(303.15 to 353.15) K and Pressures up to 19 MPa - ACS Publications

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Densities and Volumetric Characteristics of Binary System of CO2 + Decane from (303.15 to 353.15) K and Pressures up to 19 MPa Yongchen Song, Weiwei Jian, Yi Zhang,* Yong Shen, Yangchun Zhan, Jiafei Zhao, Yu Liu, and Dayong Wang Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy and Power Engineering, Dalian University of Technology, Dalian, Liaoning, 116024, P. R. China ABSTRACT: Densities of CO2 + decane binary mixtures were measured by using the magnetic suspension balance (MSB) at different CO2 mole fractions, x1 = 0.2361, 0.4698, 0.7100, 0.7725, and 0.8690 with temperatures from (303.15 to 353.15) K and pressures from (8 to 19) MPa. Excess molar volumes were calculated from the density data. The experimental results revealed that the density of CO2 + decane mixtures increases with increasing pressure and decreases with increasing temperature. The density of mixtures increases with increasing CO2 concentration first and then decreases at higher CO2 concentration and higher temperature. A crossover phenomenon with compositions is observed, and the crossover pressure increases with temperature. The excess molar volumes of this mixture display more negative values with increasing temperature at 18 MPa and less negative values with increasing pressure at 313.15 K. Moreover, the mixture densities have been predicted with GERG2008 and a modified Benedict−Webb−Rubin−Starling (BWRS) model. The validities of the two models have been tested by predicting density data in this work and comparing with previous literature.

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mixture densities at different compositions.5 Nishiumi’s equation combined with Lee−Kelser mixing rules presented by Bessières et al. gave a good prediction for their own experimental data, but the prediction results for other experimental data need to be confirmed.4 In this study, density measurements about CO2 + decane system have been conducted in the pressure range (8 to 19) MPa and temperature range (303.15 to 353.15) K at five compositions x1 = 0.2361, 0.4698, 0.7100, 0.7725, and 0.8690 by a magnetic suspension balance (MSB). Comparisons of the data with two density models, a modified Benedict−Webb−Rubin− Starling (BWRS) equation of state in which the binary interaction parameter was expressed as a function of CO2 mole fraction, and the GERG-2008 model sponsored by the Group Européen de Recherche Gazières are presented.

INTRODUCTION Injecting carbon dioxide into depleted oil/gas fields has been considered as one promising option for enhancing oil recovery and caused increasing attention in recent years.1 The thermodynamic characterization of CO2 + oil mixtures such as phase composition, volumetric characteristics, and densities in wide temperature and pressure ranges need to be investigated for the CO2 displacement process. The density of CO2 + oil solution is a key parameter for CO2-EOR which determines the diffusion and migration of CO2 in the reservoir.2 As we know, decane is one of typical components in petroleum which has similar thermal physical properties such as surface tension and viscosity with petroleum, so it can be used as a model fuel instead of petroleum in research. Researchers have investigated the densities of CO2 + decane mixtures before. Cullick and Mathis measured the density of this binary mixtures in the range (310 to 403) K and (7 to 30) MPa with x1 = 0.15, 0.301, 0.505, 0.649, and 0.85.3 Bessières et al. measured the density of this system from (308.15 to 368.15) K and (20 to 40) MPa with x1 = 0.15, 0.30, 0.51, 0.66, 0.78, and 0.84.4 Zúñiga-Moreno et al. reported densities from (313 to 363) K up to 25 MPa at x1 = 0.0551, 0.2369, 0.4536, 0.8114, and 0.9663.5 But this is not sufficient for evaluating the consistency of these data because the measurement conditions and CO2 concentrations are different from each other. Therefore, more experimental data with high accuracy are required for the density of CO2 + decane mixtures. The density models of CO2 + decane mixtures have been discussed before. Zúnĩ ga-Moreno et al. proposed a five-parameter empirical equation to correlate the © 2012 American Chemical Society

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EXPERIMENTAL SECTION Materials. The CO2 and N2 are supplied by Dalian Da-te Gas Co., Ltd. with a nominal purity of 99.99 mol % and 99.999 mol %, respectively. Decane is supplied from TCI (Shanghai) Development Co., Ltd. with purity of a nominal 99.1 %. The materials above are used for density measurement without further purification. The details of chemicals used in this work are stated in Table 1. Apparatus and Procedure. The magnetic suspension balance (MSB) manufactured by Rubotherm Präzisionsmesstechnik Received: April 24, 2012 Accepted: October 23, 2012 Published: November 6, 2012 3399

dx.doi.org/10.1021/je300388b | J. Chem. Eng. Data 2012, 57, 3399−3407

Journal of Chemical & Engineering Data

Article

mixtures during measurement. The mass and volume calibration of the sinker could ensure the accuracy of density data. The accuracy and reliability of the experimental system are tested by measuring the densities of deionized water and N2; the specific details are stated in our previous study (Zhang et al.6). During the measurement, first the temperature is regulated to a stable condition, and a certain amount of CO2 is injected into the measuring cell; the density of CO2 ρCO2 is then measured. Then decane is injected, and the circulation pump (AKICO, Japan) starts working to accelerate the CO2 dissolution. The uniform state of CO2 + decane system is judged by the stable pressure and the readout of mixture density data from MSB. It usually takes (1 to 2) days for the dissolution of CO2 into decane solution. After CO2 is dissolved into decane completely, the density of CO2 + decane mixtures ρmix is measured. After a data point measurement, the experimental pressure is adjusted with intervals of 2 MPa up to 19 MPa by changing the volumes of a piston container (b in Figure 1), which also could maintain the CO2 concentration unchanged in the measuring cell. The other experimental temperature can be continued using the same procedures with 10 K steps. Experimental Principle. The basic principle of density measurement by MSB is the Archimedean principle. The principle is illustrated in Figure 1, where F1, F2, and F3 are the values of sinker measured by MSB at the experimental condition, the buoyancy of sinker induced by the fluid, and the value of sinker in vacuum, respectively.

Table 1. Purity of Chemicals Used in This Study and Their Details chemical name

source

purification method

mole fraction purity

nitrogen

Dalian Da-te Gas Co., Ltd.

none

0.99999

carbon dioxide

Dalian Da-te Gas Co., Ltd.

none

0.9999

decane

TCI Development Co., Ltd.

none

0.991a

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

a

The purity of decane (0.991) is different from mole or mass fraction; the purity depends on the sensitivity of the FID detector in the GC (gas chromatography).

GmbH can be operated in the temperature range from (253 to 423) K and pressures up to 20 MPa. A schematic diagram of MSB appears as Figure 1. The core units of MSB consist of a measuring cell, an electromagnet, a permanent magnet, and a microbalance. The electromagnet is attached to the bottom of the balance, which maintains a freely suspended state of the permanent magnet via an electronic control unit. The permanent magnet is located within the measuring cell and connected with sinker by the load decoupling device. The microbalance is isolated from the measuring cell and exists at ambient conditions, so the measurement could be realized under high temperature and pressure conditions. The temperature in the measuring cell is controlled by a JULABO FP 50-ME refrigerated/heating circulator with a double-walled thermostatic jacket, which is filled with circulating oil. The pressure is measured by a pressure probe (20 MPa, reproducibility 0.08 %) connecting the gas tube with a T-piece. The resolutions of experimental quantities presented in this work are ± 0.01 K for T and ± 10−5 g for m in the range of reported data. Before the measurement, the leakage detection of the whole system should be performed to prevent the leakage of CO2 + decane

F1 + F2 = F3

(1)

m∗g + ρgv = mg

(2)

ρ = (m − m∗)g /v

(3)

In eq 2, m* is the apparent mass of sinker obtained from MSB, v is the volume of sinker at experimental condition which can be calibrated accurately from its known volume v0 at specified reference conditions in Zhang et al.,6 m is the true mass of sinker in vacuum, and ρ is the fluid density to be measured. Therefore the fluid density could be calculated from eq 3.

Figure 1. Schematic diagram of experimental apparatus. The piston pump (a) used to inject decane and the piston pump (b) used to adjust the pressure during measurements are shown. 3400



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Table 2. Experimental Densities and Excess Molar Volumes of CO2 + Decane Mixtures and Density Deviations Calculated from the Modified BWRS EOS Proposed in This Worka T

P

K

MPa

303.16 303.16 303.16 303.17 303.16 303.17 303.15 313.15 313.14 313.16 313.15 313.13 313.13 313.14 323.18 323.18 323.15 323.16 323.15 323.13 323.15 333.13 333.15 333.15 333.13 333.13 333.15 333.13 343.25 343.25 343.21 343.24 343.24 343.23 343.26 353.13 353.11 353.10 353.11 353.13 353.12 353.06

7.980 9.974 12.020 14.016 16.018 18.023 19.014 7.987 10.008 12.002 14.013 16.010 18.008 19.018 8.000 9.965 12.025 14.034 16.022 18.027 19.016 8.017 10.019 12.027 14.026 16.022 18.023 19.022 8.005 10.011 12.007 14.012 16.011 18.019 19.024 8.013 10.031 12.021 14.011 16.016 18.021 19.016

303.16 303.15 303.15 303.15 303.15 303.15 303.15 313.10 313.12 313.11 313.06 313.07 313.09 313.09

8.015 9.993 11.989 13.995 15.978 17.988 19.005 8.010 10.005 11.987 13.974 15.987 17.989 19.001

ρ g·cm

ρcal −3

g·cm

−3

x1 = 0.2361 0.74010 0.73901 0.74173 0.74052 0.74335 0.74204 0.74491 0.74347 0.74643 0.74489 0.74792 0.74627 0.74864 0.74696 0.73205 0.73058 0.73381 0.73226 0.73550 0.73386 0.73719 0.73545 0.73882 0.73700 0.74041 0.73851 0.74118 0.73924 0.72385 0.72208 0.72574 0.72384 0.72766 0.72569 0.72945 0.72740 0.73117 0.72907 0.73288 0.73073 0.73369 0.73151 0.71558 0.71353 0.71765 0.71551 0.71964 0.71745 0.72158 0.71934 0.72345 0.72115 0.72524 0.72290 0.72615 0.72379 0.70717 0.70474 0.70951 0.70694 0.71178 0.70909 0.71397 0.71111 0.71611 0.71309 0.71814 0.71503 0.71917 0.71595 0.69840 0.69607 0.70096 0.69852 0.70337 0.70083 0.70570 0.70305 0.70798 0.70520 0.71021 0.70729 0.71131 0.70835 x1 = 0.4698 0.75062 0.75457 0.75273 0.75677 0.75478 0.75892 0.75680 0.76101 0.75873 0.76300 0.76063 0.76496 0.76162 0.76593 0.74128 0.74378 0.74354 0.74626 0.74573 0.74865 0.74792 0.75099 0.75001 0.75324 0.75203 0.75537 0.75305 0.75643

V mE (ρcal − ρ)/ρ

T −1

cm ·mol 3

−0.15% −0.16% −0.18% −0.19% −0.21% −0.22% −0.22% −0.20% −0.21% −0.22% −0.24% −0.25% −0.26% −0.26% −0.24% −0.26% −0.27% −0.28% −0.29% −0.29% −0.30% −0.29% −0.30% −0.30% −0.31% −0.32% −0.32% −0.33% −0.34% −0.36% −0.38% −0.40% −0.42% −0.43% −0.45% −0.33% −0.35% −0.36% −0.38% −0.39% −0.41% −0.42%

−3.04 −1.73 −1.13 −0.76 −0.49 −0.28 −0.18 −25.50 −4.52 −2.55 −1.73 −1.23 −0.88 −0.73 −34.75 −15.08 −5.54 −3.33 −2.32 −1.70 −1.48 −41.35 −23.14 −11.33 −6.06 −3.96 −2.85 −2.47 −46.82 −29.08 −17.32 −10.18 −6.51 −4.59 −3.99 −51.24 −33.37 −21.76 −14.05 −9.27 −6.51 −5.56

0.53% 0.54% 0.55% 0.56% 0.56% 0.57% 0.57% 0.34% 0.37% 0.39% 0.41% 0.43% 0.44% 0.45%

−4.86 −2.39 −1.29 −0.59 −0.11 0.27 0.42 −48.84 −7.86 −4.00 −2.44 −1.49 −0.85 −0.60 3401

ρ

P

K

MPa

323.15 323.15 323.17 323.19 323.17 323.15 323.15 333.19 333.14 333.13 333.13 333.13 333.12 343.13 343.18 343.10 343.19 343.11 343.14 343.11 353.13 353.12 353.13 353.09 353.06 353.09 353.12

8.008 9.979 12.015 13.986 15.984 18.000 19.002 7.979 9.933 11.987 13.997 15.964 17.971 8.074 9.933 12.072 13.921 16.088 18.000 19.117 8.042 10.093 12.051 14.010 16.037 18.081 19.059

313.00 313.00 313.01 313.00 313.03 313.01 323.02 323.12 323.15 323.09 323.11 323.02 333.12 333.09 333.10 333.13 333.15 333.12 343.02 343.02 343.12 343.13 343.13 352.97 353.01 353.26 353.14 353.12 362.92

7.975 9.941 11.688 13.966 16.024 18.022 7.998 9.935 11.971 14.027 16.036 18.226 8.094 10.021 11.957 14.047 16.044 18.053 10.240 12.281 14.000 16.033 18.000 9.877 11.994 14.128 15.978 17.940 12.052

g·cm

ρcal −3

g·cm

−3

x1 = 0.4698 0.73172 0.73261 0.73415 0.73540 0.73655 0.73814 0.73880 0.74067 0.74107 0.74316 0.74327 0.74559 0.74434 0.74675 0.72190 0.72109 0.72457 0.72429 0.72721 0.72744 0.72970 0.73035 0.73207 0.73306 0.73442 0.73573 0.71230 0.70949 0.71494 0.71286 0.71801 0.71664 0.72036 0.71956 0.72326 0.72299 0.72557 0.72576 0.72699 0.72737 0.70224 0.69712 0.70542 0.70147 0.70835 0.70531 0.71117 0.70895 0.71408 0.71249 0.71681 0.71578 0.71806 0.71729 x1 = 0.7100 0.76324 0.77813 0.76744 0.78265 0.77091 0.78639 0.77530 0.79099 0.77896 0.79479 0.78243 0.79837 0.74745 0.75894 0.75226 0.76434 0.75686 0.76959 0.76143 0.77463 0.76546 0.77906 0.76963 0.78372 0.73025 0.73762 0.73644 0.74487 0.74169 0.75120 0.74685 0.75727 0.75160 0.76252 0.75613 0.76748 0.72054 0.72380 0.72649 0.73233 0.73099 0.73840 0.73612 0.74499 0.74108 0.75076 0.70661 0.69560 0.71136 0.70829 0.71578 0.71803 0.71992 0.72584 0.72510 0.73290 0.69895 0.68173

VmE (ρcal − ρ)/ρ

cm ·mol−1

0.12% 0.17% 0.22% 0.25% 0.28% 0.31% 0.32% −0.11% −0.04% 0.03% 0.09% 0.13% 0.18% −0.39% −0.29% −0.19% −0.11% −0.04% 0.03% 0.05% −0.73% −0.56% −0.43% −0.31% −0.22% −0.14% −0.11%

−68.37 −28.59 −9.95 −5.60 −3.63 −2.44 −2.01 −81.99 −46.17 −21.68 −11.04 −6.90 −4.69 −90.45 −57.64 −32.48 −19.34 −11.33 −7.79 −6.42 −100.19 −64.43 −41.88 −26.76 −17.13 −11.58 −9.81

1.95% 1.98% 2.01% 2.02% 2.03% 2.04% 1.54% 1.61% 1.68% 1.73% 1.78% 1.83% 1.01% 1.14% 1.28% 1.39% 1.45% 1.50% 0.45% 0.80% 1.01% 1.20% 1.31% −1.56% −0.43% 0.31% 0.82% 1.08% −2.46%

−74.90 −12.39 −6.90 −4.18 −2.86 −1.98 −103.02 −43.97 −15.32 −8.52 −5.72 −3.93 −119.09 −66.95 −32.66 −16.26 −10.26 −7.16 −78.98 −45.12 −27.73 −16.79 −11.43 −100.22 −62.61 −38.26 −25.06 −16.97 −73.08

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Article

Table 2. continued

a

T

P

ρ

ρcal

K

MPa

g·cm−3

g·cm−3

363.28 363.08 362.99

14.095 16.052 18.094

303.27 303.23 303.28 303.24 303.28 303.32 313.33 313.20 313.31 313.17 313.06 313.17 323.21 323.25 323.13 323.28 323.28 323.2 333.36 333.36 333.19 333.28 333.15 343.80 344.00 343.99

7.996 10.003 12.025 13.984 16.026 18.105 8.029 10.072 12.031 14.050 16.061 18.069 8.116 10.032 12.041 14.061 16.123 18.068 10.019 12.043 13.987 15.978 18.111 12.013 14.040 16.060

x1 = 0.7100 0.70289 0.69457 0.70718 0.70543 0.71219 0.71468 x1 = 0.7725 0.79202 0.80831 0.79770 0.81331 0.80302 0.81781 0.80797 0.82204 0.81270 0.82603 0.81722 0.82987 0.77030 0.78580 0.77789 0.79253 0.78401 0.79785 0.79026 0.80338 0.79582 0.80840 0.80067 0.81267 0.74917 0.76074 0.75519 0.76882 0.76221 0.77652 0.76877 0.78279 0.77631 0.78887 0.78220 0.79427 0.73247 0.74097 0.73943 0.75144 0.74806 0.76027 0.75553 0.76755 0.76310 0.77492 0.72065 0.72069 0.72714 0.73277 0.73512 0.74304

V mE

T

P

ρ

ρcal

(ρcal − ρ)/ρ

cm3·mol−1

K

MPa

g·cm−3

g·cm−3

−1.18% −0.25% 0.35%

−48.97 −33.21 −22.76

2.06% 1.96% 1.84% 1.74% 1.64% 1.55% 2.01% 1.88% 1.77% 1.66% 1.58% 1.50% 1.54% 1.80% 1.88% 1.82% 1.62% 1.54% 1.16% 1.62% 1.63% 1.59% 1.55% 0.01% 0.77% 1.08%

−9.23 −5.23 −3.64 −2.72 −2.08 −1.61 −80.38 −13.17 −7.42 −5.09 −3.77 −2.95 −107.41 −45.38 −15.90 −9.22 −6.41 −4.83 −72.32 −33.97 −17.42 −11.00 −7.58 −53.28 −30.03 −18.19

344.03 353.46 353.44 353.45 353.38

18.036 12.001 14.011 16.015 18.050

303.04 303.31 303.36 303.31 303.37 303.31 313.36 313.27 313.33 313.31 313.37 313.23 323.30 323.34 323.38 323.29 323.30 333.22 333.19 333.20 343.23 343.16 352.99

8.019 10.032 12.023 14.034 16.021 18.050 7.992 10.003 12.002 14.001 16.041 18.019 10.012 11.994 13.996 16.015 18.075 14.072 15.933 18.078 16.061 18.048 18.036

x1 = 0.7725 0.74369 0.75139 0.70190 0.68336 0.70931 0.70361 0.71770 0.71783 0.72534 0.72946 x1 = 0.8690 0.79859 0.82210 0.80757 0.83062 0.81616 0.83864 0.82426 0.84612 0.83123 0.85251 0.83810 0.85878 0.76259 0.77670 0.77639 0.79327 0.78726 0.80541 0.79682 0.81573 0.80504 0.82455 0.81262 0.83266 0.74087 0.74038 0.75566 0.76333 0.76770 0.77948 0.77840 0.79265 0.78776 0.80348 0.74519 0.73454 0.75434 0.75379 0.76305 0.77026 0.73438 0.70551 0.74236 0.73009 0.71770 0.68159

VmE (ρcal − ρ)/ρ

cm3·mol−1

1.04% −2.64% −0.80% 0.02% 0.57%

−12.53 −67.00 −41.80 −26.58 −17.72

2.94% 2.85% 2.75% 2.65% 2.56% 2.47% 1.85% 2.17% 2.31% 2.37% 2.42% 2.47% −0.07% 1.01% 1.53% 1.83% 2.00% −1.43% −0.07% 0.95% −3.93% −1.65% −5.03%

−8.58 −4.72 −3.13 −2.20 −1.61 −1.18 −90.49 −13.60 −6.90 −4.47 −3.13 −2.24 −50.55 −16.52 −8.93 −5.80 −4.10 −17.66 −10.93 −7.05 −18.69 −12.18 −18.18

ρ and ρcal are the experimental densities in the measurement and calculated densities by the modified BWRS EOS. Standard uncertainties u are u(T) = 0.01 K, u(P) = 0.003 MPa, and u(x1) = 0.0003, and the combined expanded uncertainties of measured densities are U(ρ) = 2·0.24 kg·m−3 (level of confidence = 0.95, k = 2).

During the experiment, not only the density of CO2 + decane mixtures could be measured accurately, but also the CO2 concentration in the mixtures x1 can be obtained from eq 4: ρCO V1 2

x1 =

44.01 ρmix V2 − ρCO V1 2

142.28

+

ρCO V1 2

44.01

ρCO V1 2

=

44.01 ρmix (V1 + ΔV ) − ρCO V1 2

142.28 ρCO

+

ρCO V1 2

44.01

2

≈

44.01 ρmix − ρCO

2

142.28

+

ρCO

2

44.01

(4)

In eq 4, V1 is the volume of measuring cell after injecting CO2, and V2 and ρmix are the volume of measuring cell and the density of CO2 + decane mixtures after CO2 dissolved into the decane solution completely. The volume change ΔV can be ignored during the calculation, because the influence of ΔV on x1 is very small which has been verified in Song et al.7 Then we could obtain the mixture density by a series of measurements at different CO2 concentrations.

Figure 2. Comparison of experimental densities CO2 + decane mixtures reported in this work and Zúñiga-Moreno et al.5 at 313.15 K at x1 = 0.2361: ■, this work; ○, Zúñiga-Moreno et al.5

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RESULTS AND DISCUSSION Densities of CO2 + decane binary mixtures are presented in Table 2 for CO2 concentration x1 = 0.2361, 0.4698, 0.7100, 0.7725, 3402



Article

Figure 3. Density of CO2 + decane 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 = 0.2361; ○, x1= 0.4698; ▼, x1 = 0.7100; □, x1 = 0.7725; ▲, x1 = 0.8690.

decane molecules, and the number of molecules increase per unit volume, so the densities of mixture increase almost linearly with increasing pressure. Meanwhile, at higher CO2 concentrations, the property of mixture is inclined to CO2, and the density variations of CO2 rise sharply with increasing pressure. Meanwhile, due to the lower molecular weight of CO2 than that of decane, the density decreases with the increase of CO2 content within a certain CO2 concentration range. Thus it can be observed that, before the crossover, the mixture density with a CO2 mole fraction of 0.8690 is lower than that of 0.7100 and 0.7725. The densities of CO2 + decane mixtures decrease with increasing temperature in Figure 4, and a crossover is observed due to the different slopes depending on the CO2 concentration in the mixture. Density versus CO2 Mole Fraction. As shown in Figure 5, the density of CO2 + decane mixtures increases with increasing CO2 mole fraction first, while it decreases at higher CO2 concentrations and higher temperatures. This behavior was also mentioned in the study of Zúñiga-Moreno et al.,5 which did not give the reasons. The reason may be that the properties of this binary mixture are approximate to CO2 at higher CO2 concentrations, and the density of CO2 is much lower than decane at high temperatures. Moreover, for the temperatures at which densities appear to drop increase with increasing pressures, the phenomenon is accordance with the crossover mentioned above. Note that, at a constant temperature, mixtures with high CO2

and 0.8690. The uncertainties for the measured densities are calculated by using the partial differential equation expressed as eq 5: Uc(ρ) =

⎛ ∂ρ ⎞2 2 ⎛ ∂ρ ⎞2 2 ⎛ ∂ρ ⎞2 2 ⎜ ⎟ U ⎟ U +⎜ + ⎜ ⎟ Uv ⎝ ∂m ⎠ m ⎝ ∂m* ⎠ m * ⎝ ∂v ⎠

(5)

m, m*, and v are the same in eq 3, Um, Um*, and Uv represent the uncertainty of measured density caused by m, m*, and v, respectively. Uc(ρ) is the uncertainty of measured density. Density versus Pressure and Temperature. The experimental results are compared with the densities reported in Zúñiga-Moreno et al.5 and plotted in Figure 2. It is noticeable that these two sets of data are consistent with each other, with the average relative error of 0.123 % at x1 = 0.2361. From Figure 3, it can be seen that the dissolution of CO2 increases the density of decane. The results reveal that the densities of this binary mixtures increase with increasing pressure. The densities versus pressure present a linear relationship when CO2 mole fractions are low, such as 0.2361 and 0.4698. But when CO2 mole fractions rise to 0.7100 or larger, the density variation shows a peculiar behavior. A crossover with the compositions appears, and the crossover pressure shifts to higher pressures with increasing temperature. The explanation is maybe that the density characters of CO2 + decane mixtures are approximate to the component with high content in the mixture. When the mixture is CO2-poor, the CO2 molecules insert into the gap of 3403



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Figure 4. Density of CO2 + decane mixtures versus temperature at different pressures P: a, 12 MPa; b, 14 MPa; c, 16 MPa; d, 18 MPa; ◊, x1 = 0; ◀, x1 = 0.2361; ○, x1 = 0.4698; ▼, x1 = 0.7100; □, x1 = 0.7725; ▲, x1 = 0.8690.

The excess volume appears to reach a minimum value at x1 = 0.8690 nearby, which shows that the nonideality of the mixtures is affected by the amount of CO2. Calculation from a Modified BWRS Equation of State. Densities of CO2 + decane mixtures are calculated by an improved BWRS equation of state, which was proposed by Nishiumi et al.12 as the function of temperature and molar density is given by eq 7.

mole fractions have not achieved miscibility when the pressure is lower than the minimum miscible pressure. Thus the measurement can not be performed, and the lack of density data at high CO2 concentration (for example: when x1 is 0.8690, lack of density data at 333.15 K, 343.15 K, and 353.15 K at 12 MPa) is shown in Figure 5. Excess Molar Volume. The excess molar volumes of CO2 + decane binary mixture are calculated according to eq 6. Vm E =

x1M1 + x 2M 2 − (x1v1 + x 2v2) ρmix

⎛ C D E ⎞ P = ρRT + ⎜B0 RT − A 0 − 02 + 30 − 04 ⎟ρ2 ⎝ T ⎠ T T ⎛ ⎞ f d e + ⎜bRT − a − − 4 − 23 ⎟ρ3 ⎝ T T T ⎠ ⎛ f ⎞ d e + α ⎜a + + 4 + 23 ⎟ρ6 ⎝ T T T ⎠

(6)

where x1 and x2 are the mole fractions of CO2 and decane, respectively, ρmix is the density of the mixture measured, v1 and v2 are molar volumes of CO2 and decane, and M1 and M2 are the molar weights of CO2 and decane, respectively. The excess molar volume is observed to be mostly negative over the entire composition range in Figures 6 and 7, where the excess molar volume is plotted as a function of x1 at 18 MPa at different temperatures and at 313.15 K at different pressures. From Figures 6 and 7 it can be seen that the curves display negative increasing with increasing temperature but are less negative with increasing pressure. This trend was observed in many CO2 + hydrocarbon systems such as CO2 + decane mixtures in Cullick and Mathis3 and CO2 + toluene/acetone/pentane/ethanol mixtures.8−11

+

⎛ c g h ⎞ + 8 + 17 ⎟ρ3 (1 + γρ2 )exp( −γρ2 ) ⎝ T2 T T ⎠

⎜

(7)

In eq 7, there are 15 coefficients obtained by adding four suitable coefficients to the BWRS equation. For mixtures these coefficients are calculated from coefficients of the pure component combine with corresponding mixing rules. In this work, we focus on the binary interaction parameter used in the mixing rule. 3404



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Figure 5. Density of CO2 + decane mixtures versus CO2 mole fraction at different pressures P: a, 12 MPa; b, 14 MPa; c, 16 MPa; d, 18 MPa; 303.15 K; □, 313.15 K; ▼, 323.15 K; ○, 333.15 K; ◀, 343.15 K; ◊, 353.15 K.

▲,

The following four coefficients A0, C0, D0, and E0 are calculated with the binary interaction parameter in the BWRS13 equation. A0 =

∑ ∑ xixjA 0i1/2A 0j1/2(1 − kij) i

C0 =

j

(9)

∑ ∑ xixjD0i1/2D0j1/2(−kij)4 i

E0 =

(8)

∑ ∑ xixjC0i1/2C0j1/2(1 − kij)3 i

D0 =

j

j

(10)

∑ ∑ xixjE0i1/2E0j1/2(1 − kij)5 i

j

(11)

In eqs 8 to 11, i and j are indices for the components, and the summations range from i = 1 to i = n and j = 1 to j = n, where n is the total number of components. xi and xj are the mole fractions of the ith component. A0i, C0i, and so forth are the pure component parameters for the ith which can be expressed as the functions of component acentric factor ωi, critical temperature Tci, and critical density ρci. For the pure fluid, kij is equal to zero, and the coefficients are obtained from the critical parameters of pure component without the mixing rule. The formulas and the corresponding mixing rules for other

Figure 6. Excess molar volume of CO2 + decane mixtures at 18 MPa at different temperatures T: ▲, 303.15 K; □, 313.15 K; ▼, 323.15 K; ○, 333.15 K; ◀, 343.15 K; ◊, 353.15 K.

coefficients are the same with Nishiumi et al.12 and Starling and Han.13 The binary interaction parameter kij for A0, C0, D0, and E0 in the mixing rule has a significant impact on vapor−liquid 3405



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for this work. The results predicted using the correlation of kij and the constant kij = 0.05 (the interaction parameter for CO2 + decane mixtures given in BWRS equation of state14 is 0.05) for different experimental data are plotted in Figure 8.

Figure 7. Excess molar volume of CO2 + decane mixtures at 313.15 K at different pressures P: □, 8 MPa; ◀, 10 MPa; ○, 12 MPa; ▼, 14 MPa; ◊, 16 MPa; ▶, 18 MPa.

equilibrium prediction.14 It is found that the density relative deviations calculated with the same kij value are largely different at different CO2 concentrations. Thus, in this study, the correlation of kij and CO2 mole fraction x1 is developed as eq 12: kij = 1.7092e−3.803x1

Figure 8. Relative deviation of experimental densities of CO2 + decane mixtures from those calculated by different models: ○, ●, this work at 313.15 K; △, ▲, Bessières et al.4 at 308.15 K; ☆, ★, Zúñiga-Moreno et al.5 at 313.15 K. Closed and open symbols are for deviations using the modified BWRS equation of state with kij = 0.05 and correlation of kij and x1 proposed in this work, respectively.

(12)

The equation is correlated from the optimal kij values at different CO2 mole fractions based on our experimental data and previous literature.3−5 At a constant CO2 mole fraction, the optimal kij can be obtained by minimizing the absolute average deviations (AAD) between the experimental data and the prediction result. Then the correlation is established by fitting the optimal kij values and CO2 mole fraction x1. The optimal kij values and AAD values are presented in Table 3, with the best

The relative errors calculated by the modified BWRS model are inferior to ± 0.5 % when CO2 mole fraction is less than 0.7. The results indicate that the accuracy has been improved by using the correlation of kij and could be appropriate to an extensive application. Calculation from the GERG-2008 Equation of State. The equation of state was adopted under the name GERG2008 by GERG (Group Européen de Recherche Gazières) as the international reference equation of state for natural gases. This equation of state covers the whole fluid regions (gas, liquid, supercritical region, liquid−vapor phase boundaries) consist up to 21 components. The GERG-2008 is explicit in the reduced Helmholtz energy depending on the density, the temperature, and the composition; thus all thermodynamic properties can be calculated from combinations of the derivatives. In this work, we focus on the density of CO2 + decane mixtures that calculated from eqs 13 to 15.

Table 3. Optimal kij Values and Absolute Average Deviations (%) of the Density Predicted by Different Modelsa reference this work this work this work this work this work Bessières et al.4 Bessières et al.4 Bessières et al.4 Bessières et al.4 Bessières et al.4 Bessières et al.4 Zúñiga-Moreno Zúñiga-Moreno Zúñiga-Moreno Zúñiga-Moreno Zúñiga-Moreno

et et et et et

al.5 al.5 al.5 al.5 al.5

x1

kij

AAD1

AAD2

AAD3

0.2361 0.4698 0.7100 0.7725 0.8690 0.1500 0.3000 0.5100 0.6600 0.7800 0.8400 0.0551 0.2369 0.4536 0.8114 0.9663

0.6963 0.2864 0.1148 0.0906 0.0627 0.9662 0.5461 0.2457 0.1389 0.0880 0.0701 1.3861 0.6943 0.3045 0.0781 0.0433

0.30 0.31 1.35 1.48 2.14 0.14 0.44 0.17 0.23 1.09 1.42 0.88 0.21 0.37 1.89 1.96

2.05 3.86 4.89 4.51 3.21 1.39 2.05 3.01 2.58 3.06 2.35 1.50 2.22 3.33 4.09 2.48

0.75 1.50 0.80 0.57 0.99 0.67 1.12 0.99 0.32 0.30 0.30 0.26 0.87 1.06 1.01 5.38

N−1

α r (δ , τ , x ) =

N

∑ xiαoir (δ , τ) + ∑ ∑

xixjFijαijr(δ , τ )

i=1 j=i+1

(13)

a AAD1 are the results predicted by the modified BWRS equation of state with the correlation of kij and x1 proposed in this work; AAD2 are the results predicted by the modified BWRS equation of station with the constant kij = 0.05; AAD3 are the results predicted with the GERG-2008 model.

p(δ , τ , x ) = 1 + δαδr ρRT

(14)

⎛ ∂α r ⎞ ⎟ αδr = ⎜ ⎝ ∂δ ⎠τ ,x

(15)

where α and are the residual part of the reduced Helmholtz free energy for the mixture and component i, δ and τ are the reduced mixture density and the inverse reduced mixture temperature, xi and xj indicate for the mole fraction of the components i and j where N is the maximum value of the components. r

AAD are 0.14 % and 0.21 % for Bessières et al.4 and ZúñigaMoreno et al.,5 respectively, and the maximum AAD is 2.14 % 3406

αroi



Article

The adjustable factor Fij in eq 13 equals zero for CO2 + decane mixtures. The equation of state of αroi and corresponding coefficients are detailed in Kunz and Wagner.15 The absolute average deviations between the measured densities and the GERG-2008 model for CO2 + decane mixtures are also presented in Table 3. It shows that the accuracy of our model is better than the GERG-2008 model when the CO2 mole fraction is less than 0.5, but for some high CO2 mole fractions the GERG2008 model is more accurate. The relative deviations between the different experimental data and GERG-2008 model are also plotted in Figure 9. As we can see, most of data are fitted very well.

Program on Key Basic Research Project (No. 2011CB707304), Research Fund for the Doctoral Program of Higher Education of China (No. 20100041120040), Liaoning Provincial Natural Science Foundation of China (No. 201202028), and the Fundamental Research Funds for the Central Universities. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are thankful for the editor’s kind work and are grateful for the constructive comments from the reviewers. Special thanks are given to O. Kunz and W. Wagner for providing us with their unpublished GERG-2008 model.

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(1) Yan, W.; Huang, S.; Stenby, E. H. Measurement and modeling of CO2 solubility in NaCl brine and CO2-saturated NaCl brine density. Int. J. Greenhouse Gas Control 2011, 5, 1460−1477. (2) Chang, L.; Wang, C.; Zhang, Y.; Sha, Z.; Song, Y. Research progress on the density of CO2 model oil system. J. Environ. Sci. Technol. 2012, 34, 140−143. (3) Cullick, A. S.; Mathis, M. L. Densities and Viscosities of Mixtures of Carbon Dioxide and n-Decane from 310 to 403 K and 7 to 30 MPa. J. Chem. Eng. Data 1984, 29, 393−396. (4) Bessières, D.; Saint-Guirons, H.; Daridon, J. L. Volumetric Behavior of Decane + Carbon Dioxide at High Pressures. Measurements and Calculation. J. Chem. Eng. Data 2001, 46, 1136−1139. (5) 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. (6) 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. (7) Song, Y.; Chen, B.; Shen, S. Density and state function of CO2 salt water solution in underground condition. J. Therm. Sci. Technol. 2003, 2, 358−364. (8) Kiran, E.; Pöhler, H.; Xiong, Y. Volumetric properties of pentane + carbon dioxide at high pressures. J. Chem. Eng. Data 1996b, 41, 158− 165. (9) Pöhler, H.; Kiran, E. Volumetric properties of carbon dioxide + toluene at high pressures. J. Chem. Eng. Data 1996, 41, 482−486. (10) Pöhler, H.; Kiran, E. Volumetric properties of carbon dioxide + acetone at high pressures. J. Chem. Eng. Data 1997, 42, 379−383. (11) Kiran, E.; Pöhler, H.; Xiong, Y. Volumetric properties of pentane + carbon dioxide at high pressures. J. Chem. Eng. Data 1996, 41, 158−165. (12) Nishiumi, H.; Saïto, S. An improved generalized BWR equation of state applicable to low reduced temperatures. J. Chem. Eng. Jpn. 1975, 8, 356−360. (13) Starling, K. E.; Han, M. S. Thermo data refined for LPG. Hydrocarbon Process 1972, 51, 129−132. (14) Starling, K. E.; Han, M. S. Thermo data refined for LPG. Hydrocarbon Process 1972, 51, 107−115. (15) Kunz, O.; Wagner, W. The GERG-2008 Wide-Range Equation of State for Natural Gases and Other Mixtures: An Expansion of GERG-2004. J. Chem. Eng. Data 2012, 10.1021/je300655b.

Figure 9. Relative deviation of experimental densities of binary mixtures from those calculated by the modified BWRS and GERG2008 models: ○, ●, this work at 313.15 K; △, ▲, Bessières et al.4 at 308.15 K; ☆, ★, Zúñiga-Moreno et al.5 at 313.15 K. Closed and open symbols are for deviations using the GERG-2008 model and the modified BWRS equation of state proposed in this work, respectively.

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CONCLUSIONS In this work, densities of CO2 + decane binary mixtures are reported covering five different CO2 concentrations (x1 = 0.2361, 0.4698, 0.7100, 0.7725, and 0.8690) at temperatures from (303.15 to 353.15) K and pressures from (8 to 19) MPa by a magnetic suspension balance. The following conclusions were obtained: (1) The dissolution of CO2 increases the densities of decane solution. (2) For a constant pressure, the density of mixtures increases with increasing CO2 mole fraction first and then decreases at higher CO2 concentration and higher temperature. (3) A crossover phenomenon with compositions is observed, and the crossover pressure increases with temperature. (4) The excess molar volumes of this mixtures display a negative value increasing with increasing temperature and a less negative value with increasing pressure. (5) The densities calculated by the modified BWRS and GERG2008 models are fitted generally well at low CO2 mole fractions. The relative errors predicted with the modified BWRS model are less than ± 0.5 % when the CO2 mole fraction is less than 0.7.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

This work has been supported by National Natural Science Foundation of China (Nos. 51006016, 51006017), National 3407


(303.15 to 353.15) K and Pressures up to 19 MPa - ACS Publications

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