Thermodynamic data for cryogenic carbon dioxide capture from natural gas: A review

Cryogenics 102 (2019) 85–104

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Cryogenics journal homepage: www.elsevier.com/locate/cryogenics

Review article

Thermodynamic data for cryogenic carbon dioxide capture from natural gas: A review

T

Muhammad Babara, Mohamad Azmi Bustamb, , Abulhassan Alic, Abdulhalim Shah Mauludd, Umar Shafiqa, Ahmad Mukhtara, Syed Nasir Shahe, Khuram Maqsoodc, Nurhayati Mellond, Azmi M. Shariffa ⁎

a

CO2 Research Center (CO2RES), Department of Chemical Engineering, Universiti Teknologi PETRONAS, Malaysia Center of Research in Ionic Liquids (CORIL), Department of Chemical Engineering, Universiti Teknologi PETRONAS, Malaysia c Department of Chemical Engineering, University of Jeddah, Jeddah, Saudi Arabia d Center of Contaminant Management (CenCo), Department of Chemical Engineering, Universiti Teknologi PETRONAS, Malaysia e Department of Chemical Engineering, University of Engineering and Technology, Taxila, Pakistan b

ARTICLE INFO

ABSTRACT

Keywords: Natural gas Cryogenic technology CO2 removal Phase equilibria Hydrocarbons

The increasing global energy demand has compelled the researchers to utilize the undeveloped contaminated natural gas (N.G) reservoirs. However, due to the emissions standards established by environmental regulatory authorities, N.G treatment has become more crucial. Amongst the established CO2 separation strategies, the cryogenic CO2 removal techniques are promising due to environmentally friendliness, high N.G purification, low footprint values, no chemical reaction involved and capable of handling N.G with high CO2 content. Design and operation of a cryogenic process require accurate thermodynamic knowledge along with the understanding of the phase behavior of CO2 with light alkanes to make the process cost–effective. Furthermore, the study of frosting and liquefaction behavior of CO2 or CO2–alkanes mixture is significant for the energy minimization and smooth operation of the cryogenic CO2 removal from N.G. This paper provides a critical review of the available experimental and predicted thermodynamic data for CO2–alkanes mixtures at different conditions. The significance of pressure–temperature (PT), pressure–composition (P–xy), and temperature–composition (T–xy) phase diagrams for CO2–alkane mixtures are discussed in this paper. This paper also describes the use of the equation of states (EoS) for predicting the thermodynamic phase behavior of the CO2 mixtures. This review will help the researchers in designing more efficient, economical, and sustainable cryogenic CO2 capture processes.

1. Introduction From the last few decades, the world is fastly becoming a global village due to the increasing energy requirement across the world. The energy and its related services are significant to satisfy human social and economic developments. Currently, CO2 emission from the energy sources and environmental issues have attracted global concern. Nowadays, renewable energy sources are becoming the most significant energy wellsprings. However, as these technologies are still in the nascent stages, therefore are unable to fulfill the high energy requirement of the 21st century. Hence, for the next few decades, fossil–based fuels will be dominant over the other energy sources of the world [1-3]. Among the fossil fuels, natural gas (N.G) is considered as the cleanest fossil fuel and has become one of the primary global energy sources [4-

6]. The projected average annual rise in N.G consumption from 2002 to 2030 is around 3.4% [7]. Although N.G is considered as an environmentally friendly fuel, still, its quality strongly depends upon the geological conditions, deposit type, and the well–depth [8]. N.G primarily consists of Methane along with some higher hydrocarbons (H.C), and contaminants like CO2, N2, H2S, and He [9]. CO2 is one of the major greenhouse gases in N.G, and its concentration may vary from 5% to 90% [10-15]. Malaysia alone has about 13 trillion standard cubic feet (136.11 cubic kilometers) of unexplored high CO2 content (87 mol %) N.G reservoirs [16]. The acceptable standard specification for CO2 in N.G is usually less than 2% to avoid pipelines corrosion and other environmental problems [17-21]. Fig. 1 presents the standard U.S pipeline specifications for N.G delivery. Therefore, the removal of CO2 from the N.G is vital for improving the N.G quality and production of

⁎ Corresponding author at: Center of Research in Ionic Liquids (CORIL), Department of Chemical Engineering, Universiti Teknologi PETRONAS, Bandar Seri Iskandar 31750, Perak, Malaysia. E-mail address: [email protected] (M.A. Bustam).

https://doi.org/10.1016/j.cryogenics.2019.07.004 Received 25 March 2019; Received in revised form 29 June 2019; Accepted 17 July 2019 Available online 17 July 2019 0011-2275/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature

PCP-SAFT: Perturbed–Chain Polar Statistical Associating Fluid Theory P: Pressure Po: Vapor pressure PSRK: Predictive Soave-Redlich-Kwong P-xy: Pressure-composition S: Solid phase S–V: Solid–Vapor S–L: Solid–Liquid S–L–V: Solid–Liquid–Vapor S–L–E: Solid–liquid equilibrium SRK: Soave-Redlich-Kwong T: Temperature T-xy: Temperature-composition u: Standard uncertainty ur: Relative standard uncertainty V: Vapor Phase V–L: Vapor–Liquid x: Liquid–phase mole fraction y: Vapor–phase mole fraction

AD: Absolute Deviation AAD: Absolute Average Deviation ANN: Artificial-Neural-Network CCS: Carbon Capture and Sequestration CPA: Cubic plus association EoS: Equation of State GERG-2008: Groupe Européen de Recherches Gazières, GPA–RR: Gas Processors Association Research Report H.C: Hydrocarbon KLSSP: Kohn and Luks Solids Solubility Program L: Liquid phase MAD: Maximum Absolute Deviation NGL: Natural Gas Liquids NRTL: Non-Random Two-Liquid N.G: Natural Gas SRK: Soave–Redlich–Kwong NLFHB: Non-random Lattice Fluids Hydrogen Bond PC-SAFT: Perturbed Chain Statistical Associating Fluid Theory environmentally friendly energy source [22].

[43]. In the last few decades of the 20th–century, membrane separation has turned out to be well–established technology for N.G purification [44]. One of the key advantages is that they can remove bulk impurities from N.G [45-47]. However, the main constraints associated with the membranes technology are the lack of selectivity, hydrocarbon losses, large footprint, high energy consumption, and the high cost of membranes pretreatment [48]. Cryogenic technology has been known for an extended period as an

1.1. CO2 capture technologies Carbon capture and sequestration (CCS) has a crucial performance in controlling the pre and post–combustion CO2–emission to the atmosphere [26-33]. The leading CCS technologies are Absorption, Adsorption, Membranes, and cryogenic CO2 capture processes [34]. A brief classification of CO2 capture technologies based on CO2 capturing techniques are illustrated in Fig. 2 [35]. CO2 absorption is divided into two main types, physical absorption, and chemical absorption. In physical absorption, the solubility of CO2 in a solvent is the driving force for the CO2 separation. While chemical absorption is based on the chemical affinity of a solvent to dissolve CO2 [36-39]. The notable drawbacks of physical absorption are low solubility and selectivity of CO2, high pressure–drop, and high energy requirement. Similarly, limitations with chemical absorption are the involvement of a chemical reaction, high power requirement for the solvent regeneration, not capable of handling high content of CO2 content N.G, and the release of captured CO2 to the atmosphere [40]. In N.G industry the term CO2 adsorption refers to the purification process in which the CO2 from the feed N.G is removed by using a solid surface (adsorbent). CO2 adhesion on the adsorbent is done by bringing the gas stream and the solid surface in contact with each other. The difference in the adsorbent affinities for the various N.G components offers a straightforward means of purification [41,42]. However, limitations to volatile organics, low resistance to high–pressure changes, the potential for a fire at the bed, low removal capacity and higher operating cost are the noteworthy limitations of adsorption technology

MEA

Chemical

Caustics

Others

Absorption

Selexol

Physical

Rectisol

Others Alumina

CO2 Capture Technologies

Adsorbed Beds

Zeolites

Activated Carbon

Adsorption

Pressure swing

Regeneration Method

Temperature Swing

Washing

Conventional V-L

V-L Ryan Holmes

Stirling Coolers

Cryogenic

Non-Conventional V-S

V-S Packed Bed Heat Exchangers

Control Freeze Zone

0 2 % CO 10 92 95 % HC

Hybrid

%H S

2 7% H

CryoCell HCDN

O

PolyPhenyleneOxide

Gas separation

4 % Total inerts Membrane

Gas Absorption Ceramic Bed System

Fig. 1. U.S. pipeline composition specifications for N.G delivery [23-25].

Fig. 2. CO2 removal technologies [35]. 86

PolyDimethylsiloxane Polypropylene

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available approach for CO2 removal from N.G [49]. However, this technology was not extensively studied due to the typical concept of high expected cooling duty [50,51]. Recently, along with the introduction of cryogenic hybrid technologies, researchers have found some optimal solutions to minimize the energy requirements for cryogenic CO2 capture, which make this technology more attractive [5278]. Cryogenic separation technologies require 30% less energy as compared to the other conventional N.G purification processes [79]. Fig. 3 illustrates the energy requirements per kg CO2 removal for the available conventional technologies [80]. Together with the advantage of low energy requirements, cryogenic technology also offers low footprints, less hydrocarbon losses, high product purity, no chemical reaction involved, and applicability for high CO2 content gaseous mixtures at any pressure, which make it dominant over the other technologies [81,82].

2.2. General phase diagram for the CO2–CH4 system A general P–T phase envelope for the binary CO2–CH4 mixture is presented in Fig. 5. The points A and B represent the triple points of CH4 and CO2, respectively. Curve BC shows the liquid CO2 vapor pressure while CD represents the critical locus. The region below and above the line BC is V and V–L phase, respectively. The area under the 3–phase locus (curve AB) presents the S–V phase. Moreover, Fig. 5 illustrates a general description of the thermodynamic phase study of binary CO2–CH4 mixture. However, changing the CO2 concentration in the mixture will affect the components of the phase envelope. 2.3. Effect of CO2 content on CO2–CH4 phase envelope The effect of CO2 concentration on the P–T phase envelope of binary CO2–CH4 system is illustrated in Fig. 6. The pressure and temperature conditions for the dew and bubble points changes with varying CO2 content in a gaseous mixture [48,91]. Fig. 6 illustrates different CO2–CH4 binary mixtures having 10, 20, 40, 60, and 80 mol % CO2 and balance CH4 [35]. It can be observed from the P–T phase envelope that every mixture with a specific CO2 content has a distinct critical point with different pressure and temperature conditions. With increasing CH4 content in the binary mixture, the temperature of the dew and bubble points at constant pressure decreases, and vice versa. Moreover, the change in composition also affects the CO2 frost lines. Two types of thermodynamic phase data are available in the literature for N.G with different CO2 content. First is the experimental thermodynamic data obtained for some specific CO2–H.C mixtures, while Second is the predicted or calculated thermodynamic data, that is obtained either by using simulators or EoS for a particular CO2–H.C mixture. In the current study, the reported experimental and predicted PT, T–xy, and P–xy thermodynamic phase data for the binary CO2–CH4 and ternary CO2–CH4–H.C mixtures are explored. The scope of this review covers the S–V and L–V thermodynamic phase data and CO2 frost point study for the binary and ternary gaseous mixtures. The effect of pressure and temperature on the liquefaction and solidification of CO2 are also discussed. The applications of different simulators and equations of state (EoS) for the generation of thermodynamic phase data are also analyzed. The current review is classified into five major sections. The first section provides a general introduction to N.G and CCS technologies. The second section deliberates the importance of thermodynamics in cryogenic CO2 separation and phase equilibria. The available experimental and predicted thermodynamic phase data for the binary and ternary mixture are discussed in the third section. Key findings of the current review, along with the future recommendations, are discussed in the fourth section. Section 5 provides a conclusion of the current review.

2. Importance of phase equilibria in cryogenic separation Designing a cryogenic CO2 capture process requires an accurate thermodynamic phase study of the gaseous mixtures. Phase equilibria are the comprehensive graphical study of different phases of a material relating to some thermodynamic properties [83]. Generally, temperature, pressure, and mole fractions are expressed in the thermodynamic phase diagrams. These diagrams can be classified into two major types, two–dimensional and three–dimensional graphs [84-86]. In the two–dimensional graphs, only two quantities are plotted on the x and y–axes. While the three–dimensional graph has three quantities (commonly temperature, pressure, and mole fraction) on x, y, and z–axes. Three–dimensional charts are more comprehensive, which provide a critical study that intensively benefits the CO2 removal from N.G. If properly designed, the cryogenic CO2 capture from natural gas requires 30% less energy as compared to the other conventional technologies. For designing an efficient and economical cryogenic CO₂ capture process, a precise thermodynamic study is very crucial [87,88]. It assists in generating the pressure and temperature conditions for the bubble and dew point curves, 3–phase locus, and CO2 freeze–out line for the CO2 gaseous mixtures. To produce highly purified N.G, meeting the international pipeline specifications (CO2 < 2 mol%), it is mandatory to generate more accurate phase envelopes for the CO2–N.G gaseous mixtures. The increasing demand for the cryogenic CO₂ removal from N.G has developed a drastic need for the researchers to obtain more precise thermodynamic data for CO₂–N.G mixtures. Phase change has a vital role in the cryogenic CO2 capture from N.G. S–V and L–V binary phase regions are the regions where cryogenic CO2 capture may occur. For investigating the thermodynamic phase behavior of CO2-N.G mixture, it is mandatory to understand the P-T phase envelope qualitatively, and quantitatively. 2.1. Qualitative P–T phase envelope

Cryogenics [89, 90]

Fig. 4 presents a qualitative P–T phase envelope for a binary gaseous mixture. In the diagram, the curve BDF represents 3–phase locus for the binary system. FG line shows the freeze–out line for the component with a lower freezing point. The frost or snow line, which is the borderline of two–phase V–S and single vapor phase, is represented by line AB. The dew point curve, represented by line BC, shows the boundary distinguishing two–phase V–L from the single vapor phase. Curve CD represents the bubble point line, which is a border between the liquid phase and the binary–phase V–L region. The critical point of the mixture is represented by C. Freezing or melting line, which is the boundary between two–phase L–S and the liquid phase, is represented by line DE. Moreover, any change in the composition of the gaseous mixture will affect the position of the dew and bubble points, CO2 freeze–out line, frost line, triple point, and the critical point.

Membranes [87, 88] Adsorbents [84, 86] Absorbents [84, 85]

0

1

2 3 4 Energy requirements / MJe.Kg -1 CO2

5

6

Fig. 3. Energy requirement for various CO2 capture technologies (MJe.Kg-1CO₂) [80]. 87

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10

G

E

6

Solid + Liquid

7

Solid-Solid

Pressure / MPa

8

5 4

1

Liquid

Bubble point curve

C

Liquid + Vapor

D

3 2

isotherms at temperatures between 271.48 and 199.82 K and a pressure range from 0.689–6.895 MPa. Fig. 7 illustrates the P–T phase envelope obtained by Donnelley and Katz for CO2–CH4 system. Six different compositions with CO2 contents ranging from 0–88% are highlighted along with experimentally determined 3–phase locus for the binary mixture up to 194.27 K. The authors deduced that any change in CO2 concentration in the binary mixture has a significant effect on the bubble and dew points. Moreover, the authors also found that the critical locus of the binary mixture lies between the individual critical points of pure CO2 and CH4. Additionally, it was also pointed out that at any pressure, no CO2 solidification would occur in the mixtures containing less than 4 mol % CO2. The thermodynamic phase equilibria for binary CO2–CH4 system was also experimentally investigated by Pikaar [94]. The author examined S–L and S–V equilibria for a composition range of 1–20 mol % CO2 using a non–sampling approach. Three–phase locus was investigated in a temperature range of 143.15–203.15 K. Boiling, dew, and CO2–freezing points were measured to identify the V–L, V–S, and L–S equilibrium of the CO2–CH4 mixture. The author used a pressure up to 10.1325 MPa and a temperature range between 113.15 and 210.15 K to determine the V–S and L–S equilibrium. In Fig. 8, experimental data of the L-V and S–V region obtained by Pikaar for binary CO2–CH4 mixture is illustrated. However, when compared with Donnelly and Katz data at low temperature (206.15 and 200.15 K), the author observed a disagreement in pressure (≈ 4.053 MPa). Furthermore, Pikaar also highlighted that the 3–phase locus determined by Donnelly and Katz is incorrect below 206.15 K. Sterner extended the previous research work on the binary CO2–CH4 system to a lower temperature and experimentally determined the solid region boundaries near Methane’s critical temperature [95]. The author used a binary CO2–CH4 mixture having CO2 mole fraction of 0.019–0.052. Isothermal P–xy diagrams of the V–L regions at 205.37, 202.59, and 199.82 K were obtained. Isobaric T–xy phase envelopes were also generated at 4.482 and 5.171 MPa. The isobar at 4.482 MPa covers a temperature range between 211.48 and 189.82 K, and at 5.171 MPa covers the entire temperature range for the V–L equilibrium from 288.71–199.82 K. Fig. 9 (a) shows the composition (CO2 concentration) at the three–phase locus, and while Fig. 9 (b) presents the triple point locus of the binary system. The disagreement between Sterner’s 3–phase locus data and those of Donnelly and Katz, Pikaar, and Wang data are also illustrated in Fig. 9 [95 93,94,96]. Sterner explained the disagreement between Donnelly and Katz extrapolated data, Pikaar, and Wang data in two ways. In a T–xy graph (Fig. 9(a)), the author pointed out that below 194.27 K, where Donnelley’s extrapolation starts, the error in the liquid composition is increasing, which indicates the unreliability of Donnelley’s extrapolation. In the extrapolation, the pressure measurements by Donnelly & Katz was low by about 0.517 MPa [93]. A remarkable similarity between Donnelly’s experimental data and Wang's data was also noted [93,96]. The P–T graph in Fig. 9 (b) shows that there is an excellent agreement between the three–phase locus experimental data obtained by Sterner and Pikaar, However, Donnelley’s three–phase locus data is at higher temperature or conversely lower in pressure than Sterner’s data. Experimental investigation of the three–phase locus for binary CH4–CO2 system was also carried out by Davis et al. [92]. P–T phase

V-L Critical Point

CO2 Freezout line

9

H

F

3-Phase Locus Solid + Vapor

B

Vapor

A

0 273

Dew point curve

293

313 333 Temperature / K

353

373

Fig. 4. Qualitative P–T diagram for a binary gaseous system [89].

Fig. 5. General phase diagram for the CO₂−CH₄ system [90].

Fig. 6. Effect of CO2 concentration on the P–T phase envelope [48,92-94].

3. Available thermodynamic phase equilibrium data for CO2–H.C mixtures 3.1. Binary CO2–CH4 mixture

Table 1 Critical conditions for CH4–CO2 system [93].

3.1.1. Experimental thermodynamic study Donnelly and Katz in 1954 experimentally studied the thermodynamic phase behavior of the binary CH4–CO2 mixture [93]. The author analyzed 3–phase locus by experimentally determining the thermodynamic phase envelope of binary CO2–CH4 mixtures with different CO2 content. Table 1 shows the composition of the CO2–CH4 mixtures along with its critical points, obtained by Donnelly & Katz. The authors also evaluated V–L phase equilibrium for seven 88

CO2 mole fraction

Critical temperature/K

Critical pressure/MPa

1.00 0.88 0.705 0.543 0.18 0.00

304.26 286.48 273.7 256.49 222.04 190.93

7.398 8.377 8.618 8.44 6.791 4.640

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Fig. 7. P–T phase diagram for the CO2–CH4 system [93].

Fig. 9. (a) 3–phase compositions of CO2–CH4 system (b) Triple point locus of CO2–CH4 system.

of CO2 with light hydrocarbon because of the presence of interaction effects [100].

Fig. 8. Pikaar’s diagram for CH4–CO2 binary mixture [94].

2

x i Aoi1/2

Ao =

envelope along the S–L–V locus was determined for a temperature range between the triple point of CO2 (216.55 K) up to 97.05 K, and pressure range between 0.028 and 4.87 MPa. The author found a dissimilarity of the obtained 3–phase locus data with the S–L–V data of Donnelly and Katz below 205.37 K [93]. However, the author observed an outstanding agreement with the S–L–V data of Sterner, excluding the highest temperature (200 K) [95]. For S–V study the author used temperature in the range of 140.93–208.21 K and corresponding compositions between 0.12 and 11.73 mol % CO2. The author also determined the composition of the liquid phase on 3–phase locus through crystal formation, using eleven different mixtures with CO2 contents between 0.16 and 20.5 mol%. A graphical comparison of the data obtained by Devis et al. with Sterner, Kurata, and Donnelly & Katz is presented in Fig. 10 [92,93,95,97]. It was observed that below 205.37 K, the deviation between Donnelley & Katz and Davis et al. increases [92,93]. Geni Kaminishi et al. further studied the V–L equilibria for binary CO2–CH4 mixture at a temperature of 223.15–293.15 K and pressure up to 20.265 MPa [98]. V–L equilibrium, along with the available literature data, were used in finding the usefulness of the Benedict–Webb–Rubin (BWR) equation for predicting V–L equilibria. The V–L equilibrium prediction of the BWR equation was satisfactory for inorganic mixtures, excluding the critical region, while the usage of Leland et al. was unsatisfactory [99]. Moreover, the data obtained by Geni Kaminishi et al. at different temperatures, e.g. 233.15, 253.15, and 283.15 K is presented in Fig. 11. The author observed a considerable disagreement between the theoretically calculated results and experimental results, as shown in Fig. 11. Joffe and Zudkevitch indicated the failure of the combination rule identical to Eq. (1) for the constants in the Redlich–Kwong for mixtures

2

Bo =

i

x i Boi

x i Coi1/2

Co =

i

i

3

x i ai1/3

a=

3

xi bi1/3 )

b=(

3

i

i 2

=

xi i

x i ci1/3

c=

1/2 i

3

=

xi

1/3 i

i

(1)

where A o, Bo , Co , a, b, c, , and γ are the constants of BWR equation, x is the mole fraction of component ‘i’ in the liquid phase. Stotler and Benedict [101] have proposed a modified combination rule for A o as

Fig. 10. Davis S–L–V envelop for CH4–CO2 system [92]. 89

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whole isotherm. A good agreement was observed in comparison with the data obtained by Davalos et al., as shown in Fig. 14 [103]. The vapor phase comparison also showed an excellent similarity up to 5.066 MPa, but at high pressures, small deviations were found. The author indicated that the sampling procedure in the previous research was responsible for the slight variations in some of the high–pressure vapor–phase data. The author conducted three tests and found that the results were in excellent internal consistency. The calculated value of 3.198 MPa for the vapor pressure of CO2 is in good agreement with the value of 3.203 MPa from Myers and Van Dusen adjusted to the International Practical Temperature Scale of 1968 (IPTS–68) [108]. Stephen et al. described the bubble–point compositions of binary CH4–CO2 in the low–temperature region [109]. The author measured the V–L equilibrium as a function of pressure on seven isotherms at 219.26, 210.15, 203.15, 193.15, 183.15, 173.15, and 153.15 K for plotting the ‘k’ values at constant temperature and pressure. A small disagreement was observed between the obtained results and that of Hwang et al., which steadily decreases with reducing CO2 concentration until 193.15 K, where the results are almost similar [105]. Therefore, below 193.15 K, no comparison was made between the two research works. The risk of any severe error between 183.15 and 173.15 K was prevented by the excellent extrapolation of the liquid–phase data to the correctly known vapor pressure of pure CH4. Fig. 15 shows the comparison of P–xy data obtained by Stephen at 219.26, 210.15, 203.15, and 193.15 K with the data obtained by Hwang et al. at the same conditions. Table 3 shows a comparison of data obtained by Stephen’s et al. [109] and Hwang’s et al. [105] at the mentioned conditions. The minimum and maximum percentage deviation between the set of data is 6.5% and −2.5%, respectively. Shen et al. experimentally investigated the CO2 frost point formation in the binary CO2–CH4 mixtures [111]. Table 11 shows the Pressure and temperature conditions used by the author to determine the CO2 solubilities in liquid CH4. To validate the established model, the author compared the data obtained with the experimental data reported by Davis et al. [92]. It was concluded that the CO2 solubility in saturated liquid CH4 increases with increasing temperature. For the obtained experimental data, the author found an AAD of 4.14% in comparison with the experimental data of Davis et al., as shown in Table 4 [92].

10 9 8 Pressure / MPa

7 6 5 4 BWR equation origional Katz 233.15 K Katz 253.15 K BWR eqn. m=0.88 Present work 233.15 K Present work 253.15 K Present work 283.15 K

3 2 1 0

0

0.2

0.4

0.6

0.8

1

Mole fraction of CH4

Fig. 11. Geni Kaminishi et al. P–xy diagram for the CO2–CH4 system [98].

given in Eq. (2).

Ao = x12 Ao1 + 2x1 x2 m Ao1 Ao2 + x 22 Ao2

(2)

For the binary CO2–CH4 system, the coefficient ‘m’ is given in Table 2. These modifications boost the reliability of this research for the inorganic mixtures except in the vicinity of its critical point conditions. Sexena and Robinson experimentally studied the V–L equilibrium for the binary CO2–CH4 mixture [102]. Experiments were carried out at temperatures 266.48, 277.59 and 310.93 K, and pressures 2.758, 5.516, and 8.274 MPa. For the binary CO2–CH4 system, the authors found an excellent agreement of their data with the previously available experimental data, including Donnelly & Katz. However, a disagreement was observed with the data obtained by Wang and McKetta at 244.26 and 277.59 K for pressures 2.758, 5.516, and 8.274 MPa. Davolos et al. extended the research work of Gen Kaminishi and studied V–L equilibrium for the binary CH4–CO2 system at a temperature of 270 K and pressure ranging from 1.317 MPa to 8.106 MPa [103]. V–L equilibria were investigated for CH4–CO2 at different temperatures i.e. 230, 250, and 270 K. The author used a graphical method for evaluating the reliability of low–pressure binary results for both liquid and vapor phase, while for high–pressure data, the authors used the numerical method of orthogonal arrangement. Pressure difference against liquid composition was plotted to check the authenticity of the liquid–phase measurements. Ordinary isotherm was obtained for a CH4–CO2 binary system having one of the components above its critical point. The estimated critical pressures for these isotherms were 7.164, 8.167, and 8.582 MPa at 230, 250, and 270 K, respectively. These values were in good agreement with critical locus values reported by previous researchers [104]. Fig. 12 shows the P–xy graph obtained by Davolos et al. for the above–mentioned composition and conditions. Hwang et al. experimentally studied the vapor phase concentration of binary CH4–CO2 system along the V–L isotherms surrounding the S–V region for a temperature range between 153.15 and 219.25 K and a pressure range from 3–phase locus to the critical point of CH4 [105]. The author observed an intensification in the data in the vicinity of the critical point of CH4. P–xy for isotherms from 193.15–219.26 K was plotted using the frost–point data reported by Pikaar [94,105]. P–T relation for the binary CH4–CO2 mixture was obtained at dew point curves. Fig. 13 shows the data obtained by Hwang et al. along with the other available set of experimental data for the binary CO2–CH4 mixtures [105]. Hwang et al. observed a disagreement of the obtained data with the results of Neumann and Walch and Donnelly & Katz [93,106]. A linear isotherm was obtained below the critical point of CH4. The obtained isotherms were in good agreement with those obtained by Neumann and Walch at 186.15 and 173.35 K. However, a disagreement was observed for the curves at 183.25 and 178.75 K [106]. V–L equilibrium for CH4–CO2 binary systems at 270 K and over the entire pressure range from 3.242 to 12.362 MPa was experimentally studied by Fahad et al. [107]. Fig. 14 shows the data obtained for the

3.1.2. Predicted/Calculated phase equilibria Computer simulators having vast applications in the design, control, and optimization of gas processing facilities have attracted the researcher’s interest. By using these simulators, thermodynamic properties for the desired mixtures can be predicted. The basic principle behind these simulators is the use of an equation of state to model the phase equilibria [112]. Nowadays predicting and correlating the thermodynamic properties and phase equilibria using EoS is considered significant. Deficiency of data for CO2 ternary systems and significant variances for the binary CH4–CO2 system between different data sources makes the modelling work more meaningful. Valuable equations of states will predict the properties of complex and compounds with specific interaction as well as pure fluids [113]. Aleksander et al. calculated the V–L equilibrium for the CO2–CH4 mixtures and correlated it to the critical loci of the binary system [114]. Table 2 Correlation factor ‘m ’ for CO2–CH4 system. System

Temperature/K

Pressure/MPa

‘m ’

CO2–CH4

283.15

71.94 81.87 36.98 62.01

0.920 0.850 0.893 0.908

233.15

90

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9

7

8

5

6 Pressure / MPa

Pressure / MPa

7 5 4 3 2

230 K

1

250 K

0

Vapor Pressure of CO Stephen et al. data Hwang et al.

6

0.1

0.2

0.3 0.4 0.5 Mole fraction CH4

0.6

0.7

3 2

270 K

0

4

1

0.8

0

0

0.1

0.2

0.3

Fig. 12. Davolos et al. V–L equilibria in the CH4–CO2 system.

0.4 0.5 0.6 Mole fraction CH4

0.7

0.8

0.9

1

Fig. 15. Stephen et al. P–xy diagram for binary CO2–CH4, for temperatures above the critical temperature of CH4 [110]. Table 3 Comparison of Stephen's work and Hwang's data. T/K

219.27 210.38 203.15 193.15

Fig. 13. Hwang et al. P–xy comparison with reported literature [93,105,106]. 9

Pressure / Mpa

7 6 5 4 3

4.826 5.515 6.205 5.515 5.171 5.308 4.309 4.412 4.481 4.619

Mole fraction of CO2 in the vapor phase Hwang et al.

Stephen’s data

Difference

% Difference

0.205 0.2003 0.211 0.148 0.1054 0.110 0.0512 0.0446 0.0409 0.0323

0.1922 0.885 0.1973 0.1412 0.1025 0.1064 0.0510 0.0457 0.0418 0.0331

0.0128 0.0118 0.0137 0.0068 0.0029 0.0036 0.0002 −0.0011 −0.0009 −0.0008

6.2 5.9 6.5 4.6 2.8 3.3 0.4 −2.5 −2.2 −2.5

Table 4 Shen et al. [111] Exp. Mole fraction solubilities of CO2 in pure Liquid CH4.

Davolos et al. Fahad et al.

8

P/MPa

T/K

P/MPa

x (Shen et al.)

112.0 124.0 129.7 135.2 139.4 144.5 150.4 162.0 169.9 AAD

0.093 0.241 0.350 0.489 0.617 0.800 1.055 1.718 2.315

0.000213 0.000823 0.001413 0.002479 0.003678 0.005665 0.008225 0.017640 0.028960 4.14%

x (Davis et al.)

0.0016 0.0025 0.0037 0.0058 0.0093 0.0183 0.0290

Standard uncertainties u are u(T)= ± 0.11 K, u(P)= ± 7 kPa, ur( x )= ± 0.011 for x2 > 1000 ppm and ur( x )= ± 0.016 for x2 less than 1000 ppm. 0

0.05

0.1

0.15

0.2 0.25 Mol fraction CH4

0.3

0.35

0.4

0.45

Table 5 Alexander et al. critical locus values for CH4–CO2 system.

Fig. 14. Fahad et al. P–xy diagram for CH4–CO2 binary mixture.

The ordering effect was minimized in the critical region by using an EoS with a semi–empirical correction. The calculated data has an excellent comparison with the data of Kurata et al. Table 5 and Fig. 16 shows the comparison of the data obtained by Alexender et al. with the reported literature data [109,115]. The author also found an excellent agreement with the data obtained by Arai et al., Kaminishi et al., and Somait & Kidnay except in the vicinity of the critical locus [98,107,115]. A deviation was observed between the obtained data of vapor compositions and those reported by Davalos et al. [103]. Supercooled liquids and signified liquid–liquid equilibrium below 193.15 K, with the

Observed values x1 Tc/K

Pc/MPa

ρc/mol. L-1

Calculated valuesa x1 Pc/MPa

ρc/mol. L-1

0.166b 0.300b 0.475b 0.748c 0.974c 1

8.16b 8.55b 8.35b 6.47c 4.74c 4.604d

11.7b 12.2b 12.45b — — 10.1d

0.18 0.325 0.495 0.76 0.97 1

11.2 11.5 11.8 11.4 — 10.1

a b c d

91

288.15 273.15 253.15 219.26 193.15 190.58d

calculated at given Tc. Arai et al. [115]. Mraw et al. [109]. selected values.

8.45 8.80 8.45 6.47 4.68 4.60

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10

temperature for dry ice was predicted to within approximately 1 K. Concerns in calculating CO2 solidification conditions using a constant composition approach were also discussed, since this may yield results that do not represent true equilibrium. Table 7 shows the comparison of the ProMax predicted data for the vapor composition along the 3–phase locus with the reported experimental data in literature [92]. For the vapor composition along the 3–phase locus, for the ProMax simulator, the author found an AD, AAD, and MAD of –2.17 K, 2.55 and 11.1 K, respectively. Fig. 18 shows the comparison of the CO2 freeze–out temperature predicted by PROSIM and ProMax with the experimental data. The AD, AAD, and MAD for ProMax and PROSIM were 0.83, 1.0, 2.27 K and 1.55, 2.66, 7.22 K, respectively. In addition to 3–phase locus the CO2 frost and freezing lines for the binary CO2–CH4 mixtures having 1%, 3%, 5%, 10%, and 20% CO2 were also predicted and compared with the experimental data reported in the literature [92-94]. Tang and Gross modelled CH4–CO2 system by using the Perturbed–Chain Polar Statistical Associating Fluid Theory (PCP–SAFT) EoS [123]. V–L, L–L, V–S, and L–S phase equilibria were modelled over a vast range of pressures and temperatures. The author found an excellent agreement of the data predicted by PC–SAFT and PCP–SAFT EoS with the reported experimental data. It was also proposed that dry ice formation can be minimized by adding heavier hydrocarbons to the binary CH4–CO2 system during the cryogenic processes. Thermodynamic calculations for predicting the CO2 solidification was appropriately formulated by Tim and Chaffin [124]. The authors explained procedures for heat exchangers, expanders and columns. The established thermodynamic models were competent for predicting the CO2 freeze–out temperature for CH4–CO2 binary mixture in GPA RR–10 with an uncertainty (u) of 1.44 K while dealing data from other sources this uncertainty (u) may reach to 5.2 K. For verifying the freezing point predictions, the authors back–checked their results with real data from several operating plants. From these operating data, the authors have built simulation models for several different plants which have operated very near at their known CO2 freezing points. Table 8 shows the comparison of the predicted and real plant CO2 freezing data. The predicted freeze temperatures agree quite well with the observed plant CO2 freeze–out temperatures for all the four facilities. Excellent agreement was found between the GPSA CO2 freezing predictions and that obtained by Tim and Chaffin. To avoid pitfalls in many unit operations, the author defined the temperature safety margin by altering the thermodynamic calculations to the needs of the specific unit operation. Antoine equation based conventional model for calculating the CO2 freeze–out temperature in L–S equilibrium for binary CO2–CH4 mixtures was used by Yajun et al. [125]. The developed model has high accuracy in the V–S equilibrium than that in the L–S equilibrium. The L–S equilibrium model based on the Antoine equation for calculating

Exp. data of Arai et al.

273.15 K

9

Exp. Data of Mraw et al.

8

Pressure / MPa

7 6 5 4 3

Subcooled liquid mixtures

2 1 0

0

0.2

0.4 0.6 Mol fraction Methane

0.8

1

Fig. 16. Alexender et al. P–xy data for CH4–CO2 mixture.

assumptions that the mixture does not freeze, were also calculated. Using B1 = 150 and B2 = 20 in Eq. (3) the author also calculated V–L critical curves and found dissimilarities between the calculated critical compositions at given Tc and the observed values.

µor = RT

B1

TC

2 T x j . exp[ B2 (

)2]

(3)

and = 0.74048V o , where Vo indicates the close–packed volume, is the molar density of the system, and Δμ shows the chemical potential. The superscript “or” shows the ordering effect, R is the ideal gas constant, B1 and B2 are the systems dependent constants, ' and '' are the constants, xj is mole fractions, ΔTc is always chosen positive, and T is the temperature. Cheung and Zander formulated S–L equilibrium in the binary mixtures of CO2 with CH4, C2H6, and C3H8 [116]. The author used a temperature range between 87.4 and 194.6 K. The author determined the L–S equilibrium and linked the obtained thermodynamic phase data with available literature data. The author also studied the multicomponent mixtures based on their available binary data in the literature and found a good agreement. However, any experimental pressure value for S–L equilibria in CH4–CO2 binary system at different temperatures was not calculated. Leigh et al. calculated the V–L equilibria of the binary CO2–CH4 system at 230 & 270 K, using PR EoS [112]. At 270 K, the author compared the calculated results with the reported literature data, as shown in Fig. 17 [104,107,117]. The author pointed out a high accuracy of PR predictions at the low pressures and vice versa near the critical points. The CO2 freezing temperature was modelled using several commercial process simulators by Eggeman and Chafin [118,119]. The authors used NRTL and PR EoS for modelling L–S equilibria for CO2–CH4 binary mixtures, from GPA research report RR–10 with a ± 1.4 K uncertainty [120]. However, it was claimed that this uncertainty may rise to ± 5.2 K using any other data sources. Table 6 shows a comparison of the data obtained by Chafin et al. with the available experimental and commercial simulator’s data for the binary system CO2–CH4 [119]. A significant variation was observed between the process simulator results and experimental data. PR model is comparable to that of the NRTL model in the 172.04 K region but deviates in other areas. The MAD calculated by the author from the GPA RR–10 data was 1.4 K [121]. ProMax simulator was utilized by Hlavinka et al. to study the modelling of solid phase behavior in natural gas processing [122]. The authors mainly focused on dry ice formation, analogue with hydrate formation, and description of the phase equilibria at different P and T conditions. The authors related the predicted results from simulation with selected experimental data sets. The emergent formation

Peng Robinson EoS Leigh et al. Somait and Kidnay Al-Sahhaf et al.

9

Pressure / MPa

8 7 6 5 4 3

0

0.1

0.2

0.3

Mol fraction / CH4

Fig. 17. Leigh et al. P–xy data for CO2–CH4 270 K. 92

0.4

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Table 6 Eggeman and Chaffin CH4–CO2 binary freezing comparison [119]. Mole Fraction CH4

Mole Fraction CO2

0.9984 0.9975 0.9963 0.9942 0.9907 0.9817 0.9706 0.9415 0.8992 0.8461 0.7950 Maximum Absolute Deviation

Temperature/K

0.0016 0.0025 0.0037 0.0058 0.0093 0.0183 0.0294 0.0585 0.1008 0.1539 0.2050

Exp.

Simulator A

Simulator B

Simulator C

Eggeman et al. data

49.85 56.85 64.45 73.65 84.15 105.15 119.25 141.35 154.15 167.95 175.75

76.85 86.25 94.35 104.15 115.05 133.15 145.85 165.05 180.25 185.05 173.75 17.17

33.95 43.85 53.05 64.35 77.25 97.65 113.25 138.05 182.35 191.05 189.55 15.67

36.75 46.15 55.05 66.05 115.15 133.15 112.25 165.05 180.25 185.15 173.75 17.22

46.95 55.85 64.15 74.45 85.95 104.25 118.25 140.05 156.75 167.65 173.65 1.44

solid CO2 fugacity was replaced by a new thermodynamic method of reference state of the hypothetical fluid. Based on the accuracy of CO2 freezing temperature the authors improved phase–equilibrium model based on European gas research group, GERG–2008 having the Antoine equation in V–S equilibrium model, while the reference state method in L–S equilibrium model proved to be the best one. The comparison of predicted results for a complex natural gas system with the reported experimental data showed higher accuracy. Replacing the model based on the Antoine equation by the method of reference state of hypothetical fluid model in LSE, the average relative deviation of CO2 freezing temperature of CH4–CO2 binary systems by RK–Soave, PR, and GERG–2008 was reduced by 36.05%, 38.27%, and 85.66%, respectively. Phase equilibria of the binary CO2–CH4 system by two different methods was determined by Riva et al. [126]. In the first approach, the author used an EoS for representing the fugacity of the fluid phases, and for solid phase fugacity, an independent model was used. The Second approach was using an EoS capable of representing all the three phases at the same time. To enhance the description of the reported experimental L–S, V–S and V–L–S equilibrium data, binary interaction parameters have been abated for both the models. Model–2 shows slightly lower deviations with reference to the experimental values as compared to Model–1. At a specific CO2 mole fraction for L–S equilibrium, model–1 gives an improved illustration of SLE temperature, while at a fixed temperature model–2 is better in calculating CO2 mole fraction. Model–2 also performs slightly better for the representation of V–S equilibrium. Agrawal and Laverman calculated the frost points of CH4–CO2 binary mixtures for five different compositions ranging from 0.02–10 mol% CO2 [90]. The uncertainty in the composition may vary from 0.01 mol % to 0.1 mol %, while in temperature and pressure is 0.278 Kand 0.00345 MPa, respectively. Using the published literature for S–V equilibrium, the author made theoretical predictions of frost points using theory applicable to S–V equilibria. The author found an excellent agreement of the predicted frost point values for CH4–CO2 mixtures with Pikaar’s data, as shown in Figs. 19. Tan T et al. measured the V–S equilibria for the CO2–CH4 binary mixture by using a non–sampling visual observation technique [127]. The authors also determined CO2 frost points for the binary CH4–CO2 mixtures having 1.00%, 1.91%, and 2.93% moles of CO2. The selected pressures and temperature range for experiments were 0.962–3.01 MPa and 168.6–187.7 K, respectively. At constant CO2 composition, the effect of C2H6 and N2 addition to the CO2–CH4 binary on the CO2 frost point was also examined. The authors also give a comparison of the obtained data with the data reported by Pikaar, Agrawal, and Laverman at higher pressures, as shown in Fig. 20 [90,94]. It was observed that the frost points obtained for the CH4–CO2 binary matched more closely to the data obtained by Pikaar than that of Agrawal and Laverman

Table 7 CO2 freezeout predictions for Davis et al. vapor compositions measured along the 3–Phase locus in the CO2–CH4 system [122]. Vapor mole % CO2

Temperature/K

0.12 0.63 1.08 1.72 2.79 3.67 5.65 11.73 Average Deviation Average Absolute Deviation Maximum Absolute Deviation

Experimental

ProMax

140.93 165.6 175.88 177.6 183.99 188.71 193.65 205.71

152.1 168.38 174.32 179.65 185.49 188.88 194.49 205.99 −2.17 2.56 11.17

220

Temperature / K

200 180 160 Experimental ProMax PROSIM

140 120

0

0.1

0.2

0.3

0.4 0.5 0.6 Liquid CO2 /mol%

0.7

0.8

0.9

1

Fig. 18. Liquid Compositions measured along the S–L–V locus in the CO2–CH4 system. Table 8 Comparison of actual plant freezing vs. Chaffin et al. data. Plant#

Observed plant freeze Temp./K

Predicted freeze–out Temp./K (Chaffin et al.)

Absolute Deviation/K

Limiting Freezing Criteria

1 2 3 4

171.93 176.37 178.98 190.37

174.43 177.04 179.21 190.82

2.50 0.67 0.22 0.44

LSE VSE VSE LSE

93

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V–L equilibrium for the binary CO2–CH4 mixtures at 293 K was measured by Xu et al. using modified PR EoS [129]. The author observed an excellent agreement of the calculated data with the data reported by Arai et al. for the CH4–CO2 system at 288.15 K, [115]. Xu et al. performed two graphical tests for the thermodynamic evaluation of the binary data [129]. Fig. 21 shows the P–xy graph obtained by the author, along with the data obtained by Arai et al. and predicted data obtained by PR EoS. For analyzing the vapor composition, measurement enhancement factor (E) method, as shown in Eq. (5) was used.

E = Py (2) Ps (2)

(5)

10 9

Fig. 19a. Comparison of experimental and calculated frost points for CH4–CO2 system.

8

Pressure / MPa

7 6 5 4 3

288.15 K Arai et al.

2

288.5 K Xu et al. research work.

1

Correlated by Modified PR EoS.

0

293.4 K Xu et al. research work.

0

0.5

1

1.5 2 2.5 Mole fraction Methane

3

3.5

4

Fig. 21. V–L equilibrium for CH4–CO2 system obtained by Xu et al. [129].

ZareNezhad used PR EoS for calculation of CO2 frost point for the CO2–CH4 liquid and vapor mixtures at the cryogenic operating conditions [130]. To express the CO2–CH4 interactions at cryogenic conditions, the author derived a semi–empirical quadratic temperature dependent kij correlation from NGL Plants data. The AAD of the proposed thermodynamic model in prediction of CO2 freezing point in the S-V and S-L region was 0.23 % and 0.38 %, respectively. The overall AAD of the proposed model was found to be about 0.26 %. The proposed model can be used for accurate prediction of CO2 freezing temperatures of CO2–CH4 mixtures at cold sections of demethanization system of NGL extraction plants. The binary CO2–CH4 mixture having different CO2 concentrations, e.g., 40, 60, 75 & 90% were studied by Babar et al. [35]. The study aimed to identify CO2 solid formation and its quantification. PR EoS in Aspen HYSYS simulator was employed to predict the thermodynamic phase data for the binary mixture. The author presented P–T and T–xy phase diagrams for the identification and quantification of CO2 solid formation, respectively. The phase behavior of binary mixtures of CO2, N2, and H2S with nalkanes (C1–C5) was also studied by Aparicio Martinez and Hall using PC–SAFT EoS [131]. V–L–L three–phase line of binary CO2 with nC13H28 at 310.8 K was obtained with different kij values. Using the PC–SAFT EoS with different kij value, the authors also modelled pure compound vapor pressures, V–L critical points, and experimental V–L–L equilibria curve. However, no solid phase study was not conducted. PC–SAFT EoS along with Variable Range Statistical Associating Fluid Theory (VR–SAFT) was employed for modeling binary mixtures of CO2 with C3H8, n-C4H10, n-C5H12, n-C6H14, n-C7H16, n-C8H18, n-C10H22, n-C12H26, n-C14H30, n- C20H42, n-C22H46, n-C28H58, n-C32H66, n-C36H74, and n-C44H90 by Thi et al. [132]. V-L equilibria results were obtained and compared for both of the PC–SAFT and VR–SAFT EoS. Temperature and pressure range for the overall modelling was between 230–664 K and 0–40.0 MPa, respectively. From the comparison, it was found that PC–SAFT is comparatively most reliable for CO2–n-alkane system. Gross and Sadowski [133,134] also used PC–SAFT EoS for modelling V–L

Fig. 19b. Calculated frost points for CH4–CO2 system. 4

Agrawal and Laverman data for 0.97% CO

3.5

Pikaar's data for 1% CO Tan T et al. data for 1% CO

Pressure/MPa

3

Agrawal and Laverman data for 3.07% CO

2.5

Pikaar's data for 3% CO Tan T et al. data for 2.93% CO

2 1.5 1 0.5 0

150

155

160

165 Temperature/K

170

175

180

Fig. 20. Comparison of data obtained by Tan T. with Pikaar and Agrawal et al. [90,94,127].

[90,94]. Moreover, the author also highlighted the presence of some systematic errors in the data reported by Agrawal and Laverman at higher pressures [90]. Zhang et al. also provides a modelling technique for the calculation of CO2 frost points in CO2–CH4 binary system, for a wide range of CO2 concentration ranging from 0.108 to 0.542–mol % [128]. The author verified the calculated results by a set of published experimental data for the CO2 frost point. A solid fugacity model based on pure CO2 sublimation pressure was used to model the conditions for dry ice formation. CO2 frost points were predicted by the obtained thermodynamic model for the binary CO2–CH4 mixtures. By comparing the calculated data and experimental data, a good agreement was found with a maximum temperature deviation of 1.3 K, which depicts the reliability of the developed model. 94

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equilibria for CO2–n-alkane (CH4, C3H8, C4H10, n-C5H12, and n-C7H16). Wibawa et al. evaluated the performances of PR EoS with the classical mixing rules to calculate S–V and L–V equilibrium of binary CH4-CO2 system [135]. In S–V study, based on the reported experimental data, the author proposed a new binary interaction parameter values (kij) for the binary CH4–CO2 mixture. It was observed that the proposed kij enhanced the accuracy of PR EoS from (2.18% to 0.26%), (0.88% to 0.70%) and (0.61% to 0.44%) at CO2 composition of 1%, 1.91% and 2.93%, respectively. Shen et al. used PR and SRK EoS to model the CO2 frost point formation in the binary CO2–CH4 mixtures [111]. The author obtained two temperature-dependent correlations for the interaction parameter, kij, for the binary CH4–CO2 system by the experimental data for a temperature range of 112 to170 K and pressure up to 3 MPa. To validate the established model, the author compared the obtained data with the published experimental data of Davis et al. [92]. The author found that AAD decreases from 2.78% to 2.53% for the PR EOS and from 7.33% to 2.67% for the SRK EoS. The proposed temperature dependent (kij) correlations were more suitable for S–L phase equilibrium calculations on CH4–CO2 system in a temperature range of 112–170 K. Calculation techniques, for calculation of the phase equilibrium, e.g., SRK, PR and PC–SAFT EoS, and for critical temperature estimation, e.g., MF, CVF, CP, GT, RK, MW and GC methods of binary CH4–CO2 was summarized by Guo et al. based on the reported literature [136]. The author described that in the phase equilibrium study of binary CH4–CO2, the results obtained by PR EoS were more accurate. For the prediction of critical point of the binary mixture having low CH4 content (< 50%), all the estimation methods except Group Contribution method gave the results close to the experimental data, while GC method produced lower values. While in the region with high CH4 composition (> 60%), only MF and CP methods gave the most accurate results. Soo et al. compared the predictive models, e.g., SRK, CPA, GERG–008, PC–SAFT, and NLFHB EoS in calculating the phase equilibria of CO2–CH4 binary mixtures [137]. The author explained the inadequacy and effectiveness of each EoS model. V–L equilibria for the binary CO2–CH4 mixture was obtained and compared with the reported experimental data at 250, 270, and 293.4 K. GERG–2008 correlates both BP and DP with an uncertainty of 3%. PSRK, CPA, and NLFHB show similar degrees of accuracy when averaging the vapor and liquid composition deviations. The author also reported the P–T diagram of the binary CO2–CH4 mixture in CO2–loaded phase and mentioned that all types of EoS provide satisfactory results compared with experimental data. A detailed modelling study on the phase behavior of CO2–H.C systems over a vast range of temperatures and pressures was conducted by Ozturk et al. [138]. The authors used PC–SAFT EoS to model the complete phase diagram for the binary CO2–CH4 system. It was found that the PC–SAFT EoS can accurately predict the VLE, SVE, and SLE of CO2–CH4 system using a single set of temperature and pressure independent binary interaction parameters. The author also studied the outcome of C2H6 and C4H10 addition on the SLE of CO2–CH4. An inconsistency in the SLE experimental data of CO2–CH4 systems were also reported. The reported work by Ozturk et al. will help the researchers in precisely predicting the solid-fluid equilibria of CO2 in natural gas and for optimum design of cryogenic processes. Ali et al. investigated the CO2 solidification in binary CO2–CH4 mixtures and established a predictive model using the artificial neural network (ANN) technique [91]. The ANN model developed by the authors was successfully used for the V-S and V–L–S equilibrium study in a binary CH4–CO2 mixture. Binary CO2–CH4 mixtures with CO2 concentration in a range of 1–54.2 mol% were studied in a temperature range of 223.15 to 73.15 K. The author did not validate the model in the L–S region due to insufficient experimental data in this region. Furthermore, the author described that the developed model could be helpful in design calculations for the cryogenic CO2 capture process

from the binary CH4–CO2 binary mixture. Shen et al. used ThermoFAST to predict the thermodynamic data for the binary CH4-CO2 mixture [139]. The author investigated the binary mixture in a temperature range of 140–270 K for a complete range of CO2 mole fraction. For both ThermoFAST and KLSSP, the author found maximum deviations with the data of Pikaar [94], where a variation of up to 14 K and 23 K was observed for ThermoFAST and KLSSP, respectively. At low CO2 concentrations within KLSSP’s range of validity, the tuned ThermoFAST model has a root-mean-squared deviation (rmsd) of only 2.2 K, which was 16.4 K for the KLSSP model. Including the 41 additional conditions measured by Pikaar [94] at low CO2 concentrations, the overall rmsd of the models over this range increases to 3.0 K and 16.2 K for ThermoFAST and KLSSP, respectively. 3.2. Multicomponent CO2 mixtures with light alkanes 3.2.1. Experimental thermodynamic data Although CH4 is the most crucial component of natural gas, yet it may also contain other hydrocarbons. Therefore, the present work also presents the study of ternary mixtures having CO2–CH4 along with other hydrocarbons. Reported literature based on the thermodynamic phase study of ternary CO2–CH4–H.C mixture is also critically reviewed in the present article. The equilibrium compositions of liquid and vapor phases for the ternary CH4–CO2–C4H10 system at temperatures 310.93, 277.59, 244.26 K, and pressure 2.758, 5.516, and 8.274 MPa at each temperature was determined by Saxena et al. [102]. The authors observed a disagreement of the data obtained with the data reported by Wang et al. [96] for the ternary mixture at 277.59 K and 300.73 K at 5.516 MPa, and for 244.26 K and 300.73 K, 5.516, at 8.274 MPa. The existence of CH4–CO2 binary vapor and liquid phase equilibrium were also reported at the conditions indicated in the published literature. However, at the same conditions, Wang and McKetta rejected the survival of the CH4–CO2 binary in two phases. Phase compositions were measured along the S–L–V locus for multicomponent mixtures of CO2 containing CH4, C2H6, C3H8, and C4H10, at temperatures less than 216.55 K (triple point of CO2) by Kurata et al. [140]. The phase samples from the equilibrium cell kept at certain equilibrium conditions were analyzed to determine the phase compositions. The standard uncertainty in the temperature and pressure was about 0.167 K and 0.00345 MPa, respectively. Chromatographic calibration data showed the extreme relative uncertainty to be 3.2 mol %. The presence of heavier hydrocarbons in the system had a negligible effect on molal concentrations of CO2 and CH4. Molal equilibrium ratios for hydrocarbons in the presence of solid CO2 were consistently higher than those of hydrocarbon systems without CO2 at the same temperature and pressure ranges higher than 199.82 K. Table 9 shows the scope of Kurata et al. experimental work. Robert et al. analyzed the CO2–CH4–C2H6 ternary system and calculated V–L compositions for each mixture in V–L–S equilibrium [141]. A ternary phase diagram, shown in Fig. 22, at 199.8 K and 1.90 MPa, was obtained. S–L equilibrium data for the CO2–C2H5 from this study, S–V equilibrium data for CO2–CH4 mixture from Donnelly & Katz and Davis et al. and V–L equilibrium data for binary CH4–C2H5 from Kobayashi et al. were used to construct the ternary phase diagram Table 9 Ranges of variables investigated by Kurata et al. [140]. System studied

Temperature/K

CO2–CH4–C3H8

208.21, 165.21, 210.21, 210.21, 210.21,

CO2–CH4–n-C4H10 CO2–C2H6–C3H8 CO2–CH4–C2H6–C3H8

95

205.21, 150.21 208.21, 205.21, 205.21,

Composition parameter 200.21, 185.21,

0.35, 0.65

205.21, 185.21 200.21, 190.21 200.21, 190.21

0.35, 0.60, 0.75 0.35, 0.65 0.28, 0.68

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Fig. 22. (a). CO2–CH4–C2H6 phase diagram at 199.8 K and 1.9 MPa. (b) Liquid-phase compositions for S–L–V equilibria in the CO2–CH4–C2H6 system.

cryogenic processes to remove CO2 from a multicomponent natural gas mixture. The author presented Eq. (4) for predicting CO2 solubility in CH4–C2H6 mixtures.

x2 = (1

) x 2CH4 + x 2C2 H6 + (1

)(

1

2

(4)

)

Where stands for mole fraction ethane x 2CH4 andx 2C2 H6 shows CO2 mole fractions in the binary mixtures of CO2–CH4 and CO2–C2H6 in S–L–V equilibrium, and 1and 2 denotes the empirical functions of temperature. Hsi and Lu studied three ternary systems of CH4–H2S–nC4H10, CH4–CO2–nC4H10, and H2S–CO2–CH4 at 310.93 K and 5.516 MPa, 277.59 K and 5.516 MPa, and 310.93 K and 8.274 MPa, respectively [143]. From Fig. 23, it can be observed that the reported experimental data by Saxena et al. and Wang et al. for the CH4–CO2–C4H10 ternary system at 277.59 K and 5.515 MPa are not in agreement [96,102]. While the author observed a remarkable similarity between the experimental equilibrium composition and the predicted data. The predicted values in the region of high CO2 concentration and low CO2 concentration region are in satisfactory compliance with that reported by Saxena et al. and Wang et al. data respectively [96,102]. Davolos et al. reported the V–L equilibrium for the CH4–C2H6–CO2 ternary system at 250 K and pressures of 1.317–8.106 MPa [103]. Table 10 shows the data obtained by Davolos et al. for the ternary system at 250 K for different pressures [103]. An attractive property of

Fig. 23. Hsi and Lu predicted data with experimental ternary V–L equilibria for CH4–CO2–n-C4H10 system at 277.59 K and 5.516 MPa.

[93,142]. Robert et al. also studied the liquid phase compositions for S–L–V equilibria in CO2–CH4–C2H5 system [141]. The author mentioned that solid CO2 is more soluble in mixtures of Methane and Ethane than in either of the pure components, at least over a temperature range of 313.0 K. These understandings could be very helpful in designing the Table 10 V–L equilibrium for the ternary system CH4–C2H6–CO2 at 250 K [103]. P/MPa

YCH₄

YC₂H₆

YCO₂

XCH₄

XC₂H₆

XCO₂

K

2.127

0.0265 0.1728 0.1602 0.2500 0.0288 0.0374 0.0400 0.0235

0.4432 0.5700 0.5615 0.6200 0.2007 0.1700 0.1600 0.2154

0.5303 0.2572 0.2783 0.1300 0.7715 0.7926 0.8000 0.761 1

0.0033 …. …. 0.0352 …. 0.0020 0.0022 …

0.4512 …. …. 0.7898 … 0.1198 0.0986 …

0.5455 …. …. 0.1750 …. 0.8782 0.8992 …

2.533

0.3521 0.3264 0.1901 0.1323 0.1387 0.1701 0.2464

0.5377 0.5264 0.4148 0.2937 0.2601 0.1623 0.4730

0.1 102 0.1472 0.3951 0.5740 0.6012 0.6676 0.2806

0.0999 0.0950 0.0508 0.0298 0.0282 0.0247 …

0.818 9 0.8097 0.5792 0.3157 0.2662 0.1392 …

3.040

0.4021 0.2605 0.2580 0.3025 0.2630 0.3448

0.4531 0.2845 0.2420 0.0935 0.2270 0.4182

0.1448 0.4550 0.5000 0.6040 0.5100 0.2370

0.1351 0.0705 0.0685 … 0.0520 0.1203

0.7350 0.3741 0.3250 0.2495 0.6652

96

KC₂H₆

KCO₂

8.030 …. … 7.102 …. 18.70 18.18 …

0.9823 … … 0.7850 …. 1.419 1.623 ….

0.9721 ….. ….. 0.7429 ….. 0.9025 0.8897 …..

0.0812 0.0953 0.3700 0.6545 0.7056 0.8361 …

3.525 3.436 3.742 4.439 4.918 6.887 …

0.6566 0.6501 0.7162 0.9303 0.9771 1.1660

1.357 1.545 1.068 0.8770 0.8520 0.7985 …

0.1300 0.5554 0.6064 … 0.7085 0.214 5

2.976 3.695 3.766 … 5.058 2.966

0.6165 0.7605 0.7446 … 0.9098 0.6287

1.1138 0.8192 0.8245 … 0.7198 1.1050

CH₄

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the ternary system observed by the author was the behavior of the minimum in the vapor curve. At 2.127 MPa pressure was plotted against mole fraction of Ethane, the graph was a straight line at the minimum in the vapor curve beginning at the C2H6–CO2 azeotrope. Xu et al. studied V–L equilibrium for the ternary system of N2–CH4–CO2 at a temperature of 293 K and pressure 6.04, 6.25, 7.15, and 8.26 MPa [129]. The data obtained were correlated with available experimental data for the same systems. Original PR EoS, along with its modified form, was used for the thermodynamic data prediction. Introduction of the temperature–dependent fluid–specific parameters in the modified PR EoS shows dominance over the original PR EoS for the V–L equilibrium correlation for the ternary N2–CH4–CO2 system. Le et al. experimentally studied frost point for the ternary CH4–CO2–C2H6 mixture at 0.997% and 1.99% mole fraction of Ethane, as shown in Table 11 [127]. The CO2 mole fraction of the two ternaries was kept reasonably like the binary containing 1.91% mole fraction of CO2 so that the effect of Ethane can be easily observed. By adding Ethane to the binary CO2–CH4 mixture, a slight increase in the frost point of the system was found. However, N2 addition to the binary CH4–CO2 system showed that desublimation of CO2 also occurred at higher pressures than the binary CH4–CO2 system.

Garcia et al. modelled the PVT behavior and critical phenomena in CO2–n-alkane (C2–nC20) systems [144]. The author used the Perturbed Chain Statistical Associating Fluid Theory (PC–SAFT) EoS with a transferable binary interaction parameter, kij. Vapor pressures of pure components, V–L and L–L critical lines for binary mixtures of CO2 with C2H6, C3H8, n-C4H10, n-C5H12, n-C6H14, n-C8H18, n-C12H26, n-C13H28, and n-C14H30 were determined using PC–SAFT EoS. The author used pressure up to 50 MPa and temperature from 200 to 700 K for the thermodynamic study. The author showed the reliability of the PC–SAFT EoS to model the phase behavior of CO2-n-alkane systems to obtain satisfactory results for the global phase equilibria and PVT behavior. V–L equilibrium for the ternary CO2–CH4–N2 system was measured at two different conditions by Taher and Al–sahhaf [117]. First at a temperature of 230 K and pressure 6.205, 8.619 and 9.652 MPa, and second at a temperature of 250 K and pressure 8.963 and 10.342 MPa. To predict the thermodynamic data, PR and the Patel–Teja (PT) EoS were used. The authors used PR EoS with generalized parameters and fluid–specific temperature–dependent parameters. Excellent agreement was found in the data obtained by all the three methods. The selected system had two non–hydrocarbons components; therefore, it was not perfectly correlated in the critical region. The author concluded from the study that the predictions of fluid–specific PP and the PT equations were almost the same as those of the original PR EoS. SAFT model was used to model V–L equilibria of a gaseous mixture of CO2 with n-alkanes (n-C3 to n-C44) by Passarello et al. [145]. V–L equilibria for different CO2–alkane mixtures was modelled for a vast temperature range (220–573.45 K). The authors also determined a PT phase envelope for pure CO2. To ensure the reliability of the EoS, a comparison between predicted and reported experimental data was made, and an excellent similarity was observed. Jeffrey et al. predicted V–L equilibria of the ternary system of CO2 with alkanes [146]. The authors used grand canonical histogram–reweighting Monte Carlo simulations for obtaining phase diagrams for the binary and ternary CO2-H.C mixtures, and Gibbs Ensemble Monte Carlo (GEMC) technique for studying the phase behavior of ternary CO2–C3H8–N2 mixture. Pressure–temperature selected for the thermodynamic study of the ternary mixture were 270 K and 6.0 MPa. The authors used 150 molecules and 104 Monte Carlo (MC) cycles for simulation through GEMC. The obtained results were averaged over next 5 × 104 MC. From the calculation for the ternary system, it was observed that phase behavior; the molecular simulation could also be used for the thermodynamic study to a high precision without needing particular binary interaction parameters. Global fluid-phase behavior along with critical phenomena for a mixture of CO2 with n-alkane (C2H6 to n-C16H34) using Statistical Association Fluid Theory of Variable Ranged (SAFT-VR) EoS was studied by Blass and Galindo [147]. The temperatures and pressures ranges used by the author were from 200 to 700 K and 0 to 60.0 MPa, respectively. The author only provided the V–L equilibria, critical

Table 11 Le et al. Frost Point P & T data for CH4(1) + CO2(2) + C2H6(3). x2 = 1.95%, x3 = 97.053%

x2 = 1.96%, x3 = 96.05%

T/K

P/MPa

T/K

P/MPa

173.6 173.9 174.2 176.3 176.7 176.7 178.4 178.9 178.9 182.4 182.9 183.0

1.2677 1.2925 1.3447 1.5665 1.5931 1.6030 1.8096 1.7786 1.8254 2.2299 2.1792 2.2372

174.8 175.1 175.3 177.0 177.4 177.4 179.6 179.9 180.2 183.3 183.6 183.6

1.3146 1.3207 1.3073 1.6364 1.6520 1.6240 1.8385 1.8316 1.8481 2.2202 2.2227 2.2503

3.2.2. Predicted/calculated thermodynamic data Ternary CO2–CH4–C3H8 system under two different conditions was studied by Leigh et al. [112]. The author investigated the V–L equilibrium of the system at a temperature of 230 K and pressures of 0.8, 4.0, and 7.0 MPa, and then at a temperature of 270 K and pressure 2.8, 5.5, and 8.0 MPa. Ternary measurements were calculated using the binary interaction parameter kij in the PR EoS, obtained by the binary V–L equilibrium data regression. Fig. 24 shows the ternary phase envelopes obtained by the author for the CH4–CO2–C3H8 mixture.

Fig. 24. Leigh et al. data for the ternary mixture. 97

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CO2 freeze out line needs to be studied in detail. Table 14 shows the summary of all the data reported in this paper along with their scope and literature gaps.

Table 12 AAD obtained with both with SRK and with PR, for multicomponent CO2 mixtures. Mixture

AAD SRK

AAD PR

CO2–CH4–C2H6 CO2–CH4–C3H8 CO2–CH4–nC4H10 CO2–C2H6–C3H8 CO2–CH4–C2H6–C3H8

0.0288 0.0202 0.044 0.0535 0.0204

0.0236 0.0217 0.0391 0.056 0.022

4.1. Simulation work The literature reported in Section 3 shows the reliability of the commercially available simulation tools for the prediction of thermodynamic data for the CO2 gaseous mixtures. It will help the researchers to save the energy required for the thermodynamic study at cryogenic conditions. The use of process simulators also requires very less time for the thermodynamic study and hence their use is considered as time efficient. However, every simulator has some limitations; for example, Aspen Hysys simulator can only determine the CO2 solid formation and is unable to quantify the solidification. For overcoming these limitations, some new mathematical solutions need to be developed for the study. It is therefore also recommended to further investigate the thermodynamic phase study with more accurate experimental data.

Table 13 AAD obtained with both with SRK and with PR, for Binary CO2 mixtures. Mixture

AAD SRK

AAD PR

CO2–CH4 CO2–C2H6 CO2–C3H8 CO2–n-C4H10 CO2–n-C5H12 CO2–n-C6H14

0.0471 0.0115 0.0248 0.0374 0.0543 0.0714

0.0487 0.0111 0.0259 0.0348 0.0537 0.0713

4.2. Future scenarios Due to the increasing energy demand for energy, a continuous supply of energy is needed to fulfill the global requirement. Therefore, the contaminated natural gas reservoirs need to be explored. As discussed earlier, that proper thermodynamic study is very crucial for designing an energy and performance efficient cryogenic process for CO2 capture. It is costly and time consuming to study the thermodynamic phase behavior experimentally. In the future, therefore, the use of computer simulator and EoS will play a significant role in the thermodynamic study of the natural gas mixture. As per the natural gas compositions of many N.G wells, the models for high CO2 content and multicomponent N.G mixtures need to be developed in the future. Also, the quantification of CO2 dry ice formation needs to be modelled. The limitations with many available models need to be resolved for proper thermodynamic study.

behaviors, liquid–liquid, and vapor–liquid–liquid phase equilibria and did not investigate the solid phase. Thermodynamic methodology for the prediction of S–V–L equilibrium of CO2 mixtures with n-alkanes based on SRK and PR cubic EoS was developed by Guido et al. [148]. The research work was mainly focused on the comprehensive investigation of the method abilities for multicomponent systems. For the prediction of CO2 solubility in mixtures with n-alkanes, the authors used Cubic EoS. For an accurate solubility curve for both binary and multicomponent mixtures of CO2, the authors introduced adaptive parameters. The authenticity of the predicted data by the adopted methodology was done by comparing it with the published solubility data. Table 12 and Table 13 presents the AAD of the proposed method, both with SRK and with PR for the multicomponent and binary mixtures of CO2, respectively. CO2 frost points for binary CH4–CO2 and ternary CH4–CO2–C2H6 mixtures were measured over a vast range of temperature, pressure, and compositions by Xiong et al. [149]. The calculations were done by fugacity balance model based on PR EoS with van der Waals mixing rule. The author presented the reliability of PR EoS based model by showing a remarkable similarity of the calculated results with reported experimental data [127]. Xiong et al. showed that the effect of both Nitrogen and ethane on CO2 frost point is negligible. But, for the ternary mixture of CH4–CO2–N2 with 3% and 5% Nitrogen, the maximum pressure for CO2 frosting increases with Nitrogen content. However, in the CH4–CO2–C2H6 ternary mixture having 3% and 5% ethane, it decreases with ethane content. A new tool called ThermoFAST for prediction of solids formation in complex multicomponent systems and producing full phase diagrams were presented by Baker et al. [139]. The established model was capable of rapid prediction of S-L, S-V, and S-L-V equilibrium conditions. The author tuned the model to the available solid–fluid equilibrium literature data for 58 CO2–N.G mixtures. The author found that ThermoFAST a minimum and maximum root-mean standard deviation of 1.0 and 2.9 K, respectively, compared to KLSSP, which was 8.0 and 20.7 K, respectively.

5. Conclusions The Importance of cryogenic CO2 capture from natural gas is described in this review. The main advantage of cryogenic CO2 capture processes is high product purity. Cryogenic CO2 capture processes are also considered as green technologies because CO2 capture takes place without any organic solvents. Designing a cryogenic CO2 capture process require proper thermodynamic phase study of the gaseous mixture. Reported literature shows that cryogenic CO2 capture by phase separation has been investigated for a range of selected capture conditions for flue gases and synthesis gases. The present work is an attempt to critically analyze the published thermodynamic data and to identify the inconsistencies in the existing thermodynamic data available for the binary CO2-CH4 mixtures, and multicomponent mixtures containing CO2-CH4. In this review, PT, P-xy, and T-xy thermodynamic phase studies for the mentioned mixtures are summarized. This work also highlights the importance of computer simulators and EoS in the thermodynamic study of the N.G mixture. In the current work, some discrepancies have been reported among the available experimental thermodynamic phase data. For example, at high pressures, the deviations between Donnelly’s and Mraw’s data for CO2-CH4 can be up to 20% for the CO2 concentration in the vapor phase. Also, there is not satisfactory agreement among the S-L-V locus study of Donnelley and Sterner at high pressures. Therefore, more experimental work is needed to verify the reliability of these measurements. The predicted and calculated thermodynamic data revealed that using a calibrated binary interaction parameter kij, the cubic EoS can predict appropriate PVTxy results for CO2-CH4 mixtures. The equation is however studied mostly for thermodynamic phase study involving

4. Discussions In the last few decades cryogenic natural gas purification is getting more concentration in the research field. Most of the available literature covers the phase equilibrium data for the binary CO2–CH4 mixture. The addition of other higher hydrocarbons to the binary system needs to be studied. Most of the thermodynamic data is available in the L–V twophase region; however, very limited data is available for the S–V region. 98

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Table 14 Summary of experimental literature. Scope Composition

Research Gaps P & T Conditions

Section 1: Experimental thermodynamic study of Binary CO2 mixtures with n-alkanes T = 271.48–199.82 K Binary CO2–CH4 mixture P = 0.689–6.895 MPa Binary CO2–CH4 mixture

T = 210.15–113.15 K P = up to 10.1325 MPa

Binary CO2–CH4 mixture

T = 288.71–189.82 K P = 4.482 and 5.171 MPa

Binary CO2–CH4 mixture

T = 208.21–90.93 K P = 0.358–4.888 MPa

Binary mixtures of CO2 with the CH4, C2H6, and C3H8

T = 87.4–194.6 K

CH4–CO2 binary mixture

T = 223.15–293.15 K P = up to 20.265 MPa

CH4–CO2 Binary system

T = 266.48, 277.59 and 310.93 K P = 2.758, 5.516, and 8.274 MPa

CO2 mixtures with CH4, C2H6, C3H8, and C4H10

T = 210.21 to 150.21 K P = 0.903 to 3.049 MPa

Ternary CO2–CH4–C2H6 mixture

T = above 166 K P = 0.898 to 3.049 MPa

Binary CO2–C4H10 mixture

T = 223.71 to 444.25 K P = 0.138 to 7.929 MPa

Binary CO2–CH4 mixture

T = 250, 230, and 270 K P = 1.317 to 8.106 MPa T = 219.26 to 153.15 K P = 2.027 to 6.033 MPa T = 270 K P = 3.242 to 12.365 MPa T = 219.26 to 153.15 K P: 0.582 to 6.447 MPa

Binary CO2–CH4 mixture Binary CO2–CH4 mixture Binary CO2–CH4 mixture Binary CO2–CH4 mixture

T: 194 K P = 0.616 to 8.755 MPa

Binary CO2–CH4 mixture

T: 225 to 400 K P = 2.0 to 35.0 MPa

Ternary system N2–CO2–CH4

T: 250 to 230 K P: 6.205, 8.619, 8.963, 9.652, and 10.342 MPa T: 288.5 and 293.4 K P: 5.12, to 8.15 MPa

CO2–CH4 and N2–CH4–CO2 systems Binary CO2–CH4 mixture CO2 mixture with n-alkanes (n-C3 to n-C44) Ternary CH4–CO2–C3H8 system Binary CO2–CH4 mixture Binary CO2 mixtures with n-alkanes (C1–C5)

Binary CO2–CH4 mixture

Ref.

T = 137.59 to 198.09 K P = 0.172 to 2.785 MPa T: 220 to 573.45 K P = 0.1 MP up to Critical pressure T = 270 and 230 K, P = 0.8, 2.8, 4.0, 5.5, 7.0, and 8.0 MPa T = 210.37 to 129.71 K P = 0 to 4.82 MPa T: 310.8 K P = up to 3.2 MPa T: 168.6 to 187.7 K P: 0.962 to 3.01 MPa

- No discussion on phase envelope of the multicomponent mixture. - Limited study of 3–phase locus - No discussion about L–V region and CO2 freezeout line. - Low CO2 content studied. - No discussion about L–V region and CO2 freezeout line. - Three phase locus for different CO2 concentration was not discussed. - Effect of composition on 3–phase locus not discussed. - Only binary mixture studied. - No experimental pressure values for binary CO2–CH4 isotherms. - PT phase envelope was not included. - Only V–L equilibria studied, 3–phase locus and S–V, and S–L equilibria was not reported. - Only binary mixture studied. - No data is reported for the 3–phase locus of the ternary mixture. - No discussions about S–V region or CO2 freeze out data. - P–T phase envelope not discussed. - 3–phase locus for different CO2 content was not reported. - No experimental work was carried out for the validation of predicted data. - Phase equilibria were not studied at high pressure. - The author does not include cryogenic conditions. - Binary phase equilibria were not studied. - Only L–V region was studied. - Cryogenic conditions were not studied. - Only V–L region was focused. - Low CO2 content was studied. - Only V–L region was focused in this work. - Cryogenic conditions were not discussed. - No data was shown for the effect of the addition of other H.C to CO2–CH4 mixture. - Only CO2 liquid formation was focused. - Only P–xy phase envelope was reposted for CO2–CH4 mixture. - No discussion on multicomponent N.G–CO2 mixture - This research mainly focused on densities. - Phase envelope and cryogenic conditions not discussed. - Small temperature range was covered. - Only high pressures were discussed, no work has been performed on atmospheric pressure. - Cryogenic conditions were not studied. - Multicomponent N.G mixtures were not studied. - NG with high CO2 content was not studied. - Frost point at high pressure was not studied. - Only V–L region was studied. - No data about CO2–CH4 binary mixture was reported. - Only V–L equilibria was studied. - No description was given for CO2 freeze out. - Only binary CO2–CH4 mixture was studied. - Only solid CO2 formation was discussed. - V–L phase region was studied only. - No discussions were given about CO2 solidification. - No experimental study at cryogenic conditions. - Low CO2 content mixture studied. - High pressures operations were not studied.

[93] [94] [95]

[92] [116] [98] [102]

[140] [141]

[143] [103] [105] [107] [109] [114]

[150] [117] [129] [90] [145] [112] [119,124] [131]

[127]

(continued on next page)

99

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Table 14 (continued) Scope

Research Gaps

Composition

P & T Conditions

Binary CO2–CH4 mixture

T = 121 to 222 K P = 0.229 to 4.8 MPa T = 112 to 170 K P = 0.093 to 2.315 MPa

Binary CO2-CH4 mixture

Section 2: Predicted/calculated thermodynamic study of Binary CO2 mixtures with n-alkanes Binary CO2–CH4 mixture T = 283.15 K and 233.15 K P = 3.698 to 8.187 MPa Binary CO2–CH4 mixture

T = 194 K P = 0.616 to 8.755 MPa

Binary mixtures of CO2 with the CH4, C2H6, and C3H8

T = 87.4 to 194.6 K

Binary CO2–CH4 mixture

T = 230 and 270 K P = 3 to 9 MPa

Binary CO2–CH4 mixture

T = 210.37 to 129.71 K P = 0 to 4.82 MPa T = 88.71 to 304.26 K P = 0 to 8.481 MPa

Binary CO2–CH4 mixture Binary CO2–CH4 mixture Binary CO2-CH4 mixture Binary CO2–CH4 mixture

T = 210 to 305 K P = 0.5 to 8.0 MPa T = 120 to 180 K P = 1 to 3.5 MPa T = 208.21 to 90.93 K P = 0.358 to 4.888 MPa

Binary CO2–CH4 mixture

T = 120 to 200 K P = 1 to 6 MPa

Binary CO2–CH4 mixture

T = 168.6 to 187.7 K P = 0.962 to 3.01 MPa T = 121 to 222 K P = 0.229 to 4.8 MPa T = 293 K P = 0 to 9 MPa T = 160 to 210 K P = 0.5 to 3 MPa

Binary CO2–CH4 mixture Binary CO2-CH4 Binary CO2-CH4

Binary CO2-CH4 Binary CO2 mixtures with n-alkanes (C1–C5)

T = 93 K to 270 K P = 0.1 to 4.8 MPa T = 310.8 K P = up to 3.2 MPa

Binary mixtures of CO2 with C3H8 to C8H18, and n-C10H22, nC12H26, n-C14H30, n- C20H42, n-C22H46, n-C28H58, nC32H66, n-C36H74, and n-C44H90

T = 230 to 664 K P = up to 40.0 MPa

CO2 mixtures with n-alkane (CH4, C3H8, C4H10, n-C5H12, and n-C7H16)

T = 450 K P = up to 100.0 MPa

Binary CO2-CH4

T = 155 to 215 K P = 0.1 to 2 MPa

Binary CO2-CH4 mixture

T = 112 to170 K Pressure up to 3 MPa

Binary CO2-CH4 mixture

T = 230 and 270 K P = 0.5 to 8.6 MPa 250, 270, and 293.4 K

Binary CO2-CH4 mixture Binary CO2-CH4 mixture Binary CO2-CH4 mixture

T = 144.3 to 288.0 K P = 3.45 MPa, 4.64 MPa, 4.93 MPa T = 223.15–73.15 K

Ref.

- No data has been reposted for L–V region - Only binary mixture has been studied. - Only S-L was studied, and no data has been reposted for S–V and L–V region

[128] [111]

- The cryogenic temperature was not studied. - No study was included about P–T phase envelope. - Only P–xy phase envelope was reported for CO2–CH4 mixture. - No discussion on multicomponent N.G–CO2 mixture - No proper experimental pressure values validation for binary CO2–CH4 isotherms. - Phase equilibria not addressed. - The research work was focused on the L-V study and did not provide any data about CO2 solidification. - Only binary CO2–CH4 mixture was studied. - Only solid CO2 formation was discussed. - Only binary CO2–CH4 mixture was studied. - No description was given on the effect of composition on three phase loci. - No discussion about 3–phase locus. - Only binary CO2–alkane mixtures were studied. - CO2 freeze-out in V-S and L-S was modelled. - No calculation was done for 3-phase locus. - Only Binary CO2–CH4 mixture has been discussed. - Variation of 3–phase locus with changing CO2 concentration was not discussed. - The effect of composition on the CO2 frost point was not examined. - Very low CO2 concentration was studied. - Low CO2 content was studied.

[101]

- No data was reposted for L–V region - Only binary mixture was studied. - No data was provided for CO2 solidification.

[128]

- Low CO2 content was used for CO2 frost points modelling. - No data was provided for the CO2 solid formation at high pressures. - PR EoS state was used, and no experimental work was performed for the study. - V–L–L phase region was studied only. - No idea was given about CO2 solidification. - No experimental study at cryogenic conditions. - No discussion was given about CO2 solidification. - Phase envelop was not discussed at cryogenic conditions. - CO2 solid formation was not discussed. - Phase envelopes were not obtained at cryogenic temperatures. - Low CO2 content was used for CO2 frost points modelling - No experimental data were reported for CO2 solidification. - No data were reported for dry ice formation at high pressures. - Only SLV was investigated for the binary system. - No data was reported for the CO2 solidification. - Only P-xy was reported for the binary mixture - Only VLE was studied, and no data was provided for the CO2 freeze-out or frosting. - CO2 freezing was investigated for binary CO2CH4 having low CO2 content. - No experimental study was performed for the CO2 solidification. - The model was not validated in the SL region.

[130]

[114]

[116] [112] [118,119] [122] [123] [125] [126]

[90] [127]

[129]

[35] [131] [132]

[133,134] [135]

[111]

[136] [137] [138] [91]

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Table 14 (continued) Scope

Research Gaps

Composition

P & T Conditions

Binary CO2–CH4 mixture

T = 110–210 K P = 0.1–4 MPa

section 3: Experimental thermodynamic study of Multicomponent CO2 mixtures Ternary CH4–CO2–C4H10 mixture T = 310.93, 277.59, 244.26 K P = 2.758, 5.516, and 8.274 MPa CO2 mixtures with CH4, C2H6, C3H8, and C4H10

T = 150.5–208.21 K

CO2–CH4–C2H6

T = 199.8 K P = 1.90 MPa

CH4–H2S–nC4H10, CH4–CO2–nC4H10, H2S–CO2–CH4

T = 310.93 K, P = 5.516 MPa, T = 277.59 K, P = 5.516 MPa, T = 310.93 K, P = 8.274 MPa

CH4–C2H6–CO2

T = 250 K P = 1.317–8.106 MPa

N2–CH4–CO2 CH4–CO2–C2H6

Section 4: Predicted/Calculated thermodynamic study of Multicomponent CO2 mixtures CO2–CH4–C3H8 T = 230, 270 K P = 0.8, 2.8, 4.0, 5.5, 7.0, and 8.0 MPa CO2 mixture with n-alkane (C2–C20) CO2–CH4–N2

T = 200–700 K Pressure up to 50.0 MPa

CO2 mixtures with n-alkanes (n-C3 to n-C44)

T = 220–573.45 K

Ternary CO2–N2–C3H8 mixture

T = 270 K P = 6.0 MPa

CO2 with n-alkane (C2H6 to n-C16H34)

T = 200–700 K P = 0–60.0 MPa T = 150–210 K P = 0.358–5.25 MPa

CO2 mixtures with CH4, C2H6, C3H8, C4H10, C5H12, C6H14 Ternary CO2–CH4–C3H8 CH4–CO2–C2H6

T = 153.15–193.15 K P = up to 3 MPa

solid phase for the binary CO2-CH4 mixtures with low CO2 content, and not for multicomponent mixtures and CO2 rich N.G mixtures. Therefore, to ensure appropriate data for proper development of future EoS, more experimental investigation about the PVTxy properties of the CO2 rich natural gas, including both binary and multi-component mixtures is recommended in this review. Furthermore, before developing a proper model for the CCS, identification of the standard accuracy according to the demands of process design and operation is of vital importance. This work will help researchers to enhance the CO2 capture efficiency of the cryogenic processes. The designing and optimization of a more efficient cryogenic process should be a goal for the future. Moreover, a reference EoS for CCS should be developed in the future.

Ref.

- Only S-V equilibria were studied.

[139]

- High CO2 content in the ternary mixture needs to be studied. - The ternary mixture needs to be studied at cryogenic conditions. - CO2 solidification at high pressures was not studied. - High CO2 content in the mixture was not studied. - CO2 freeze-out in the ternary mixture was not studied. - High CO2 content in the ternary mixture needs to be studied. - S-V in the system was not studied. - PT phase envelop for the ternary system was not provided. - Only V-L equilibrium was investigated. - No data was provided for the CO2 solidification. - Low-temperature investigation was not done for the system. - Only V-L equilibrium was studied. - Gaseous mixture with low CO2 content was studied. - CO2 freeze-out at high pressures was not investigated.

[102]

- The study was not conducted at cryogenic conditions. - Only V-L was investigated. - No experimental data was obtained for the mixtures at cryogenic conditions. - CO2 solid formation was not studied in the ternary system. - Only L-V equilibrium was studied for the system, S-L, and S-V at cryogenic conditions need to be investigated. - Phase envelope at cryogenic temperatures was not studied. - High content CO2 natural gas was not studied. - Solid phase formation was not studied. - Phase envelope for CO2–CH4 was not studied. - Low CO2 content was studied only. - Full range of PT phase envelope for the mixtures was not discussed. - CO2 solidification at high Pressures and high CO2 content need to be investigated.

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Acknowledgement The authors gratefully acknowledge the financial and infrastructural help from CO2RES center and Department of Chemical Engineering, Universiti Teknologi PETRONAS, Malaysia. Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.cryogenics.2019.07.004. References [1] Tuinier M, van Sint Annaland M, Kramer GJ, Kuipers J. Cryogenic CO2 capture using dynamically operated packed beds. Chem Eng Sci 2010;65:114–9. [2] Yousef AM, El-Maghlany WM, Eldrainy YA, Attia A. New approach for Biogas purification using cryogenic separation and distillation process for CO2 capture. Energy 2018;156:328–51. [3] Abunowara M, Elgarni M. carbon dioxide capture from flue gases by solid sorbents. Energy Procedia 2013;37:16–24.

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 101

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