures with low CO2 concentrations, the variation of density with pressure at a constant temperature was linear. Meanwhile, the slope (density versus 1479



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Figure 3. Density of the CO2 + tetradecane mixtures versus pressure at different temperatures T: a, 313.15 K; b, 323.15 K; c, 333.15 K; d, 343.15 K; ■, x1 = 0; ○, x1 = 0.2469;▲, x1 = 0.5241; ▽, x1 = 0.7534; ◀, x1 = 0.8773.

Figure 4. Density of the CO2 + tetradecane mixtures versus temperature at different pressures P: a, 12 MPa; b, 14 MPa; c, 16 MPa; d, 18 MPa; ■, x1 = 0; ○, x1 = 0.2469; ▲, x1 = 0.5241; ▽, x1 = 0.7534; ◀, x1 = 0.8773.

decreased with the CO2 mole fraction. The decrease in density with CO2 concentration is directly displayed in Figure 5. The behavior in Figure 5d shows that, at 343.15 K and 353.15 K, density increased with CO2 concentration at first and then decreased until the CO2 concentration reached a certain value.

The decrease in density tended to occur at higher temperatures in Figure 5 because the density of CO2 is much lower and more strongly affected by higher temperatures. A decrease in mixture density will cause the CO2 to float upward in the oil reservoir, which is not beneficial for oil recovery and CO2 storage safety. 1480



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Figure 5. Density of the CO2 + tetradecane mixtures versus CO2 mole fraction at different temperatures and pressures: a, 12 MPa; b, 14 MPa; c, 16 MPa; d, 18 MPa; ■, T = 313.15 K; ○, T = 323.15 K; ▲, T = 333.15 K; ▽, T = 343.15 K; ◀, T = 353.15 K.

of pure tetradecane and the CO2 + tetradecane mixtures by the following expression:

The experimental densities for the CO2 + tetradecane mixtures were compared with the densities of CO2 + decane and CO2 + dodecane reported by Song et al.10 and Zhang et al.,16 respectively. As shown in Figure 6, densities were plotted

vmE =

x1M1 + x 2M 2 − (x1v1 + x 2v2) ρmix

(7)

where M, x, and v are the molecular weight, mole fraction, and molar volume, respectively. The subscripts 1 and 2 represent the components CO2 and tetradecane, respectively. ρmix is the density of the mixtures measured in this work. The molar volumes of CO2 were recorded from the NIST database, and that of tetradecane was calculated from the measured densities ρ2 (v2 = M2/ρ2, ρ2 is the density of tetradecane). The excess molar volumes are plotted as a function of the CO2 mole fraction at 313.15 K and 12 MPa in Figure 7. Negative values of the excess molar volumes were obtained for the CO2 + tetradecane mixtures over the entire compositions, which implies nonideal properties of the binary system and the interaction between CO2 and tetradecane. Fandiño et al.17 studied the excess molar volumes of CO2 + decane solutions and concluded that negative values were attributed to strong interactions and molecular sizes between CO2 and decane. There may be some similar phenomena in the volumetric behavior of the CO2 + tetradecane mixtures. In Figure 7, there was a maximum negative value at a CO2 mole fraction between 0.7 and 1. The maximum negative values indicate the marked packing effect of the CO2 + tetradecane mixtures and the strong molecular interactions in the mixing process. This behavior has also been observed in other CO2 + alkane (i.e., CO2 + decane,10 CO2 + dodecane,16 CO2 + tridecane18) binary systems. The excess molar volume was also compared for the CO2 + decane, CO2 + dodecane, and CO2 + tetradecane mixtures. As shown in Figure 7, the excess molar volumes of CO2 + decane were larger than those of CO2 + dodecane, and the values for

Figure 6. Density of the CO2 + alkane mixtures versus pressure at 313.15 K. ■, CO2 + tetradecane, x1 = 0.2469; ○, CO2 + dodecane,16 x1 = 0.2497; ▲, CO2 + decane,10 x1 = 0.2361.

as a function of pressure for binary mixtures of similar CO2 mole fractions (x1 ≈ 0.25), and at 313.15 K, the densities of the CO2 + alkane mixtures increased with the carbon number of the alkane. Densities of CO2 + tetradecane were higher than that of CO2 + decane and CO2 + dodecane, and the slope of the density versus pressure were similar for the three different binary mixtures. Excess Molar Volume. The excess molar volumes of the binary systems were calculated from the experimental densities 1481



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a ̃hs =

⎞ ⎛ζ 3 ζ2 3 1 ⎡⎢ 3ζ1ζ2 ⎜ 22 − ζ0⎟ + + 2 ζ0 ⎢⎣ 1 − ζ3 ζ3(1 − ζ3) ⎠ ⎝ ζ3 ⎤ ln(1 − ζ3)⎥ ⎥⎦

giihs =

(12)

⎛ di ⎞2 2ζ2 2 3d ζ2 1 ⎜ ⎟ + i + ⎝ 2 ⎠ (1 − ζ3)3 (1 − ζ3) 2 (1 − ζ3)2 (13)

a disp ̃ = −2πρI1(η , m) ∑ ∑ xixjmimj i

where ρ is the total number density of molecules. The temperature-dependent effective segment diameter di of component i is given by

4. DENSITY PREDICTION Equation of State. PC-SAFT and tPC-PSAFT predicted the densities of the CO2 + tetradecane binary mixtures. The PC-SAFT19 equation of state is a modified SAFT20,21 equation of state, which is developed by applying the perturbation theory of Baker and Henderson22 to a hard-chain reference fluid. In PC-SAFT, a new dispersion term is derived, and a hard-chain fluid serves as a reference, rather than the spherical molecules in the SAFT20 equation of state. The tPC-PSAFT developed by Karakatsani and Economou23 equation of state is an extension of PC-SAFT to explicitly account for polar interactions. The tPC-PSAFT equation of state has been described in detail elsewhere,23,24 and only a brief introduction of tPC-PSAFT is mentioned here. tPC-PSAFT is usually expressed as a sum of the reduced residual Helmholtz free energy ãres:

⎡ ε ⎞⎤ ⎛ di = σi⎢1 − 0.12 exp⎜ −3 i ⎟⎥ ⎝ kT ⎠⎦ ⎣

a ̃polar = m

(8)

a ̃ind = m

i

m=

∑ ximi i

a 2̃ polar 1 − a3̃ polar /a 2̃ polar

(17)

a 2̃ ind 1 − a3̃ ind /a 2̃ ind

(18)

where the subscripts 2 and 3 are the second- and third-order perturbation terms, respectively. The exact formulas of ã2polar, ã3polar, ã2ind, and ã3ind can be found in Karakatsani and Economou.23,24 For an association component, PC-SAFT requires five parameters that are typically fitted to the experimental data: the number of segments, m; the chain segment diameter, σ; the energy dispersion interactions between segments, ε/k; the association energy between sites A and B, εAB/k; and the volume of the association interactions between sites A and B, κAB. For tPC-PSAFT, two additional parameters were taken into account: the effective polar segment diameter σp and the dipole μ or the quadrupole Q. For the nonpolar components, tPC-PSAFT was reduced to the PC-SAFT equation of state.26 The models were extended to mixtures using appropriate mixing and combining rules for the various parameters. The

(9)

For the mixture, the reduced Helmholtz free energies of the hard-chain and dispersion terms were given in PC-SAFT theory,19 as shown in eqs 10 to 14:

∑ xi(mi − 1)ln(giihs)

(16)

where σi and εi/k are the temperature-independent segment diameter and the segment energy parameter, respectively, of component i. I1 and I2 in eq 14 are calculated from the power series in density, and C1 is given as a function of m and ζ3. The detailed expression of I1, I2, and C1 can be found in Gross and Sadowski.19 The pioneering work of Stell and coworks is used25 for polar and induced polar interactions:

where ãhc, ãdisp, ãassoc, ãpolar, and ãind in the right-hand side of eq 8 are the reduced Helmholtz free energy of the hard-chain term, dispersion term, association interaction, polar interaction, and induced polar interactions, respectively. For nonassociation fluids, such as CO2 and tetradecane, the reduced residual Helmholtz free energy ãres reduces to

a ̃hc = ma ̃hs −

(14)

where m is the mean segment number in the mixture. xi, mi, and giihs are the mole fraction, the number of segments, and the radial distribution function, respectively, of the component i, and ζ0, ζ1, ζ2, and ζ3 could be defined as π n = 0, 1, 2, 3 ζn = ρ ∑ ximidin 6 i (15)

the CO2 + tetradecane mixtures were smallest. Consequently, the interaction between CO2 and tetradecane molecules was the strongest, and it may be more difficult for CO2 to extract tetradecane from the petroleum. In other words, CO2 smoothly enhances oil recovery when petroleum contains lighter alkanes.

a ̃res = a ̃hc + a disp ̃ + a ̃polar + a ̃ind

kT

σij 3

⎛ εij ⎞2 − πρmC1I2(η , m) ∑ ∑ xixjmimj⎜ ⎟ σij 3 ⎝ kT ⎠ i j

Figure 7. Excess molar volumes for the system CO2 + alkane mixtures at 12 MPa and 313.15 K: ■, CO2 + decane;10 ○, CO2 + dodecane;16 ▲, CO2 + tetradecane.

a ̃res = a ̃hc + a disp + a ̃polar + a ̃ind ̃ + a assoc ̃

j

εij

(10)

(11) 1482



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standard mixing rule for the mean segment number m in the mixtures is m = x1m1 + x 2m2 (19)

n

F = min ∑

εij =

1 (σi + σj) 2

(21)

Table 5. Parameters of Pure Tetradecane Used in PC-SAFT

The binary interaction parameter kij was used to correct the segment−segment interactions for these unlike segments. Density calculations with the PC-SAFT and tPC-PSAFT equations of state were the same as the method in Song et al.11 Parameters of CO2 and Tetradecane. In PC-SAFT, CO2 and tetradecane were both modeled as nonassociation and nonpolar molecules, and only three parameters (segment number m, segment diameter σ, and segment energy parameter ε/k) of these two components were considered. In tPCPSAFT, CO2 was modeled as a nonassociation component with a quadrupole−quadrupole interaction, and tetradecane was the same as in PC-SAFT. tPC-PSAFT was reduced to PC-SAFT for the nonpolar component. Thus, the parameters of tetradecane in tPC-PSAFT were the same as in PC-SAFT, and four parameters (segment number m, segment diameter σ, segment energy parameter ε/k, the quadrupole Q) of CO2 should be taken into account. Within the same temperature range, the average absolute deviation of the CO2 density calculated with parameters from Gross and Sadowski19 and Diamantonis and Economou27 were 2.73 % and 0.83 %, respectively. Thus, the parameters of CO2 in PC-SAFT were those referred to by Diamantonis and Economou.27 In tPC-PSAFT, the CO2 parameters were taken from Karakatsani and Economou.24 The CO2 parameters used in this work are given in Table 4, and the density AADs calculated with the PC-SAFT and tPC− PSAFT equations of state were 0.83 % and 0.49 %, respectively.

this work G-S PC-SAFT HTHP PC-SAFT

PC-SAFT tPC-PSAFTa

σ

ε/k

AADb (%)

2.6037 1.912

2.555 2.854

151.04 157.97

0.83 0.49

m

σ

ε/k

AADa (%)

8.8207 5.9002 8.5081

3.4404 3.9396 3.4946

235.8651 254.21 240.9176

0.01 0.12 0.6

a

The AADs in the density of tetradecane were calculated from the experimental data and predicted densities of the various models.

Density Predictions for Pure Tetradecane. The PCSAFT prediction results for three sets of parameters are plotted in Figure 8. From 313.15 K to 353.15 K and 10 MPa to 19

Table 4. Parameters of CO2 Used in PC-SAFT and tPCPSAFT m

(22)

where ρi,exp and ρi,cal refer to the experimental and calculated densities, respectively. n is the number of experimental data. The three different sets of tetradecane parameters (G-S PCSAFT, HTHP PC-SAFT, new values proposed in this work) are listed in Table 5.

(20)

εiεj (1 − kij)

ρi ,exp

i=1

Conventional combining rules were employed to determine the parameter for a pair of unlike segments: σij =

ρi ,exp − ρi ,cal

Figure 8. Comparison of the PC-SAFT predictions with different sets of parameters for tetradecane. Solid lines, new parameters in this work; dashed lines, G-S PC-SAFT parameters; dotted lines, HTHP PCSAFT parameters. The scatter points are the experimental densities measured in this work: ■, 313.15 K; ◁, 323.15 K; ●, 333.15 K; ○, 343.15 K; ▶, 353.15 K.

Q = 4.3 D, and σp = 2.974 Å. bThe AADs in the density of CO2 for PC-SAFT and tPC-PSAFT were recorded from Diamantonis and Economou27 and Karakatsani and Economou.24

a

MPa, the results predicted by the new parameters proposed in this work agreed well with the experimental densities. The PCSAFT predictions using parameters recommended by G-S PCSAFT overestimated the density with pressures higher than 12 MPa. The HTHP PC-SAFT generally performed poorly in calculating tetradecane density in this temperature range. The maximum RDs (relative deviations) in tetradecane densities calculated by G-S PC-SAFT, HTHP PC-SAFT and the new parameters were 0.28 %, −0.63 %, and 0.02 %, respectively. The AADs (absolute average deviations) were 0.12 %, 0.6 %, and 0.01 % for G-S PC-SAFT, HTHP PC-SAFT, and the new parameters, respectively. The RD and AAD can be defined as

There are two sets of PC-SAFT parameters for tetradecane to date: that derived by Gross and Sadowski19 (G-S PC-SAFT), who fit PC-SAFT to the vapor pressure curve, and those parameters predicted by the correlations in Burgess et al.,28 namely, HTHP PC-SAFT. The correlations were obtained by regressing the parameters of selected n-alkanes for which literature density data were available and then plotting the parameters as a function of molecular weight. However, the regressions of the correlations were not included in the density data of tetradecane because no available data of tetradecane has been reported. In this work, new values for the tetradecane PCSAFT parameters m, σ, and ε/k were obtained by fitting experimental density data measured in this work to tetradecane directly. The following function was used to determine the PCSAFT parameters fit to the density data:

RD% = 1483

100(ρcal − ρexp ) ρexp

(23) DOI: 10.1021/acs.jced.5b00049 J. Chem. Eng. Data 2015, 60, 1476−1486


Article

Figure 9. (a) Relative deviations of tetradecane in the literature predicted by PC-SAFT with the new parameters. ■, Kariznovi et al.;8 ★, Gawronska et al.;12 ◆, Khasanshin et al.;13 ○, Kariznovi et al.;15 ▼, Nourozieh et al.;29 ▲, Zhang et al.;30 ◁, Alcart et al.;31 □, Valencia et al.32 (b) Densities of tetradecane in the literature. ■, Kariznovi et al.,8 323.2 K; ○, △, ▽, Kariznovi et al.,15 296.6 K, 313.3 K, and 333.3 K; ◀, ▷, Nourozieh et al.,29 294.8 K and 324 K.

AAD% =

100 n

n

∑

Table 6. Coefficients of Equations 25 and 26 for kij in PCSAFT and tPC-PSAFT

ρi ,cal − ρi ,exp

i

ρi ,exp

(24) a b

where ρi,exp and ρi,cal are the same as in eq 22. For the literature tetradecane density data, PC-SAFT predictions with the new parameters also gave reasonable agreement with the experimental measurements. As shown in Figure 9a, the maximum deviation was limited to 0.2 %, except for densities from Nourozieh et al.29 There might be some disagreement between densities of Nourozieh et al.29 and those reported by other studies because the slope of the density versus pressure line was different from the other data (Figure 9b). In general, PC-SAFT combined with the new parameters could accurately predict the densities of tetradecane from 296.6 K to 353.15 K and below 19 MPa. Density Predictions for Binary Mixtures. The new parameters for tetradecane were used to calculate the densities of the CO2 + tetradecane mixture by PC-SAFT and tPCPSAFT. The adjustable binary interaction parameter kij in eq 21 is crucial for the density calculation of the CO2 + tetradecane binary mixtures. In this work, the constant kij values of the CO2 + tetradecane solutions were regressed from the experimental densities from PC-SAFT and tPC-PSAFT, which were 0.159 and 0.25, respectively. The regression of kij according to the objective function was the same as eq 22. However, the relative density deviations calculated with a constant kij value varied with the CO2 mole fraction. Thus, in this study, kij was correlated as a function of the CO2 mole fraction for the PCSAFT and tPC-PSAFT, as in eqs 25 and 26: kij1 = a1 + a 2x12.5 + a3/ln(x1)

(25)

kij2 = b1 + b2x1 + b3/x1

(26)

1

2

3

−1.94710 −0.06369

7.03805 −0.07305

0.38803 0.32559

densities. Then, the correlation was established by fitting a series of optimal kij values and the CO2 mole fraction x1. PC-SAFT and tPC-PSAFT with different kij values were named as four different cases listed in Table 7. Cases 1 and 3 were defined as the predictions by PC-SAFT and tPC-PSAFT combined with the constant kij value, and cases 2 and 4 were the predictions with these two equations of state combined with the improved correlation of kij. The calculated results of the different cases are shown in Table 7 and Figure 10. In the measured temperature and pressure ranges, the AADs in the CO2 + tetradecane densities calculated by cases 1 to 4 were 2.92 %, 2.31 %, 2.46 %, and 0.24 %, respectively. Case 3 gave better predictions than case 1, highlighting the necessity of considering the quadrupole of CO2. As shown in Figure 10, PC-SAFT gave negative deviations, and tPC-PSAFT gave positive deviations. The accuracies of tPC-PSAFT were markedly improved by the correlated binary interaction parameter kij, but PC-SAFT was slightly improved by the correlated kij. This once again highlights the importance of the quadrupole of CO2 when calculating the density of the CO2 + tetradecane solution. The tPC-PSAFT equation combined with the correlated kij values gave the best agreement with the experimental densities, with a maximum relative deviation less than 2 %. Figure 11 shows the prediction results of the CO2 + tetradecane solution at x1 = 0.5241 by case 4, which gave satisfactory predictions with experimental measurements from 313.15 K to 353.15 K and 10 MPa to 19 MPa.

5. CONCLUSIONS In this work, new measurements of the compressed liquid densities for CO2 + tetradecane binary mixtures were reported from 313 to 353 K and 10 to 19 MPa over a wide interval of compositions. The PC-SAFT and tPC−PSAFT equations of state calculated densities of the CO2 + tetradecane solutions, tPC−PSAFT combined with the correlation of kij and the CO2

where the superscripts 1 and 2 in kij are indices of the PC-SAFT and tPC−PSAFT equations of state. The coefficients of eqs 25 and 26 are listed in Table 6. These two equations were correlated according to the following procedures. At a constant CO2 concentration, an optimal kij was obtained by minimizing the AADs between the experimental and the calculated 1484



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Table 7. Values of kij Used in PC-SAFT and tPC-PSAFT and the AAD % of Density Predictions by Different Cases

a

case

EOS

kij

AAD x1 = 0.2469

AAD x1 = 0.5241

AAD x1 = 0.7534

AAD x1 = 0.8773

averagea

1 2 3 4

PC-SAFT PC-SAFT tPC-PSAFT tPC-PSAFT

0.159 eq 25 0.25 eq 26

6.74 6.01 4.02 0.17

3.85 1.77 3.54 0.01

1.46 1.48 2.04 0.3

0.52 0.53 0.59 0.44

2.92 2.31 2.46 0.24

Representing the AAD of all data for each case.

prediction, and PC-SAFT gave a poor prediction with this correlation, highlighting the necessity of including the quadrupole of CO2.

■

AUTHOR INFORMATION

Corresponding Authors

*Fax: 0086411-84708015. E-mail: [email protected]. *E-mail: [email protected]. Funding

This paper was supported by the National Program on Key Basic Research Project (No. 2011CB707304), the Fundamental Research Funds for the Central Universities (DUT15LAB22), and the China Scholarship Council. Notes

The authors declare no competing financial interest.

■ ■

Figure 10. Relative deviations of the experimental densities of the CO2 + tetradecane mixtures from those calculated from the various cases listed in Table 7 at 18 MPa and 313.15 K to 353.15 K: ▲, case 1; △, case 2; ●, case 3; ○, case 4.

ACKNOWLEDGMENTS The authors thank the editor and reviewers for their valuable comments. REFERENCES

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Figure 11. Calculation results of the CO2 + tetradecane solution by case 4 at x1 = 0.5241. ◀, 313.15 K; ▽, 323.15 K; ▲, 333.15 K; ○, 343.15 K; ■, 353.15 K; dotted lines, calculated by case 4.

mole fraction gave a satisfactory prediction in the reported temperature and pressure ranges. The following conclusions can be drawn from this study. (1) The intersection effect was observed for binary mixtures with high CO2 concentrations, and the intersection of pressure increased with temperature. (2) At higher temperatures, densities of CO2 + tetradecane increased with CO2 concentration at first and then decreased at higher CO2 mole fractions. (3) The excess molar volumes of CO2 + tetradecane were negative over the entire range of compositions, and the maximum negative values were with compositions rich in CO2. (4) For pure tetradecane, new PCSAFT parameters were regressed from the experimental densities with an AAD of 0.01%. For the density prediction of the CO2 + tetradecane system, tPC−PSAFT combined with the correlation of kij and the CO2 mole fraction gave the best 1485



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