Determination of CO2 Solubility in Saturated Liquid CH4 + N2 and

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Determination of CO2 Solubility in Saturated Liquid CH4 + N2 and CH4 + C2H6 Mixtures above Atmospheric Pressure Taotao Shen, Ting Gao, Wensheng Lin,* and Anzhong Gu Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, Shanghai 200240, China ABSTRACT: Accurate CO2 solubility data are crucial for putting a proposal of pressurized liquefied natural gas (PLNG) project into practice. A solid−liquid equilibrium (SLE) apparatus, which is based on the static−analytic method, has been set up to measure the solubility of carbon dioxide in saturated liquid CH4/CH4 + N2/CH4 + C2H6 in the pressure region from atmospheric up to 3 MPa, corresponding to the temperature region from (112 to 170) K. In addition, Peng− Robinson (PR) and Suave−Redlich−Kwong (SRK) equationsof-state (EOS) are selected to calculate the solubility of carbon dioxide in CH4 + N2 and CH4 + C2H6 mixtures, and the results are consistent with the experimental data in the whole region. Two temperature-dependent correlations for the interaction coefficients kij on CH4 + CO2 system are derived by the experimental data for PR and SRK EOS, which can improve the calculation accuracy of the binary and ternary solid−liquid phase equilibrium.

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INTRODUCTION Oceans are rich in natural gas resources, and LNG (liquefied natural gas) technology is often considered the most promising option for offshore natural gas production and transmitting, as the volume of natural gas will reduce to 1/600 after liquefaction. The idea of offshore liquefied natural gas usually refers to the FPSO (floating production storage and offloading) concept of offshore oil exploitation. In a proposed LNG-FPSO, the gas is purified, liquefied, stored, and finally offloaded to an LNG carrier. Although there are no serious problems in the technical aspects, the investors are still very cautious about building an LNG-FPSO due to the relatively high investment comparing to a conventional onshore LNG plant. Accordingly, reducing the footprint of LNG plants will be the key of the maritime LNG plant.1,2 Papka et al. proposed the PLNG (pressurized LNG)3 technology; that is, liquefied natural gas was liquefied and stored at a relatively high pressure [(1.0 to 2.0) MPa], corresponding to an increased condensation temperature [about (−100 to −120) °C]. On one hand, the increase of condensation temperature can reduce the required cold energy and the heat transfer area during liquefaction. On the other hand, a higher temperature can increase the solubility of CO2 in LNG [increased from less than 100 ppm to (1 to 3) %], which make it possible to cancel the CO2 pretreatment device in the liquefied natural gas system. Therefore, the decrease of the cold box area, especially the cancellation of the CO2 pretreatment unit, will substantially reduce the investment and the footprint of the whole system4,5 which make the offshore plants economically practical. Thus, in the PLNG temperature region, the precise CO2 solubility data in the LNG are essential to the © 2012 American Chemical Society

decision whether the PLNG technology can be applied to offshore platforms or not. From the middle of last century, experts began to measure the solubility of carbon dioxide in the cryogenic liquid by experimental methods. Fedorova6 calculated the solubility of carbon dioxide in liquid oxygen and liquid nitrogen according to ideal solution theory. At the same time, he did some experiments and found that the theoretical calculations are more than 100 times larger than the experimental values. Donnelly and Katz7 measured the three phase loci for the CH4−CO2 binary system over the temperature range of (194.4 to 215.2) K. Pikaar8 used a constant volume cell to measure three phase locus points for the CH4−CO2 binary system over a range of approximately (143 to 200) K. Additionally, solid− liquid equilibria along (113.4, 132.5, 152.7, 173, 183, 189, and 193) K isotherms were acquired in the saturation cell. Davis et al.9 performed a series of experiments on the CH4−CO2 system and got the solubility of carbon dioxide in methane at temperatures ranging from (129.65 to 201.26) K. De Stefani et al.10 measured the solubility of nitrous and carbon dioxide in liquid oxygen at temperatures between (90 and 110) K using a static−analytic method. In 2003, they designed a new device named “atomiser-injector” which was used to determine the CO2−N2O cosolubility in liquid oxygen at 90.44 K.11 ZareNezhad and Eggeman12 used the Peng−Robinson equation of state (PR EOS) to predict CO2 freezing points of hydrocarbon liquid and vapor mixtures at cryogenic conditions of gas plants. The overall average absolute relative Received: April 5, 2012 Accepted: July 6, 2012 Published: July 18, 2012 2296

dx.doi.org/10.1021/je3002859 | J. Chem. Eng. Data 2012, 57, 2296−2303

Journal of Chemical & Engineering Data

Article

Figure 1. Cryogenic solid−liquid equilibrium apparatus. 1, cryostat; 2, thermostat; 3, equilibrium cell; 4, heating wire; 5, platinum resistance thermometer; 6, level controller; 7, liquid nitrogen vessel; 8, digital indicator; 9, pressure transducer; 10, buffer tank; 11, PID temperature regulator; 12, gas chromatograph; 13, vacuum pump; 14, solvent reserve; 15, solute reserve; 16, insulation materials.

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EXPERIMENTAL SECTION Currently, three main methods are used in the measurement of solid solubility in cryogenic liquids: the synthetic−optical method, the evaporation method, and the static−analytic method. All three methods are suitable for measuring the substances with a relatively high solubility (between 10−1 and 10−4 mole fraction); however, to measure very low solubility (lower than 10−4 mole fraction), the static−analytic method is better.16 The static−analytic method can be divided into the static spectroscopic analytic method and the chromatographic analytic method according to the different manner of analysis. The chromatographic analytic method is often adopted for the organic systems.16 Referring to the commonly used method of solid solubility measurement in liquid oxygen, the chromatographic analytic method was selected to measure the solubility of CO2 in liquid CH4 + N2 and CH4 + C2H6 mixtures. Chemicals. Carbon dioxide, methane, nitrogen, and ethane used in these measurements are provided by Shanghai Wetry Standard Gas Company with the following purities: Carbon dioxide: mole fraction purity > 99.995 %, Methane: mole fraction purity > 99.99 %, Nitrogen: mole fraction purity > 99.999 %, Ethane: mole fraction purity > 99.99 %. Apparatus. The principle of the experiment is as follows. Appropriate amounts of solvent and excess solute CO2 gas are

deviation between the experimental and the predicted CO2 freezing temperatures for this binary system is 0.26 %. Carter and Lucks13 presented a strategy for describing all of the solid− liquid phase equilibria of a binary mixture, by combining a classical equation-of-state with a general mathematical artifice for the fugacity of the solid phase. Zhang and Solbraa14 simulated the solubility of carbon dioxide and heavy hydrocarbons in the natural gas by use of software NeqSim15 at low temperatures, and the simulation result agreed well with experimental data. As can be seen from the above literatures, only a few authors engaged in work directly related to the solubility of CO2 in LNG, and their work only involved the solubility of CO2 in pure methane, without considering the influence of other components of natural gas, such as nitrogen and ethane. As an attempt to fill this gap, the experimental method was adopted in this paper to measure the CO2 solubility in liquid CH4 + N2 and CH4 + C2H6 mixtures in the PLNG temperature region [(112 to 170) K]. At the same time, a proper theoretical calculation method was selected to calculate the solid−liquid phase equilibrium, and the binary interaction coefficient between CH4 and CO2 was associated by a combination of experimental data and theoretical results. 2297



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consequently the pressure in the equilibrium cell decrease, more solvent gas is loaded to ensure that the liquefied fluid is enough to fill 2/3 of the cell. The expected temperature is reached after about (2 to 3) h, with helium introduced into the thermostat to shorten the time of equilibrium. Equilibrium is assumed when the temperature fluctuation of equilibrium cell is less than 0.1 K and the total pressure fluctuation remains within 0.001 MPa during a period of 1 h. Then, liquid samples are drawn through a sampler capillary and analyzed. It is essential that the samples accurately represent the component of the solution. The buffer tank is vacuumized several times before loading the sample, and then, the gas in the buffer tank is used to purge the chromatograph more than three times. For each equilibrium temperature at least 10 samples are withdrawn and analyzed to check for measurement repeatability.

introduced into the equilibrium cell. Then, the temperature is lowered, and gas in equilibrium cell is liquefied. Several hours later, the system reaches solid−liquid phase equilibrium. A small amount of the solution is sampled and sent into the gas chromatograph for analysis. The CO2 concentration in the sample is the solubility of CO2 in the solvent. The experimental apparatus used in the present work is shown schematically in Figure 1. A stainless steel thermostat (capacity: about 5.5 L) is suspended in a cryostat partially filled with liquid nitrogen. The thermostat is cooled by vapor that arises from the liquid nitrogen. A heating wire with the maximum power of 150 W wrapped around the thermostat provides heat for the experiment. In this way, liquid nitrogen acts as the cold reservoir, while a heating wire connected to a PID thermal regulator is used to achieve temperature stability within 0.1 K. Therefore, a relatively constant temperature field is provided to the equilibrium cell (capacity: about 350 mL). Less than 0.3 g of microsamples (to avoid disturbance of the thermodynamic equilibrium) are drawn each time through a capillary with an internal diameter of 1 mm plunging into the equilibrium cell. After gasification and depressurization in the evacuated buffer tank, a 1 mL gas sample is sent into the gas chromatograph detector. The cryostat is a 100 L double-enveloped vessel. The level of liquid nitrogen is monitored using a level controller. In this study, four GFD film platinum resistance thermometers with range of (55 to 300) K are used to measure the temperature (one in the equilibrium cell, the other three in the top, in the middle, and in the bottom of the thermostat, respectively). The uncertainties of these thermometers are ± 0.1 K, calibrated by Chinese Academy of Science Cryogenic Measurement Station. The uncertainty of the temperature indicator is ± 0.01 K, so the total uncertainty of temperature measurement in this study is u(T) = ± 0.11 K. The pressure in equilibrium cell is measured by the NS-I1 type pressure transducer which works from (0 to 6) MPa. The pressure transducer is calibrated by Shanghai TM Automation Instruments Company achieving a relative uncertainty of ± 0.1 %. The uncertainty of the pressure indicator is ±1 kPa, so the total maximum uncertainty of pressure measurement in this work is u(p) = ± (6 MPa × 0.1 % + 1 kPa) = ± 7 kPa. The samples are analyzed using a gas chromatograph (GC 1690) equipped with a thermal conductivity detector (TCD) for constant measurement (x2 > 1000 ppm) and a flame ionization detector (FID) for trace measurement (x2 < 1000 ppm). The uncertainty of components measurement is mainly derived from the standard gas and the column analysis. In this work, the relative uncertainty of the column is ± 0.001. The relative uncertainties of the standard gas are ± 0.01 when x2 > 1000 ppm and ± 0.015 when x2 < 1000 ppm, respectively. So the relative deviations of components measured are ur(x) = ± 0.011 for TCD and ur(x) = ± 0.016 for FID. Procedure. The experimental procedure consists of the following main steps: (1) filling of the equilibrium cell; (2) regulating the cell temperature to achieve the desired equilibrium conditions; (3) sampling and analyses. At room temperature, the equilibrium cell and its loading lines are evacuated. Then, the cell is partially loaded with solvent gas (CH4/CH4 + N2/CH4 + C2H6) and excessive CO2, to reach a pressure of 5.5 MPa. Afterward, the cryostat is filled with liquid nitrogen up to 20 cm, and the PID thermal regulator is opened to set a desired temperature by adjusting the heating power of the heating wire. As the temperature and

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EXPERIMENTAL RESULTS The experimental solid−liquid equilibrium data for CH4 + CO2 binary system, CH4 + N2 + CO2 ternary system, and CH4 + C2H6 + CO2 ternary system were measured in the PLNG temperature region [(112 to 170) K] and at pressures up to 3 MPa. CH4 + CO2 Binary System. Methane is the most important component of natural gas. In this paper, SLE measurements on the CH4 + CO2 binary system were performed for comparison with experimental results of Davis et al.,9 to verify the reliability of the experimental apparatus which would be used to measure the solid−liquid equilibrium of CH4 + N2 + CO2 and CH4 + C2H6 + CO2 ternary systems. In this work, the test temperature points are (112.0, 124.0, 129.7, 135.2, 139.4, 144.5, 150.4, 162.0, and 169.9) K, respectively. For each temperature at least 10 samples are drawn and analyzed. The data were averaged as the solubility at each temperature. The experimental data on CH4 + CO2 binary system of this work, and those of Davis et al.,9 are presented in Table 1. Table 1. Experimental Mole Fraction Solubilities of CO2 (2) in Pure Liquid CH4 (1) at Temperature T and Pressure pa T/K

p/MPa

x (this work)

x (Davis et al.9)

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

0.0016 0.0025 0.0037 0.0058 0.0093 0.0183 0.0290 4.14 %

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 < 1000 ppm. a

First, we can draw a conclusion from Table 1 that the solubility of carbon dioxide in saturated liquid methane increases with temperature increasing.When T = 145 K, the solubility of carbon dioxide in methane reaches 0.5 %, which is approximately 25 times higher than that at atmospheric pressure. This means that a natural gas liquefaction process running at 145 K may allow CO2 content as high as 0.5 % and 2298



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decreases with the increase of nitrogen content when the temperature is higher than 140 K. CH4 + C2H6 + CO2 Ternary System. Ethane is another common component in natural gas, whose proportion may be up to 10 % or higher. So the solubility of carbon dioxide in 98 mol % CH4 + 2 mol % C2H6, 95 mol % CH4 + 5 mol % C2H6, and 90 mol % CH4 + 10 mol % C2H6 mixtures have been measured, and the results are shown in Table 3.

the CO2 removal unit in an LNG plant may be minimized or even canceled. As can be seen from Table 1., the experimental data of this study are very close to the data of Davis et al.9 with the 4.14 % average absolute deviation. Consequently, the experimental apparatus made for this study can be used further to measure CO2 solubility in CH4 + N2 and CH4 + C2H6 mixtures. CH4 + N2 + CO2 Ternary System. Beside methane, nitrogen is a common component of natural gas. Due to the great difference of the molecular structure between N2 and CH4, the solubility of CO2 in CH4 + N2 may be obviously different from that in pure CH4. The nitrogen content in the conventional natural gas is usually less than 5 %. To better understand the impact to CO2 solubility by adding nitrogen, three mixtures, which are 98 mol % CH4 + 2 mol % N2, 95 mol % CH4 + 5 mol % N2, and 90 mol % CH4 + 10 mol % N2, were selected in the experiment. The experimental results are shown in Table 2.

Table 3. Experimental Mole Fraction Solubilities of CO2 (2) in Liquid CH4 (1) + C2H6 (3) Mixtures at Temperature T and Pressure pa solvent

T/K

p/MPa

x

98 % CH4 + 2 % C2H6

120.0 124.0 129.7 135.2 139.4 144.5 150.4 162.0 169.9 120.0 124.0 129.7 135.2 139.4 144.5 150.4 162.0 169.9 120.0 124.0 129.7 135.2 139.4 144.5 150.4 162.0 169.9

0.175 0.233 0.342 0.473 0.590 0.770 1.012 1.632 2.228 0.171 0.229 0.331 0.459 0.578 0.745 0.982 1.588 2.155 0.162 0.218 0.315 0.437 0.548 0.708 0.930 1.488 2.006

0.000577 0.000821 0.00155 0.00263 0.00384 0.00574 0.00854 0.0186 0.0303 0.000601 0.000945 0.00157 0.00267 0.00389 0.00604 0.00873 0.0193 0.0319 0.000624 0.000956 0.00159 0.00273 0.00395 0.00623 0.00923 0.0198 0.0331

Table 2. Experimental Mole Fraction Solubilities of CO2 (2) in Liquid CH4 (1) + N2 (3) Mixtures at Temperature T and Pressure pa solvent

T/K

p/MPa

x

98 % CH4 + 2 % N2

112.0 124.0 129.7 135.2 139.4 144.5 150.4 162.0 169.9 112.0 124.0 129.7 135.2 139.4 144.5 150.4 162.0 169.9 112.0 124.0 129.7 135.2 139.4 144.5 150.4 162.0 169.9

0.155 0.326 0.446 0.596 0.724 0.929 1.168 1.845 2.421 0.268 0.418 0.545 0.725 0.880 1.095 1.385 2.097 2.685 0.318 0.580 0.748 0.968 1.146 1.397 1.678 2.448 3.150

0.000225 0.000889 0.00150 0.00250 0.00370 0.00550 0.00821 0.0175 0.0277 0.000238 0.000909 0.00158 0.00256 0.00375 0.00542 0.00820 0.0162 0.0268 0.000254 0.000917 0.00159 0.00265 0.00377 0.00537 0.00816 0.0159 0.0252

95 % CH4 + 5 % N2

90 % CH4 + 10 % N2

95 % CH4 + 5 % C2H6

90 % CH4 + 10 % C2H6

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 < 1000 ppm. The compositions expressed as “%” in the table are mole-based. a

The trend of carbon dioxide solubility in CH4 + C2H6 mixtures increased with temperature increasing is the same as the previous two sets of experimental data. In the whole temperature range, adding ethane in methane will increase the solubility of carbon dioxide in liquid CH4 + C2H6 mixtures. The increase of CO2 solubility is not proportional to the amount of ethane; instead, it is like a logarithmic relation.

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 < 1000 ppm. The compositions expressed as “%” in the table are mole-based a

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THEORETICAL CALCULATIONS Experimental measurement is the most reliable means to obtain the solid−liquid equilibrium data. However, it is impossible to get the experimental data for the infinite kinds of mixture under infinite kinds of temperature and pressure conditions. Therefore, it is necessary to find an appropriate theoretical model that suitable to calculate the solubility of CO2 in CH4 + N2 and CH4 + C2H6 mixtures. In a previous paper,16 the solution method and the equation of state (EOS) methods were adopted to calculate the solubility of CO2 in pure methane. Results derived

From Table 2, we can see that the solubility of carbon dioxide in CH4 + N2 mixture also increases with temperature increasing. But the change of CO2 solubility along with the increase of nitrogen content seems interesting. When temperature is lower than 140 K, the increase of nitrogen content in methane will slightly increase the solubility of carbon dioxide in liquid CH4 + N2 mixtures. On the contrary, the solubility of carbon dioxide 2299



Article 2 ⎡ ⎛ ⎛ T ⎞0.5⎞⎤ R2Tc2i ⎢ ⎥ ⎜ ⎟ 1 + mi⎜1 − ⎜ ⎟ ⎟ ai = 0.45724 pci ⎢⎣ ⎝ Tci ⎠ ⎠⎥⎦ ⎝

from the regular solution method gradually deviated much from the experimental values at relative high temperature. So EOS methods are selected for the solubility calculations in this paper. Basic Principle. To perform solid−fluid phase equilibria between a ternary fluid phase (species 1, 2, and 3) and a pure solid phase (species 2), one solves the fugacity balance for species 2 between the phases: f 2l (T , p , x 2) = f 2s (T , p)

bi = 0.0778

kij

φ21p

N2 C2H6

p=

(5)

3

RT a − Vm − b Vm(Vm + b)

z 3 − z 2 + (A − B − B2 )z − AB = 0

(6)

N

a=

N

∑ ∑ xixj(aiaj)0.5 (1 − kij) i=1 j=1

= x12a1 + x 22a 2 + x32a3 + 2x1x 2(a1a 2)0.5 (1 − k12)

N

+ 2x1x3(a1a3)0.5 (1 − k13) + 2x3x 2(a3a 2)0.5 (1 − k 32)

∑ ∑ xixj(aiaj)0.5 (1 − kij) i=1 j=1

(15)

x 22a 2

+

x32a3

0.5

N

+ 2x1x 2(a1a 2) (1 − k12)

b=

0.5

+ 2x1x3(a1a3) (1 − k13) + 2x3x 2(a3a 2)0.5 (1 − k 32)

2 ⎡ ⎛ ⎛ T ⎞0.5⎞⎤ R2Tc2i ⎢ 1 + mi⎜⎜1 − ⎜ ⎟ ⎟⎟⎥ ai = 0.42748 pci ⎢⎣ ⎝ Tci ⎠ ⎠⎥⎦ ⎝

N

∑ xibi = x1b1 + x2b2 + x3b3 i=1

∑ xibi = x1b1 + x2b2 + x3b3 i=1

(7)

b=

(14)

where A = (ap/R T ), B = (bp/RT)

where A = (ap/R T ), B = (bp/RT). To apply such an EOS to mixtures, mixing rules are used to calculate the values of a and b of the mixtures. Classical mixing rules are used in this study

+

(13)

2 2

2 2

=

(12)

It can also be written in cubic form 2

=0

x12a1

0.05 0.05

where a2̅ = 2x1a12 + 2x2a2 + 2x3a23 = 2x2a2 + 2x1(a1a2) (1 − k12) + 2x3(a2a3)0.5(1 − k23). Suave−Redlich−Kwong (SRK) EOS. Calculating the solubility by the SRK EOS13 is similar to the PR EOS, just a different form of equations. The standard form of SRK EOS is

z − (1 − B)z + (A − 3B − 2B)z − (AB − B − B )

a=

−0.02 0.1298

0.1298

0.5

Equation 5 can also be written in cubic form

N

−0.02

⎛ z + ( 2 + 1)B ⎞⎞ ln⎜ ⎟⎟ ⎝ z − ( 2 − 1)B ⎠⎠

(4)

2

0.0998 + 5.4835/T − 36.134/T2 0.036 0.00224

C2H6 0.00224

⎛b b ⎞ A ⎛ a 2̅ ⎜ − 2⎟ φ2l = exp⎜ 2 (z − 1) − ln(z − B) − 2 2B⎝ a b⎠ ⎝b

PR EOS. We chose a standard form of PR EOS12,17 for solid−liquid equilibrium calculations, since it is widely used to model natural gas processing systems. This equation can be written as

2

N2 0.036

Using the PR EOS, the fugacity coefficient of a component in the mixture can be evaluated by the following equation:

where the fugacity coefficient can be evaluated using the EOS. The linear regression analysis of experimental solid CO2 vapor pressure data12 in the form of ln ps2 versus 1/T with the overall average absolute deviation (AAD) of 0.1 % gives

RT a − Vm − b Vm(Vm + b) + b(Vm − b)

CO2 0.0998 + 5.4835/T − 36.134/T2

CO2

(3)

p2s = 9.44· 108 exp( −3108.2/T )

CH4

CH4

φ2sp2s exp(V2(p − p2s )/R /T )

3

(11)

Table 4. kij among CH4, CO2, N2, and C2H6 by PR EOS (2)

where x2 is the mole fraction of CO2 in liquid phase, φl2 the liquid phase partial fugacity coefficient for CO2, p the system pressure in Pa, ps2 the saturated vapor pressure of solid CO2 at system temperature in Pa, φs2 the fugacity coefficient of pure CO2 at system temperature, and V2 the molar volume of solid CO2. With the simplification, we can obtain

p=

(10)

The mole fraction of component i is represented by xi, and ωi is the eccentric factor of component i. kij is the binary interaction parameter characterizing molecular interactions between molecules i and j, listed in Table 4. kij among CH4 and CO2 is derived from ZareNezhad et al.,12 and the rest of the data come from the software HYSYS.

where subscript 1 refers to the solvent CH4, subscript 2 refers to the solute CO2, subscript 3 refers to the solvent N2 (or C2H6), and fs and f l are the fugacity of pure solid and liquid, respectively. According to the definition of fugacity coefficient, eq 1 becomes

x2 =

RTci pci

mi = 0.37464 + 1.5422ωi − 0.26992ωi2

(1)

⎛ V2(p − p s ) ⎞ 2 ⎟ φ2lpx 2 = φ2sp2s exp⎜ RT ⎠ ⎝

(9)

(8) 2300

(16)

(17)


Journal of Chemical & Engineering Data bi = 0.08664

Article

RTci pci

(18)

mi = 0.480 + 1.574ωi − 0.176ωi2

(19)

kij among CH4, CO2, N2, and C2H6 for the SRK EOS are derived from HYSYS, which are listed in Table 5. Table 5. kij among CH4, CO2, N2, and C2H6 by SRK EOS kij

CH4

CH4 CO2 N2 C2H6

CO2 0.0956

0.0956 0.0312 0.00224

−0.0171 0.1401

N2

C2H6

0.0312 −0.0171

0.00224 0.1401 0.0319

0.0319

So, using the SRK equation of state, the fugacity coefficient of a component in the mixture can be evaluated by the following equation:

Figure 2. Comparison of CO2 (2) solubility in 95 mol % CH4 (1) + 5 mol % N2 (3) mixtures by different methods.

⎛b φ2l(T , P , x 2) = exp⎜ 2 (z − 1) − ln(z − B) ⎝b −

b ⎞ ⎛ A ⎛ a 2̅ B ⎞⎞ ⎜ − 2 ⎟ln⎜1 + ⎟⎟ B⎝ a b⎠ ⎝ z ⎠⎠

equation are closer to experimental data than SRK EOS. Because the binary interaction coefficient kCH4−CO2used in PR EOS is a function of temperature fitted by ZareNezhad et al.,12 kCH4−CO2 used in SRK EOS is only the constant from HYSYS. CH4 + C2H6 + CO2 System. PR EOS and SRK EOS were also selected to calculate the solubility of carbon dioxide in liquid CH4 + C2H6 mixtures. The temperature range was (112 to 170) K, and the ratio of ethane in the mixture ranged from 0.5 % to 20 %. The AAD of calculating results and experimental data on the CH4 + C2H6 + CO2 ternary system presented in Table 7. In addition, the solubility of CO2 in 95 mol % CH4 + 5 mol % C2H6 mixtures by the two methods and the experimental data are drawn in Figure 3.

(20)

where a2̅ = 2x1a12 + 2x2a2 + 2x3a23 = 2x2a2 + 2x1(a1a2) (1 − k12) + 2x3(a2a3)0.5(1 − k23). The fugacity coefficient of pure solid CO2 is as follows 0.5

⎛ A ⎛ B ⎞⎞ φ2s(T , P) = exp⎜z − 1 − ln(z − B) + ln⎜1 + ⎟⎟ ⎝ ⎝ B z ⎠⎠ (21)

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THEORETICAL RESULTS AND DISCUSSION CH4 + N2 + CO2 System. PR EOS and SRK EOS were used to calculate the solubility of carbon dioxide in liquid CH4 + N2 mixtures in this paper. The temperature range was (112 to 170) K, and the proportion of nitrogen in the mixtures ranged from 0.5 % to 20 %. For comparison, the AAD of calculating results and experimental data on CH4 + N2 + CO2 ternary system by two different EOS methods are shown in Table 6.

Table 7. AAD of Calculating Results and Experimental Data on CH4 + C2H6 + CO2 Ternary System x3/(x1 + x3) 0 0.02 0.05 0.10

PR EOS 2.78 3.51 2.27 3.67

% % % %

SRK EOS 7.33 5.27 5.82 10.07

% % % %

Table 6. AAD of Calculating Results and Experimental Data on CH4 + N2 + CO2 Ternary System x3/(x1 + x3) 0 0.02 0.05 0.10

PR EOS 2.78 3.16 4.29 3.68

% % % %

SRK EOS 7.33 5.95 6.51 7.32

% % % %

First, we can draw the following conclusion from Table 6 that the calculating results of carbon dioxide solubility in CH4 + N2 mixtures adopted by PR and SRK EOS are relatively consistent with the experimental data. The AADs between experimental data and the calculating results of PR EOS are smaller than that of the SRK EOS, which is generally predictable under the present conditions. For better analysis and comparison, the solubility of CO2 in 95 mol % CH4 + 5 mol % N2 mixtures by different theoretical methods and experimental data is plotted in Figure 2, from which we can obtain that the calculating results of the PR

Figure 3. Comparison of CO2 (2) solubility in 95 mol % CH4 (1) + 5 mol % C2H6 (3) mixtures by different methods. 2301



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kij = 0.0956 + 5.649/T + 107.48/T 2

Both of the calculating carbon dioxide solubilities in CH4 + C2H6 mixtures by the PR and SRK EOS are relatively close to the experimental data with most of the AAD < 10 %. Similar to the ternary system CH4 + N2 + CO2, the calculating results of PR are also slightly better than that of SRK by comparison of the AAD. An accurate kij correlation plays a key role for the solid−liquid phase equilibrium calculation by the EOS.

To verify the applicability and accuracy of new kij obtained in the present work, the calculating results of carbon dioxide solubility in CH4 and CH4 + N2 by different kij are presented in Table 8.

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Table 8. AAD of CO2 Solubility in Liquid CH4 + N2 Mixtures Calculated by Different kij

BINARY INTERACTION COEFFICIENT The binary interaction coefficient is an empirical parameter to adjust the deviation between the actual state and the ideal state. It does not have a strict theoretical foundation; instead, it is associated by the experimental data. In the present work, two temperature-dependent kCH4−CO2 correlations are proposed by a least-squares method for the PR EOS and SRK EOS, respectively. Suppose that the data points are (xi, yi) (i = 0, 1, ..., m), and Φ is the nth degree polynomial (n ⩽ m). The idea is to model a function

PR EOS

∑ ak ·xik ∈ Φ

(22)

k=0

Meet that m

I=

n

∑ [∑ ak ·xik − yi ]2 i=0

= min (23)

k=0

Pn(x) is the least-squares fitting polynomial. The condition for I to be a minimum is that m

n

∂I = 2 ∑ [∑ ak ·xik − yi ]xij = 0 ∂aj i=0 k=0

(24)

m

∑ xi i=0 m

∑ xi2 i=0

⋮ m

∑ xin+ 1 i=0

⎞ ⎛ m ⎞ ⎟ ⎜ ∑ yi ⎟ ⎟ ⎜ i=0 ⎟ i=0 ⎟ ⎟⎛ a 0 ⎞ ⎜ m m ⎟ ⎜ n + 1 ⎟⎜ ⎟ ... ∑ xi ⎟⎜ a1 ⎟ ⎜ ∑ xiyi ⎟ i=0 ⎟ ⎟⎜ ⋮ ⎟ = ⎜ i = 0 ⋱ ⋮ ⎟⎜⎝ a ⎟⎠ ⎜ ⋮ ⎟ ⎟ ⎟ n ⎜ m m ⎟ ⎟ ⎜ n ... ∑ xi2n ⎟ ⎜∑ xi yi ⎟ ⎠ ⎠ ⎝ i=0 i=0

∑ xin

(25)

A temperature-dependent kij is presented by referring to the forms of ZareNezhad et al.12 and Zhu et al.,18 which have a high accuracy of calculating. kij = a0 + a1/T + a 2 /T 2

(26)

At room temperature, kij is 0.1 for PR EOS and 0.0956 for SRK EOS on CH4 + CO2 binary system, so a0 are valued at 0.1 and 0.0956 for PR EOS and SRK EOS, respectively. The kij of each temperature can be obtained according to the experimental data. Then, coefficients of a1 and a2 can be fitted by the least-squares method. Equations 27 and 28 are the new kij for PR EOS and SRK EOS, respectively. kij = 0.1 + 2.3454/T + 326.03/T 2

new kij

kij (HYSYS)

new kij

0 0.02 0.05 0.10

2.78 % 3.16 % 4.29 % 3.68 %

2.53 % 2.38 % 3.40 % 3.29 %

7.33 % 5.95 % 6.51 % 7.32 %

2.67 % 2.20 % 3.49 % 3.49 %

CONCLUSION In this paper, a new experimental apparatus has been designed and set up to measure the solubility of carbon dioxide in cryogenic liquid, which is based on the static−analytic method. The experimental apparatus, together with the equations-ofstate methods, are adopted to determine the solubility of carbon dioxide in liquid CH4 + N2 and CH4 + C2H6 mixtures above atmospheric pressure. The following conclusions are drawn from the results. (1) Experiments show that, for the CH4 + N2+CO2 ternary system, the addition of nitrogen in methane will slightly increase the CO2 solubility in liquid CH4 + N2 mixtures when T < 140 K, while the CO2 solubility decreases with the increase of nitrogen when T > 140 K. For the CH4 + C2H6 + CO2 ternary system, adding ethane in methane will increase the solubility of carbon dioxide in liquid CH4 + C2H6 mixtures in the whole temperature range. (2) The equations-of-state method is adopted to calculate the CO2 solubility in liquid CH4 + N2 and CH4 + C2H6 mixtures. Results obtained from PR and SRK EOS are consistent with the experimental data in the whole temperature region, while the results of PR EOS are better. (3) Two quadratic temperature-dependent kCH4−CO2 correlations are derived from the experimental data. The AAD between the model by new kij and the experimental data are within 2.53 % for PR EOS and 2.67 % for SRK EOS,

m

...

x3/(x1 + x3)

■

where j = 0, 1, ..., n, and a0, a1, ..., an can be calculated from the following matrix: ⎛ ⎜m + 1 ⎜ ⎜ m ⎜ ⎜ ∑ xi ⎜ i=0 ⎜ ⋮ ⎜ ⎜ m n ⎜ ∑ xi ⎝ i=0

SRK EOS

kij12

From Table 8, the calculating results by the new kij are closer to experimental data than those by the former kij on CH4 + CO2 binary system. The average absolute deviation decreases from 2.78 % to 2.53 % for the PR EOS and from 7.33 % to 2.67 % for the SRK EOS. Therefore, the new temperaturedependent kij correlations are more suitable for solid−liquid phase equilibrium calculations on yjr CH4 + CO2 system in (112 to 170) K temperature regions. In addition, for the ternary system, the calculated CO2 solubility in the CH4 + N2 liquid mixture by the new kij has a higher accuracy than that by the previous kij, especially in the calculation of the SRK EOS. For example, in the calculation of 95 mol % CH4 + 5 mol % N2 mixture, the AAD is reduced more than 3 % for the SRK EOS. Consequently, the new kij also can improve the calculation accuracy of the ternary solid−liquid phase equilibrium.

n

Pn(xi) =

(28)

(27) 2302



Article

(17) Peng, D. Y.; Robinson, D. B. A new tow-constant equation of state. Ind. Eng. Chem. Fundam. 1976, 15, 59−64. (18) Zhu, H. B.; Gong, M. Q.; Zhang, Y.; Wu, J. F. Review of the research on interaction coefficients used in two cubic equations of state for phase equilibria predictions. Cryogenics 2005, No. 5, 7−12.

both of which improve the calculation accuracy of the ternary solid−liquid phase equilibrium. (4) Experimental data and theoretical results show that, when T > 145 K, the CO2 solubility in liquid CH4 + N2 and CH4 + C2H6 mixtures will be higher than 0.5 %. This means that an LNG plant running at 145K or higher may allow CO2 content higher than 0.5 %, and consequently, the CO2 removal unit in an LNG plant may be minimized or even canceled.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-21-34206533; fax: +86-21-34206814; e-mail address: [email protected]. Funding

The authors are grateful to the support of China’s National Natural Science Fund (No. 51076098). Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Birol, F. World energy prospects and challenges. Aust. Econ. Rev. 2006, 39 (No.2), 190−195. (2) Barclay, M.; Denton, N. Selecting offshore LNG processes. LNG J. 2005, 10, 4−36. (3) Papka, S. D.; Gentry, M. C.; Leger, A. T. Pressurized LNG: A new technology for gas commercialization. Proceedings of the 15th International Offshore and Polar Engineering Conference, Seoul, South Korea, 2005. (4) Anon. Pressurised LNG: An alternative way to transport gas. Nav. Arch. 2005, No. No.6, 20−28. (5) Fairchild, D. P.; Smith, P. P.; Biery, N. E.; Farah, A. M.; Lillig, D. B.; Jackson, T. S.; Sisak, W. J. Pressurized LNG: Prototype container fabrication. Proceedings of the 15th International Offshore and Polar Engineering Conference, Seoul, South Korea, 2005. (6) Fedorova, M. F. The solubility of C2H2 and CO2 in liquid nitrogen and oxygen. Zh. Fiz. Khim. 1940, 14, 422−426. (7) Donnelly, H. G.; Katz, D. L. Phase equilibria in the carbon dioxide-methane system. Ind. Eng. Chem. 1954, 46 (No.3), 511−517. (8) Pikaar, M. J. A study of phase equilibria in hydrocarbon-CO2 systems. Ph.D. Thesis, University of London, London, 1959. (9) Davis, J. A.; Rodewald, N.; Kurata, F. Solid-liquid-vapor phase behavior of the methane-carbon dioxide system. AIChE J. 1962, 8 (4), 537−539. (10) De Stefani, V.; Baba-Ahmed, A.; Valtz, A.; Meneses, D.; Richon, D. Solubility measurements for carbon dioxide and nitrous oxide in liquid oxygen at temperatures down to 90 K. Fluid Phase Equilib. 2002, 200, 19−30. (11) De Stefani, V.; Baba-Ahmed, A.; Richon, D. Experimental determination of carbon dioxide and nitrous oxide co-solubility in liquid oxygen. Fluid Phase Equilib. 2003, 207, 131−142. (12) 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, 840−845. (13) Carter, K.; Luks, K. D. Extending a classical EOS correlation to represent solid−fluid phase equilibria. Fluid Phase Equilib. 2006, 243, 151−155. (14) Zhang, L. M.; Solbraa, E. Solid phase behavior in offshore natural gas liquefaction concepts. CIESC J. 2009, 60, 44−49. (15) Solbraa, E. Equilibrium and non-equilibrium thermodynamics of natural gas processing. Ph.D. Thesis, Norwegian University of Science and Technology, Trondheim, 2002. (16) Shen, T. T.; Lin, W. S. Calculation of carbon dioxide solubility in saturated liquid methane. Proceedings of the 9th Asian Thermophysical Properties Conference, Beijing, China, 2010. 2303


Determination of CO2 Solubility in Saturated Liquid CH4 + N2 and

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