Methane and carbon dioxide solubility in 1,2-propylene glycol at temperatures ranging from 303 to 423 K and pressures up to 12 MPa

Fluid Phase Equilibria 289 (2010) 185–190

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Methane and carbon dioxide solubility in 1,2-propylene glycol at temperatures ranging from 303 to 423 K and pressures up to 12 MPa A.C. Galvão ∗ , A.Z. Francesconi School of Chemical Engineering, University of Campinas – UNICAMP, P.O. Box 6066, 13083-970, Campinas – SP, Brazil

a r t i c l e

i n f o

Article history: Received 27 June 2009 Received in revised form 9 December 2009 Accepted 11 December 2009 Available online 16 December 2009 Keywords: Gas solubility Henry’s constant Methane Carbon dioxide 1,2-Propylene glycol

a b s t r a c t This work reports solubility data of methane and carbon dioxide in 1,2-propylene glycol and the Henry’s law constant of each solute in the studied solvent at saturation pressure. The measurements were performed at 303, 323, 373, 398 and 423.15 K and pressures up to 4.5 MPa for carbon dioxide solubility and pressures up to 12.1 MPa for methane solubility. The experiments were performed in an autoclave type phase equilibrium apparatus using the total pressure method (synthetic method). All investigated systems show an increase of gas-solubility with the increase of pressure. A decrease of carbon dioxide solubility with the increase of temperature and an increase of methane solubility with the increase of temperature was observed. From the variation of solubility with temperature, partial molar enthalpy and entropy change of the solute for each mixture were calculated. © 2009 Elsevier B.V. All rights reserved.

1. Introduction Glycols are a class of chemical compounds widely used with different purposes. Due to their low vapor pressure and affinity with water, they are applied as dehydrating agents in the purification of gaseous streams. Unfortunately, the use of glycols as a dehydrating agent comes with an unwelcome effect, the glycol also dissolves an amount of the gaseous components. This effect drops the water removing efficiency and the dissolved gas is lost. The knowledge about the amount of the dissolved gas is helpful for choosing the adequate dehydrating agent and to design, to operate and to optimize an effective dehydration system. Despite the importance and applicability of gas solubility in glycols, the availability of data and research, especially at higher temperatures and pressures is still low. All the data reported are related to the solubility of gases in ethylene glycol [1–5], diethylene glycol [2,6–8] and triethylene glycol [9]. It was not found data of gas solubility in 1,2-propylene glycol. The scarcity of gas solubility data in glycols encouraged the study presented in this work. Another motivation for the study deals with fundamental research, since studies of gas–liquid solubility provide important information for the understanding of the solubility mechanism and also help in the development of models and theories.

∗ Corresponding author. Tel.: +55 19 3521 3951/3289 8147; fax: +55 19 3521 3894. E-mail address: [email protected] (A.C. Galvão). 0378-3812/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2009.12.006

The following sections show the method, experimental results and conclusions about the binary mixtures investigated. 2. Experimental 2.1. Apparatus and method The autoclave used to perform the experiments is part of a commercial apparatus named Barnes Volumetric Hydrothermal System, model RA-1A-1 produced by LECO® Co. (USA). Distilled water under laboratory conditions was used to verify the autoclave volume. After several measurements a volume of 1128 cm3 (uncertainty ± 2 cm3 ) was found. The equilibrium temperature inside the autoclave was measured with a J type thermocouple (uncertainty ± 0.3 K) previously calibrated with a Pt-100 thermometer (Guildline® , model 9540, resolution 0.001 K) as reference. The pressure inside the cell was measured by a Heise® bourdon gauge (uncertainty ± 0.035 MPa). To calibrate the bourdon gauge, the vapor pressure of water for temperatures up to its critical temperature was measured and the data were compared with those provided by IAPWS (The International Association for the Properties of Water and Steam) [10]. The experimental procedure is the following: first of all a known amount of solute and degassed solvent is fed into an evacuated autoclave. After that, the desired temperature is set and when the mixture reaches equilibrium, the temperature and pressure values are recorded. Next, the temperature of the system is increased to obtain a new phase equilibrium state and so on until the desired range of temperature is covered. The heating system is turned off

186

A.C. Galvão, A.Z. Francesconi / Fluid Phase Equilibria 289 (2010) 185–190

and when the autoclave reaches room temperature, a new amount of gas is added. The heating system is turned on and equilibrium states are reached again. The process is repeated for each gas load placed into the cell. A detailed description of the apparatus and experimental procedure is given elsewhere [11].

Eq. (9) can be written as

P

v¯ ∞ 2

ˆ G y2 P = x2 H2,1 exp  2

RT

dP

(10)

P sat 1

For component 1 it is assumed that

2.2. Materials The reagent 1,2-propylene glycol (purity 0.999 mol fraction) was supplied by Merck (Germany), the gases carbon dioxide (analytical grade) and methane (purity 0.995 mol fraction) were supplied by White Martins (Brazil). None of the reagents used in this work received further purification except degassing. The degassing of 1,2-propylene glycol was performed prior to use by a method similar of that suggested by Van Ness and Abbott [12]. The purity of the liquid reagent was checked by performing density and refractive index measurements at 293.15 K and the results were compared with those available in the literature. To perform density measurements a vibrating-tube densimeter (Anton Paar® , model DMA 55, uncertainty ± 1 × 10−5 g cm−3 ) was used. To perform refractive index measurements a refractometer (Atago® , model 3T, uncertainty ± 1 × 10−4 ) was used. The analyses results showed that the values agree well with literature data.

P

v1

ˆ G y1 P = x1 sat P sat exp  1 1 1

RT

dP

(11)

P sat 1

x2 = 1 − x1

(1)

y2 = 1 − y1

(2)

nT1 = nL1 + nG 1

(3)

The success of the method applied in this work depends on the models used to calculate all variables involved. Among all variables, the fugacity coefficients play the most important role and the choice of an appropriate approach to calculate them makes all the difference. The appropriate approach to calculate fugacity coefficients is closely related to the mixing rules applied to describe solute–solvent interaction. Due to the different chemical nature of the components 1,2-propylene glycol, carbon dioxide and methane, the use of an EoS/GE (Equation of State/Excess Gibbs Energy) model seems to be the an appropriate approach. The only one problem is to estimate the adjustable parameters of the EoS/GE model and a reasonable solution for that would be to use a predictive model. The PSRK [13,14] is the most used model although as the asymmetry of the system increases the prediction becomes poorer. In those cases, even at higher temperatures and pressures, the LCVM model shows better results [15–17]. The LCVM model developed by Boukouvalas et al. [18] is a linear combination of Vidal [19] and Michelsen [20] mixing rules associated with the UNIFAC method and applied to the modified Peng–Robinson equation of state [21]. In accordance with the model, the fugacity coefficient is described by Eqs. (12) and (13)   √   ¯ V + (1 + 2)b ˆ i = bi PV −1 − ln P(V − b) − ˛ ln  (12) √i ln √ RT b RT 2 2 V + (1 − 2)b

nT2 = nL2 + nG 2

(4)

˛ ¯i =

2.3. Thermodynamic framework and data reduction Calculus of composition in the liquid phase consists of solving simultaneously a system of equations involving a mass balance and relations of phase equilibrium for both components. The mass balance is written by the equations below:

nG 1 =

y1 PV G RTZ G

(5)

nG 2 =

y2 PV G RTZ G

(6)

x1 =

nL1 nL1

(7)

+ nL2

When phase equilibrium is attained ˆ G yi P = xi i f 0  i i

(8)

ˆ G y2 P =  ∗ x2 H2,1 exp  2 2

v¯ ∞ 2 RT

AV

+

1− AM

ln i +

1− AM





ln

b b + i − 1 + ˛i bi b

(13)

The LCVM mixing rule has three constants,  = 0.36, AM = −0.52 and AV = −0.623. To use these constants, the original UNIFAC method [22] must be used to calculate the activity coefficient  i and the excess Gibbs energy GE . The parameters for mixtures are calculated as follows: ˛=



AV

+

1− AM

 GE

RT

+

1− AM



xi ln

b  bi

+

xi ˛i

(14)

a = bRT˛

(15)

b=

(16)



xi bi



ai = 0.45724 dP



For pure components the parameters are given as:

For the solute Eq. (8) can be written as

P



(9)

P sat 1

in which H2,1 is the Henry’s constant at the saturation pressure of solvent and 2∗ is the activity coefficient of solute by the unsymmetric convention (2∗ → 1 as x2 → 0). Usually the amount of a gas dissolved in a liquid has little magnitude and thus the influence of the solute activity coefficient may be neglected. Although it is important to be aware that in cases wherein the mole fraction of a gas in the liquid phase reaches more than 10%, the calculus should be reevaluated or a pseudo-Henry’s law constant (the product of 2∗ by H2,1 ) should be applied. Neglecting the solute activity coefficient

R2 TC2 PC



f (TR )

(17)

Table 1 Constants of f(TR ), critical properties and acentric factor used to calculate gas solubility.

C1 C2 C3 TC (K) PC (MPa) VC (cm3 mol−1 ) ω

CH4

CO2

HOCH2 CH(CH3 )OH

0.49258 – – 190.6 4.6 99.0 0.0080

0.82550 0.16755 −1.70390 304.2 7.4 94.0 0.2252

1.35125 – – 676.4 5.9 237.0 0.5928

A.C. Galvão, A.Z. Francesconi / Fluid Phase Equilibria 289 (2010) 185–190 Table 2 Experimental values of solvent and solute amounts (expressed in mass) along with equilibrium temperatures and pressures.

˛i =

CH4 + HOCH2 CH(CH3 )OH (solvent (g): 967.79) First load (g): 2.05

Second load (g): 4.76

T (K)

P (MPa)

T (K)

P (MPa)

297.92 323.85 353.58 393.53 423.97

0.9258 1.0470 1.1816 1.3499 1.4980

302.62 323.85 357.89 393.23 426.37

2.1778 2.4202 2.7971 3.1673 3.5375

T (K)

P (MPa)

T (K)

P (MPa)

300.92 323.55 353.78 397.94 423.57

3.6519 4.0760 4.6616 5.5299 6.0146

296.32 323.35 353.48 393.13 425.07

5.0049 5.7924 6.6810 7.8791 8.8215

CH4 + HOCH2 CH(CH3 )OH (solvent (g): 967.79) Fifth load (g): 16.03 P (MPa)

299.62 323.45 353.48 393.43 424.37

6.7685 7.7781 9.0436 10.7937 12.1534

(18)

ai bi RT

(19)

The dimensionless function f(TR ) is calculated as suggested by Mathias and Copeman [23] and it depends on the magnitude of the reduced temperature. If TR ≤ 1:

f (TR ) = [1 + C1 (1 −





TR ) + C2 (1 −

TR )]



2

TR ) + C3 (1 −



3 2

TR ) ]

2

(20)

(21)

The constants C1 , C2 and C3 along with critical properties, acentric factor and UNIFAC parameters are available for a large number of components in the supplementary data file of Horstmann et al. [24]. Table 1 shows the properties and constants of each pure component used in this work. The total pressure method applied in this work is described in detail by Breman et al. [25]. 3. Results and discussion

CO2 + HOCH2 CH(CH3 )OH (solvent (g): 954.92) First load (g): 5.10

Second load (g): 13.25

T (K)

P (MPa)

T (K)

P (MPa)

300.12 323.95 348.18 385.72 424.47

0.3402 0.4075 0.4749 0.5960 0.6768

301.32 325.35 354.49 394.13 427.27

0.6431 0.8249 1.0470 1.3499 1.5518

CO2 + HOCH2 CH(CH3 )OH (solvent (g): 954.92) Third load (g): 24.59

C

PC

If TR > 1:

Fourth load (g): 11.77

T (K)

 RT 

f (TR ) = [1 + C1 (1 −

CH4 + HOCH2 CH(CH3 )OH (solvent (g): 967.79) Third load (g): 8.13

bi = 0.0778

187

Fourth load (g): 42.46

T (K)

P (MPa)

T (K)

P (MPa)

299.72 324.35 354.08 394.43 426.97

1.0807 1.4037 1.8211 2.3596 2.7298

300.42 324.95 354.49 394.63 426.77

1.7403 2.3663 3.0663 3.9548 4.5674

Table 2 presents the primary experimental data used to calculate gas–liquid solubility, namely the temperature and pressure at equilibrium and the amount of solvent and each load of solute placed into the cell. The isochoric data are linearly correlated indicating that the gaseous phase contains just methane or carbon dioxide. That behavior is explained by the low vapor pressure of 1,2-propylene glycol. The calculated solubility of methane and carbon dioxide in 1,2-propylene glycol against pressure, at different temperatures, is shown in Table 3. The uncertainty of gas mole fraction in the liquid phase was estimated by analyzing the influence of T, P, V and n uncertainties on the mole fraction. It was found an average uncertainty of ±1% of the calculated value. For all studied temperatures the solubility of methane and carbon dioxide increases with pressure. A linear correlation for the solubility data against pressure for each temperature was observed. Figs. 1 and 2 show the data for each isotherm; for isobaric conditions in the range under investigation, the solubility of methane increases and the solubility of carbon dioxide decreases with temperature. Table 4 shows the Henry’s law constant for each solute in 1,2-propylene glycol at studied temperatures and solvent saturation pressure. As expected, the H2,1 values for methane

Table 3 Experimental results for the solubility of methane and carbon dioxide in 1,2-propylene glycol against pressure for all studied temperatures. 303.15 K

323.15 K

373.15 K

398.15 K

423.15 K

P (MPa)

x2

P (MPa)

x2

P (MPa)

x2

P (MPa)

x2

P (MPa)

x2

CH4 + HOCH2 CH(CH3 )OH 0.9537 2.1803 3.6747 5.1953 6.9089

0.0018 0.0041 0.0066 0.0096 0.0132

1.0437 2.3983 4.0607 5.7893 7.7729

0.0021 0.0048 0.0078 0.0112 0.0150

1.2687 2.9433 5.0257 7.2743 9.9329

0.0033 0.0074 0.0124 0.0176 0.0234

1.3812 3.2158 5.5082 8.0168 11.0129

0.0040 0.0092 0.0154 0.0220 0.0293

1.4937 3.4883 5.9907 8.7593 12.0929

0.0049 0.0113 0.0190 0.0272 0.0363

CO2 + HOCH2 CH(CH3 )OH 0.3621 0.6664 1.1375 1.8597

0.0063 0.0184 0.0344 0.0588

0.4181 0.8124 1.3995 2.3077

0.0063 0.0181 0.0338 0.0577

0.5581 1.1774 2.0545 3.4277

0.0065 0.0181 0.0339 0.0581

0.6281 1.3599 2.3820 3.9877

0.0068 0.0186 0.0347 0.0596

0.6981 1.5424 2.7095 4.5477

0.0072 0.0193 0.0360 0.0619

188

A.C. Galvão, A.Z. Francesconi / Fluid Phase Equilibria 289 (2010) 185–190 Table 4 Henry’s constant of methane and carbon dioxide in 1,2-propylene glycol at solvent saturation pressure for all studied temperatures. T (K)

H2,1 (P1sat ) (MPa)

303.15 323.15 373.15 398.15 423.15

544 490 377 332 298

CH4

CO2 ± ± ± ± ±

14 13 11 10 8

50 53 58 60 62

± ± ± ± ±

1 1 2 2 2

with the thermodynamic relations [26]:

 

Fig. 1. Methane solubility (mole fraction) in 1,2-propylene glycol as a function of pressure; () 303.15 K, () 323.15 K, () 373.15 K, () 398.15 K, () 423.15 K, and (—) linear fit.

Fig. 2. Carbon dioxide solubility (mole fraction) in 1,2-propylene glycol as a function of pressure; () 303.15 K, () 323.15 K, () 373.15 K, () 398.15 K, () 423.15 K, and (—) linear fit.

∂ ln x2 ∂ ln T

=−



P

= P

h¯ 2 R

¯s2 R

(22)

(23)

After rearranging the above equations, the dependence of solubility with temperature may be written in a more convenient way as follows:

 

decrease with temperature and for carbon dioxide the values increase with temperature. The influence of temperature on Henry’s law constant is presented in Fig. 3 that plots the natural logarithm of Henry’s law constant against inverse temperature. The dissolution of a gas in a liquid is a phenomenon based on molecular interaction, the solubility mechanism is not known, although an analyze of the temperature effect on solubility provides information about molecular interaction. The temperature effect on solubility for mixtures where the solvent is nonvolatile and the gas mole fraction in the liquid phase is small may be related to partial molar enthalpy and entropy change of the solute in accordance

∂ ln x2 ∂1/T

∂ ln x2 ∂T ∂ ln x2 ∂T



=

h¯ 2 RT 2

(24)

=

¯s2 RT

(25)

P

P

Table 5 presents calculated values of these two quantities as a function of temperature at some smoothed pressure values. The tabulated information shows that upon dissolution, methane exhibits positive enthalpy and entropy changes, indicating that its solubility increases disorder in the mixture and the interaction among molecules of solute and solvent is weak. On the other hand, the dissolution of carbon dioxide, however, exhibits negative enthalpy and entropy changes, indicating stronger molecular interactions among solute and solvent molecules. One possible explanation for this behavior could be due to the large quadrupolar moment and linear shape of carbon dioxide.

Fig. 3. Dependence of Henry’s law constant with temperature; () carbon dioxide, () methane, and (—) linear fit.

A.C. Galvão, A.Z. Francesconi / Fluid Phase Equilibria 289 (2010) 185–190 Table 5 Partial molar enthalpy and entropy change of the solute in the liquid phase for all studied temperatures and different pressures. P (MPa)

T (K)

h¯ 2 (kJ mol−1 )

¯s2 (J mol−1 K−1 )

CH4 + HOCH2 CH(CH3 )OH 3 303.15 3 323.15 3 373.15 3 398.15 3 423.15 6 303.15 6 323.15 6 373.15 6 398.15 6 423.15 9 303.15 9 323.15 9 373.15 9 398.15 9 423.15 12 303.15 12 323.15 12 373.15 12 398.15 12 423.15

2.8 3.5 5.8 7.2 8.8 2.1 2.8 5.4 7.0 9.0 1.8 2.6 5.2 6.9 9.0 1.7 2.5 5.1 6.9 9.0

9.2 10.8 15.4 18.1 20.9 6.8 8.7 14.4 17.6 21.2 6.0 8.0 14.0 17.5 21.2 5.5 7.6 13.8 17.4 21.3

CO2 + HOCH2 CH(CH3 )OH 1 303.15 1 323.15 1 373.15 1 398.15 1 423.15 2 303.15 2 323.15 2 373.15 2 398.15 2 423.15 3 303.15 3 323.15 3 373.15 3 398.15 3 423.15 4 303.15 4 323.15 4 373.15 4 398.15 4 423.15

−9.7 −9.5 −7.8 −6.1 −3.8 −9.5 −9.4 −7.7 −6.0 −3.7 −9.4 −9.3 −7.6 −6.0 −3.7 −9.4 −9.3 −7.6 −6.0 −3.7

−32.0 −29.6 −21.0 −15.4 −9.0 −31.3 −29.0 −20.6 −15.1 −8.8 −31.1 −28.8 −20.5 −15.1 −8.8 −31.1 −28.7 −20.4 −15.0 −8.8

4. Conclusion Analyzing the data of gas–liquid solubility, it is observed that for the range of pressure and temperature studied the carbon dioxide is more soluble than methane in 1,2-propylene glycol. The results of carbon dioxide solubility decreasing with temperature indicate that the interaction among molecules of solute and solvent is exothermic (h¯ 2 < 0). For mixtures containing methane, the increase of solubility with temperature indicates an endothermic effect (h¯ 2 > 0). List of symbols x liquid mole fraction y gas mole fraction n amount of substance P equilibrium pressure or desired pressure V volume R universal gas constant T equilibrium temperature or desired temperature Z compressibility factor H Henry’s law constant h¯ partial molar enthalpy s¯ partial molar entropy C1 constant of the equation suggested by Mathias and Copeman

C2 C3 AV AM f0 a b

v v¯

189

constant of the equation suggested by Mathias and Copeman constant of the equation suggested by Mathias and Copeman constant of the LCVM mixing rule constant of the LCVM mixing rule fugacity at reference state energy parameter of the equation of state co-volume parameter of the equation of state molar volume partial molar volume

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