Partial vapor pressure of CO2 and H2S over aqueous methyldiethanolamine solutions

Fluid Phase Equilibria 172 (2000) 261–277

Partial vapor pressure of CO2 and H2S over aqueousmethyldiethanolamine solutions

B. Lemoinea, Yi-Gui Li b, R. Cadoursa, C. Boualloua, D. Richona,∗a Centre Réacteurs et Processus, Ecole Nationale Supérieure des Mines de Paris, 60 Bd. Saint-Michel, 75006 Paris, France

b Department of Chemical Engineering, Tsinghua University, Beijing 100084, PR China

Received 9 July 1999; accepted 30 May 2000

Abstract

A new apparatus is presented to measure low partial vapor pressures of acid gas. New measurements are given forcarbon dioxide and hydrogen sulfide into aqueous solutions of methyldiethanolamine (MDEA). Large discrepanciesamong the measured VLE data and the slopes of their solubility curves are found between the authors due tosystematic experimental errors, and particularly in the low acid loading regions. Different modeling approaches areproposed herein. © 2000 Elsevier Science B.V. All rights reserved.

Keywords:Apparatus; Acid gas solubility data; MDEA; Carbon dioxide; Hydrogen sulfide; Modeling

1. Introduction

Aqueous solutions of alkanolamines are commonly used for acid gases removal from gaseous streams.H2S and CO2 are absorbed into the solution and desorbed from the solution by steam stripping. Mo-noethanolamine (MEA) and diethanolamine (DEA) have been the most widely used amines in gas treat-ing processes. Methyldiethanolamine (MDEA) solutions with the advantages of H2S selective removal,and lower enthalpy of reaction and vapor pressure than primary or secondary alkanolamines solutionshas found an increased use. The design of such separation equipment also requires the knowledge ofvapor–liquid equilibrium as deviation from equilibrium provides the force to drive the kinetically con-trolled process. There have been a great number of investigations of the solubility of CO2 and H2S inMDEA aqueous solutions. Only a few studies have reported experimental data for very low gas loadings.Jou et al. [1,11,13] and Rogers et al. [15] have reported CO2 and H2S solubility in 35 wt.% MDEAsolutions at 313 and 373 K, and H2S solubility in 50 wt.% MDEA solution at 313 K for acid gas loadingslower than 0.1 mol of gas per mole of amine.

∗ Corresponding author. Tel.:+331-64694965; fax:+331-64694968.E-mail address:[email protected] (D. Richon).

0378-3812/00/$20.00 © 2000 Elsevier Science B.V. All rights reserved.PII: S0378-3812(00)00383-6

262 B. Lemoine et al. / Fluid Phase Equilibria 172 (2000) 261–277

Nomenclature

A interaction parameter between and among neutral moleculesAx Debye–Hückel parameter on a mole fraction basisa,b coefficients for interaction parametersB interaction parameter between ionsF objective functionIx ionic strength on mole fraction basisP partial pressure (Pa or kPa)T absolute temperature (K)W interaction parameter between and among neutral and ionic speciesX liquid phase mole fraction based on the true species, molecular and ionicZ valency of an ion

Greek lettersα Pitzer universal constantγ activity coefficient in mole fraction baseδ average relative deviation of partial pressure (%)ρ Pitzer parameter relating to the hard-core collision diameter between ions

Superscript∗ unsymmetric convention

Subscripts1 MDEA2 H2OM MDEAH+

X HCO3− or HS−

cal calculated valueex experimental value

This paper describes an apparatus developed to measure acid gas solubility in amine aqueous solutions.Solubility of CO2 and H2S have been measured in the temperature range 297–314 K, with acid gasloadings in the range 0.0083–0.2625 mol of gas per mole of amine, and with 11.83–23.63 wt.% MDEAaqueous solutions. Experimental results are reported and compared with literature data. The correlationand prediction for the above systems in this low acid loading region are also established.

2. Experimental

The equilibrium apparatus (see Fig. 1) is composed of a glass cylinder closed at each extremity bytwo stainless steel flanges. Two Viton gaskets ensure adequate sealing and avoid glass–metal contact.

B. Lemoine et al. / Fluid Phase Equilibria 172 (2000) 261–277 263

Fig. 1. Flow diagram of the apparatus for small differential vapor pressure measurements. ASM: variable speed motor, CI:component inlet, DPT: differential pressure transducer, EC: equilibrium cell, GC: glass cylinder, Hg: mercury, LB: liquid bath,LP: liquid phase, MR: magnetic rod, MWG: movable washer gasket, O: Oven, PA: pressure actuator, PP: platinum probe, S:septum, TR: temperature regulation, Va P: vacuum pump and VP: vapor phase.

The cell is provided with two propellers supported by a shaft maintained vertically by two sapphirebearings on the metallic flanges. The shaft is driven magnetically and the liquid phase and the vaporphase are agitated simultaneously. This technique avoids leaking, friction and heat generation, whichappear when using stems crossing the cell bottom and top. The propellers’ speed is maintained constant at100 rpm.

The upper flange is equipped with a septum for liquid and gas loading. This septum is covered withmercury in order to avoid gas diffusion and then leaking. A tube passing through this flange is used todegas the cell. The cell is provided with a differential pressure transducer, working in the range 0–1500 Pa.The pressure transducer is from MKS, type 315B 0–11 mmHg full scale, it is fitted with a MKS type272 temperature controller and a MKS type 270 signal conditioner. It has a calibration certificate within0.03 Pa from MKS. In our laboratory we have performed some additional calibrations against a mercurymanometer and we have confirmed the accuracy of the MKS calibration within the mercury manometer


accuracy, i.e. within 2×10−2 mmHg which is our own limiting accuracy and do not affect the real precisionannounced by the manufacturer within the considered measuring range. The transducer is thermostatedat 407 K, in order to avoid liquid condensation in the measuring chamber. A microcomputer fitted withan acquisition card is used to record the pressure transducer signal.

The lower flange is equipped with a movable container to trap a liquid sample, which will act as areference. The sealing of this reference container is obtained by a Viton disk. The volume of the sampletrapped in this way is about 1% of the total volume of the aqueous solution.

The whole cell is placed in a thermostated liquid bath. The liquid bath temperature and the equilibriumtemperature are measured by a platinum probe. The injection of various volumes of gas in the cell yieldsthe total volume available for gas and liquid in the equilibrium cell. This volume corresponding to thecell volume and to the pressure transducer volume is estimated at (68.9±0.1)×10−6 m3. The transducervolume is given by the constructor: 4.0×10−6 m3.

This apparatus presents several advantages. First, the experimental procedure avoids analysis of thegas and liquid phases. The gas loading is calculated from the volumes and the amounts of gas and liquidintroduced in the cell. Second, no inert gas was added to measure acid gas solubility for low partialpressures. This technique avoids gas phase resistance and diminishes the time to reach the equilibriumconditions. Third, we used a small liquid volume, between 12 and 15 cm3. This volume is small incomparison with the liquid volumes, generally encountered in the literature, above 100 cm3. By avoidingsampling methods, the liquid volume in our apparatus remains constant during the experiment. Thistechnique avoids liquid reinjection during the experiments to maintain the liquid volume constant [2].The most important advantage of this apparatus is that the acid gas partial pressures are directly obtained inthe range 0–11 mmHg. The gas phase composition at low sour gas partial pressure is generally obtainedby chromatographic analyses in the literature. This technique implies the addition of an inert gas toget a sufficient pressure allowing to sample the gas phase, and introduces uncertainties through thechromatographic measurements [3].

Water and MDEA are degassed independently, and mixed under a vacuum in desired proportions. Theamounts of water and MDEA are known separately by differential weighings within 0.01 g. The aqueousmixture is introduced inside the degassed equilibrium cell by gravity and under a vacuum through ahypodermic needle introduced in the septum. Accurate differential weighings within 2×10−2 g of theglass flask before and after the transfer yields the mass of solution present in the cell. The accuracy ofthe solvent composition is within 10−4 in weight fractions.

The liquid phase volume,Vintroduced, is obtained through the density correlation of Al-Ghawas et al. [4].Then stirring is started, about 2100 rpm at the beginning, to reach thermodynamic equilibrium and reducedat 100 rpm during measurements. When thermal equilibrium is reached, a liquid sample is isolated in themovable washer gasket moved upward by a pneumatic actuator. One of the entrances of the differentialtransducer is then closed. In this way, the closed arm of the pressure transducer works as a reference forwater–MDEA mixture. We assume that due to low acid gas content the differential pressure, which ismeasured, is the acid gas partial pressure.

Given volumes of acid gases are then introduced through the septum with calibrated chromatographicsyringes. The amount of acid gas introduced is known from the volume introduced at room temperatureT0 and atmospheric pressureP0

Nacid gases introduced=P0Vintroduced

RT0(1)


At the beginning, the differential pressure is very high, but decreases as acid gases dissolve with thehelp of vigorous stirring. The pressure decrease down to its equilibrium value is recorded as a functionof time. The equilibrium is reached within 4 h with CO2 injection, and 45 min with H2S injection. Thistime difference is explained by the different kinetic mechanisms involved in each case. The reactionbetween MDEA and H2S implies a proton transfer. It is generally considered instantaneous compared tothe transfer mechanism. CO2 cannot react directly with a tertiary amine. The Donaldson and Nguyen [5]mechanism is the most accepted one to describe the reaction involved in the CO2 absorption into aqueoussolutions of tertiary amines. This theory leads to a finite rate reaction mechanism. The different reactionrates between the MDEA and CO2 or H2S explain the selectivity of aqueous solutions of MDEA withrespect to hydrogen sulfide. The amount of acid gas absorbed is then obtained from

Nacid gases absorbed=Nacid gases introduced− PVgas phase

RTequilibrium cell− PVtransducer

RTtransducer(2)

The thermal gradient between the equilibrium cell and the transducer is also neglected. The equilibriumsolution loading is then obtained by

loading=Nacid gases absorbed

VliquidCMDEA(3)

whereVliquid andCMDEA are the liquid phase volume and the MDEA concentration in the aqueous solution.The relative accuracy on the acid gas loading, in the worst case, is 5×10−2 for CO2 or H2S. This is this

uncertainty which is the most important on the determination of the partial vapor pressure of either CO2

or H2S. We can conclude the partial vapor pressures given in this paper have an uncertainty of not morethan 5×10−2 which is the maximum reached only after several consecutive loading.

The solubilities of CO2 in 23.63 wt.% MDEA aqueous solutions at 298 K are given in Table 1. At thistemperature the CO2 partial pressures were from 12 to 1636 Pa.

The solubilities of H2S in 23.63 wt.% at 313 K and 11.83 wt.% MDEA aqueous solutions at 298 K aregiven in Table 2. At this temperature the H2S partial pressures were from 23 to 1611 Pa.

Table 1CO2 solubility into MDEA aqueous solutions

T (K) MDEA (wt.%) Loading (molCO2/molMDEA) PCO2 (Pa)

297.70 23.63 0.0171 20297.70 23.63 0.0342 62297.72 23.63 0.0512 114297.71 23.63 0.0648 165297.71 23.63 0.0853 256297.71 23.63 0.0971 304297.70 23.63 0.1126 402297.72 23.63 0.1295 477297.73 23.63 0.1361 546297.72 23.63 0.1617 716297.70 23.63 0.2042 1075297.72 23.63 0.2550 1593297.67 23.63 0.2625 1636


Table 2H2S solubility into MDEA aqueous solutions

T (K) MDEA (wt.%) Loading (molH2S/molMDEA) PH2S (Pa)

313.08 23.63 0.0151 40313.09 23.63 0.0301 113313.11 23.63 0.0452 224313.13 23.63 0.0601 355313.13 23.63 0.0754 509313.12 23.63 0.1049 887313.14 23.63 0.1346 1352313.12 23.63 0.1494 1611313.11 23.63 0.0356 183313.27 23.63 0.0497 291313.25 23.63 0.0638 416313.19 23.63 0.0920 735313.25 23.63 0.1201 1128298.15 11.83 0.0101 31298.16 11.83 0.0202 66298.16 11.83 0.0606 176298.15 11.83 0.1010 329298.17 11.83 0.1208 423298.13 11.83 0.1610 661297.95 11.83 0.2011 945298.16 11.83 0.2411 1278298.16 11.83 0.2610 1468299.34 11.83 0.0154 23298.16 11.83 0.0233 49298.17 11.83 0.0308 71298.13 11.83 0.0463 129298.16 11.83 0.0770 218298.17 11.83 0.1384 482298.15 11.83 0.2299 1091

3. Thermodynamic expression

Li and Mather [6] used the simplified Clegg–Pitzer equations [7] to correlate the solubility data forMDEA–CO2–H2O and MDEA–H2S–H2O systems over a wide range of solvent concentration (12–50 wt.%MDEA aqueous solutions), temperature (298–393 K), partial pressure of acid gases (0.001–5290 kPa) andacid gas loading (0.001–1.0 mol CO2 or H2S/mol MDEA) from different authors. They have shown thatthe simplified Clegg–Pitzer [7] equations are capable of correlation and prediction of the solubility ofan acid gas in a mixed solvent system with chemical equilibria. They found the experimental VLE datameasured from different authors in the same temperature and the same initial MDEA concentration werenot coincident with each other due to the measurement errors, which decreased the accuracy of the cor-relation and prediction by use of these equations. In this work, we still use the simplified Clegg–Pitzerequation [7]. We took three options. One is to use the interaction parameters regressed from Li and Mather[6] to predict the above VLE experimental data. The second is to re-regress the Clegg–Pitzer parameters


by use of our own experimental VLE data only in the low temperature and low acid gas loading regions.The third option is to re-regress the Clegg–Pitzer parameters by incorporating our experimental data withthose from other authors in the whole temperature and acid gas loading ranges. The results from threemethods are compared.

The chemical equilibria considered in this work are the same as those of Li and Mather [6]

CO2 + 2H2O⇔K1

H3O+ + HCO3

−

H2S+ H2O⇔K2

H3O+ + HS−

H2O + MDEAH+⇔K3

H3O+ + MDEA

The chemical equilibrium constants for the above reactions and the Henry constants for CO2 andH2S used here are the same as in the paper of Li and Mather [6] and are only temperature depen-dent. In our material balance we considered the ionic species of MDEAH+, HCO3

− and HS− and theneutral species of H2O, MDEA, CO2 and H2S and neglected the ionic species of CO3

2−, S2−, OH−

and H3O+ in the aqueous phase. (From Posey–Rochelle [8] the equilibrium concentrations of CO32−

even in 50% MDEA solution and acid loading near 1 at 313 K are less than 1 mol% in liquid phase,explicitly the concentration of CO32− is 100 times lower than the concentration of HCO3

− for load-ings lower than 0.3, which is our interest range.) In our calculation of the activity coefficients of thecomponents in aqueous phase, the neutral species of dissolved free gases (CO2 and H2S) are also ne-glected, because their concentrations are low. We also neglect the non-ideality of the gas phase as inLi–Mather’s paper [6]. Only the activity coefficients for H2O, MDEA, MDEAH+, HCO3

− and HS− inaqueous phase are involved in our calculation for the non-ideality of the liquid phase. In this work, bothwater and MDEA are treated as solvents. The reference state (or standard state) associated with eachsolvent is the pure liquid at the system temperature and pressure. The adopted reference state for theionic species and molecular solutes (CO2 and H2S) is the ideal, infinitely dilute aqueous solution (with-out MDEA) at the system temperature and pressure. Thus, we can use the Henry constants of CO2 andH2S in pure water without any additional approximate assumption. The chemical equilibrium constantsin this work should adopt the same reference states for each component in equilibrium. According toour simplified Clegg–Pitzer equations, the activity coefficient expressions for each component are asfollows:

ln γ1 = 2AxI3/2x

1 + ρI1/2x

− xMxXBMX exp(−αI 1/2x ) + A12(1 − 2x1)x

22 + 2A21x1x2(1 − x1)

+(1 − x1)x1W1,MX − x2x1W2,MX (4)

ln γ2 = 2AxI3/2x

1 + ρI1/2x

− xMxXBMX exp(−αI 1/2x ) + A21(1 − 2x2)x

21 + 2A12x1x2(1 − x2)

+(1 − x2)xIW2,MX − x1xIW1,MX (5)


ln γ ∗M = −z2

MAx

[2

ρln(1 + ρI 1/2

x ) + I1/2x (1 − 2Ix/z

2M)

1 + ρI1/2x

]+ xXBMXg(αI 1/2

x )

−xMxXBMX

[z2

Mg(αI1/2x )

2Ix

+(

1 − z2M

2Ix

)exp(−αI 1/2

x )

]− 2x1x2(A12x2 + A21x1)

+x1(1 − xI )W1,MX + x2(1 − xI )W2,MX − W2,MX (6)

if zM = zX, ln γ ∗X = ln γ ∗

M

Here the subscripts 1, 2, 3, M and X represent MDEA, H2O, CO2 (or H2S), MDEAH+ and HCO3− (or

HS−), respectively. In the above equations the concentrations for the equilibrated components in the liquidphase are expressed as mole or ionic fractions (x). Asterisk (∗) represents the infinitely dilute aqueoussolution without amine as the reference state. Theγ values without asterisk (∗) represent the pure solventliquid as reference state.

xI = xM + xX = 1 − x1 − x2

g(x) = 2[1 − (1 + x)exp(−x)]

x2

Ix = xMz2M + xXz2

X

2

Ax = Aφ

(∑n

Cn

)1/2

Aφ = 0.391

(78.54× 298.15

DmT

)3/2(dm

0.99702

)1/2

ρ = 2150

(18.02dm

∑n

(Cn

1000DmT

))1/2

Dm =∑

n

φnDn

φn = CnVn∑nCnVn

αI 1/2x = 2I 1/2 =

(∑i

z2i Ci

)1/2

(7)

Here Ix and I are the ionic strength expressed in ionic fraction and molarity, respectively.Ax is theDebye–Hückel parameter on a mole fraction basis andAφ is the original Debye–Hückel parameter [9],which is a function of temperature (T), density (dm) and dielectric constant (Dm) of the mixed solvents(MDEA+H2O). The parameterρ is related to the hard-core collision diameter, or distance of closestapproach, of ions in solution.φn is the volume fraction of solventn andVn is the molar volume of the


pure solventn. The temperature and concentration (weight percentage) dependence of the density ofaqueous MDEA solution was re-regressed in this work as polynomial expression from the experimentaldensity data of Teng et al. [10]. The temperature dependence of the dielectric constants for pure H2O andpure MDEA were listed in the paper of Li and Mather [6]. The molar concentration is expressed asC inaqueous phase.

The equations for the material balance and the calculation of the chemical equilibria are shown inAppendix A.

4. Data regression

For each ternary system, the regressed interaction parameters areBMX , W1,MX andW2,MX , which are alltemperature dependent asB (or Wor A)=a+b/T. The interaction parametersA12 andA21, which are alsotemperature dependent, are parameters between solvent molecules MDEA and H2O. The definitions ofthese interaction parameters are expressed in Clegg and Pitzer’s original paper [7]. The objective functionused in this study is as follows:

F = 1

n

∑n

|pcal − pex|pex

At first, we used all the interaction parameters regressed from Li and Mather [6] to predict our ownexperimental VLE data. The prediction results in low acid loading regions (α<0.30 mol CO2 or H2S/molMDEA) are listed in Tables 3 and 4 and also shown on Figs. 2 and 3. It can be seen that the prediction resultsfor our own experimental VLE data are acceptable. The model represents well our data at 23 MDEA wt.%and those of Jou et al. [11] at 48 MDEA wt.%, but not those at 23 MDEA wt.% from Jou et al. [11]. Theslope of our experimental curve (d logP/d logα) is smaller than those from Jou et al. [11] in the low acidloading region.

The other option is to re-regress all the interaction parameters of the Clegg–Pitzer equation in the lowacid loading region in the temperature of 298 and 313 K for the MDEA–CO2–H2O and MDEA–H2S–H2Oternary systems. The correlation results were bad. We have selected the systems for which the correlation

Table 3Prediction results for the MDEA–CO2–H2O ternary system with Li–Mather parameters [6]

Reference MDEA concentration (wt.%) Temperature (K) Data points δ% (prediction)a

This work 23.63 298 13 7.84[2] 23.3 313 7 14.8[2] 48.8 313 5 45.4[11] 23.3 298 4 99.7[11] 23.3 313 6 41.7[1] 35.0 313 18 19.0[11] 48.8 298 5 26.0[11] 48.8 313 6 15.3[15] 23.0 313, 323 20 25.6[15] 50.0 313 14 47.8

a δ% = (1/n)∑ |(pcal − pex)|/pex × 100.


Table 4Prediction results for the MDEA–H2S–H2O ternary system with Li–Mather parameters [6]

Reference MDEA concentration (wt.%) Temperature (K) Data points δ% (prediction)a

This work 11.83 298 16 33.0This work 23.63 313 13 17.5[11] 11.8 298 4 224.9[11] 11.8 313 5 152.5[11] 23.3 313 9 100.8[1] 35.0 313 19 23.8[1] 48.8 313 14 41.2[15] 50.0 313 10 56.3

a δ% = (1/n)∑ |(pcal − pex)|/pex × 100.

lead to small deviations. All our experimental VLE data together with those of Austgen et al. [2] were usedto make the correlation. The correlation results are good. But we cannot use these parameters to predictthe VLE data in high temperature range (up to 393 K) and high acid loading (α>0.3) for both ternarywith high MDEA concentration (35–50 wt.% MDEA). Since in our correlation the high temperature forboth ternary systems, the high concentration of MDEA for MDEA–H2S–H2O system and the high acidloading region were not involved, we do not list the correlation and prediction results here again.

Generally, the industry requires parameters, which are valid in the whole temperature, acid gas loadingand amine concentration ranges. So we have to re-regress the parameters by use of the experimental datacovering the wide ranges of temperature from 298 to 393 K and the acid gas loading from 0.001 to about1.0 and the MDEA concentration from 10 to 50 wt.%. We used the method of Weiland et al. [12] to discardsome ‘bad’ data points. Here we only considered the Debye–Hückel term and theA12 andA21 terms for

Fig. 2. Comparison of predicted and experimental values of CO2 partial pressure for MDEA–CO2–H2O system at 298 K withLi–Mather parameters [6].


Fig. 3. Comparison of predicted and experimental values of H2S partial pressure for MDEA–H2S–H2O system with Li–Matherparameters [6].

the non-ideality of MDEA–H2O system. The average deviation of the correlation is still very large due tosystematic experimental errors. So we have to plot a lot of equilibrium curves at the same temperaturesand the same MDEA initial concentrations but from different authors and decided to discard some setsof data far away from the most of the data. Our third option is to re-regress the Clegg–Pitzer parameterswith the selected experimental data from Jou et al. [1,11,13], MacGregor–Mather [3], Huang–Ng [14],Rogers et al. [15] and ours. The correlation results are listed in Tables 5 and 6 and are shown in Figs. 4–8.

Table 5Experimental solubility data used to re-regress the interaction parameters and the correlation results for the MDEA–CO2–H2Oternary system

Reference MDEA concentration (wt.%) Temperature (K) Data points δ% (correlation)a

This work 23.63 298 13 8.28[3] 23.3 313 4 20.7[13] 30.0 298, 313, 353, 393 24 26.6[1] 35.0 313, 373 32 23.5[11] 23.3 313, 343, 373, 393 27 27.7[14] 23.1 313, 343, 373, 393 21 21.5[14] 50.0 313, 343, 373, 393 34 17.3[15] 23.0 313, 323 20 62.7[15] 50.0 313 14 43.5

Total 202 28.7

a δ% = (1/n)∑ |(pcal − pex)|/pex × 100.


Table 6Experimental solubility data used to re-regress the interaction parameters and the correlation results for the MDEA–H2S–H2Oternary system

Reference MDEA concentration (wt.%) Temperature (K) Data points δ% (correlation)a

This work 11.83 298 16 5.34This work 23.63 313 13 27.7[3] 23.3 313 20 23.7[1] 35.0 313, 373 28 20.4[1] 48.8 313 12 19.5[11] 23.3 313, 373 17 55.1[14] 23.1 313, 373, 393 9 25.4[13] 50.0 313, 343, 373, 393 26 17.6[15] 50.0 313 10 22.3

Total 151 24.1

a δ% = (1/n)∑ |(pcal − pex)|/pex × 100.

The interaction parameters with their temperature coefficients thus regressed are listed in Tables 7 and8. The interaction parameters between solventsA12 andA21 are the same as those in Li–Mather’s paper[6] and are not listed here again. From the tables and figures it can be seen that the correlation resultsare fair for our data and are poor for the Rogers et al. [15] data. But they are still good for the Jou’s data[1,13]. From these figures it can be seen also that the discrepancies between the experimental data of Jouet al. [11] and ours are serious in low acid loading particularly in 50% MDEA solution. The slope of theexperimental curves from Rogers et al. [15] is located between those from Huang–Ng [14] and Jou et al.[11]. The slope from ours is located near that of Huang–Ng [14].

Fig. 4. Comparison of correlated and experimental values of CO2 partial pressure for 23% MDEA–CO2–H2O system with newparameters.





Fig. 7. Comparison of correlated and experimental values of H2S partial pressure for 23% MDEA–H2S–H2O system with newparameters.

Fig. 8. Comparison of correlated and experimental values of H2S partial pressure for 50% MDEA–H2S–H2O system with newparameters.


Table 7Refitted values of interaction parameters for MDEA–CO2–H2O systema

a b B(or W)b (at 313 K)

BMX 106.302 −59515.65 −83.75275W1,MX 15.43094 −4443.233 1.242103W2,MX −7.014513 1100.45 −3.500382

a Subscripts: 1=MDEA, 2=H2O, M=MDEAH+ and X=HCO3−.

b B (or W)=a+b/T.

Table 8Refitted values of interaction parameters for MDEA–H2S–H2O systema

a b B(or W)b (at 313 K)

BMX 536.4005 −188076.2 −64.19418W1,MX 8.648682 −2366.862 1.090444W2,MX 2.077459 −1182.494 −1.698668

a Subscripts: 1=MDEA, 2=H2O, M=MDEAH+ and X=HCO3−.

b B (or W)=a+b/T.

5. Conclusions

An original apparatus has been designed and used here to measure very low partial vapor pressures ofacid gases over MDEA aqueous solutions. Data obtained within 1 Pa are compared with data availablefrom literature. There are large discrepancies among the measured VLE data and the slopes of theirsolubility curves from different authors due to systematic experimental errors, particularly in the low acidloading regions. The original Li–Mather parameters [6] can be used to predict our experimental VLE datain low acid loading regions (α<0.30). The simplified Clegg–Pitzer equation can be used only to correlateour own experimental low acid loading and low temperature VLE data with good accuracy. But theparameters thus obtained cannot be used to predict the VLE data in high temperature range (up to 373 K)and high acid loading (α>0.3). In this case, the prediction capability will be limited. Our experimentalVLE data can be incorporated with those from MacGregor and Mather [3], Jou et al. [1,11,13], Huang andNg [14] and Rogers et al. [15] to re-regress the interaction parameters with acceptable correlation resultsin the very wide ranges of temperature (298–393 K), acid loading (0.001–1.0) and MDEA concentration(11.83–50.0 wt.%), which is very useful to the gas purification process.

Appendix A

The equations for the material balance and the calculation of the chemical equilibria

CO2 + MDEA + H2O⇔K4

MDEAH+ + HCO3−

are as follows.


For MDEA–CO2–H2O ternary system:

K4 = K1

K3= xMγ ∗

MxXγ ∗X

x1γ1x2γ2x3γ∗3

K4X = xMxX

x1x2x3= K4γ1γ2γ

∗3

γMγ ∗X

= CMCX(C1 + C2 + C3 + CM + CX)

C1C2C3

C1 = C01 − CM

C2 = C02 − CM

C3 = C01α − CM

CX = CM

(K4X − 1)C3M + [C0

2 + C01(1 + α)](1 − K4X)C2

M

+ [C02 + (C0

1 + C02)α]K4XC0

1CM − C01C

02αK4X = 0

whereK4X is the apparent chemical equilibrium constant, which changes with the concentration of eachspecies,C0 the initial concentration in aqueous solution,α the CO2 loading (total mol of CO2/mol oforiginal MDEA) in liquid phase. The equilibrated concentrations of MDEAH+ and the free dissolvedCO2 can be obtained by solving the above cubic equation with Newton iterative method based on thechemical equilibrium and material balance.

pCO2 = HCO2x3γ∗3 = HCO2xMγ ∗

MxXγ ∗X

K4x1γ1x2γ2

K4 = K1

K3

In the expression ofK4, we used the Henry’s constant of CO2 (HCO2) instead of thex3γ∗3 term. So we did

not calculate the activity and activity coefficient of CO2 in the liquid phase.For MDEA–H2S–H2O ternary system:

H2S+ MDEA⇔K5

MDEAH+ + HS−

K5 = K2

K3= xMγ ∗

MxXγ ∗X

x1γ1x3γ∗3

K5X = xMxX

x1x3= K5γ1γ

∗3

γ ∗Mγ ∗

X

= CMCX

C1C3

C1 = C01 − CM

C2 = C02

C3 = C01α − CM

CX = CM


whereK5X is the apparent chemical equilibrium constant, which is dependent on the concentration of eachspecies,α the H2S loading (total mol of H2S/mol of original MDEA) in liquid phase. The equilibratedconcentrations of MDEAH+ and the free dissolved H2S can be obtained by solving the following quadraticequation:

(1 − K5X)C2M + K5XC0

1(1 + α)CM + K5XC01α = 0

pH2S = HH2Sx3γ∗3 = HH2SxMγ ∗

MxXγ ∗X

K5x1γ1

We also used the Henry’s constant of H2S (HH2S) instead of thex3γ∗3 term. So we did not calculate the

activity and activity coefficient of H2S in liquid phase directly.As shown above, only the activity coefficients for H2O, MDEA, MDEAH+, HCO3

− and HS− areinvolved in our calculation for non-ideal mixed solvent system. Thus, our material balances are simplerthan the traditional Kent–Eisenberg model [16].

References

[1] F.-Y. Jou, J.J. Carroll, A.E. Mather, F.D. Otto, Can. J. Chem. Eng. 71 (1993) 264–268.[2] D.M. Austgen, G.T. Rochelle, C.-C. Chen, Ind. Eng. Chem. Res. 30 (1991) 543–555.[3] R.J. MacGregor, A.E. Mather, Can. J. Chem. Eng. 69 (1991) 1357–1366.[4] H.A. Al-Ghawas, D.P. Hagewiesche, G. Ruiz-Ibanez, O.C. Sandall, J. Chem. Eng. Data 34 (1989) 385–391.[5] T.L. Donaldson, Y.N. Nguyen, Ind. Eng. Chem. Fundamentals 19 (1980) 260–266.[6] Y.-G. Li, A.E. Mather, Ind. Eng. Chem. Res. 36 (1997) 2760–2765.[7] S.L. Clegg, K.S. Pitzer, J. Phys. Chem. 96 (1992) 3513–3520.[8] M.L. Posey, G.T. Rochelle, Ind. Eng. Chem. Res. 36 (9) (1997) 3944–3953.[9] K.S. Pitzer, Ion interaction approach theory and data correlation, in: K.S. Pitzer (Ed.), Activity Coefficients in Electrolyte

Solutions, 2nd Edition, CRC Press, Boca Raton, FL, 1991 (Chapter 3).[10] T.-T. Teng, Y. Maham, L.G. Hepler, A.E. Mather, Physical Properties of Aqueous Solutions of MDEA, DEA and Their

Mixtures, in: Proceedings of the 2nd International Symposium on Thermodynamics in Chemical Engineering and Industry,Beijing, China, 1994.

[11] F.-Y. Jou, A.E. Mather, F.D. Otto, Ind. Eng. Chem. Process Des. Dev. 21 (1982) 539–544.[12] R.H. Weiland, T. Chakravarty, A.E. Mather, Ind. Eng. Chem. Res. 32 (7) (1993) 1419–1430.[13] F.-Y. Jou, F.D. Otto, A.E. Mather, Ind. Eng. Chem. Res. 33 (1994) 2002–2005.[14] S.-H. Huang, H.-J. Ng, Final Report to the Gas Research Institute, GRI-95/0126, February 1996.[15] W.J. Rogers, J.A. Bullin, R.R. Davidson, AIChE J. 44 (11) (1998) 2423–2430.[16] R.L. Kent, B. Eisenberg, Hydrocarbon Process 55 (2) (1976) 87–90.

Documents

Partial vapor pressure of CO2 and H2S over aqueous methyldiethanolamine solutions