Ind. Eng. Chem. Res. 2007, 46, 6053-6060
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CORRELATIONS Electrolyte UNIQUAC-NRF Model to Study the Solubility of Acid Gases in Alkanolamines Ali Haghtalab* and Mohammad Dehghani Tafti Chemical Engineering Department, Tarbiat Modarres UniVersity, Tehran, Iran
Thermodynamic modeling of solubility of acid gases in aqueous alkanolamine solutions is essential in design of the absorbers for sweetening of natural gas. A thermodynamic consistent model was developed for calculation of the vapor-liquid equilibria in acid gases (H2S and CO2)-alkanolamine-water system. This model accounts for both chemical and phase equilibria in liquid and vapor phases. For nonideality of species in the liquid phase, the UNIQUAC-NRF equation with ion-pair approach was applied. For long-range interaction, the Pitzer-Debye-Hu¨ckel term was used. The model was applied for correlation of the solubility of acid gases in binary and ternary aqueous solutions of monoethanolamine (MEA) and methyldiethanolamine (MDEA). Also, prediction of the solubility of acid gases in binary and ternary aqueous solution of 2-amino-2-methyl1-propanol (AMP) was investigated. A general correlation function in terms of temperature was used for each parameter so that the model can be applied to predict the solubility of acid gases in the alkanolamines at the other temperatures. The results obtained by this model are in very good agreement with experimental data. 1. Introduction Aqueous solutions of alkanolamines are used to remove carbon dioxide and hydrogen sulfide from natural gas and oil refineries plants. Monoethanolamine (MEA) has been the most widely employed gas treating alkanolamine solvent due to its high reactivity, low cost, ease of reclamation, and low solubility of hydrocarbons.1 The disadvantage includes a high enthalpy of reaction with carbon dioxide and formation of carbomate. Methyldiethanolamine (MDEA) solution frequently is used for selective removal of H2S from gas streams which contain both CO2 and H2S. However, MDEA is also useful for bulk CO2 removal because of the low heat of reaction with acid gases, which leads to lower energy requirement for regeneration. Recently, 2-amino-2-methyl-1-propanol (AMP) has been considered as a sterically hindered stable amine for higher cyclic absorption capacity for CO2. AMP does not form a stable carbomate, so bicarbonate and carbonate ions may be present in the solution in larger amounts than carbomate ions. Design of gas-treating operation requires knowledge of vapor-liquid equilibria (VLE) of the aqueous acid gas-alkanolamine system. In an early thermodynamic model, Kent-Eisenberg1 used apparent an chemical equilibrium constant neglecting the activity coefficient of species in the liquid phase. Using Guggenheim’s equation for calculation of the activity coefficient, Deshmukh and Mather2 applied the Edwards et al.3 approach to correlate the solubility of H2S and CO2 in MEA solution. Chakravarty et al.4 extended the model of Dushmukh and Mather for mixed amines. Austgen et al.5 used Chen’s electrolyte-NRTL6 equation in the context of a VLE model for representation activity coefficients of all species, ionic and molecular in an acid gas* To whom correspondence should be addressed. Chemical Engineering Department, Faculty of Engineering, Tarbiat Modarres University, P.O. Box: 14115-175, Tehran, Iran. Tel.: +9821 88011001. Fax: +9821 88004565. E-mail:
[email protected].
MEA-water system. Li and Mather7 applied the Clegg-Pitzer8 equation to correlate solubility of acid gases in MEA and MDEA aqueous solutions. Kaewsichan et al.9 applied electrolyteUNIQUAC for an acid gas-alkanolamine-water system. Kundu et al.10 used a modified Clegg-Pitzer model for the solubility of CO2 in AMP aqueous solution. Pazuki et. al applied the UNIQUAC-NRF to modeling the solubility of CO2 in aqueous ammonia solution at low temperature.11 The objective of the present work is to develop the electrolyteUNIQUAC-NRF model that correlates the solubility of CO2 and H2S in aqueous solutions of MEA, MDEA, and AMP. In fact, we applied the molecular activity coefficient model UNIQUAC-NRF12 for an electrolyte system based on interaction of ion pairs with molecular species. 2. Thermodynamic Framework 2.1. Standard State. In this work, both water and alkanolamine are treated as solvents. The standard state associated with each solvent is pure liquid at the temperature and pressure of system. The adopted standard state for an ionic (ion-pair) solute is an ideal, infinitely dilute aqueous solution (infinity dilute in solute and alkanolamine) at the system temperature and pressure. Finally, the reference state chosen for molecular solutes (CO2 and H2S) is also an ideal, infinitely dilute aqueous solution at the system temperature and pressure. This leads to the following unsymmetrical convention for normalization of the activity coefficient. Solvent:
γs f 1 as xs f 1 Pair ions and molecular solutes:
γ/i f 1 as xi f 0 and xs*w ) 0
10.1021/ie070259r CCC: $37.00 © 2007 American Chemical Society Published on Web 07/27/2007
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Ind. Eng. Chem. Res., Vol. 46, No. 18, 2007
where the subscript s refers to any nonaqueous solvent, i refers to ionic or neutral solutes, and w refers to water. The activity coefficients of all species are assumed to be independent of pressure. 2.2. Chemical Equilibria. In aqueous solution, CO2 and H2S react with MDEA, AMP, and MEA to produce a number of ionic complex species as in the following equilibrium reactions: K1
CO2 + 2H2O 798 H3O+ + HCO3-
(1)
K2
H2S + H2O 798 H3O+ + HS-
(2)
K3
H2O + MDEAH+ 798 H3O+ + MDEA
3. Activity Coefficient The molar excess Gibbs energy of an electrolyte system is assumed to consist of short-range (gSR) and long-range (gLR) terms:
gE gLR gSR ) + RT RT RT
(12)
For short-range interaction, with the ion-pair assumption, the UNIQUAC-NRF equation as a nonelectrolyte model with both combinatorial and residual terms is expressed as
( ) ( )
gE gSR ) RT RT
(3)
+
C
gE RT
(13)
R
where the combinatorial term is written as
K4
H2O + AMPH+ 798 H3O+ + AMP +
K5
(4)
+
H2O + MEAH 798 H3O + MEA
(5)
In addition, in aqueous solutions of MEA, the carbomate is formed as follows: K6
-
-
H2O + RNHCOO 798 MEA + HCO3
∏i (γixi)V
ij
j ) 1, .., 6
(7)
where xi and γi are the mole fraction and activity coefficient of species i and υij is the stoichiometric coefficient for component i in reaction j. In this work, the chemical equilibrium constant is expressed as a function of temperature:
ln Kj ) C1 + C2/T + C3 ln T + C4T
(8)
For simplicity, we neglected the molecular species of CO2 and H2S and the ionic species of CO32- and S2- in the aqueous phase, because their concentrations are very low in comparison with the other species dissolved in a mixed alkanolamine-water system. 2.3. Phase Equilibria. The nonideality of the gas phase was neglected, so the fugacity of molecular species (H2S and CO2) in liquid phase can be written as follows:
fi ) xiHiγi (i ) CO2 or H2S)
(9)
where Henry’s law represents a reference state and “H” refers to Henry’s constant. We assumed that the solubility of molecular species in the liquid phase is ideal, so the partial pressure of dioxide carbon is expressed as follows:
Pi ) xiHi
C
∑ i)1
xi ln
+
xi
[∑ ]
Z
n
2
i)1
θi
qixi ln
φi i ) ions and molecules (14)
So, the combinatorial activity coefficient was presented:
θi φi n Z + qi ln + li xjlj xi 2 φi xi j)1
φi
ln γCi ) ln
∑
(11)
where the coefficients C1-C4 of both eqs 8 and 11 have been taken from the work of Austgen et.al.13
(15)
The volume fraction, area fraction, and li are written as follows:
φi )
rixi n
; θi )
rjxj ∑ j)1
qixi n
; li ) (ri - qi)z/2 - (ri - 1)
qjxj ∑ j)1
(16)
The residual term, the UNIQUAC-NRF equation of molar excess Gibbs energy, was obtained as follows:12
() gE
[
n
)
RT
∑ i)1
R
]
Γji
n
qixi ln Γii +
θj ln ∑ Γ j)1 j*i
(17)
ii
So by proper differentiation of eq 17, the residual activity coefficient equation was obtained:
[
n
ln γRi ) qi 1 + ln Γii -
(1 - θi)
n
∑ i*j j)1
θj ln
θjΓij + ∑ j)1
( ) ΓijΓji
-
ΓiiΓjj
1
n
n
∑∑ l)1
2 k)1
θkθl ln
k*j l*k,i
( )] ΓklΓlk
ΓkkΓll
(18)
where the nonrandom factor was obtained as
(10)
The units of Henry’s constant is Pascals, and its temperature dependence is expressed by the same function form as eq 8.
ln Hi ) C1 + C2/T + C3 ln T + C4T
RT
φi
n
)
(6)
The equation governing chemical equilibria may be written as follows:
Kj )
() gE
Γij )
τij
∑k θkτkj
(19)
Γii ) Γji/τji
(20)
τij ) exp(-aij)
(21)
Ind. Eng. Chem. Res., Vol. 46, No. 18, 2007 6055
where τij or aij are the adjustable energy parameters. Thus, eq 18 can be used for calculation of the activity coefficients of ion-pair and molecular species. In modeling of the electrolyte system, we assumed that the cations and anions to form ion pairs,14 for instance, the MEAH+ and HS- ions form an ion pair as MEAH+-HS-. For an electrolyte solution containing n cations and m anions, then “m × n” ion pairs can be formed. So, the probability of formation of an ion pair, cZaaZc, is calculated as
pcZaaZc )
zc[czc]
×
za[aza] (22)
∑i zi[cz ] ∑j zj[az ] i
ln γ/,PDH ) -zi2Ax i
[
) ln γPDH n
2AxIx3/2
1
(zi2xi) ∑ 2 i
(32)
The variable Ax is the Debye-Hu¨ckel parameter on a mole fraction basis:
Ax ) Aφ(
(23)
∑n (Cn)1/2
(33)
where Cn is the molar concentration of the solvent n. The Aφ is the original Debye-Hu¨ckel parameter,16 which is given by following function:
where
∑i zi[cz ] + ∑j zj[az ]]
(24)
j
The volume (r) and surface (q) parameters of an ion pair were calculated as the following:
qcZaaZc ) zaqc + zcqa and rcZaaZc ) zarc + zcra
Aφ ) 0.391
(
)(
78.54‚298.15 DmT
3/2
dm 0.99702
(25)
On the other hand, the residual activity coefficient of the ion pairs is expressed as
a
c
za zc ln γRc + ln γRa z c + za zc + za
(26)
where γc and γa are the activity coefficient of cation and anion, respectively. For a univalent-univalent ion-pair system, one can assume the following:
ln γcRZ aZ ) ln γRc ) ln γRa a
(27)
ln γ j Rc )
( ) ( )
∑a
[czaazc]
[cz a′z ] ∑ a′ a′
ln γ j Ra )
F ) 2150
(
∑c
a
(28) c
c
[czaazc]
[c′z az ] ∑ c′ a
ln γcRZ aZ
1/2
(34)
)
∑n Cn
1000DmT
3/2
(35)
where dm and Dm are the density and dielectric constant for the mixed solvent m which can be calculated by using the following equations:18,19
Dm )
dm )
∑n (φnDn)
(∑ ) wn
n
c
On the other hand, due to presence of the common ions in the system, one may define the average activity coefficient of the common ion in terms of the activity coefficient of the ion pair as follows:
)
The parameter F is related to the hard-core collision, or distance of closest approach, of ion and solution, which is given by Pitzer and Li17 as follows:
18.02dm
ln γcRZ aZ )
(31)
1 + FIx1/2
where the mole fraction ionic strength is defined as
Ix )
[cZaaZc] ) pcZaaZc × Ct
i
]
Ix1/2(1 - 2Ix/zi2) 2 ln(1 + FIx1/2) + F 1 + FIx1/2 (30)
j
where the values in the brackets show the concentration of cation and anion species. Thus, using the electroneutrality of the system, Σizi[czi] ) Σjzj[azj], the concentration of the ion pair can be obtained:
1 Ct ) [ 2
for both molecular and ionic species, respectively, were used:15
(36)
-1
dn
(37)
where φn is the volume fraction of solvent n
φn )
CnVn C mV m ∑ m
(38)
The Vn is the molar volume of the pure solvent n. The temperature dependences of the density and dielectric constant are taken from the work of Li and Mather.7 4. Determining Interaction Parameters
ln γcRZ aZ a
(29) c
c′
For the long-range term, the Pitzer-Debye-Hu¨ckel equations
The surface and volume parameters for molecular and ionic species are shown in Table 1. The surface and volume parameters of ions were calculated by using the method which was presented by Marcus.25 The structural parameters of molecular species were obtained from Hysys software. For calculation of the parameters of the complex ions such as
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Table 1. Values of the Surface and Volume Parameters for the Species species
q
r
H2O AMP MEA MDEA HSHCO3H+ MEAH+ MDEAH+ AMPH+
1.4 4.132 2.976 5.5 1.2966 0.7364 0.0272 3.0032 5.5272 4.1592
0.92 4.391 3.0436 5.8841 1.4744 0.6311 0.0043 3.0479 5.8884 4.3953
Table 2. Values of the Coefficient of Binary Interaction Parameters for the MDEA + H2O and MEA + H2O Systems n-n′
τnn′
ann′
bnn′
H2O-MDEA MDEA-H2O H2O-MEA MEA-H2O
τ12 τ21 τ13 τ31
-0.838383 -2.610744 0.660048 0.658168
955.2726 1414.1518 583.3513 -125.4741
Figure 1. Solubility of CO2 in 30% MDEA aqueous solutions at 25, 40, 80, and 120 °C.
Table 3. Coefficients of the Interaction Parameters for Ternary Systems MDEA-CO2-H2O, MDEA-H2S-H2O, and MEA-H2S-H2Oa parameter aij
coefficient eij
hij
gij
a1,MX aMX,1 a2,MX aMX,2
MDEA-CO2-H2O -1446.734 217501.538 -613.077 99572.087 -1690.878 252779.285 -488.295 337317.245
-1245.757 -1538.007 -2361.371 -11622.319
a1,MY aMY,1 a2,MY aMY,2
MDEA-H2O-H2S -114564.830 33812093.800 -20108.794 5876593.750 12848.205 -3798549.080 8216.813 -2522721.740
53809.637 9209.629 -7168.985 -4253.858
MEA-H2O-H2S a1,NY aNY,1 a3,NY aNY,3
-1286.787 1449.575 -4640.282 -2015.828
326901.911 -316623.318 1323304.076 725037.373
10856.080 -6174.742 30185.299 13071.348
a 1 ) H O, 2 ) MDEA, 3 ) MEA, M ) MDEAH+, N ) MEAH+, X 2 ) HCO3-, Y ) HS-.
MDEAH+, we used an addition method as follows: rMDEAH+ ) rH+ + rMDEA, qMDEAH+ ) qH+ + qMDEA. 4.1. Binary System. For MEA + H2O and MDEA + H2O binary systems, the binary parameters of the UNIQUAC-NRF equation (τij) were calculated by using the NRTL5 binary interaction parameters. In fact, due to the inaccessibility of the binary activity coefficient data, the values of the activity coefficient were reproduced from the NRTL energy parameters. So, the binary interaction parameters were assumed to be dependent on temperature and correlated by the following relation:
τnn′ ) ann′ +
bnn′ T
(39)
Figure 2. Solubility of H2S in 4.28 molar MDEA aqueous solutions at 25, 40, 70, 100 and 120 °C.
4.2. Ternary Systems. To determine the binary interaction parameters of the ion-pairs and molecular species in the UNIQUAC-NRF equation, we used the solubility data of the aqueous single gas-single amine system over a wide range of temperatures and gas loadings. So, the following relation for the interaction parameters in terms of temperature are used:
aij ) eij +
[
hij T - T0 T + gij + ln 0 T T T
]
(40)
where e, h, and g are the coefficients of the interaction parameters and the value of T0 is 298.15 K. By combining eqs 1 and 3, for the MDEA-CO2-H2O system, one can obtain the following: K1/K3
Table 2 shows the binary parameters and the fitted coefficients for MEA and MDEA systems. Since no reliable experimental data for the binary system AMP-H2O are available, the solvent-solvent interaction parameters were optimized using the solubility data for the ternary AMP-CO2-H2O system.10
CO2 + H2O + MDEA 798 MDEAH+ + HCO3-
(41)
Only four true species, two neutral-solvent and two ionic species, exist in this ternary system, and we may assume that all the dissolved CO2 is converted into HCO3- ions. The concentration of each species can be obtained by the electroneutrality condition
Ind. Eng. Chem. Res., Vol. 46, No. 18, 2007 6057
Figure 3. Solubility of H2S in 5 M MEA aqueous solutions at 25, 40, and 60 °C.
Figure 4. Solubility of H2S in 5 molar MEA aqueous solutions at 80, 100, and 120 °C.
and mass balance equations as the following:
CMDEAH+ ) CHCO3- ) C0MDEAR
(42)
C0MDEA ) CMDEA + CMDEAH+
(43)
CH0 2O ) CH2O + CMDEAH+
(44)
where the superscript “0” presents the initial concentration of the compounds and the variable R is the CO2 loading in the equilibrated liquid phase, expressed in moles of CO2 per mole of the amine. By writing the equilibrium constant for the reaction 41 and using eq 10, the following relation for partial pressure of CO2 is obtained:
PCO2 )
HCO2K2xMγ/M xXγ/X K1x1γ1x2γ2
(45)
where subindexes 1, 2, M, and X represent H2O, MDEA, MDEAH+, and HCO3-, respectively. So, the objective function σ for optimization of the interaction parameters is the following:
σ)
(PCO2)cal - (PCO2)exp | (PCO2)exp
∑|
(46)
Figure 5. Comparison of the calculated and experimental partial pressure of CO2 over aqueous MDEA solution.
Figure 6. Comparison of the calculated and experimental partial pressure of H2S over aqueous MDEA solution.
The same relations as in eqs 41-46 can be written for the MDEA-H2S-H2O and MEA-H2S-H2O systems. By global optimization of experimental VLE data, the interaction parameters were calculated and shown in Table 3. Figures 1-4 show the partial pressure of CO2 and H2S versus the loading for the aqueous ternary systems of MDEA + CO2, MDEA-H2S, and MEA + H2S, respectively. As one can observe, the agreement between experimental data and the calculated values are very good. Figures 5-7 show the experimental partial pressure of CO2 and H2S versus the calculated partial pressures for the systems MDEA-CO2-H2O, MDEA-H2S-H2O, and MEA-H2SH2O, respectively. As one can see, the deviations are very low. Similar calculations were performed for the AMP-CO2H2O system; however, using general relation 40, globally all six interaction parameters were optimized and are shown in Table 4. One should be noted that the data of solubility of CO2 in 24% AMP aqueous solutions at 30, 40, and 50 °C were used for optimization. The results of the partial pressure vs the CO2 loading are shown in Figure 8. To investigate the predictability of the model, the interaction parameters were used to calculate the solubility of CO2 in 30% AMP aqueous solutions at 30, 40, and 50 °C, and the results
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Figure 7. Comparison of the calculated and experimental partial pressure of H2S over aqueous MEA solution.
Figure 9. Solubility of CO2 in 30% AMP aqueous solutions at 30, 40, and 50 °C.
Figure 8. Solubility of CO2 in 24% AMP aqueous solutions at 30, 40, and 50 °C. Table 4. Coefficients of the Interaction Parameters for Ternary System AMP-CO2-H2Oa parameter
a
Figure 10. Solubility of CO2 in 30% molar MEA aqueous solutions at 25, 40, 60, and 80 °C.
coefficient
Table 5. Coefficients of the Interaction Parameters for Ternary System H2O-MEA-CO2a
τij or aij
eij
hij
gij
τ1,4 τ4,1 a1,LX aLX,1 a4,LX aLX,4
-22998.287 -57.739 297.2891 -50165.002 -1241.067 -12108.269
6315800 15895 -180250 13696000 271610 3402800
10722.807 32.187 -310.110 23354.678 464.378 5812.456
parameter
1 ) H2O, 4 ) AMP, L ) AMPH+, X ) HCO3-.
are shown in Figure 9. As one can observe, the predicted results are in very good agreement with experiment. To study the MEA-H2O-CO2 system, the electroneutrality condition and mass balance relations for this system can be written as follows:
a
coefficient
aij
eij × 10-4
hij × 10-6
gij × 10-3
a1,NX aNX,1 a1,NV aNV,1 a2,NX aNX,2 a2,NV aNV,2 aNX,NV aNV,NX
1.2093 22.175 -35.263 30.618 -6.6856 12.366 41.162 -23.416 -15.406 102.85
-4.4078 -65.478 104.49 -90.608 19.019 -37.052 -123.00 70.136 45.132 -306.38
-5.0063 -107.26 171.73 -149.91 32.809 -59.589 -194.46 107.75 76.693 -495.69
1 ) H2O, 2 ) MEA, N ) MEAH+, X ) HCO3-, V ) RNHCOO-.
CMEAH+ ) CRNHOO- + CHCO3-
(47)
In addition, we assumed that all the dissolved CO2 is converted into HCO3- and carbomate, so one can write the following:
C0MEA ) CMEA + CMEAH+ + CRNHCOO-
(48)
CRNHCOO- + CHCO3- ) C0MEARCO2
CH0 2O ) CH2O + C0MEARCO2 + CRNHCOO-
(49)
Using eq 6, the equilibrium constant equation for carbomate
(50)
Ind. Eng. Chem. Res., Vol. 46, No. 18, 2007 6059 Table 6. Average Deviation of the Partial Pressure of Acid Gases in the Aqueous Alkanolamine Solutionsa E-NRTL
Clegg-Pitzer
system
no. of parameters
no. of coefficients (parameters)
1 2 3 4 5
8 8 8 8 12
10 (5) 10 (5) 10 (5) 10 (5) 20 (8)
UNIQUAC-NRF δb
(%)
20.1[24] 26.5 [24] 14.3 [10] 13..5 [7]
no. of coefficients (parameters)
δb (%)
16 (6) 16 (6) 16 (6) 16 (6) 38 (12)
8.68 8.82 5.19 8.26 11.59
a 1 ) MDEA + H O + CO , 2 ) MDEA + H O + H S, 3 ) MEA-H O-H S, 4 ) AMP + H O + CO , 5 ) MEA-H O-CO . b δ (%) ) 100(1/n) 2 2 2 2 2 2 2 2 2 2 n |[(PCO2)cal - (PCO2)exp]/(PCO2)exp|. Σi)1
Figure 11. Comparison of the calculated and experimental partial pressure of CO2 over aqueous MEA solution.
formation can be written as
K6 )
x3γ3xXγ/X
(51)
x1γ1xVγ/V
where 1, 3, N, X, and V represent H2O, MEA, MEAH+, HCO3-, and RNHCOO-, respectively. One can define the mole fraction equilibrium constant as
x 3x X ) (KX)6 ) K6/Kγ x1xV
(52)
where the Kγ denotes the activity coefficient equilibrium constant. Combining eqs 1 and 5 and applying the Henry’s law, we can write the following:
(PCO2)1 )
HCO2K5xNγ/NxXγ/X K1x1γ1x3γ3
(53)
HCO2K5K6xNγ/NxVγ/V K1(x3γ3)2
(54)
Finally, using eqs 53 and 54, the following objective function was applied to correlating the experimental data:
σ)
∑
(PCO2)cal,1 - (PCO2)exp |+ (PCO2)exp
|
5. Conclusion Using the ion-pair assumption, the UNIQUAC-NRF activity coefficient equation was applied to model the solubility of acid gases in binary aqueous solutions of MEA, MDEA, and AMP. The model successfully correlated the experimental data in the whole range of temperatures and concentrations. The model can be used for prediction of solubility of acid gases in the alkanolamines and also may be used in equilibrium stage design calculation of the absorption columns for gas-sweetening processes. Nomenclature
Similarly using eqs 1, 5, and 6,
(PCO2)2 )
five main species consist of two neutral solvents, one cation, and two anions existing in the solution. Having this extra species, one may not be able to calculate the concentration of species directly with the available equations. So, by substitution of eqs 47-50 into eq 52 a quadratic equation can be obtained, and by solving this equation, the concentration of carbomate was calculated. However for the initial iteration, we assumed a initial guess for (KX)6. Using eq 55, the Marquardt-Levenberg approach was applied for optimization of interaction parameters. Table 5 shows the interaction parameters for the H2O-MEACO2 system, and Figure 10 shows the results of plotting the partial pressure of CO2 versus the loading. Also, Figure 11 shows the deviation of the partial pressure of CO2 for this system. The results of the model were compared with the E-NRTL and Clegg-Pitzer models and are shown in Table 6. This table shows the number of the interaction parameters for E-NRTL and both the coefficients and interaction parameters in the bracket for the Clegg-Pitzer and UNIQUAC-NRF models. Also, the deviation from the experimental partial pressures for the three models is shown. As one can see, the present model in some cases shows good accuracy with less parameters in comparison with the E-NRTL mode. Moreover, the model presents better precision with more parameters in comparison with the Clegg-Pitzer model. It should be noted that for system 1, Li and Mather7 used nearly the same data points with a deviation of 7.32%.
∑
(PCO2)cal,2 - (PCO2)exp | (PCO2)exp (55)
|
Due to formation of carbomate in the MEA-H2O-CO2 system,
Aφ ) Debye-Hu¨ckel parameter for osmotic coefficient Ax ) Debye-Hu¨ckel parameter on a mole fraction basis a ) interaction parameter of UNIQUAC-NRF C1, C2, C3, C4 ) the coefficients of eqs 7 and 10 C ) molar concentration D ) dielectric constant d ) density, g/mL σ ) objective function gE ) molar excess Gibbs free energy H ) Henry’s constant, Pa Ix ) ionic strength on a mole fraction basis K ) thermodynamic chemical equilibrium constant
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Kx ) apparent chemical equilibrium constant, expressed in mole fraction Kγ ) apparent chemical equilibrium constant, expressed in activity coefficients P ) partial pressure, Pa or kPa q ) area parameter r ) volume parameter T ) absolute temperature, K t ) temperature, °C V ) molar volume wn ) mass fraction x ) liquid-phase mole fraction based on true molecular and ionic species z ) valence of an ion Greek Letters R ) CO2 or H2S loading in liquid phase, mol of gas/mol of amine F ) hard-core collision diameter τ ) binary interaction parameter between solvent and water molecules θi ) area fraction of species i φi ) volume fraction of species i γ ) activity coefficient Superscripts 0 ) initial concentration and temperature / ) unsymmetrical convention PDH ) Pitzer-Debye-Hu¨ckel LR )long range SR ) short range C ) combinatorial R ) residual Subscripts a, X, Y, V ) anion c, N, L ) cation i, j ) ion species m ) mixed solvent system n, s ) neutral solvent species w, 1 ) water 2 ) MDEA 3 ) MEA 4 ) AMP M ) MDEAH+ N ) MEAH+ L ) AMPH+ X ) HCO3V ) RNHCOOcal ) calculated corr ) correlation exp ) experiment pre ) prediction Literature Cited (1) Kent, R. L.; Eisenberg, B. Better Data for Amine Treating. Hydrocarb. Process 1976, 55 (2), 87. (2) Deshmukh, R. D.; Mather, A. E. A Mathematical Model for Equilibrium Solubility of Hydrogen Sulfide and Carbon Dioxide in Aqueous Alkanolamine Solutions. Chem. Eng. Sci. 1981, 36, 355.
(3) Edwards, T. J.; Newman, J.; Prausnitz, J. M. Thermodynamics of Aqueous Solutions Containing Volatile Weak Electrolytes. AIChE J. 1975, 21 (2), 248. (4) Chakravarty, T.; Phukan, U. K.; Weiland, R. H. Reaction of Acid Gases with Mixtures of Amines. Chem. Eng. Prog. 1985, 81 (4), 32. (5) Austgen, D. M.; Rochelle, G. T.; Peng, X.; Chen, C. C. Model of Vapor-Liquid Equilibria for Aqueous Acid Gas-Alkanolamine Systems Using the Electrolyte NRTL Equation. Ind. Eng. Chem. Res. 1989, 28, 1060. (6) Mock, B.; Evans, L. B.; Chen, C. C. Thermodynamic Representation of Phase Equilibria of Mixed-Solvent Electrolyte Systems. AIChE J. 1986, 32 (10), 1655. (7) Li, Y. G., Mather, A. E. The Correlation and Prediction of the Solubility of Carbon Dioxide in a Mixed Alkanolamine Solution. Ind. Eng. Chem. Res. 1994, 33, 2006. (8) Clegg, S. L.; Pitzer, K. S. Thermodynamics of Multicomponent, Miscible, Ionic Solutions: Generalized Equations for Symmetrical Electrolytes. J. Phys. Chem. 1992, 96, 3513. (9) Kaewsichan, L.; Al-Bofersen, O.; Yesavage, V. F.; Selim, M. S. Predictions of the Solubility of Acid Gases in Monoethanolamine (MEA) and Methyldiethanolamine (MDEA) Solutions using the ElectrolyteUNIQUAC Model. Fluid Phase Equilib. 2001, 183-184, 159. (10) Kundu, M.; Mandal, B. P.; Bandyopadyay, S. S. Vapor-Liquid Equilibrium of CO2 in Aqueous Solution of 2-Amino-2-methyl-1-propanol. J. Chem. Eng. Data 2003, 48, 789. (11) Pazuki, G. R.; Pahlevanzadeh, H.; Ahooei, M. Solubility of CO2 in aqueous ammonia solution at low temperature. Fluid Phase Equilib. 2006, 242, 57. (12) Haghtalab, A.; Asadollahi, M. A. An excess Gibbs Energy model to study the phase behavior of aqueous Two-Phase system of Polyethenglycol + dextran. Fluid Phase Equilib. 2000, 171, 77. (13) Austgen, D. M.; Rochelle, G. T.; Chen, C. 4. Model of VaporLiquid Equilibria for Aqueous Acid Gas-Alkanolamine Systems. 2. Representation of H2S and CO2 Solubility in Aqueous MDEA and CO2 Solubility in Aqueous Mixtures of MDEA with MEA or DEA. Ind. Eng. Chem. Res. 1991, 30, 543. (14) Dehghani Tafti, M. Solubility of Acid Gases (CO2 & H2S) in Aqueous Solution of Alkanolamine. Master Thesis, Tarbiat Modarres Un, Iran, 2005. (15) Pitzer, K. S.; Simonson, J. M. Thermodynamics of Multicomponent, Miscible, Ionic Systems: Theory and Equations. J. Phys. Chem. 1986, 90, 3005. (16) Pitzer, K. S. Thermodynamics of Electrolytes. I. Theoretical Basis and General Equations. J. Phys. Chem. 1973, 77 (2), 268. (17) Pitzer, K. S.; Li, Y. G. Thermodynamics of Aqueous Sodium Chloride to 823 K and 1 kilobar. Proc. Natl. Acad. Sci. U.S.A. 1983, 80, 7689. (18) Raatschen, W.; Harvey, A. H.; Prausnitz, J. M. Equation of State for Solutions of Electrolytes in Mixed Solvents. Fluid Phase Equilib. 1987, 38, 19. (19) Qian, W.-M.; Li, Y.-G.; Mather, A. E. Correlation and Prediction of the Solubility of CO2 and H2S in an Aqueous Solution of Methyldiethanolamine and Sulfolane. Ind. Eng. Chem. Res. 1995, 34, 2545. (20) Jou, F.-Y.; Otto, F. D.; Mather, A. E. Vapor-Liquid Equilibrium of Carbon Dioxide in Aqueous Mixtures of Monoethanolamine and Methyldiethanolamine. Ind. Eng. Chem. Res. 1994, 33, 2002. (21) Jou, F. Y.; Mather, A. E.; Otto, F. D. Solubility of H2S and CO2 in Aqueous Methyldiethanolamine Solutions. Ind. Eng. Chem., Process Des. DeV. 1982, 21, 539. (22) Lee, J. I.; Otto, F. D.; Mather, E. Equilibrium in Hydrogen SulfideMonoethanolamine-Water System. J. Chem. Eng. Data 1976, 21, 2, 207. (23) Jou, F.-Y.; Mather, A. E.; Otto, F. D. The Solubility of CO2 in a 30 wt% Monoethanolamine Solution, Can. J. Chem. Eng. 1995, 73, 140. (24) Li, Y. G.; Mather, A. E. Correlation and Prediction of the Solubility of the H2S and CO2 Carbon Dioxide in Aqueous Solution of Methyldiethanolamine. Ind. Eng. Chem. Res 1997, 36, 2760. (25) Marcus, Y. Ion Properties; Marcel Dekker Inc.: New York, 1997.
ReceiVed for reView February 19, 2007 ReVised manuscript receiVed May 24, 2007 Accepted June 8, 2007 IE070259R
