Physical & Chemical Solubility of CO2

5/20/2018 Physical & Chemical Solubility of CO2

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.Fluid Phase Equilibria 168 2000 241258

www.elsevier.nlrlocaterflu

Physical and chemical solubility of carbon dioxide in aqueousmethyldiethanolamine

Sanjay Bishnoi, Gary T. Rochelle )

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

Received 15 February 1999; accepted 8 December 1999

Abstract

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 i

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

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

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

of carbon dioxide as a function of loading because of this discrepancy in the data. The electrolyteNRTL mode

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

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

high temperature and high loading are needed for industrially important MDEA concentrations. The N O2analogy 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:ElectrolyteNRTL 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 oindustries, including the processing of natural gas and the removal of CO from synthesis gas in th

2

production of hydrogen or ammonia. With the recognition of CO as a greenhouse gas, anothe2

important application of this technology is CO removal from combustion gases at power plants o2manufacturing facilities.

)

Corresponding author. Fax: q1-512-475-7824. . .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. .P I I : S 0 3 7 8 - 3 8 1 2 0 0 0 0 3 0 3 - 4


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( )S. Bishnoi, G.T. Rochelle r Fluid Phase Equilibria 168 2000 241258242

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

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

2

equilibrium distribution of species in the solution. Since free CO is only a very small fraction of th2

.total CO concentration free plus reacted , it is calculated using a chemical and phase equilibrium2routine. The development of such a routine requires experimental data of the chemical and physicasolubility of carbon dioxide in aqueous alkanolamine solutions along with a thermodynamic framework to account for the reaction of carbon dioxide with the alkanolamines, and liquid and gas phasnon-idealities. The physical solubility of carbon dioxide cannot be directly measured in aqueoualkanolamines since it reacts with the solution. Therefore, the nitrous oxide analogy is used to infethe physical solubility of carbon dioxide.

.The chemical solubility of CO in aqueous methyldiethanolamine MDEA solutions has bee2

studied by several investigators. Experimental data for the equilibrium partial pressure of carbow xdioxide over aqueous MDEA has been obtained by several investigators 27 . All data obtaine

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

w xelectrolyteNRTL framework within Aspen Pluse 23 to model the vaporliquid equilibrium ow xcarbon dioxide over aqueous MDEA. Posey 9 extended Austgens efforts by measuring an

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

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

The physical solubility of CO in aqueous MDEA has been studied primarily through th2

experimental use of the nitrous oxide analogy with MDEA solutions from 0 to 4.28 M anw xtemperatures of 158C to 608C 1013 . Other investigators have measured the solubility of N O i

2

w xloaded solutions of MDEA 1416 .The contribution of this work is to bring the study of physical and chemical solubility together an

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

.discrepancy is illustrated in Section 4.1. Data are presented Section 4.1 for CO and N O solubilit2 2

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

2

and to quantify the salting out tendency of carbon dioxide in aqueous MDEA solutions as a functioof 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. Th2

electrolyteNRTL model has been used with a different reference state for solutes in order to predicthe 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 ardescribed in Section 3. The algorithm used for chemical and physical solubility is presented alonwith parameters obtained by regression of VLE and physical solubility data using GREG, an iterativ

w xregression package developed by Caracotsios 17 .


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( )S. Bishnoi, G.T. Rochelle r Fluid Phase Equilibria 168 2000 241258 24

2. Equilibrium model

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

CO q 2H O l HCOyq H Oq 1 2 2 3 3

HCOyq H O l CO2yq H Oq 2 3 2 3 3

MDEAHqq H Ol

MDEAq H Oq 3 2 3

2H Ol

OHyq H Oq. 4 2 3w xValues of the equilibrium and Henrys law constants are the same as Posey 9 , and are no

included here for brevity. The model solves for liquid mole fractions of all components chemica. .equilibrium and gas phase partial pressures of each molecular component phase equilibrium give

the 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 liqui

phase and the second calculating the resulting composition of the gas phase. The liquid phas

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

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

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

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

using the gas phase algorithm. This algorithm starts by assuming an ideal gas and calculates the totaand partial pressure of each component based on physical equilibrium. Fugacity coefficients are thesolved for iteratively until the total pressure does not change. Since the electrolyteNRTL model hano dependence of pressure on activity coefficients, no liquid phase iteration must be made after thgas 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 thspecies in consideration is a solvent, solute or ionic species. Different reference states are used in thi

work than in the work of Posey and Austgen. In their work, the reference state of solvents is the pursolvent at the system temperature and pressure. Solutes are considered to be at their reference state ainfinite dilution in the mixed, loaded solvent. For example, the activity coefficient of carbon dioxidin a 50-wt.% mixture of water and MDEA approaches 1.0 as the mole fraction of carbon dioxidapproaches zero in the solution. The reference state of ionic species is considered to be infinitdilution in the aqueous phase instead of the mixed solvent.


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Fig. 1. Description of model algorithm.

A major inconsistency resulting from the previous reference states is the normalization oequilibrium constants. Equilibrium constants involving the solute contain the activity coefficient othe solute and must, therefore, be normalized consistently with the reference state of the solute. Sinc

the 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 aqueou

phase in order to account for the change in carbon dioxide activity as a function of amine strength. Ithis work, the reference states of solvent molecules and of ionic species remain the same as in th

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


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

gi

)g s . 5 i `gi

.The activity coefficients in Eq. 5 are calculated from the expressions for the excess Gibbs frew xenergy as described by the electrolyteNRTL model and as discussed in the works of Austgen 8 anw xPosey 9 .

2.2. System non-idealities

This work uses the electrolyteNRTL model to account for liquid phase non-idealities. Thw xelectrolyteNRTL model was first proposed by Chen et al. 20 . The original work was applicable t

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

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

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

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

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

i

parameters of the electrolyteNRTL model are defined differently than in the work of Posey anAustgen. In this work, tvalues for salt pairrmolecule and moleculersalt pair interactions are give

.by Eq. 6 whereT is 353.15 K.ave

1 1tsA qB y 6 /T T

ave

BtsA q 7

T

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

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 o

pressure and brought out of the integration. This treatment is consistent with the models of Austgen ew x w xal. 5 and Posey and Rochelle 18 . The partial molar volumes of solvents are calculated as the molaw volume of the pure solvent in order to be consistent with its reference state. The Rackett equation 25

is used to calculate these volumes. The partial molar volume of solutes is calculated at infinitw xdilution in the solvent by using the BrelviOConnell model 26 . In typical acid gas VLE, th

pressures are low enough that the Poynting corrections of all species are very small.


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Gas phase deviations from ideal gas behavior are dealt with using the SoaveRedlichKwon . . w xSRK equation of state EOS 27 . Typical pressures and gas compositions in VLE of carbon dioxidover 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 totacarbon dioxide that is not reacted. Since carbon dioxide reacts with the amine, an analogy is drawbetween the solubility of nitrous oxide and that of carbon dioxide. The ratio of the solubility onitrous oxide in a given solvent to that of carbon dioxide in the same solvent is considered to be constant at a given temperature.

w xThe N O analogy was first proposed by Clarke 28 . He argued that since N O and CO hav2 2 2

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

.shown in Fig. 2 for the solubility of N O in aqueous solutions of MDEA which are loaded wit2

carbon dioxide. These experiments show a strong salting out tendency for carbon dioxide witincreasing loading. In this work, the apparatus used by Toman has been reconstructed and experiments 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 iaqueous MDEA solutions that show opposite trends for the increaserdecrease of physical solubilitof 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 ha2

typically been expressed as a Henrys law constant in the solvent being studied. This is done b

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


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

PisolventH s . 8 i

xi

.Note that Eq. 8 is a simplification from the rigorous definition of the Henrys law constant since w

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

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

Hsolventi)g s 9 i H O2H

i

. solvent .In Eq. 9 , H is calculated from Eq. 8 and then normalized by the Henrys law constant of thi

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

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 ga

displaced into a liquid. The liquid is originally unsaturated with respect to the solute gas and the gas iclosed with respect to the atmosphere, therefore, the solubility or the Henrys constant may bmeasured by the volume of gas displaced.

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


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The mercury reservoir is open to the atmosphere on one side and the level of mercury in the burettis adjusted by moving the reservoir up and down on a clamp stand. By doing so, we can ensure thathe pressure in the burette is always atmospheric. This ensures that any difference in the mercury leveis 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 taland has an inside diameter of 5 cm. Tygon tubing connects the mercury reservoir to the burette. Th

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

flask is extremely short and is made of Teflon tubing. The head assembly of the flask is made of glasbut 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 magnetic stirrer. Although the original apparatus built by Toman had a temperature bath, experimentin the current work were run at ambient temperature. Since the vapor pressure of water is low aambient 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 closinvalve 5. The burette is then charged with gas by opening valves 1 and 2 and flowing gas through th

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

4. Results

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

2

in aqueous MDEA solutions neutralized by sulfuric acid.Parameters are estimated for the electrolyteNRTL model, such that the physical solubility o

carbon dioxide, as measured by the N O analogy, is predicted by the model. ElectrolyteNRT2

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

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 metho

were verified by studying the solubility of carbon dioxide in water, nitrous oxide in water, and nitrouoxide in aqueous alkanolamines and comparing the results with other investigators. The Henryconstant extracted from this apparatus matches other investigators within 510%. It is believed thathese deviations are because the apparatus is not temperature controlled and temperature variations o"0.58C were seen between experiments. The results do, however, match qualitative results and trendof other investigators very well. The activity coefficient of carbon dioxide increases, and hence th


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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 g2 4

y1 y1 . . .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 1.4825 50 N O 0.5 133.7 3.03

2

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 alsdecreases with increased salt concentration. The nitrous oxide analogy provides a good estimation othe solubility of carbon dioxide in these cases, well within the precision of the apparatus. The resultwill 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 increasinsalt concentration. Chemical solubility data taken by some investigators, however, are not consisten

w xwith this trend. Analysis of the chemical solubility data at loadings greater than 1.0 2 7 shows thathe partial pressure of carbon dioxide is extremely sensitive to loading. The activity coefficientherefore, is also extremely sensitive to loading at these conditions and sometimes shows either 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 thloading 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 thactivity coefficient of CO .

2

f y PCO CO2 2)

g s . 10 CO ` )2 P y P .CO H O2 2

x H expCO CO2 2 /RT

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

.subtracting the total carbon dioxide concentration from the amine concentration. Eq. 10 shows thaif we can provide good models to predict the partial molar volume of carbon dioxide at infinitdilution and the fugacity coefficient of carbon dioxide, we can calculate the activity coefficient ocarbon dioxide with respect to its reference state at infinite dilution in water. The results of thes

calculations are summarized in Table 2 for several VLE data points. The fugacity coefficients in thescalculations are calculated using the SRK EOS and the Poynting corrections are calculated using thBrelviOConnell model. The points in Table 2 represent a cross-section of data from differeninvestigators, different amine concentrations and different temperatures and show that a discrepancbetween the salting out and salting in tendency for carbon dioxide in MDEA solutions at high loadinis present at different experimental conditions.


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Table 2

Calculation of activity coefficient from high loading VLE data

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

. .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 workwas to determine which trend was consistent with the N O analogy. The N O analogy may not be

2 2

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

protonated amine and therefore salting in. The experiments conducted in this work, howeveconfirm the N O analogy in loaded MDEA solutions. This is also consistent with the phase behavio

2

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

There is also the possibility of having errors in the physical property packages used to calculate thactivity coefficient in Table 2. The pressures dealt with in this work, however, were not very high anthe 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 coefficienshould not result in major changes to the analysis above. The BrelviOConnell relationship fo

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

The error in reported loading could be another reason. Most investigators withdrew samples of thliquid and used a barium salt to precipitate barium carbonate and determine the total amount of carbodioxide. An error of 510% in the loading determination at high loading would resolve most of thdifferences described above. Although 510% error is in the higher region of the error considered bmost 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 consisteninformation about the activity coefficient of carbon dioxide from data at high loading. Since onlVLE data were regressed, the models of Posey and Austgen show a salting in tendency for carbo

dioxide which is strongly temperature dependent since the majority of the equilibrium data shows thitendency as well. .The current regression only examines one response partial pressure . Based on these arguments,

was decided to eliminate all high loading VLE points from the regression. The high loading regimwas 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.


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4.2. Regression results

w xN O solubility data in unloaded MDEA solutions 1012 were regressed independently of VL2

data. The result of this regression was the MDEArCO parameter that accounts for the decrease i2

CO solubility with increasing MDEA concentration. With this parameter fixed at its regressed value2

the VLE data for CO in MDEA solutions was regressed. The data regressed in this work are th2

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

w 4.28 M, and temperature from 298 to 393 K. These are primarily the data sets of Jou et al. 2 4w x w x w x Austgen 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. Th3 2 2

q y w MDEAH OH rH O parameter was adjusted to match the conductivity data obtained by Posey 92

With these parameters fixed, the regression was performed again and final parameters were obtainedThe results of the regression of vaporliquid 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 aw xwas seen by Posey 9 . The overall spread of the data may seem worse than that of Posey at fir

glance but this is because the error in his regression was distributed between partial pressure anloading. 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 pointeout in the previous sections. Model calculations were performed in order to compare the model to thdata at these conditions. The results of these calculations are presented in Fig. 5. Some points tha

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 predictionusing the N O analogy match the data of Bhairi quite well even though they were not included in th

2

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


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Fig. 5. Comparison of experimental and predicted values of CO vapor pressure over loaded solutions of MDEA. Data no2

included in regression.

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

3

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

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

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

Parameters not listed have default values of the electrolyteNRTL model. These are as follows: AB parameters are 0, for A parameters, all moleculermolecule are 0, all waterrsalt pair are 8.0, a

. salt pairrwater are y4, all molecule other than waterrsalt pair are 15, all salt pairrmolecule othe.than water are 8. All moleculermolecule, waterrsalt pair, and salt pairrwater non-randomnes

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

correlation between some pairs of parameters is present because of the default parameters. Most of thregressed parameters are not correlated. Because of the newly introduced dependence of t otemperature, the Aand B parameters are not strongly correlated as they were in the work of Austgew 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 carbodioxide in order to compare the results to experimental data and previous models. Fig. 6 shows th


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Table 3

Regressed parameter values of the electrolyteNRTL model: this work compared to Posey .ts AqB 1r Ty1r T for salt pairrmolecule and moleculersalt pair.

ave

.ts Aq Br T for moleculermolecule.

Parameter A B tat 408C

This work Posey

q y .H O C5 HCO 9.645"0.398 0 9.65 7.502 3q y .C5 HCO H O y4.483"0.173 652.4"107.3 y4.25 y3.603 2q y .C5 HCO MDEA y6.211"0.208 y3056.8"317.9 y7.32 y5.80

3q 2y .C5 CO MDEA 24.49"3.6 0 24.49 y2.00

3q y .C5 OH H O y5.16 0 y5.16 y5.60

2q y .C5 HCO CO y8.08 2840.8 y7.05 0

3 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 solutionsN O solubility data are also presented in this figure. In general, the model does a good job o

2

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

2

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

Predictions were also made to determine how the model fit the N O data in loaded solutions an2

.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 highetemperature.

Model predictions at industrially important conditions were also performed. The partial pressurw xand activity coefficient of carbon dioxide are compared to Posey 9 at 408C, 808C and 1208C in 5

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

2

Table 4

Variancerco-variance matrix: correlation of regressed parameters

1 2 3 4 5

q y

. .1 H Or C5 HCO A2 3q y . .2 C5 HCO rH O A y0.983 2

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

q y . .4 C5 HCO rMDEA A y0.88 0.89 0.443

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

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


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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 tw2

different models at moderate loadings.

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


15/18


Fig. 8. Model partial pressure predictions.

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

3

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


16/18


w xparameters that are introduced in this work. Chang 30 studied the sensitivity of the partial pressurto each of the electrolyteNRTL parameters. He found that the partial pressure at 408C is no

q y. .sensitive to the C5 HCO rCO parameter except at very high loading around 1.0 . At 1208C3 2

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

3 2

w x q y.of Posey 9 . The only other parameters important at these conditions are the H Or C5 HCO an2 3

q y

.C5 HCO rH O parameters. These parameters, therefore, adjust to account for the change in th3 2 q y.C5 HCO rCO parameters.3 2

q y.The C5 HCO rCO parameter is based on a temperature extrapolation of data at 408C an3 2

608C. The prediction of the model would increase significantly if there were reliable N O solubilit2

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

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

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 th

2

work support the salting out tendency of carbon dioxide with increasing ionic strength. The datobtained 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 mannethe reference state for solutes should be defined as infinite dilution in the aqueous state. Havinperformed this, the new model predicts free CO concentrations in accordance with the N O analog

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 t

be quite sensitive to experimental errors of the loading. As a result, it is difficult to obtain informatioabout 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 loade2

solutions. There is a need for VLE data at industrially important conditions carbon dioxide over 5.wt.% MDEA solutions at 1208C .

6. List of symbols

Hx Henrys law constant for solute i in solvent x, atm ly1 moly1iP pressure, PaP) vapor pressure of x, Pa

x

R universal gas constant, 8.314 J moly1 Ky1


17/18


T temperature, K

` 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 electrolyteNRTL 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 oTexas at Austin and other industrial sponsors for financial support of this work.

References

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University of Texas, 1998.w x .2 F.Y. Jou, A.E. Mather, F.D. Otto, Ind. Eng. Chem. Process Des. Dev. 21 1982 539544.w x .3 F.Y. Jou, J.J. Caroll, A.E. Mather, F.D. Otto, Can. J. Chem. Eng. 71 1993 264268.w x .4 F.Y. Jou, F.D. Otto, A.E. Mather, Ind. Eng. Chem. Res. 29 1994 20022005.w x .5 D.M. Austgen, G.T. Rochelle, X. Peng, C.C. Chen, Ind. Eng. Chem. Res. 28 1989 10601073.w x6 B. Ho, R. Eguren, Presented at the 1988 AIChE Spring National Meeting, March 6 10, 1988.w x7 A. Bhairi, Experimental equilibrium between acid gases and ethanolamine solutions, PhD Dissertation, Oklahoma Sta

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Physical & Chemical Solubility of CO2

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