Measurement and Correlation of High Pressure Phase Equilibria for

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX-XXX

pubs.acs.org/jced

Measurement and Correlation of High Pressure Phase Equilibria for CO2 + Alkanes and CO2 + Crude Oil Systems Xia Gui,*,†,‡ Wei Wang,† Qiang Gao,† Zhi Yun,† Maohong Fan,‡ and Zuhua Chen§ †

College of Chemical Engineering, Nanjing Tech University, Nanjing, Jiangsu 210009, PR China Department of Chemical Engineering, University of Wyoming, Laramie, Wyoming 82071, United States § Research Institute of Exploration & Development, East China Company, SINOPEC, Nanjing, Jiangsu 210009, PR China ‡

ABSTRACT: An analytical apparatus with improved recirculating and sampling mechanisms was presented to investigate phase behavior of binary and multicomponent systems, which effectively avoided undesirable pressure gradients across the cell and serious disturbance of equilibrium during sampling procedure. Two one-channel magnetic recirculation pumps were designed and built to provide better mass transfer between the coexisting phases. Two six-port switching valves were used for sampling, quantitative fluid injection, and online compositional analysis by gas chromatography. The apparatus was validated by means of isothermal vapor−liquid equilibrium data for CO2 + hexane, and the results were found to be in good agreement with the literature data. High pressure phase equilibria data of CO2 + n-alkanes and CO2 + crude oil + n-alkanes were measured from 353.15 to 373.15 K. Three thermodynamic models of RR, PRSV, and YQE, based on Peng−Robinson and a modified quartic equation of state coupled with various mixing rules, were suggested to represent phase equilibrium. Calculations were compared with experimental values for evaluating the predictive ability of these proposed equations. Analysis of the results confirmed that the YQE model was superior to all the other equations examined and worked well in describing phase behavior of complex real fluids.

1. INTRODUCTION Global climate change mainly caused by CO2 has become one of most important and pressing environmental issues today.1,2 Carbon capture and storage (CCS) is currently acknowledged as a highly innovative and promising technology to help mitigate climate change.3 However, previous studies have shown that significant drawbacks are associated with CCS options that capture CO2 from fossil energy power plants or industrial facilities and then store it underground. In particular, the application of geological storage may be confronted with high investment costs, limited storage capacity, potential leakage of CO2, and problems with public acceptance of onshore storage locations.4−6 Compared with CCS, carbon capture and utilization (CCU) seems to be more acceptable and feasible, which plays a large, critical, and unique role in dealing with global carbon dioxide emissions as well as reusing CO2 beneficially for various purposes.7 In view of the practical importance and inherent advantages, commercial utilization of the captured CO2 as working fluid or as feedstock in chemical processes and biotechnological applications has received widespread attention with international action from governments and industries.8,9 Over the past few decades, a multitude of available technologies to reuse CO2 have emerged, including CO2-based enhanced oil and gas recovery (CO2-EOR and EGR), enhanced coal bed methane (CO2-ECBM), fertilizer, cement, algae, and plastics production.10−12 Among them, CO2-based enhanced oil recovery (CO2-EOR), accounting for nearly 6% of U.S. oil © XXXX American Chemical Society

production, is probably the most well developed type of reuse.13 It is estimated that roughly 65% of crude oil remains in the reservoir after primary and secondary recoveries.14 CO2-based enhanced oil recovery (CO2-EOR), also referred to as tertiary recovery, can effectively maintain or increase the reservoir pressure for extracting more oil from a mature oilfield.15 Since the early 1970s, CO2 has been increasingly injected into depleted oilfields to recover additional oil from existing sources. The first industrial-scale CO2-EOR project at the SACROC unit (Kelly-Snyder field, Scurry County, West Texas) was launched in 1972.16 Until now, the United States has led the world in both the number and the volume of CO2-EOR oil production. The technical success of the CO2-EOR project, coupled with current energy crisis, provides an attractive alternative for countries with heavy and extra-heavy oil resources, such as China and Canada. A typical CO2-EOR represents the process by which CO2 is injected into depleting oil fields for the purpose of oil swelling and viscosity reduction. Both of the two characteristics help to improve sweep efficiency and then facilitate additional oil recovery. A full understanding of the physical and chemical properties of CO2 with crude oil as well as the miscibility between Received: June 8, 2017 Accepted: September 29, 2017

A

DOI: 10.1021/acs.jced.7b00517 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

of CO2 solubility in crude oil are still a question of practical importance and theoretical interest. In this paper, an analytical experimental apparatus with improved recirculating and sampling mechanisms was constructed to investigate the phase equilibrium data of CO2 and hydrocarbons at reservoir conditions. A series of phase equilibria data for CO2 + n-alkanes and CO2 + crude oil + n-alkanes were measured for testing thermodynamic models rigorously under representative conditions of temperature, pressure, and composition. Three thermodynamic models of RR, PRSV, and YQE, based on Peng−Robinson and modified quartic equations of state coupled with various mixing rules, were suggested to represent phase equilibrium in both the binary and multicomponent systems. Calculations were compared with experimental data for evaluating the predictive ability of these proposed equations.

them, together with their effects on oil recovery, is extremely crucial for practical design, construction, operating condition optimization, and industrialization of CO2-EOR projects. One of the major parameters that remarkably affect the microscopic and macroscopic sweep efficiency is the phase equilibrium data of CO2 in multicomponent systems.17−19 Moreover, high pressure phase equilibria of systems containing hydrocarbons and CO2 are also of interest in a wide range of industrial processes, such as coal to liquids production, petroleum processing, hydrotreatment of aqueous waste streams, and supercritical fluid extraction.20−23 Therefore, getting a better grasp of phase behavior and its effects on oil recovery efficiency mechanisms has a huge impact on the success of CO2-EOR projects and many other industrial fields. Most of the phase equilibrium data can be determined by experimental studies and available software packages or correlations. In fact, large amounts of such data and models have existed in the literature, covering the binary systems of CO2 and hydrocarbons. A large majority of pertinent works are primarily based on the binary system of CO2−alkane, CO2−bitumen, and the rest are chiefly related to ternary mixtures of alkanes−CO2−water.24−31 The available phase equilibrium data for mixtures of CO2 with multicomponent hydrocarbons is very limited in view of the diversity of the hydrocarbons and the ranges of temperature and pressure investigated.32 Thus, more reliable experimental methods and precise high-pressure high-temperature phase behavior data are required, particularly in the range of operating conditions suitable for CO2-EOR. Furthermore, in order to gain some interrelated thermosphysical properties of multicomponent mixtures and a deeper comprehension of phase behavior, various mathematical correlations have been developed, ranging from empirical and semiempirical models, to molecular-based theories.33 In general, such proposed thermodynamic models and mathematical correlations perform very well in terms of estimating the CO2 solubility in binary systems but require numerous experiments and much useful information for each pure component. Cubic equations of states (EOS) are commonly employed to describe thermodynamic properties and phase equilibrium of pure fluids or mixtures over wide temperature and pressure ranges. Since the introduction of the van der Waals equation of state in 1873, considerable time and effort has been expended to improve the reliability and versatility of previous EOS. Soave−Redlich−Kwong (SRK) EOS and Peng−Robinson (PR) EOS are the two widely accepted models in the field of oil and gas.34,35 In most cases, the accuracy of the EOS calculation tends to be very sensitive to a temperaturedependent interaction parameter so that an explicit determination of all the interaction parameters for all possible binary combinations is required. Recently, Jaubert and co-workers developed a group contribution method (GCM) allowing the estimation of the temperature-dependent binary interaction parameter kij in PR EOS, thereby creating a new predictive model PPR78.36−43 The PPR78 model has been tested against known data for many binary mixtures, and the results are found to be in good agreement with experiment. In addition, a series of revised group-contribution equations of state (GC-EOS) from many later studies also show a similar performance to PPR78. In contrast to other models, GC-EOS appears to have good predictability especially for particular ranges of operating conditions and fluid properties. However, these predictive EOS models have not yet been extensively tested against multicomponent equilibrium data. Therefore, detailed investigations

2. EXPERIMENTAL SECTION 2.1. Materials. The CO2 was sourced from a high purity CO2 cylinder (with a volume fraction of 99.99%, SanLe Gas in Nanjing). The crude oil, a mixture of more than 30 hydrocarbons including alkanes, branched-alkanes, cyclo-alkanes, and aromatics, was provided by East China Branch and Petroleum Bureau of Sinopec Group. Basic physical properties and carbon number distribution of the crude oil sample were presented in Table 1 and Table 2, which were from East China Branch and Table 1. Basic Properties of the Crude Oil Sample average molecular weight

density at 298.15 K

refractive index

pour point

276 g·mol−1

0.886 g·cm−3

1.4497

312.15 K

Table 2. Compositional Analysis and Carbon Number Distribution of the Crude Oil carbon numbers

mole %

carbon numbers

mole %

C1 C2 n-C3 i-C3 C4 n-C5 i-C5 C6 C7 C8 C9 C10

10.29 0.36 0.45 0.08 0.16 1.80 0.04 1.48 2.62 5.59 6.12 4.73

C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22

3.80 3.38 3.38 2.80 3.16 2.68 2.37 2.88 3.66 2.41 2.14 2.11

carbon numbers

mole %

C23 C24 C25 C26 C27 C28 C29 C30+ N2 CO2

2.15 1.95 1.87 1.90 1.77 1.71 1.90 16.95 0.97 0.34

Petroleum Bureau of Sinopec Group. Alkanes including hexane (C7H16), octane (C8H18), nonane (C9H20), decane (C10H22), undecane (C11H24), dodecane (C12H26), tridecane (C13H28), tetradecane (C14H30), pentadecane (C15H32), and hexadecane (C16H34) were purchased from Aladdin-Reagent Company in Shanghai. The purity was determined by HPLC (shimadzu LC-20A), and the mass fraction is higher than 99.9%. All components were used without further purification. Detailed information on materials used in this study is listed in Table 3. 2.2. Apparatus. A number of different investigative techniques have been attempted to represent the phase behavior of multicomponent mixtures under high-pressure and high-temperature conditions. These techniques are generally classified as B



Article

Table 3. Sample Provenance Table materials hexane octane nonane decane undecane dodecane tridecane tetradecane pentadecane hexadecane CO2

CAS 110-54-3

purity

0.999 (mass fraction) 111-65-9 0.999 (mass fraction) 111-84-2 0.999 (mass fraction) 124-18-5 0.999 (mass fraction) 1120-21-4 0.999 (mass fraction) 112-40-3 0.999 (mass fraction) 629-50-5 0.999 (mass fraction) 629-59-4 0.999 (mass fraction) 629-62-9 0.999 (mass fraction) 544-76-3 0.999 (mass fraction) 124-38-9 0.9999 (volume fraction)

source Aladdin-Reagent Company Aladdin-Reagent Company Aladdin-Reagent Company Aladdin-Reagent Company Aladdin-Reagent Company Aladdin-Reagent Company Aladdin-Reagent Company Aladdin-Reagent Company Aladdin-Reagent Company Aladdin-Reagent Company SanLe Gas

purification method none none none

Figure 2. Schematic diagram of the designed pump. 1, nonmagnetic steel casing; 2, permanent magnet ferrite bricks; 3, magnetic steel piston; 4, synthetic ruby balls.

none none

samples from liquid and vapor phases, which is applicable to the analytic mode of experiment. Therefore, an analytical apparatus with improved recirculating and sampling systems was proposed to investigate phase equilibrium. The apparatus constructed for measuring CO2 solubility consisted of six major parts: a CO2 cylinder, a gas buffer tank (100 mL, 100 MPa), a high pressure syringe pump (0−1 L/h, 50 MPa), a high pressure view-cell (45 mL, 50 MPa), two magnetic recirculation pumps, and a gas chromatograph. Complete sets of equipment were provided by Hongbo Machinery Manufacturing Co., Ltd., in Jiangsu Province. A simplified schematic diagram of the apparatus used in this work is depicted in Figure 1. It should be noted that the facility design was based on an integration of the constant-volume and recirculation method.49−51 A high pressure syringe pump equipped with a cooling jacket was utilized to liquefy CO2 and deliver supercritical liquid with great accuracy and reliability. As a complementary device, the gas buffer tank was built for transforming CO2 into either liquid or gas more flexibly. The gas buffer tank was connected to an external recirculating temperature-controlled bath (253.15 to 393.15 K),

none none none none none none

direct (analytical) or indirect (synthetic) sampling methods, depending on how composition is determined. Comprehensive reviews have covered new and important experimental mechanics techniques in Fonseca (2011), Dohrn (2010), Christove (2002), Dohrn (1995), and Fornari (1990).44−48 Challenges encountered in attaining accurate measurement of vapor−liquid equilibrium data mainly include two issues: (1) ensure that equilibrium has been reached; (2) avoid disturbing the equilibrium condition when withdrawing representative

Figure 1. Schematic diagram of the designed apparatus. 1, CO2 gas cylinder; 2, gas buffer tank; 3, high-pressure view-cell; 4, liquid injector; 5, solvent tank; 6, magnetic recirculation pump; 7, liquid sampling valve; 8, gas sampling valve; 9, carrier gas; 10, gas purifier; 11, rotameter; 12, gas chromatograph; 13, check valve; 14, safety valve; 15, cooling system; 16, liquid CO2 pump; 17, high pressure syringe pump; 18, vacuum pump; P1−P3, pressure transducer; T1−T2, resistance thermometer. C



Article

Table 4. Phase Equilibrium Data for CO2 (1) + Hexane (2) Systema T = 313.15 K

Table 5. Phase Equilibrium Data for CO2 (1) + Octane (2) Systema

T = 353.15 K

P, MPa

x1

y1

P, MPa

x1

y1

0.93 1.39 2.42 3.05 3.68 4.26 5.20 5.99 6.50 6.83

0.1094 0.1681 0.2770 0.3555 0.4620 0.5674 0.7180 0.7704 0.7961 0.8570

0.9299 0.9331 0.9581 0.9668 0.9726 0.9765 0.9809 0.9834 0.9847 0.9855

1.56 2.32 2.87 3.98 4.92 5.92 6.86 7.67 8.52 9.70 10.58

0.1313 0.1804 0.2371 0.3164 0.3631 0.4412 0.4962 0.5713 0.623 0.7057 0.7714

0.9053 0.9341 0.9512 0.9481 0.9523 0.9556 0.9468 0.9417 0.9434 0.9392 0.9241

T, K

P, MPa

x1

y1

K1

K2

353.15

1.71 2.95 4.46 6.42 7.71 8.45 11.96 13.03 2.88 3.94 5.83 7.26 9.64 11.65 12.76 13.87 3.01 4.24 6.11 8.49 9.41 10.47 11.71 12.81 13.77

0.1453 0.2415 0.3591 0.4936 0.5778 0.6232 0.8255 0.9148 0.2047 0.2753 0.3920 0.4756 0.6051 0.7094 0.7805 0.8550 0.1851 0.2545 0.3556 0.4735 0.5169 0.5657 0.6218 0.6851 0.8292

0.9809 0.9862 0.9880 0.9875 0.9861 0.9847 0.9674 0.9452 0.9807 0.9832 0.9839 0.9829 0.9781 0.9692 0.9539 0.9315 0.9749 0.9768 0.9774 0.9734 0.9700 0.9669 0.9620 0.9490 0.9082

6.7508 4.0836 2.7513 2.0006 1.7066 1.5801 1.1719 1.0332 4.7898 3.5718 2.5098 2.0667 1.6164 1.3662 1.2222 1.0895 5.2669 3.8381 2.7486 2.0558 1.8766 1.7092 1.5471 1.3852 1.0953

0.0224 0.0182 0.0187 0.0247 0.0329 0.0406 0.1868 0.6432 0.0243 0.0232 0.0265 0.0326 0.0555 0.1060 0.2099 0.4724 0.0308 0.0310 0.0351 0.0505 0.0621 0.0762 0.1005 0.1620 0.5375

363.15

a Standard uncertainties u are u(T) = 0.10 K, u(P) = 0.01 MPa, and uc(x1) = uc(y1) = 0.0512.

373.15


Table 6. Phase Equilibrium Data for CO2 (1) + Nonane (2) Systema Figure 3. P−x−y phase diagram for CO2 (1) + hexane (2) at 313.15 and 353.15 K. The filled symbols correspond to published experimental data; the open symbols represented the data gathered during this work. ▲, 313.15 K; △, 313.15 K; ■, 353.15 K; □, 353.15 K.

and the phase transition of CO2 between gas and liquid can be achieved at relatively lower temperatures. Meanwhile, the amount of CO2 introduced into a high-pressure view-cell can be calculated from the pressure variation inside the gas buffer tank, and this method is especially applicable to low and mediumpressure applications.1,50−52 Here, the gas buffer tank was recommended for determining the phase behavior under extended operating conditions. A high pressure view-cell with a constant volume of 45 mL was presented for investigation of multiphase equilibrium, which contained two sapphire windows for a clear view of the interior, an absolute pressure transducer, and a standard platinum resistance thermometer. An optical rail located below the cell was used to mount a camera and front and back illumination devices. It was therefore possible to adjust the position of the camera and facilitate the detection of phase changes. The maximum allowable working pressure and temperature were 50 MPa and 523.15 K, respectively. In order to provide better mixing of different phases and to ensure the attainment of equilibrium, two one-channel magnetic recirculation pumps, shown in Figure 2, were designed and built. The magnetic recirculation pump was constructed

T, K

P, MPa

x1

y1

K1

K2

353.15

2.14 3.72 5.35 6.80 8.63 10.06 11.95 12.86 2.02 3.22 4.49 6.47 8.99 11.17 13.12 14.01 2.11 3.51 4.89 6.38 7.67 9.74 11.15 12.58 14.84

0.1781 0.2976 0.4135 0.5201 0.6306 0.7168 0.8352 0.9027 0.1745 0.2703 0.3640 0.4969 0.6430 0.7515 0.8528 0.9262 0.1465 0.2382 0.3198 0.4063 0.4752 0.5773 0.6470 0.7298 0.8683

0.9946 0.9955 0.9953 0.9945 0.9925 0.9892 0.9784 0.9709 0.9886 0.9910 0.9917 0.9912 0.9884 0.9833 0.9790 0.9650 0.9873 0.9891 0.9894 0.9898 0.9887 0.9861 0.9832 0.9758 0.9335

5.5845 3.3451 2.4070 1.9121 1.5739 1.3800 1.1715 1.0756 5.6662 3.6670 2.7243 1.9946 1.5357 1.3084 1.1479 1.0419 6.7392 4.1524 3.0938 2.4361 2.0806 1.7081 1.5196 1.3371 1.0751

0.0066 0.0064 0.0080 0.0115 0.0203 0.0381 0.1311 0.2991 0.0138 0.0123 0.0131 0.0175 0.0326 0.0672 0.1427 0.4741 0.0149 0.0143 0.0156 0.0172 0.0215 0.0329 0.0476 0.0895 0.5049

363.15

373.15


D



Article

Table 7. Phase Equilibrium Data for CO2 (1) + Decane (2) Systemta

Table 9. Phase Equilibrium Data for CO2 (1) + Dodecane (2) Systema

T, K

P, MPa

x1

y1

K1

K2

T, K

P, MPa

x1

y1

K1

K2

353.15

2.92 4.24 6.12 8.46 10.58 12.07 13.57 14.59 2.93 4.39 7.30 10.15 12.17 14.21 15.40 3.33 5.46 6.32 8.51 10.52 11.89 13.57 15.29

0.2179 0.3071 0.4246 0.5573 0.6675 0.7419 0.8179 0.8777 0.2077 0.3015 0.4673 0.6099 0.7016 0.8004 0.8595 0.2138 0.3359 0.3403 0.4872 0.5758 0.6321 0.7002 0.7915

0.9966 0.9968 0.9963 0.9948 0.9917 0.9873 0.9784 0.9647 0.9951 0.9955 0.9945 0.9914 0.9868 0.9844 0.9738 0.9937 0.9932 0.9930 0.9917 0.9876 0.9830 0.9783 0.9638

4.5722 3.2454 2.3466 1.7852 1.4856 1.3306 1.1961 1.0991 4.7911 3.3023 2.1283 1.6255 1.4065 1.2299 1.1331 4.6478 2.9568 2.9180 2.0355 1.7152 1.5551 1.3972 1.2177

0.0044 0.0046 0.0064 0.0117 0.0249 0.0492 0.1187 0.2887 0.0062 0.0064 0.0103 0.0221 0.0442 0.0784 0.1864 0.0080 0.0102 0.0106 0.0162 0.0292 0.0462 0.0724 0.1736

353.15

1.17 2.47 3.34 5.98 8.35 10.27 12.49 14.37 1.69 3.77 4.87 6.72 8.93 10.61 12.93 14.40 16.54 3.49 4.93 6.62 8.06 9.62 11.11 12.59 13.83 15.02 15.79 17.54

0.1034 0.2091 0.2764 0.4604 0.6034 0.7067 0.8139 0.8925 0.1372 0.2886 0.3608 0.4726 0.5919 0.6727 0.7728 0.8349 0.9194 0.2348 0.3197 0.4106 0.4825 0.5526 0.6158 0.6738 0.7205 0.7615 0.7865 0.8451

0.9997 0.9997 0.9997 0.9996 0.9992 0.9985 0.9963 0.9914 0.9996 0.9996 0.9995 0.9993 0.9988 0.9982 0.9961 0.9854 0.9739 0.9954 0.9959 0.9962 0.9964 0.9964 0.9952 0.9931 0.9905 0.9846 0.9772 0.9584

9.6707 4.7803 3.6167 2.1713 1.6559 1.4128 1.2242 1.1108 7.2850 3.4639 2.7704 2.1143 1.6875 1.4839 1.2889 1.1933 1.0843 4.2393 3.1151 3.1151 2.0651 1.8031 1.6161 1.4739 1.3747 1.2929 1.2425 1.1341

0.0003 0.0004 0.0004 0.0007 0.0020 0.0051 0.0199 0.0799 0.0004 0.0006 0.0008 0.00133 0.00294 0.0055 0.01717 0.0219 0.03789 0.0060 0.0060 0.0064 0.0069 0.0081 0.0125 0.0212 0.0339 0.0646 0.1068 0.2686

363.15

373.15

363.15

373.15

a

Standard uncertainties u are u(T) = 0.10 K, u(P) = 0.01 MPa, and uc(x1) = uc(y1) = 0.0512.

Table 8. Phase Equilibrium Data for CO2 (1) + Undecane (2) Systema T, K

P, MPa

x1

y1

K1

K2

353.15

2.86 3.99 5.83 7.08 8.51 10.43 11.86 12.92 14.47 1.99 3.86 6.02 7.59 10.39 12.46 13.95 3.64 5.57 7.04 8.49 9.82 11.53 13.14 15.14 16.31

0.1919 0.3213 0.4852 0.5857 0.6683 0.7631 0.8301 0.8658 0.9348 0.1552 0.2869 0.4223 0.5110 0.6526 0.7449 0.7986 0.2248 0.3282 0.3985 0.4628 0.5191 0.5852 0.6407 0.7151 0.7615

0.9979 0.9981 0.9979 0.9973 0.9964 0.9944 0.9911 0.9879 0.9872 0.9967 0.9973 0.9971 0.9964 0.9939 0.9901 0.9849 0.9962 0.9965 0.9958 0.9950 0.9934 0.9918 0.9894 0.9805 0.9595

5.2013 3.1066 2.0569 1.7026 1.4909 1.3032 1.1939 1.1411 1.0668 6.4242 3.4754 2.3610 1.9497 1.5230 1.3291 1.2459 4.4315 3.0363 2.4989 2.1500 1.9137 1.6948 1.5443 1.3711 1.2600

0.0026 0.0028 0.0041 0.0065 0.0109 0.0236 0.0524 0.0742 0.1613 0.0039 0.0038 0.0050 0.0074 0.0176 0.0388 0.0612 0.0049 0.0052 0.0069 0.0093 0.0137 0.0197 0.0295 0.0683 0.1704

363.15

373.15


The liquid was pumped through one magnetic recirculation pump, while vapor was sucked into another one simultaneously. The recirculation of both liquid and vapor was advantageous to significantly promote mass transfer and obviously reduce the equilibrium time. Another serious drawback of the existing apparatuses is that the withdrawal of the representative samples from the cell can easily modify the equilibrium of the system, and their transport to analytical devices might change their homogeneity. When sampling the liquid phase in a volatile/nonvolatile system, the lighter component in the liquid phase flashes preferentially to the heavier component. A liquid mixture, containing relatively light and heavy components, undergoes a distillation process when it is throttled across a valve from a high pressure region to a low pressure region or to an evacuated space. As a result, the concentration of the light component in the throttled liquid passing through the valve has a higher concentration of light component than the liquid upstream of the valve. The sample obtained for analysis is not a representative sample of the equilibrium liquid phase. Thus, most previous research dealing with a complex system centered on a synthetic apparatus and tried to avoid sampling. By contrast, the analysis of the equilibrium composition presented in this study was accomplished by taking a small amount of the circulating phases through two customized 6-port 2-pos valves (Cheminert, model C2-2206EH3Y, VICI AG International) which were connected online to a gas chromatograph (model SP6890, Rainbow Chemical Instrument

a

Standard uncertainties u are u(T) = 0.10 K, u(P) = 0.01 MPa, uc(x1) = uc(y1) = 0.0512.

using permanent magnet ferrite bricks surrounding a nonmagnetic steel casing and housed inside a magnetic steel piston. E



Article

Table 10. Phase Equilibrium Data for CO2 (1) + Tridecane (2) Systema

Table 11. Phase Equilibrium Data for CO2 (1) + Tetradecane (2) Systema

T, K

P, MPa

x1

y1

K1

K2

T, K

P, MPa

x1

y1

K1

K2

353.15

0.95 2.54 3.67 5.54 7.12 8.83 10.37 12.08 14.01 1.81 3.77 4.81 6.67 8.48 11.07 12.38 13.75 1.80 3.39 5.15 7.88 10.14 12.45 14.55

0.0909 0.2321 0.3256 0.4682 0.5759 0.6793 0.7604 0.8349 0.9036 0.1425 0.2822 0.3507 0.4634 0.5622 0.6876 0.7442 0.7992 0.1137 0.2052 0.2961 0.4206 0.5090 0.5878 0.6507

0.9993 0.9995 0.9995 0.9993 0.9991 0.9985 0.9976 0.9957 0.9906 0.9992 0.9992 0.9992 0.9989 0.9984 0.9969 0.9955 0.9930 0.9987 0.9990 0.9988 0.9983 0.9975 0.9959 0.9933

10.9834 4.3059 3.0695 2.1345 1.7349 1.4699 1.3119 1.1925 1.0963 7.0106 3.5403 2.8489 2.1557 1.7759 1.4498 1.3377 1.2425 8.7799 4.8674 3.3737 2.3737 1.9596 1.6944 1.5266

0.0006 0.0007 0.0007 0.0013 0.0021 0.0047 0.0100 0.0261 0.0975 0.0009 0.0011 0.0012 0.0021 0.0036 0.0099 0.0176 0.0349 0.0015 0.0013 0.0017 0.0029 0.0051 0.0099 0.0192

353.15

1.02 2.59 4.03 6.21 8.71 10.83 12.13 13.13 14.49 15.03 15.60 15.68 1.21 3.60 5.71 8.72 9.95 11.47 12.78 14.14 15.54 16.64 1.71 2.81 3.72 7.21 10.16 12.70 16.00 18.81 20.86

0.0787 0.1921 0.2878 0.4195 0.5529 0.6536 0.7115 0.7552 0.8150 0.8401 0.8691 0.8732 0.0871 0.2429 0.3639 0.5136 0.5676 0.6300 0.6805 0.7301 0.7804 0.8212 0.1042 0.1657 0.2131 0.3731 0.4818 0.5577 0.6818 0.7318 0.7833

0.9997 0.9997 0.9997 0.9995 0.9990 0.9979 0.9966 0.9948 0.9906 0.9878 0.9833 0.9825 0.9995 0.9996 0.9994 0.9988 0.9984 0.9974 0.9961 0.9939 0.9902 0.9853 0.9993 0.9994 0.9994 0.9990 0.9982 0.9967 0.9871 0.9813 0.9752

12.7018 5.2029 3.4733 2.3828 1.8069 1.5267 1.4007 1.3172 1.2155 1.1759 1.1315 1.1254 11.4812 4.1149 2.7461 1.9447 1.7591 1.5831 1.4638 1.3615 1.2695 1.2016 9.5902 6.0314 4.6898 2.6776 2.0718 1.7872 1.4476 1.3405 1.2448

0.0003 0.0004 0.0005 0.0009 0.0022 0.0061 0.0118 0.0213 0.0508 0.0763 0.1275 0.1378 0.0005 0.0006 0.0009 0.0025 0.0037 0.0070 0.0122 0.0226 0.0446 0.0817 0.0007 0.0007 0.0008 0.0016 0.0035 0.0075 0.0408 0.0708 0.1154

363.15

373.15

363.15

373.15


Co., Ltd. in Shandong Province). The liquid or vapor flow was injected into the corresponding sampling loop while the 6-port valve was switched out of the gas chromatograph path. After the sampling loop was entirely filled with the extracted sample, the 6-port valve was switched back to the recirculation loop, and then the remaining sample was pushed back into the cell. All of these characteristics had potential to reduce the fluctuation of pressure and differential vaporization due to the sampling procedure. On this basis, the use of circuits, recirculation pumps, and 6-port valves not only helped to minimize the disturbance of equilibrium but also obtained reliable samplings and repeatable results. All the high-pressure view-cell, magnetic recirculation pumps, sampling valves, and stainless steel tubes were encased in a 20 mm thick jacket and 50 mm thick asbestos insulation layer. These jackets were connected to a constant temperature circulator, which could be set from 253.15 to 523.15 K. The pressure and temperature were measured by precision pressure transducers and resistance thermometers with a platinum probe, respectively. The calibration was done in a range of temperatures from 253.15 to 523.15 K, and the final uncertainty of the temperature measurements was estimated to be 0.10 K. The accuracies of the pressure transducers were factory calibrated and certified to 0.01 MPa at full scale. 2.3. Experimental Procedures. The apparatus was cleaned with 2-propanol and followed by purging several times with low pressure CO2 before starting the experiment. After a 24 h pressure maintaining test, the whole system was evacuated down to 7 kPa, and the computer began to record the temperature and pressure of the system continuously. When the gas pressures were stabilized within a few hours, CO2 was introduced from a high pressure cylinder (1) into the buffer

373.15

a


tank (2). At the same time, the temperature was set to a needed value by an external recirculating temperature-controlled bath. A total of 30 mL of n-alkane or hydrocarbons was injected into the view-cell (3) with the help of the vacuum inside the cell, and CO2 was charged into the view-cell (3) from the buffer tank (2). In this way, the amount of CO2 introduced in each injection step could be estimated from the difference between the pressure of the buffer tank (2) before and after loading. The multicomponent mixtures in the cell were then countercurrently recirculated to accelerate the attainment of equilibrium. The vapor was sucked into one magnetic recirculation pump (6) and bubbled from the bottom of the cell (V1−V2− 8−V3−6−V4), passing through all the coexisting liquid phases. The liquid was pumped through the other and dropped from the top of the cell (V6−6−V7−7−V8−V9), passing through the vapor space above the cell. The time required to achieve thermodynamic equilibrium, as determined from pressure measurements at operating temperature, was about 1.5 to 2 h under continuous recirculating. The pressure of the cell was then decreased in small decrements, each followed by a further equilibration period. In the case of mixed systems at equilibrium, it was usual practice to start sampling simultaneously from the two circulating phases. At least three or four samples from both vapor and liquid phases would be taken to minimize sample F



Article

Table 12. Phase Equilibrium Data for CO2 (1) + Pentadecane (2) Systema

Table 13. Phase Equilibrium Data for CO2 (1) + Hexadecane (2) Systema

T, K

P, MPa

x1

y1

K1

K2

T, K

P, MPa

x1

y1

K1

K2

353.15

1.04 2.50 3.85 5.81 7.12 8.60 9.62 10.59 11.80 12.87 13.51 14.36 1.27 4.29 6.29 7.93 9.13 10.87 11.67 12.94 13.04 14.17 14.73 2.05 3.87 6.30 7.76 8.58 10.31 11.58 13.03 14.41 15.43 16.06

0.0879 0.2032 0.3022 0.4298 0.5087 0.5908 0.6445 0.6925 0.7508 0.7987 0.8271 0.8621 0.1035 0.3184 0.4297 0.5290 0.5889 0.6682 0.7015 0.7516 0.7563 0.7927 0.8152 0.1522 0.2718 0.4118 0.4857 0.5247 0.6007 0.6517 0.7066 0.7563 0.7927 0.8152

0.9985 0.9982 0.9985 0.9981 0.9993 0.9990 0.9988 0.9982 0.9971 0.9957 0.9925 0.9883 0.9994 0.9995 0.9994 0.9991 0.9988 0.9982 0.9977 0.9967 0.9966 0.9964 0.9951 0.9997 0.9997 0.9995 0.9994 0.9992 0.9987 0.9981 0.997 0.9953 0.9933 0.9916

10.8180 4.8435 3.2942 2.3222 1.9644 1.6909 1.5497 1.4414 1.3281 1.2467 1.1999 1.1464 9.6560 3.1386 2.3259 1.8887 1.6960 1.4939 1.4222 1.3261 1.3177 1.2576 1.2232 6.5671 3.6774 2.4270 2.0578 1.9044 1.6627 1.5315 1.4110 1.3161 1.2531 1.2164

0.0538 0.0198 0.0065 0.0033 0.0014 0.0024 0.0034 0.0058 0.0116 0.0214 0.0434 0.0848 0.0007 0.0007 0.0011 0.0019 0.0029 0.0054 0.0077 0.0133 0.0140 0.0151 0.0157 0.0003 0.0004 0.0009 0.0012 0.0017 0.0033 0.0054 0.0102 0.0193 0.0323 0.0454

353.15

1.55 3.27 4.57 6.62 8.28 9.92 10.53 11.59 12.87 13.72 2.83 5.33 6.29 7.99 9.84 10.84 12.26 13.53 14.67 15.83 16.52 2.41 4.21 6.04 6.66 7.72 11.28 14.10 16.51 18.56

0.1074 0.2195 0.2997 0.4188 0.5093 0.5949 0.6255 0.6772 0.7386 0.7787 0.1826 0.3287 0.3804 0.4686 0.5591 0.6058 0.6694 0.7221 0.7609 0.8060 0.8305 0.1426 0.2400 0.3315 0.3610 0.4098 0.5594 0.6651 0.7499 0.8198

0.9999 0.9999 0.9999 0.9998 0.9997 0.9996 0.9994 0.9990 0.9983 0.9975 0.9999 0.9998 0.9998 0.9997 0.9995 0.9993 0.9988 0.9972 0.9955 0.9939 0.9921 0.9999 0.9998 0.9998 0.9998 0.9997 0.9991 0.9978 0.9952 0.9909

9.3125 4.5549 3.3366 2.3872 1.9627 1.6803 1.5978 1.4752 1.3516 1.2810 5.4751 3.0416 2.6286 2.1335 1.7877 1.6496 1.4922 1.3782 1.3084 1.2356 1.1993 7.0135 4.1665 3.0164 2.7695 2.4395 1.7860 1.5002 1.327 1.2087

0.0001 0.0001 0.0001 0.0003 0.0006 0.0010 0.0016 0.0031 0.0065 0.0113 0.0001 0.0003 0.0003 0.0006 0.0011 0.0018 0.0036 0.0173 0.0186 0.0211 0.0231 0.0001 0.0003 0.0003 0.0003 0.0005 0.0020 0.0066 0.0192 0.0505

363.15

373.15

363.15

373.15

a


tetradecane, pentadecane, and hexadecane) were performed at 353.15, 363.15, and 373.15 K. Multicomponent phase equilibrium of CO2 + crude oil + n-alkanes (hexane, octane, nonane, undecane, and dodecane) was measured under a representative reservoir temperature of 373.15 K. Experimental results and Ki (Ki = yi/xi, partitioning coefficient of component i) are listed in Tables 5−14. The standard uncertainty estimation in phase composition measurements was evaluated by contributions of the calibration of the chromatograph, pressure, and temperature measurements. The combined standard uncertainty of the composition measurements was therefore obtained as follows:49,55

a


cross-contamination or entrainment during sampling procedure. Moreover, the special design of the magnetic recirculation pump and the small volume of the sampling loops were capable of preventing undesirable pressure gradients across the viewcell and serious disturbance of the equilibrium. The analytical system and procedure reported in the literature was performed to determine the compositions of phases in equilibrium.48

⎛ ∂x ⎞2 ⎛ ∂x ⎞2 uc 2(xi) = ⎜ i ⎟ u 2(p) + ⎜ i ⎟ u 2(T ) ⎝ ∂T ⎠ ⎝ ∂p ⎠

3. EXPERIMENTAL RESULTS AND DISCUSSION 3.1. Validation of the Apparatus. The mixture of CO2 + hexane was chosen to validate the apparatus through comparison with published experimental data. The equilibrium temperature T, equilibrium pressure P, CO2 mole fraction x1 in liquid phase, and CO2 mole fraction y1 in vapor phase are listed in Table 4. Results for vapor−liquid equilibrium comparison of CO2 + hexane are plotted in Figure 3. Good agreement was found between the experimental values and those reported in the literature, which indicated that the apparatus was reliable and effective for measuring the phase equilibrium data.53,54 3.2. Experimental Results for CO2 + n-Alkanes and CO2 + Crude Oil + n-Alkanes. Studies for CO2 + n-alkanes (octane, nonane, decane, undecane, dodecane, tridecane,

⎛ ∂x ∂nj ⎞2 ⎟⎟ u 2(Aj) + ∑ ⎜⎜ i ∂ n ∂ A j j⎠ j=1 ⎝ 2

(1)

Here, uc(xi) represents the standard uncertainty of the composition and u(Aj) is the standard uncertainty related to the calibration of the chromatograph for component, u(T) = 0.1 K, u(P) = 0.01 MPa. The relative standard uncertainties for the chromatographic were within 0.0203 for each component. The maximum standard uncertainty (maximum error, correlated uncertainty) of liquid and vapor phase composition measurements was estimated to be about 0.0512. G



Article

Table 14. Phase Equilibrium Data for CO2 (1) + Multicomponent System (2) at 373.15 Ka P, MPa 4.37 6.03 9.20 11.48 13.27 15.38 4.49 6.43 8.69 10.38 12.44 14.34 0.6085 0.7068 0.7567 0.7836 0.8306 0.8465 3.53 6.04 8.93 10.65 12.66 14.84 0.5331 0.6666 0.7281 0.7615 0.7875 0.8082

x1

y1

P, MPa

x1

Crude Oil + Hexane (1% mass fraction) 0.7105 0.9455 17.11 0.8978 0.7854 0.9606 18.85 0.9053 0.8351 0.9742 20.29 0.9082 0.8657 0.9793 21.58 0.9171 0.8773 0.9822 23.08 0.9217 0.8859 0.9846 24.30 0.9453 Crude Oil + Octane (1% mass fraction) 0.6399 0.9863 16.72 0.8783 0.7548 0.9906 18.46 0.8894 0.8005 0.9931 20.05 0.9002 0.8227 0.9942 21.33 0.9044 0.8442 0.9952 23.52 0.9184 0.8665 0.9958 24.10 0.9280 Crude Oil + Nonane (1% mass fraction) 4.72 0.9348 0.8656 17.52 6.71 0.9541 0.8780 19.47 8.72 0.9647 0.8943 21.77 10.56 0.9709 0.9137 23.84 13.57 0.9774 0.9280 24.90 15.68 0.9804 Crude Oil + Undecane (1% mass fraction) 0.5388 0.9210 16.35 0.8418 0.6629 0.95399 18.34 0.8614 0.7327 0.96896 20.34 0.8758 0.7721 0.9740 21.92 0.8931 0.8002 0.9781 23.12 0.9057 0.8278 0.9813 24.90 0.9280 Crude Oil + Dodecane (1% mass fraction) 3.56 0.9133 0.8359 18.72 6.80 0.9547 0.8521 20.23 9.84 0.9687 0.8664 21.82 11.64 0.9736 0.8809 23.12 14.35 0.9786 0.9057 24.98 16.25 0.9811

y1 0.9862 0.9874 0.9883 0.9890 0.9897 0.9874 0.9964 0.9967 0.9970 0.9972 0.9975 0.9711

Figure 5. Comparison of experimental and published equilibria data for CO2 (1) + n-alkanes (2) at 373.15 K. The filled symbols correspond to published experimental data; the open symbols represented the data gathered during this work.

0.9825 0.9843 0.98592 0.9802 0.9711

Table 15. Summary of the Models Used To Represent CO2 + Alkanes Phase Equilibrium

0.9831 0.9849 0.9864 0.9874 0.9803 0.9711 0.9836 0.9848 0.9859 0.9843 0.9802

abbreviation

EOS

mixing rules

parameter numbers

YQE-1 PR-1 PR-2 PR-3 PRSV-1 PR-LCVM

quartic equation PR PR PR PRSV PR

VDW-167 VDW-168 VDW-267,68 Panagiotopoulos−Reid69 VDW-167 LCVM70

1 1 2 2 1 2

The new phase equilibria data for CO2 + n-alkanes were compared with selected literature values determined by using different research methods.56−61 Figure 4 and Figure 5 showed that the VLE data obtained were found to be inconsistent with published values, and the standard deviations for the pressure and vapor compositions in comparison with the reported literature data were found to be within 5%.


4. MODELS, THEORY, AND CALCULATIONS An accurate characterization of fluid properties and phase behavior is critical for practical design, construction, optimization, and industrialization in various industrial and scientific applications. However, prediction of the phase behavior of real reservoir fluids is extremely difficult owing to the complex intermolecular forces of attraction and repulsion. Equations of state (EOS) are typically used to determine the properties, phase conditions, and composition of vapor−liquid coexistence. The accuracy of EOS depends on its ability to model the attractions and the repulsions between molecules over a wide range of temperatures and pressures. Soave−Redlich−Kwong (SRK) and Peng−Robinson (PR) equations of state, derived from the basic ideal gas law along with other corrections, are more preferred in the oil, gas, petroleum, and petrochemical applications because of their high precision, high reliability, and greater simplicity. Considering the complicated compositional characteristics of crude oil, three thermodynamic models of PR, PRSV-1, and YQE coupled with various mixing rules were chosen to investigate phase equilibrium in binary and multicomponent systems.

Figure 4. Comparison of experimental and published equilibria data for CO2 (1) + n-alkanes (2) at 353.15 K. The filled symbols correspond to published experimental data; the open symbols represented the data gathered during this work. H



Article

Table 16. BIP of CO2 + Alkanes Calculated by PR-1, PR-2, and PR-3 EOS PR-1 systems

PR-2

k12

k12

n12

k12

k21

353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15

0.0732 0.0818 0.0915 0.1141 0.0594 0.1076 0.1069 0.1193 0.1205 0.0213 0.0765 0.1099 0.1321 0.1006 0.0713 0.0480 0.0200 0.0701 0.1464 0.0809 0.1199 0.0608 0.0983 0.0759 0.0987 0.1088 0.0276

0.2529 0.1076 0.2236 0.1792 0.2294 0.2481 0.0563 0.1173 0.1891 0.1590 0.1474 0.1822 0.1047 0.1059 0.1136 0.1200 0.0725 0.1093 0.0519 0.1516 0.0587 0.1071 0.1211 0.1103 0.1243 0.0891 0.1099

−0.0618 −0.0982 −0.1559 −0.1379 −0.0465 −0.0695 −0.1857 −0.1385 −0.1033 −0.0653 −0.0988 −0.087 −0.0814 −0.0793 −0.0765 −0.0695 −0.1144 −0.1120 −0.1295 −0.0912 −0.1352 −0.0623 −0.0915 −0.1254 −0.0717 −0.1065 −0.1702

0.1910 −0.0686 0.0529 0.0655 0.6949 0.1237 0.0007 0.4975 0.0123 0.0031 0.2748 0.1007 0.1812 0.1664 0.0571 0.1243 0.2810 0.1450 −0.0066 0.1702 0.0299 0.0981 0.1209 0.1049 0.0308 0.0234 0.2028

0.0602 0.1375 0.1432 0.1080 −0.0390 0.0888 0.1297 0.0115 0.1341 0.0513 0.0337 0.1199 0.0067 0.0293 0.1010 0.0797 −0.0308 0.1277 0.1637 0.0644 0.1957 0.0703 0.0578 0.0831 0.1224 0.1329 −0.0114

n-octane

n-nonane

n-decane

n-undecane

n-dodecane

n-tridecane

n-tetradecane

n-pentadecane

n-hexadecane

4.1. PR and PRSV-1 Models. The Peng−Robison (PR) EOS is generally recommended to determine phase boundaries and the phase conditions of complex mixtures containing supercritical fluid. The PR standard EOS is represented in eq 2. p=

a(T ) RT − v−b v(v + b) + b(v − b)

(3)

α(TR ) = [1 + m(1 − TR 0.5)]2

(4)

m = 0.37464 + 1.5422ω − 0.26922ω 2

(5)

RTc Pc

m = (0.378893 + 1.4897135ω − 0.171318482ω 2 ⎡ ⎛ T ⎞0.5⎤⎡ ⎛ T ⎞⎤ + 0.0196554ω3) + k1⎢1 + ⎜ ⎟ ⎥⎢0.7 − ⎜ ⎟⎥ ⎢⎣ ⎝ Tc ⎠ ⎥⎦⎢⎣ ⎝ Tc ⎠⎥⎦ (8)

where k1 is an adjustable parameter characteristic of each pure component and the optimization of k1 values was performed using a particular set of critical constants. 4.2. YQE ModelA Modified Quartic Equation of State. A modified quartic version of generalized EOS based on our previous studies is proposed to describe thermodynamic properties for the chosen mixtures.2,64 Both the repulsive term of cubic chain-of-rotators (CCOR) EOS and the attractive term of Patel−Teja (PT) EOS are introduced into the quartic EOS. The presented EOS therefore has the following form:65,66

(2)

⎛ R2T 2 ⎞ c ⎟ a(T ) = 0.45724⎜⎜ ⎟α(TR ) ⎝ pc ⎠

b = 0.07780

PR-3

temperature (K)

z=

where p is the pressure, T is the temperature, v is the molar volume, Tc is the critical temperature, Pc is the critical pressure, R is the universal gas constant, ω is the acentric factor, and TR (TR = T/Tc) is the reduced temperature. Stryjek and Vera proposed the following modified temperature dependent function α(TR) for the PR EOS to extend the range of applicability to polar components:62,63 2

α(TR ) = [1 + m(1 − TR )]

(9)

where z is the compressibility factor, v is the molar volume, and a, b, and c are the parameters.

(6)

0.5

v + 0.77b av − v − 0.42b v(v + b) + (v − b)c

a = acα(TR )

(10)

ac = Ωa

RTc Pc

(11)

b = Ωb

RTc Pc

(12)

RTc Pc

(13)

c = Ωc

(7) I



Article

where

Ωc =

Ωa = 3ζ 2 + 3Z0ζ + 0.42Ω b 2 + 1.42Ω bΩc + 1.77Ω b + Ωc

(14)

Ω b Ωc

(17) (18)

λ(TR), a function of reduced temperature, is expressed as eq 19.

ζ3

(15) 2

Ω b = 0.030889 − 2.31047ζ + 9.25722ζ − 16.6452ζ 4

ζ 3 + 0.77Ω b 2

ζ = Zcλ(TR )

2

z 0 = 0.77

ζ 3 − 3ζ 4 − 0.58ζ 3Ω b

+ 15.24ζ − 5.5797ζ

0.12 ⎧ ] + S2(1 − TR )0.5 TR < 1 ⎪1 + S [2 − (1 − T ) 1 R λ(TR ) = ⎨ ⎪ TR ≥ 1 ⎩1

3

5

(19)

At the critical point, λ(TR) = 1 and ζ = Zc.

(16)

⎧⎡ ⎤2 ⎪ ⎢1 + S ⎛⎜ 1 ⎞⎟ − S (1 − T 2)⎥ TR < 1.5 3 4 R 0.5 ⎪ ⎢⎣ ⎥⎦ ⎝ TR ⎠ ⎪ ⎪ α(TR ) = ⎨1 TR = 1 ⎪ ⎪ ⎡ k (1 − T 0.3) + k (1 − T 0.5)2 + k (1 − T 0.2)3 ⎤ R 2 R 3 R ⎥ TR > 1.5 ⎪ exp⎢ 1 0.5 ⎪ ⎣ T ⎦ R ⎩

For nonpolar substances, S1, S2, S3, and S4 are calculated by eqs 21−24:

was the best-fit model in describing phase equilibrium for both binary and multicomponent systems. The predictions of the YQE-1 model for CO2 (1) + alkanes (2) at T = 353.15, 363.15, and 373.15 K are shown along with the experimental data in Figure 6 and Figure 7. The results showed that the calculated solubility data by YQE-1 were in reasonably good agreement

S1 = −0.0135804 + 0.140845ω − 0.102508ω 2 + 0.199674ω3

(21)

S2 = 0.499075 + 0.184235ω − 0.301733ω 2 + 0.481977 ω3

(22) 2

Table 17. BIP of CO2 + Alkanes Calculated by YQE, PRSV-1, and PR-LCVM EOS

3

S3 = 1.72879 + 0.601242ω + 1.5677ω − 1.04434ω

YQE-1

PRSV-1

temperature (K)

k12

k12

g12

g12

353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15

0.8967 0.8772 0.8576 0.8757 0.9215 0.8895 0.8660 0.8715 0.8658 0.9014 0.8758 0.8461 0.8841 0.8852 0.8780 0.9200 0.8976 0.8553 0.8839 0.8837 0.8572 0.8707 0.8600 0.8934 0.9484 0.9566 0.9519

0.0833 0.1127 0.1199 0.1048 0.0537 0.1048 0.1078 0.1067 0.1218 0.0448 0.0798 0.1211 0.0648 0.0666 0.1049 0.0995 0.0185 0.1328 0.1127 0.0947 0.1252 0.0675 0.0892 0.0890 0.1127 0.1133 0.0444

−1964.2 5961.1 7118.3 1430.2 949.9 −2499.5 1529.2 2078.8 −2311.0 2957.6 −1145.4 −117.6 524.7 −2929.3 −2396.5 −3060.6 −255.8 −658.6 770.3 9974.3 −923.1 −3651.2 2282.1 9757.9 1152.1 9997.4 2843.5

1734.3 −1964.2 −3758.2 −1555.4 −2315.1 2192.3 −1657.0 −2321.5 2092.3 −3477.0 1084.2 −850.8 383.3 2517.6 807.5 2576.6 −918.4 −42.2 237.4 −4937 883.2 2977.8 −1818.9 −4961.4 −475.9 −4463.4 −3378.5

(23)

S4 = 0.110836 − 0.175204ω + 0.393393ω 2 − 0.0641687 ω3

(20)

systems n-octane

(24)

4.3. Comparison with Experiment. In order to extend a thermodynamic equation to mixtures, the characteristic constants of an equation of state must be obtained using mixing rules. A summary of models with various mixing rules used in this work are presented in Table 15. Binary interaction parameter (BIP), an adjustable parameter, was used in equations of phase equilibrium to help calibrate the extent of nonideality of a given mixture. All component parameters were obtained by regression analysis of the respective experimental solubility data in this work. Values of BIP for the EOS described in Sections 4.1 and 4.2 are given in Tables 16 and 17. As for the PR-LCVM model, g12 and g21 were interaction parameters for the NRTL equation. Furthermore, the concordance between the experimental data and the calculated values was established by average absolute relative deviation (AARD), which was generally used to evaluate the predictive effectiveness of these proposed models. The AARD for each binary system are given in Tables 18 and 19. For all investigated systems the values of AARD are lower than 20%. The PR-LCVM model gave a good representation for equilibrium pressure and CO2 mole fraction in the gas phase with an overall AARD of 3.74% and 0.16%. The YQE-1 model also gives an excellent agreement of equilibrium pressure and CO2 mole fraction in the gas phase with an overall AARD of 3.54% and 0.15%, respectively. Comparisons showed that the YQE-1

n-nonane

n-decane

n-undecane

n-dodecane

n-tridecane

n-tetradecane

n-pentadecane

n-hexadecane

J

PR-LCVM



Article

Table 18. Derivation Analysis of Equilibrium Pressure for CO2 + Alkanes AARDp (%) systems n-octane

n-nonane

n-decane

n-undecane

n-dodecane

n-tridecane

n-tetradecane

n-pentadecane

n-hexadecane

temperature (K)

YQE-1

PR-1

PR-2

PR-3

PRSV-1

PR-LCVM

353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15

2.37 3.55 2.46 4.34 3.94 4.74 3.65 6.79 2.31 3.15 6.01 3.02 5.45 6.18 3.41 4.94 5.01 5.46 1.62 1.27 1.66 1.26 2.58 1.39 3.14 3.24 2.53

2.95 4.41 3.21 6.49 6.97 4.98 3.99 8.82 2.54 4.15 6.86 3.30 6.79 11.62 3.95 5.93 5.78 5.66 1.89 3.74 2.00 1.34 3.53 2.67 3.11 4.02 3.36

2.60 4.31 3.23 6.33 6.20 8.09 3.96 7.81 2.56 4.29 7.06 2.36 6.52 7.35 3.42 5.64 7.41 5.62 1.83 3.53 2.18 1.49 3.18 2.57 3.16 6.51 3.46

3.85 5.18 3.68 6.63 18.14 8.98 3.98 14.95 3.36 4.56 10.67 4.29 10.52 10.23 3.43 7.97 10.25 6.28 2.20 4.52 5.66 4.14 3.68 3.73 3.23 6.61 3.66

2.40 4.22 3.10 5.49 6.52 4.94 3.91 7.17 2.41 3.83 6.33 3.45 6.21 7.16 3.42 4.96 5.75 6.12 1.72 2.49 1.85 1.44 2.78 3.68 3.06 3.99 3.18

2.39 3.56 2.73 5.03 4.26 4.80 3.65 6.79 2.38 3.20 6.25 3.36 5.47 6.19 3.40 4.96 5.54 5.72 1.62 1.63 1.83 1.43 2.73 2.84 2.67 3.31 3.17

Table 19. Derivation Analysis of CO2 Mole Fraction in Gas Phase for CO2 + Alkanes AARDy (%) systems n-octane

n-nonane

n-decane

n-undecane

n-dodecane

n-tridecane

n-tetradecane

n-pentadecane

n-hexadecane

temperature (K)

YQE-1

PR-1

PR-2

PR-3

PRSV-1

PR-LCVM

353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15 353.15 363.15 373.15

0.13 0.11 0.16 0.13 0.24 0.19 0.16 0.18 0.13 0.10 0.16 0.14 0.12 0.13 0.16 0.15 0.16 0.13 0.10 0.16 0.11 0.14 0.15 0.11 0.16 0.16 0.18

0.48 0.17 0.46 0.14 0.42 0.32 0.22 0.28 0.28 0.14 0.17 0.19 0.27 0.17 0.19 0.19 0.20 0.12 0.21 0.18 0.20 0.19 0.10 0.32 0.21 0.21 0.18

0.18 0.14 0.45 0.13 0.34 0.22 0.21 0.22 0.19 0.14 0.17 0.11 0.17 0.18 0.21 0.18 0.18 0.11 0.22 0.16 0.16 0.17 0.18 0.32 0.17 0.16 0.22

0.54 0.26 0.57 0.23 0.52 0.41 0.22 0.30 0.33 0.25 0.21 0.43 0.36 0.19 0.34 0.28 0.31 0.24 0.34 0.37 0.30 0.21 0.24 0.50 0.42 0.50 0.41

0.17 0.15 0.36 0.13 0.32 0.13 0.12 0.18 0.16 0.12 0.13 0.13 0.16 0.15 0.18 0.16 0.15 0.11 0.15 0.14 0.13 0.18 0.16 0.20 0.12 0.14 0.19

0.14 0.13 0.18 0.17 0.23 0.20 0.21 0.17 0.15 0.11 0.16 0.13 0.15 0.14 0.18 0.13 0.19 0.15 0.12 0.16 0.13 0.14 0.15 0.11 0.19 0.17 0.19

K



Article

Figure 6. Experimental data and calculated phase equilibrium behavior for CO2 (1) + n-alkanes (2). The filled symbols correspond to experimental data in this work; the solid lines () represent the calculated data by the YQE-1 model.

with the experimental ones. All the analysis demonstrated that the YQE-1 model was clearly the best choice here. 4.4. Group Contribution Method and Prediction of Multicomponent Systems. The largest obstacle in efficient design of processes dealing with hydrocarbons, such as enhanced oil recovery, pipeline transportation, petroleum processing, and refining, is the difficulty in precise prediction of their phase behavior and some thermodynamic properties. All experimental determinations of these properties proved to be difficult and subject to high uncertainty on account of technical equipment and thermal decomposition. It can be said that the presence of a complex mixture with diverse constituents, proportions, and molecular properties undoubtedly poses additional challenges on the accuracy of mathematical models. Group contribution method (GCM), also known as fragmental constants, is a technique to relate thermodynamic and other properties to molecular structures, such as single atom,

atom pairs, atom-centered substructures, molecular fragments, functional groups, and so on. Such a method appears to be as accurate as the experimental data used to establish the group contributions and has a wide range of applicability. In this work, it was assumed that a certain property of heavy crude oil sample is a function of six different groups.71 The number and types of the chosen functional groups contributing to the molecular diversity are listed in Table 20. The chemical structure of crude oil fractions can be calculated using semiempirical correlations of n−d−M−LP, in which available information about the linear programming (LP) of the crude oil composition, refractive index (n), molecular weight (M), and relative density (d) were all taken into account. The n−d−M method can be expressed as the following:72−79

L

W = (d − 0.851) − 1.11(n − 1.475)

(25)

V = 2.51(n − 1.475) − (d − 0.851)

(26)



Article

Figure 7. Experimental data and calculated phase equilibrium behavior for CO2 (1) + n-alkanes (2). The filled symbols correspond to experimental data in this work; the solid lines () represent the calculated data by the YQE-1 model.

Table 20. Group Composition of the Crude Oil

when W < 0,

Table 21. BIP and ADD for CO2 (1) + Crude Oil (2) + Alkanes (3) Calculated by YQE-1 systems

kij

AARDP (%) AARDY (%)

k12 = 0.9879; k13 = 0.8720; k23 = 0.9753 crude oil + octane k12 = 0.9951; k13 = 0.8643; k23 = 0.9626 crude oil + nonane k12 = 0.9865; k13 = 0.8526; k23 = 0.9578 crude oil + undecane k12 = 0.9912; k13 = 0.8387; k23 = 0.9437 crude oil + dodecane k12 = 0.9987; k13 = 0.8921; k23 = 0.9515 crude oil + hexane

3.65

0.24

4.31

0.29

2.97

0.19

4.03

0.23

3.15

0.16

C R = 1440W − 3S + 10600/M

(30)

C N% = C R % − CA %

(31)

C P% = 1 − C R %

(32)

where S is the number of sulfur, CA is the aromatic ring carbons, CR is the cycloalkane ring carbons, and CA%, CR%, CP%, and CN% are the percentage of carbon atoms on the aromatic ring, total ring, cycloalkane ring, and alkyl chain, respectively. The critical properties required for the applied equation were estimated by Constantinou−Gani (G-C) group contribution method on a two-level basis according to the following model:80,81

when V > 0,

CA = 430V + 3660/M

(27)

Tc = 181.728 × ln(∑ niΔTci +

when V < 0,

CA = 670V + 3660/M

(28)

Pc = 0.13705 + 0.1

when W > 0,

C R = 820W − 3S + 10000/M

(29)

× (0.100220 + M

∑ niΔpci

∑ njΔTcj)

+

∑ njΔpcj )−2

(33)

(34)



Article

best-fit model in describing multicomponent phase equilibrium, which could bring positive impacts on technological developments of CO2 reuse.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (X. Gui). ORCID

Maohong Fan: 0000-0003-1334-7292 Funding

This research is supported by the National Natural Science Foundation of China (NSFC 21306088), National Natural Science Foundation of China (NSFC 21676145), and Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD, China).

Figure 8. Experimental data and calculated phase equilibrium behavior for CO2 (1) + crude oil (2) + alkanes (3) at 373.15 K. The filled symbols correspond to experimental data in this work; the solid lines () represent the calculated data by the YQE-1 model.

ω = 0.4085 × (1.1507 +

∑ niωi + A ∑ njωj)

Notes

The authors declare no competing financial interest.

■

(35)

REFERENCES

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The entire methodology was established without a consideration of the neighboring group participation ability. Ci is the contribution of a first-order group type i, Cj is the contribution of a second-order group type j, and the value of A generally accepted is 0. The calculated critical properties of crude oil were Tc = 903 K, Pc = 0.87 MPa, and ω = 1.05. The AARD were listed together with the adjustable BIP parameters for CO2 + crude oil + alkanes (1% mass fraction) in Table 21. All component parameters were obtained by fitting them on its experimental solubility data. The phase equilibrium behavior for CO2 + crude oil + alkanes was simulated by using YQE-1 under the representative oil reservoir temperature 373.15 K. From Figure 8, the calculated values were found to be in good agreement with the experimental data and simultaneously showed that the YQE-1 approach can be used to model multicomponent system equilibrium with better correlation accuracy.

5. CONCLUSIONS An analytical apparatus was presented to investigate phase behavior of complex real fluids. Special considerations should be taken into account for apparatus design, which greatly influenced the reliability and accuracy of phase equilibrium data. Flexible design of the magnetic recirculation pumps and the small volume of sampling loops effectively prevented undesirable pressure gradients across the equilibrium cell and serious disturbance of the equilibrium during the sampling procedure. The apparatus was validated by means of isothermal vapor−liquid equilibrium data for CO2 + hexane at temperatures of T = 313.15 K and T = 353.15 K. High pressure phase equilibria data of CO2 + alkanes and CO2 + crude oil + alkanes were measured from 353.15 to 373.15 K. Three thermodynamic models of RR, PRSV, and YQE, based on the Peng− Robinson and a modified quartic equations of state coupled with various mixing rules, were suggested to represent phase equilibrium in both binary and multicomponent systems. The concordance between the experimental data and the calculated values for all investigated systems was evaluated by AARD. Analysis results showed that the YQE-1 model was the N



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