Rigorous Modeling of the Acid Gas Heat of Absorption in

2044

Energy & Fuels 2007, 21, 2044-2055

Rigorous Modeling of the Acid Gas Heat of Absorption in Alkanolamine Solutions Emilie Blanchon le Bouhelec,† Pascal Mougin,*,† Alain Barreau,† and Roland Solimando‡ De´ partement Thermodynamique et Mode´ lisation Mole´ culaire, Institut Franç ais du Pe´ trole, 1 et 4 aVenue de Bois Pre´ au, 92850 Rueil-Malmaison Cedex, France, and Laboratoire de Thermodynamique des Milieux Polyphase´ s, Nancy UniVersite´ s, INPL-ENSIC, 1 rue GrandVille, 54000 Nancy, France ReceiVed NoVember 14, 2006. ReVised Manuscript ReceiVed March 14, 2007

In this work, we are interested in the estimation of CO2 and H2S heats of absorption in aqueous solutions of alkanolamine: monoethanolamine (MEA), diethanolamine (DEA), and methyldiethanolamine (MDEA). Two methods can be used to calculate the heat release during the absorption phenomenon. The easier which consists of applying the integration of the Gibbs-Helmholtz expression remains inaccurate. The second one, more rigorous, evaluates the heat transfer through an internal energy balance for an open system. The balance expression contains partial molar enthalpies of species in the liquid phase which are calculated from the electrolyte nonrandom-two-liquid (NRTL) excess Gibbs energy model. The calculations carried out in this method can be considered as predictive regarding the NRTL model because its interaction parameters were previously and solely fitted on vapor-liquid equilibrium (VLE) data and not on experimental heat of absorption data. The comparison between both methods and experimental data for the three alkanolamines shows the contribution of this rigorous calculation to better estimate both properties (i.e., solubility and heat) and its usefulness to improve processes. Heats of absorption calculated with the second method can be used in addition to VLE data to fit NRTL parameters. This procedure leads to less-correlated parameters and allows extrapolating the model with more confidence.

Introduction At its extraction, natural gas contains carbon dioxide and hydrogen sulfide that must be removed. Today’s processes are mainly based on chemical absorption of acid gases by aqueous solutions of alkanolamines.1 Both acid gases are weak electrolytes and they partially dissociate in the aqueous phase to form a complex mixture of molecular and ionic species. In a closed system at constant temperature and pressure, physical equilibrium governs the distribution of molecular species between the liquid phase and the vapor phase. Simultaneously, in the liquid phase, alkanolamine reacts with CO2 and H2S, either through acid-base buffer mechanisms or through a direct reaction of CO2 with primary or secondary alkanolamine to produce ionic species (Appendix A): physical and chemical equilibrium are highly coupled. Representation of the vapor-liquid equilibrium (VLE) behavior of acid gas-alkanolamine-water systems is made complex by the large number of chemical reactions which occur in the system. It requires that both physical and chemical equilibria be accounted for in a thermodynamically rigorous way. Many studies can be assessed in the literature concerning the VLE representation of acid gas-alkanolamine-water systems: the practical but limited model2 or a more rigorous approach.3 More sophisticated models can be used for wider * To whom correspondence concerning this article should be addressed. E-mail: [email protected]. † Institut Franc ¸ ais du Pe´trole. ‡ Nancy Universite ´ s. (1) Astarita, G.; Savage, D. W.; Bisio, A. Gas treating with chemical solVents; Wiley: New York, 1983. (2) Kent, R.; Eisenberg, B. Better data from amine treating. Hydrocarbon Process. 1976, 55, 87-90.

ranges of temperature, pressure, and acid gas loading (Rag ) mole of acid gas per mole of alkanolamine in the liquid phase) than correlative models: the heterogeneous approach4 or the electrolyte equation of state.5 VLE studies cannot be used alone for engineering applications such as design and simulation of industrial acid gas removal units. The heat of absorption, which governs the temperature profile in the absorber and in the regenerator, can be also taken into account. Indeed, from an economic point of view, reasonable even accurate estimates of this quantity might save energy, especially during the regeneration of the loaded solvent.6 There are numerous new studies on experimental data of acid gas solubility over various solutions of alkanolamine7-10 and on their modeling.11-13 Only few works are related to the heat of absorption measurements and modeling. (3) Desmukh, R. D.; Mather, A. E. A mathematical model for equilibrium solubility of hydrogen sulphide and carbon dioxide in aqueous alkanolamine solutions. Chem. Eng. Sci. 1981, 36, 355-362. (4) Austgen, D. M. A model of vapor-liquid equilibria for acid gasalkanolamine-water systems. Ph.D. Thesis, The University of Texas, Austin, TX, 1989. (5) Chunxi, L.; Fu¨rst, W. Representation of CO2 and H2S solubility in aqueous MDEA solutions using an Electrolyte equation of state. Chem. Eng. Sci. 2000, 55, 2975-2988. (6) Sakwattanapong, R.; Aroonwilas, A.; Veawab, A. Behavior of reboiler heat duty for CO2 capture plants using regenerable single and blended alkanolamines. Ind. Eng. Chem. Res. 2005, 44, 4465-4473. (7) Pe´rez-Salado Kamps, A.; Balaban, A.; Jo¨decke, M.; Kuranov, G.; Smirnova, N. A.; Maurer, G. Solubility of single gases carbon dioxide and hydrogen sulfide in aqueous solutions of methyldiethanolamine at temperatures from 313 to 393 K and pressures up to 7.6 MPa: new experimental data and model extension. Ind. Eng. Chem. Res. 2001, 40, 696-706. (8) Sidi-Boumedine, R.; Horstmann, S.; Fischer, K.; Provost, E.; Fu¨rst, W.; Gmehling, J. Experimental determination of carbon dioxide solubility data in aqueous alkanolamine solutions. Fluid Phase Equilib. 2004, 218, 85-94.

10.1021/ef0605706 CCC: $37.00 © 2007 American Chemical Society Published on Web 05/17/2007

Alkanolamine Solution Acid Gas Heat of Absorption

Two methods can be used to measure the experimental data of heat of absorption. Batch calorimetry consists of introducing an amount of acid gas in the solvent and measuring heat release due to this adding. Flow calorimetry consists in feeding simultaneously but separately into the calorimeter both materials (acid gas and solvent) at flow rates required to obtain the desired acid gas loading and then measuring the heat release when steady state is reached. Most measurements assessed in literature were determined by flow calorimetry14-16 except those of Carson et al.17 The standard deviation of their experimental results is about 5%. Concerning the modeling part, most of refs 16 and 18-20 come from a correlative approach. They applied the Gibbs-Helmholtz relation which consists of differentiating acid gas partial pressure with respect to temperature for aqueous solutions of alkanolamine (diethanolamine (DEA) or methyldiethanolamine (MDEA)) loaded with H2S or CO2. Although it has been shown that it was an approximate form,21 this method remains widely used for acid gas + alkanolamine reacting systems. Lee22 developed a method to calculate simultaneously species concentration profiles and heat of absorption where MSA theory was combined with the UNIFAC model. The computational method was not detailed, but calculations led to the conclusion that the heat of reaction dominated the total heat effects. In the paper of Oscarson et al.,15 the heat of absorption is obtained by subtracting the enthalpy of the reactant stream from the enthalpy of the product stream and partial molar enthalpies (9) Sidi-Boumedine, R.; Horstmann, S.; Fischer, K.; Provost, E.; Fu¨rst, W.; Gmehling, J. Experimental determination of hydrogen sulfide solubility data in aqueous alkanolamine solutions. Fluid Phase Equilib. 2004, 218, 149-155. (10) Ma’mun, S.; Nilsen, R.; Svendsen, H. F. Solubility of carbon dioxide in 30 mass % monoethanolamine and 50 mass % methyldiethanolamine solutions. J. Chem. Eng. Data 2005, 50, 630-634. (11) Park, S. H.; Lee, K. B.; Hyun, J. C.; Kim, S. H. Correlation and prediction of the solubility of carbon dioxide in aqueous alkanolamine and mixed alkanolamine solutions. Ind. Eng. Chem. Res. 2002, 41, 1658-1665. (12) Sidi-Boumedine, R. Etude des syste`mes gaz acide/alcanolamine/ eau: mesures coupleés de composition de la phase liquide et de solubilite´. Ph.D. Thesis, Ecole des Mines de Paris, Paris, France, 2003. (13) Vrachnos, A.; Voutsas, E.; Magoulas, K.; Lygeros, A. Thermodynamics of acid gas-MDEA-water systems. Ind. Eng. Chem. Res. 2004, 43, 2798-2804. (14) Van Dam, R.; Christensen, J.J.; Izatt, R.M.; Oscarson, J.L. GPA Project 821, Enthalpies of solution of H2S in aqueous diethanolamine solutions; report no. 114, Gas Processors Association, May 1988. (15) Oscarson, J. L.; Chen, X.; Izatt, R. M. GPA Project 821, A thermodynamically consistent model for the prediction of solubilities and enthalpies of solution of acid gases in aqueous alkanolamine solutions; report no. 130, Gas Processors Association, August 1995. (16) Mathonat, C. Calorime´trie de me´lange, a` ećoulement, a` tempe´ratures et pressions e´leveés. Application a` l’e´tude de l’e´limination du dioxyde de carbone a` l’aide de solutions aqueuses d’alcanolamines. Ph.D. Thesis, Universite´ Blaise Pascal, Clermont-Ferrand, France, 1995. (17) Carson, J. K.; Marsh, K. N.; Mather, A. E. Enthalpy of solution of carbon dioxide in (water + monoethanolamine, or diethanolamine, or N-methyldiethanolamine) and (water + monoethanolamine + N-methyldiethanolamine) at T ) 298.15 K. J. Chem. Thermodyn. 2000, 32, 12851296. (18) Jou, F-Y.; Otto, F. D.; Mather, A. E. Vapor-liquid equilibrium of carbon dioxide in aqueous mixtures of monoethanolamine and methyldiethanolamine. Ind. Eng. Chem. Res. 1994, 33, 2002-2005. (19) Posey, M. L. Thermodynamic model for acid gas loaded aqueous alkanolamine solutions. Ph.D. Thesis, The University of Texas, Austin, TX, 1996. (20) Gabrielsen, J.; Michelsen, M. L.; Stenby, E. H.; Kontogeorgis, G. M. A model for estimating CO2 solubility in aqueous alkanolamines. Ind. Eng. Chem. Res. 2005, 44, 3348-3354. (21) Sherwood, A. E.; Prausnitz, J. M. The heat of solution of gases at high pressure. AIChE J. 1962, 8, 519-521. (22) Lee, L. L. Thermodynamic modeling of acid gas treating systems and industrial applications. Proceedings of the 2001 Laurence Reid Gas Conditioning Conference, Norman, OK, 2001; pp 371-395.

Energy & Fuels, Vol. 21, No. 4, 2007 2045

are calculated by differentiation of the Pitzer equation.23 A set of parameters was regressed by the authors on their own heat of absorption data for the following systems: CO2-DEA-H2O, CO2-MDEA-H2O, H2S-DEA-H2O, and H2S-MDEA-H2O. The thermodynamic model used in the present paper is a heterogeneous approach:24 the liquid phase is described by the electrolyte-nonrandom-two-liquid (NRTL) model, and the vapor phase is modeled by the Peng-Robinson25 equation of state. A reactive flash algorithm has been developed to calculate both acid gas partial pressures and liquid composition. The aim of the present work is to provide a thermodynamic model which can accurately predict both solubilities and heats of absorption over the ranges of temperature, pressure, and solvent composition of those found in the gas processing industry. ElectrolyteNRTL parameters were fitted solely on VLE data and then used to calculate the heats of absorption of CO2 or H2S in aqueous DEA, MDEA, and monoethanolamine (MEA) solutions. Calculation is performed according to two different methods: (1) using the Gibbs-Helmholtz relation and (2) using a rigorous balance. Both methods are compared with experimental data to check their validity. We also discuss the use of enthalpy data in addition to VLE data to improve the determination of electrolyte-NRTL parameters. Both methods named above are first detailed. Then, modeling results are shown and described. First Method: Heat of Absorption from Acid Gas Partial Pressure During the acid gas absorption phenomenon, the integral heat of absorption (∆Hint) at a loading R and at temperature T corresponds to the heat release due to the absorption of acid gas from a clean alkanolamine solution to an R-loaded solution. It is given by the following:

∆Hint(R,T) )

∫0R∆Hdiff(R′) dR′

1 R

(1)

∆Hdiff is the heat release during the change of acid gas loading dR′. It can be calculated from solubility data by application of the Gibbs-Helmholtz expression

( )

∂ ln Pag ∆Hdiff )1 R ∂ T

(2)

xag

in which Pag is the acid gas partial pressure and xag is its molar fraction in the liquid phase. Integral heats of absorption at the loading point are compared with experimental values. This requires acid gas partial pressures at any loading and temperature. Differentiations and integrations are carried out numerically. The first-order finite difference method is used for differentiation. For integration, the trapezium method and the Simpson method were tested separately. The calculation for a given acid gas loading is not direct as it always requires the calculation of heats of absorption at lower loadings. Although this approximate method is not accurate in the case of such (23) Edwards, T. J.; Maurer, G.; Newman, J.; Prausnitz, J. M. Vaporliquid equilibria in multicomponent aqueous solutions of volatile weak electrolytes. AIChE J. 1978, 24, 966-976. (24) Barreau, A.; Blanchon le Bouhelec, E.; Habchi Tounsi, K. N.; Mougin, P.; Lecomte, F. Absorption of H2S and CO2 in alkanolamine aqueous solution: experimental data and modeling with the ElectrolyteNRTL model. Oil Gas Sci. Technol. 2006, 61, 345-361. (25) Peng, D. Y.; Robinson, D. B. A new two-constant equation of state. Ind. Eng. Chem. Fundam. 1976, 15, 59-64.

2046 Energy & Fuels, Vol. 21, No. 4, 2007

Blanchon le Bouhelec et al.

systems, it can be easily implemented and is used by many authors.16,18-20 Second Method: Rigorous Internal Energy Balance The main purpose of this work is to develop a direct and rigorous calculation of the heat of absorption. This method consists of modeling a calorimetric experiment with internal energy balance which refers to a liquid-phase changing from an acid gas free liquid phase (initial state) to a final state where acid gas has been absorbed. Infinitesimal change of internal energy occurring during the process can be written as the following expression:

dU ) δQ + δW + hVag dn

(3)

Where, δQ and δW are respectively the elementary quantity of heat exchanged and the elementary work. The term dn is the elementary quantity of substance of acid gas transferred from the storage, and hVag is its molar enthalpy in the vapor phase. In our particular case, there is no mechanical work but heat is exchanged during the acid gas transfer and absorption. Assuming that pressure and temperature in the acid gas storage remain constant (i.e.,hVag is constant during the transfer) and introducing enthalpy, the integration of eq 3 leads to the following expression for the heat of absorption (Qabs):

Qabs ) HF - HI - (PFVF - PIVI) - hVag‚ntotal ag

(4)

ntotal ag

where is the total acid gas number of moles (ionic and molecular species) in the liquid phase. Total enthalpies HI and HF are calculated from partial molar enthalpies of all species respectively in the initial state (aqueous solution of alkanolamine) and in the final state (liquid phase containing water, alkanolamine, absorbed acid gas, and ionic species produced by acid gas reactions). P and V are the total pressure and volume in the final and initial states. Therefore, the final expression of heat of absorption per mole of acid gas is given by

Qabs ntotal ag

)

∑i

nFi

ntotal ag

hhFi

-

∑j

nIj

hhIj -

ntotal ag

1 ntotal ag

(PFVF - PIVI) - hVag (5)

where nFi and ntotal ag are calculated with our flash algorithm. The subscripts j and i denote species at the initial state and at final state, respectively. Each term of eq 5 is detailed in the following parts. Enthalpy in the Liquid Phase. The terms hhIi and hhFi are the partial molar enthalpies of the species i in the liquid phase at the initial state and final state, respectively. Their expressions are given by the following equation:

hhLi

)

hh#i

+

hhL,mixing i

(

#

)

∂µi (T,P)/RT ) -RT ∂T 2

-

P,ni

( )

RT2

∂ ln γ/i ∂T

P,ni

(6)

Here, hh#i is the partial molar enthalpy in the reference state and hhL,mixing is the mixing term. Also, µ#i (T,P) is the reference term i of chemical potential in the liquid phase:

µ#i (T,P) ) aT3 + bT2 + cT + d

(7)

The coefficients of eq 7 are detailed in Table 1. They are calculated from the literature26 when they are available and by considering the action mass balance laws of chemical reactions. As the chemical potentials are known with a reference state, we assume that alkanolamines have theirs potentials equal to zero. Details of the mathematical treatment can be found in our previous work.24 Carbamate equilibrium constants for MEA and for DEA are treated as constants determined from experimental data27-29 whereas they are often considered as adjustable parameters.4 MEACOO- and DEACOO- are the carbamate species related to MEA and DEA, respectively. MEAH+, DEAH+, and MDEAH+ are the protonated alkanolamines related to MEA, DEA, and MDEA, respectively. The partial molar enthalpy of mixing is calculated by differentiation of the natural logarithm of the activity coefficient of species i with respect to temperature. It depends on the thermodynamic model used to describe the liquid phase. In this work, we focus on the electrolyte-NRTL model which is a generalized excess Gibbs energy model that accounts for molecular/ionic interactions between all liquid-phase species.30,31 The model postulates that the excess Gibbs energy, expressed in unsymmetric convention regarding the reference state, gE*, is the sum of two contributions (water is the solvent): E* gE* ) gE* PDH + gNRTL

(8)

E* The first one, gPDH , is related to the long-range interactions between ions. They are described by the Pitzer-Debye-Hu¨ckel expression.32 The second contribution, gE* NRTL, is related to the short-range interactions between all the species. The NRTL theory33 is adopted to account for them. Details of the model can be found in the work of Chen et al.30 and Chen and Evans,31 and details of the equilibrium pressure calculation can be found in Barreau et al.24 The adjustable parameters of the model are the NRTL local interaction terms. Three types of adjustable interaction parameters, τij, are considered: molecule-molecule (τmm′, τm′m ), molecule-ion pair (τmca, τcam), and ion pair-ion pair with common cation or anion (τcaca′, τca′ca, τcac′a, τc′aca) where m represents a molecular species, a an anionic species, and c a cationic species. When no acid gases are present, this model reduces to the NRTL form. The acid gas-water parameters were taken from the work of Chen and Evans.31 Data from binary systems were

(26) Barner, H. E.; Scheurman, R. V. Handbook of thermochemical data for compounds and aqueous species; Wiley: New York, 1978. (27) Chan, H. M.; Danckwerts, P. V. Equilibrium of MEA and DEA with bicarbonate and carbamate. Chem. Eng. Sci. 1981, 36, 229-230. (28) Barth, D. Mećanismes des reáctions du gaz carbonique avec des amino-alcools en solutions aqueuses : e´tude cine´tique et thermodynamique. Ph.D. Thesis, Universite´ de Nancy I, Nancy, France, 1984. (29) Aroua, M. K.; Benamor, A.; Haji-Sulaiman, M. Z. Temperature dependency of the equilibrium constant for the formation carbamate from diethanolamine. J. Chem. Eng. Data 1997, 42, 692-696. (30) Chen, C. C.; Britt, H. I.; Boston, J. F.; Evans, L. B. Local composition model for excess Gibbs energy of electrolyte systems. AIChE J. 1982, 28, 588-596. (31) Chen, C. C.; Evans, L. B. A local composition model for the excess Gibbs energy of aqueous electrolyte systems. AIChE J. 1986, 32, 444454. (32) Pitzer, K. S. Electrolytes, From dilute solutions to fused salts. J. Am. Chem. Soc. 1980, 102, 2902-2906. (33) Renon, H.; Prausnitz, J. M. Local compositions in thermodynamic excess functions for liquid mixtures. AIChE J. 1968, 14, 135-144.



Table 1. Temperature Dependence Parameters of the Reference Term of Chemical Potential µ#i (kcal/mol) compound

a

b

c

d

temp range (K)

H2O alkanolamine CO2 H2S OHHCO3CO32 HSS2DEACOOMEACOODEAH+ MEAH+ MDEAH+

0 0 7.8941 × 10-8 -2.8613 × 10-8 3.4174 × 10-7 0 -1.0693 × 10-7 0 0 0 0 -1.1049 × 10-8 0 -1.9481 × 10-8

-1.13 × 10-5 0 -1.4855 × 10-4 6.7216 × 10-6 -3.5418 × 10-4 2.69 × 10-5 2.2618 × 10-4 5.72 × 10-5 4.574 × 10-5 3.82 × 10-5 3.82 × 10-5 2.3745 × 10-5 2.7226 × 10-6 4.1864 × 10-5

4.5945 × 10-2 0 1.0001 × 10-1 4.0845 × 10-2 1.94 × 10-1 7.7375 × 10-2 2.2448 × 10-2 1.7490 × 10-2 3.777 × 10-2 3.7846 × 10-2 3.6095 × 10-2 -1.8374 × 10-2 -4.5479 × 10-3 -3.0742 × 102

-6.939 × 101 0 -1.0858 × 102 -2.5749 × 101 -7.0785 × 101 -1.6339 × 102 -1.4784 × 102 -1.4539 × 101 -1.3502 -9.9240 × 101 -9.9774 × 101 -8.4082 -1.1796 × 101 -5.6713

298.15-573.15 298.15-573.15 298.15-498.15 298.15-573.15 298.15-573.15 298.15-573.15 273.15-323.15 298.15-573.15 298.15-343.15 298.15-358.15 298.15-348.15 298.15-423.15 298.15-323.15 298.15-423.15

Table 2. Representation of Acid Gas Partial Pressures in (Water-Alkanolamine) Systems Using Our Model temp range (K)

Pag range (MPa)

rmsd (%)

data sources

CO2-DEA-H2O

system

298.15-394.3

9.8 × 10-6-6.89

5.2-49.6

22.3

H2S-DEA-H2O

298.15-393.15

9.3 × 10-7-3.41

20.6-50

24.0

CO2-MDEA-H2O

297.7-393.15

1.4 × 10-7-5.87

5-25.7

25.7

H2S-MDEA-H2O

298.15-388.7

1.4 × 10-5-1.54

11.8-46.8

23.7

CO2-MEA-H2O

298.15-393.15

1.2 × 10-3-6.8

6-30.7

22.7

H2S-MEA-H2O

298.15-413.15

1.0 × 10-5-4.2

15.3-30.7

28.3

Lee et al.42 Lawson and Garst43 Lal et al.44 Maddox et al.45 Maddox and Elizondo46 Lee et al.47 Lawson and Garst43 Huang and Ng48 Jou et al.49 Rhoo et al.50 Lemoine et al.51 Rogers et al.52 Maddox et al.45 Sidi-Boumedine12 Jou et al.53 MacGregor and Mather54 Lemoine et al.51 Li and Shen55 Maddox et al.45 Sidi-Boumedine12 Huang and Ng48 Jones et al.56 Park et al.57 Lee et al.58 Lee et al.59 Maddox et al.45 Lawson and Garst43 Lee et al.58 Lee et al.59 Maddox et al.45 Huang and Ng48 Jones et al.56

used to fit parameters of DEA-water,34,35 MDEA-water,36,37 and MEA-water.38-40 All other binary interactions were assumed to be zero. Ion pair-ion pair parameters were set to (34) Abedinzadegan Abdi, M.; Meisen, A. A novel process for diethanolamine recovery from partially degraded solutions. Process description and phase equilibria of the DEA-BHEP-THEED-Hexadecane system. Ind. Eng. Chem. Res. 1999, 38, 3096-3104. (35) Horstmann, S.; Mougin, P.; Fischer, K.; Gmelhing, J.; Lecomte, F. Phase equilibrium and excess enthalpy data for the system methanol + 2,2′diethanolamine + water. J. Chem. Eng. Data 2002, 47, 14961501. (36) Xu, S.; Qing, S.; Zhen, Z.; Zhang, C.; Carroll, J. J. Vapor pressure measurements of aqueous N-methyldiethanolamine solutions. Fluid Phase Equilib. 1991, 67, 197-201. (37) Lemoine, B. Absorption de gaz acides par des solutions aqueuses de MDEA. Acquisition de donneés et de parame`tres cine´tiques et thermodynamiques en vue d’applications industrielles. Ph.D. Thesis, Ecole des Mines de Paris, Paris, France, 1995. (38) Nath, A.; Bender, E. Isothermal vapor-liquid equilibria of binary and ternary mixtures containing alcohol, alkanolamine, and water with a new static device. J. Chem. Eng. Data 1983, 28, 370-375. (39) Touhara, H.; Okazaki, S.; Okino, F.; Tanaka, H.; Ikari, K.; Nakanishi, K. Thermodynamic properties of aqueous mixtures of hydrophilic compounds 2. aminoethanol and its methyl derivatives. J. Chem. Thermodyn. 1982, 14, 145-146.

amine conc (wt %)

zero without affecting the representation of VLE data.31 Molecule-ion pair and ion pair-molecule parameters are determined on ternary systems experimental data. Unregressed parameters are set to default values:31 τwater-ca ) 8.0, τca-water ) -4.0, τDEA-ca ) τacidgas-ca ) 15.0, and τca-DEA ) τca-acidgas ) -8.0. The nonrandomness parameters are assumed to be symmetric (Rij ) Rji). Following the work of Chen and Evans,31 they are fixed at 0.2 for molecule-molecule interactions and for waterion pair interactions except for the water-alkanolamine binary system (set at 0.47). Alkanolamine-ion pair and acid gas-ion pair interactions41 are fixed at 0.1. (40) Tochigi, K.; Akimoto, K.; Ochi, K.; Liu, F.; Kawase, Y. Isothermal vapor-liquid equilibria for water + 2-aminoethanol + dimethyl sulfoxide and its constituent three binary systems. J. Chem. Eng. Data 1999, 44, 588590. (41) Mock, B. L.; Evans, L. B.; Chen, C. C. Thermodynamic representation of phase equilibria of mixed-solvent electrolyte systems. AIChE J. 1986, 32, 1655-1664. (42) Lee, J. I.; Otto, F. D.; Mather, A. E. Solubility of carbon dioxide in aqueous diethanolamine solutions at high pressures. J. Chem. Eng. Data 1972, 17, 465-468.



Table 3. Electrolyte-NRTL Parameters for MEA Solutions

Table 4. Electrolyte-NRTL Parameters for DEA Solutions

regressed parameters

τ(0)

τ(1)


τ(0)

τ(1)

τwater-MEAH ,OH τMEAH+,OH--water τwater-MEAH+,HCO3τMEAH+,HCO3-,water τwater-MEAH+,CO32τMEAH+,CO32-,water τwater-MEAH+,MEACOOτMEAH+,MEACOO--water τMEA-MEAH+,OHτMEAH+,OH--MEA τMEA-MEAH+,MEACOOτMEAH+,MEACOO--MEA τCO2-MEAH+,OHτH3O+,OH--MEA τMEAH+,HCO3--MEA τMEAH+,CO32--MEA τwater-MEAH+,OHτMEAH+,OH--water τwater-MEAH+,HSτMEAH+,HS--water τwater-MEAH+,S2τMEA-H3O+,S2τMEA-MEAH+,OHτMEA-MEAH+,HSτMEAH+,HS--MEA τH2S-H3O+,OHτH2S-H3O+,HSτH2S-H3O+,S2τH3O+,OH--MEA τMEAH+,OH--H2S τMEAH+,HS--H2S

1.6050 179.77 -102.47 33.030 20.219 90.476 -3.7235 -4.37 -175.990 257.04 63.59 -4.342 123.9 100.0 22.574 -4.745 3.247 -4.0125 -6.207 2.25 5.484 -1.859 2.22 -1.730 0.759 1.711 16.41 14.8 1.591 -11.01 1.287

213.29 -964.1 2338.1 744.2 167.95 default 861.8 298.2 0.8716 default default 2305.1 -1.67 -0.499 794.6 default 0.91984 0.1245 -3.045 0.0859 default default default 1.644 1.5204 default default default default 2.402 default

τwater-DEAH τDEAH+,HCO3 -water τDEAH+,HCO3--DEA τwater-DEAH+,DEACOOτDEAH+,DEACOO--water τDEAH+,DEACOO--DEA τwater-DEAH+,HSτDEAH+,HS--water τDEAH+,HS--DEA

-9.1861 -6.4923 20.99382 1.02875 -5.27408 -0.19209 1.3073 -4.195 -8.601

-41.933 -394.76 37.854 -52.336 -482.06 37.195 11.885 -68.18 -92.03

+

-

+

,HCO3-

Table 5. Electrolyte-NRTL Parameters for MDEA Solutions

τ1kl T

τ(0)

τ(1)

τwater-MDEAH+,HCO3τMDEAH+,HCO3--water τCO2-MDEAH+,HCO3τMDEAH+,HCO3--CO2 τMDEA-MDEAH+,HCO3τMDEAH+,HCO3--MDEA τwater-MDEAH+,HSτMDEAH+,HS--water τH2S-MDEAH+,HSτMDEA-MDEAH+,HSτMDEAH+,HS--MDEA

-5.3685 -6.6389 15.815 -5.2696 15.527 -9.5559 -3.858 0.142 -0.1201 -1.719 -7.140

577.53 64.776 -22.479 -0.57735 25.005 213.61 -65.58 540.6 5.931 105.42 181.6

Table 6. Temperature Dependence Parameters of Henry’s Constant (Pa) solute H2S CO2

After determining molecule-molecule binary parameters, ternary systems are studied to fit the best values of interaction parameters by data regression. The parameters are first-order temperature dependent:

τkl ) τ0kl +


(9)

C1

C2

F)

∑i

(

Piexp,ag

)

hVag(T,P) ) h#ag(T,P°) + RT2

2

(10)

Root-mean-square deviations (rmsds) between calculated and experimental values of acid gas partial pressures are given in Table 2. Regressed parameters values are given in Tables 3-5 for MEA, DEA, and MDEA solutions, respectively. The calculation of (∂ ln γ/i /∂T)P,ni in the unsymmetric convention is presented in Appendix B. (43) Lawson, J. D.; Garst, A. W. Gas sweetening data: equilibrium solubility of hydrogen sulfide and carbon dioxide in aqueous monoethanolamine and aqueous diethanolamine solutions. J. Chem. Eng. Data 1976, 21, 20-30. (44) Lal, D.; Otto, F. D.; Mather, A. E. The solubility of H2S and CO2 in a diethanolamine solution at low partial pressures. Can. J. Chem. Eng. Data 1985, 63, 681-685. (45) Maddox, R. N.; Bhairi, A. H.; Diers, J. R.; Thomas, P. A. GPA Project 841, Equilibrium solubility of carbon dioxide or hydrogen sulfide in aqueous solutions of monoethanolamine, diglycolamine, diethanolamine and methydiethanolamine; Gas Processors Association, March 1987. (46) Maddox, R. N.; Elizondo, E. M. GPA Project 841. Equilibrium solubility of carbon dioxide in aqueous solutions of diethanolamines al low partial pressures; report no. 104, Gas Processors Association, June 1989. (47) Lee, J. I.; Otto, F. D.; Mather, A. E. Partial pressures of hydrogen sulfide over aqueous diethanolamine solutions. J. Chem. Eng. Data 1973, 18, 420.

C4

temp range (K)

According to Barreau et al.,24 this model can be used for predictive calculations of species concentration profiles in the liquid phase: good agreement is obtained between experimental12 and calculated values. In this work, we suggest extending the validation of this model over the heat of absorption experimental data. Enthalpy in the Vapor Phase. The acid gas molar enthalpy in the vapor phase can be expressed by the following expression:

And the objective function is the following:

Piexp,ag - Pcal,ag i

C3

358.138 -13236.8 -55.0551 0.059565 273.15-423.15 170.7126 -8477.711 -21.9574 0.005781 273.15-423.15

[(

)

sat

w d ln HPag,w dT

(

)

∂ ln φag(T,P) ∂T

]

P,nag

(11)

in which the fugacity coefficient of acid gas, ln φag, is calculated from the Peng and Robinson25 equation of state. Henry’s sat w , coming from the work of Edwards et al.23 and constants HPag,w 60 Chen et al., are detailed in Table 6. The reference term of (48) Huang, S. H.; Ng, H. J. GPA Project 911, Solubility of H2S and CO2 in alkanolamines; report no. 155, Gas Processors Association, September 1995. (49) Jou, F-Y.; Mather, A. E.; Otto, F. D. Solubility of H2S and CO2 in aqueous methyldiethanolamine solutions. Ind. Eng. Chem. Process Des. DeV. 1982, 21, 539-544. (50) Rho, S. W.; Yoo, K. P.; Lee, J. S.; Nam, S. C.; Son, J. E.; Min, B. M. Solubility of CO2 in aqueous methyldiethanolamine solution. J. Chem. Eng. Data 1997, 42, 1161-1164. (51) Lemoine, B.; Li, Y. G.; Cadours, R.; Bouallou, C.; Richon, D. Partial vapor pressure of CO2 and H2S over aqueous methyldiethanolamine solutions. Fluid Phase Equilib. 2000, 172, 261-277. (52) Rogers, W. J.; Bullin, J. A.; Davison, R. R. FTIR measurements of acid-gas-methyldiethanolamine systems. AIChE J. 1998, 44, 24232430. (53) Jou, F-Y.; Carroll, J. J.; Mather, A. E.; Otto, F. D. The solubility of carbon dioxyde and hydrogen sulphide in a 35 wt% aqueous solution of methyldiethanolamine. Can. J. Chem. Eng. 1993, 71, 264-267. (54) MacGregor, R. S.; Mather, A. E. Equilibrium solubility of H2S and CO2 and their mixtures in a mixed solvent. Can. J. Chem. Eng. Data 1991, 69, 1357-1366.



Figure 1. Heats of absorption of H2S in a 30 wt % DEA aqueous solution at 299.82 K: Comparison of modeling curves with experimental data.15

molar enthalpy in the liquid phase, h#ag(T,P°), is determined by differentiation of µ#i (T,P)/RT with respect to temperature. Expansion Term. The expansion term of eq 5 depends on volumes and pressures at the initial state and final state. Pressures are calculated by our VLE model (PI is the solvent bubble pressure, and PF is the equilibrium pressure). A correlative model has been developed to express the volume of loaded aqueous solutions of alkanolamines. It is expressed as follows:

VF ) V I + υ j agnLag

(12)

VI can be calculated from the solvent’s characteristics: alkanolamine weight fraction, molar weight, and density of the solvent which is evaluated from the work of Amarare`ne et al.61 Here, j ag nLag is the acid gas number of moles in the liquid phase, and υ is the acid gas partial molar volume in the water + alkanolamine solvent: they were fitted on experimental data (of the work of Rinker et al.62 for H2S and Weiland et al.63 for CO2). (55) Li, M. H.; Shen, K. P. Solubility of hydrogen sulfide in aqueous mixtures of monoethanolamine with N-methyldiethanolamine. J. Chem. Eng. Data 1993, 38, 105-108. (56) Jones, J. H.; Froning, H. R.; Claytor, E. E. Solubility of acidic gases in aqueous monoethanolamine. J. Chem. Eng. Data 1959, 4, 85-92. (57) Park, S. B.; Shim, C. S.; Lee, H.; Lee, K. H. Solubilities of carbon dioxide in the aqueous potassium carbonate and potassium carbonate-poly(ethylene glycol) solutions. Fluid Phase Equilib. 1997, 134, 141-149. (58) Lee, J. I.; Otto, F. D.; Mather, A. E. The solubility of H2S and CO2 in aqueous monoethanolamine solutions. Can. J. Chem. Eng. Data 1974, 52, 803-805. (59) Lee, J. I.; Otto, F. D.; Mather, A. E. Equilibrium in hydrogen sulfide-monoethanolamine-water system. J. Chem. Eng. Data 1976, 21, 207-208. (60) Chen, C. C.; Britt, H. I.; Boston, J. F.; Evans, L. B. Extension and application of the Pitzer equation for vapor-liquid equilibrium of aqueous electrolyte systems with molecular solutes, AIChE J. 1979, 25, 820-831. (61) Amarare`ne, F.; Balz, P.; Bouallou, C.; Cadours, R.; Lecomte, F.; Mougin, P.; Richon, D. Densities of hybrid solvents: diethanolamine + water + methanol and N-methyl-diethanolamine + water + methanol at temperature ranging 283.15 to 353.15 K. J. Chem. Eng. Data 2003, 48, 1565-1570. (62) Rinker, E. B.; Colussi, A. T.; McKnight, N. L.; Sandall, O. C. Effect of hydrogen sulfide loading on the density and viscosity of aqueous solutions of methyldiethanolamine. J. Chem. Eng. Data 2000, 45, 254-256. (63) Weiland, R. H.; Dingman, J. C.; Cronin, D. B.; Browning, G. J. Density and viscosity of some partialy carbonated aqueous alkanolamine solutions and their blends. J. Chem. Eng. Data 1998, 43, 378-382.

Equation 12 has been calculated for different [water + alkanolamine + acid gas] systems at various temperature, solvent composition, and acid gas loading conditions and varies between 0.1 and 1.0 kJ/acid gas mol: it is in the same order of magnitude as experimental uncertainties; therefore, it is preferable not to neglect it. The equations described above are integrated into our reactive flash algorithm24 which solves the chemical equilibrium (i.e., the composition of the liquid phase) by a nonstoichiometric Gibbs energy minimization approach and then determines the composition of the vapor phase through a bubble point calculation. This approach allows us to use the same computational method for all systems. Aqueous solutions of DEA, MDEA, and MEA loaded with CO2 or H2S were studied, and binary parameters of the electrolyte-NRTL were fitted on VLE data. Acid gas partial pressures and liquid-phase compositions were represented satisfactorily. With these sets of parameters, heats of absorption are directly predicted without numerical differentiation and integration existing in the first method. Modeling Results Heats of absorption of H2S in an aqueous solution of DEA are plotted in Figures 1 and 2. For the Gibbs-Helmholtz method, we tested the trapezium and the Simpson integration methods. The comparison with experimental data15 clearly shows a better agreement between experimental data and our rigorous calculation than for the differentiation method. Calculation by differentiation shows uncertainties, especially when H2S loadings (and H2S partial pressures) increase: at 299.82 K (Figure 1), average absolute relative deviations (AARDs) between experimental and calculated values are similar for the rigorous method and the Simpson method and twice more for the trapezium method; at 399.82 K (Figure 2), AARDs obtained with the Simpson method are four times greater than those with the rigorous method and twice more if the trapezium method is used. In Figure 3, the use of a 3-point Gaussian quadrature method shows some inaccuracies although the temperature dependence is in good agreement with experimental data. A 4-point Gaussian quadrature gives a similar result. The Gibbs-Helmholtz method should be used as an acceptable and easy estimation of the heat of absorption but in this case an improved integration method, such as Simpson or Gauss



Figure 2. Heats of absorption of H2S in a 30 wt % DEA aqueous solution at 399.82 K: Comparison of modeling curves with experimental data.15

Figure 3. Heats of absorption of CO2 in a 20 wt % MDEA aqueous solution at 298.15 K: Comparison of modeling curves with experimental data.17

quadrature, must be employed in order to reduce all numerical uncertainties. However, the rigorous method must be preferred in order to describe the influence of weak parameters such as temperature or alkanolamine concentration on the heat of absorption. Comparing the results obtained in Figures 1 and 2, we can notice that the heats of absorption are temperature dependent and that the Gibbs-Helmholtz method becomes less and less accurate as temperature increases. Figure 3 is an other example of a better agreement between our rigorous method and experimental data17 (AARD ≈ 3%) than the Gibbs-Helmholtz expression (AARD ≈ 10%) at very low loadings for the [water + MDEA + CO2] system. Figure 4 compares our rigorous calculation with experimental data15 at 299.82 K in the case of the [water + DEA + CO2] system at different DEA concentrations and for a wide range of acid gas loadings. We can notice a very weak DEA concentration dependence for loadings greater than 0.8 (physical regime absorption) whereas for lower loadings (chemical regime absorption), this dependence is stronger and the maximum difference at a given loading is about 3 kJ/mol CO2 in this region. Data at very low CO2 loadings17 is satisfactorily modeled. We can also notice from this figure that the dependence of heat of absorption with loading is very well reproduced

to high values of gas loadings (1.1). The AARD between experimental data and calculated values is 1.3%. The process of absorption of CO2 in DEA solvent can be investigated considering simultaneously the shape of the calculated curve with the rigorous method in Figure 4, and the concentrations of all species as reported in Figure 5. A chemical absorption regime mainly due to the chemical property of DEA occurs at low loadings (up to 0.6 and 0.7). When CO2 loading increases, it can be noticed from Figure 5 that DEA is consumed by two main reactions: acid-base reaction and formation of carbamate ion DEACOO- for loadings up to 0.4 and 0.5 and then destruction of carbamate. Experimental data12 confirms the existence of a maximum concentration value of carbamate for loading close to 0.5 and 0.6 as shown in Figures 5 and 6. For higher loadings (greater than 0.6 and 0.7), the absorption process should become less and less chemical because alkanolamine begins to be fully charged as can be seen in Figure 5 and the absorption process becomes mainly physical for loadings close to and greater than 1. Concerning the [water + DEA + H2S] system, as there is no carbamate formation, the chemical regime in the absorption process is only due to DEA consumption by acid-base reaction. In this system, the physical regime begins for high H2S loadings: close to 0.8 according to calculation with the Gibbs-



Figure 4. Heats of absorption of CO2 in DEA aqueous solutions at 299.82 K: Comparison of modeling curves with experimental data at 298.15 K17 and 299.82 K.15

Figure 5. Liquid-phase composition of 30 wt % DEA aqueous solution loaded with CO2 at 299.82 K. Compositions are calculated with the VLE model.

Figure 6. Carbamate concentration at 298.15 K: Comparison between our model calculations and infrared experimental data.12

Helmholtz method and close to 1 if our rigorous method is employed (Figure 1). ReactiVity Comparison between DEA, MEA, and MDEA. MEA and MDEA are two other alkanolamines commonly used in industry. The first one is a primary alkanolamine and reacts directly with CO2 to form carbamate like DEA. The second

one is a tertiary alkanolamine and does not have hydrogen attached to nitrogen. Then, it does not react as the other two alkanolamines and no carbamate is formed. These different chemical behaviors can be clearly noticed on the heat of absorption curves. Heats of absorption of CO2 in aqueous solutions containing the same number of moles of each



Figure 7. Heats of absorption of CO2 in 30.08 wt % DEA, 32.78 wt.% MDEA, and 20 wt % MEA aqueous solutions at 298.15 K: Comparison of modeling curve with experimental data17 for MEA.

Figure 8. Heats of absorption corresponding to each reaction calculated by our rigorous calculation for a 30 wt % DEA solution loaded with CO2 at 299.82 K.

alkanolamine are plotted in Figure 7. It is obvious that Qabs values are more exothermic in the case of MEA and DEA than for MDEA. The difference between MEA and DEA can be due to the fact that MEA is less sterically hindered than DEA. In the same figure, experimental data17 is plotted and is relatively well reproduced with calculations. Enthalpies of each acid-base reaction for the [water + DEA + CO2] and [water + MEA + CO2] systems are respectively plotted in Figures 8 and 9. These results can be compared because the mole number of alkanolamine is the same in each case: it is evident that MEA carbamation and MEA protonation are the two reactions which make total heat of absorption more exothermic with MEA than with DEA. HCO3- dissociation is quite similar in both cases. Moreover, the change in the MEA carbamation shape for loadings close to 0.5 and 0.6 is clearer than in DEA case. Concerning H2S, the difference between the two alkanolamines is less and is only due to the nature of the chemical compound. Figure 10 shows the results for aqueous solutions of DEA, MDEA, and MEA at the same molar concentration and loaded with H2S. In the chemical region absorption, the difference between MDEA and DEA curves and between DEA and MEA curves is about 7 kJ/mol H2S

whereas with CO2, there is a 20 kJ/mol CO2 difference between MDEA and DEA curves and twice less between DEA and MEA curves. Influence of Heat of Absorption Data in the Determination of Electrolyte-NRTL Parameters. Direct and rigorous internal energy balance allows the determination of electrolyte-NRTL parameters which is not possible with the Gibbs-Helmholtz method (which employs numerical differentiations and integrals). Experimental data of the heat of absorption for the [water + DEA + CO2] and [water + DEA + H2S] systems is also used to fit electrolyte-NRTL parameters in addition to experimental partial pressure data. The resulting objective function is weighted (ω1 is the weight applied in our optimization process) to take into account both types of data:

∑i

F ) ω1

(

)

Piexp,ag - Pcal,ag i Piexp,ag

2

+

∑j

(1 - ω1)

(

)

exp cal Qabs,j - Qabs,j exp Qabs,j

2

(14)



Figure 9. Heats of absorption corresponding to each reaction calculated by our rigorous calculation for a 19.9 wt % MEA solution loaded with CO2 at 299.82 K.

Figure 10. Heats of absorption of H2S in 20.55 wt % DEA, 22.66 wt % MDEA, and 15.31 wt % MEA aqueous solutions at 298.15 K.

The quality of the regression is given by a parameter correlation matrix. It is calculated for each system and for the following ω1 values: ω1 ) 1 and ω1 ) 0.8. For the [water + DEA + H2S] systems, over 78 correlation coefficient values, the number of high values of correlation coefficients dropped by 80% when experimental heat of absorption data is introduced. Concerning the [water + DEA + CO2] system, the difference is less obvious due to a higher number of electrolyte-NRTL parameters. In this case, 20% of the parameters became less correlated using both heats of absorption and VLE data in the optimization procedure. Conclusions In the context of improving today’s processes of acid gases (H2S and CO2) removal by alkanolamine solutions, it can be necessary to calculate heats of absorption in addition to VLE equilibrium, kinetics, and hydrodynamics. A rigorous method has been developed for this goal. It consists of an internal balance for an open system and depends on the thermodynamic model to describe the liquid-phase nonideality. The results presented use the electrolyte-NRTL model and are predictive as binary parameters of the model were only fitted on VLE data. The agreement with experimental data is satisfac-

tory for the systems under study: [water + DEA + H2S or CO2], [water + MDEA + H2S or CO2], and [water + MEA + H2S or CO2]. This approach allows determining the influence of temperature or alkanolamine concentration on the heat of absorption whereas it has generally been considered to be a constant. Moreover, it is shown that this rigorous method leads to more accurate calculation than the usual simplified Gibbs-Helmholtz method. In another way, the rigorous method can be used to fit simultaneously electrolyte-NRTL parameters using both VLE and enthalpy data. The use of experimental heat of absorption data in addition to VLE data leads to less-correlated parameters than generally found and allows extrapolating the model with more confidence. This thermodynamic study form a multidisciplinary whole as it can calculate directly and simultaneously acid gas partial pressures, liquid-phase composition, and heats of absorption. Acknowledgment. The authors express their thanks to N. Ettlili and J.C. Brevot for their helpful work done on MDEA and MEA systems, respectively, during their internship.



Appendix A

Molecular Species. NRTL Term

Chemical Dissociations

d ln γNRTL m

2H2O T HO- + H3O+

(1)

CO2 + 2H2O T HCO3- + H3O+

(2)

HCO3- + H2O T CO32- + H3O+

(3)

dT

Xa

∑∑W X c

(4)

a

Vca

HS- + H2O T S2- + H3O+

(5)

-

R1R2NCOO- + H2O T R1R2NH + HCO3

( )

j

Vm )

V′m )

∑

U′ca )

j jm

∑ j

Uac )

∑X G

Vac )

j

U′ac )

ja,caτja,ca

∑X G j

∑X

∑

a

∑X G′

j ja,ac

∑X (G′ j

V′ac )

ja,ca

and Wc )

a

∑X

x

() [ -3/2

Vca

)]

Vca2 -

+

Vac2

ja,caτja,ca

+ Gja,caτ′ja,ca)

∑X G′

(

τma,ca -

)

Uac

(

τ′ma,ca -

+

Vac

c

dT

za

-

a′

)

[∑ [

Xc U′ac

c

-

Wc Vac

Uac

Vca

]

+

τma,ca -

+

U′ac

+

)]]

Uac‚V′ac

Vac

Vac2

G′am

V′ac +

Vac2

Xm

m

Vm

τam -

Gam Um Gam U′m Um V′m τam + τ′am + V′m Vm Vm Vm V 2 Vm2 m G′ac,a′c

Wa

Vca′

τac,a′c -

Uca′

-

Gac,a′c‚V′ca′

Vca′

Vca′

τac,a′c -

Vca′2

τ′ac,a′c -

d ln γ∞a

[

) za G′awτaw + Gaw • τ′aw +

U′ca′ Vca′

Aφ ) Pitzer parameter D ) dielectric constant e ) electron charge F ) objective function g ) molar Gibbs energy h ) molar enthalpy H ) enthalpy

1

+

+

Uca′

Vca′

Uca′

V′ca′ Vca′2

∑c

∑c xcτ′wa,ca

Xc

Nomenclature

3 (DwT)-3/2 - D′wxFw(DwT)5/2 2 2xFw

)

Uca

[ ( G′ma,ca

a

c

Vac

-

]∑[( ) ( ) ( )] ∑∑ [ ( ) ( ( )]] NRTL 1 d ln γa

dT

j ja,ca

j

F′w

τmc,ac -

Xc

c

)]

Vm′2

(

∑∑W X a

Gma,ca‚V′ac

Vm′

Vca2

)

Um′‚V′m′

+

Gmc,ac‚V′ca

-

Uca‚V′ca

c

2πN e 1000 k

Uca

U′m′

Vm′

Infinite Dilution Term.

PDH Term. This term is the same for molecular and ionic species. The only temperature-dependent parameter is Aφ:

dAφ 1 ) dT 3

Vm′

τmc,ac -

+

τ′mm′ -

Gac,a′c

Xj(G′ja,caτjc,ac + Gjc,acτ′jc,ac)

j

j

Wa )

j jm

j

j

Gmm′

Vm′

Vca

)

+

Vm′

Um′

Anions (To Obtain Formulae for Cations, One Must Change a to c). NRTL Term.

c

j

V′ca )

XjGjc,ac

m′

τmm′ -

d ln γ∞m ) [τ′wm + G′mw‚τmw + Gmw‚τ′mw] dT

Xc

j

XjGjc,acτjc,ac

U′ca

Um′

[ ( G′mm′

m′

Infinite Dilution Term.

Xa′

+ Gjmτ′jm)

∑X G′

j

Uca )

jm jm

j

j

Uca )

j

Vm2

Vac

Vm

∑X (G′ τ

∑X G′

τ′mc,ac -

Vac

Um

∂A A′ ) ∂T P,ni U′m )

∑X

+

Gma,ca

Differentiation of the Natural Logarithm of the ElectrolyteNRTL Activity Coefficient with Respect to Temperature. Definition of Intermediary Functions.

jmτjm

Um‚V′m

(7)

Appendix B

j

Vca

(6)

R1R2R3N is the alkanolamine chemical formula: - Monoethanolamine: R1 ) R2 ) H and R3 ) CH2-CH2OH; primary alkanolamine - Diethanolamine: R1 ) H and R2 ) R3 ) CH2-CH2-OH; secondary alkanolamine - Methyldiethanolamine: R1 ) CH3 and R2 ) R3 ) CH2CH2-OH; tertiary alkanolamine

∑X G

τmm′ -

Uac

R1R2R3NH+ + H2O T R1R2R3N + H3O+

Um )

(

-

Vm

G′mc,ac

c

a

Gmc,ac

[

U′m

) ( [ ( )

(

Gmm′‚V′m Vm′2

H2S + H2O T HS- + H3O+

)

]

+

Alkanolamine Solution Acid Gas Heat of Absorption sat

HPi,jj ) Henry’s constant of solute i in solvent j at its saturation pressure k ) Boltzmann constant n ) moles N ) Avogadro’s number P ) pressure Q ) heat R ) ideal gas constant T ) temperature U ) internal energy V ) molar volume V ) volume W ) work x ) liquid-phase mole fraction Greek Letters R ) loading; NRTL nonrandomness factor γ ) activity coefficient φ ) fugacity coefficient µ ) chemical potential F ) density τ ) binary parameter ω ) mass composition ω1 ) weigh factor in objective function Subscripts a ) anion ag ) acid gas abs ) absorption c ) cation diff ) differential

Energy & Fuels, Vol. 21, No. 4, 2007 2055 F ) final I ) initial int ) integral m ) molecule w ) water Superscripts cal ) calculated E ) excess exp ) experimental L ) liquid mixing ) mixing sat ) saturation total ) total V ) vapor ° ) reference state # ) liquid reference state * ) unsymetric convention ∞ ) infinite dilution Acronyms DEA ) diethanolamine MEA ) monoethanolamine MDEA ) methyldiethanolamine NRTL ) nonrandom two liquids PDH ) Pitzer-Debye-Hu¨ckel AARD ) average absolute relative deviation rmsd ) root-mean-square deviation EF0605706

Rigorous Modeling of the Acid Gas Heat of Absorption in

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