SAFT prediction of vapour-liquid equilibria of mixtures containing carbon dioxide and aqueous monoethanolamine or diethanolamine

Fluid Phase Equilibria 158–160 Ž1999. 175–181

SAFT prediction of vapour-liquid equilibria of mixtures containing carbon dioxide and aqueous monoethanolamine or diethanolamine J.K. Button a , K.E. Gubbins

b, )

a

b

School of Chemical Engineering, Cornell UniÕersity, Ithaca, NY, 14583, USA Department of Chemical Engineering, North Carolina State UniÕersity, 113 Riddick Laboratories, Raleigh, NC, 27695-7905, USA Received 31 March 1998; accepted 1 February 1999

Abstract We extend the Statistical Associating Fluid Theory, SAFT, to vapour-liquid equilibria of fluid mixtures in which all components hydrogen bond. We refit parameters for carbon dioxide and water to obtain better agreement with experiment, and more consistency with parameters for other associating molecules. For monoethanolamine and diethanolamine, we obtain deviations in the individual mole fractions of 1 to 2% between the SAFT predictions and the smoothed experimental data. For aqueous mixtures we determine values of the single temperature-independent binary parameters, and then use these parameters to predict phase equilibria of ternary aqueous mixtures of monoethanolamine or diethanolamine with carbon dioxide. Our results deviate an average of 0.01 in mole fraction units from the experimental mole fractions. The SAFT equation slightly overpredicts the amount of alkanolamine, and underpredicts the amount of carbon dioxide in the liquid mixture. Small deviations in the liquid mole fraction produce large deviations in the carbon dioxide loading ratio, the ratio of moles of carbon dioxide to moles of alkanolamine in the liquid, giving average deviations of 43%. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Vapour-liquid equilibrium; Hydrogen bonding; Alkanolamine; Carbon dioxide; SAFT equation of state

1. Introduction The Statistical Associating Fluid Theory Ž SAFT. equation of state w1,2x is a molecular based equation that is designed to account for effects of molecular association Ž H-bonding, charge transfer, etc.. and chain flexibility, in addition to the more usual effects due to repulsive and dispersion interactions. The equation is expressed as the sum of contributions to the free energy Ž or, equivalently, )

Corresponding author. Tel.: q1-919-513-2262; fax: q1-919-515-3465; e-mail: [email protected]

0378-3812r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 Ž 9 9 . 0 0 1 5 0 - 8

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J.K. Button, K.E. Gubbinsr Fluid Phase Equilibria 158–160 (1999) 175–181

contributions to the pressure. from repulsionrdispersion, chain formation and association. The association and chain contribution terms are based on a theory due to Wertheim w3x. Since the equation has a rigorous statistical mechanical basis, it is possible to test it for various model interaction potentials against molecular simulations. Such comparisons have shown the equation to be accurate for a variety of molecular types, including polar, associating and chain molecules w4x. Huang and Radosz w5x showed successful applications of the equation to a wide range of pure and mixed fluids in which association occurred, and since then a large number of successful applications have been reported; work up to 1996 has been reviewed w4x. Several modifications to the original theory have been proposed and have been discussed elsewhere w4x. In this paper we apply SAFT in its original form w5,6x to study alkanolamines and their mixtures with water and carbon dioxide. Chains of hard spheres are used to describe the molecular shape, with off-centre square well sites to mimic the association centres in each molecule. For associating pure fluids there are 5 adjustable parameters. For binary mixtures one unlike-pair energy parameter is fitted; this parameter is independent of temperature. Without any further fitting, the equation of state uses these parameters to predict ternary phase equilibria. Unlike some other theories of associating fluids, the SAFT equation of state is not restricted in the number of association sites per molecule, nor does it require knowledge of chemical reaction equations and temperature-dependent equilibrium constants.

2. Potential models and parameters 2.1. Pure components The first step in the application of the SAFT equation of state to multicomponent mixtures is the determination of pure component parameters. The first parameter is the number of hard spheres m that form a molecule. This is treated as an adjustable parameter, and need not have an integer value. The volume of a mole of these spheres when closely packed, Õ 00 , the second parameter, sets their size. Although Huang and Radosz w5x allowed Õ 00 to vary in their application of the SAFT equation of state to a large variety of pure components, we do not adjust Õ 00 , setting it to 12.0 for all components. The third pure-component parameter is the segment energy, u 0 , which determines segment–segment interactions. Off-centre square-well association sites are used to represent the short-ranged, highly directional nature of hydrogen bonds. Two parameters, ´ and k , the square-well depth and width, determine the hydrogen bonding strength and the association contribution to the residual Helmholtz free energy. Huang and Radosz w5,6x fit SAFT parameters for carbon dioxide without any hydrogen bonding sites. However, carbon dioxide has a strong quadrupole moment and forms a complex with alkanolamines. We have refit carbon dioxide to the same experimental points from Vargaftik w7x, adding four association sites. For water we also use four association sites, one for each hydrogen and for each of the lone pair of electrons on oxygen. Since Huang and Radosz w5x used three association sites, we refit parameters to the same experimental points from Vargaftik w7x. We made two additional changes to the pure-component parameters for carbon dioxide and water for greater consistency with other associating fluids. We set the volume of the hard spheres to 12.0 mlrmole instead of 10.0 mlrmole, and for carbon dioxide

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we used 10 instead of 40 for e which controls the temperature behaviour of segment–segment interactions w5x. The pure-component data for the two alkanolamines, monoethanolamine and diethanolamine, are smoothed and extrapolated data regressed from a number of experimental sources w8x. Since these alkanolamines have either one or two alcohol functional groups as well as an amine functional group, they form many different hydrogen bonds as pure fluids and in multicomponent mixtures. Instead of assigning different association parameters to bonds formed by nitrogen atoms than to those formed by oxygen atoms, which would be in keeping with the known differences in these bond strengths, we use one set of hydrogen bonding parameters for each alkanolamine with a single association site for the two sets of lone pairs on oxygen. We adopt these simplifications in this work to limit the number of adjustable parameters. 2.2. Binary mixtures We fit a single temperature-independent binary parameter over a range of temperatures to minimize deviations of the calculated mole fractions from experimental points. The binary parameter determines the segment–segment interactions of unlike molecules. Each of these binary mixtures contains two components which self-associate, that is form intermolecular hydrogen bonds between like pair molecules. Combining two self-associating fluids produces cross-association’s; new H-bonds between unlike molecules. We expect the cross-associations to differ in strength from the self-associations of the pure components. In order to keep the number of adjustable parameters small, we simplify these interactions by assuming the cross-association parameters to be the geometric means of the association parameters for each of the pure components.

3. Results 3.1. Pure fluids The parameter values and average absolute deviations for predicted pressure and molar liquid volume for the four pure fluids are summarized in Table 1. For carbon dioxide, the average absolute deviations of 0.8 and 0.6% for the pressure and molar liquid volume, respectively are significantly better than those obtained by Huang and Radosz w5x, which were 2.8 and 0.9%. The association

Table 1 Pure fluid potential parameters and average absolute deviations in the predicted vapour pressure Ž P . and saturated molar liquid volumes ŽLV. Pure fluid

Sites

m

u 0 rK

´ rK

k

T rK

D Pr%

DLVr%

Carbon dioxide Water Monoethanolamine Diethanolamine

4 4 5 6

1.650 1.047 3.000 4.699

196.7 504.4 307.1 268.0

657.4 1365.0 1556.1 1762.6

0.00925 0.02408 0.02664 0.05553

220–290 303–613 310–630 350–570

0.8 1.2 1.3 1.9

0.6 3.6 1.2 1.0

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Table 2 Binary parameters, k i j , showing temperatures and pressures used in fitting, together with average absolute deviations in liquid mole fraction, D x Binary mixture

ki j

T rK

PrMPa

Dx

Water–carbon dioxide Monoethanolamine–water Diethanolamine–water

y0.24 y0.09 y0.08

423, 473, 523 333, 351, 364 373, 473

10.0 0.0002–0.0691 0.08–1.52

0.001 0.02 0.03

parameters for carbon dioxide are smaller than those for water and the alkanolamines, as would be expected since the quadrupole interaction is not as strong as a hydrogen bond. For water, despite the changes we have made to the model, we obtain very similar results to those of Huang and Radosz. The monethanolamine and diethanolamine molecules are larger than carbon dioxide and water, and so have correspondingly larger values for the number of hard sphere segments m. Since alkanolamines as a class of molecules have high boiling points, we also expect them to have strong hydrogen bonds, and therefore higher values of the association parameters ´ and k than for carbon dioxide and water. 3.2. Binary mixtures We consider three binary mixtures, aqueous carbon dioxide and two aqueous alkanolamines. Data for carbon dioxide–water come from Takenouchi and Kennedy w9x, for water–monoethanolmine from Nath and Bender w10x, and for diethanolamine–water from Wilding et al. w11x. Calculations were performed by carrying out an isothermal, isobaric flash calculation, using an iterative Rachford–Rice Newton–Raphson algorithm which converges to give liquid and vapour mole fractions. The SAFT equation of state calculates residual Helmholtz free energies and therefore fugacity coefficients, which give the vapour fractions used in the Rachford–Rice algorithm.

Fig. 1. SAFT calculations Žsolid lines. for the binary water–monoethanolamine mixture showing agreement with experimental points at three temperatures, 333 K Žcrosses., 351 K Žtriangles., and 364 K Ždiamonds..

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Table 3 Results for alkanolamine–water–carbon dioxide mixtures, showing average absolute deviations in the liquid mole fractions for alkanolamine ŽA., water ŽW. and carbon dioxide ŽC. Ternary mixture

PrMPa

T rK

Dx A

Dx W

Dx C

Monoethanolamine–H 2 O–CO 2 Ethanolamine–H 2 O–CO 2

2.2 6.8

353–413 393–413

0.006 0.006

0.010 0.013

0.009 0.020

The binary parameters for the mixtures studied, and the corresponding average absolute deviations in the mole fraction are shown in Table 2. Results for the binary mixture monoethanolamine–water are shown in Fig. 1 for a range of temperatures and mole fractions. Similar results are obtained for the other two binary mixtures. 3.3. Ternary mixtures The data for alkanolamine–water–carbon dioxide mixtures is taken from Lee et al. w12,13x. We have converted the data, which is in the form of alkanolamine molarity, and ratio of moles of carbon dioxide to moles of alkanolamine in the liquid, to liquid mole fractions for the three components. For the data studied, the liquid is almost entirely water and the vapour almost entirely carbon dioxide. Using the binary results and no new adjustable parameters, we have predicted liquid mole fractions for the ternary mixtures, as shown in Table 3. Since we did not fit the binary carbon dioxide–alkanolamine mixtures, we have set those binary energy parameters equal to the geometric mean of the like pair values. The pure and binary parameters for the SAFT equation of state as we have fitted them result in alkanolamine liquid mole fractions that are consistently higher, and carbon dioxide

Fig. 2. Deviation of calculated from experimental liquid mole fractions for monoethanolamine Žasterisks. and carbon dioxide Žsquares. in the ternary aqueous mixture at a carbon dioxide partial pressure of 2.2 MPa and temperatures ranging from 353 to 413 K.

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liquid mole fractions that are generally lower than the experimental liquid mole fractions. The fit is similar to that for the binary water–alkanolamine mixtures, with similar liquid mole fraction deviations. However, the results for carbon dioxide loading, the ratio of liquid moles of carbon dioxide to moles of alkanolamine, are sensitive to small errors in the predicted mole fractions, and deviate as much as 87% from the experimental points. As an average, the carbon dioxide loading for the monoethanolamine mixture is 62% too low, and for the diethanolamine mixture it is 24% too low. Our results for liquid mole fractions of alkanolamine and carbon dioxide in the monethanolamine ternary mixtures are shown in Fig. 2.

4. Conclusions We have developed approximate molecular models for use in the SAFT equation of state for monoethanolamine and diethanolamine, obtaining results that agree with experimental vapour-liquid equilibria to within a few percent, as well as improved parameter values for carbon dioxide and water. We have extended SAFT to cover cross-associating mixtures, and find good agreement for three binary aqueous mixtures. Our ternary predictions for carbon dioxide in aqueous monoethanolamine or diethanolamine are similarly good with respect to deviation of predicted liquid mole fraction from experimental points, but small deviations in these mole fractions lead to large deviations of our calculated carbon dioxide loading ratios from experimental values.

5. List of symbols ki j m P T ui j Dx ´ k Õ 00

binary parameter number of hard-sphere segments in a molecule pressure, MPa temperature, K segment energy, K deviation in liquid mole fraction depth of square-well association site, K width of square-well association site, fraction of hard-sphere volume volume of mole of hard-sphere segments, mlrmole

Acknowledgements It is a pleasure to thank M. Radosz for sending data on alkanolamines and for helpful discussions. We are grateful to the U.S. Department of Energy for support of this work through grant no. DE-FG02-98ER14847.

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