Ind. Eng. Chem. Res. 1993,32, 1419-1430
1419
GENERAL RESEARCH Solubility of Carbon Dioxide and Hydrogen Sulfide in Aqueous Alkanolamines Ralph H. Weiland,’ Tanmoy Chakravarty? and Alan E. Mather* Department of Chemical Engineering, The University of Newcastle, Callaghan, NSW 2308, Australia The Deshmukh-Mather thermodynamic model has been fitted t o all available, public, phaseequilibrium data for COZ and HzS in aqueous solutions of monoethanolamine, diethanolamine, diglycolamine, and N-methyldiethanolamine. The fitting was done for both acid gases simultaneously, and the best numerical values of the most important interaction parameters for each amine were obtained. Although the method used for data regression did not provide a statistical measure of the goodness of fit, the regressed model forms a unified basis for evaluating the large amount of data collected over the past 50 years and it results in a rational approach t o performing vapor-liquid equilibrium calculations in a computationally affordable, thermodynamically sound manner.
Introduction The availability of accurate information on the equilibrium solubility of carbon dioxide and hydrogen sulfide, both individually and together, in aqueous solutions of various alkanolamines is of the utmost importance in the design of gas-treating units. Amines of broad, current interest include monoethanolamine (MEA), diethanolamine (DEA), diglycolamine (DGA), and N-methyldiethanolamine (MDEA). While over 6000 solubility measurements have been reported in some 28 separate publications, the data taken as a whole have yet to be analyzed in a consistent manner and on a thermodynamically rational basis. Solubilities have been measured over wide ranges of temperature, solution loadings with respect to the acid gases (solution loading is the number of moles acid gas per mole of amine),and amine concentrations, but the majority of the data are crowded in the middle loading range. Although the measurements can most accurately and easily be made at modest solution loadings, the production of high-purity gases (ppm impurities) requires solubility data at very low loadings. Unfortunately, the relatively small amount of data available at these low loadings tends to be of rather poor precision, and possibly of poor accuracy, too. Thus, there is a need for all the available data to be correlated in terms of a fairly general model of the solution thermodynamics so that solubility predictions can be confidently made where data do not exist or where they are of poor quality. The earliest attempt to model vapor-liquid equilibrium in COz-HZS-amine-water systems was made by Klyamer et al. (1973). Like all later models, this model uses an activity coefficientapproach to the excess Gibbs free energy and is based on chemical reaction equilibrium in the liquid phase. The activity coefficients of all species are taken equal to each other and to depend only on the total ionic strength in a way given by the Debye-Huckel limiting law. No interactions between species were used, and the
* Author to whom correspondence should be addressed. t
Bechtel Corporation, Houston, TX. Departmentof Chemical Engineering, University of Alberta,
Edmonton, Alberta, Canada T6G 2G6.
activity coefficients and fugacity Coefficients of the free acid gases were taken to be unity. This relatively simple model was quickly followed by the even simpler approach of Kent and Eisenberg (1975). The Kent-Eisenberg correlation is essentially the model of Klyamer et al. in the limit of unit activity coefficients. This model has become popular among practitioners because it correlates the data fairly well while retaining extreme computational simplicity. This model takes all activity coefficients and fugacity coefficients to be unity (ideal solutions and idealgases) and forces agreement with experimental measurement by regressing the reaction equilibrium constants for the amine protonation reaction (RR’R”N + HzO = RR’R’’NH+ + OH-) and the carbamate formation reaction (COZ + 2RR’R”N = RR’R”NH+ RR’R”NCO0-) to give apparent equilibrium constants. The Kent-Eisenberg model has several deficiencies: the fit is good only in the narrow loading range from 0.2 to 0.7 mol of acid gas/mol of amine, the model gives inaccurate results for the solubility of mixed acid gases (as distinct from the single acid gas data used for fitting), and the model is unsuccessful for tertiary amines because they do not form carbamates at all so that no free parameters are available for fitting. One requirement of any model for acid-gas-amine systems is that it be of greater rigor than the simple approaches of Klyamer et al. (1973) and Kent and Eisenberg (19751, yet algebraically simple enough that it is computationally efficient and attractive to do largescale calculations (such as for columns). Blended amine systems have become increasingly widely used over the past 5 years, and certainly any model worth considering must be able to be extended to such solvents. There are currently two candidates: (i) the model of Deshmukh and Mather (1981) and (ii) the electrolyte-NRTL model of Chen and Evans (1986). Austgen’s (1989)implementation of the electrolyte-NRTL model is, like the DeshmukhMather model, thermodynamically rigorous but it is somewhat more complex and is certainly more expensive computationally (Austgen, 1990). Both models are readily extendable to chemical systems containing multiple amines. We have chosen the Deshmukh-Mather model for this work because (i) it meets our requirements of
0888-588519312632-1419$04.00/0 0 1993 American Chemical Society
+
1420 Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993
thermodynamic soundness and broad generality and (ii) it does so at a computationally affordable price. In the original work of Deshmukh and Mather (1981), interaction parameters for specific pairs of species were fitted only to the data of Lee et al. (1976a,b) for COS!and H2S in MEA solutions. No other data relevant to MEA were used in the fitting, and all other amines were ignored. What fitting was done was based on minimizing the sum of squares of the differences between measured and model partial pressures. Because partial pressures span as much as 8 orders of magnitude, the simple sum-of-squares minimization unduly weighted the high partial pressure data relative to the data at low partial pressures. This was doubly unfortunate because it is precisely at the low partial pressure end of the spectrum where greatest accuracy is needed in order to deal successfully with the high-purity (lean amine, low acid-gas partial pressure) end of an absorption tower. It is very important in model regressions of this type that the minimization be done on the basis of equal weighting of all data regardless of their individual magnitudes. The Deshmukh-Mather model is rigorous and and of sufficient generality to be extremely useful. The primary parameters of the model, the reaction equilibrium constants,are available from independent measurements, and even by themselves, they yield a set of model predictions in fair quantitative agreement with the data. Additionally, there are enough interaction parameters to allowthe model to be fine tuned to the data with a degree of accuracy far in excess of the reliability inherent in the data themselves. Furthermore, the model exhibits the right kind of behavior in the limit of low solution loadings. Thus, one might expect it to extrapolate reliably to partial pressures below the range of the measured data. Of considerable commercial importance, it is readily extendable to mixtures containing two (or more) amines, an area of currently high and growing interest. Deshmukh and Mather’s original implementation used Brown’s method for solving the system of equations. They found that such enormous computational effort was required that it seemed unlikely for the model to find use in column design and simulation. However, Chakravarty (1985) used Newton’s method to solve the equations and he found convergence to be quite rapid. Indeed, computation times were sufficiently short to allow the Deshmukh-Mather model to be incorporated into absorption and regeneration column simulation programs (Sardar and Weiland, 1984) based on the masstransfer-rate approach. Thus, there is every reason that the Deshmukh-Mather model should find increased use in process design and simulation work.
General Equations for Acid-Gas Equilibria in Alkanolamines In the system HzS-COzamine-water, the following 12 species are postulated to exist in solution: H2S, HS-, S”, COz, HC03-, COS%,RR’RTOO-, RR’R”N, RR’R’’NH+, H20, H+, and OH-. Here, RR’R”N represents the amine and the R, R’, and R” groups may be mobile protons or hydrocarbon groups depending on the amine in question. For a tertiary amine, for example, R, R’, and R” are all organicgroups, whereas for secondary amines the R”group is a bound hydrogen atom, and for primary amines both R’ and R” are bound hydrogen atoms. In general terms, the equilibrium distribution of COZ and HzS between an aqueous alkanolamine solution and a vapor phase is determined by the solution of a set of equations comprising (i) three species balances, one for each of HzS, COZ,and the amine (S, C, and N), (ii) seven
reaction equilibrium equations for the dissociation of various species in solution, (iii) an equation of electroneutrality, and (iv) isofugacity statements for each species which is present in both phases. The following are the equilibrium chemical reactions relevant to acid-gas alkanolamine systems: dissociation of alkanolamine RR’R”N
+ H,O
= RR’R’’NH+
+ OH-
dissociation of water H,O = H+
+ OH-
dissociation of hydrogen sulfide
+
H2S = H+ HSdissociation of bisulfide ion
HS- = H+ + sZ hydrolysis of carbon dioxide
+ H,O
CO,
= H+
+ HCO,
dissociation of bicarbonate ion
+
HCO; = H+ CO,” carbamate formation (except tertiary amines) CO,
+ 2 RR’R’’N = RR’R’’NH+ + RR’R”NCO0-
Mathematically, the corresponding equilibrium constants are defined in terms of activity coefficients, y, and molalities, m:
(3)
(4) ~H+mH+YHCOs-mHC08-
Kco, =
~cO,mco,aw yH+mH+yCO,%mCOa%
KHCO,-
KAmc,
=
=
YHCO,-~HCO~-
yAmH+mAmH+YAmcmmAmcoo. 2
yllm
2
mAm ~cO,mco,
(5)
(6) (7)
Here, the subscript Am refers to the molecular amine and the definition of molality is based on water being the sole solvent (amines are taken as solutes). The definition of the liquid phase is completed by four balance equations: one for electrical charge neutrality
Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 1421
m w + + m ~ =+~
H C O+ ~m -
b c w + OH- + m ~ +5 2mco,P-+ 2msa- (8)
and one for each of amine,
m k = m b + m b H + + mbcoo-
(9)
hydrogen sulfide,
mkaHps = m v + mH9-+ mss
(10)
and carbon dioxide
mkaCOl = mCO, + mHC08- + mAmCOO- + mCO,% (11) Here, m k indicates total concentration of the amine in all its forms (i.e., the initial, acid-gas-free amine concentration) and a is the loading of the acid gas in question (moles of acid gas per mole of total amine). The vapor and liquid phases are connected by isofugacity equations. In this work, we have assumed that the amine is nonvolatile (relative to the other molecular species), an assumption that can be easily relaxed if necessary. We assume a physical solubility (Henry's law) relation for the (noncondensible) acid gases and a vapor pressure relation for water. (If the system contains other volatile species, such as hydrocarbons, these can be accounted for by additional isofugacity relations baaed, for example, on Henry's law for sparingly soluble components,or on vapor pressures for condensibles.) Thus, the following relations apply: @JH+YH$' = Y H ~ ~ H Z ~ H H (12) ~ ~
@Jcoyco,p = Yco,~colHco,
$y>= a x t 4 r texp[P(P - C t ) / R T I
(13) (14)
where 4 is the fugacity coefficient, y is mole fraction, H is a Henry's constant for the acid gas in pure water, P is the total pressure, and a, is the activity of water. The exponential term in eq 14 is the Poynting correction. Deshmukh-Mather Model The Deshmukh-Mather model is basically a method for calculating the excess Gibbs free energy function using an activity coefficient approach, and it is based on an extension of the Debye-Htickel (1923) theory. As suggested by Edwards et al. (197% it uses the form of equation for activity coefficients of the solute species proposed by Guggenheim and Stokes (1958) and Scatchard (1961): -2.303A,~:I"~
In yi = 1
+ BUI'J~
+2C~ijmj
(15)
Here, A, is the Debye-Htickel limiting slope (0.509 at 25 "C in water), B is a function of temperature and the dielectric constant of the solvent (water), and I is the ionic strength, defined as (16)
in which Z j is the charge number on the ion. The quantity a is an adjustable parameter measured in angstrom units which roughly corresponds to the effective size of the hydrated ions, and the Bijrepresent the net effect of various short-range two-body forces between different molecular and ionic solutes. The summation in the second term is taken over all solute pairs but excludes interactions between solutes and the solvent,water (j # w). Physically,
the fiist term on the right represents the contribution of electrostatic forces; the second term represents short-range van der Waals forces. This model performs reasonably well in fitting data for dilute solutions; however, for concentrated solutions of weak electrolytes (above 10 M concentration), Pitzer's correlation (Pitzer, 1973) performs better. Nevertheless, we have used the extended DebyeHtickel theory for a number of reasons: First, this is the form invariably used while obtaining the dissociation constants of various species. [See, for example, Kruykov (1974) for the dissociation constant for bisulfide ion, Bates and Pinching (1951) for amine dissociation, and Cuta et al. (1954) for the dissociation constant of bicarbonate ion.] Second, it reduces to the well-known Setschenow (1889) equation for the salting-out effect caused by moleculeion interactions, and third, it gives the correct limiting behavior for solutions of low ionic strength. [The limiting behavior of solutions at low ionic strength is different with the Pitzer and modified Pitzer (Chen et al., 1979) forms because the Debye-Hiickel limiting slope is not the same as the Pitzer-Debye-Htickel limiting slope (see Ananthaswamy and Atkinson, 198411. In any case, one of the goals of this work is to provide a fully-regressed model that can be extended to blended, or mixed, amine systems. The approach of Guggenheim and Stokes allows this to be done using only single-amineparameters; the use of Pitzer's correlation would require an unmanageably large number of additional parameters. Two further approximations have been made in this work: the Poynting correction has been ignored and the activity of water has been taken equal to its mole fraction. The reference state for water is pure liquid water at the system temperature and pressure, and for solutes it is a hypothetical ideal solution of unit molality. Fugacity coefficients have been estimated using the Peng-Robinson equation of state. Thermodynamic Parameters The thermodynamic parameters needed for the model are (i) equilibrium constants for all chemical reactions, (ii) Henry's constants for the two acid gases in pure water, (iii) fugacity coefficients for all gas-phase species (HzS, C02, and water), and (iv) activity Coefficients for all solute species. Model regression is to be achieved by selection of numerical values for the important interaction parameters in the activity coefficient model. Thus, we need data and methods for the first three items. All Henry's law solubility constants and chemical reaction equilibrium constants can be expressed in the form In K = a / T + b In T + c + d T + e p (17) Values of the constants in this equation are listed in Table I for all relevant equilibria (except for the dissociation of water) along with error estimates and literature sources of the data. For water, the reaction equilibrium constant (Olofsson, 1975) In K, = -328379.9lT
- 4229.195 In T + 20501.02448 + + 2.649539(104)P -
22.4345T - 2.985025(10-2)'la
1 . 0 5 9 6 5 ( 1 0 4 ) ~(18)
is valid over the temperature range from 0 to 145 "C with a probable error of 1.0-1.7% (based on a comparison between correlated and measured values at temperatures where data exist). Values used for the parameter a in eq 15 are listed in Table 11.
1422 Ind. Eng. Chem. Res., Vol. 32,No. 7, 1993 Table I. Constants in Correlating Equation for Various Reaction Equilibrium and Solubility Constants parameter K b (MEA)
1Wa -6166.115 65b
0
K b @EA)
-4214.076 10
0
K b (DGA) K b (MDEA) Kbcoo- (MEA) K b c w (DEA) Kbcoo. (DGA) KHES KHS-
Kco,
KHC~-
Hco,
d We -7.798 625 0 -0.OOO 984 815 6 0 C
-16.187 633 7
0.009 961 210 0 0
-6079.6 0 -8.2502 0 0 0 -39.166 97 0.04236757 9124.36 0 -34.208 8 0.131 493 9 6801.72909 0 -8.5022397 0 10213. 0 -16.543 8 0 -13919.6 0 238.709 -37.744 -6661.171 0 -17.149 8 0.005 788 7 17262.0 -67.341 4 406.820 7 0.04431786 6433.628 -2.245 836 16.961 285 -0.044 584 35 -4379.847 741 0 43.643 503 -23.873 488 8 -4778.603386
"Is
b
0
45.353 452
-28.978 205
temp range ("C) 0-50 0-50
0-50 25-60 -1.999 91 18-120 0 18-100 0 18-70 0 0-276 0 25-150 0 25-250 0 0-218 0 0-350 0 0
0
0-330
eatdo error literature sources l-5%c Bates and Pinching (1951); Antelo et al. (1984) 2-5d Bower et al. (1962); Antelo et al. (1984) 2-5 Dingman et al. (1983) 25 Barth et al. (1981) this work this work this work 21-55% Rao (1976);Barber0 (1982) 35-85% Kruykov et al. (1974) 2-30% Ryzhenko (1963);Read (1975) 5-10% Cuta (1964); Ryzhenko (1963) 1-5% Zel'venskii (1973); Wiebe (1939); Ellis (1959) 6%d Lee and Mather (1977)
Error limits were obtained by comparing parameter values calculated from the correlations with measured valuee at those temperatures where data exist. b Parameters are given to many digits if the correlation was converted from a loglo base to a natural logarithm. c Experimental values from different sources differ by 18-19%. Standard deviation of fit as reported by source. a
Table 11. Effective Ionic Size, a, Used in Eq 16-from Butler (1964) ionic species ionic size (A) H+ 9.0 OH3.0 HS3.0 SZ 5.0 HCOs4.0 COS" 5.0 carbamate of MEA 4.5 DEA 6.0 DGA 6.0
The Peng-Robinson equation of state was used for fugacity calculations in the vapor phase. The only interaction considered was the one between C02 and HzS, for which we assigned the value 6ij = 0.1 in the relation ai, = (1 - 6jj)(aiaj)'/2(Robinson et al., 1985).
Selection of Interaction Parameters for Fitting There is an extremely large number of possible interactions in acid-gas alkanolamine systems. For example, for a primary or secondary amine with two acid gases, there are 78 possible interactions (even allowing for symmetry). In a blended amine system in which both amines can form carbamates there are 120 possible interactions. Discarding interactions between ions of the same charge (Le., net positive or negative) reduces these figures somewhat (to 62 and 97 in the above examples), but not enough to make the fitting of the remaining parameters a realistic goal. All interactions between like-charged ions (Bransted, 19221,all self-interactions of molecular species (with the sole exception of molecular amine with itself), and all interactions between water and its ionization products with other species were set to zero. This still leaves 27 parameters for a two-acid-gas, carbamate-forming system. To reduce further the number of parameters to a manageable set, interactions between the acid gases and other components were disregarded for the primary and secondary amine systems; this was justified after the fact by computer experiments in which nonzero values of the parameters were found to have negligible effect on calculated partial pressures. This is a result that one might expect on the basis of the concentrations of most of these
species being quite small (so that even if their interactions were strong, they would make negligible contribution to the total interaction term in eq 15). This reduced the number of interactions to 12of which 7 are the interactions of molecular amine with itself and with the 6 ionic species present in the liquid, and 5 are interactions of protonated amine with the 5 other ionic components. Further computer experiments allowed four interactions to be dropped from further consideration, leaving the following parameters to be fitted to the data for MEA, DEA, and DGA: AmH+-HSAmH+-HCOi AmH+-CO; AmH+-AmCOOAm-HsAm-HCO; Am-AmCOOAm-Am In the case of MDEA, inclusion of interactions between protonated amine and molecular H2S and C02 was found to reduce the error of the fit (the objective function) by some 15%, so they were included in the parameter set. Thus, for MDEA the following set of interactions was fitted: AmH+-H2S AmH+-HSAmH+-CO, AmH+-HCO; Am-HSAm-HC0,AXI-HCO,~ Am-Am (As will become evident in subsequent sections, even some
Ind. Eng. Chem. Res., Vol. 32, No. 7,1993 1423 of the interactions included in the above sets proved to have marginal to insignificant effect on the size of the minimized objective function, as indicated by their small values relative to others.)
Least-Squares Data Regression The thermodynamic model, involving as it does the calculation of activity coefficients from a detailed knowledge of the ionic makeup of the solution and the calculation of fugacities of the gas using the Peng-Robinson equation of state, is relatively complex and computationally expensive compared with the simple models of Klyamer et al. (1973) and Kent and Eisenberg (1975). The model is also highly nonlinear, making data regression a decidely nontrivial task. The approach taken here was to define an objective function in terms of a normalized sum of squares of deviations between experimental and fitted data and to seek the minimum of this function by algorithmic selection of values for a set of interaction parameters. The procedure used for finding the optimum set of parameter values was Davidon's method. Davidon's (1959) method is an efficient, unconstrained, minimization algorithm that begins the minimization along the steepest descents direction, and as the minimum is approached, it gradually switches to Newton's method of minimization. Search directions are maintained conjugate throughout the procedure. Thus, Davidon's method is initiallylinearly convergent, but as the minimization proceeds, it becomes quadratically convergent. Conjugate search directions are generated using approximations to the Hessian matrix as the conjugate basis. (Conjugate search directions are directions that are orthogonal with respect to a nonorthogonal set of basis vectors for the space in which the minimization is being carried out.) The inverse Hessian (matrix) is approximated using a quasi-Newton update formula that adds a rank-one update based on the most recent search direction plus a further correction to maintain the search along conjugate directions. Although symmetry is not a requirement for Davidon's method, the method as implemented made good use of the fact that the interactions themselves are symmetric (i.e., P i j = pji) by using a symmetric Hessian matrix. The derivative information required by the method was obtained numerically. (To use analytical derivatives, mass balance and electroneutrality equations would have to be included as constraints for every data point-12 variables per point-resulting in an enormously large system of equations.)
Objective Function for Minimization We seek numerical values for the interaction parameters that will minimize the difference between the measured values of equilibrium partial pressures of the acid gases over the solutions, and the values calculated from the model. It must be remembered, however, that these partial pressures span some 8 orders of magnitude so that simply minimizing the sum of the squares of the differences between measured and fitted values would weight the high partial pressure data almost to the exclusion of the low partial pressure end of the spectrum. The low partial pressure (low solvent loading) data are the very data that are most critical in determining equipment performance. What is needed is an objective function that will weight all data equally. The simplest such unbiased objective
function has the following as a typical term: [(measured) - (calculated)12 (19) (measured)(calculated) The denominator is designed to give equal weight to all the data, regardless of the magnitude of the measured quantity. Thus, for each data point &e., for each measured value of the partial pressure of HzS and/or COZ)the contributions of H2S and COz were calculated andsummed, forming the discrepancy function, Fi, for that measurement:
The objective function is the sum of the individual discrepancy functions:
Elimination of "Bad"Data from Data Sets As expected, it was normal to find at least a few measurements in any set of data (defined as the data in a single publication) that deviated greatly from the majority. There was no way to determine beforehand which measurements within a given data set were errant and which data sets were more or less reliable than the rest. Preliminary calculations preparatory to doing the actual fitting showed, however, that even with all interactions put to zero, the vast majority of the data for any particular amine did not differ from calculated partial pressures by more than 40 or 50 % although high loading data were frequently skewed one way or the other from the line of perfect agreement. Therefore, the procedure adopted here was to discard immediately any data for which the calculated partial pressures differed by a factor of 3 or more from the measured values (4 or more in the case of DGA so as to preserve as much data as possible from an already small collection). (The vast majority of the data appeared to be reproduced reasonably well by the model without interaction parameters at all, the interactions being used only to improve an already fairly close fit. Therefore, one might look at the zero-interaction model predictions as closely approximating the data themselves. As a result, when we saw that a few of the measurements differed from the vast majority by factors of 3,4, or more, we took that to indicate that these data were rogue measurements, and discarded them. I t would have been preferable to make the decision to discard data by a direct comparison between measurements themselves, without the intervention of a model; however, the large number of parameters varying from measurement to measurement made this impossible. The alternative of using the zero interaction model to represent the data was the only one available.) It was absolutely essential to eliminate those data that were obviously discrepant and which would cause the fitting procedure to fail (diverge); some 12-16% of the data in the MEA, DEA, DGA, and MDEA data sets were discarded in this way. For a given amine, the model was then fitted to all the remaining data. It was usual for the fitting procedure eventually to reach a stage where it ceased to make any further progress in reducing the objective function even though the gradient vector was nonzero. For example, two successivevalues of the objectivefunction
1424 Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 Table 111. Sources of MEA Data total points reference points used comments Atwood et al. (1957) 23 23 H2Sonly 76 54 mixedgas Isaacs et al. (1980) 141 137 mixedgas Jones et al. (1959) 102 99 mixedgas Lawson and Garst (1976) 103 92 CO2andH2S Lee et al. (1974) 124 71 mixedgas Lee et al. (1975) 96 90 HzS only Lee et al. (1976a) 209 158 mixedgas Lee et al. (1976b) 227 218 C02only Lee et al. (1976~) Leibush and Shneerson (1950) 43 38 mixedgas Maddox et al. (1987) 78 60 CO2andH2S Mason and Dodge (1936) 87 67 C02only Muhlbauer and Monaghan (1957) 145 107 mixed gas Nasir and Mather (1977a) 37 30 mixedgas Nasir and Mather (1977b) 69 38 COzandH2S Riegger et al. (1944) 189 189 H&only Shen and Li (1992) 61 61 CO2only total
1738
1532
Table IV. Interaction Parameter Values for MEA AmH+-HS26.6175 AmH+-HCOa7.9786 AmH+-COss 0.2238 AmH+-AmCOO-5.7057 Am-HS-18.4323 Am-HCOs-0.9027 Am-AmCOO-1.7020 Am-Am 13.7760
successive iterations. When this occurred, the individual interaction parameter values were changing by 0.05% or less per iteration. At this level, the difference between consecutive values of a typical partial pressure was evident only in the third or fourth significant figures (well below the average 30% error level of the experimental data themselves). It must be remembered that the bulk of "fitting" has already been done when correlations for equilibrium constants are established. The adjustment of interaction parameters should be viewed as fine tuning of the model to achieve the best possible fit. Therefore, the fiiding that the goodness of fit was relatively insensitive to substantial changes in the interaction parameters is exactly what one should expect. It is also noted in passing that in view of the large number of parameters being fitted and the weak sensitivity of the fit to perturbations in individual parameter values, physical significance should not be attached to individual interaction-parameter values, or even to their signs.
MEA Data
for MDEA were 321.5343 and 321.5351 while successive values of the interaction parameters were within 0.05% of each other; at this stage the procedure was stopped. The fit was examined point by point to check for any data that were wildly discrepant with the fit (and would, therefore, unduly skew it), but no such data were found for any of the amines. Although the factor of 3 criterion (factor of 4 for DGA) used in the preliminary screening was arbitrary, it was selected for two reasons: first, this value made it easy to spot noncompliant data and, second, it did not force the rejection of a very large fraction of the original data; i.e., it allowed most of the data to be retained, eliminating only the most discrepant measurements. Convergence Criterion Convergence was reached when progress in reducing the objective function ceased being made in several
Sources of data, the total number of measurements, the number of measurements falling within the acceptance criterion above, and comments on the type of data are shown in Table 111. A measurement here refers to the partial pressure(s) measured in a single experiment as reported by the authors. Thus, a measurement may refer to a single acid gas or a pair of acid gases, depending on the number of acid gases contained in the amine solution being used. Interaction parameters and fitting statistics are shown in Tables IV and V, respectively, and parity plots of all the data, whether used in the fitting or not, are shown in Figure 1for HzS and Figure 2 for COz. (The quantity of data is so large that placing it all on a single plot for each acid-gas-amine combination would render it unreadable. However, Figure la-c, for example, should be viewed together .) In looking a t the overall statistics of the fit (Table V), it is apparent that the mean value of the ratios of measured predicted partial pressures is not unity, despite the fact that the total error of the fit as defined by eqs 19-21 has been minimized. The reason for this is that the partial pressure ratio is bounded from below by zero, and from above by infinity. Therefore, the partial pressure ratio distribution is not normal; rather, it is skewed to the right
Table V. Numbers of Data Points Fitted, Mean Values of MeasuredFitted Partial Pressure Ratios, and Their Standard Deviations for MEA data source Atwood et al. (1957) Isaacs et al. (1980) Jones et al. (1959) Lawson and Garst (1976) Lee et al. (1974) Lee et al. (1975) Lee et al. (1976a) Lee et al. (1976b) Lee et al. (1976~) Leibush and Shneerson (1950) Maddox et al. (1987) Mason and Dodge (1936) Muhlbauer & Monaghan (1957) Nasir and Mather (1977a) Nasir and Mather (1977b) Riegger et al. (1944) Shen and Li (1992) overall
co2
no. data 23 38 87 76 50 80 90 150
H2S mean 1.168 0.689 0.722 0.995 1.257 1.699 0.922 1.535
U
no. data
mean
U
0.452 0.101 0.140 0.362 0.485 0.511 0.258 0.513
50
102 35 45 82
0.658 0.674 0.627 1.089 1.677
0.209 0.21 0.198 0.323 1.014
40 13
1.153 0.862
0.472 0.201
84 30 17 189
1.004 1.611 0.729 0.720
0.186 0.366 0.233 0.131
132 218 4 49 71 83 30
1.332 0.993 0.909 0.843 0.667 1.136 1.235 0.893
0.529 0.304 0.262 0.316 0.224 0.519 0.330 0.275
61
1.091
0.476
950
1.063
0.452
966
1.011
0.464
21
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'
L
106
Calculated Partial Pressure H,S (Pa)
107
z
B N
8E
105
VI
e!
-
LL
;
0
103
.-
i I 10'
1 o3
10'
107
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105
t
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e i
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' . ' " ""' t""' S h n 8 Li (1992) Nasir & Malher (1977a) Muhlbauer 8 Monaghan(1957) Mason 8 Dodpe (1936) Maddox et al. (1987)
"'I
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I
.e'
0 I
n
eo-
I"
'
Calculated Partial Pressure CO, (Pa)
0
l o
"' 103
Calculated Partial Pressure H,S (Pa)
Nasir & Malhr (r9Tla) MUMbauer & Monaghan(1957)
'
102
104
106
tN
1001 100
I
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1 02
' " ' I
'
I
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'
1 o4
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' " J
106
Calculated Partial Pressure H,S (Pa) Calculated Partial Pressure CO, (Pa)
Figure 1. (a, top-e, bottom) Parity plots for H2S-MEA data.
Figure 2. (a, top-c, bottom) Parity plots for COrMEA data.
and the mean is almost invariably somewhat greater than unity, a fact that is evident from examining the overall statistics for each of the four amines (Tables V, VIII, XI, and XIV). When lookingat means on an author-by-author basis, they should be compared with the overall average for the particular acid-gas-amine pair. From Table V it can be seen that the data of Jones et al. (19591, Isaacs et al. (19801, and Riegger et al. (1944) lie more than two standard deviations below the mean for the H2S-MEA data as a whole and that the COz data of these authors are
only slightly less than two standard deviations from the mean. Interestingly, nearly 30% of the Isaacs data were already rejected before the model was regressed. The rest of the data shown in Table V are of varying quality, as measured by the standard deviation for each data set. For example, the data of Lee et al. (1975) exhibit quite a bit more scatter than most, especially considering that over 40% of the original data had already been rejected prior to the fitting.
1426 Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 Table VI. Sources of DEA Data total reference points Atwood et al. (1957) 15 Fries and Newman (1991) 28 Ho and Eguren (1988) 55 Kennard and Meisen (1984) 156 172 Lal et al. (1985) Lawson and Garst (1976) 381 Lee et al. (1973a) 107 Lee et al. (1973b) 119 227 Lee et al. (1974) Leibush and Shneerson (1950) 58 Maddox et al. (1987) 27 Mason and Dodge (1936) 68
points used 14 20 36 141 158 329 78 104 214 58 26 66
1413
1244
total
Lee et al. (1974) Lee et ai (1 973b)
comments HzS only HzS only mixed gas C02 only mixed gas mixed gas mixed gas HzS only mixed gas mixed gas C02 only COz only
Lee et al (1973a) Ho & Eguren (1988) Fries & Newman (1991) Atwood et al (1957)
-I
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0
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IV
Table VII. Interaction Parameter Values for DEA AmH+-HS27.1859 AmH+-HC037.0973 AmH+-C03" 0.4542 AmH+-AmCOO2.7478 Am-HS-21.2732 h-HCO30.6493 Am-AmCOO-1.6789 Am-Am 4.3115
N
1 o3
10'
105
10'
Calculated Partial pressure H,S (Pa)
.
0
-
DEA Data Data sources, the total number of measurements, the number of measurements falling within the acceptance criterion, and comments on the type of data are shown in Table VI. Interaction parameter values are given in Table VII, regression statistics are shown in Table VIII, and calculated partial pressures are shown plotted against measured values in Figure 3 for HzS and Figure 4 for COZfor all the data. The HzSdata of Lal et al. (1985)appear to be sufficiently far removed from the totality (more than two standard deviations below the mean of all the H2S-DEA data) to justify removal. However, the standard deviation for these data is extremely low (indicating a rather high degree of precision in the measurements), lending a note of caution to such a recommendation. The data of Kennard and Meisen (1984) are also considerably below the mean for the COpDEA data. This may be because their measurements were taken at much higher temperatures than others, from 100 to 205 "C, with 77% of the data at 120 "C and above, i.e., at temperatures well above those normally encountered in solution regenerators and outside the range of the data to which some of the equilibrium constants have been fitted (see Table I). However, apart from a few measurements that deviate markedly from the
.
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. ...,
,...
.
.
Leibush & Shneerson (1950) Lawson & Garst (1976) La1 et al. (1985)
I
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DGA Data Data sources, the total number of measurements, the
Table VIII. Numbers of Data Points Fitted, Mean Values of Measured:Fitted Partial Pressure Ratios, and Their Standard Deviations for DEA data source Atwood et al. (1957) Fries and Newman (1991) Ho and Eguren (1988) Kennard and Meisen (1984) Lal et al. (1985) Lawson and Garst (1976) Lee et al. (1973a) Lee et al. (1973b) Lee et al. (1974) Leibush and Shneerson (1950) Maddox et al. (1987) Mason and Dodge (1936) overall
coz
no. data 14 20 16
HzS mean 1.324 1.626 1.237
0.899 0.676 0.381
116 264 77 104 210 58
0.693 0.974 1.371 1.413 1.233 1.015
879
1.117
no. data
mean
0
0.166 0.460 0.547 0.427 0.386 0.292
37 141 129 154 59 59 214 14 26 66
0.683 0.631 0.932 0.984 1.588 1.420 0.949 1.394 0.778
0.366 0.294 0.259 0.498 0.559 0.765 0.475 0.317 0.374 0.227
0.491
897
1.088
0.551
0
1.662
Ind. Eng. Chem. Res., Vol. 32,No. 7,1993 1427 io7[
107
.....
.....
. . . . I
.....
-..,
....I
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Martin et al. (1978) Maddox el al. (1 987) Dingman et al. (1983)
Z $ e
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105
10''
10'
io5
103
1o7
Calculated Partial Pressure H,S (Pa)
Calculated Partial Pressure CO, (Pa)
Figure 5. Parity plot for H2S-DGA data. 108
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Mason & Dodge (1936) Maddox et al (1987) Leibush & Shneerson (1950) Lawson & Garst (1976) La1 et al (1985) Kennard 8 Meisen (1984)
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102
106
IO"
103 10''
Calculated Partial Pressure CO, (Pa)
1o3
IO'
1o5
to7
Calculated Partial Pressure CO, (Pa)
Figure 4. (a, top; b, bottom) Parity plots for C02-DEA data.
Figure 6. Parity plot for COrDGA data.
Table IX. Sources of DGA Data reference total points points used Dingmau et al. (1983) 192 160 109 102 Maddox et al. (1987) 84 84 Martin et al. (1978)
Table XI. Numbers of Data Points Fitted, Mean Values of MeasuredFitted Partial Pressure Ratios, and Their Standard Deviations for DGA
~
tQtal
385
comments mixedgas COzaudHzS COzaudHzS
346
Table X. Interaction Parameter Values for DGA 50.1535 AmH+-HS26.5206 AmH+-HCOs0.2658 AmH+-COa"1.3694 AmH+-AmCOO4.6081 Am-HS-0.7488 Am-HCOa-1.3599 Am-Amcoo-28.3608 Am-Am
number of measurementa falling within the acceptance criterion for fitting, and comments on the type of data are shown in Table IX. Interaction parameter values are given in Table X, regression statistics are listed in Table XI, and calculated partial pressures are shown plotted against measured values in Figures 5 and 6 for H2S and COz, respectively, for all the available data, both those used in the fitting and those excluded from it. The available DGA data appear to be all of roughly the same quality, and as can be seen from Figures 3 and 4,they cover a wide range of partial pressures (corresponding to solution loadings as
HzS coz no. no. data source data mean u data mean u Dingmanetal. (1983) 144 1.093 0.369 126 1.073 0.470 Maddoxetal. (1987) 62 0.885 0.423 40 1.100 0.380 Martinet al. (1978) 39 1.349 0.347 45 1.416 0.592 overall
245
1.138 0.467 211
Table XII. Sources of MDEA Data total reference points Chakma and Meisen (1987) 36 Ho and Eguren (1988) 33 Jou et al. (1982) 273 Jou et al. (1986) 193 74 Bhairi et al. (1984) 74 Maddox et al. (1987) MacGregor and Mather (1991) 32 Shen and Li (1992) 45 total
760
points used 35 19 204 174 69 74 32 34
1.150 0.477
comments COzonly mixedgas COzandHzS mixedgas COzandHzS COzandHzS HzSonly COzonly
641
low as 0.001 for H2S and 0.02 for C02). Unfortunately, only the data of Dingman et al. (1983) cover the low loadings and it would be useful for more data on DGA to be taken.
1428 Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 106:
'
'
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'
' " 8
" "
'
" ' 7
'
'
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' " I
'
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e MacGregor & Mather (1991) Jou et a1 (1982)
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32
MacGregor 8 Mather (1991) Jou et al. (1982) Ho 8 Eguren (1988) Chakma 8 Meisen (1987)
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106
Calculated Partial Pressure CO, (Pa) Calculated Partial Pressure H,S (Pa) ,n7
.
. . ...
.
. . ..
.
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. . . ..
. . ...
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.
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ai. (1984)
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103
'
105
'
10'
Calculated Partial Pressure CO, (Pa)
Figure 8. (a, top; b, bottom) parity plots for COzMDEA data.
AmH+-HZS AmH+-HSAmH+-C02 AmH+-HC03Am-HSAm-HC03-
h-cos" Am-Am
-26.1265 -58.6444 67.8732 -98.1594 -76.6213 -1.4492 185.5448 -82.8487
MDEA Data Data sources, the total number of measurements, the number of measurements falling within the acceptance criterion above, and comments on the type of data are shown in Table XII.
Interaction parameter values are given in Table XIII, statistical information relevant to each data set is provided in Table XIV, and calculated partial pressures are ehown plotted against measured values in Figure 7 for HzS and Figure 8 for COz for all the data available. With the exception of the smallamount of data provided by Ho and Eguren (1988) and Shen and Li (19921, all the MDEA data appear to be of good quality. We note, however, that about 25% of the data of Jou et al. (1982) were omitted from the regression because they deviated by more than a factor of 3 from the majority. A possible reason is that the MDEA used in that study was of unknown purity and it may have contained other amines coproduced during manufacture.
Table XIV. Numbers of Data Points Fitted, Mean Values of MeasuredFitted Partial Pressure Ratios, and Standard Deviations for MDEA data source Chakma and Meisen (1987) Ho and Eguren (1988) Jou et al. (1982) Jou et al. (1986) Bhairi et al. (1984) Maddox et al. (1987) MacGregor and Mather (1991) Shen and Li (1992) overall
no. data
17 128
HzS mean
coz (I
30 16 27
1.770 0.820 1.091 1.001 0.970 0.757
0.663 0.221 0.296 0.291 0.112 0.165
360
0.958
0.290
155
no. data 36 25 95 141 44 54 5 45
mean 1.074 1.529 1.207 1.156 1.098 1.115 1.394 0.852
0.259 0.740 0.539 0.412 0.283 0.364 0.387 0.646
398
1.088
0.369
a
Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 1429 Concluding Remarks The Deshmukh-Mather model has been fitted to all public-domain data on the solubility of H2S and CO2 in aqueous solutions of MEA, DEA, DGA, and MDEA. An unconstrained minimization procedure was used to minimize an unbiased measure of the discrepancy between the model and the data. The data themselves span a wide range of temperatures, amine concentrations, and solution loadings. The interaction parameters found here provide a unified basis for doing vapor-liquid equilibrium calculations using a computationally-affordable, thermodynamically-sound model. The Deshmukh-Mather model provided a sound approach to the preliminary screening of data so that the final values of the interaction parameters we have reported probably give as accurate a representation of the data as one is likely to achieve. This model also provides a good basis for extrapolation outside the range of existing data in those rare instances when such is necessary. It would appear from our analysis that, with the possible exception of DGA, there is little or nothing to be gained from the taking of further data on the solubility of H2S and C02 in these amines, even a t low solution loadings-for MEA, DEA, and MDEA there is already a large quantity of reliable data at low loadings. Admittedly, the low loading data exhibit more scatter; however, we feel that the preliminary screening performed on each data set has weeded out badly errant measurements, leaving the large core of high-quality data used in the final fit. For DGA, some benefit might accrue from making further measurements at low loadings and at the higher temperatures encountered in gas-treating applications using this solvent. Acknowledgment This work was supported in part by the Gas Research Institute (Howard Meyer, Project Manager, Chicago, IL) under subcontract to Fluor Daniel, Inc., and by Dow Chemical U.S.A. T.C. gratefully acknowledges the f i a n cial support of a Dow Chemical Fellowship. The authors thank Fluor Daniel, Inc., for permission to publish. The objective function for minimization was suggested by Dr. Stephen C. Smelser, Fluor Daniel, Inc., Irvine, CA.
Greek Symbols &j = parameter for the interaction of species i with species j W-l, kg/gmol) y = activity coefficient 4 = fugacity coefficient Subscripts
Am = amine AmH+ = protonated amine AmCOO- = carbamate of the amine w = water Superscripts O = total in all forms calc = value calculated by model meas = experimentally measured value sat = saturation value
Literature Cited Ananthaswamy, J.; Atkinson, G. Thermodynamics of Concentrated Electrolyte Mixtures. 4. Pitzer-Debye-HBckel Limiting Slopes for Water from 0 to 100 "C and from 1 Atmosphere to 1 kbar. J. Chem. Eng. Data 1984,29,81-87. Antelo, J. M.; Arce, F.; Casado, J.; Sastre, A.; Varela, J. Protonation Constants of Mono-, Di-, and Triethanolamine. Influence of Ionic Composition of the Mixture. J.Chem. Eng. Data 1984,29,10-11. Atwood, K.; Arnold, M. R.; Kindrick, R. C. Equilibria for the System Ethanolamine-Hydrogen SulfidsWater. Znd. Eng. Chem. 1957, 49 (9), 1439-1444.
Austgen, D. M. A Model for Vapor-Liquid Equilibria for Acid GasAlkanolamine-Water Systems. Ph.D. Thesis, University of Texas at Austin, Austin, TX, 1989. Auatgen, D. M. Private communication, 1990. Barbero, J. A.; McCurdy, K. G.; Tremaine, P. R. Apparent Molal Heat Capacities and Volumes of Aqueous Hydrogen Sulfide and Sodium Hydrogen Sulfide near 25 "C; the Temperature Dependence of HzS Ionization. Can. J. Chem. 1982,80, 1872-1880. Barth, D.; Tondre, C.; Lappai, G.; Delpuech, J. J. Kinetic study of Carbon Dioxide Reaction with Tertiary Amines in Aqueous Solutions. J. Phys. Chem. 1981,85, 3660-3667. Bates, R. G.; Pinching, G. D. Acidic Dimxiation Constant and Related Thermodynamic Quantities for Monoethanolammonium Ion in Water from 0 OC to 50 "C. J. Res. Natl. Bur. Stand. 1951,46, 349-352.
Bhairi, A.; Mains, G. J.; Maddox, R. N. Experimental Measurements of Equilibrium between COa or HzS and Ethanolamine Solutions. Paper Presented at AIChE National Meeting, Atlanta, GA, March 11-14,1984.
Nomenclature a = activity, ionic size (A) in eq
15, or constant (K)in eq 17 A, = Debye-Htickel limiting slope in eq 15 Am = amine b = constant in eq 17 B = function of temperature in eq 15 c = constant in eq 17 d = constant in eq 17 e = constant in eq 17 Fi = discrepancy of the ith measurement Fobj = objective function H = Henry's law constant (Pa/mole fraction) I = ionic strength (m) K = equilibrium constant (various units but based on kmol/
L)
m = molality (kmovkg) p = partial pressure (Pa) P = total pressure (Pa) Ct= saturation pressure of water (Pa) R = universal gas constant T = absolute temperature (K) 0 = partial molar volume y = vapor-phase mole fraction zi = absolute charge of ith ionic species
Bower, V. E.; Robinson, R. A.; Bates, R. G. Acidic Dissociation Constant and Related Thermodynamic Quantities for Diethanolammonium Ion in Water from 0 "C to 50 "C. J. Res. Natl. Bur. Stand. 1962, 66A, 71-75. Bransted, J. N. Studies on Solubility. IV. Principle of Specific Interaction of Ions. J. Am. Chem. SOC.1922,44, 877-898. Butler, J. N. Ionic Equilibrium; Addison-Wesley: Boston, MA, 1964. Chakma, A.; Meisen, A. Solubility of COz in Aqueous Methyldiethanolamine and Nfl-Bis(hydroryethy1)piperazine Solutions. Ind. Eng. Chem. Res. 1987,26, 2461-2466. Chakravarty, T. Solubility Calculations for Acid Gases in Amine Blends. Ph.D. Thesis, Clarkson University, Potsdam, NY, 1985. Chen, C. C.; Evans, L. B. A Local Composition Model for the Excess Gibbs Energy of Aqueous Electrolyte Systems. AIChE J. 1986, 32,444-454.
Cuta, F.; Strafelda, F. The Second Dissociation Constant of Carbonic Acid between 60 and 90". Chem. Listy 1954,48, 1308-1313. Davidon, W. C. Variable Metric Method for Minimization. AEC Res. Dev. Rep. December 1959, ANL-5990. Debye, P.; Htickel, E. The Theory of Electrolytes. I. Lowering of Freezing Point and Related Phenomena. Phys. 2.1923,24,185206.
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, 355-362.
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Received for review August 26, 1992 Revised manuscript receiued February 19, 1993 Accepted March 18, 1993
