Ind. Eng. Chem. Res. 1999, 38, 3473-3480
3473
Representation of CO2 and H2S Absorption by Aqueous Solutions of Diethanolamine Using an Electrolyte Equation of State Ge´ raldine Valle´ e,† Pascal Mougin,‡ Sophie Jullian,‡ and Walter Fu 1 rst*,† Laboratoire Re´ acteurs et Processus, ENSMP-ENSTA, 32 Bd. Victor, 75739 Paris Cedex 15, France, and IFP, 1-4 Av de Bois-Pre´ au, 92506 Rueil Malmaison, France
The electrolyte equation of state published in 1993 by Fu¨rst and Renon (AIChE J. 1993, 39, 335) has been applied to the representation of CO2 and H2S solubility in diethaloamine (DEA) aqueous solutions. This equation of state extends the classical Redlich-Kwong-Soave equation of state associated with a Wong-Sandler mixing rule to the case of systems containing ions. The study of binary systems allowed us to determine the parameters of the nonelectrolyte part of the equation of state. The ionic parameters have been fitted from experimental solubility data covering a wide range of experimental conditions (temperature range, 25-100 °C; amine concentration, from 0.5 to 3.5 M; loadings up to 2.34 molCO2/molamine). With the assumption used in previous applications of our model to various electrolyte systems, the adjusted ionic parameters are interaction ones involving protonated amine and anions as well as molecular compounds. The resulting model represents experimental data with deviations consistent with the experimental ones and close to the deviations obtained in previous studies. 1. Introduction
three contributions:
The amine equilibria representation has been extensively studied during the 2 recent past decades. It may be related to the large number of industrial operation units using various amines solutions for the absorption of acid gases. On one hand, great part of the published papers were devoted to solubility determinations. On the other hand, few papers were devoted to the presentation of models for the representation of solubility data. Furthermore, most of them, including the most recent ones, were based on γ-φ approaches,2-8 although equations of state seem to be more adapted to the representation of the solubilities of gases. Up to now only few electrolyte equations of state have been applied to the representation of acid gases solubilities in alkanolamine solutions.9,10 The aim of this paper is to represent CO2 and H2S absorption in DEA (diethanolamine) aqueous solutions using our electrolyte equation of state. This equation was initially applied to strong aqueous electrolyte solutions1 and then applied to the nonaqueous electrolyte systems11 and to mixed solvent systems.12 After a short introduction of the main features of our model, the consistence of the available experimental data will be discussed. The determination of the adjustable parameters will then be detailed and the representation results discussed. 2. Equations of the Electrolyte Equation of State The model used in the present study is an electrolyte equation of state (EOS) and has already been described in a previous paper;1 hence, we are only giving hereafter the basic equations of the model. They are derived from a development of the Helmholtz energy which contains * To whom correspondence should be addressed. E-mail:
[email protected]. Phone: (33) 145524417. Fax: (33) 145525587. † ENSMP-ENSTA. ‡ IFP.
a - ast ∆a ∆a ∆a ∆a ) ) + + RT RT RT NE RT LR RT SR
( ) ( )
( )
( )
(1)
2.1. Nonelectrolyte Part of the Equation of State. The model may be considered an extension of a nonelectrolyte equation of state to the representation of solutions containing ions. Hence, the first term (NE) of eq 1 is similar to the expression of the Helmholtz energy associated with a nonelectrolyte cubic equation of state, the Redlich-Kwong-Soave EOS in our case:
() ∆a
RT
NE
)
∑k
xk ln
(
xkRT
)
Pst(ν - b)
aSR
+
RTb
ln
( ) ν
ν+b
(2)
In the following, as in eq 2, indices k or l mean that the summation is over all species. In contrast, i and j will be assigned to the ionic species, the summation over molecular species being expressed by the use of m or n indices. In this expression, the ionic effect is limited to the dilution effect and to the use of an ionic contribution in addition to the molecular contribution bm to the covolume:
b ) bm +
∑i xibi
(3)
Equation 3 introduces ionic covolumes bi which are adjustable parameters. The other adjustable parameters involved in eq 2 are dependent on the nonelectrolyte mixing rule chosen. In the studied systems, molecular species with low polarity, like CO2 and H2S, are dissolved in a polar solvent. Hence, an efficient mixing rule is needed and we choose to use the Wong-Sandler mixing rule13 because of the large successful applications of this formalism. Thus, the attractive term aSR and the nonelectrolytic part of covolume bm are calculated by the following expressions:
10.1021/ie980777p CCC: $18.00 © 1999 American Chemical Society Published on Web 07/22/1999
3474 Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999
bm )
(
∑ ∑xmxn m n 1-
bm + bn
[∑ (∑ m
aSR RT
) bm
k
)
xaman(1 - kmn)
-
2
RT am
gE
]
(4)
xm bmRT ln 2RT ak
gE
)
xk bkRT ln 2RT
)
RT
[ ]
xm ∑ m
∑n xnτnmGnm
σi ) (5)
(6)
∑n xnGnm
with Gnm ) exp(-Rnmτnm) and R˙nm ) Rmn. 2.2. Ionic Part of the Equation of State. The second term on the right-hand side of eq 1 is the longrange (LR) interaction contribution and is based on the nonprimitive Mean Spherical Approximation (MSA) approach,15
( ) ∆a
RT
LR
)-
RLR2 4π
xiZi2Γ
∑i 1 + Γσ
+
Γ3ν 3πN
i
(7)
where the shielding parameter Γ is given by
( )
xi
∑i ν
4Γ2 ) RLR2
Zi
2
1 + Γσi
(8)
and
RLR2
e2N ) 0DRT
(9)
The dielectric constant of the solution takes into account the influence of the ions through Pottel’s expression,
( ) 1 - ξ′′3 ξ′′3 1+ 2
D ) 1 + (Ds - 1)
(10)
where Ds is the solvent dielectric constant and is deduced from the various molecular contribution Dm by
Ds )
xmDm ∑ m xm ∑ m
6bi Nπ
(12)
The last term in eq 1 expresses the short-range interactions involving ionic species,
( ) ∆a
)
RT
xkxlWkl
∑k ∑l ν(1 - ξ )
(13)
3
where at least one of species k and l is an ion. In this equation, ξ3 is expressed as in eq 11 but the summation is, in this case, over both ionic and molecular species. In eq 13, another type of adjustable parameter appears which is a symmetrical interaction parameter Wij. Hence, the model contains two types of ionic adjustable parameters which are anionic (ba) and cationic (bc) covolumes and symmetrical interaction parameters between a cation and a solvent (Wcs) and between a cation and an anion (Wac). The other interaction parameters are considered negligible because of charge repulsion effects (Wcc′ and Waa′) and because we supposed that solvation interactions involving anions (WaS) are low compared to the solvation of cations. Fu¨rst and Renon1 have shown that all the ionic parameters could be, for strong simple electrolyte systems, related to experimental properties characterizing solvation: Stokes diameters σSc for cations and Pauling diameters σPa for anions. These relations involve six correlation parameters, λ1λ6:
bc ) λ1(σSc )3 + λ2
(14)
ba ) λ1(σPa )3 + λ2
(15)
Wcs ) λ3σSc + λ4
(16)
Wac ) λ5(σSc + σPa )4 + λ6
(17)
The main changes, if compared to the model previously published,1 concern the use of the Wong-Sandler mixing rule (obviously no mixing rule is needed in the case of strong electrolyte systems in one solvent) and the drop of volume translation parameters. The actual values being λ1 ) 0.0982, λ2 ) 7.003, λ3 ) 77.22, λ4 ) -25.314, λ5 ) -0.05813, and λ6 ) -44.383, using the set of data published in 1993. The deviation is very close to the previous one (2.8% instead of 2.86%). It must be noticed that in the correlations (14)-(17) the diameters are expressed in 10-10 m and the b and W parameters in SI units (m3/mol). 3. Database Analysis
In eq 10, ξ3′′ is defined by
ξ′′3 )
x 3
where the pure component ai parameter is calculated using Schwartzentruber’s expression.14 The excess Gibbs energy was evaluated from the nonrandom two-liquid (NRTL) model:
gE
well as ionic species. In both cases, to reduce the number of adjusted values, these parameters are estimated. The diameters of molecular compounds are deduced from literature values or are estimated. In the case of ionic diameters, we have assumed that they could be deduced from the ionic covolumes by
Nπ
xiσi3
6
ν
∑i
(11)
In the LR expression, a pure component parameter σk is involved which is a diameter relative to molecular as
The first step of the study, before the determination of the adjustable parameter values, is to obtain a database with consistent values of experimental acid gases solubilities. This is especially important in the case of acid gases absorption because a lot of data have been published by various authors. In 1993, Weiland
Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999 3475 Table 1. Experimental Data Used in the Present Study DEA concns (mol/L or wt %)
pressure range (kPa)
acid gases loadings
point no.
25-100 40-100 25 38-108
DEA-H2O-CO2 0.5, 2, 3.5 M 2M 0.5, 2 M 25 wt %
0.68-6890 0.0098-1.125 6.82-2011.6 2-4370
0.035-2.34 0.042-0.3669 0.6-2 0.035-2.34
101 8 20 30
25-100 40, 100 38-108
DEA-H2O-H2S 2, 3.5 M 0.7-2109 2M 0.007-3.2 25 wt % 0.001-3706
refs
T (°C)
Lee et al.17 Lal et al.20 Bhairi21 Lawson and Garst38 Lee et al.18,19 Lal et al.20 Lawson and Garst38
et al.16 have published an analysis of CO2 and H2S solubility data in aqueous solutions of various amines. It appears to be very difficult to disregard any data set. In many cases, only few pieces of data of each data set are obviously inconsistent with the whole collection of available values. Our aim was to test our electrolyte equation of state on the acid gases solubilities, so we have selected data sets covering a large range of experimental conditions. Among the data published, the values given by Lee17-19 cover a large range of experimental conditions. However, studying the internal consistency of these data, we have noticed strange behaviors in the case of H2S solubilities: the H2S partial pressure variation as a function of the loading, at a DEA concentration of 0.5 M, is crossing the curve relative to 2 M DEA concentration. So, the values corresponding to DEA ) 0.5 M have been ignored. Some of the values published by Lee et al.17-19 are in fact extrapolated values. To evaluate the quality of these extrapolations, we have compared these solubilities with the experimental values of Lal et al.20 It appears that the measurements of Lal et al. show significant discrepancies with the series of Lee et al.17-19 at the same experimental conditions. We have also taken away a few extrapolated values from Lee et al. to make the series of these two different authors consistent. Table 1 summarizes the data used in our data treatment. They also include, besides the values of Lee et al. and those of Lal et al., the values published by Bhairi21 which also cover a large range of temperatures and acid gases loadings. 4. Application of the Electrolyte Equation of State to the Solubility Equilibria 4.1. Determination of the Nonionic Parameters. 4.1.1. Pure Component Parameters. The pure component parameters involved in the nonelectrolyte part of the equation of state are deduced from the critical properties of the various compounds. Among the molecular species considered in this study, the only unusual one is diethanolamine (DEA). Its critical characteristics (Tc ) 715 K and Pc ) 32.7 bar) and the value of the acentric factor (ω ) 0.1) are taken from the work of Daubert and Danner.22 The expression of the attractive parameters is taken from Schwartzentruber and Renon14 and involves three polar parameters which were obtained by fitting vapor pressure data of pure components over a large temperature range. The fitted parameters are given in Table 2. Although the main contribution of the dielectric constant of the solution is due to water, we have taken into account other molecular contributions through a
0.064-1.54 0.007-0.21 0.03-1.58
94 13 88
Table 2. Polarity Parameters for Pure Molecular Component component H2O DEA CO2 H2S
p1
p2
p3
temp. range (°C) refs
0.07598 -1.3555 0 0.09862 0 -1.663 0.04136 -1.3158 0 0.01857 0 -2.078
0-300 28 to 269 -56 to 31 -60.4 to 75
23 1 23 23
simple linear mixing rule, the molecular contributions themselves being temperature-dependent:
Dm )
D(0) m
D(1) m (3) 2 (4) 3 + (18) + D(2) m T + Dm T + Dm T T
The values of the Dm parameters used during this work are given in Table 3. As we have no data concerning H2S, a low value has been used in this case because it is a molecule with low polarity. The last pure component parameters involved in our equations are the diameters appearing in the SR term. As said above, these parameters are estimated from the molecule structure (DEA) or taken from previous studies, as in the case of the water molecule15 or identified to literature values as for H2S and CO2 (Lennard-Jones diameters). The corresponding values are reported in Table 4. 4.1.2. Determination of Interaction Parameters from the Study of Binary Systems. Because we have used a Wong-Sandler mixing rule with a NRTL expression for the excess Gibbs energy, we have to introduce three interaction parameters (kij, τij, and τji) per binary system. The nonrandom parameter Rij was fixed at 0.2 for all the binary interactions to reduce the number of adjustable parameters. To cover a large temperature range, we have introduced the following temperature dependence for the kij and τij parameters: (1) kmn ) k(0) mn + kmnT +
τmn ) τ(0) mn +
τ(1) mn T
k(2) mn T
(19)
(20)
The coefficients of these correlations were determined from the regression of vapor-liquid equilibrium (VLE) data of the various binary systems. H2O-CO2 interactions parameters have been deduced from a data treatment of the partial pressure data from Houghton27 which are available in the 25-100 °C temperature range. The experimental CO2 partial pressure data are represented within 3%. In the same way, we have determined the interaction parameters relative to the binary H2O-H2S by fitting experimental VLE data28,29 in a large range of pressure (from 43 to 1300
3476 Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999 Table 3. Temperature Dependence of the Dielectric Constant for Pure Component D(0)
component
D(1)
-19.29 -5.95 0.50 2
H2O DEA CO2 H2S
D(2)
D(3) 10-2
-1.96 × -6.21 × 10-6 1.37 × 10-3 0
29814.5 9276.38 34.97 0
Table 4. Pure Molecular Components Diameters component
H2O
DEA
H2S
CO2
σ (Å)
2.52
4.5
3.62
3.94
Table 5. Binary Interaction Parameter k H2O-CO2 H2O-H2S H2O-DEA
k(0)
k(1)
k(2)
temp. range (°C)
17.044 -0.7072 -12.18
-0.0406 0.00304 0.01379
-956.21 -172.92 2435.59
0-100 15-105 25-160
Table 6. Binary NRTL Parameter τ H2O-CO2 CO2-H2O H2O-H2S H2S-H2O H2O-DEA DEA-H2O
τ(0)
τ(1)
25.243 92.467 1.927 -7.522 19.158 1.6106
-7735.6 -23751.1 89 3536.07 -4646.1 -853.33
kPa) and temperature (10-167 °C). The fitted values of these are listed in Tables 5 and 6. The root-meansquare deviation obtained is 3.4%. Vapor pressure data relative to the H2O-DEA system have been published by Kennard and Meisen.30 Other experimental values have been used by some authors,2,3 but we have no access to these data. However, it is possible to calculate the pseudodata using Austgen’s expressions and parameters.2,3 It appears that there is a large discrepancy between these pseudodata and Kennard and Meisen’s values.30 The values issued from the calculations are consistent with a quite ideal behavior, as in the case of other water-amine systems, so we have decided to fit the pseudodata obtained using Augsten’s expressions.2,3 The same approach was previously used by other authors6 in the case of other amines. As far as we know, no data concerning the DEA-H2S or DEA-CO2 systems are available. So, the corresponding parameters must be fitted from ternary data. 4.2. Application of the Electrolyte EOS to the Absorption of Acid Gas in Aqueous DEA Solutions. 4.2.1. Results of the Data Treatment. We are dealing with a chemical absorption. We have to take into account various chemical equilibria. These equilibria are acid-base ones and also, because we are considering a secondary amine, carbamate formation equilibria. All the chemical reactions considered are presented in Table 7. The associated chemical constants, defined in the mole fraction scale with a reference state corresponding to infinite dilution in water, are also given in Table 7 through the parameters defining the temperature dependence of the chemical equilibria:
ln K ) K(0) + K(1)/T + K(2) ln T + K(3)T
(21)
All the chemical constants have been taken from the literature, except for the carbamate formation. In this case the given value is deduced from a global data treatment which is obviously strongly connected to the choice of the activity coefficient model. Hence, for consistency purposes, this constant has been adjusted
1.32 × 0 0 0
10-4
D(4) -0.31 × 0 0 0
10-6
temp. range (°C)
refs
0-100 0-90 25-350
24 25 26
by regression of the experimental data relative to the DEA-H2O-CO2 system. Our electrolyte equation of state involves three types of ionic parameters: the ionic covolume, the interaction parameters between ions and molecules, and those between two different ions. To reduce the number of fitted parameters, we adopted the following assumptions: (1) The covolumes of ionic species (see Table 8) are calculated using correlations (14) and (15), the solvated diameters being the ones used in a preceding study.9 These diameters are estimated in the case of species containing amines, starting from the DEA diameter reported in Table 4. For other species, we used literature values, the sources being specified in Table 4. However, it has to be pointed out that, in the modeling, the diameter values are sensitive only if they are associated with sufficiently concentrated ions, which is the case for HCO3-, HS-, DEAH+, and the carbamate anion. (2) As in previous papers devoted to the application of this electrolyte equation of state, we did not take into account anion-molecule interaction parameters. (3) Moreover, the influence of CO32- and S2- species being small, because they have low concentrations, the DEAH+-CO32- and DEAH+-S2- interaction parameters have been disregarded. In the application of our equation to the representation of strong electrolyte systems, we have correlated the various parameters applying relations (14)-(17). In the present case, the problem is different because the experimental value of the solvation diameter of the cationic species (protonated amine) is not available and has to be determined in relation to the data representation. Furthermore, because we intend to represent data over a large temperature range, a temperature dependence of the W interaction parameters has to be taken into account, which is not the case of the covolumes. Hence, for the W parameters, the correlations will give sensitive parameters only over a part of the temperature range taken into account. This explains that we have restricted the use of the correlations to the covolumes. Consequently, in addition to the equilibrium constant of carbamate formation and the acid gas-DEA parameter of the Wong-Sandler mixing rule, seven interaction parameters (DEAH+-H2O, DEAH+-DEA, DEAH+CO2, DEAH+-H2S, DEAH+-HCO3-, DEAH+-DEACOO-, and DEAH+-HS-) have to be determined from the data treatment of ternary systems. Furthermore, because we are considering solubility data over a large temperature range, a temperature dependence of the interaction parameters has to be included in the model: (1) Wkl ) W(0) kl + Wkl
1 (T1 - 298.15 ) + W (298.15T - T + T (22) ln 298.15) (2) kl
We regressed simultaneously the solubility data of H2S and CO2 in DEA aqueous solutions because some adjustable parameters are involved in both systems. However, it has to be pointed out that defining the
Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999 3477 Table 7. Temperature Dependence of Equilibrium Constants K(0)
K(1)
K(2)
K(3)
source
2H2O ) + CO2 + 2H2O ) HCO3- + H3O+ HCO3- + H2O ) CO32- + H3O+ H2S + H2O ) HS- + H3O+ HS- + H2O ) S2- + H3O+ DEAH+ + H2O ) DEA + H3O+ DEACOO- + H2O ) DEA + HCO3-
132.899 231.465 216.049 214.582 -32 -51.021 11.1743
-13445.9 -12095.1 -12431.7 -12995.4 -3338.0 -3302.998 -5117.42
-22.4773 -36.7816 -35.4819 -33.5471 0 6.7927 -0.03023
0 0 0 0 0 -0.00357 6.666e-4
31 32 32 32 32 a b
From a fitting of experimental values.33-35
b
reaction H3O+
a
OH-
Adjusted in this study using VLE data relative to the CO2-DEA-water system.
Table 8. Estimated Ionic Diameters and Corresponding Calculated Covolumes ionic species
solvated diameter (10-10 m)
source
calculated covolume (m3/K‚mol)
DEAH+ HCO3CO32HSS2carbamate H3O+ OH-
4.4 3.12 3.7 3.6 3.5 6 4.06 3.52
a 36 36 36 36 a 1 36
0.0157 0.00981 0.01198 0.01155 0.01115 0.02965 0.0137 0.01123
a
Estimated from the molecule structure.
Table 9. Adjusted Values of the kij Parameters Involved in the Wong-Sandler Mixing Rule k(0) DEA-CO2 DEA-H2S
6.71665 2.7715
k(1)
Figure 1. Solubility of CO2 in a 2 M DEA aqueous solution at 25, 50, 75, and 100 °C.
k(2) 10-3
0.0159 × 0.01834 × 10-3
0.0634 × 10-3 0.0585 × 10-3
Table 10. Adjusted Values of the NRTL τij Parameters DEA-CO2 CO2-DEA DEA-H2S H2S-DEA
τ(0)
τ(1)
-0.965 -0.661 -1.0067 -0.5005
1317.63 -718.08 1282.48 -666.416
Table 11. Adjusted Wkl Interaction Parameters interaction
W(0)
W(1)
W(2)
DEAH+-water DEAH+-DEA DEAH+-CO2 DEAH+-H2S DEAH+-HCO3DEAH+-DEACOODEAH+-HS-
0.0859 0.08363 -0.09446 -0.2059 -0.0746 -0.2469 -0.2061
-36.854 580.423 38.388 -352.632 20.752 24.943 289.041
-2.646 -23.579 -4.938 -12.882 -6.368 -2.202 2.618
objective function in the case of acid gas solubility in amine solutions is a real problem because the experimental pressure range extends from few Pa to several bar. Furthermore, no experimental deviations are given in the various experimental papers, and inconsistency problems suggest high data uncertainties, at least for some of the data sets. To avoid giving a very large weight to low pressures or, on the contrary, to highpressure data, we used relative deviation except for lowpressure data where absolute deviations are used.The parameters obtained are presented with their temperature dependence in Tables 9-11. The results of the CO2 and H2S solubility representation are illustrated in Figures 1-4. The average relative deviations associated with CO2 partial pressures is 20.6%, while this value is less than 15% for the partial pressure of H2S. These relative deviations may appear high, but it is of the same order of magnitude as the deviations obtained by other authors in the representation of gases solubilities in amine aqueous solutions. For example, Li and Mather8 obtained a deviation varying from 15.2% to 51% in the case of the representation of
Figure 2. Solubility of CO2 in a 3.5 M DEA aqueous solution at 25, 50, 75, and 100 °C.
Figure 3. Solubility of H2S in 2 M DEA aqueous solution at 25, 50, 75, and 100 °C.
equilibrium partial pressure of CO2 and H2S over Methyl Diethanolamine (MDEA) aqueous solutions, using a modified Clegg-Pitzer36 model. The reason for some high deviations may be related to some “residual” discrepancies between the various data considered. For instance, in Figure 2, we can notice that large deviations
3478 Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999
Figure 6. Prediction of the solubility of CO2 in 2.45 M DEA aqueous solutions (Lawson and Garst values) at 310-366 K. Figure 4. Solubility of H2S in a 3.5 M DEA aqueous solution at 25, 50, 75, and 100 °C.
Figure 5. Prediction of the solubility of H2S in 2.45 M DEA aqueous solutions (Lawson and Garst values) at 310-366 K.
correspond to low loadings of CO2, and this may be related to the fact that the data regressed in this range of loading were not real experimental values but obtained by extrapolation of experimental data. 4.2.2. Representation of Other Data Sets Relative to the CO2 and H2S Solubilities in DEA Aqueous Solutions. As the parameters of our model have been determined using a limited number of experimental solubility sets, we have applied, without any change, our equation to the representation of other data sets to ensure that our data choice has no drastic influence on the validity of our representation. The above fitted interaction parameters were used to predict Lawson and Garst38 solubility data of ternary systems which were not included in our regressed database. The results of CO2 and H2S partial pressure representation by our equation of state, associated with the mean relative deviations of 14.4 and 20.6%, respectively, are illustrated in Figures 5 and 6. We can see in Figure 6 that the partial pressure of CO2 calculated by our model in 25 wt % DEA aqueous solution is in good agreement with the experimental data of Lawson and Garst.38 However, the experimental solubility of H2S in the same system is poorly represented, especially in the middle range of acid gas loading. Our model was used to predict the solubility of acid gas mixtures in DEA aqueous solutions without introducing a new parameter or fitting, again, the above adjusted parameters. The VLE data for DEA-CO2H2S-H2O we used are listed in Table 12.
Figure 7. Comparison of predicted and measured CO2 partial pressure for acid gas mixtures over 2 and 2.45 M DEA aqueous solutions at different temperatures.
Figure 8. Comparison of predicted and measured H2S partial pressure for acid gas mixtures over 2 and 2.45 M DEA aqueous solutions at different temperatures.
The prediction results are shown in Figures 7 and 8. The quality of the prediction depends on the data series we have considered. As shown in Figure 8, the H2S partial pressure data of Lee et al.39 are predicted with an average relative deviation equal to about 23%, while the discrepancy between experimental and calculated CO2 partial pressures of this set of data are larger. In contrast, the prediction results for CO2 in 25 wt % DEA from Lal et al.20 are represented with a relative average deviation equal to 35% while the H2S partial pressures calculated by our model are systematically much larger than the experimental values. The CO2 and H2S solubility data
Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999 3479 Table 12. Source of Data for the Quaternary DEA-CO2-H2S-H2O System refs Lawson and Lee et al.39 Lal et al.20
Garst38
T (K)
concn DEA
PH2S (kPa)
PCO2 (kPa)
H2S loading
CO2 loading
310-366 323 313.15-373.15
25 wt % 2M 2M
0.01-1486 0.886-1505 0.06-5.73
2.2-2900 0.22-5764 0.05-6.47
0.042-1 0.1-1 0.018-0.25
0.11-0.9 0.1-1.22 0.08-0.22
Table 13. Carbamate Decomposition Constant at Various Temperatures: Comparison of Our Values (Converted in the Molarity Scale) and Those of Literature authors Austgen2,3 Planche and Fu¨rst9 this work
25 °C
40 °C
100 °C
0.491 0.167 0.141
0.748 0.3918 0.54125
3.142 2.5762 4.6
from Lal et al. are both poorly predicted by our model. This is certainly due to the fact that these data are obtained at very low acid gas loadings and our regressed database contains just a few pieces of data. 5. Conclusion The aim of this work has been to apply an electrolyte equation of state previously tested only on strong aqueous or nonaqueous electrolyte solutions to the representation of CO2 and H2S acid gases solubility in DEA aqueous solutions. After an analysis of published data to obtain a consistent database, we have represented the CO2 and H2S solubility in aqueous solutions of DEA, adjusting only seven ionic parameters (and their temperature dependence) over a large range of experimental conditions. A precise comparison of the deviations obtained by the various authors in regard to the number of adjusted parameters is not easy because the experimental conditions and data sets considered in the various studies differ from each other. However, it may be said that the quality of our representation is very similar to what has been obtained by other authors with about the same number of adjustable parameters. Another possible comparison concern the parameters obtained. Obviously, because the models are very different, the only significant comparison concerns the chemical constant associated with the carbamate formation. From Table 13, it may be seen that, although our value has a more pronounced temperature dependence, it is consistent with other adjusted values. However, it must be pointed out that our approach significantly differs from previous ones because we used an equation of state instead of an excess Gibbs energy model. This method is especially interesting because it could easily be extended to the calculation of the solubility of other gases and could therefore be a useful tool for column design and optimization. Modelings could also be useful as a guide for the analysis of data consistency because, being self-consistent, they are often more efficient than simple methods (graphical analysis, for instance). Furthermore, they may be applied, whatever the experimental conditions are (temperature, amine concentration, and gas loadings) considered in the various data sets. This explains that Weiland et al.16 applied the Deshmukh-Mather model to a screening of the acid gas solubility data. Hence, it could be interesting to compare our results to the conclusions given by Weiland et al., especially in the case of low loadings where the data uncertainty is maximum. In the case of CO2 solubility, the equilibrium pressure at low loadings is well-represented by our expression in the case of Lal et al.20 and Lawson and Garst38 data sets. This is consistent with Weiland et al. results.
However, in the case of Lee’s data,17 we have observed systematic deviations when the loading is less than about 0.2. In this case, the comparison with Weiland et al.’s results is impossible because, if this data set is mentioned in the reference section, it is not included in the data fitting. For H2S data, we have a good representation of all equilibrium pressures at low loadings. The comparison of our results with Weiland et al.’s in the case of a mixed gas system is not really pertinent because, in the present work, we have considered CO2 and H2S solubility data and then extended it to acid gas mixtures instead of making a data fitting using all the data, as in Weiland et al.’s work: this could explain the difference observed in the representation of CO2 solubility. With our approach, a good representation of H2S solubility in mixed gas systems is obtained (Figure 8). On the contrary, the calculated CO2 pressures (Figure 7) in mixed gas systems is lower than the experimental ones, especially in the case of Lee et al.39 data. This suggests some consistency problems for the CO2 solubility in a ternary (CO2-DEA-water) system and when mixed gases are considered. Acknowledgment The authors are grateful to the IFP for financial support. Nomenclature a ) Helmholtz energy aSR ) attractive parameter b ) covolume D ) dielectric constant Ds ) solvent dielectric constant e ) protonic charge G ) NRTL parameter ge ) excess Gibbs energy K ) chemical constant N ) Avogadro’s number p ) polarity parameters P ) pressure R ) gas constant T ) absolute temperature v ) molar volume x ) mole fraction W ) interaction parameter defined in eq 13 Greek Symbols R ) NRTL nonrandom parameter RLR ) defined in eq 9 0 ) permittivity of free space λ ) correlation parameters σ ) diameter τ ) NRTL interaction parameters ξ ) defined in eq 11 Subscripts a ) relative to anion c ) relative to cation i, j ) relative to ionic species k, l ) relative to all species m, n ) relative to molecular species LR ) long-range term
3480 Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999 NE ) nonelectrolyte term SR ) solvation term Superscripts (0), (1), (2), (3), (4) ) temperature-dependence parameters S ) Stockes diameter P ) Pauling diameter st ) standard state
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Received for review December 11, 1998 Revised manuscript received May 6, 1999 Accepted May 20, 1999 IE980777P
