Application of Highly Accurate Phase-Equilibrium Models for CO2

Article pubs.acs.org/IECR

Application of Highly Accurate Phase-Equilibrium Models for CO2 Freezing Prediction of Natural Gas System Yajun Li,* Canteng Gong, and Yue Li Key Lab of Heat Transfer Enhancement and Energy Conservation of the Ministry of Education, South China University of Technology, Shaw Engineering Building, 381 Wushan Road, 510640 Guangzhou, Guangdong, P. R. China ABSTRACT: It is of great engineering significance to find an accurate model to predict CO2 freezing and avoid plugging in the light hydrocarbon separation process of natural gas. Research starts from CO2 freezing in simple CH4−CO2 binary systems. By use of a traditional model based on the Antoine equation, the calculated freezing temperature in liquid−solid equilibrium (LSE) is not as accurate as that in vapor−solid equilibrium (VSE). Then a new thermodynamic method of reference state of hypothetical fluid is used to replace LSE model based on the Antoine equation to calculate solid CO2 fugacity. The improved phase-equilibrium model based on GERG-2008 is proved to be the most accurate one to calculate CO2 freezing temperature, in which the Antoine equation is used in VSE model while reference state method is used in LSE model. Compared with experimental data, the calculated results also show a higher accuracy in complex natural gas system. Besides, the improved phase-equilibrium model is applied in the actual light hydrocarbon separation process to research the CO2 freezing phenomenon, which explains wide applicability of the new model. likely to solidify from gas and liquid and finally precipitate. Solid CO2 is most likely to form at these locations in the process which is shown in Figure 1. Once the CO2 freezing and plugging occur, the equipment will be jammed and the whole process has to be shut down, which will have a great influence on the normal operation of the light hydrocarbon separation device.2−6 Therefore, the design of separation devices and the operating condition should take CO2 freezing temperature into consideration to avoid CO2 freezing in actual production process. At present, most of the research about CO2 freezing temperature focuses on the simple CH4−CO2 binary systems. In these works,7−9 phase-equilibrium model is established based on the thermodynamic criterion that CO2 fugacity in partial phase is equal to each other. The equation of state (EoS) such as Peng−Robinson (PR), RK−Soave, Lee−Kester− Plocker is mainly used for calculation. Moreover, CO2 freezing temperature by the phase-equilibrium model is compared with the experimental data, which reveal that PR equation shows a higher accuracy and then is used the most;7,8 ZareNezhad9 designed an iterative algorithm to optimize the binary interaction parameters in PR equation, which then are put into the phase-equilibrium model for calculation. The results show a higher accuracy. In addition to the widely used method of EoS, CO2 freezing can be predicted by using an activity coefficient model. W. S. Lin et al.10 used the regular-solubility

1. INTRODUCTION Ethylene yield is an important index that measures the development level of petrochemical industry of a country. In China, the equivalent consumption of ethylene shows an increasing tendency over the years and is twice as much as its production capacity. The supply gap of ethylene is rather large: almost half of the ethylene depends on import due to the resource lack in China.1 There exist abundant high value hydrocarbon resources such as ethane and propane, which can be cracked to prepare ethylene. It helps to relieve the dilemma in China that ethylene is in short supply and has a large external dependency. So the light hydrocarbon in natural gas must be recycled and reused. Light hydrocarbon separation of natural gas is a process in which CH4 is separated from the heavier component such as C2H6, C3H8, C4H10, etc. in demethanizer column. Natural gas is a mixture containing not only hydrocarbon gases such as C1−5 but also non-hydrocarbon gases like N2 and CO2. Due to the limited solubility of CO2 in vapor and liquid, solid CO2 starts to generate and precipitate if the content of CO2 in vapor or liquid exceeds its saturated solubility in the separation process. The formation of solid CO2 is closely related to the composition of feed gas and the operating condition of system. When system pressure is settled, the temperature at which the solid CO2 begins to form rises with content of CO2 in feed gas; when the composition of feed gas is settled, the temperature margin of CO2 freezing decreases with operating pressure. It means that the possibility of forming solid CO2 increases. In the separation process to recycle light hydrocarbon, all the streams are under cryogenic condition and the operating temperature can reach −90 to −100 °C, under which CO2 is © XXXX American Chemical Society

Received: January 24, 2016 Revised: April 22, 2016 Accepted: April 29, 2016

A

DOI: 10.1021/acs.iecr.6b00339 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

Figure 1. Actual process of hydrocarbon separation.

2. COMPARISON BETWEEN DIFFERENT EOSS FOR CALCULATING CO2 FREEZING TEMPERATURE Calculations of CO2 freezing temperature are based on the vapor−solid and liquid−solid equilibrium (VSE and LSE) model according to thermodynamic criterion that fugacity of CO2 in partial phase is equal when the system attains phase equilibrium. Fugacity of CO2 in vapor, liquid, and solid can respectively be calculated by eqs 1, 2, and 3.

theory and the modified Scatchard−Hildebrand equation to calculate the solubility of solid CO2 in saturated liquid methane based on ideal solution. Activity coefficient model is applicable to multicomponent mixtures and is capable of handling the expected level of nonideality. However, it does have some limitations.3 Thus, there is hardly any research that uses activity coefficient model to predict CO2 freezing in natural gas systems. With the deepening of the research on natural gas, Kunz et al.11 proposed a new EoS named GERG-2008 which can be used in natural gas systems. It has been proved that gas properties calculated by the equation are rather accurate. Florian et al.12and Gong et al.13 compare GERG-2008 EoS with traditional EoS such as PR, RK−Soave and LK−Plocker, and the analysis indicates highly accuracy and wide applicability of GERG-2008. To sum up, the research on CO2 freezing mostly focus on the simple CH4−CO2 binary systems and CO2 freezing temperature is calculated by traditional phase-equilibrium model. In view of the present research situation, this article starts from CO2 freezing phenomenon in simple CH4−CO2 binary systems and then proposes GERG-2008 EoS to calculate CO2 freezing temperature in multicomponent natural gas systems. Besides, referring to the reference state method which is widely used for the calculation of solid solubility, the method of reference state of hypothetical fluid is designed to calculate fugacity of pure solid CO2, which is a big improvement to the traditional LSE model. Then the improved model is applied in the multicomponent natural systems to predict CO2 freezing. After a great amount of calculation, the data are compared with the experiment data from literature. It can be concluded that the results are more accurate when the improved phaseequilibrium model is adopted for calculating CO2 freezing temperature under different conditions. What’s more, the model is more suitable for actual complex multicomponent natural gas systems. Then the new model is applied in the light hydrocarbon separation process of natural gas, which indicates its wide applicability.

V

V ̂ fCO = yCO ϕCO p 2

2

(1)

2

L

L ̂ fCO = xCO2ϕCO p

(2)

⎡VS ⎤ ̂S = ϕ Sat p Sat exp⎢ CO2 (p − pSat )⎥ fCO CO2 CO2 CO2 ⎥ 2 ⎢⎣ RT ⎦

(3)

2

2

When vapor−solid and liquid−solid systems where solid CO2 is generated reach equilibrium, the phase-equilibrium model can be established as follows to calculate CO2 freezing temperature under different pressures. ⎧ ⎡ S ⎤ ⎪ y ϕ V p = ϕ Sat pSat exp⎢ V CO2 (p − pSat )⎥ CO2 CO2 CO2 ⎥ ⎪ CO2 CO2 ⎢⎣ RT ⎦ ⎪ ⎨ ⎡VS ⎤ ⎪ L Sat Sat ⎢ CO2 (p − pSat )⎥ ⎪ xCO ϕCO = ϕ exp p p CO2 CO2 CO2 ⎥ ⎪ 2 2 ⎢⎣ RT ⎦ ⎩

(4)

fi ̂ = f (p ,V ,T )

(5)

T < TTP

(6)

where eq 4 represents the VSE and LSE, eq 5 shows that fugacity is calculated by EoS, and eq 6 demonstrates the constraint that freezing temperature must be lower than the triple-point temperature if the solid CO2 were to exist stably. The saturated vapor pressure of pure solid CO2 can be calculated by the Antoine equation shown as eq 7. B


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Industrial & Engineering Chemistry Research ⎤ ⎡ ⎛1⎞ Sat PCO = exp⎢ −3108.2⎜ ⎟ + 20.6654⎥ 2 ⎝T ⎠ ⎦ ⎣

(7)

The fugacity of CO2 in both vapor and liquid phase can be solved by EoS that is widely applicable in natural gas system. At present, RK−Soave, PR EoS, and so on are commonly used to calculate the thermodynamic properties of natural gas while GERG-2008 is a newly developed and original thermodynamic EoS, but it has not been found that there are researchers who apply it in calculating CO2 freezing temperature. On the basis of the established phase-equilibrium model, RK−Soave, PR, and GERG-2008 EoSs are used to simulate CO2 freezing temperature in both vapor and liquid phases in different CH4−CO2 binary systems. The calculated freezing temperatures by the models based on three EoSs are obtained by Aspen Plus. EoSs and their parameters in Aspen Plus are taken from the literature.11,14−16 Then the simulated results are compared with the experimental data from literature17 to check the accuracy of the EoSs above. The simulation process chooses CH4−CO2 binary vapor systems in which the molar concentrations of CO2 are respectively 2%, 4%, 6% and the CH4−CO2 binary liquid systems in which the concentration of CO2 differs. Then the deviation analysis is carried out, and the results are shown in Figures 2−5.

Figure 4. Deviation of freezing temperature in vapor for CO2−CH4 binary system in which CO2 mole fraction is 6%.

Figure 5. Deviation of simulated CO2 freezing temperature in liquid phase for CO2−CH4 binary system.

deviation between the simulated and experimental data in vapor at different CO2 concentrations. In Figure 5, the abscissa represents the concentration of CO2 in CH4−CO2 system while the ordinate represents percentage deviation between the simulated and experimental data in liquid at different CO2 concentrations. Judging from Figures 2−4, all three equations show a high accuracy on the CO2 freezing temperature in vapor of CH4− CO2 binary systems, and the relative deviation of RK−Soave, PR, and GERG-2008 is respectively 0.279%, 0.239%, and 0.220%, the maximum of which is less than 0.5%. However, the deviation of CO2 freezing temperature in liquid is rather large and the relative deviation of RK−Soave, PR, and GERG-2008 is respectively 4.779%, 4.442%, and 1.122% as shown in Figure 5. Nevertheless, the relative deviations by GERG-2008 stabilize within 1.5%. In a few words, GERG-2008 shows a higher accuracy about CO2 freezing temperature in both vapor and liquid phases compared to the other equations.


3. IMPROVEMENT ON THE PREDICTION MODEL ABOUT CO2 FREEZING TEMPERATURE In the simulation process above, the fugacity coefficient of pure solid CO2 is calculated by model based on the Antoine equation. This model is derived from three segments integral based on VSE. The integral path is shown in Figure 6 and described as eq 8:18 the component is compressed from 0 to saturate pressure ps, then phase transition from vapor to solid


In Figures 2−4, the abscissa represents pressure of the CH4− CO2 system while the ordinate represents the percentage C


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Industrial & Engineering Chemistry Research S fCO (T ,P) 2

RT ln

L (T ,P) fCO

= ΔHa → d(T ,P) − T ΔSa → d(T ,P) (11)

2

Since enthalpy and entropy are state functions, enthalpy and entropy changes are only related to initial and final state. So the Gibbs free energy change from “a” to “d” can be calculated by another path: a → b → c → d.

Figure 6. Compressed process of CO2 from vapor to solid.

Ha → d = ΔHa → b + ΔHb → c + ΔHc → d

occurs, and at last it is further compressed from saturated vapor pressure ps to the system pressure p. f is ⎞

⎛ RT ln ϕi = RT ln⎜ ⎟ = ⎝ p⎠ ⎛ ps ⎞ + RT Δ⎜⎜ln s ⎟⎟ + ⎝ fi ⎠

∫p

S

∫0

p⎛

S

p

⎜V is ⎝

=

⎛ RT ⎞ ⎜Vi − ⎟ dp p ⎠ ⎝

RT ⎞ − ⎟ dp p ⎠

=

∫T

TTP

cpL dT − ΔHTP +

=

=

T

cpS dT

TP

TTP

(cpL − cpS) dT − ΔHTP

(12)

∫T ∫T

TTP

TTP

cpL

ΔHTP dT − + T TTP

(cpL − cpS)

dT −

T

∫T

T

TP

cpS T

dT

ΔHTP TTP

(13)

Suppose cLp and cSp are constant and will not change with temperature and a new equation can be obtained after transformation by putting eqs 12 and 13 into eq 11: ln

(9)

According to eq 9, fugacity can be calculated by way of Gibbs free energy. In order to get the solid fugacity of pure component in specific condition, a hypothetical liquid-state point that has the same temperature and pressure can be chosen at first. Then the properties at actual solid-state point can be calculated according to the thermodynamic cycle. It is shown in Figure 7, where “d” is the actual solid point while “a”

S fCO (T ,P) 2

L fCO (T ,P) 2

=

Δcp(TTP − T ) TTP ⎞ ΔHTP ⎛ ⎜1 − ⎟ + RTTP ⎝ T ⎠ RT −

Δcp R

ln

TTP T

(14)

In conclusion, fugacity of solid CO2 can be calculated as follows: ⎡ ΔH ⎛ T ⎞ S L TP ⎜ fCO (T ,P) = fCO (T ,P) exp⎢ 1 − TP ⎟ 2 2 ⎢⎣ RTTP ⎝ T ⎠ +

Δcp(TTP − T ) TR

−

Δcp R

ln

TTP ⎤ ⎥ T ⎥⎦

(15)

where the temperature, enthalpy change, and heat capacity difference at triple point can all be found in literature; so long as the fugacity of hypothetical fluid can be solved by EoS, the solid fugacity of the component under this condition can also be calculated.20 To test the accuracy of the method of reference state of hypothetical fluid on calculating fugacity of pure solid component, the model based on the Antoine equation is substituted by the new method, and results of deviation analysis on the freezing temperature of CH4−CO2 binary systems in liquid phase are shown in Figure 8. Judging from Figure 8, the relative deviations of RK−Soave, PR, and GERG-2008 are respectively 3.056%, 2.742%, and 0.160% by the new method. Compared to the results by the model based on the Antoine equation, average relative deviation was reduced by 36.05%, 36.05%, and 85.66%. It is obvious that the average relative deviations of the three equations are greatly reduced and the accuracy of GERG-2008 increases the most.

Figure 7. Thermodynamic cycle of hypothetical fluid as reference state.

is the hypothetical fluid point. The process from “a” to “d” is a phase transition process. “b” and “c” are reference points. Since data at the triple point such as temperature and pressure are easy to get, the triple point is chosen as the reference point. The Gibbs free energy change from “a” to “d” can be represented as follows: ΔGa → d(T ,P) = ΔHa → d(T ,P) − T ΔSa → d(T ,P)

∫T

Sa → d = ΔSa → b + ΔS b → c + ΔSc → d

(8)

Thus, it can be preferred that it is because the Antoine method is based on the VSE that the simulated results of CO2 freezing temperature in vapor are accurate but the deviation of freezing temperature in liquid is rather large. Aiming at the dilemma that CO2 freezing temperature in liquid calculated by model based on Antoine equation is not accurate enough, the method of reference state19 is used in this article to solve the fugacity of pure solid CO2 in the LSE model. This method has already been widely applied in calculating the solid solubility in liquid. Fugacity and Gibbs free energy satisfy the following equation:18 dGi = RT d ln fi

∫T

(10)

By combining eqs 9 and 10, it is easy to get D


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Industrial & Engineering Chemistry Research

Table 2. Deviation Analysis of CO2 Freezing Temperature Calculated by Different EoSs in Natural Gas System deviation

RK−Soave

relative deviation in vapor phase, % average relative deviation (%) in liquid phase (δ1/δ2) max absolute deviation (K) in liquid phase (δ1/δ2)

PR

GERG-2008

2.174

2.074

1.849

2.683/1.841

2.703/1.878

0.648/0.606

5.84/4.36

5.93/4.49

2.25/1.16

calculation CO2 freezing temperature in vapor in natural gas systems. However, no matter which equation is chosen, when the new method is adopted, instead of the traditional model based on Antoine equation to calculate solid CO2 fugacity, the results by the improved LSE model are more accurate. What’s more, GERG-2008 possesses the highest calculating accuracy. Compared to CH4−CO2 binary systems, the components of natural gas are more complex and the mutual influence between the components is rather large, so the accuracy of phaseequilibrium on natural gas systems is inferior to that on simple CH4−CO2 binary systems.

Figure 8. Deviation of simulated CO2 freezing temperature in liquid phase for CO2−CH4 binary system.

4. SIMULATION ON CO2 FREEZING TEMPERATURE OF MULTICOMPONENT NATURAL GAS SYSTEM Considering that natural gas is a complex mixture containing many components, it is rather difficult to measure the actual CO2 freezing temperature of natural gas systems. It is necessary to establish phase-equilibrium model to calculate CO2 freezing temperature, which can provide reference for engineering design and actual process plant. In this article, both model based on Antoine and the new method named reference state of hypothetical fluid are combined with phase-equilibrium model to simulate the freezing situation in natural gas systems. Moreover, CO2 freezing temperatures in both vapor and liquid are compared with the experimental data from GPSA,21 which are shown in Table 1. In Table 1, there are four natural gas systems and the compositions are represented by lists of mole fractions 1−4. The first three systems are in LSE. T1 and T2 respectively represent CO2 freezing temperature calculated by LSE model based on the Antoine equation and the reference state of hypothetical fluid; the fourth system is in VSE and CO2 freezing temperature in vapor is calculated by model based on Antoine equation. Deviations are reported in Table 2. In Table 2, δ1 and δ2 respectively represent the deviation of freezing temperature in liquid by model based on Antoine equation and the new method. According to the deviation analysis, the three equations all possess high accuracy on

5. APPLICATION TO ACTUAL LIGHT HYDROCARBON SEPARATION The improved phase-equilibrium model is then used to calculate CO2 freezing temperature in the actual light hydrocarbon separation process and provides proper and safe parameters for the separation devices. The light hydrocarbon separation process is shown in Figure 1. The components of natural gas in pipeline are shown in Table 3. In the whole separation process, the freezing temperature margin of demethanizer is the smallest. In other words, the CO2 freezing risk of demethanizer is the largest; thus, it is chosen as the calculating example. The operating conditions of demethanizer are list in Table 4. The purpose of recovery process of light hydrocarbon is to recycle C2H6 at high recovery and avoid CO2 freezing at the same time. High recovery relies on sufficient cold source, which requires that the operation should be under cryogenic conditions. Thus, system pressure should be as small as possible on premise of avoiding CO2 freezing. In general, the operating pressure of demethanizer is 0.7−3.2 MPa.22 Under the designed condition of demethanizer, CO2 composition profile is drawn for the feed in Table 3. The

Table 1. Comparison between Simulated CO2 Freezing Temperature and Experimental Data in Both Vapor and Liquid Phases in Natural Gas System under 2.2 MPa component

mole fraction 1, % in liquid

N2 CO2 C1 C2 C3 C4+

0.38 3.44 90.35 5.03 0.69 0.11

actual CO2 freezing temp, K temp (K) simulated by RK−Soave (T1/T2) temp (K) simulated by PR (T1/T2) temp (K) simulated by GERG-2008 (T1/T2)



mole fraction 4, % in vapor

0.31 5.49 85.64 7.65 0.79 0.12 mole fraction 1

0.29 6.82 80.29 11.54 0.92 0.14 mole fraction 2

mole fraction 3

168.15 164.36/165.84 164.41/165.86 168.46/169.76

176.48 171.95/173.41 171.88/173.32 175.57/176.91

180.93 175.09/176.57 175.00/176.44 178.68/179.8

E

1.42 1.13 96.38 1.03 0.04 Trace mole fraction 4 169.26 172.94 172.77 172.39


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Industrial & Engineering Chemistry Research Table 3. Components and Contents of Natural Gas in Pipeline components contents (x%)

C1

C2

C3

iC4

nC4

iC5

nC5

CO2

N2

90.036

4.825

1.306

0.555

0.2

0.23

0.047

2.01

0.791

margins between solubility line and CO2 profile line. It means that the CO2 freezing would occur at lower operating pressure. Then the freezing in the demethanizer at 3.0 MPa is analyzed in detail in Figures 11 and 12. According to the CO2

Table 4. Operating Conditions Demethanizer in Our Research conditions designed pressure: 2.8−3.5 MPa processing capability: 60 × 104 N m3/h number of theoretical stages: 25 feed stage: 1st, 12th, and 15th feed rate: 574.3 kmol/h, 179.8 kmol/h, 1993.8 kmol/h feed temp: 177.7 K, 182.1 K, 183.5 K

simulation of the demethanizer is also carried out by Aspen Plus. The results are shown in Figures 9 and 10.

Figure 11. CO2 freezing in vapor in demethanizer.

Figure 9. Solubility line and CO2 profile in stages of demethanizer in vapor phase under 2.8 MPa.

Figure 12. CO2 freezing in liquid in demethanizer.

concentration and temperature on each stage, the operating line of demethanizer can be drawn out. Also, the freezing line of vapor and liquid phase can be drawn by data of CO2 concentration and CO2 freezing temperature in both vapor and liquid phase. Then whether CO 2 will freeze in demethanizer can be judged by whether the freezing line intersects the operating line. In Figure 11, the abscissa represents the temperature on each stage; the ordinate in the left side represents CO2 mole fraction on each stage, and the other on the right side represents stages of the column. It is easy to find that at the CO2 concentration of point C, freezing margin between A and B is the smallest. Points A and B respectively represent the temperature on stage and corresponding freezing temperature. Since point A is found, a vertical line (isothermal) can be drawn and intersect the temperature profile line at point D. Then a horizontal line is drawn from point D to intersect the right y-axis at point E. That is the stage at which CO2 freezing is most likely to take place. The analysis of CO2 freezing in liquid is the same. Then it comes to the conclusion that the minimum freezing temperature margin is 3.25 °C in vapor and 3.64 °C in liquid; furthermore it can be judged that CO2 freezing in both vapor and liquid is most likely to occur on 19th stage.

Figure 10. Solubility line and CO2 profile in stages of demethanizer in vapor phase under 3.0 MPa.

As shown in Figure 9, the two lines intersect each other. It is indicated that there is a region where CO2 composition crosses the solid formation barrier. In Figure 10, there are certain F


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Industrial & Engineering Chemistry Research As for the whole demethanizer, so long as the freezing temperature margin is higher than 0, CO2 freezing can be avoided. In line with industry practice, the freezing temperature margin is usually kept at 3 °C in the hydrocarbon separation process to ensure the safe and stable run of facilities.23 So setting 3.0 MPa as the operating pressure of demethanizer can avoid CO2 freezing and meet the process requirements.

■

6. CONCLUSION (1) Aiming at the reason why CO2 freezing temperature in LSE by the model based on Antoine is not accurate enough, the improved phase-equilibrium model in which method of reference state of hypothetical fluid is introduced to calculate fugacity of solid CO2. The average relative deviation of CO2 freezing temperature in liquid of CH4−CO2 binary systems by RK−Soave, PR, and GERG-2008 is respectively reduced by 36.05%, 38.27%, and 85.66% if the model based on the Antoine equation is replaced by the method of reference state of hypothetical fluid in LSE model. (2) When the improved phase-equilibrium model is extended to natural gas systems, results reveal that GERG-2008 always shows a high accuracy on predicting CO2 freezing temperature in both vapor and liquid; no matter which equation is chosen, when the new method is adopted, taking the place of the traditional model based on Antoine equation, the results calculated by the improved LSE model are more accurate. (3) Establishing highly accurate phase-equilibrium model helps to predict and avoid CO2 freezing under actual working conditions. Also, it can provide theoretical reference for the design of light hydrocarbon recovery process which has been analyzed in detail by a case of light hydrocarbon separation.

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ϕVCO2 = vapor phase fugacity coefficient for CO2, dimensionless ϕLCO2 = liquid phase fugacity coefficient for CO2 in the liquid mixture, dimensionless Sat ϕSat CO2 = fugacity coefficient for pure CO2 vapor at PCO2, dimensionless

REFERENCES

(1) Li, Y. J.; Luo, H. Integration of light hydrocarbons cryogenic separation process in refinery based on LNG cold energy utilization. Chem. Eng. Res. Des. 2015, 93, 632−639. (2) Fernández, L.; Bandoni, J. A.; Eliceche, A. M.; Brignole, E. A. Optimization of ethane extraction plants from natural gas containing carbon dioxide. Gas Sep. Purif. 1991, 5 (4), 229−234. (3) Eggeman, T.; Chafin, S. Pitfalls of CO2 freezing prediction. Presented at the 82nd Annual Convention of the Gas Processors Association, San Antonio, TX, U.S., 2003. (4) Eggeman, T.; Chafin, S. Beware the pitfalls of CO2 freezing prediction. Chem. Eng. Prog. 2005, 101 (3), 39−44. (5) Cheng, Z. H. Research on CO2 freeze blocking law and solutions for demethanizing tower in natural gas processing plant. Mod. Chem. Ind. 2010, 30 (8), 80−82. (6) Hlavinka, M. W.; Hernandez, V. N.; McCartney, D. Proper interpretation of freezing and hydrate prediction results from process simulation. Presented at the 85th GPA Annual Convention Proceedings, Grapevine, TX, U.S., 2006. (7) ZareNezhad, B.; Eggeman, T. Application of Peng−Rabinson equation of state for CO2 freezing prediction of hydrocarbon mixtures at cryogenic conditions of gas plants. Cryogenics 2006, 46 (12), 840− 845. (8) Xiong, X. J.; Lin, W. S.; Gu, A. Z. Prediction of CO2 frosting temperature in CH4-CO2 binary system. Chem. Eng. Oil Gas 2012, 41 (2), 176−178. (9) ZareNezhad, B. Prediction of CO2 freezing points for the mixtures of CO2-CH4 at cryogenic conditions of NGL extraction plants. Korean J. Chem. Eng. 2006, 23 (5), 827−831. (10) Shen, T. T.; Lin, W. S. Calculation of carbon dioxide solubility in saturated liquid methane. Presented at the Annual Academic Conference of Refrigeration Institute, Shanghai, China, 2009. (11) Kunz, O.; Wagner, W. The GERG-2008 wide-range equation of state for natural g ases and other mixtures: an expansion of GERG2004. J. Chem. Eng. Data 2012, 57 (11), 3032−3091. (12) Dauber, F.; Span, R. Modelling liquefied-natural-gas processes using highly accurate property models. Appl. Energy 2012, 97, 822− 827. (13) Gong, K. Q.; Wang, Z. Z.; Jia, Y. Y. Generalization of Thermodynamic Research of LNG and Other Mixtures Storage and Transportation Process. Sci. Technol. Eng. 2013, 35, 10549−10559. (14) Soave, G. Equilibrium constants from a modified RedlichKwong equation of state. Chem. Eng. Sci. 1972, 27 (6), 1197−1203. (15) Peng, D. Y.; Robinson, D. B. A new two-constant equation of state. Ind. Eng. Chem. Fundam. 1976, 15 (1), 59−64. (16) Kunz, O.; Klimeck, R.; Wagner, W.; Jaeschke, M. The GERG2004 wide-range equation of state for natural gases and other mixtures. GERG TM15 2007; Groupe Européen de Recherches Gazières, 2007. (17) Kurata, F. Solubility of Solid Carbon Dioxide in Pure Light Hydrocarbons and Mixtures of Light Hydrocarbons; Gas Processors Association, 1974. (18) Ma, P. S.; Xia, S. Q.; Qiu, T.; Chen, X. N. Tutorial in Chemical Thermodynamics; Higher Education Press: Beijing, China, 2011; p 75. (19) Shi, Y. H. Chemical Engineering Thermodynamics; East China University of Science Press: Shanghai, China, 2007; pp 153−154. (20) De Guido, G.; Langè, S.; Moioli, S.; Pellegrini, L. A. Thermodynamic method for the prediction of solid CO2 formation from multicomponent mixtures. Process Saf. Environ. Prot. 2014, 92 (1), 70−79. (21) Gas Processors Association. GPSA Engineering Data Book, 11th ed.; Gas Processors Suppliers Association, Tulsa, OK, 1998.

AUTHOR INFORMATION

Corresponding Author

*Tel: 86-020-87112044. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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NOMENCLATURE = liquid CO2 heat capacity, J·K−1 = solid CO2 heat capacity, J·K−1 Δcp = heat capacity difference, J·K−1 fi ̂ = fugacity of component i, kPa s f ̂ = solid fugacity of component i, kPa cLp cSp

i

Gi = Gibbs free energy of component i, J·mol−1 ΔHTP = enthalpy of fusion at triple point, J·K−1 P = system pressure, kPa Psi = saturated vapor pressure of component i, kPa PSat CO2 = saturated vapor pressure of solid CO2 at system temperature, kPa R = universal gas constant, 8.314 J·(K·mol)−1 Si = entropy of component i, J·(K·mol)−1 T = temperature at which solid CO2 forms, K TTP = CO2 triple point temperature, 216.55 K Vi = molar volume of vapor component i, cm3·mol−1 Vsi = molar volume of solid component i, cm3·mol−1 3 −1 VSat CO2 = molar volume of solid CO2, cm ·mol xCO2 = mole fraction of CO2 in liquid phase, dimensionless yCO2 = mole fraction of CO2 in vapor phase, dimensionless ϕi = fugacity coefficient for component i G


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Industrial & Engineering Chemistry Research (22) Wang, Y. D. Natural Gas Processing Principle and Craft; China Petrochemical Press: Beijing, China, 2007; p 184. (23) Jiang, H.; He, Y. X.; Zhu, C. A. Forecast model for solid CO2 formation conditions in a CH4-CO2 system. Nat. Gas Ind. 2011, 31 (9), 112−114.

H


Application of Highly Accurate Phase-Equilibrium Models for CO2

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