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Ž .Fluid Phase Equilibria 168 2000 241–258

www.elsevier.nlrlocaterfluid

Physical and chemical solubility of carbon dioxide in aqueousmethyldiethanolamine

Sanjay Bishnoi, Gary T. Rochelle )

Department of Chemical Engineering, The UniÕersity of Texas at Austin, 26th and Speedway, Austin, TX 78712-1062, USA

Received 15 February 1999; accepted 8 December 1999

Abstract

Ž .Inconsistent trends for the physical solubility of carbon dioxide in aqueous methyldiethanolamine MDEA

are presented. These inconsistencies are found between data sets for the chemical solubility of carbon dioxide in

aqueous MDEA. In order to rationalize this inconsistency, data are presented for the solubility of nitrous oxide

and carbon dioxide in MDEA solutions neutralized with sulfuric acid. The physical solubility is seen to decrease

with increasing ionic strength. Previously published models show the incorrect trend for the physical solubility

of carbon dioxide as a function of loading because of this discrepancy in the data. The electrolyte–NRTL model

was successfully used to model the chemical and physical solubility of carbon dioxide in MDEA by defining the

reference state for solutes as infinite dilution in the aqueous phase instead of the mixed solvent. VLE data at

high temperature and high loading are needed for industrially important MDEA concentrations. The N O2

analogy needs to be studied further in solutions at high and moderate loading as a function of temperature.

q 2000 Elsevier Science B.V. All rights reserved.

Keywords: Electrolyte–NRTL model; Reference state; Carbon dioxide; Aqueous methyldiethanolamine; N O analogy2

1. Introduction

Chemical absorption of acid gases by alkanolamines has found application in a wide variety of industries, including the processing of natural gas and the removal of CO from synthesis gas in the

2

production of hydrogen or ammonia. With the recognition of CO as a greenhouse gas, another2

important application of this technology is CO removal from combustion gases at power plants or2

manufacturing facilities.

)

Corresponding author. Fax: q1-512-475-7824.Ž . Ž . E-mail addresses: [email protected] S. Bishnoi , [email protected] G.T. Rochelle .

0378-3812r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.Ž .P I I : S 0 3 7 8 - 3 8 1 2 0 0 0 0 3 0 3 - 4



( )S. Bishnoi, G.T. Rochelle r Fluid Phase Equilibria 168 2000 241–258 242

The finite chemical kinetics associated with the reaction of carbon dioxide with alkanolaminesw xresult in low stage efficiencies in staged and packed contactors 1 . Understanding acid gas contactors,

therefore, requires an understanding of several aspects of mass transfer with associated chemicalreaction, including the quantification of the driving force for mass transfer. The driving force is givenby the gradient of the free CO concentration in the liquid boundary layer that largely depends on the

2

equilibrium distribution of species in the solution. Since free CO is only a very small fraction of the2

Ž .total CO concentration free plus reacted , it is calculated using a chemical and phase equilibrium2

routine. The development of such a routine requires experimental data of the chemical and physicalsolubility of carbon dioxide in aqueous alkanolamine solutions along with a thermodynamic frame-work to account for the reaction of carbon dioxide with the alkanolamines, and liquid and gas phasenon-idealities. The physical solubility of carbon dioxide cannot be directly measured in aqueousalkanolamines since it reacts with the solution. Therefore, the nitrous oxide analogy is used to inferthe physical solubility of carbon dioxide.

Ž .The chemical solubility of CO in aqueous methyldiethanolamine MDEA solutions has been2

studied by several investigators. Experimental data for the equilibrium partial pressure of carbonw xdioxide over aqueous MDEA has been obtained by several investigators 2–7 . All data obtained

w xcovers amine concentrations up to 4.28 M and temperatures from 258C to 1208C. Austgen 8 used the

w xelectrolyte–NRTL framework within Aspen Pluse 23 to model the vapor–liquid equilibrium of w xcarbon dioxide over aqueous MDEA. Posey 9 extended Austgen’s efforts by measuring and

modeling the excess Gibbs free energy of mixtures of water and MDEA. He did so by measuring thefreezing point depression and heat of mixing of water and MDEA. This improved the estimation of

ŽMDEA non-idealities and greatly improved model predictions at low loading moles carbon dioxide.per moles amine .

The physical solubility of CO in aqueous MDEA has been studied primarily through the2

experimental use of the nitrous oxide analogy with MDEA solutions from 0 to 4.28 M andw xtemperatures of 158C to 608C 10–13 . Other investigators have measured the solubility of N O in

2

w xloaded solutions of MDEA 14–16 .The contribution of this work is to bring the study of physical and chemical solubility together and

produce equilibrium models that represent both sets of data in a thermodynamically consistentmanner. In doing so, it is recognized that different data sets for the chemical solubility of carbondioxide in aqueous MDEA show opposite trends for physical solubility as a function of loading. This

Ž .discrepancy is illustrated in Section 4.1. Data are presented Section 4.1 for CO and N O solubility2 2

in aqueous MDEA solutions neutralized with sulfuric acid in order to resolve this discrepancy. Thegoal and result of these experiments is to verify the N O analogy in ionic, aqueous MDEA solutions

2

and to quantify the salting out tendency of carbon dioxide in aqueous MDEA solutions as a functionof carbon dioxide loading.

w xAs a consequence of this discrepancy, previously published models 8,9 for CO rMDEArH O2 2

VLE show the incorrect trend for the physical solubility of CO as a function of loading. The2

electrolyte–NRTL model has been used with a different reference state for solutes in order to predictthe correct trend. The new model is described in Section 2 while a quantification of the error betweenthe old models and new model is made in Section 4.3. Experimental methods and apparatus aredescribed in Section 3. The algorithm used for chemical and physical solubility is presented alongwith parameters obtained by regression of VLE and physical solubility data using GREG, an iterative

w xregression package developed by Caracotsios 17 .




2. Equilibrium model

w xThe equilibrium model is similar to that presented by Austgen et al. 5 and Posey and Rochellew x18 . The dissociation of carbon dioxide to form bicarbonate and carbonate ions is considered alongwith the protonation of the amine. These reactions are summarized as follows.

CO q 2H O l HCOyq H Oq 1Ž .2 2 3 3

HCOyq H O l CO2yq H Oq 2Ž .3 2 3 3

MDEAHqq H Ol

MDEAq H Oq 3Ž .2 3

2H Ol

OHyq H Oq. 4Ž .2 3

w xValues of the equilibrium and Henry’s law constants are the same as Posey 9 , and are notŽincluded here for brevity. The model solves for liquid mole fractions of all components chemical

. Ž .equilibrium and gas phase partial pressures of each molecular component phase equilibrium giventhe solution temperature, loading, and amine concentration on an acid gas-free basis.

The model is composed of two separate algorithms: the first calculating the speciation of the liquidphase and the second calculating the resulting composition of the gas phase. The liquid phase

speciation algorithm reads the loading, temperature, and acid gas-free composition of the solventŽ .amine strength and mole fraction of water . The liquid speciation algorithm uses the Smith and

w xMissen non-stoichiometric algorithm 19 , a variation of the RAND algorithm, to determine theconcentration of all species in the liquid phase. This algorithm assumes that the standard chemicalpotential of each species in solution is known and minimizes the Gibbs free energy subject to theconstraint of the mass balance of the system. The Smith and Missen method solves the constrainedoptimization problem using the method of Lagrangian multipliers.

The use of any non-stoichiometric method requires that we know the standard state chemicalw xpotential. Austgen 8 devised a technique to determine the standard state potential in acid gas systems

using the equilibrium constants.Once the speciation has been determined, the partial pressure of each component is calculated

using the gas phase algorithm. This algorithm starts by assuming an ideal gas and calculates the totaland partial pressure of each component based on physical equilibrium. Fugacity coefficients are thensolved for iteratively until the total pressure does not change. Since the electrolyte–NRTL model hasno dependence of pressure on activity coefficients, no liquid phase iteration must be made after thegas phase is converged. Fig. 1 shows a simplified block diagram of the algorithm.

2.1. Reference states used in this work

In this work and in previous works, different reference states are used depending on whether thespecies in consideration is a solvent, solute or ionic species. Different reference states are used in thiswork than in the work of Posey and Austgen. In their work, the reference state of solvents is the puresolvent at the system temperature and pressure. Solutes are considered to be at their reference state atinfinite dilution in the mixed, loaded solvent. For example, the activity coefficient of carbon dioxidein a 50-wt.% mixture of water and MDEA approaches 1.0 as the mole fraction of carbon dioxideapproaches zero in the solution. The reference state of ionic species is considered to be infinitedilution in the aqueous phase instead of the mixed solvent.




Fig. 1. Description of model algorithm.

A major inconsistency resulting from the previous reference states is the normalization of equilibrium constants. Equilibrium constants involving the solute contain the activity coefficient of the solute and must, therefore, be normalized consistently with the reference state of the solute. Sincethe reference state of carbon dioxide changes with MDEA concentration in the works of Posey andAustgen, a different set of equilibrium constants must be used for each MDEA concentration.

To overcome this, the reference state of solutes has been changed to infinite dilution in the aqueousphase in order to account for the change in carbon dioxide activity as a function of amine strength. Inthis work, the reference states of solvent molecules and of ionic species remain the same as in the

w x w xwork of Austgen 8 and Posey 9 . Activity coefficients of ionic species and solutes are calculated in




the same manner as solvent molecules, however, they are then normalized by the activity coefficientof the same species at infinite dilution in the aqueous phase. The activity coefficient of ionic speciesand solutes then becomes:

g i

)g s . 5Ž .i `g i

Ž .The activity coefficients in Eq. 5 are calculated from the expressions for the excess Gibbs freew xenergy as described by the electrolyte–NRTL model and as discussed in the works of Austgen 8 andw xPosey 9 .

2.2. System non-idealities

This work uses the electrolyte–NRTL model to account for liquid phase non-idealities. Thew xelectrolyte–NRTL model was first proposed by Chen et al. 20 . The original work was applicable to

w xaqueous systems of single, completely dissociated electrolytes. Chen and Evans 21 extended thew xoriginal work to represent multi-component electrolytes. Mock et al. 22 showed that the effect of

salts on multi-solvent systems could be predicted using the NRTL model. Mock was primarily

interested in the activities of multiple solvents as a function of ionic strength.The electrolyte–NRTL model uses an expression for the excess Gibbs free energy of a solution that

contains three terms: a long-range Debye–Huckel term to account for ionic forces, a Born term tocorrect the reference state of ionic species from infinite dilution in the solvent to infinite dilution inwater, and a short-range NRTL term analogous to the NRTL model proposed by Renon and Prausnitzw x24 . The excess Gibbs free energy model used in this work is the same as that described by Posey

Ž .and Austgen. The only change is the reference state for solutes which is now calculated by Eq. 5 ,where g ` is the activity coefficient of solute i at infinite dilution in water. The binary interaction

i

parameters of the electrolyte–NRTL model are defined differently than in the work of Posey andAustgen. In this work, t values for salt pairrmolecule and moleculersalt pair interactions are given

Ž .by Eq. 6 where T is 353.15 K.ave

1 1t s A q B y 6Ž .ž /T T

ave

Bt s A q 7Ž .

T

Ž . w x w xEq. 7 is consistent with the treatment of Austgen 8 and Posey 9 and is used formoleculermolecule interactions. Expressions for the excess Gibbs free energy for molecular and ionic

w x w xspecies are given in Austgen 8 and Posey 9 and are not repeated here.Poynting corrections are calculated by assuming that the partial molar volumes are independent of

pressure and brought out of the integration. This treatment is consistent with the models of Austgen etw x w xal. 5 and Posey and Rochelle 18 . The partial molar volumes of solvents are calculated as the molar

w xvolume of the pure solvent in order to be consistent with its reference state. The Rackett equation 25is used to calculate these volumes. The partial molar volume of solutes is calculated at infinite

w xdilution in the solvent by using the Brelvi–O’Connell model 26 . In typical acid gas VLE, thepressures are low enough that the Poynting corrections of all species are very small.




Gas phase deviations from ideal gas behavior are dealt with using the Soave–Redlich–KwongŽ . Ž . w xSRK equation of state EOS 27 . Typical pressures and gas compositions in VLE of carbon dioxideover alkanolamines or in industrial gas treating are dealt with well with the SRK EOS.

3. Physical solubility of carbon dioxide

The physical solubility of carbon dioxide in aqueous alkanolamines refers to the portion of the totalcarbon dioxide that is not reacted. Since carbon dioxide reacts with the amine, an analogy is drawnbetween the solubility of nitrous oxide and that of carbon dioxide. The ratio of the solubility of nitrous oxide in a given solvent to that of carbon dioxide in the same solvent is considered to be aconstant at a given temperature.

w xThe N O analogy was first proposed by Clarke 28 . He argued that since N O and CO have2 2 2

similar molecular weights and electronic configuration, they would interact with solvents in the samew xmanner and therefore have similar solubility. Toman and Rochelle 14 present experimental data

Ž .shown in Fig. 2 for the solubility of N O in aqueous solutions of MDEA which are loaded with2

carbon dioxide. These experiments show a strong ‘salting out’ tendency for carbon dioxide withincreasing loading. In this work, the apparatus used by Toman has been reconstructed and experi-ments are performed to analyze the validity of the N O analogy in neutralized aqueous MDEA

2

solutions. This was done to rationalize the inconsistency of VLE data sets for carbon dioxide inaqueous MDEA solutions that show opposite trends for the increaserdecrease of physical solubilityof carbon dioxide with increasing loading in aqueous MDEA solutions.

The solubility of gases in liquids has been expressed in several ways. N O analogy data has2

typically been expressed as a Henry’s law constant in the solvent being studied. This is done by

w xFig. 2. Salting out of N O in aqueous MDEA loaded with CO . Data are from Toman and Rochelle 14 .2 2




assuming that pressure and solution non-idealities are negligible at the low pressures and composi-tions of solute gas in the liquid. The Henry’s law constant may then be expressed as:

Pisolvent H s . 8Ž .i

xi

Ž .Note that Eq. 8 is a simplification from the rigorous definition of the Henry’s law constant since we

are not taking the limit as the mole fraction of the solute approaches zero. Instead, the mole fraction atŽ .the experimental conditions is low enough that the Henry’s law constant calculated by Eq. 8 wouldŽ .not have any significant error. The Henry’s law constant obtained by Eq. 8 has the reference state of

infinite dilution in the solvent, not necessarily in the aqueous phase. In this work, the reference stateused for modeling purposes is the infinitely dilute aqueous phase. In this case, we can express thesolubility of the gas in terms of an activity coefficient.

H solvent

i)g s 9Ž .i H O2 H

i

Ž . solvent Ž .In Eq. 9 , H is calculated from Eq. 8 and then normalized by the Henry’s law constant of thei

same solute in water. In this way, the solubility is expressed as an activity coefficient with the

reference state of infinite dilution in water.

3.1. Experimental apparatus and procedure

The experimental apparatus used to measure the solubility of nitrous oxide and carbon dioxide inw xthis work is shown in Fig. 3 14 . The principle of the apparatus is to measure the volume of gas

displaced into a liquid. The liquid is originally unsaturated with respect to the solute gas and the gas isclosed with respect to the atmosphere, therefore, the solubility or the Henry’s constant may bemeasured by the volume of gas displaced.

Fig. 3. Experimental apparatus for N O and CO solubility measurement.2 2




The mercury reservoir is open to the atmosphere on one side and the level of mercury in the buretteis adjusted by moving the reservoir up and down on a clamp stand. By doing so, we can ensure thatthe pressure in the burette is always atmospheric. This ensures that any difference in the mercury levelis due to gas that has been absorbed into the liquid.

The apparatus is composed of a thick-walled glass mercury reservoir. The reservoir is 15 cm talland has an inside diameter of 5 cm. Tygon tubing connects the mercury reservoir to the burette. The

burette is a 100-ml glass burette with 0.1-ml graduations. The burette is also connected to a gasrotameter with tygon tubing that is connected to a pressure-regulated gas cylinder. Stainless steelŽ .tubing 1r8 in. connects the burette to the three-way valve. The line from the three-way valve to the

flask is extremely short and is made of Teflon tubing. The head assembly of the flask is made of glassbut has a hole with Teflon tube inserted in it. Teflon tubing of a smaller size forms the dipstick andthe assembly is sealed with vacuum grease. The flask is a 50-ml Pyrex glass flask and is stirred with amagnetic stirrer. Although the original apparatus built by Toman had a temperature bath, experimentsin the current work were run at ambient temperature. Since the vapor pressure of water is low atambient temperatures, no pre-saturation of the gas with water was performed.

An experiment is run by filling the vessel with the solution to be studied and isolating it by closingvalve 5. The burette is then charged with gas by opening valves 1 and 2 and flowing gas through the

system by opening valve 5 from the gas burette to vent. Once all the air has been displaced from theburette and it is charged with the solute gas to be studied, the gas and liquid side are brought intocontact. Valves 3 and 4 are opened, bringing the mercury piston in contact with the gas to bedisplaced. The amount of gas displaced is measured by examining the initial and final readings of themercury level in the burette.

4. Results

The results of experiments on the solubility of carbon dioxide and nitrous oxide in neutralizedamines verify that the N O analogy provides an adequate way to infer the solubility of carbon dioxide

2

in aqueous MDEA solutions neutralized by sulfuric acid.Parameters are estimated for the electrolyte–NRTL model, such that the physical solubility of

carbon dioxide, as measured by the N O analogy, is predicted by the model. Electrolyte–NRTL2

w xparameters similar to those of Posey 9 are regressed to match the overall system VLE data. Theresulting model represents both the physical solubility of carbon dioxide from the N O analogy and

2

the VLE data for carbon dioxide over aqueous solutions of MDEA.

4.1. Experimental results

Table 1 shows the results of the experiments performed in this work. The apparatus and methodwere verified by studying the solubility of carbon dioxide in water, nitrous oxide in water, and nitrousoxide in aqueous alkanolamines and comparing the results with other investigators. The Henry’sconstant extracted from this apparatus matches other investigators within 5–10%. It is believed thatthese deviations are because the apparatus is not temperature controlled and temperature variations of "0.58C were seen between experiments. The results do, however, match qualitative results and trendsof other investigators very well. The activity coefficient of carbon dioxide increases, and hence the




Table 1

Nitrous oxide and carbon dioxide solubility: experimental results at 298 K. Neutralization by sulfuric acid

)w x w xExperiment MDEA Solute gas H SO H g 2 4

y1 y1Ž . Ž . Ž .number acid-free wt.% molrmol MDEA atm l mol

1 0 N O 0 44.2 1.002

2 20 N O 0 47.9 1.082

3 50 N O 0 54.8 1.242

4 20 N O 0.5 65.5 1.482

5 50 N O 0.5 133.7 3.032

6 0 CO 0 34.2 1.002

7 20 CO 0.5 51.4 1.502

8 50 CO 0.5 95.3 2.782

solubility decreases with amine concentration. The solubility of nitrous oxide and carbon dioxide alsodecreases with increased salt concentration. The nitrous oxide analogy provides a good estimation of the solubility of carbon dioxide in these cases, well within the precision of the apparatus. The resultswill be compared to model predictions and presented in Section 4.3.

A definite ‘salting out’ tendency is seen by both nitrous oxide and carbon dioxide with increasingsalt concentration. Chemical solubility data taken by some investigators, however, are not consistent

w xwith this trend. Analysis of the chemical solubility data at loadings greater than 1.0 2– 7 shows thatthe partial pressure of carbon dioxide is extremely sensitive to loading. The activity coefficient,therefore, is also extremely sensitive to loading at these conditions and sometimes shows either a‘salting out’ or a ‘salting in’ effect. It becomes extremely hard to gain any information on the activitycoefficient based on chemical solubility data at high loading since a small experimental error in theloading results in a large error in the reported partial pressure of carbon dioxide.

Consider the general equation for phase equilibrium of carbon dioxide, rearranged here for theactivity coefficient of CO .

2

f y PCO CO2 2)

g s . 10Ž .CO ` )2Õ P y PŽ .CO H O2 2

x H expCO CO2 2 ž / RT

For a chemical solubility data point, the loading of the solution, the amine strength, and the partialpressure of carbon dioxide are usually known. Since the amine is completely neutralized by theabsorbed acid gases at loadings greater than 1.0, we can calculate the free carbon dioxide by

Ž .subtracting the total carbon dioxide concentration from the amine concentration. Eq. 10 shows thatif we can provide good models to predict the partial molar volume of carbon dioxide at infinitedilution and the fugacity coefficient of carbon dioxide, we can calculate the activity coefficient of carbon dioxide with respect to its reference state at infinite dilution in water. The results of thesecalculations are summarized in Table 2 for several VLE data points. The fugacity coefficients in thesecalculations are calculated using the SRK EOS and the Poynting corrections are calculated using theBrelvi–O’Connell model. The points in Table 2 represent a cross-section of data from differentinvestigators, different amine concentrations and different temperatures and show that a discrepancybetween the salting out and salting in tendency for carbon dioxide in MDEA solutions at high loadingis present at different experimental conditions.




Table 2

Calculation of activity coefficient from high loading VLE data

)w x Ž .Temperature MDEA Loading X P kPa g Sourcefree CO CO CO2 2 2

Ž . Ž .K wt.%

w x298 23.4 1.146 6.13Ey3 698 0.67 Jou et al. 2w x298 50 1.115 1.28Ey2 1190 0.52 Jou et al. 2w x343 50 1.187 2.64Ey2 5590 0.55 Jou et al. 2

w x298 35 1.498 2.78Ey2 1.49E4 1.92 Jou et al. 4w x313 23.4 1.376 1.53Ey2 3440 0.81 Ho and Eguren 6

w x298 23.4 1.34 1.43Ey2 4860 1.52 Bhairi 7w x323 23.4 1.222 9.30Ey3 4650 1.39 Bhairi 7

There could be many reasons for the discrepancy of the VLE data obtained. One goal of this work was to determine which trend was consistent with the N O analogy. The N O analogy may not be a

2 2

good indication of the physical solubility of carbon dioxide in loaded amine solutions. Since thecharge structure of the two molecules is different, carbon dioxide may be associating with the

protonated amine and therefore ‘salting in’. The experiments conducted in this work, however,confirm the N O analogy in loaded MDEA solutions. This is also consistent with the phase behavior

2

w xof carbon dioxide in other salt solutions. Stewart and Munjal 29 studied the solubility of carbondioxide in synthetic sea water and synthetic sea water concentrates, and determined that carbondioxide ‘salts out’ with increasing ionic strength. The salts in the synthetic sea water were primarilysodium chloride, magnesium chloride, magnesium sulfate, and calcium chloride.

There is also the possibility of having errors in the physical property packages used to calculate theactivity coefficient in Table 2. The pressures dealt with in this work, however, were not very high andthe gas phase at these pressures was almost pure carbon dioxide. Under these conditions, the SRKEOS yields accurate results and any errors associated with the calculation of the fugacity coefficientshould not result in major changes to the analysis above. The Brelvi–O’Connell relationship for

infinite dilution volumes is approximate, however, the Poynting corrections calculated in this analysiswere only fractions of a percent and should not be important.

The error in reported loading could be another reason. Most investigators withdrew samples of theliquid and used a barium salt to precipitate barium carbonate and determine the total amount of carbondioxide. An error of 5–10% in the loading determination at high loading would resolve most of thedifferences described above. Although 5–10% error is in the higher region of the error considered bymost investigators, it is likely that this is what leads to the discrepancy seen above.

A conclusion that can be drawn from this analysis is that it is not possible to obtain consistentinformation about the activity coefficient of carbon dioxide from data at high loading. Since onlyVLE data were regressed, the models of Posey and Austgen show a salting in tendency for carbondioxide which is strongly temperature dependent since the majority of the equilibrium data shows thistendency as well.

Ž .The current regression only examines one response partial pressure . Based on these arguments, itwas decided to eliminate all high loading VLE points from the regression. The high loading regimewas modeled using information gathered about the activity of carbon dioxide through the N O

2

analogy and the other thermodynamic models discussed in this work.




4.2. Regression results

w xN O solubility data in unloaded MDEA solutions 10–12 were regressed independently of VLE2

data. The result of this regression was the MDEArCO parameter that accounts for the decrease in2

CO solubility with increasing MDEA concentration. With this parameter fixed at its regressed value,2

the VLE data for CO in MDEA solutions was regressed. The data regressed in this work are the2

w xsame sets as those regressed by Posey 9 , with the exception of the data with loading greater than 1.The data include loading conditions from 0.0001 to approximately 1, MDEA concentration from 1 to

w x4.28 M, and temperature from 298 to 393 K. These are primarily the data sets of Jou et al. 2– 4 ,w x w x w x qAustgen et al. 5 , Ho and Eguren 6 , and Bhairi 7 . After the first regression, the MDEAH

HCOyrCO parameters were adjusted to account for the N O solubility in loaded solutions. The3 2 2

q y w xMDEAH OH rH O parameter was adjusted to match the conductivity data obtained by Posey 9 .2

With these parameters fixed, the regression was performed again and final parameters were obtained.The results of the regression of vapor–liquid equilibrium data are shown in Fig. 4 as a parity plot.

Most of the data fits between the 0.5 and 2 region with the same systematic error at low loading asw xwas seen by Posey 9 . The overall spread of the data may seem worse than that of Posey at first

glance but this is because the error in his regression was distributed between partial pressure andloading. In this work, only the partial pressure was adjusted and therefore reflects all the error.

The VLE data at high loading was intentionally left out due to the inconsistencies that were pointedout in the previous sections. Model calculations were performed in order to compare the model to thedata at these conditions. The results of these calculations are presented in Fig. 5. Some points that

w xshowed large deviations are not shown. These are primarily points taken by Jou et al. 2 in 50 wt.%MDEA. These points were also left out of the Posey regression. It is seen that the model predictionsusing the N O analogy match the data of Bhairi quite well even though they were not included in the

2

Fig. 4. Comparison of experimental and predicted values of CO vapor pressure over loaded solutions of MDEA.2




Fig. 5. Comparison of experimental and predicted values of CO vapor pressure over loaded solutions of MDEA. Data not2

included in regression.

regression. The Jou data are consistently lower than the Bhairi data and the model predictions.Determination of loading was done very differently by each experimentalist. Jou et al. precipitated allthe absorbed carbon dioxide as BaCO and then titrated it with HCl. Bhairi calculated the loading of

3

the aqueous MDEA solution by knowing how much gas is initially in the cell and measuring thepressure decrease over the course of the experiment. The loading is then determined by closing theoverall material balance for the equilibrium cell.

w xThe parameters obtained are of a different form than those obtained by Posey 9 since this work has changed the temperature dependence of the interaction parameters. Parameters obtained are

summarized in Table 3 along with t values at 408C. Parameters where the standard deviation is notlisted were not regressed.

Parameters not listed have default values of the electrolyte–NRTL model. These are as follows: All B parameters are 0, for A parameters, all moleculermolecule are 0, all waterrsalt pair are 8.0, all

Ž . Žsalt pairrwater are y4, all molecule other than water rsalt pair are 15, all salt pairrmolecule other.than water are 8. All moleculermolecule, waterrsalt pair, and salt pairrwater non-randomness

parameters are 0.2. All other non-randomness parameters are 0.1.Ž .Another measure of the regression is the variancercovariance matrix Table 4 . The high

correlation between some pairs of parameters is present because of the default parameters. Most of theregressed parameters are not correlated. Because of the newly introduced dependence of t ontemperature, the A and B parameters are not strongly correlated as they were in the work of Austgen

w x w x y8 and Posey 9 . However, the A parameters involving HCO are strongly correlated.3

4.3. Model predictions

The resulting model has been used to calculate activity coefficients and partial pressures of carbondioxide in order to compare the results to experimental data and previous models. Fig. 6 shows the




Table 3

Regressed parameter values of the electrolyte–NRTL model: this work compared to PoseyŽ .t s Aq B 1r T y1r T for salt pairrmolecule and moleculersalt pair.

ave

Ž .t s Aq Br T for moleculermolecule.

Parameter A B t at 408C

This work Posey

q yŽ .H O C5 HCO 9.645"0.398 0 9.65 7.502 3

q yŽ .C5 HCO H O y4.483"0.173 652.4"107.3 y4.25 y3.603 2

q yŽ .C5 HCO MDEA y6.211"0.208 y3056.8"317.9 y7.32 y5.803

q 2yŽ .C5 CO MDEA 24.49"3.6 0 24.49 y2.003

q yŽ .C5 OH H O y5.16 0 y5.16 y5.602

q yŽ .C5 HCO CO y8.08 2840.8 y7.05 03 2

CO MDEA 1.637"0.213 0 1.64 02

H O CO 0 0 0 y0.372 2

CO H O 0 0 0 y0.372 2

aH O MDEA 9.473 y1902.4 3.40 3.402

aMDEA H O y2.173 y147.4 y2.64 y2.642

aObtained by Posey.

model prediction of the activity coefficient of carbon dioxide in unloaded aqueous MDEA solutions.N O solubility data are also presented in this figure. In general, the model does a good job of

2

representing the physical solubility in unloaded solutions. It should be noted that there are notemperature dependent terms for CO rMDEA interactions, yet the model predicts the correct

2

temperature dependence of the activity coefficient due to the relationship between the excess Gibbsfree energy and the activity coefficient.

Predictions were also made to determine how the model fit the N O data in loaded solutions and2

Ž .neutralized amines Fig. 7 . The model predicts the solubility well; however, the lack of N O2

solubility data in loaded solutions at higher temperature leads to uncertain predictions at highertemperature.

Model predictions at industrially important conditions were also performed. The partial pressurew xand activity coefficient of carbon dioxide are compared to Posey 9 at 408C, 808C and 1208C in 50

wt.% MDEA. Fig. 8 shows the partial pressure comparison and Fig. 9 shows the comparison of theactivity coefficient as calculated by this work and by Posey. It can be seen that the activity coefficienttrends downward in the model by Posey while the trend predicted by the N O analogy and by this

2

Table 4

Variancerco-variance matrix: correlation of regressed parameters

1 2 3 4 5

q yŽ . Ž .1 H Or C5 HCO A2 3

q yŽ . Ž .2 C5 HCO rH O A y0.983 2

q yŽ . Ž .3 C5 HCO rH O B y0.59 0.533 2

q yŽ . Ž .4 C5 HCO rMDEA A y0.88 0.89 0.443

q yŽ . Ž .5 C5 HCO rMDEA B y0.12 0.09 0.35 y0.113

q 2yŽ . Ž .6 C5 CO rH O A y0.01 0.01 0.01 0.08 0.193 2




Fig. 6. Physical solubility in unloaded solutions: model comparison to N O analogy data.2

work is upwards. This will make up to a factor of 5 difference in the free CO calculated by the two2

different models at moderate loadings.

Fig. 7. Physical solubility in loaded solutions: model comparison to N O analogy data.2




Fig. 8. Model partial pressure predictions.

The partial pressure predictions of this model match those of Posey well except at very highŽ . Ž q y.loading at high temperature 1208C . This may be explained by the new C5 HCO rCO

3 2

Fig. 9. Model predictions of the activity coefficient of carbon dioxide in 50 wt.% MDEA.




w xparameters that are introduced in this work. Chang 30 studied the sensitivity of the partial pressureto each of the electrolyte–NRTL parameters. He found that the partial pressure at 408C is not

Ž q y. Ž .sensitive to the C5 HCO rCO parameter except at very high loading around 1.0 . At 1208C,3 2

Ž .however, these parameters become important at moderate loading around 0.5 . For this reason,Ž q y.setting the C5 HCO rCO parameter modified the model fit at high temperature compared to that

3 2

w x Ž q y.of Posey 9 . The only other parameters important at these conditions are the H Or C5 HCO and2 3

Ž q y.C5 HCO rH O parameters. These parameters, therefore, adjust to account for the change in the3 2

Ž q y.C5 HCO rCO parameters.3 2

Ž q y.The C5 HCO rCO parameter is based on a temperature extrapolation of data at 408C and3 2

608C. The prediction of the model would increase significantly if there were reliable N O solubility2

data in loaded solutions at higher temperature. There has been much discussion about the validity of w xacid gas VLE data at high loading. Posey 9 did not regress many of the VLE data points based on

the author’s own questioning of the data. The model of Posey predicts a much flatter VLE curvearound loading of 1.0 at higher temperature than at lower temperature. This is not the case in thiswork that raises the question of whether this is due to a high temperature interaction between freeCO and the amine solution, or whether the VLE data is not indicative of the true behavior of the

2

system.

5. Conclusions

Analysis of several data sets for the chemical solubility of carbon dioxide in aqueous MDEA showinconsistent trends for the physical solubility of CO with loading. Experiments performed in this

2

work support the salting out tendency of carbon dioxide with increasing ionic strength. The dataobtained confirms the validity of the N O analogy in neutralized solutions of aqueous MDEA.

2

In order to model the physical and chemical solubility in a thermodynamically consistent manner,the reference state for solutes should be defined as infinite dilution in the aqueous state. Havingperformed this, the new model predicts free CO concentrations in accordance with the N O analogy

2 2

w xand makes up to a factor of 4 correction to previous models 8,9 .The modeling work performed leads to several conclusions. VLE data at high loading is shown to

be quite sensitive to experimental errors of the loading. As a result, it is difficult to obtain informationabout the activity coefficient of carbon dioxide in loaded alkanolamine solutions. There are very fewdata points that quantify the temperature dependence of N O solubility in loaded aqueous MDEA

2

solutions. It is recommended that the N O analogy be studied at higher temperatures and in loaded2

Žsolutions. There is a need for VLE data at industrially important conditions carbon dioxide over 50.wt.% MDEA solutions at 1208C .

6. List of symbols

H x Henry’s law constant for solute i in solvent x, atm ly1 moly1i

P pressure, PaP) vapor pressure of x, Pa

x

R universal gas constant, 8.314 J moly1 Ky1




T temperature, K

Õ` partial molar volume of i at infinite dilution, cm3 moly1i

x liquid phase mole fractioni

y gas phase mole fractioni

Greek letters

F fugacity coefficienti

t electrolyte–NRTL interaction parametersg activity coefficient with reference state of pure component at system T and P

i

g ) activity coefficient with reference state of infinite dilutioni

g ` activity coefficient evaluated at infinite dilutioni

Acknowledgements

The authors would like to acknowledge the Separations Research Program at the University of Texas at Austin and other industrial sponsors for financial support of this work.

References

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physical chemistry solubility of co2

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