Solubility of n-alkanes in supercritical CO2 at diverse temperature and pressure

Journal of CO2 Utilization 9 (2015) 29–38

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Solubility of n-alkanes in supercritical CO2 at diverse temperature and pressure Qingzhao Shi, Lishuai Jing, Weihong Qiao * State Key Laboratory of Fine Chemicals, School of Chemical Engineering, Dalian University of Technology, Dalian 116024, PR China

A R T I C L E I N F O

A B S T R A C T

Article history: Received 14 October 2014 Received in revised form 25 November 2014 Accepted 1 December 2014 Available online

Poor solubility of heavy hydrocarbons in CO2 has limited the application of CO2-EOR (enhanced oil recovery) in modern oil recovery industry to some extent. Therefore, it is crucial to investigate the solubility regularity of different hydrocarbons in supercritical carbon dioxide (scCO2) in the first place. In this paper, our objective is to explore the solubility of n-alkanes (C6H14–C18H38) in scCO2. To measure cloud point pressures, the experiment utilizes high-pressure view chamber, and results for accuracy and repeatability of the experimental method and instrument are evidently positive. Then, cloud point pressures for n-alkanes from 318 K to 343 K show a proximately linear and positive correlation with the temperature; they also increase with expanding chain length of n-alkanes. In addition, the result of x (molar fraction of n-alkane at cloud point pressure) indicates that x has a positive correlation with the pressure at identical temperature, and when pressure is constant, temperature increase will reduce x. Finally, relationship studies between density of CO2 and x reveal that, density of CO2 has a positive influence on the solubility of n-alkane, and the Chrastil model corrects ln r and ln S data. The measured data align with the Chrastil model, with a maximum AARD value of 9.85%. ß 2014 Elsevier Ltd. All rights reserved.

Keywords: scCO2 Solubility n-Alkane Cloud point pressure

1. Introduction Enhanced oil recovery processes have become increasingly important to the petroleum industry. Among numerous EOR methods, CO2-EOR is known as a promising, green, and economical oil recovery technology. It could recover 6–18% original oil in place after secondary oil recovery by oil viscosity reduction, oil swelling effect, interfacial tension reduction, and light-hydrocarbons extraction, etc. Furthermore, CO2-EOR could lighten greenhouse effect by injecting CO2 into oil reservoirs and storing it underground [1–8]. Due to its low polarity, low dielectric constant, and relative high density at supercritical state, CO2 is a good solvent for petroleum [9,10]. After being stored underground, liquid CO2 can effectively extract light (e.g., C3–C8) hydrocarbons from original light crude oil, leaving a much larger amount of heavy hydrocarbons flowing through the reservoir [2,11]. Studies by Meng Cao et al. show that, as the injection volume of CO2 increase, produced oil becomes lighter and lighter [1]. This is because hydrocarbons’ polarity

* Corresponding author. Tel.: +86 84986023; fax: +86 41184986232. E-mail address: [email protected] (W. Qiao). http://dx.doi.org/10.1016/j.jcou.2014.12.002 2212-9820/ß 2014 Elsevier Ltd. All rights reserved.

increases with their length. As a result, solubility of hydrocarbons in CO2 decreases. Owning to the fact that lighter hydrocarbons are easier to dissolve into CO2, the heavier hydrocarbons are left behind when CO2 passes through the reservoir. Besides, experimental studies indicate that the oil recovery factor will decrease if the C5–C19 mole fractions in the crude oil dwindle [1]. CO2-EOR is preferred to be used in light and medium oil reservoirs because of miscibility restriction [2,4,12,13]. Moreover, asphaltene precipitation, caused by extracting phenomenon, makes the next stage of oil recovery even more difficult [3,13– 16]. It is helpful to solve the problem with the settlement of heavy hydrocarbons’ solubility problem, which would be a significant step towards improving the CO2-EOR efficiency. Therefore, solubility of varying hydrocarbons in scCO2 deserves careful investigation [17]. Field of high pressure CO2-alkane systems phase equilibrium at elevated temperature and pressure has received the greatest attention [18–26]. Karen Chandler et al. reported capacity factors for n-alkanes (C9H20–C36H74) in CO2. The experimental temperature and pressure range are 308.2–348.2 K and 100–240 bar, respectively. The estimated solubility for solid n-alkanes (C24H50–C36H74) in CO2 is calculated from the capacity factors [18]. Eun-Joo Choi et al. measured critical point data (dew points and bubble points) of

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CO2/hexane, CO2/heptane, CO2/octane, and CO2/nonane, mole fractions of CO2 ranges from 0.974 to 0.834, and experimental temperature and pressure are up to 395.7 K and 153.41 bar, respectively [19]. Other phase equilibriums of systems like hexane/CO2 [20], octane/CO2 [21], decane/CO2 [22,23], dodecane/ CO2 [24], and tetradecane/CO2 [25], etc. were studied as well. Bo Wang et al. measured the solubility of hexane and other compounds containing Cl, F, or aromatic nucleus in scCO2. They discussed the effect of polar substitute on solubility of the compound in scCO2. Also, the dependence of solutes’ solubility on binary system density was investigated [27]. Zihao Yang et al. researched on the solubility of CO2 in hexane, octane, decane, and cyclohexane, and he looked at the effect of alkane molecular structure on volume expansion of CO2/alkanes system, basing on the data of CO2 solubility in alkanes [5]. Besides the aforementioned researches on phase equilibrium and intersolubility between alkanes and CO2 from different workers, Ali Zolghadr et al. measured the minimum miscible pressure (MMP) of heptane and hexadecane by vanishing interfacial tension technique to determine the effect of temperature and pressure on interfacial tension, which also represents, to some extent, their solubility in CO2 [28]. However, to make the study more systematic, we delve into the solubility of hydrocarbons in scCO2. There are literature data for systems similar to ours from other works: solubility of octane in CO2 at 333 K from Ref. [25], n-decane in scCO2 at 344.15 K, and n-hexadecane in the same solvent, at 308.15 K, both in the range 8–13 MPa [26]. In this study, we compare our experimental results with the above systems, using the literature data. Chrastil, Bartle, Sung and Shim and many other workers proposed different semi-empirical models to correlate solute’s solubility in CO2 with density of CO2 [29–36]. These models are simple to use because it is not necessary to employ physicochemical properties. Instead, semi-empirical models were employed and widely used to provide correlations of the experimental solubility in scCO2 with density of CO2. These models are density-based methods in which the effects of temperature and pressure are considered crucial. These models also indicate that there is a linear relationship between solvent density and solute’s solubility. Chrastil first develops a model to correlate the solute solubility in scCO2 with density of CO2, and this model is now commonly used by other researchers [29]. The equation is as follows: ln S ¼ k ln r þ

m þn T

Table 1 Provenance and purity of all chemical used in this study. Chemical used

Provenance

Purity

CO2 n-Hexane n-Octane n-Decane n-Dodecane n-Tetradecane n-Hexadecan n-Octadecane

Dalian Gas Co. Ltd. Tianjin Fuyu Fine Chemical Co. Ltd. Tianjin Bodi Chemical Company Tianjin Guangfu Fine Chemical Research Institute Tianjin Kemiou Chemical Reagent Co. Ltd. Tianjin Guangfu Fine Chemical Research Institute Merck-Schuchardt Aladdin Industrial Corporation

99.5% 98.0% 99.0% 99.0% 98.0% 99.0% 99.5% 98.0%

2. Experiment 2.1. Materials Provenance and purity of all chemical used in this study are included in Table 1. Carbon dioxide with a purity greater than 99.5% was purchased from Dalian Gas Co. Ltd.; n-hexane (AR) was supplied by Tianjin Fuyu Fine Chemical Co. Ltd.; n-octane (AR) was imparted by Tianjin Bodi Chemical Company; n-decane (AR) and ntetradecane (AR) were purchased from Tianjin Guangfu Fine Chemical Research Institute; n-dodecane (AR) was provided by Tianjin Kemiou Chemical Reagent Co. Ltd.; n-hexadecane (GC) and n-octadecane (AR) were purchased from Merck-Schuchardt and Aladdin Industrial Corporation separately. 2.2. Apparatus and procedure Fig. 1 demonstrates the schematic diagram of the applied experimental setup for solubility measurement. Main part of this apparatus is a fixed-volume (59.42 ml) high-pressure-view chamber (maximum working pressure and temperature of the chamber are 32 MPa and 423 K, respectively), which consists of two crossing sapphire windows. A pressure transducer with 0.001 MPa accuracy and a temperature controller with an accuracy of 1 8C monitor control the pressure and temperature of the cell. A rotation controller with maximum 1200 r/min speed is installed under the cell. Before each solubility test, the cell is cleaned and dried by acetone. Then add a desired amount of the solvent into the cell. To discharge air in the system, open the CO2 entrance gently to let in

(1)

where r (kg/m3) is the density of CO2, and T (K) the system temperature; k, m and n are characteristic constants; S (kg/m3) is the solubility of the solute, which can be calculated using the formula below: S¼

rM 1 x ½M 0 ð1-xÞ

(2)

where M0 and M1 are the molar weight of CO2 and the solute, respectively, x is molar fraction of the solute in the binary system. One objective of this study is to examine the solubility of n-alkanes (C6–C18), which help us to have a better understanding on how much hydrocarbon could dissolve into the scCO2. Furthermore, temperature and pressure effects on the solubility of n-alkanes as well as the correlations between CO2 density and n-alkanes solubility are primary objectives as well. And the solubility results correlate with Chrastil model.

Fig. 1. Schematic diagram of experimental apparatus for solubility test in scCO2. (1) High pressure view cell; (2) temperature and rotate speed controller; (3) temperature sensor; (4) CO2 delivery pump; (5) coolant system; (6) entrance to the cell; (7) relief port.

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Fig. 2. Pictures of 5.21 g n-hexane’s dissolubility in scCO2 at 318 K: (a) n-hexane; (b) n-hexane + CO2 under 5.445 MPa; (c) n-hexane + CO2 under 5.445 MPa, stirrer is on; (d) nhexane + CO2 under 7.712 MPa, stirrer is on; (e) n-hexane + CO2 under 8.630 MPa, stirrer is on.

some CO2 first, then close the entrance and open the relief port. The above procedure has to be repeated three times to make sure the air was drained thoroughly. Afterwards, inject enough CO2 into the cell, set the target temperature, and start the stirrer. After the cell stays at a stable temperature, pump CO2 into the system until a clear transparent single phase is formed. Keep stirring until the cell reaches an equilibrium condition. Cloud point of the binary system is measured by slow depressurization (0.005 MPa/s) of the system. Gently let out some CO2 by operating the relief port. During the depressurization, at the cloud point, the precipitation of compound out of single-phase solution induces cloudiness in the high-pressure cell, which could be detected visually. System pressure at this point is recorded as the cloud point pressure of the solvent. Solubility can be calculated from Eq. (3) below: x ð%Þ ¼

ðm1 =M 1 Þ  100 ½m1 =M 1 þ ðv0 r0 Þ=M 0 

(3)

where x is the mole fraction of solute in the binary system; m1 stands for the weight of solute; M1 and M0 are molecular weights of Table 2 Comparison of the cloud point pressures of n-hexane between our experiment and Ref. [27] results at 328 K. No.

1 2 3 4 5

Experimental results

Reference results

P/MPa

x

P/MPa

x

8.930 8.915 8.824 8.467 7.310

0.0620 0.0522 0.0476 0.0371 0.0295

8.95 8.93 8.86 8.48 7.22

0.0618 0.0520 0.0471 0.0373 0.0304

Fig. 3. Accuracy test: comparison of cloud point pressures between reference and experiment.

solute and CO2, respectively; v0 stands for the volume of the cell, r0 stands for the density of CO2. The National Institute of Standards and Technology database software Refprop provides the densities of scCO2. S could be calculated using Eq. (2) by substituting x value at certain temperature. Plugging in different values of S and temperatures, to which S corresponds, and we will have k, m, and n. 3. Results and discussion 3.1. Accuracy and repeatability test Fig. 2 shows the condition of n-hexane (5.21 g)/CO2 binary system under different pressures at 318 K. Picture a illustrates nhexane in the cell. After gently injecting CO2 into the cell, we notice the liquid level raises (picture b), which is caused by some CO2 dissolved into the n-hexane phase. Picture b and c shows that it is a Table 3 Cloud point pressure results for C14H30 (0.01 mol) at temperatures from 318 K to 343 K. MPa

318 K

323 K

328 K

333 K

338 K

343 K

1 2 3 Average Average deviation

10.394 10.392 10.379 10.388 0.622%

11.424 11.459 11.493 11.459 2.311%

12.420 12.412 12.386 12.406 1.333%

13.401 13.416 13.402 13.406 0.644%

14.372 14.359 14.370 14.367 0.533%

15.189 15.174 15.220 15.194 1.711%

C8H18,

C10H22,

C12H26,

C14H30,

Fig. 4. Cloud point pressures of: C6H14, C16H34 and, & C18H38.

32

Q. Shi et al. / Journal of CO2 Utilization 9 (2015) 29–38

Fig. 5. Cloud point pressures for n-alkanes with different molar mass: (a) C10H22; (b) C12H26; (c) C14H30; (d) C16H34; (e): C18H38.

two-phase system at 5.445 MPa. Additionally, the system appearance changes from turbid (d, 7.712 MPa) to transparent (e, 8.630 MPa) by adding more CO2 into the cell. A comparative analysis between results of this study and previous experiments shows that, as summarized in Table 2 and

Fig. 3, the difference between our experiment results and that of Ref. [27] is small, indicating that solubility determined in our lab is reliable. Moreover, for C8H18 at 333 K, its molar fraction in CO2 is 0.0454 at 10.327 MPa in our experiment, and according to Ref. [25], the result shows no much difference, which is 0.0617 at 10.48 MPa.

Q. Shi et al. / Journal of CO2 Utilization 9 (2015) 29–38 Table 5 (Continued )

Table 4 The k, m, n values for C10H22–C18H38.

C10H22 C12H26 C14H30 C16H34 C18H38

T

P (MPa)

r (kg/m3)

xexp (%)

k

m

n

338 K

11.18 13.25 8.42 8.32 7.58

30,645 62,220 2827 39,206 19,328

29.77 58.69 40 68.91 12.76

12.626 13.033 13.107 13.338 13.657

425.14 451.09 455.7 469.79 488.44

0.86 1.62 2.38 3.05 4.35

14.33 28.67 43.00 57.33 86.00

0.89 1.81 2.04 2.94 4.63

343 K

13.341 13.734 13.925 14.202 14.436 AARDx% = 5.90%

422.11 443.74 454.00 468.49 480.33

0.87 1.64 2.39 3.06 4.42

14.33 28.67 43.00 57.33 86.00

0.86 1.61 2.14 3.15 4.27

9.981 10.394 10.503 10.953 11.035

499.71 553.20 564.56 602.59 608.33

0.74 1.32 1.93 2.40 3.52

16.69 33.39 50.08 66.78 100.16

0.70 1.47 1.70 2.71 2.90

323 K

10.845 11.424 11.569 12.038 12.218

489.07 545.33 557.00 589.43 600.05

0.75 1.34 1.96 2.45 3.57

16.69 33.39 50.08 66.78 100.16

0.73 1.59 1.84 2.74 3.10

328 K

11.718 12.420 12.627 13.150 13.488

483.54 537.74 551.32 581.39 598.08

0.76 1.36 1.97 2.48 3.58

16.69 33.39 50.08 66.78 100.16

0.72 1.56 1.87 2.74 3.35

333 K

12.522 13.401 13.942 14.251 14.459

475.00 531.50 548.00 574.84 584.00

0.77 1.37 1.99 2.51 3.66

16.69 33.39 50.08 66.78 100.16

0.75 1.66 2.05 2.87 3.20

338 K

13.341 14.372 14.701 15.131 15.534

470.00 526.37 542.00 560.76 576.82

0.78 1.39 2.01 2.57 3.71

16.69 33.39 50.08 66.78 100.16

0.76 1.73 2.13 2.72 3.32

14.195 15.189 15.595 15.914 16.395 AARDx% = 9.85%

468.13 515.72 533.00 545.75 563.62

0.78 1.42 2.04 2.64 3.79

16.69 33.39 50.08 66.78 100.16

0.74 1.62 2.12 2.55 3.30

11.085 12.046 12.960 13.829 15.108

611.69 661.65 694.03 717.72 745.25

0.60 1.11 1.58 2.02 2.89

19.06 38.11 57.16 76.22 114.33

0.60 1.13 1.66 2.16 2.91

323 K

12.002 13.091 13.856 14.592 15.940

587.20 641.70 669.17 690.67 722.05

0.63 1.14 1.63 2.10 2.98

19.06 38.11 57.16 76.22 114.33

0.60 1.20 1.66 2.12 2.98

328 K

12.913 14.171 14.858 15.951 16.904

568.46 626.77 650.53 681.17 702.96

0.65 1.17 1.68 2.13 3.06

19.06 38.11 57.16 76.22 114.33

0.64 1.26 1.64 2.26 2.81

333 K

13.652 14.959 15.994 16.640 17.734

545.38 604.07 638.66 656.67 682.70

0.67 1.21 1.71 2.20 3.15

19.06 38.11 57.16 76.22 114.33

0.66 1.29 1.86 2.23 2.86

338 K

14.602 15.880 16.737 17.495 18.381

537.40 589.55 617.42 638.56 660.04

0.68 1.24 1.77 2.27 3.26

19.06 38.11 57.16 76.22 114.33

0.62 1.26 1.79 2.31 2.96

Table 5 Data of solubility of n-alkanes at temperature form 318 K to 343 K, and density of CO2 at respective conditions.

r (kg/m3)

xexp (%)

9.185 9.308 9.451 9.528 9.618

366.34 385.77 409.94 423.43 439.36

1.00 1.88 3.49 4.98 6.32

11.97 23.94 47.87 71.81 95.74

1.04 1.15 3.35 4.65 6.73

9.783 9.918 10.162 10.261 10.393

361.49 377.02 406.55 418.87 435.35

1.01 1.93 3.51 5.04 6.37

11.97 23.94 47.87 71.81 95.74

1.10 2.08 3.47 4.63 6.66

10.325 10.491 10.75 10.918 10.985

353.99 368.93 393.12 409.18 415.62

1.04 1.97 3.63 5.14 6.65

11.97 23.94 47.87 71.81 95.74

1.09 2.19 3.47 5.36 6.33

10.849 11.046 11.437 11.64 11.691

348.02 362.60 392.52 408.33 412.31

1.05 2.00 3.64 5.16 6.70

11.97 23.94 47.87 71.81 95.74

1.12 1.69 3.73 5.48 6.01

11.299 11.635 11.959 12.189 12.545

339.41 360.55 381.50 396.55 419.85

1.08 2.01 3.74 5.30 6.58

11.97 23.94 47.87 71.81 95.74

1.14 1.97 3.26 4.57 7.46

11.811 12.251 12.608 12.912 13.091 AARDx% = 7.67%

336.49 360.7 380.77 397.98 408.09

1.09 2.01 3.74 5.29 6.77

11.97 23.94 47.87 71.81 95.74

1.06 2.09 3.52 5.34 6.73

T C10H22 318 K

323 K

328 K

333 K

338 K

P (MPa)

343 K

C12H26 318 K

323 K

328 K

333 K

33

S

xcal (%)

9.601 9.779 9.826 9.901 10.02

436.35 467.30 475.15 487.31 505.53

0.84 1.56 2.28 2.95 4.21

14.33 28.67 43.00 57.33 86.00

0.82 1.78 2.15 2.85 4.28

10.371 10.618 10.658 10.748 10.92

432.61 462.09 467.65 478.13 497.25

0.85 1.57 2.32 3.00 4.28

14.33 28.67 43.00 57.33 86.00

0.82 1.86 2.10 2.74 4.35

11.136 11.453 11.534 11.649 11.837

430.11 459.93 467.30 477.54 493.62

0.85 1.58 2.32 3.01 4.31

14.33 28.67 43.00 57.33 86.00

0.84 1.88 2.28 2.96 4.38

11.892 12.22 12.34 12.529 12.703

427.90 452.94 461.84 475.50 487.63

0.86 1.61 2.35 3.02 4.36

14.33 28.67 43.00 57.33 86.00

0.83 1.69 2.15 3.08 4.20

C14H30 318 K

343 K

C16H34 318 K

S

xcal (%)

Q. Shi et al. / Journal of CO2 Utilization 9 (2015) 29–38

34 Table 5 (Continued )

3.2. Solubility of n-alkanes in scCO2 r (kg/m3)

xexp (%)

S

xcal (%)

515.63 574.11 611.36 628.07 641.71

0.716 1.27 1.78 2.30 3.34

19.06 38.11 57.16 76.22 114.33

0.68 1.38 2.08 2.47 2.84

12.475 13.804 15.075 16.231 17.370

678.09 717.11 744.62 764.83 781.77

0.54 0.77 0.98 1.20 1.40

21.41 32.12 42.83 53.54 64.24

0.54 0.79 1.01 1.20 1.39

323 K

13.635 14.706 15.826 17.042 17.895

661.87 693.67 719.70 742.68 756.51

0.56 0.79 1.02 1.23 1.45

21.41 32.12 42.83 53.54 64.24

0.56 0.77 1.00 1.24 1.41

328 K

14.553 15.382 16.533 17.661 18.769

640.50 666.13 694.92 717.95 737.12

0.57 0.83 1.05 1.27 1.48

21.41 32.12 42.83 53.54 64.24

0.61 0.79 1.04 1.29 1.53

333 K

15.306 16.288 17.394 18.482 19.514

616.60 647.15 675.12 698.02 716.66

0.60 0.85 1.08 1.31 1.53

21.41 32.12 42.83 53.54 64.24

0.62 0.84 1.09 1.33 1.57

338 K

16.207 17.585 18.351 19.170 20.273

600.75 640.89 659.36 676.86 697.53

0.61 0.86 1.11 1.35 1.57

21.41 32.12 42.83 53.54 64.24

0.62 0.94 1.13 1.34 1.63

16.971 18.180 19.293 20.045 20.862 AARDx% = 2.51%

583.08 618.16 645.04 660.94 676.56

0.63 0.89 1.13 1.38 1.62

21.41 32.12 42.83 53.54 64.24

0.60 0.87 1.13 1.32 1.53

T

P (MPa)

343 K

15.187 16.698 17.926 18.569 19.145 AARDx%=5.23%

C18H38 318 K

343 K

C14H30 (0.01 mol) was chosen for repeatability test. Cloud point pressures of C14H30 were tested three times from 318 K to 343 K, and the results are reported in Table 3. The average deviation is less than 2.311%, which demonstrates that the experimental results have an excellent repetition.

Fig. 6. Comparison between solubility data of references and our experiment.

There are three intermolecular forces that affect the solubility of n-alkane in CO2: (1) the force between two CO2 molecules; (2) the force between two alkane molecules; (3) the force between CO2 molecule and alkane molecule. Strengthening of the first two forces works against the dissolution, in contrast, strengthening of the forces between CO2 and alkane molecules will benefit the dissolution of alkane in CO2. All these forces are affected by changes in alkane, temperature, and pressure etc., which have impacts on the solubility. 3.2.1. Carbon chain length effect on solubility of n-alkanes in scCO2 To investigate the role of carbon chain length in solubility of n-alkanes, the cloud point pressures of C6H14–C18H38 are measured separately at 318 K, 323 K, 328 K, 333 K, 338 K and 343 K. Fig. 4 shows the cloud point pressure–temperature curves for different n-alkanes in scCO2. The quantity of addition in C10H22 to C18H38 is 0.01 mol, while C8H18 and C6H14 are added 0.02 mol and 0.05 mol, respectively. Attributed to that, cloud point pressures of C8H18 and C6H14 are below 7.37 MPa (critical pressure of CO2) if only adding 0.01 mol. As it can be seen in Fig. 4, the cloud point pressure increases as molecular chain length grows. This is because molecule chain length expansion increases instantaneous dipole of n-alkane in CO2, and strengthen the Vander Waals forces among alkane molecules. So the longer the molecule chain length is, the harder it is to dissolve n-alkane in CO2. There is approximately a 53% increase in cloud point pressure, as the chain carbon number increases by 8 (cloud point pressures for C10H22 and C18H38 are 12.251 MPa and 18.802 MPa, respectively). 3.2.2. Temperature and pressure effect on solubility of n-alkanes in scCO2 Another objective of this study is to investigate the effects of temperature and pressure on the solubility of n-alkanes in scCO2. For this purpose, cloud point pressures for different amount of n-alkanes are denoted in Fig. 5 and Table 5. Mass of CO2 is calculated with volume and density of CO2 at given temperature and pressure, and the corresponding molar fraction x of n-alkane in CO2 can be calculated with Eq. (3), shown in Table 5. The results are compared with those from Refs. [23,26], shown in Fig. 6. It shows that data from this experiment align with the data that were previously reported. The x in % for each alkane is plotted as a function of pressure in Fig. 7. According to Fig. 7, for example, increasing of pressure from 9.185 MPa to 9.618 MPa brings about a fivefold increase in x (for C10H22 at 318 K). We can conclude that higher pressure raises x when temperature is constant. And this can be explained by the fact that force generated by pressure squeezes the alkane molecules into the CO2 phase, which contributes to solubility. When pressure is held constant, temperature increase will abate x. For example, as temperature increases from 323 K to 328 K (for C10H22 at around 10.25 MPa), x decreases from about 6.5% to 1.0%. Higher temperature leads to the decrease in intermolecular forces between CO2 and n-alkane molecules, as well as those of two alkane molecules. However, the former decreases faster than the latter. Temperature and pressure influences on x of C10H22–C18H38 differ by the chain length incline. It is worth noting that, the x value of C10H22 is about seven times of the value of C12H26 (at about 9.5 MPa, 318 K), the fact that the difference is only 2 carbon numbers indicates that the carbon chain length exerts a tremendous influence on their solubility.

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35

Fig. 7. Changes of molar fractions for different alkanes at cloud point with pressure at different temperature: (a) C10H22; (b) C12H26; (c) C14H30; (d) C16H34; (e) C18H38. &: 318 K; : 323 K; : 328 K; : 333 K; : 338 K; : 343 K.

3.3. Correlations between CO2 density and solubility of n-alkanes Solvent strength of supercritical fluid is thought to be related with its density: increase in density would increase the solvent strength at a constant temperature. CO2 density to x curves is plotted and shown in Fig. 8. As seen in Fig. 8, x value raises with density of CO2, showing that the solubility of n-alkanes has some influence on the density of CO2. Higher temperature raises better solubility when CO2 density is constant. According to Chrastil semi-empirical equation, there is a linear relationship between solvent density and solute’s solubility. With x value in hand, S can be calculated by Eq. (2), and the results are listed in Table 5. The corresponding ln r–ln S are shown in Fig. 9,

and a data-fitting line (shown in Fig. 9) from Eq. (1) gives the corresponding k, m, and n values listed in Table 4. The xcal (x calculated by Chrastil model) and xexp (x from experiment) are compared in Table 5. The average absolute relative deviation (AARD) between them can be calculated by Eq. (4) below: AARD ¼

P

 jðxi;cal  xi;exp Þ=xi;exp j  100% n

(4)

From Table 5, AARD values of n-alkanes are 7.67%, 5.90%, 9.85%, 5.23%, and 2.51%, respectively. The maximum AARD is 9.85% for C14H30, which demonstrates that the experimental data perfectly agree with the data from Chrastil model.

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Fig. 8. Changes of molar fraction for different alkanes with density of CO2 at cloud points: (a) C10H22; (b) C12H26; (c) C14H30; (d) C16H34; (e) C18H38: 328 K; : 333 K; : 338 K; : 343 K.

4. Conclusions The experimental study on the solubility of n-alkanes in CO2 at 318–343 K demonstrated that alkane’s solubility has a direct relation with pressure and CO2 density, while it has inverse relation with chain length and temperature. The cloud point pressure of n-alkanes exhibits a positive liner trend with temperature; it also increases with the chain length of nalkane, attributed to that molecule chain length growth

318 K;

: 323 K;

:

increases instantaneous dipole of n-alkane in CO2, and strengthen Vander Waals forces among alkane molecules. We find that x increases with pressure at the same temperature, and when pressure is constant, temperature increase will induce x reduction. The relationships between CO2 density and x illustrates that n-alkane solubility has direct impact on CO2 density. The experimental data show good agreement with those corrected by Chrastil model, and the maximum AARD value is 9.85%.

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Fig. 9. Logarithmic relationships between S and the density of pure CO2 (the points are data from experiment, and the lines are data fitted by Chrastil model). (a) C10H22; (b) C12H26; (c) C14H30; (d) C16H34; (e) C18H38. : 318 K; : 323 K; : 328 K; : 333 K; : 338 K; : 343 K.

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