Density and Volumetric Behavior of CO2 + Undecane System from

Article pubs.acs.org/jced

Density and Volumetric Behavior of CO2 + Undecane System from 313.15 to 353.15 K and Pressures up to 19 MPa Yi Zhang, Lulu Wang, Shuyang Liu, Yongchen Song,* Yu Liu, and Lanlan Jiang 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, China ABSTRACT: Densities of compressed CO2 + undecane binary mixtures were measured using a magnetic suspension balance (MSB). Measurements were made at temperatures ranging from 313.15 to 353.15 K and pressures ranging from 8 to 19 MPa at CO2 mole fractions (x1) of 0, 0.2483, 0.4641, 0.6797, and 0.8874. The mixture densities were found to increase linearly with pressure and decrease with temperature; this behavior is similar to that of CO2 + decane or dodecane mixtures. The mixture densities show a crossover with composition when the CO2 mole fraction is high. The densities of alkanes increase almost linearly with carbon number, as do the densities of CO2 + alkane mixtures. With the of CO2 mole fraction, the mixture densities increase at first, then decrease. The increase of pressure makes the excess molar volume less negative, whereas the increase of temperature makes it more negative. Densities calculated from the perturbed hard chain equation of state (PHSC EOS) with improved parameters are in good agreement with the experimental densities. Adopting the constant binary interaction parameter kij for different alkanes in the PHSC EOS slightly enlarge the model deviation but simplifies the calculation. of 0.38%.11 Later, Zhang et al. improved the PHSC EOS to predict the densities of the CO2 + dodecane system, yielding an AAD of 0.52%.12 In summary, the predictions of PHSC EOS for binary mixtures are of considerable precision. In this work, the density of CO2 + undecane system was measured at five compositions in the pressures ranging from 8 to 19 MPa and temperatures ranging from 303.15 to 353.15 K by a magnetic suspension balance (MSB). Furthermore, the PHSC EOS with improved parameters was used to represent the experimental densities.

1. INTRODUCTION As a result of increasing greenhouse gas emissions, the global warming has accelerated in recent years. Consequently, it is imperative to reduce the release rate of CO2 to mitigate greenhouse effect.1 Recognized as a promising way to ensure cost-efficient avoidance of CO2 emission to the atmosphere,2 CO2 capture and storage (CCS) consists of separating CO2 from the emission sources and transporting and storing the captured CO2 underground.3 Furthermore, CO2-enhanced oil recovery (EOR) has been increasingly adopted in large-scale CO2 storage projects for its commercial advantages.4 To design and optimize the CO2 displacement process, properties such as density, phase behavior, and viscosities of mixtures of CO2 and hydrocarbons must be known.5 Undecane is a midlength chain alkane and a typical component of crude oil.6 Thus, the properties of CO2 + undecane mixture are of great research value. Nevertheless, few data concerning the property of CO2 + undecane system are available in the literature. Albo et al. measured the density of undecane at temperatures between 278 and 318 K and pressures up to 60 MPa.7 Camacho−Camacho studied the vapor−liquid equilibrium for the CO2 + undecane systems at four temperatures (315, 344, 373, and 418 K) and pressures up to 20 MPa;8 however, the density of this system has not been measured. Sharafi et al. employed the PHSC EOS to calculate the densities of R32-R134a mixtures and the absolute average deviation (AAD) was 1.08%;9 Hosseini et al. applied the PHSC EOS to model the density of ionic liquids and obtained an AAD of 0.24%.10 Further more, Valavi et al. used the PHSC EOS to predict the density of an acid and peptide solution with an AAD © XXXX American Chemical Society

2. EXPERIMENTAL SECTION Materials. The details of materials used in this experiment are listed in Table 1. All materials were used as received without any further purification. The impurities of undecane were found Table 1. Details of Pure Compounds Used in This Study chemical

CAS no.

source

nitrogen

7727−37−9

carbon dioxide undecane

124−38−9

Dalian Da-te Gas co., Ltd. Dalian Da-te Gas co., Ltd. Tokyo Chemical Industry Co., Ltd. (TCI)

112−40−3

mole fraction purity

molecular weight

0.99999

28.01

0.9999

44.01

0.996

156.31

Received: January 10, 2016 Accepted: July 4, 2016

A

DOI: 10.1021/acs.jced.6b00026 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Figure 1. Schematic diagram of the apparatus. The piston pump (a) was used to inject undecane, and the piston pump (b) was used to adjust pressure during measurements.

Experimental Principal. Archimedes’ principle indicates that the upward buoyant force that exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces. On the basis of this principle, the fluid density can be obtained from eq 1

to be decane, dodecane, tridecane, tetramethylbenzene and other hydrocarbons. The average carbon number of the impurities was around 11, and thus, the effect of impurities on the experiments can be ignored. Apparatus. The main experimental apparatus used to measure density, shown schematically in Figure 1, was a magnetic suspension balance (MSB) manufactured by Rubotherm Präzisionsmesstechnik GmbH. The MSB can be operated in the temperature range from 253 to 423 K and at pressures up to 20 MPa. A permanent magnet, an electronic magnet, a sinker, and a measuring cell constitute the core parts of the MSB. The sinker is made of titanium alloy, a highly corrosion resistant material. The mass of the sinker was 19 g and its volume is 4.2265 cm3 at 20 °C (details provided by the manufacturer.) The electronic magnet, which is attached to the bottom of the microbalance, could maintain a freely suspended state via an electric control unit. Through magnetic coupling, the measuring force is transmitted from the permanent magnet, which is located inside the measuring cell to the microbalance without contact. Because the substance to be measured is isolated from the microbalance, the measurement can be conducted under high temperature and pressure conditions. A JULABO FP 50 ME refrigerated/heating circulator was used to control the temperature. The measuring cell was covered with a double-walled thermostatic jacket that was filled with circulating oil. The temperature and pressure were measured by a Pt 100 temperature probe with a resolution of 0.01 K and a pressure probe (20 MPa, reproducibility 0.08%), respectively. A circulating pump (AKICO, Japan) was used to accelerate the dissolution of CO2 into undecane. The booster pump was used to pressurize nitrogen to the exact pressure in leakage detection of the experimental system. A vacuum pump reduced the pressure to 0.07 bar before the start of the experiment. To prevent the system pressure from reaching 220 bar (the pressure limit of the measuring cell), a rupture disc was installed. Piston pump (a) was used to inject undecane, and piston pump (b) was used to adjust the pressure in the measuring cell during measurements.

ρ=

m−W V

(1)

In this equation, ρ is the density of the fluid in the measuring cell, m is the mass of the sinker in vacuum, W is the apparent mass of the sinker weighed in a fluid-filled measuring cell, and V is the volume of the sinker at temperature T and pressure P. V can be obtained accurately from its known volume, V0, at specified reference conditions (T0, P0) from the expression ⎤ ⎡ 1 V = V0⎢1 + αT (T − T0) − (P − P0)⎥ κT ⎦ ⎣

(2)

where αT and kT are the isobaric thermal expansion coefficient and the isothermal compressibility modulus, respectively. For the sinker material, both αT and kT are functions of temperature, and these can be acquired from the manufacturer of the MSB.13 Procedures. Prior to the measurements, leakage detection over the whole system was carried out to ensure that the CO2 leakage could not occur during measurement. The mass and volume of the sinker must be calibrated because this affects the accuracy of the obtained density data. Zhang et al. have tested the accuracy and reliability of this experimental system by measuring the densities of deionized water and N2; the maximum deviations were found to be 0.03% and 0.05%, respectively.13 The procedure of using the MSB to measure the densities of CO2 + alkane mixtures has been stated in detail in our previous work.12 It is important to note that the experimental pressure range is greater than 14 MPa and the pressure interval is 1 MPa when the temperature is greater than 343.15 K because the miscible pressure is greater at high temperatures. B



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Table 2. Experimental Densities ρ of Undecane at Temperature T and Pressure P in This Worka

The concentration of CO2 strongly affects the density of the CO2 + undecane mixture. Therefore, to find the relationship between the concentration of CO2 in the solution and the solution density, the value of the CO2 concentration must be known accurately. The following expression can be used to obtain the CO2 mole fraction, x1 ρCO V1 2

m1 =

x1 =

ρmix V2

=

ρCO V1 2

ρmix (V1 + ΔV )

≈

ρCO V1 2

ρmix V1

=

ρCO

2

ρmix

(3)

m1 44.01 1 − m1 156.31

+

m1 44.01

(4)

In eq 3, m1 is the CO2 mass fraction and V1 is the volume of the measuring cell filled with CO2; ρmix and V2 are the density of CO2 + undecane and the volume of the measuring cell after CO2 is completely dissolved into the undecane, respectively. First, CO2 was injected into the measuring cell, and the density, ρCO2, was measured. Then undecane was injected to the measuring cell and after the CO2 was completely dissolved, the mixture density ρmix was measured. The volume change, ΔV, has little influence on the mole fraction, so ΔV can be ignored.14 The CO2 mass fraction, m1, can be obtained as eq 3. The molecular weights of CO2 and undecane are 44.01 and 156.31, respectively. The CO2 mole fraction, x1, can be converted from m1 using eq 4. Then, having determined these values, a series of measurements to obtain the densities of mixtures at different pressures and temperatures were conducted.

T

P

ρ

T

P

ρ

K

MPa

g·cm−3

K

MPa

g·cm−3

313.24 313.18 313.19 313.22 313.23 313.19 313.17 323.24 323.22 323.23 323.23 323.19 323.19 323.18 333.14 333.16 333.13 333.15 333.12 333.12 333.14

8.029 9.997 12.016 14.009 16.006 18.013 19.009 7.997 10.009 12.003 14.022 16.026 17.995 19.002 8.001 10.001 12.007 14.012 16.003 17.990 19.027

0.73314 0.73469 0.73618 0.73762 0.73905 0.74050 0.74121 0.72603 0.72767 0.72924 0.73080 0.73235 0.73380 0.73454 0.71868 0.72038 0.72207 0.72370 0.72532 0.72687 0.72766

343.29 343.29 343.26 343.28 343.25 343.26 343.30 343.27 343.25 343.27 343.28 353.33 353.35 353.31 353.16 353.32 353.33 353.32 353.34 353.31 353.33 353.32

7.989 9.998 11.021 11.999 13.005 14.019 14.998 15.997 16.996 18.006 19.019 7.993 9.996 11.002 12.003 13.007 14.003 14.999 16.001 17.012 18.010 19.024

0.71151 0.71333 0.71427 0.71512 0.71600 0.71686 0.71766 0.71851 0.71936 0.72027 0.72098 0.70436 0.70627 0.70725 0.70819 0.70908 0.70998 0.71086 0.71173 0.71263 0.71348 0.71435

a Standard uncertainties u are u(T) = 0.01 K, u(P) = 0.001 MPa, and u(ρ) = 0.16 × 10−3 g·cm−3.

3. RESULTS AND DISCUSSION First, the compressed liquid densities of undecane are reported, and the variation oof the density with temperature and pressure are listed in Table 2. Albo et al. measured the density of undecane at temperatures between 278 and 318 K and pressures up to 60 MPa.7 A comparison between the two sets of experimental data is shown in Figure 2. The density value of undecane at 313.15 K and 19 MPa from our experiment and undecane density value at 318 K and 20 MPa from Albo et al.7 are close to each other. The trends of density versus pressure are similar. However, a direct comparison cannot be made because these data are reported at different temperatures and pressures. The uncertainties of the measured densities and CO2 mole fraction are calculated using the equations ⎛ ∂ρm ⎞2 2 ⎛ ∂ρm ⎞2 2 ⎛ ∂ρm ⎞2 2 ⎜ ⎟ um + ⎜ ⎟ um * + ⎜ ⎟ uv ⎝ ∂m ⎠ ⎝ ∂m* ⎠ ⎝ ∂v ⎠

u ρm =

2 ⎛ ∂v ⎞2 2 ⎛ ∂v ⎞ 2 ⎜ ⎟ u + ⎜ ⎟ up ⎝ ∂T ⎠ T ⎝ ∂p ⎠

uv =

2

2

(5)

(6)

uT =

uT1 + uT 2

uP =

uP12 + uP 2 2

(8)

ux =

⎛ ∂x ⎞2 ⎛ ∂x ⎞2 2 ⎟⎟ u ρ2 ⎜⎜ ⎟⎟ u ρ + ⎜⎜ ⎝ ∂ρ1 ⎠ 1 ⎝ ∂ρm ⎠ m

(9)

2

Figure 2. Comparison of experimental densities of undecane in this work and Albo et al.: □, ○, △, ◇, and ☆ represent the density from Albo et al. at 278 K, 288 K, 298 K, 308 K, and 318 K, respectively;7 ■, ●, ▲, ◆, and ★ represent the density from this work 313 K, 323 K, 333 K, 343 K, and 353 K, respectively.

In eqs 5 to 9, m and m* are the masses of the sinker in a vacuum and the apparent mass of the sinker, respectively. v is the volume of the sinker at experimental conditions. uρm, uP, uT, and ux are the uncertainties of ρm, P, T, and CO2 mole fraction, x1, respectively. uT1 and uT2 are the uncertainties aroused by repeat measurements and accuracy of temperature probe. Uncertainties for T and P are 0.01 K and 0.001 MPa, respectively. The uncertainties for the measured undecane densities, CO2 + undecane mixture densities and CO2 mole

(7)

C



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Table 3. Experimental Densities ρ and Excess Molar Volumes VmE at Temperature T, Pressure P, and CO2 Mole Fraction x1 for the CO2 + Undecane Mixturesa T

P

K

MPa

313.21 313.21 313.20 313.18 313.19 313.21 313.18 323.27 323.20 323.14 323.23 323.20 323.20 323.23 333.06 333.14 333.16 333.17 333.05 333.06 333.07 343.32 343.24 343.30 343.19 343.39 343.20 343.26 343.30 343.20 343.40 343.34 353.40 353.12 353.08 353.43 353.13 353.34 353.35 353.14 353.31 353.33 353.40 353.35 353.14 353.31

8.004 10.007 12.013 13.999 16.008 18.002 18.977 8.000 9.999 11.997 14.011 16.011 18.000 19.001 8.008 10.000 12.018 14.013 15.991 18.013 19.007 7.999 10.010 11.002 12.000 13.010 14.004 14.997 16.007 17.005 18.008 19.012 7.998 10.003 11.003 12.003 13.017 14.014 14.995 16.002 16.999 18.011 19.017 14.995 16.002 16.999

313.25 313.24 313.24 313.29 313.23 313.23 313.22 323.17 323.26 323.26

7.997 10.003 12.000 14.002 16.004 17.996 19.000 7.997 10.008 12.004

ρ g·cm

VmE −3

x1 = 0.2483 0.74068 0.74245 0.74422 0.74592 0.74758 0.74916 0.74997 0.73265 0.73459 0.73647 0.73822 0.73999 0.74172 0.74254 0.72469 0.72664 0.72860 0.73050 0.73243 0.73427 0.73515 0.71646 0.71869 0.71969 0.72079 0.72168 0.72281 0.72376 0.72472 0.72576 0.72658 0.72757 0.70829 0.71071 0.71186 0.71278 0.71401 0.71502 0.71605 0.71714 0.71815 0.71915 0.72008 0.71605 0.71714 0.71815 x1 = 0.4641 0.75891 0.76159 0.76415 0.76659 0.76905 0.77137 0.77252 0.74766 0.75042 0.75318

T −1

cm ·mol 3

−27.2 −4.84 −2.24 −0.97 −0.02 0.75 1.07 −37.84 −15.92 −5.69 −2.84 −1.34 −0.27 0.17 −44.71 −25.05 −11.99 −5.94 −3.2 −1.58 −0.96 −50.89 −31.41 −24.37 −18.47 −13.92 −10.35 −7.83 −5.97 −4.55 −3.48 −2.57 −56.09 −36.52 −29.4 −23.72 −18.65 −14.84 −11.77 −9.15 −7.29 −5.74 −4.5 −11.77 −9.15 −7.29 −51.54 −10.13 −5.93 −4.11 −2.92 −2.05 −1.67 −70.24 −30.08 −11.73

D

P

K

MPa

343.35 343.32 353.31 353.33 353.41 353.09 353.39 353.23 353.19 353.4 353.44 353.13 353.38

17.999 19.002 8.017 9.996 11.004 11.995 13.004 14.005 14.997 16.003 16.998 17.994 19.001

313.18 313.2 313.21 313.21 313.18 313.24 313.19 323.19 323.2 323.3 323.25 323.11 323.17 333.14 333.17 333.23 333.07 333.14 343.21 343.25 343.27 343.28 343.28 343.27 343.28 343.37 353.44 353.34 353.44 353.42 353.44

8.001 10.002 12.003 13.997 16.002 18.003 19.014 9.992 11.998 14.004 16.042 18.008 19.002 11.987 13.998 16.000 18.027 19.000 11.985 13.002 13.999 14.995 15.997 17.005 18.018 19.021 15.006 16.078 17.006 17.964 19.016

313.26 313.26 313.26 313.27 313.18 313.27 323.32 323.31 323.32 323.31 323.25

10.039 11.990 14.074 16.066 18.070 19.015 11.984 13.971 16.015 18.051 19.040

ρ g·cm

V mE −3

x1 = 0.4641 0.74125 0.74271 0.71203 0.71759 0.71934 0.72132 0.72288 0.72468 0.72633 0.72785 0.72938 0.73112 0.73250 x1 = 0.6797 0.77608 0.78554 0.79385 0.80130 0.80824 0.81433 0.81741 0.75797 0.76850 0.77717 0.78542 0.79277 0.79598 0.74590 0.75483 0.76253 0.77002 0.77323 0.72910 0.73182 0.73608 0.73994 0.74379 0.74733 0.75083 0.75380 0.70250 0.71053 0.71604 0.72219 0.72796 x1 = 0.8874 0.77399 0.78991 0.80372 0.81500 0.82537 0.82945 0.74506 0.76429 0.77989 0.79306 0.79897

cm ·mol−1 3

−8.61 −7.25 −101.38 −66.96 −54.10 −43.35 −34.91 −27.80 −22.33 −18.20 −14.97 −12.29 −10.42 −73.37 −14.19 −8.97 −7.08 −6.03 −5.36 −5.08 −41.77 −15.93 −10.10 −7.65 −6.33 −5.87 −31.31 −16.51 −10.89 −8.02 −7.17 −47.43 −35.42 −26.94 −20.94 −16.74 −13.72 −11.54 −9.90 −26.95 −21.33 −17.74 −14.96 −12.61 −12.90 −6.71 −4.43 −3.29 −2.55 −2.29 −15.35 −8.25 −5.45 −3.98 −3.48



Article

Table 3. continued T

P

K

MPa

323.17 323.15 323.27 323.26 333.17 333.16 333.16 333.19 333.16 333.14 333.21 343.31 343.34 343.30 343.30 343.31 343.41 343.27 343.25 343.26

14.005 16.006 18.003 19.006 8.004 10.004 11.998 13.997 16.006 18.003 19.000 8.003 9.998 11.003 12.002 13.003 14.002 14.997 16.001 17.011

ρ

VmE

T

−3

cm ·mol

0.75592 0.75848 0.76086 0.76209 0.73670 0.73987 0.74285 0.74571 0.74854 0.75123 0.75246 0.72539 0.72883 0.73057 0.73218 0.73377 0.73522 0.73690 0.73842 0.73990

−7.01 −4.79 −3.42 −2.85 −82.78 −46.57 −23.13 −12.4 −7.94 −5.53 −4.68 −93.22 −58.09 −45.06 −34.56 −26.31 −20.24 −15.75 −12.59 −10.28

g·cm

3

−1

P

K

MPa

333.11 333.17 333.19 333.09 333.16 343.28 343.35 343.34 343.32 343.3 343.37 353.46 353.46 353.52 353.43 353.43 353.52 353.45 353.43

12.010 14.005 16.015 18.042 19.039 14.027 15.016 16.020 17.016 18.033 19.004 16.003 17.018 18.000 19.052 15.953 17.018 17.976 18.953

ρ g·cm

V mE −3

0.70145 0.72101 0.74191 0.75898 0.76591 0.67356 0.68929 0.70238 0.71366 0.72356 0.73175 0.64930 0.66572 0.67879 0.69156 0.65124 0.66810 0.68110 0.69279

cm ·mol−1 3

−33.31 −15.30 −9.07 −6.13 −5.24 −25.95 −19.69 −15.20 −12.10 −9.83 −8.25 −21.19 −16.97 −13.90 −11.36 −21.45 −17.28 −14.18 −11.51

a Standard uncertainties u are u(x1) = 0.0005, u(T) = 0.01 K, and u(P) = 0.001 MPa and the expanded uncertainties of measured densities are u(ρ) = 0.18 × 10−3 g·cm−3.

fraction are 0.16·10−3 g·cm−3, 0.18·10−3 g·cm−3 and 0.0005, respectively. The absolute average deviation of the repeat measurements was calculated to be 0.08%. The densities of binary mixtures of CO2 (x1) and undecane (1 − x1) at x1 = 0.2483, 0.4641, 0.6797, and 0.8874 are summarized in Table 3. To test the reliability of the experimental data, a repeat experiment was conducted. Figure 3 shows similar results were produced, which meant the experimental data is reliable. Density versus Pressure and Temperature. The variations in the density of CO2 + undecane mixtures with changing pressure and temperature are shown in Figures 4 and 5, respectively. The density behavior of the binary mixture was found to be similar to that of mixtures of CO2 + decane or

dodecane: for a fixed composition, the densities of the binary mixture increased linearly with pressure at a constant temperature and decreased with temperature at a constant pressure. When the CO2 mole fraction is low (x1 = 0, 0.2483, and 0.4641), the slope of the plotted data is similar to that of pure undecane. However, when the mole fraction rose to 0.6797 or greater, the experimental density increased more sharply with pressure. Thus, a crossover phenomenon with composition is observed. And the crossover pressure seems to rise as the temperature becomes higher. This peculiar behavior, which has also been found in similar studies,15,16 can be attributed to the following: When the binary system is CO2poor, there are few CO2 molecules existing in the gap of undecane molecules resulting in poor compressibility. However, at higher CO2 mole fraction, more CO2 molecules enlarge the distance between two undecane molecules. Thus, the binary mixture becomes more compressible, resulting in a steeper slope. Density versus Carbon Number. The densities of CO2 + alkane mixtures have been widely studied in recent years. Zúñiga-Moreno et al. measured the densities of CO2 + decane mixtures from 313 to 363 K and at pressures up to 25 MPa;17 Song et al. measured the densities of CO2 + decane mixtures;18 Zhang et al. measured the densities of CO2 + dodecane and CO2 + tetradecane mixtures;12,19 Medina-Bermúdez et al. measured the densities of CO2 + tridecane mixtures.15 All the above experiments were conducted at similar temperature and pressure conditions. The densities of alkanes with different carbon number can be compared and the results are shown in Figure 6. It is clear that the densities of alkanes increase with increasing carbon number. Furthermore, when the CO2 mole fraction rises to approximately 0.25, a similar phenomenon is also observed. This can be attributed to a higher carbon number resulting in a higher molecular weight and correspondingly higher densities.

Figure 3. Comparisons between the two experiments of the mixture densities at CO2 mole fraction of 0.8874 at 353.15 K: ●, the original experiment; ■, the repeat experiment. E



Article

Figure 4. Densities of CO2 + undecane mixtures versus pressure at different temperatures: a, 313.15 K; b, 323.15 K; c, 333.15 K; d, 343.15 K; ■, x1 = 0; □, x1 = 0.2483; ●, x1 = 04641; ○, x1 = 0.6797; ▲, x1 = 0.8874.

Figure 5. Density of CO2 + undecane mixtures versus temperature at different pressures: a, 12 MPa; b, 14 MPa; c, 16 MPa; d, 19 MPa; ■, x1 = 0; □, x1 = 0.2483; ●, x1 = 04641; ○, x1 = 0.6797; ▲, x1 = 0.8874.

F



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fraction to a maximum value and then decrease. This behavior arises because the densities of the CO2 + undecane mixtures are closer to that of the component whose content is greatest and because the density of CO2 is lower than that of undecane at the same temperature and pressure. Moreover, the temperature at which the density starts to decrease tends to increase as the pressure rises from 14 to 19 MPa. Calculation from the PHSC EOS with Improved Parameters. Using the hard sphere chain as the reference system and a van der Waals attractive term as the perturbative term, the PHSC EOS derived by Song et al.20 is given as r 2aρ P = 1 + r 2bρg (d +) − (r − 1)[g (d +) − 1] − kBT ρkBT (10)

On the right side of eq 10, the first three terms represent the reference equation of state, and the forth is a van der Waals perturbation which accounts for the attractive forces. ρ = N/V is the molar density; kB is the Boltzmann’s constant; d and g(d+) represent the effective hard-sphere diameter and the pair radical distribution function of hard spheres at contact; r is the number of segments per molecule, and a and b represent the attractive forces between two nonbonded segments and the van der Waals covolume per segment, respectively. Both a and b are temperature-dependent and can be expressed with the minimum depth in the potential ε and the minimum separation distance in the pair potential, σ, as follows:

Figure 6. Comparison between experimental densities of alkanes and CO2−alkane mixtures at 333 K and 14 MPa: ■ and □ are densities of decane and CO2 + decane mixture at CO2 mol fraction x1 = 0.2369 from Zúñiga-Moreno et al.;17 ● and ○ are density of undecane and CO2 + undecane mixture at CO2 mol fraction x1 = 0.2483 in this work; ▲ and △ are densities of dodecane and CO2 + dodecane mixture at CO2 mole fraction x1 = 0.2497 from Zhang et al.;12 ☆ are densities of CO2 + tridecane mixture at CO2 mole fraction x1 = 0.2526 from Medina-Bermúdez et al.;15 ◆ and ◇ are densities of tetradecane and CO2 + tetradecane mixture at CO2 mole fraction x1 = 0.2469 from Zhang et al.19

Density versus CO2 Mole Fraction. As shown in Figure 7, the experimental densities increase with increasing CO2 mole

a=

2π 3 ⎛ kBT ⎞ ⎟ εσ Fa⎜ ⎝ sε ⎠ 3

(11)

Figure 7. Density of CO2 + undecane mixtures versus CO2 mole fraction at different pressures: a, 12 MPa; b, 14 MPa; c, 16 MPa; d, 19 MPa; ■, 313.15 K; □, 323.15 K; ●, 333.15 K; ○, 343.15 K; ▲, 353.15 K. G


Journal of Chemical & Engineering Data b=

Article

2π 3 ⎛ kBT ⎞ ⎟ εσ Fb⎜ ⎝ sε ⎠ 3

Table 5. Results of Correlation Using the PHSC EOS with s Acquired from Song et al.20 and the Improved s and the Corresponding AADa

(12)

Fa and Fb can be determined by thermodynamic properties of a simple fluid. The empirical expressions based on accurate experimental data of argon and methane21 can be expressed as ⎡ ⎛k T ⎞ ⎛ k T ⎞⎤ Fa⎜ B ⎟ = 1.8681exp⎢ −0.0619⎜ B ⎟⎥ ⎝ sε ⎠ ⎝ s ε ⎠⎦ ⎣ ⎡ ⎛ k T ⎞3/2 ⎤ + 0.6715exp⎢ −1.7317⎜ B ⎟ ⎥ ⎝ sε ⎠ ⎥⎦ ⎢⎣

material

s1

s2

AAD1

AAD2

CO2 decane undecane dodecane tetradecane

2.2677 2.8785 3.0121 3.0133 3.3248

2.5422 3.0474 3.2934 3.3919 4.0265

3.71 1.76 2.77 3.65 5.54

2.95 0.53 0.51 0.46 0.50

a 1

s is obtained from Song et al.20 and s2 is the improved s; AAD1 and AAD2 are the corresponding AAD. The CO2 + decane, CO2 + dodecane and the CO2 + tetradecane are from Song et al.18 and Zhang et al.,12,19 respectively.

(13)

⎡ ⎛k T ⎞ ⎛ k T ⎞⎤ Fb⎜ B ⎟ = 0.7303exp⎢ −0.1649⎜ B ⎟⎥ ⎝ sε ⎠ ⎝ s ε ⎠⎦ ⎣ ⎡ ⎛ k T ⎞3/2 ⎤ + 0.2697exp⎢ −2.3973⎜ B ⎟ ⎥ ⎝ sε ⎠ ⎥⎦ ⎢⎣

(14)

Considering that both Fa and Fb in terms of kBT/ε will not be suitable for molecular fluids when the increasing of the chain length raises the scaled temperature, s was introduced to circumvent this limitation. Thus, s is only affected by r and is equal to unity when r is unity. Song et al.20 have plotted s as a function of r but the precise value of s for CO2 and undecane is hard to obtain. The values of s obtained from the figure20 are 2.2677 and 3.0121 for CO2 and undecane, respectively. Table 4 Table 4. Number of Segments Per Molecule r, the Minimum Separation Distance in the Pair Potential σ, and the Minimum Depth in the Potential ε of CO2 and Undecane of PHSC EOS Used in This Work

a

substance

r

σ/Å

(ε/kB)/Ka

carbon dioxide undecane

4.275 8.409

2.228 3.270

121.7 195.0

Figure 8. Deviations of PHSC EoS with improved parameters on both data sets: solid point, experimental data from Albo et al.;7 hollow point, our experimental data.

kB is Boltzmann’s constant.

et al.7 are slightly larger than ours when pressure is less than 20 MPa. However, when pressure increases to 40 MPa or greater, deviations of Albo et al.7 increase almost linearly with pressure, reaching 5% at 60 MPa. The reason may be that the improved parameters in PHSC were obtained within the pressure ranging from 8 to 19 MPa. Density data at 40 and 60 MPa are far out of our fitting scope, so the deviations are larger. By adopting the van der Waals one-fluid (vdW1) mixing rules, the PHSC EOS can be extended to mixtures as is given in eq 16

summarizes other parameters of CO2 and undecane used in PHSC EOS supplied by Song et al.20 The AADs between the PHSC EOS and the experimental data are 3.71% and 2.77% for CO2 and undecane, respectively. Clearly, to improve the accuracy of the PHSC EOS, s must be optimized. The optimization procedure is to minimize the following objective function: N

F = min ∑ i=1

ρical − ρiexp ρi

m

P = 1 + ρ ∑ xixjrjbijgij(dij+) − ρkBT ij

exp

(15)

exp In eq 15, ρcal are the densities calculated from the i and ρi PHSC EOS with improved s parameter and the experimental densities. N is the total number of experimental data. As shown in Table 5, the optimal value of s for CO2 and undecane are 2.5422 and 3.2934, and using these values, the AADs reduced to 2.95% and 0.51%, respectively. In addition, s for decane, tetradecane, and undecane were optimized as shown in Table 5. It can be seen that the modeling results from the PHSC EOS with improved parameters are in good agreement with theexperimental data. Figure 8 presents the prediction results on density data in this work and that from Albo et al.7 using PHSC EOS with improved parameters. As shown in Figure 8, deviations of Albo

[gij(dij+) − 1] −

ρ kBT

m

∑ xi(ri − 1) i

m

∑ xixjrri jaij ij

(16)

xi is the mole fraction, and aij and bij can be calculated from eqs 11 and 12 by replacing ε and σ with εij and σij. εij and σij can be obtained from pure-component parameters by adopting the following combining rules: εij = (εiεj)1/2 (1 − kij)

σij = H

(17)

(σi + σj) 2

(18) DOI: 10.1021/acs.jced.6b00026 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

The adjustable binary interaction parameter, kij, for each pair of components can be determined by using an optimization method. gij(d+ij ) can be expressed as the Boublik−Mansoori− Carnahan−Starling equation for hard sphere mixtures22 gij(η , ξij) =

2 ξij 1 3 1 ξij + + 1−η 2 (1 − η)2 2 (1 − η)

mixtures. The AADs calculated using PHSC EOS with constant kij are also listed in Table 6. Compared to the AAD with the optimal kij, the AAD with constant kij = 0.054 are slightly larger. But the PHSC EOS with improved parameters is more convenient and is still remarkably accurate. Excess Molar Volume. The excess molar volume of the binary mixture can be defined as the difference in molar volume of the mixture and the sum of the molar volume of each component at given conditions. The excess molar volumes can be obtained from eq 23

(19)

where η is the packing fraction η=

ρ 4

m

∑ xirbi i

⎛ bibj ⎞1/3 ρ ξij = ⎜⎜ ⎟⎟ ⎝ bij ⎠ 4

⎛ 1 ⎛ 1 1⎞ 1⎞ − ⎟⎟ + x 2M 2⎜⎜ − ⎟⎟ V E = x1M1⎜⎜ ρ1 ⎠ ρ2 ⎠ ⎝ ρmix ⎝ ρmix

(20)

i m

(23)

E

∑ xirbi i 2/3

where V is the excess molar volume, M1 and x1 and M2 and x2 are the molar masses and mole fractions of CO2 and undecane, respectively, ρmix is the experimental density of the binary mixture, ρ1 is the density of CO2, and ρ2 is the density of undecane, which was calculated at a given temperature and pressure using PHSC EOS with improved parameters. As shown in Figures 9 and 10, the excess molar volumes are mostly

(21)

i

It is found that adopting different kij to calculate the densities of CO2 and undecane mixtures using the PHSC EOS with improved parameters leads to different results. Thus, the optimal kij at different CO2 mole fraction is found and listed in Table 6. For the CO2 + undecane system, the optimal value of kij varies over the CO2 mole fraction, and the correlation can be expressed as kij = 0.3727x12 − 0.3874x1 + 0.1384

(22)

Table 6. Correlation Results of the Binary Interaction Parameter kij Using PHSC EOS with Improved Parameters for Different CO2 + Alkane Systems at CO2 Mole Fraction x1 and the Corresponding AADa,b x1 0.2361 0.4698 0.7100 0.7725 0.8690 0.2497 0.5094 0.7576 0.8610

kij

AAD1

CO2 + decane 0.055 0.59 0.084 0.73 0.060 0.60 0.059 0.4 0.058 0.33 CO2 + dodecane 0.049 0.49 0.049 0.53 0.045 0.59 0.053 0.38

AAD2

x1

0.59 0.91 0.65 0.44 0.41

0.2483 0.4641 0.6797 0.8874

CO2 + undecane 0.063 0.56 0.031 0.44 0.048 1.24 0.083 1.80

0.57 0.58 1.23 2.69

0.49 0.53 0.67 0.38

0.2469 0.5241 0.7534 0.8873

CO2 + tetradecane 0.059 0.57 0.049 0.57 0.039 0.32 0.045 0.47

0.57 0.58 0.69 0.88

kij

AAD1

AAD2

Figure 9. Excess molar volume of CO2 + undecane mixtures at 333.15 K at different pressures: ■, 12 MPa; □, 14 MPa; ●, 16 MPa; ○, 18 MPa; ▲, 19 MPa.

negative over the whole range of compositions. A similar phenomenon has been reported for the CO2 + decane binary system.16 The excess molar volume is less negative with increasing pressure, as shown in Figure 9, whereas the excess molar volume becomes more negative with increasing temperature, as shown in Figure 10.

a

AAD1 are calculated with the optimal kij and AAD2 are calculated with the constant kij = 0.054. bThe CO2 + decane and the CO2 + dodecane and CO2 + tetradecane are from Song et al.18 and Zhang et al.,12,19 respectively.

The PHSC EOS with improved parameters was also applied to correlate the densities of CO2 + decane, CO2 + dodecane, and CO2 + tetradecane mixtures. The optimized kij and the corresponding AADs are listed in Table 6. With the optimal value of kij, the PHSC EOS exhibits high accuracy in predicting the densities of CO2 + alkane mixtures. However, relationship between the optimal kij and x1 for the four CO2 + alkane mixtures cannot be expressed as a universal equation. To simplify the calculation of the PHSC EOS for CO2 + alkane mixtures, the constant kij for the four CO2 + alkane in the entire CO2 mole fraction range must be determined. The optimization principle is to fit the experimental density of the four CO2 + alkane mixtures with the objective function of eq 15. The optimal constant kij is 0.054 for the four CO2 + alkane

4. CONCLUSION The densities of CO2 + undecane binary mixtures were measured at temperatures ranging from 313.15 to 353.15 K and pressures ranging from 8 to 19 MPa over a wide range of compositions (x1 = 0, 0.2483, 0.4641, 0.6797, and 0.8874) using a magnetic suspension balance (MSB). The densities were found to increase with pressure and decrease with temperature. A crossover phenomenon occurs at high CO2 mole fractions and the crossover pressure increases with increasing temperature. In addition, the densities of CO2 + alkane mixtures with approximate CO2 mole fraction increase with the carbon number of the alkane. Initially, the densities of the mixtures increase with the CO2 mole fraction and then I



Article

(7) Giuliano Albo, P. A.; Lago, S.; Romeo, R.; Lorefice, S. High pressure density and speed-of-sound measurements in n-undecane and evidence of the effects of near-field diffraction. J. Chem. Thermodyn. 2013, 58, 95−100. (8) Camacho-Camacho, L. E.; Galicia-Luna, L. A.; Elizalde-Solis, O.; Martínez-Ramírez, Z. New isothermal vapor−liquid equilibria for the CO2+n-nonane, and CO2+n-undecane systems. Fluid Phase Equilib. 2007, 259, 45−50. (9) Sharafi, Z.; Eslami, H. A modified perturbed hard-sphere-chain equation of state for liquid refrigerant mixtures. Phys. Chem. Liq. 2013, 51, 507−516. (10) Hosseini, S. M.; Alavianmehr, M. M.; Moghadasi, J. Density and isothermal compressibility of ionic liquids from perturbed hard-dimerchain equation of state. Fluid Phase Equilib. 2013, 356, 185−192. (11) Valavi, M.; Dehghani, M. R.; Shahriari, R. Capability of PHSC equation of state for thermodynamic modeling of aqueous amino acid and peptide solutions. J. Mol. Liq. 2014, 199, 21−28. (12) Zhang, Y.; Liu, Z.; Liu, W.; Zhao, J.; Yang, M.; Liu, Y.; Wang, D.; Song, Y. Measurement and Modeling of the Densities for CO2 + Dodecane System from 313.55 to 353.55 K and Pressures up to 18 MPa. J. Chem. Eng. Data 2014, 59, 3668−3676. (13) Zhang, Y.; Chang, F.; Song, Y.; Zhao, J.; Zhan, Y.; Jian, W. Density of Carbon Dioxide + Brine Solution from Tianjin Reservoir under Sequestration Conditions. J. Chem. Eng. Data 2011, 56, 565− 573. (14) Song, Y.; Chen, B.; Shen, S. Density and state function of CO2 salt water solution in underground condition. J. Therm. Sci. Technol. (China) 2003, 2, 358−364. (15) Medina-Bermúdez, M.; Saavedra-Molina, L. A.; EscamillaTiburcio, W.; Galicia-Luna, L. A.; Elizalde-Solis, O. (p, ρ,T) Behavior for the Binary Mixtures Carbon Dioxide + Heptane and Carbon Dioxide + Tridecane. J. Chem. Eng. Data 2013, 58, 1255−1264. (16) Bessières, D.; Saint-Guirons, H.; Daridon, J.-L. Volumetric Behavior of Decane + Carbon Dioxide at High Pressures. Measurement and Calculation. J. Chem. Eng. Data 2001, 46, 1136−1139. (17) Zúñiga-Moreno, A.; Galicia-Luna, L. A.; Camacho-Camacho, L. E. Compressed liquid densities and excess volumes of CO2+ decane mixtures from (313 to 363) K and pressures up to 25 MPa. J. Chem. Eng. Data 2005, 50, 1030−1037. (18) Song, Y.; Jian, W.; Zhang, Y.; Shen, Y.; Zhan, Y.; Zhao, J.; Liu, Y.; Wang, D. Densities and Volumetric Characteristics of Binary System of CO2+ Decane from (303.15 to 353.15) K and Pressures up to 19 MPa. J. Chem. Eng. Data 2012, 57, 3399−3407. (19) Zhang, Y.; Jian, W.; Song, Y.; Liu, W.; Yang, M.; Zhao, J.; Liu, Y.; Zhao, Y. (p, ρ, T) Behavior of CO2 + Tetradecane Systems: Experiments and Thermodynamic Modeling. J. Chem. Eng. Data 2015, 60, 1476−1486. (20) Song, Y.; Lambert, S. M.; Prausnitz, J. M. A perturbed hardsphere-chain equation of state for normal fluids and polymers. Ind. Eng. Chem. Res. 1994, 33, 1047−1057. (21) Favari, F.; Bertucco, A.; Elvassore, N.; Fermeglia, M. Multiphase multicomponent equilibria for mixtures containing polymers by the perturbation theory. Chem. Eng. Sci. 2000, 55, 2379−2392. (22) Sabzi, F.; Molaei, H. Sorption of CO2, C2H2 and C2H4 in HOF1a studied by PHSC equation of state. Fluid Phase Equilib. 2013, 360, 23−28.

Figure 10. Excess molar volume of CO2 + undecane mixtures at 18 MPa at different temperatures: ■, 313.15 K; □, 323.15 K; ●, 333.15 K; ○, 343.15 K; ▲, 353.15 K.

decrease at high CO2 concentrations. The excess molar volume is less negative with increasing pressure and more negative with increasing temperature. The PHSC EOS with improved parameters has sufficient accuracy to predict the densities of alkanes when using the optimized binary interaction parameter kij. Adopting the constant kij = 0.054 in calculating the densities of four CO2 + alkane mixtures will increase the AAD slightly but simplifies the calculations.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

This study has been supported by the National Natural Science Foundation of China (51576031, 51436003), the National Key Research and Development Plan of China(Grant No. 2016YFB0600804) and Fundamental Research Funds for the Central Universities (DUT15LAB22). Notes

The authors declare no competing financial interest.

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REFERENCES

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