I n d . E n g . C h e m . Res. 1989, 28, 1060-1073
1060
Model of Vapor-Liquid Equilibria for Aqueous Acid Gas-Alkanolamine Systems Using the Electrolyte-NRTL Equation? David M. Austgen and Gary T. Rochelle* Department of Chemical Engineering, T h e University of Texas at Austin, Austin, Texas 78712
Xiao Peng SINOPEC Beijing Design Institute, P.O. Box 949, Beijing, People's Republic of China
Chau-Chyun Chen Aspen Technology, Inc., 251 Vassar Street, Cambridge, Massachusetts 02139
A thermodynamically consistent model was developed for representing vapor-liquid equilibria in the acid gas (H2S,COJ-alkanolamine-water system. The model accounts for chemical equilibria in a rigorous manner. Activity coefficients are represented, with the Electrolyte-NRTL equation treating both long-range ion-ion interactions and local interactions between all true liquid-phase species. Both water and alkanolamine are treated as solvents. Adjustable parameters of the Electrolyte-NRTL equation, representing short-range binary interactions, were fitted on binary and ternary system VLE data. Calculated H2S and C 0 2 equilibria are in good agreement with most of the reported experimental data for aqueous solutions of a single acid gas in monoethanolamine (MEA) and diethanolamine (DEA) in the temperature range 25-120 "C. Without fitting additional parameters, representation of experimental equilibria for mixtures of H2Sand C 0 2 in aqueous solutions of MEA or DEA is good. Aqueous solutions of alkanolamines are widely used in absorption/stripping operations to remove acid gases, primarily hydrogen sulfide (H,S) and carbon dioxide (CO,), from a variety of source gases. H2S and COz are present in natural gas, synthesis gas, flue gas, and various refinery streams, and C02 is a byproduct of ammonia and hydrogen manufacture. The process is characterized as mass transfer enhanced by chemical reaction; the acid gases either react directly or react through an acid-base buffer mechanism with the alkanolamines to form nonvolatile ionic species. The presence of an alkanolamine, therefore, enhances the solubility of an acid gas in the aqueous phase at a constant value of the equilibrium partial pressure. Design of gas-treating operations requires knowledge of the vapor-liquid equilibria (VLE) of the aqueous acid gas-alkanolamine system. A large body of experimental vapor-liquid equilibria data for aqueous acid gas-alkanolamine systems has been reported in the literature. The data are generally limited to high acid gas loadings; little VLE data are reported in the low acid gas pressure range where it is perhaps most important. Representation of these experimental data is needed so that the design engineer can confidently and systematically interpolate and extrapolate the available data. Unfortunately, process simulation and design of gas-treating operations has been hindered by the lack of a correlation for accurately representing thermodynamic properties of concentrated aqueous electrolyte solutions. Design calculations are, therefore, often based upon empirical methods. Recent research has led to several semiempirical excess Gibbs energy models or activity coefficient models for aqueous electrolyte systems valid to ionic strengths representative of those found in industrial applications. Among them are the models of Pitzer (1973), Meissner and Tester (1972), Bromley (1973), Cruz and Renon (1978), Ball et al. (1985), Chen et al. (1982), Chen and Evans (1986),and Christensen et al. (1983). Sander et al. (1986) developed an excess Gibbs energy model to represent the salt effect on the VLE of mixed solvent systems. Mock +Presented a t the AIChE Spring National Meeting, New Orleans, LA, March 8, 1988.
et al. (1986) extended Chen's model to represent the salt effect on mixed solvent VLE. Chen and co-workers (Scauflaire et al., 1989) completed this extension to represent activity coefficients of both ionic and molecular species in mixed solvent systems. The objective of this work was to develop a VLE model that represents, within experimental accuracy, the H2Sand C02 equilibrium partial pressures reported in the literature for aqueous solutions of monoethanolamine (MEA) and diethanolamine (DEA) over the temperature range 25-120 "C and the amine concentration range 0.5-5 kmol m-3. The solution is treated as a mixed solvent system-water-alkanolamine. The model rigorously accounts for solution chemistry, allowing determination of all liquid-phase species, ionic and molecular. This is particularly important for kinetic studies and for design and simulation based on rates of mass transfer rather than equilibrium. Representation of activity coefficients is achieved with the Electrolyte-NRTL equation (Scauflaire et al., 1989) by treating ionic/molecular physical interactions. Adjustable parameters of the model, binary energy interaction parameters, were fitted on experimental binary and ternary system VLE data. Previous Models Because of the difficulty in representing activity coefficients in concentrated electrolyte solutions, early VLE models for weak electrolyte models adopted empirical approaches that did not account for physical interactions. Van Krevelen et al. (1949) proposed a method for representing H2S, COz, and NH3 equilibrium partial pressures over aqueous solutions. In equations governing chemical equilibria, they used "apparent" equilibrium constants related to component concentrations rather than activities. In effect, they set, activity coefficients of all species to unity. Apparent equilibrium constants were fitted on experimental data to functions of ionic strength. Dankwerts and McNeil (1967) used this method to calculate vapor- and liquid-phase compositions in amine-C02-H20 systems. Kent and Eisenberg (1976) used a similar approach to represent H2Sand COPequilibrium partial pressures over aqueous solutions of MEA and DEA. They also employed
0888-5885/89/2628-1060$01.50/0 [E 1989 American Chemical Society
Ind. Eng. Chem. Res., Vol. 28, No. 7, 1989 1061 apparent equilibrium constants in the equations of chemical equilibria. They used the thermodynamic or infinite dilution values (related to component activities), reported in the literature, as apparent equilibrium constants for all reactions in the system except amine protonation and carbamate reversion. For these reactions, equilibrium constants were fitted to published equilibrium partial pressure data for the ternary systems amine-H2S-H20 and amine-C02-H20 as functions of temperature. Atwood et al. (1957) proposed a method for calculating equilibrium partial pressures of H2S over aqueous alkanolamine solutions using a “mean ionic” activity coefficient. They employed rigorous chemical equilibria equations relating equilibrium constants to component activities. However, they assumed the activity coefficients of all ionic species to be equal. This single “mean ionic” activity coefficient was correlated with ionic strength. This method is essentially equivalent to the apparent equilibrium constant approach of Van Krevelen et al. (1949). Instead of lumping the effects of solution nonideality directly into equilibrium constants, they separated nonideality into an empirical parameter which was used to adjust the equilibrium constant for the affect of ionic strength. While the use of apparent equilibrium constants allows fair representation of experimental acid gas partial pressures, it has two significant drawbacks. First, the method cannot be confidently extended to solution compositions outside the range over which equilibrium constants are adjusted. Second, speciation to determine true compositions of all liquid-phase species, ionic and molecular, requires accurate representation of activity coefficients for use in equations of chemical equilibria. Speciation using apparent equilibria equations should be considered only an approximation to the true liquid-phase composition. The capability to calculate accurate values of all liquidphase species is important for design and simulation based upon rates of mass transfer and chemical reaction (Hermes and Rochelle, 1987; Sivasubramanian et al., 1985). In this approach, liquid-phase concentrations enter into kinetic expressions, affecting mass transfer a t vapor-liquid interfaces. In addition, the bulk liquid phase is generally assumed to be in a state of chemical equilibrium. Edwards et al. (1975) developed a molecular thermodynamic framework to calculate vapor-liquid compositions for dilute aqueous solutions of volatile weak electrolytes (sour water systems). They treated chemical equilibria rigorously by employing component activities rather than concentrations. Activity coefficients were represented with a Guggenheim-type equation (1935) by treating long-range ion-ion interactions and short-range solute ion-ion, ionmolecule, and molecule-molecule interactions. Molecule-molecule parameters of the model, representing binary interactions, were determined by data regression. Ion-ion binary parameters were approximated by using the procedure of Bromley (1972). Molecule-ion parameters were approximated from ion-ion and molecule-molecule parameters. Because Guggenheim’s equation is valid only to ionic strengths of approximately 0.1 m,the method was limited to weak electrolyte concentrations of less than 1 or 2 m. Deshmukh and Mather (1981) used a similar approach to calculate the solubility of H2S and C 0 2 in MEA solutions. They also used Guggenheim’s equation to represent activity coefficients. The adjustable binary interaction parameters of the model were fitted on ternary system VLE data-MEA-HzS-H20 and MEA-COZ-H20. They also adjusted the temperature dependence of two equilibrium constants on experimental data. Chakravarty
(1985) extended the model of Deshmukh and Mather to systems of mixed amines. Edwards et al. (1978) extended the range of validity of their sour water model to weak electrolyte concentrations of 10-20 m by adopting Pitzer’s model (1973) to represent activity coefficients. Pitzer’s model is an extension of Guggenheim’s equation. It is an improved treatment of the long-range ion-ion electrostatic interactions and short-range ion-ion interactions, although Edwards extended Pitzer’s model to also account for short-range ion-molecule and molecule-molecule interactions. Buetier and Renon (1978) also used Pitzer’s model with the thermodynamic framework of Edwards et al. (1975) to calculate VLE in sour water systems. These researchers accepted the binary molecule-molecule interaction parameters determined in the earlier work of Edwards and co-workers (1975) or refit the parameters on binary system data. Molecule-ion parameters were estimated by using Debye-McAulay’s electrostatic theory (Harned and Owen, 1958). While Pitzer’s Gibbs energy model excess (1973) has been shown to be valid to ionic strengths representative of those encountered in industrial uses, its application is generally limited to single-solvent, aqueous systems. The solute-solute binary interaction parameters are unknown functions of solvent composition. The amine-water system is more properly treated as a mixed solvent system of variable composition. Furthermore, Pitzer’s model contains a large number of binary and ternary temperaturedependent adjustable parameters. Approximating these parameters is difficult for a system with a large number of liquid-phase solute species, ionic and molecular, such as the amine-H2S-COz-HzO system. Dingman et al. (1983) developed a VLE model for the diglycolamine-H2S-C02-Hz0 system. The framework of the model was equivalent to the framework used by Edwards et al. (1975). Activity coefficients were developed from a combination of NRTL theory (Renon and Prausnitz, 1968), Bromley’s correlation (19731, the method of Meissner et al. (1972), and Born theory. The drawback of this approach was that the functional form of the expressions for the activity coefficient correlations was thermodynamically inconsistent. Chemistry In aqueous solutions, H2S and COz react in an acid-base buffer mechanism with alkanolamines. These equilibrium reactions can be written as chemical dissociation: ionization of water 2Hz0
-
H30+ + OH-
-
(la)
dissociation of hydrogen sulfide H 2 0 + H2S dissociation of bisulfide H 2 0 + HS-
H30+ + HS-
(24
H30+ + S2-
(34
-
dissociation of carbon dioxide 2 H z 0 + COz H30+ + HC03-
(44
dissociation of bicarbonate H 2 0 + HC03-
(54
H30+ + COS2-
-
dissociation of protonated alkanolamine HzO
+ RR’R”NH+
H30+ + RR’R”N
(6a)
In these equations, RR’R”N is the chemical formula of the alkanolamine. R represents an alkyl group, alkanol
1062 Ind. Eng. Chem. Res., Vol. 28, No. 7, 1989
group, or hydrogen. Primary and secondary amines are also known to react directly with COPto form stable carbamates. In this work, we consider the reversion of carbamate to bicarbonate instead of the direct formation of carbamate: carbamate reversion to bicarbonate RNHCOO-
+ HzO
-
RNHz
+ HC03-
(7a)
As noted by Deshmukh and Mather (1981), additional reactions are known to occur that may affect equilibrium. The amines may react with carbon dioxide to form heterocyclic compounds at high temperatures (Kennard and Meisen, 1985). The results of kinetic measurements on these reactions by Kim and Sartori (1984) suggest that these reactions may occur fast enough to affect equilibrium measurements if the carbonated alkanolamine solution being investigated is held at an elevated temperature (exceeding 100 " C ) for a substantial period of time. We chose not to include these degradation reactions in the equilibrium model because the effect of such degradation in most experimental measurements is likely to be small. Alkanolamines may also react with other acid gases that are present in lesser quantities in the source gas such as carbonyl sulfide and carbon disulfide. These reactions were also not considered in the equilibrium model.
Thermodynamic Framework The thermodynamic framework used in the model presented here is based on two types of equilibriachemical reaction/dissociation equilibria and vapor-liquid-phase equilibria for molecular species. Ionic species are treated as nonvolatile. The solution is treated as a mixed solvent system-water-alkanolamine. All other species in the liquid phase are considered to be molecular or ionic solutes. Molecular electrolytes dissociate or react in the liquid phase to produce ionic species to an extent governed by chemical equilibria. The equation governing chemical equilibria may be written as
where ai is the activity of species i. We rewrite eq 1 in terms of mole fractions, x i , and activity coefficients, yi, to give
Equation 2 is written for reactions la-7a. As mentioned above, both water and alkanolamine are treated as solvents. The standard state associated with each solvent is the pure liquid a t the system temperature and its vapor pressure. In view of the availability of literature data and the need for a common reference state for ionic species in various mixed solvent electrolyte systems, the standard state for ionic solutes is the ideal, infinitely dilute aqueous solution (infinitely dilute in solutes and alkanolamine) at the system temperature and pressure. Finally, in view of the unavailability of Henry's constants in pure alkanolamines, the reference state chosen for molecular solutes (HzSand COz) is also the ideal, infinitely dilute aqueous solution. This leads to the following unsymmetric convention for normalization of activity coefficients: for solvents, y, 1 as n, 1;for ionic and molecular solutes, yi* 1 as xw 1. This choice of standard states allows us to use equilibrium constants for reactions la-7a reported in the literature, while we treat the solution as a mixed solvent. It should be noted that a correction must be applied to equilibrium constants for reaction 6a, amine
- -- -
protonation; alkanolamines are usually treated as solutes with unsymmetrically normalized activity coefficients for equilibrium constants reported in the literature. The correction is related to the infinite dilution activity coefficient of the amine in water. Infinite dilution activity coefficients for MEA and DEA in water were estimated from published MEA-water and DEA-water binary VLE data. Phase equilibria govern the distribution of molecular species between the vapor and liquid phases. Henry's constants represent reference-state fugacities for molecular solutes (COz and HzS) yi+iP = xiyi*HiP exp
(
&"(P- PO) RT
(3)
where Hipand Dim represent the Henry's constant and partial molar volume at infinite dilution for molecular solute i in pure water a t the system temperature and at the vapor pressure of water. The partial molar volumes of H2S and COz at infinite dilution in water are estimated by the correlation of Brelvi and O'Connell (1972). The characteristic volume of the Brelvi-O'Connell correlation for water was taken from the original work of Brelvi and O'Connell and the characteristic volume of COz was fixed at its critical volume. Following Edwards et al. (1978), the characteristic volume for HzS was set a t 90% of its critical volume. For the solvent species, water and alkanolamine, vapor-liquid equilibria are given by
where us is the molar volume of the pure solvent at the system temperature and saturation pressure. Pure-component vapor pressures of water, MEA, and DEA were taken from the DIPPR data tables (Daubert and Danner, 1985). Units and Temperature Dependence. Because equilibrium constants are defined in terms of mole fractions and activity coefficients in eq 2, they are dimensionless. Equilibrium constants for reactions la-6a are available in the literature in terms of molalities. The temperature dependence of the equilibrium constants is represented in this work by the following function: In K = C1 + C z / T + C3 In T + C4T (5) Coefficients C1-CI are summarized in Table I for all reactions together with literature sources. Note that the coefficients of the first dissociation constant of HzS, the first and second dissociation constant of C 0 2 , and the dissociation constants of protonated MEA and DEA differ in one or more terms from the original sources. It was necessary to convert these equilibrium constants from a molality basis to a mole fraction basis. An additional correction was applied to protonated MEA and DEA dissociation constants (reaction 6a) because, as was mentioned previously, we apply different MEA and DEA reference states than those applied in the original literature sources. Henry's constants have units of pascals. The temperature dependence is given by the same functional form as eq 5. Parameters Cl-C4 of eq 5 for COz and HzS Henry's constants are also presented in Table I. Fugacity Coefficients. The vapor-phase fugacity coefficients in eq 3 and 4 are calculated by using the Redlich-Kwong equation of state as modified by Soave (1972). The original mixing rules used by Redlich and
Ind. Eng. Chem. Res., Vol. 28, No. 7, 1989 1063 Table I. Temperature Dependence of the Equilibrium Constants for Reactions la-7a and Henry's Constants for HIS and C02
In H,P' reaction
amine/acid gas
c,
la 2a 3a 4a 5a 6a 6a 7a 7a
MEA DEA MEA DEA
132.899 214.582 -32.0 231.465 216.049 2.1211 -13.3373 2.8898 16.5027
la 2a
HZS COZ
358.138 170.7126
or In K = C1 + C P / T+ C3 In T
+ C4T
c,
CZ
c 4
temp range, "C
Equilibrium Constants -13 445.9 -22.4773 -12 995.4 -33.5471 -3 338.0 0.0 -12092.10 -36.7816 -35.4819 -12431.70 -8 189.38 0.0 0.0 -4 218.71 -3 635.09 0.0 -1.5027 -4 068.76
0.0 0.0 0.0 0.0 0.0 -0.007 484 0.009 872 0.0 0.0
0-225 0-150 14-70 0-225 0-225 0-50 0-50 25-120 25-120
Henry's Constants -13 236.8 -55.0551 -8477.711 -21.95743
0.059 565 0.005 781
0-150 0-100
source a
b c, d
b b e
f
g g
b h
"Maurer, 1980. *Edwards et al., 1978. "Giggenbach, 1971. dMeyer et al., 1983. eBates and Pinching, 1951. fBower et al., 1962. BFitted on reported VLE data. Chen et al., 1979.
Kwong (1949) are used in this work to calculate equation-of-state parameters for gas mixtures. Activity Coefficients. The Electrolyte-NRTL equation (Chen and Evans, 1986), modified for mixed solvent electrolyte solutions (Scauflaire et al., 1989), is used to represent liquid-phase activity coefficients. This is a generalized excess Gibbs energy model that accounts for molecular/ionic interactions between all true liquid-phase species. The basic postulate of the model is that the excess Gibbs energy of a mixed solvent electrolyte system can be written as the sum of two contributions, one related to the local ion-molecule, ion-ion, and molecule-molecule interactions that exist in the immediate neighborhood of any species and the other related to the long-range ion-ion interactions that exist beyond the immediate neighborhood of a central ionic species: gex* = gex*,LR + gex*,local (6) For the long-range ion-ion interaction contribution, Chen and Evans adopted Pitzer's reformulation of the Debye-Huckel formula (Pitzer, 1980) &H
and local electroneutrality. The first of these assumptions stipulates that in the immediate neighborhood of a cation (anion) the local composition of all other cations (anions) is zero. Local electroneutrality requires that in the immediate neighborhood of a molecule the composition of cations and anions is such that the local electric charge is zero. The NRTL contribution to the Electrolfle-NRTL equation is reproduced here
Fxa% with CXaGca,m
k
where D, represents the dielectric constant of the mixed solvent and D, represents the dielectric constant of pure water. The sums of eq 7 and 8 represent the long-range contribution to the excess Gibbs energy in eq 6. Scauflaire and co-workers (1989) proposed a simple mass fraction average mixing rule to calculate dielectric constants of the mixed solvent. The local interaction contribution to the excess Gibbs energy was derived from the local composition concept of the nonrandom two-liquid hypothesis (Renon and Prausnitz, 1968) and the assumptions of like-ion repulsion
(9)
(Cxc,,)(CXkGka,c'a) C" k
= -RT(cxk)(looo/M,)'/2(4A~x/~) 1n (1 + ~ 1 , " ~ )
(7) where A , is a function of the mixed solvent dielectric constant and mixed solvent density. The reference state for ionic species implied by eq 7 is the ideal dilute state of electrolyte in the mixed solvent. However, as indicated earlier, the reference state chosen for ionic species in the context of a mixed solvent system is the ideal dilute state in water only. To account for the excess Gibbs energy of transfer from infinite dilution in the mixed solvent to infinite dilution in the aqueous phase, the Born expression (Robinson and Stokes, 1970) was introduced into the long-range interaction term
Xc!CGja,c,aTja,ca J
Gcm
=
CXcGca$m
ex,
Gam
=
cX,
a'
C
CXaaca,m a acm
=
Cxcaca,m C
ffam
EXa,
=
2xc,
a'
C
where X j = xjCj ( C j = Zj for ions; Cj = unity for molecules) a is the nonrandomness parameter, interaction parameter,
7
is the binary energy
Gjc,afc
= exp (-ffjc,alcTjc,aIc)
G j a?era
= exp ( - a j a
Gcqm
,c'aTja ,c,a)
= exp(-aca,mTca,m)
Gim= exp(-aimTim) Tmap
=
Tam
-
Tca,m
+
Tm,ca
Tmcpc
=
rcm
-
Tca,m
+
Tm,ca
Equation 9 must be normalized to reflect the proper reference states for the solute components. The sums of eq 7-9 constitute the Electrolyte-NRTL equation for mixed solvent electrolyte systems: gex*
= @IH
+ &ORN
+ g%lT+
(10)
1064 Ind. Eng. Chem. Res., Vol. 28, No. 7, 1989 Table 11. Dielectric Constants for Pure MEA and DEA (Ikada et al., 1968) MEA: D = 35.76 + 14836[1/T - 1/273.15] DEA: D = 28.01 + 9277[1/T - 1/273.15]
The activity coefficient for any species, ionic or molecular, solute or solvent, is derived from the partial derivative of the excess Gibbs energy with respect to mole number:
The parameters required by the Electrolyte-NRTL equation for the alkanolamine-H2S-C02-Hz0 system include the distance of closest approach, p , in the PitzerDebye-Huckel term and pure-component dielectric constants, D , and ionic radii, r , in the Born term. The parameters of the NRTL term are the nonrandomness factors, c y L l , and binary interaction energy parameters, ri,. In this work, the distance of closest approach term was fixed at 14.9 as suggested by Pitzer (1980). Dielectric constants for MEA and DEA were taken from Ikada et al. (1968) and treated as temperature dependent. The dielectric constants of MEA and DEA are reported as functions of temperature in Table 11. Ionic radii were assigned default values of 3 A. Following Chen and Evans (1986), the nonrandomness factor was fixed at 0.2 for moleculemolecule interactions (a,,, ) and for water-ion pair interactions (a,,,, or a,,,,). Nonrandomness factors for alkanolamine-ion pair and acid gas-ion pair interactions were fixed at 0.1 as suggested by the results of Mock et al. (1986) for nonaqueous solutions of electrolytes. Therefore, the only adjustable parameters of the Electrolyte-NRTL model are the short-range binary interaction parameters ( T m m , , T,m
