RESEARCH NOTE pubs.acs.org/IECR
Chrastil-Type Approach for Representation of Glycol Loss in Gaseous System Ali Eslamimanesh,† Amir H. Mohammadi,*,†,‡ Mohammad Yazdizadeh,§ and Dominique Richon† nergetique et Procedes, 35 Rue Saint Honore, 77305 Fontainebleau, France MINES ParisTech, CEP/TEP—Centre E Thermodynamics Research Unit, School of Chemical Engineering, University of KwaZulu-Natal, Howard College Campus, King George V Avenue, Durban 4041, South Africa § School of Chemical and Petroleum Engineering, Shiraz University, 71348-51154 Shiraz, Iran † ‡
ABSTRACT: Glycols are generally used to adjust the water dew-point in natural gas processes to avoid gas hydrate/ice/condensate formation. Their vaporization loss in gaseous systems may happen regularly in the petroleum industry. Glycols have very low solubility in the gas phase and because of difficulty of the corresponding measurement, few sets of experimental data are available in open literature and may not be fully satisfactory. In a previous work, we performed thermodynamic consistency tests in order to prepare reliable data sets for modeling purposes. Application of four widely used correlations in supercritical fluid industry, including the original Chrastil, Adachi and Lu, del Valle and Aguilera, and Mendez-Santiago and Teja, in which the effects of temperature, density of gas (solvent), and pressures on the solubility of glycol are generally taken into account, are investigated to represent the corresponding solubility of ethylene glycol and triethylene glycol in supercritical methane and carbon dioxide between 298.15 and 333.15 K and between 1.606 and 22.06 MPa. It is found that the absolute average deviations (AAD %) of the evaluated glycols solubility by the aforementioned equations from 57 investigated experimental values are around 27%, 18%, 31%, and 17%, respectively.
1. INTRODUCTION Gas hydrate, ice and/or condensate formation, is one of the inevitable problems of the existence of water in the petroleum industry.15 To avoid such problems, glycols (typically ethylene glycol and triethylene glycol) are normally contacted with the wet gas stream in dehydration units in order to absorb the gas humidity and adjust the water dew-point temperature.1,517 Therefore, substantial glycol quantities may be dissolved in the gas stream.1,5,6 These vaporization losses in the gas phase may result in higher production, transmission, and processing costs. A preliminary literature survey shows that although the experimental data of solubilities of methane and carbon dioxide in ethylene/triethylene glycol have been well-reported in the literature, the corresponding data on solubilities of ethylene/ triethylene glycol in supercritical carbon dioxide and methane are indeed scarce. To the best of our knowledge, they are limited to the measurements of Yonemoto et al.,5 Jerinic et al.,1 and Adachi et al.6 Several error sources in experimental measurements including calibration of pressure transducers, temperature probes, and detectors of gas chromatographs, other possible errors during the measurements of phase equilibria especially those dealing with low concentrations, improper design of the equipment etc. may lead to generation of unreliable experimental data. In a previous work,17 we have performed an assessment test (consistency test) on the experimental data of ethylene glycol/triethylene glycol solubility in supercritical carbon dioxide and methane to verify their reliability for use in a thermodynamic model based on the SRK EoS 18 and vdW2 mixing rules. 19 However, there is still a need for development of new methods for easy calculations of solubilities of glycols in gaseous systems. In this work, we focus r 2011 American Chemical Society
on presenting a novel approach based on the use of four commonly used Chrastil-type equations, which have been generally applied in supercritical fluid industry, to represent the solubility of ethylene and triethylene glycols (EG and TEG) in supercritical carbon dioxide and methane using the previously evaluated experimental values.2 The applied equations in this work have not been so far used to deal with the systems normally encountered in the dehydration of natural gases.
2. EQUATIONS 2.1. Chrastil. In 1982, Chrastil stated that the solute molecules associated with the gas molecules are in chemical equilibrium with the resulting complex (solvate complex) as follows:20,21 0
A 0 þ kB0 T A 0 Bk
ð1Þ
where k represents the association term, A0 denotes the solute molecule, and B0 is the gas (solvent) molecule. Therefore, the equilibrium concentration of the solute is calculated from the mass action law as follows:20,21 a k þ b ð2Þ c ¼ F exp T In eq 2, c is the concentration of a solute in a gas (g 3 dm3), F denotes the density of the gas (solvent) in g 3 dm3, T is temperature in K, and a and b are the adjustable parameters of the equation, Received: May 6, 2011 Accepted: July 28, 2011 Revised: June 19, 2011 Published: July 28, 2011 10373
dx.doi.org/10.1021/ie2009839 | Ind. Eng. Chem. Res. 2011, 50, 10373–10379
Industrial & Engineering Chemistry Research
RESEARCH NOTE
Table 1. Experimental Data Ranges for Solubility of Glycol in Supercritical Gas Treated in This Work
Table 4. Optimal Values of the Adjustable Parameters of the Adachi and Lu22 Equation
range of experimental data system
set no. N
CH4 + TEG
a
1
CO2 + TEG
2
CO2 + EG
3
*
T (K)
P (MPa)
12 298.15316.75 1.6068.697
optimal values of the parameters
y2 10
6a
1
0.2871.38
9 323.15323.15 2.75811.032 2.33137 36 308.15333.15 2.7622.06
33.45640
*
Glycol solubility (mole fraction). Number of experimental data.
Table 2. Critical Properties and Acentric Factors of the Compounds Investigated in This Study.2628 Tca (K)
Pcb (MPa)
ωc
methane
190.6
4.544
0.01083
carbon dioxide
304.2
7.280
0.22760
substance
a
set no.
ethylene glycol
719.70
7.599
0.4868
triethylene glycol
769.50
3.277
0.7587
a
bb
e1c
e2d
9.7
0.4
5.7 103
8 108
9
3
a
6240
e3e
2
5587
5.4
0.9
2.0 10
8 108
27
3 overall
4725
4.1
1.3
5.5 104
8 109
17 18
a The confidence interval is considered to be [10000 to 2000]. b The confidence interval is considered to be [20 to 20]. c The confidence interval is considered to be [0 to 5]. d The confidence interval is considered to be [105 to 102]. e The confidence interval is considered to be [1010 to 107].
Table 5. Optimal Values of the Adjustable Parameters of the del Valle and Aguilera’s23 Correlation optimal values of the parameters
Critical temperature. b Critical pressure. c Acentric factor.
set no.
Table 3. Optimal Values of the Adjustable Parameters of the Chrastil’s20 Correlation
aa
bb
dc
kd
1
5.3
5430
4300
1.11
17
4.1
6247
6700
3.59
43
3
12.7
1325
276600
3.03
ka
ab
1
1.108
5431
5.31
15
2
3.586
6246
4.09
35
3 overall
3.069
3112
10.04
32 27
|(ccalc 2 a
AAD* %
AAD = 100/(N n) where n is the number of the model parameters. The confidence interval is considered to be [0.1 to 10]. b The confidence interval is considered to be [10000 to 2000]. c The confidence interval is considered to be [20 to 20]. *
expt cexpt 2 )|/c2 ,
respectively. It has been shown that because the solvate complex is not stoichiometric in most cases, the association term (k) is a characteristic of the proposed system and can be considered as an adjustable parameter.21 2.2. Adachi and Lu. A modification to the Chrastil’s equation20 was proposed by Adachi and Lu,22 who consider the association term (k) of eq 2 as a function of gas (solvent) density as follows:22 k ¼ e1 þ e2 F þ e3 F
2
32 31
a
optimal values of the parameters bc
AAD %
2 overall
set no.
AAD %
ð3Þ
where e13 are adjustable parameters to reduce the relative deviations of the calculated results from experimental values for different solutes. Although these researchers faced some divergences in their calculation algorithm, they reported overall improvement in the calculated solubilities of different solids in supercritical carbon dioxide.22 2.3. del Valle and Aguilera. Fitting the experimental values of solubilities of vegetable oils in supercritical carbon dioxide led del Valle and Aguilera23 to present a correlation considering the effects of temperature and density of gas (solvent) as
The confidence interval is considered to be [20 to 20]. b The confidence interval is considered to be [20000 to 2000]. c The confidence interval is considered to be [3.0 105 to 2000]. d The confidence interval is considered to be [0.1 to 10].
Table 6. Optimal Values of the Adjustable Parameters of the Mendez-Santiago and Teja’s24 Correlation optimal values of the parameters set no.
a
a
bb
dc
AAD %
1
7117
166890
9
5
2
8521
228175
14
20
3 overall
7970
98834
16
25 17
The confidence interval is considered to be [10000 to 2000]. b The confidence interval is considered to be [104 to 106]. c The confidence interval is considered to be [20 to 20]. a
the following form: b d k þ 2 c ¼ F exp a þ T T
ð4Þ
where a, b, and d are the adjustable parameters determined for a system of interest. ndez-Santiago and Teja. The effects of pressure on 2.4. Me the solubilities of different solids in gases have been taken into account by Mendez-Santiago and Teja:24 1 a bF þ þ d ð5Þ y ¼ exp P T T 10374
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Industrial & Engineering Chemistry Research
RESEARCH NOTE
Table 7. The Calculated Results Using the Investigated Equations ccalc b 100
system
T (K) P (MPa) cexpt a 100 Chrastil20
ARD c/%
Adachi and
del Valle
Mendez-Santiago
Lu22
and Aguilera23
and Teja24
Adachi
del Valle
Chrastil20 and Lu22 and Aguilera23
Mendez-Santiago and Teja24
CH4 + TEG 298.15
16.06
0.004
0.003
0.004
0.003
0.004
6
0
10
8
298.15
32.43
0.006
0.008
0.006
0.007
0.006
29
2
23
1
298.15
51.32
0.010
0.013
0.010
0.013
0.011
28
0
22
1
298.15
64.85
0.015
0.018
0.015
0.017
0.015
17
0
11
0
298.15
74.85
0.021
0.021
0.020
0.020
0.022
0
5
5
4
298.15
86.12
0.029
0.025
0.028
0.024
0.029
13
3
17
1
316.75 316.75
18.8 33.13
0.015 0.022
0.011 0.021
0.013 0.020
0.011 0.020
0.015 0.024
27 5
14 11
30 9
0 6
316.75
49.03
0.033
0.034
0.030
0.032
0.035
2
8
2
7
316.75
63.92
0.044
0.046
0.044
0.044
0.044
4
0
0
0
316.75
75.05
0.055
0.056
0.058
0.053
0.058
1
6
3
5
316.75
86.97
0.067
0.066
0.079
0.064
0.078
2
17
6
15
CO2 + TEG 323.15
27.58
0.041
0.009
0.041
0.009
0.041
77
0
79
0
323.15 323.15
41.37 55.16
0.096 0.149
0.053 0.207
0.089 0.196
0.052 0.205
0.118 0.151
45 39
7 31
45 38
23 1
323.15
68.95
0.688
0.698
0.482
0.692
1.002
1
30
1
46
323.15
82.74
2.319
2.311
1.537
2.291
3.339
0
34
1
44
323.15
96.53
8.310
8.334
8.310
8.263
8.312
0
0
1
0
333.15
41.37
0.136
0.077
0.136
0.076
0.138
43
0
44
2
333.15
55.16
0.266
0.285
0.279
0.282
0.276
7
5
6
4
333.15
110.32
16.542
16.584
16.542
16.451
16.578
0
0
1
0
308.15
27.6
0.26
0.04
0.26
0.04
0.38
85
0
83
46
308.15
55.2
1.01
0.70
1.01
0.75
1.45
31
0
26
43
308.15
68.9
2.44
2.64
2.44
2.78
2.54
8
0
14
4
308.15
82.7
13.86
34.15
13.86
34.85
15.74
146
0
151
14
308.15
110.3
75.57
89.97
75.57
90.71
79.72
19
0
20
5
308.15
137.9
134.22
121.62
134.22
122.16
134.22
9
0
9
0
308.15
165.5
154.05
146.81
154.05
147.12
164.43
5
0
4
7
308.15 308.15
193.1 220.6
170.61 180.40
168.46 187.67
170.61 180.40
168.53 187.50
200.73 348.69
1 4
0 0
1 4
18 93
313.15
27.6
0.32
0.04
0.32
0.05
0.46
86
0
85
43
313.15
55.2
12.33
0.70
12.33
0.76
18.98
94
0
94
54
313.15
68.9
2.69
2.30
2.69
2.43
5.04
15
0
10
87
313.15
82.7
10.66
10.04
10.66
10.42
11.37
6
0
2
7
313.15
110.3
495.21
77.91
495.21
78.82
505.74
84
0
84
2
313.15
137.9
117.19
118.34
117.19
119.11
120.41
1
0
2
3
313.15 313.15
165.5 193.1
150.26 174.42
149.44 175.84
150.26 174.42
149.97 176.11
163.15 255.97
1 1
0 0
0 1
9 47
313.15
220.6
191.15
199.12
191.15
199.12
211.05
4
0
4
10
323.15
27.6
0.52
0.05
0.52
0.06
0.62
90
0
89
19
323.15
55.2
1.67
0.73
1.67
0.78
2.35
56
0
53
40
323.15
68.9
2.90
2.06
2.90
2.17
3.56
29
0
25
23
323.15
82.7
7.39
5.73
7.39
5.99
8.33
22
0
19
13
323.15
110.3
40.19
44.36
40.19
45.15
42.07
10
0
12
5
323.15 323.15
137.9 165.5
101.69 149.54
101.44 146.16
101.69 149.54
102.20 146.59
102.20 161.58
0 2
0 0
0 2
0 8
323.15
193.1
191.51
183.74
191.51
183.75
351.33
4
0
4
83
323.15
220.6
216.47
216.68
216.47
216.26
276.31
0
0
0
28
CO2 + EG
10375
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Industrial & Engineering Chemistry Research
RESEARCH NOTE
Table 7. Continued ccalc b 100
system
T (K) P (MPa) cexpt a 100 Chrastil20
ARD c/%
Adachi and del Valle Mendez-Santiago Adachi del Valle Mendez-Santiago Chrastil20 and Lu22 and Aguilera23 Lu22 and Aguilera23 and Teja24 and Teja24
333.15
27.6
0.82
0.06
0.82
0.07
0.88
93
0
92
7
333.15
55.2
2.10
0.78
2.10
0.83
2.31
63
0
60
10
333.15
68.9
4.18
2.02
4.18
2.12
5.05
52
0
49
21
333.15
82.7
6.76
4.86
6.76
5.06
7.26
28
0
25
7
333.15
110.3
26.44
25.21
26.44
25.69
26.44
5
0
3
0
333.15
137.9
73.84
77.02
73.84
77.41
78.71
4
0
5
7
333.15
165.5
131.82
132.53
131.82
132.31
155.20
1
0
0
18
333.15 333.15
193.1 220.6
183.23 217.05
181.87 225.85
183.23 217.05
180.86 223.99
228.73 217.05
1 4
0 0
1 3
25 0
expt expt a Experimental Glycols solubility (g 3 dm3). b Calculated Glycols solubility (g 3 dm3). c AAD = 100/(N n) |(ccalc 2 c2 )|/c2 , the mole fractions have been converted to concentrations with the unit (g 3 dm3).
Figure 1. The deviation ranges of the results form experimental values for the CH4 + TEG system. (1) The Chrastil20 equation; (2): Adachi and Lu22 equation; (3) del Valle and Aguilera23 equation; (4) MendezSantiago and Teja24 equation.
Figure 2. The deviation ranges of the results form experimental values for the CO2 + TEG system. (1) The Chrastil20 equation; (2) Adachi and Lu22 equation; (3) del Valle and Aguilera23 equation; (4) MendezSantiago and Teja24 equation.
where y denotes the solubility of solute (mole fraction), P is the pressure in MPa, and a, b, and d are the three adjustable parameters of the equation.
(NDD) mixing rules26 has been used to calculate the density of the gases (solvents) at the desired conditions (of course for calculating the density of a pure gas, the mixing rules of the model have not been applied).27 These values are freely available upon request from the authors. Detailed description of the applied EoS has been well-established elswhere.16,26,28,29 The optimal values of adjustable parameters of the applied correlations have been obtained through minimization of the following objective function: expt 100 N ccalc ci i ð6Þ OF ¼ N i ¼ 1 cexpt i
3. EXPERIMENTAL DATA To perform a reliable study of the capabilities of the aforementioned correlations in representation of the solubility of ethylene and triethylene glycols in supercritical carbon dioxide and methane, we have applied the previously evaluated corresponding experimental data.17 It should be noted that the thermodynamic consistency test has already been done only on the experimental data of solubilities of triethylene glycol in supercritical carbon dioxide and methane, due to high deviations of the applied model results for representation of corresponding solubilities of ethylene glycol. Table 1 shows the temperature, pressure, and solubility ranges, accompanied with the references of the experimental data. The critical properties and acentric factors of the investigated components are reported in Table 2. 4. METHODOLOGY A thermodynamic model based on the Valderrama-Patel Teja equation of state (VPT-EoS)25 with nondensity-dependent
∑
where N stands for the number of experimental data, i denotes the ith experimental data, and superscripts calc and expt refer to calculated and experimental solubility values, respectively. The mole fractions (y) have been converted to concentrations (c) with the unit (g 3 dm3). The differential evolution30,31 (DE) optimization strategy has been employed for calculating the optimal values of the correlation parameters since it has been already demonstrated to converge to the global optimum without sensivity to the calculation starting point.19,3234 10376
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Industrial & Engineering Chemistry Research
Figure 3. The deviation ranges of the results form experimental values for the CO2 + TEG system. (1) The Chrastil20 equation; (2) Adachi and Lu22 equation; (3) del Valle and Aguilera23 equation; (4) MendezSantiago and Teja24 equation.
5. RESULTS AND DISCUSSION Table 3 reports the optimal values of the Chrastil20 equation parameters along with the absolute average deviations (AAD %) of the calculated solubility values from experimental ones. Similarly, Tables 46 indicate the obtained results using the equations proposed by Adachi and Lu,22 del Valle and Aguilera,23 and Mendez-Santiago and Teja,24 respectively. All of the calculated results have been shown in Table 7. Furthermore, Figures 13 lead to better representation of the absolute relative deviations of the results from experimental values. Several points need to be considered regarding the reported results. First, we have used the thermodynamic consistent data available in the literature for obtaining the optimum values of the parameters of the equations for the system TEG + methane/ carbon dioxide. This fact may increase the possibility of presenting more accurate parameters of the correlations using the treated experimental data. Another element to consider is that, considering more adjustable parameters for representation, the equilibrium term (k) has a large effect on the evaluated glycols solubility in the investigated gas samples, although the values of the (e3) parameter in equation 3 are negligible in comparison with the other two (e1 and e2). As a matter of fact, the correlation presented by Adachi and Lu22 results in a good description of the physical behavior of these kinds of systems because it takes into account that the equilibrium constant varies with the density of the investigated gas (solvent). However, taking into account the effects of pressure on the solubility of investigated glycols in the gas phase by the equation proposed by Mendez-Santiago and Teja24 has almost a similar effect on the average absolute deviations of the results from experimental values. Neglecting the effects of gas (solvent) densities predictions by the VPT-EoS25 along with NDD mixing rules26 and the common errors in optimization procedure, on the obtained results would be an oversight although using the DE optimization strategy30,31 has contributed to overcome the drawbacks of other statistical procedures used in original articles, for example, in that of Adachi and Lu.22 The effect of the number of the parameters of the applied equations on the absolute average deviations of the calculated results from experimental ones should be pointed out because they are not negligible in comparison with the number of the
RESEARCH NOTE
experimental data. Moreover and as already mentioned, the solubility of glycols in the gas phase is very low, which may lead to high uncertainties in the measurements. These two facts literally reveal the importance of producing especially designed equipment based on various solubility measurement techniques and consequently generating more experimental data for use in tuning the models and obtaining the optimum model parameters as well as providing industry with enough information about the phase behavior of the investigated systems.35 Among the investigated equations, which are generally used for correlating the solubilities of different pharmaceutical compounds in supercritical carbon dioxide, the one presented by Mendez-Santiago and Teja24 and Adachi and Lu22 lead us to a generally acceptable representation of the solubility of ethylene/ triethylene glycols in supercritical CO2 and methane: AAD = 17% and 18%, respectively. However, applying the equations proposed by Chrastil20 and del Valle and Aguilera,23 leads to a rougher estimation of the corresponding solubility values. Finally, it should be mentioned that we assumed that the liquid phase is pure glycol. The presence of any other component in the liquid phase (e.g., water, etc.) will surely change our results. This is the subject of another investigation for the future.
6. CONCLUSIONS Four widely used correlations including the original Chrastil,20 Adachi and Lu,22 del Valle and Aguilera,23 and MendezSantiago and Teja,24 were used in this article to represent the solubilitiy of ethylene glycol and triethylene glycol in gaseous systems between 298.15 and 333.15 K and between 1.606 and 22.06 MPa; conditions of concern for the petroleum industry. The VPT-EoS25 with NDD mixing rules26 was used to calculate the density of the gases (solvents) at the desired conditions, and the DE optimization method30,31 was applied to obtain the optimum values of the adjustable parameters. The AAD % of the results from experimental values were found to be around 27%, 18%, 31%, and 17%, with respect to the results of the original Chrastil,20 Adachi and Lu,22 del Valle and Aguilera,23 and Mendez-Santiago and Teja24 correlations, respectively. It was demonstrated that consideration of the pressure dependency of the glycols solubility in investigated gases in such equations would contribute to highly reduce the deviations of the results from experimental values in comparison with the original Chrastil20 equation. However, taking into account the density dependency of the constant of the association between the solute and gas (solvent) molecules by the equation of Adachi and Lu’s22 also improves the accuracy of the results to a great extent. However, there is a drastic need to generate more reliable experimental data, to present more accurate and comprehensive correlations for this purpose, and design more efficient dehydration processes. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Tel.: + (33) 1 64 69 49 70. Fax: + (33) 1 64 69 49 68.
’ ACKNOWLEDGMENT The financial support of the ANR (Agence Nationale de la Recherche) and the OSEM (Orientation Strategique des Ecoles 10377
dx.doi.org/10.1021/ie2009839 |Ind. Eng. Chem. Res. 2011, 50, 10373–10379
Industrial & Engineering Chemistry Research des Mines) is gratefully acknowledged. Mr. Ali Eslamimanesh wishes to thank MINES ParisTech for providing a Ph.D. scholarship.
’ NOMENCLATURE AAD = absolute average deviation, %: expt expt AAD = (100)/(N n) |(ccalc 2 c2 )|/c2 ARD = absolute relative deviation, %: expt expt ARD = 100 |(ccalc 2 c2 )|/c2 0 A = solute molecule B0 = gas (solvent) molecule a = adjustable parameter of the correlations b = adjustable parameter of the correlations c = solubility of glycols, g 3 dm3 d = adjustable parameter of the correlations DE = differential evolution e1e3 = adjustable parameter of the Adachi and Lu’s22correlation k = association term N = number of experimental data n = number of adjustable parameters of equations NDD = nondensity dependent mixing rules OF = objective function P = pressure, MPa T = temperature, K u = parameter in eq 6 VPT-EoS = Valderrama-PatelTeja equation of state y = mole fraction of solute in gas phase Greek Letters
F = density of gas (solvent) (g 3 dm3) ω = acentric factor Subscripts
c = critical value i = ith experimental data point Superscripts
calc = calculated value expt = experimental value
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