Experimental and Modeling Study of Vapor Liquid Equilibrium for a

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Experimental and Modeling Study of Vapor Liquid Equilibrium for Methyldiethanolamine-CO2-H2S-Water Quaternary System Using Activity Coefficient Models with Corrected Equilibrium Constants Jong-Ho Moon, Jong-Seop Lee, Young Cheol Park, Jongkee Park, Dong Hyuk Chun, Jeongseok Yoo, Hun Yong Shin, and Byong Moo Min Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b04329 • Publication Date (Web): 02 Apr 2019 Downloaded from http://pubs.acs.org on April 7, 2019

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Experimental and Modeling Study of Vapor Liquid Equilibrium for Methyldiethanolamine-CO2-H2S-Water Quaternary System Using Activity Coefficient Models with Corrected Equilibrium Constants Jong-Ho Moon†, ‡, Jong-Seop Lee†, Young Cheol Park†, Jongkee Park†, Dong-Hyuk Chun†, Jeongseok Yoo§, Hun-Yong Shing, and Byoung-Moo Min†,* † ‡

Korea Institute of Energy Research, 102 Gajeong-ro, Yuseong-gu, Daejeon 34129, Korea

Chungbuk National University, 1 Chungdae-ro, Seowon-gu, Cheongju, Chungbuk 28644, Korea

§Doosan gSeoul

Heavy Industries & Construction, 10 Suji-ro, Suji-gu, Yongin, Gyeonggi 16858, Korea

National University of Science & Technology, 232 Gongneung-ro, Nowon-gu, Seoul 01811, Korea * Corresponding

author. Tel: 82-42-860-3696, E-mail: [email protected]

ABSTRACT The solubilities of CO2 and H2S mixtures in methyldiethanolamine (MDEA) aqueous solutions were investigated in the wide temperature range from 313.15 (absorption range) to 403.15 K (stripping range) using the static method. The values of equilibrium constants for amine protonation (K1), activity coefficients (γi) and fugacity coefficients (Φi) were regressed from the newly obtained experimental solubility data to correct nonideality. In order to obtain the equilibrium constants for amine protonation, modified Kent-Eisenberg model was applied. Then, two kinds of activity coefficient models, the Deshmukh–Mather model and the electrolyte nonrandom two-liquid (NRTL) model, were applied to minimize the gaps between experimental data and predicted values with newly obtained equilibrium constants. In this study, six thermodynamic models were presented by combining 1 equilibrium model and 2 activity coefficient models. Based on the best fitted solubility results, the mole fractions of all electrolytes and the pH in the liquid phase, and the heat of absorption for CO2 and H2S were evaluated. Keywords: CO2 and H2S, methyldiethanolamine (MDEA), modified Kent-Eisenberg model, Deshmukh-Mather model, Electrolyte NRTL model

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1. Introduction The removal of acid gases (H2S and CO2) from gas streams continues to be of considerable interest in the natural gas, biogas, and petrochemical industries. In particular, wet scrubbing processes (absorption column processes) using aqueous alkanolamine solutions have been widely applied for acid gas removal. To design and simulate absorption column processes, it is necessary to have precise information about acid gas solubilities in aqueous alkanolamine solutions1, 2. Four types of alkanolamines are used for CO2 or H2S absorption processes: (1) primary amines: monoethonolamine (MEA), (2) secondary amines: diethanolamine (DEA), diisopropanolamine (DIPA), (3) tertiary amines: methyldiethanolamine (MDEA), TEA (triethylamine), and (4) sterically hindered amine: 2-amino-2-methyl propanol (AMP). Among them, MDEA has been increasingly applied for acid gas removal due to its high capacity and excellent flexibility for meeting process requirements. In addition, several advantageous properties of MDEA, such as low heat of reaction, low vapor pressure, low corrosivity and low thermal degradation, can reduce operation energy and cost. Mather’s group1, 39,

Rochelle’ group2, 10, 11, Chen’s group2, 10, 12, Huttenhuis’ group13, and Yesavage’ group14 evaluated the

solubility of the CO2/H2S mixtures in the various kinds of amines including MDEA with activity coefficient models. Vapor–liquid equilibrium (VLE) modeling of acid gas–aqueous amine systems is critical for the synthesis, design, and analysis of gas sweetening plants. The thermodynamic models for representing the solubilities of CO2 and H2S in aqueous alkanolamine solutions can be categorized into three approaches. The first approach involves finding new equilibrium constants for amines, such as for amine protonation or carbamate formation. Kent and Eisenberg 15-17 proposed a very simple model that neglected activity coefficients and used apparent equilibrium constants for chemical equilibrium equations. However, the extrapolation capabilities of this model are comparatively poor. The second and third approaches use excess Gibbs energy models, namely the Deshmukh–Mather model1, 3-9, 18-20 and the electrolyte models2,

10-12, 21-25,

respectively. Deshmukh and Mather1 developed a rigorous

thermodynamic model, and the activity coefficients were calculated using the Guggenheim equation 26. Weiland et al.

9

provided values for the interaction parameters of the model for most commercially


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important amine systems. Later, Li and Mather 4 proposed a similar model, in which the Guggenheim equation was replaced by the well-known Pitzer model to calculate the activity coefficients. Chen’s group2, 10, 12, 21-23, 27, 28, Rochelle’s group2, 10, 11, and Svendsen’s group19, 20, 24 adapted the electrolyte nonrandom two-liquid (NRTL) model to the amine–water system. Kaewsichan et al.14 and Al-Rashed et al.

29

applied the electrolyte-UNIQUAC model to predict the solubilities of H2S/CO2 mixtures in

blended MEA/MDEA aqueous solutions. The measurement or the calculation of the heat of absorption is a key factor in estimating the regeneration energy of the absorption process. Also, in designing the absorption reactors, since the acidic gases (H2S and CO2) react with the basic aqueous solutions (amines), the pH of the solutions must be considered. However, there are not many studies on the calculations of the heat of absorption and the pH according to various temperature and gas composition conditions. In this study, the solubilities of CO2 and H2S mixtures in aqueous MDEA solutions were investigated in the temperature range from 313.15 to 403.15 K. In order to correct the nonideality for the solubility calculation, newly obtained equilibrium constants for amine protonation (modified Kent–Eisenberg model) were adapted with activity coefficients for the liquid phase and fugacity coefficients for the gas phase. In particular, this paper compared the Deshmukh Mather model, which represents a very simple and flexible representation, and the electrolyte NRTL model, which is a very complex and rigorous representation of local interaction. Six thermodynamic models were proposed for finding the optimal combination of equilibrium constants and activity coefficients. Then, the mole fractions of electrolytes in the liquid phase, the heats of absorption for CO2 and H2S and the pH were estimated based on the solubility prediction of the best fitted model.


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2. Experimental methods

2.1. Materials MDEA (>98%, Acros Co.) and double-distilled water were mixed to prepare the absorption solutions. The concentrations (wt%) of the aqueous MDEA solutions were 30, 40, 50 wt% (water balanced). As feed gases, pure carbon dioxide (>99.999%), pure hydrogen sulfide (>99.99%), and pure nitrogen (>99.999%) were introduced sequentially into the experimental apparatus.

2.2. Experimental procedure The solubilities of CO2 and H2S in the MDEA solutions were measured in the temperature range 313.15–403.15 K using the static method. The experimental sequence was composed of three stages: (1) cleaning and preparation, (2) acid gas absorption, and (3) analysis. In the cleaning and preparation stage, the absorption reactor was washed with nitrogen and water 3 times, and then the gases in the reactor were analyzed by gas chromatography to confirm whether any gases other than nitrogen remained in the reactor. In the acid gas absorption stage, a mixed gas (CO2/H2S/N2) was introduced into the absorption reactor 5 times for conversion from nitrogen conditions to reaction gas conditions while maintaining the reaction temperature. Keeping the temperature of the reactor constant, approximately 100 mL of the absorption solution was injected into the reactor with the high-pressure liquid syringe pump. Once the temperature of the injected solution was constant, the pressure was measured. The vapor pressure of the solution was calculated from the pressure change, the amount of solution injected, and the volume of the reactor. The obtained vapor pressure was used to calculate the partial pressure of the absorbed gas at the equilibrium pressure. When solution injection was completed, a mixed gas was introduced into the reactor. At this time, to increase the possibility of contact between the absorbent and the acid gas, a magnetic drive was used to stir the impellers installed in the gas phase and the liquid phase of the reactor. When the pressure in the absorption reactor decreased due to the absorption of H2S and CO2 in the solution and no further pressure changes were observed, the feed gas was injected into the reactor again from the gas reservoir. If there was no further pressure change, it was determined that


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the absorption equilibrium had been reached, and the pressure of the reactor was measured. Subsequently, the mixed gas (single component) in the gas reservoir was injected again into the absorption reactor. The equilibrium loading ratio, αH2S or αCO2, was calculated from the partial pressure and the absorbed amount (mole ratio) at each equilibrium point. Multicomponent experiments were performed to obtain equilibrium data for gas mixtures in the solution. Unlike in the single-component experiments, to inject the gas from the absorption reactor into the gas chromatograph, an additional syringe pump was used. In this study, the ideal gas law was used for calculating the gas absorption amounts. Then, the compression factor (Redlich–Kwong equation) was applied to account for the nonideality of the gas mixtures. Detailed device descriptions are included in the supporting material (S1. Experimental setup).

2.3. Uncertainty measurement In this study, the following equation presented by NIST30 and Kim et al.31 was used to calculate the uncertainty of pressure, temperature, and other data. Before calculating the uncertainty, the average values of the data were calculated as follows.

1

𝑛 𝑊𝑖 = 𝑛∑𝑘 = 1𝑊𝑖,𝑘

(1)

Where, 𝑊𝑖 is the average value of the experimental data at the same experimental condition. The standard uncertainty associated with 𝑊𝑖 can be calculated as follows.

𝑢(𝑤𝑖) =

(

1

1/2

(𝑤𝑖,𝑘 ― 𝑊𝑖)2) 𝑘=1

∑𝑛 𝑛(𝑛 ― 1)

Where, 𝑢(𝑤𝑖) is the uncertainty, n is the number of data.


(2)

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3. Model and optimization

3.1. Reaction Reaction equilibrium of CO2 and H2S mixture in aqueous solution of MDEA is governed by the following expression of equations

Alkanolamine (MDEA) :

MDEAH+ + H2O ↔ MDEA + H3O+

(3)

Carbon dioxide :

CO2 + 2 H2O ↔ H3O+ + HCO3-

(4)

Bicarbonate :

HCO3- + H2O ↔ H3O+ + CO32-

(5)

Water :

2H2O ↔ H3O+ + OH-

(6)

Hydrogen sulfide :

H2O + H2S ↔ HS- + H3O+

(7)

Hydrogen bisulfide :

H2O + HS- ↔

(8)

S-2 + H3O+

Thermodynamic frameworks, the equilibrium constants, Ki(-), for the above equations are described by as follows:

xMDEA xH

K1 = x K2 =

K3 =

γMDEA γH

+ 3O

MDEAH

xH

+ 3O

MDEAH +

2

xHCO ― 3

∙

xCO2x2H2O xH

+ 3O

xCO2 ― 3

∙

xHCO ― xH2O

γH

+ 3O

K5 =

K6 =

xH

+ 3O

xOH ―

x2H2O xH

+ 3O

xHS ―

xH2O xH2S xH

+ 3O

x S2 ―

xH2O xHS ―

(9)

γH2O

γHCO ― 3

(10)

γCO2 γ2H2O γH

γCO2 ―

+ 3O

3

(11)

γHCO ― γH2O

3

K4 =

+ 3O

∙ + xH O γ

3

∙

∙

∙

γH

+ 3O

γOH ―

(12)

γ2H2O γH

+ 3O

γHS ―

(13)

γH2O γH2S γH

+ 3O

γS2 ―

(14)

γH2O γHS ―


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where, xj (-) is the mole fraction, γj (-) is the activity coefficient of the species j. Along with the above equations, the following set of mass (amine, CO2, and H2S), charge (electroneutrality) balances, and mole fraction normalization (or H2O mass balance) should be satisfied simultaneously. In this study, 11 equations (6 equilibrium equations, 5 balance equations) for 11 variables (4 molecules, 2 cations, 5 anions) were solved simultaneously using iterative substitution method. Then, the obtained 11 variables were verified by substituting each equilibrium and balance equation.

xtMDEA = xMDEA + xMDEAH +

(15)

xtCO2 = αCO2 ∙ xtMDEA = xCO2 + xHCO3― + xCO23 ―

(16)

xtH2S = αH2S ∙ xtMDEA = xH2S + xHS ― + xS2 ―

(17) (18)

xMDEAH + + xH3O + = xHCO3― +2xCO23 ― + xHS ― +2xS2 ― + xOH ― 𝑛

𝑛

1 = ∑𝑗 𝑥𝑡𝑗 = ∑𝑖 = 1𝑥𝑖

(19)

where α (-) is the loading ratio (mol CO2/mol MDEA and H2S/mol MDEA). Finally the concentration of CO2 and H2S in the liquid phase can be calculated by phase equilibrium formulas considering activity, fugacity and Henry’s law.

phase equilibrium of CO2 phase equilibrium of H2S :

:

ϕCO2yCO2P = HCO2γCO2xCO2

(20)

ϕH2SyH2SP = HH2SγH2SxH2S

(21)

where Фi (-) is the fugacity coefficient, yi (-) is the vapor phase mole fraction, P (Pa) is the pressure, and the Hi (Pa) is the Henry constant of species i, respectively. In the case of fugacity coefficients, Фk, the equation suggested by Prausnitz et al.32 was used.

3.2. Equilibrium constants and Henry's constants Temperature dependencies of reaction equilibrium constants, Ki, and Henry’s constants, Hi, for species


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i can be described as below.

Equilibrium constants

ln K = A1 +

Henry's constants

ln H = B1 +

A2 B2

T + A3ln T + A4T

(22)

T + B3ln T + B4T

(23)

Temperature dependent coefficients for Ki (A1-A4) and Hi (B1-B4) are listed in Table 1 and Table 2 respectively.

Table 1. Temperature dependent coefficients (A1-A4) for reaction equilibrium constants (Ki)

0

Temp range (oC) 25-60

Schwabe et al.33

-36.7816

0

0-225

Edwards et al.34

-12431.7

-35.4819

0

0-225

Edwards et al.34

132.899

-13445.9

-22.4773

0

0-225

Edwards et al.34

K5

214.582

-12995.4

-33.5471

0

0-150

Edwards et al.34

K6

-32.0

-3338.0

0

0

14-70

Meyer et al. 35 and Giggenbach et al.35, 36

A1

A2

A3

A4

K1

-9.4165

-4234.98

0

K2

231.465

-12092.10

K3

216.049

K4

References

Table 2. Temperature dependent coefficients (B1-B4) for Henry's constants (Hi)

-0.0010454

Temp. range (oC) 0-250

Edwards et al.34

0.0595651

0-150

Edwards et al.34

B1

B2

B3

B4

HCO2

94.4914

-6789.04

11.4519

HH2S

342.595

-13236.8

-55.0551

References

3.3. None activity coefficient model: modified Kent–Eisenberg model In the case of the modified Kent–Eisenberg model, the equilibrium constant associated with amine protonation (K1 in Table 1) obtained by regression of the experimental data was used without considering the activity coefficient. The nonidealities in the liquid phase are lumped together in the K1


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value.

3.4. Activity coefficient model: Deshmukh–Mather model The Deshmukh–Mather model 1 is one of the simplest methods for calculating activity coefficients by considering long-range (electrostatic force) and short-range (van der Waals) interactions between solute species in the liquid phase.

𝐴𝑍2𝑖 𝐼

lnγ𝑖 = ― 1 + 𝐵 𝐼 +2∑𝑗𝛽𝑖,𝑗𝑚𝑗

(24)

Here, the first term is the long-range electrostatic force and the second term is the short-range van der Waals interactions. Zi is the electrical charges of species i, mj (mol/kg-solvent) is the molality of species j, A and B (≒1.2) are the function of the temperature, the density and the dielectric constant of the solvent

37.

βij is the temperature-dependent interaction parameter between the various ionic and

molecular species in the system, excluding interactions between solutes and solvent, and is represented as follows:

(25)

𝛽𝑖𝑗 = 𝑎𝑖𝑗 + 𝑏𝑖𝑗𝑇

where aij and bij are binary parameters to be estimated. The ionic interaction, I, of the solution is calculated using the following equation.

1

𝐼 = 2∑𝑚𝑗𝑍2𝑗

(26)

3.5. Activity coefficient model: Electrolyte NRTL model The electrolyte NRTL model is a versatile model for overcoming the nonideality of aqueous electrolyte systems when calculating activity coefficients. Using binary and pair parameters, the model can


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represent aqueous electrolyte systems as well as mixed solvent systems over the entire range of electrolyte concentrations. This model can be used to calculate activity coefficients for ionic species and molecular species in aqueous electrolyte systems. Basically, the electrolyte NRTL model is an excess Gibbs energy model that follows two assumptions. 1) The local composition of cations around cations is zero. 2) The local net ionic charge of cations and anions around central molecule is zero. The excess Gibbs free energy expression for this model is given by Eq. (27), which leads to Eq. (28) by applying Eq. (29).

𝐺 ∗ 𝑒𝑥 𝑅𝑇

=

ln𝛾𝑖 =

∗ 𝑒𝑥 𝐺𝑃𝐷𝐻

𝑅𝑇

[

+

∗ 𝑒𝑥 𝐺𝐵𝑜𝑟𝑛

𝑅𝑇

+

∂(𝑛𝑡𝐺 ∗ 𝑒𝑥/𝑅𝑇) ∂𝑛𝑖

]

∗ 𝑒𝑥 𝐺𝐿𝐶

(27)

𝑅𝑇

(28) 𝑇,𝑃,𝑛𝑗 ≠ 𝑖

) +lnγ𝐿𝐶 lnγ𝑖 = (lnγ𝑃𝐷𝐻 + lnγ𝐵𝑜𝑟𝑛 𝑖 𝑖 𝑖

(29)

∗ 𝑒𝑥 where 𝐺 ∗ 𝑒𝑥 is the excess Gibbs energy of the mixed solvent electrolyte system, 𝐺𝑃𝐷𝐻 is the excess ∗ 𝑒𝑥 Gibbs energy calculated using the Pitzer–Debye–Hückel formula, 𝐺𝐵𝑜𝑟𝑛 is the excess Gibbs energy ∗ 𝑒𝑥 calculated using the Born expression, and 𝐺𝐿𝐶 is the excess Gibbs energy calculated using the NRTL

hypothesis. The first two terms of Eq. (29) account for the long-range interactions and the third term accounts for the local interaction contribution 25. The long-range interaction contribution from the wellknown Pizer–Debye–Hückel model is given by:

ln γ𝑃𝐷𝐻 =― 𝑖

1/2

( ) 1000 𝑀𝑠

2 1/2 3/2 1/2 𝐴∅{(2𝑍2𝑖 /𝜌)ln(1 + 𝜌𝐼1/2 𝑥 ) + (𝑍𝑖 𝐼𝑥 ― 2𝐼𝑥 )/(1 + 𝜌𝐼𝑥 )}

(30) where 𝑀𝑠 (kg/kmol) is the solvent molecular weight, 𝐴∅ (-) is the Debye–Hückel constant for the osmotic coefficient, 𝑍𝑖 (-) is the absolute value of the ionic charge, 𝐼𝑥 (-) is the ionic strength in the mole fraction scale, and 𝜌 (-) is the closet approach parameter of the Pitzer–Debye–Hückel equation (=14.9 in this study). The Debye–Hückel constant and the ionic strength can be described as follows:


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𝑄2𝑒

3/2

( )

𝐴∅ = (1/3)(2𝜋𝑁0𝑑𝑠)1/2

(31)

𝜀𝑠𝑘𝑇

𝐼𝑥 = (1/2)∑𝑖𝑥𝑖𝑍2𝑖

(32)

where 𝑁0 (-) is Avogadro’s number (=6.02 × 1023 mol-1), 𝑑𝑠 (kg/m3) is the mass density of the solvent, 𝑄𝑒 is the absolute electronic charge (=1.602 × 10-19 C), 𝑘 is the Boltzmann constant (=1.38 × 10-23 J/K), and 𝜀𝑠 is the dielectric constant of the solvent, which, using the parameters in Table 3, can be described as:

𝜀𝑖(𝑇) = 𝐴𝑖 + 𝐵𝑖{(1/𝑇) ― (1/𝐶𝑖)}

(33)

Table 3. Temperature-dependent coefficients (𝑨𝒊,𝑩𝒊, 𝑪𝒊) for dielectric constants (𝜺𝒊(𝑻)) 𝐴𝑖

𝐵𝑖

𝐶𝑖

Reference

MDEA

21.9957

8992.68

298.15

ASPEN Databank

Water

78.54

31989.4

298.15

ASPEN Databank

The Born equation is used to account for the Gibbs energy corresponding to the transfer of ionic species from the infinite dilution state to the aqueous phase 23.

𝑄2𝑒

= 2𝑘𝑇 ln γ𝐵𝑜𝑟𝑛 𝑖

(

1

1 𝑍2𝑖

)

𝜀𝑠 ― 𝜀𝑤

𝑟𝑖 10

―2

𝑖 = 𝑐, 𝑎

(34)

where 𝜀𝑤 is dielectric constant of water and 𝑟𝑖 (Å) is the Born radius of the ionic species. The local interaction contribution from the electrolyte NRTL model, given by the following expressions, can be categorized into three types. The first type consists of a central molecular species with other molecular species, cationic species, and anionic species in the immediate neighborhood (Eq. (35)). Here, local electroneutrality is maintained. The other two types are based on the like-ion repulsion assumption and


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have either a cationic (Eq. (36)) or anionic (Eq. (37)) species as the central species, in addition to an immediate neighborhood consisting of molecular species and oppositely charged ionic species.

ln γ𝐿𝐶 𝑚

∑ 𝑋𝑗𝐺𝑗𝑚𝜏𝑗𝑚 𝑗

=

∑ 𝑋𝑘𝐺𝑘𝑚 𝑘

(

𝜏𝑚𝑐,𝑎’𝑐 ―

+

𝑋𝑚’𝐺𝑚𝑚’

∑∑ 𝑋 𝐺 𝑚’

𝑘 𝑘 𝑘𝑚’

∑ 𝑋𝑘𝐺𝑘𝑐,𝑎’𝑐𝜏𝑘𝑐,𝑎’𝑐 𝑘 ∑ 𝑋𝑘𝐺𝑘𝑐,𝑎’𝑐 𝑘

)

+

(

𝜏𝑚𝑚’ ―

∑ 𝑋𝑘𝐺𝑘𝑚’𝜏𝑘𝑚’ 𝑘

∑∑∑ 𝑎

𝑐’

∑ 𝑋𝑘𝐺𝑘𝑚’ 𝑘 𝑋𝑐’

)

∑∑∑

+

𝑐

𝑋𝑎𝐺𝑚𝑎,𝑐’𝑎

𝑋 ∑ 𝑋𝐺 𝑐’’ 𝑐’’ 𝑘 𝑘 𝑘𝑎,𝑐’𝑎

𝑎’

(

𝜏𝑚𝑎,𝑐’𝑎 ―

𝑋𝑎’

𝑋𝑐𝐺𝑚𝑐,𝑎’𝑐

𝑋 ∑ 𝑋𝐺 𝑎’’ 𝑎’’ 𝑘 𝑘 𝑘𝑐,𝑎’𝑐 ∑ 𝑋𝑘𝐺𝑘𝑎,𝑐’𝑎𝜏𝑘𝑎,𝑐’𝑎 𝑘 ∑ 𝑋𝑘𝐺𝑘𝑎,𝑐’𝑎 𝑘

)

(35)

1 ln γ𝐿𝐶 𝑐 = 𝑍𝑐

∑∑ 𝑎’

+

𝑋𝑎’ ∑𝑘𝑋𝑘𝐺𝑘𝑐,𝑎’𝑐𝜏𝑘𝑐,𝑎’𝑐 𝑋 𝑎’’ 𝑎’’

∑ 𝑋𝑘𝐺𝑘𝑐,𝑎’𝑐 𝑘

∑∑∑ 𝑎

𝑐’

𝑋𝑐’

+

∑∑ 𝑋 𝐺

(

(

∑ 𝑋𝑘𝐺𝑘𝑎,𝑐’𝑎 𝑘

𝑋𝑚𝐺𝑐𝑚

𝑚

𝑋𝑎𝐺𝑐𝑎,𝑐’𝑎

𝑋 ∑ 𝑋𝐺 𝑐’’ 𝑐’’ 𝑘 𝑘 𝑘𝑎,𝑐’𝑎

𝑘 𝑘 𝑘𝑚

𝜏𝑐𝑎,𝑐’𝑎 ―

𝜏𝑐𝑚 ―

∑ 𝑋𝑘𝐺𝑘𝑚𝜏𝑘𝑚 𝑘 ∑ 𝑋𝑘𝐺𝑘𝑚 𝑘

∑ 𝑋𝑘𝐺𝑘𝑎,𝑐’𝑎𝜏𝑘𝑎,𝑐’𝑎 𝑘

)

) (36)

1 ln γ𝐿𝐶 𝑎 = 𝑍𝑎

∑∑ 𝑐’

+

𝑋𝑐’ ∑𝑘𝑋𝑘𝐺𝑘𝑎,𝑐’𝑎𝜏𝑘𝑎,𝑐’𝑎 𝑋 𝑐’’ 𝑐’’

∑ 𝑋𝑘𝐺𝑘𝑎,𝑐’𝑎 𝑘

∑∑∑ 𝑐

𝑎’

𝑋𝑎’

+

∑∑ 𝑋 𝐺

(

(

∑ 𝑋𝑘𝐺𝑘𝑐,𝑎’𝑐 𝑘

𝑋𝑚𝐺𝑎𝑚

𝑚

𝑋𝑐𝐺𝑎𝑐,𝑎’𝑐

𝑋 ∑ 𝑋𝐺 𝑎’’ 𝑎’’ 𝑘 𝑘 𝑘𝑐,𝑎’𝑐

𝑘 𝑘 𝑘𝑚

𝜏𝑐𝑎,𝑐’𝑎 ―

𝜏𝑎𝑚 ―

∑ 𝑋𝑘𝐺𝑘𝑚𝜏𝑘𝑚 𝑘 ∑ 𝑋𝑘𝐺𝑘𝑚 𝑘

∑ 𝑋𝑘𝐺𝑘𝑐,𝑎’𝑐𝜏𝑘𝑐,𝑎’𝑐 𝑘

)

) (37)

where j and k can be a cation (c), anion (a), or molecule (m). 𝛼𝑖𝑗 is the nonrandomness factor, and 𝜏𝑖𝑗 is the interaction binary parameter for regression.

(38)

𝜏𝑖𝑗 = 𝑎𝑖𝑗 + 𝑏𝑖𝑗𝑇


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Energy & Fuels

More detailed definition of electrolyte NRTL model in this study are given in Chen’s group papers.2, 10, 12, 21-23

3.6. Solubility models The solubility data were regressed using a total of six thermodynamic models to correct the nonideality of the liquid phase. The thermodynamic models were obtained by combining the modified Kent– Eisenberg with Deshmukh–Mather and electrolyte NRTL models, as shown in Table 4. In the case of model 1, no activity coefficient models were applied and the K1 values (Eq. (22)) in the literature were used directly. Model 2 applied the modified Kent–Eisenberg model and did not consider the activity coefficients. Model 3 and 4 combine the Deshumkh-Mather model with model 1 and 2 respectively. Model 5 and 6 combines the electrolyte NRTL model with model 1 and 2 respectively. All calculations in this study, such as the equilibrium equations, activity coefficients, and fugacity coefficients, were performed using MATLAB 2018a.

Table 4. Thermodynamic models proposed in this study Model

Description

1

Use K1 values in the literatures without an activity coefficient model

2

Use K1 values extracted from the modified Kent–Eisenberg model without an activity coefficient model

3

Deshmukh–Mather model with K1 values from model 1 (literature)

4

Deshmukh–Mather model with K1 values from model 2 (K–E model)

5

Electrolyte NRTL model with K1 values from model 1 (literature)

6

Electrolyte NRTL model with K1 values from model 2 (K–E model)


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 32

3.7. Parameter regression In this study, the symmetric mean absolute percentage error (SMAPE) was used for calculating the differences between the calculated values and the experimental values.

SMAPE =

|

𝐴𝑖 ― 𝐶𝑖 100 𝑛 ∑𝑖 = 1 (𝐴 + 𝐶 )/2 𝑛 𝑖 𝑖

|

(39)

where A is the actual value, C is the calculated value, and n is the number of data points. Various parameters (K-values of the modified Kent–Eisenberg model and binary parameters of the Deshmukh– Mather and electrolyte NRTL models) were regressed as minimizing error functions, especially SMAPE.


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Energy & Fuels

4. Results and discussion

4.1. Equilibrium solubilities of CO2/H2S mixtures in aqueous MDEA Figure 1(a) and (b) show the newly obtained experimental data of equilibrium solubilities of CO2/H2S mixtures in 30 wt% MDEA aqueous solutions, Figure 1(c) and (d) show the data for 40 wt% MDEA, and Figure 1(e) and (f) show the data for 50 wt% MDEA. In Figure 1, the assigned numerical numbers (1, 2, 3, Etc.) and the assigned alphabetical letters (a, b, c, Etc.) inside each graph indicate the solubility data of each of CO2 and H2S measured in the same experiment. The uncertainties for the partial pressures (CO2 and H2S) and the reactor temperatures (absorber and reservoir) were calculated by Eq. 2. In this study, the uncertainties for pressure and temperature did not exceed 0.001 (0.1%) in all experimental ranges. Detailed solubility results and uncertainties are listed in Table S3 in supporting material.

(Figure 1)

4.2. Model evaluation Figure 1 also shows a comparison of the experimental partial pressure values for CO2 and H2S in the entire temperature range and the predicted values obtained by applying models 2–6 in Table 4. The experimental and predicted values were substituted into the SMAPE equation (Eq. (39)), and then various parameters, such as the K1 values in the modified Kent–Eisenberg model and the binary parameters in the activity coefficient models, were obtained by minimizing the SMAPE values. In the case of model 2 (Kent–Eisenberg model), the temperature-dependent constants A1–A4 for calculating the equilibrium constant K1 (Eq. (22)) were regressed and the results are listed in Table 5.

Table 5. Temperature-dependent coefficients (A1–A4) for the K1 value newly obtained using model 2 (modified Kent–Eisenberg model) A1

A2

A3

A4

Temp. range (°C)


Reference

Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 32

K1

48.083

-15805.84

0.0560

-0.0730

40–130

This study

K1

-9.4165

-4234.98

0

0

25–60

Schwabe et al.33

In models 3 and 4, which apply the Deshmukh–Mather model, a total of 110 binary parameters (aij, bij in Eq. (25)) for 11 components (4 molecules, 2 cations, and 5 anions, Table 6) were estimated. In models 5 and 6, which apply the electrolyte NRTL model, a total of 182 binary parameters (aij, bij in Eq. (38)) for 19 components (4 molecules and 10 cation–anion pairs, Table 6) were estimated. In this study, we assumed that aij = aji and bij = bji for binary parameters. In Figure 2, the red circles correspond to CO2 data and the blue squares correspond to H2S data. Symbols closer to the diagonal line indicate better correspondence between the calculated values and the experimental values. The obtained SMAPE values were 55.01% for model 2 (modified Kent– Eisenberg model), 50.05% for model 3 (Deshmukh–Mather model), 45.00% for model 4 (Deshmukh– Mather model with newly obtained K1 values from model 2), 54.33% for model 5 (electrolyte NRTL model), and 52.16% for model 6 (electrolyte NRTL model with newly obtained K1 values from model 2). In general, the SMAPE levels of 40 to 60% in a single gas, narrow temperature, and partial pressure ranges seem to be quite low. However, in mixed gas systems with wide range of temperature (313.15403.15 K) and partial pressure (0-350 kPa), the SMAPE level of 45% is sufficiently high. As can be seen in Figure 2, most of errors occur at low pressure range. The error rate can be significantly reduced by dividing the high and low pressure regions and applying the respective Henry constants. However, in order to apply solubility results to process simulations, solubility models should cover a wide range of temperature, partial pressure, and amine concentration without any discontinuities. Therefore, in this study, the Henry’s Constants in the existing literature were applied. In this study, the predicted values obtained from model 4 showed the best fit to the experimental values. The Deshmuhk Mather model with newly obtained equilibrium constant (K values), which has weak physical meaning but more flexible use of binary parameters, showed better expression of short range interaction (local interaction) than the electrolyte NRTL model, which has strong physical meaning and more binary parameters. Hereafter, only model 4 will be applied to calculate the predicted values.


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Energy & Fuels

Finding the dominant binary parameter of over hundreds parameters is very important when the activity coefficient models are applied to the prediction of gaseous mixture solubility. In general, the most dominant parameters for calculating activity coefficients in the MDEA-CO2-H2S-Water system are CO2-MDEA, CO2-MDEAH+, HCO3--MDEA, HCO3--MDEAH+, H2S-MDEA, H2S-MDEAH+, HS-MDEA, HS--MDEAH+. However, since the physical meaning of binary parameters for short range interaction in Deshmukh Mather model and electrolyte NRTL model is quite weaker than equilibrium constants (K1 values), obtained binary parameters are listed in the supporting material.

(Figure 2)

Table 6. Components of binary parameters for calculating local interactions in the activity coefficient models Deshmukh–Mather model Components:

MDEA, H2O, CO2, H2S (4 molecules) H3O+, MDEAH+ (2 cations) OH-, HCO3-, CO32-, S-2, HS- (5 anions)

Electrolyte NRTL model Components:

MDEA, H2O, CO2, H2S (4 molecules) MDEAH+–OH-, MDEAH+–HCO3-, MDEAH+–CO32-, MDEAH+–S-2, MDEAH+–HS-, H3O+–OH-, H3O+–HCO3-, H3O+–CO32-, H3O+–S-2, H3O+–HS-, (10 cation–anion pairs)

4.3. Liquid-phase concentrations Figure 3 shows the liquid-phase concentrations predicted using model 4 for CO2–H2S-loaded 30 wt% MDEA aqueous solutions at 323.15 K. Figure 3(a) shows the changes in the mole fractions for a total of 11 components (4 molecules, 2 cations, and 5 anions) when the H2S loading is fixed to 0.2 (mol/mol), and similarly, Figure 3(b) shows the changes in the mole fractions when the CO2 loading is fixed to 0.2 (mol/mol). As shown in Figure 3(a) and 3(b), the components that mainly affect the solubility behavior


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

are the apparent components (MDEA, H2O, CO2, and H2S) and some true components (MDEAH+, HCO3-, and HS-), whereas the influence of the remaining components (H3O+, OH-, CO32-, and S-2) is negligible. However, to calculate the CO2 and H2S solubilities accurately, all the equilibrium, material balance, and charge balance (electroneutrality) equations must be solved simultaneously with consideration of the fugacity coefficients and activity coefficients for all 11 components. None of the components should be ignored. For example, if the loading ratio of CO2 or H2S changes, the concentration of H3O+, which is a very important factor in determining the pH of the aqueous solution, also changes very minutely. Therefore, accurate calculations for trace amounts of electrolytes such as H3O+, which can calculate the pH, become very important. In addition, the calculated mole fraction must satisfy the mass balance equations (Eqs. (15)–(17)) and charge balance equation (Eq. (18)) within the specified tolerance.

(Figure 3)

4.4. pH and heat of absorption Figs. 4 and 5 show 3D solubility plots for CO2/H2S mixtures in 30 wt% MDEA aqueous solutions at 323.15 and 383.15 K, respectively. In the 3D plots, the x-axis represents CO2 loading, the y-axis represents H2S loading, and the z-axis represents the partial pressures of (a) CO2 and (b) H2S. The red circles and blue squares show the experimentally determined partial pressures of CO2 and H2S, respectively, and meshes correspond to the results calculated using model 4. In this study, CO2 and H2S solubility experiments were conducted for various MDEA concentrations in the temperature range 313.15–403.15 K. Using a total of 113 experimental data sets (Table S2), the K1 values and the binary parameter sets of the Deshmukh–Mather model and the electrolyte NRTL model were calculated. This approach allowed the prediction of the CO2 and H2S solubilities with the concentrations of 11 components for all experimental conditions.


Page 18 of 32

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Energy & Fuels

(Figure 4) & (Figure 5)

The prediction of pH in aqueous amine solutions provides very meaningful information about the inside of a column during the operation of a wet scrubbing process. Substitution of the mole fraction and activity coefficient of H3O+ into Eq. (40) allowed the pH of the liquid phase to be calculated.

𝑝𝐻 = ― 𝑙𝑜𝑔10(𝑥𝐻3𝑂 + ∙ 𝛾𝐻3𝑂 + )

(40)

Figure 6 shows predicted 3D plots for the pH of 30 wt% MDEA aqueous solutions at 323.15 and 383.15 K using model 4. The x-axis represents CO2 molarity (mol CO2/L solution), the y-axis represents H2S molarity, and the z-axis represents the pH of the liquid phase. In the case of pH, molarity was used instead of CO2 or H2S loading for a more intuitive understanding. The range of pH values was approximately 7.5–10.2 at the low temperature (323.15 K) and approximately 7.2–8.7 at the high temperature (383.15 K). The higher the temperature, the stronger the acidity of the aqueous solution, whereas the lower the temperature, the stronger the basicity. This result could be anticipated, as increasing the loading of an acidic gas, such as CO2 or H2S, is expected to decrease the pH in the liquid phase.

(Figure 6)

The heat of absorption is also a very important factor in estimating the regeneration energy for amine wet scrubbing processes. The heats of absorption for CO2 and H2S can be simply estimated using the Gibbs–Helmholtz relationship, as shown in Eq. (41) 22.

― ∆𝐻𝑎𝑑𝑠, 𝐶𝑂2 𝑅

=

[ )] 𝑑𝑙𝑛𝑃𝐶𝑂2 1 𝑑( 𝑇

& 𝑞𝐶𝑂2

― ∆𝐻𝑎𝑑𝑠,𝐻2𝑆 𝑅

=

[ )] 𝑑𝑙𝑛𝑃𝐻2𝑆 1 𝑑( 𝑇

(41) 𝑞𝐻2𝑆


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The partial pressures of CO2 and H2S were calculated by setting d(1/T) = 0.1 (temperature difference) and applying model 4, and then the heats of adsorption were calculated for the entire CO2 and H2S loading ranges. The estimated heats of absorption for CO2 and H2S in 30 wt% MDEA aqueous solutions at 323.15 K are shown in Figure 7 as 3D plots. The x-axis represents CO2 loading, the y-axis represents H2S loading, and the z-axis represents the heats of absorption of (a) CO2 and (b) H2S. As shown in Figure 7, the change in the adsorption heat of CO2 was larger than that of H2S. The heat of adsorption of CO2 was in the range 30–100 kJ/mol CO2, whereas that of H2S was in the range 10–65 kJ/mol H2S in the CO2/H2S mixture.

(Figure 7)


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Energy & Fuels

5. Conclusions

In this study, the solubilities of CO2 and H2S mixtures in 30, 40, and 50 wt% MDEA aqueous solutions in the temperature range 313.15–403.15 K were investigated experimentally and through modeling. The partial pressures of CO2 and H2S, the mole fraction of the liquid phase, the pH, and the heats of absorption for all amine concentrations, temperatures, and CO2 and H2S loading conditions were calculated by applying the modified Kent–Eisenberg model incorporated with the Deshmukh–Mather model and the electrolyte NRTL model. Equilibrium constants for amine protonation (K1) were regressed by applying the experimental data to the modified Kent–Eisenberg model (model 2 in this study). Then binary parameter of activity coefficients in the Deshmukh-Mather model and the electrolyte NRTL model were regressed. The best fit to the experimental data was obtained by applying the newly obtained equilibrium constants (K1 values) to the Deshmukh–Mather model (model 4 in this study). The obtained SMAPE (symmetric mean absolute percentage error) value was 45.00% for model 4 for all solubility data range in this study. The Deshmuhk Mather model, which has weak physical meaning but more flexible use of binary parameters, showed better expression of short range interaction (local interaction) than the electrolyte NRTL model, which has strong physical meaning and more binary parameters. Based on model 4, the range of calculated pH values was approximately 7.5–10.2 at low temperature (323.15 K) and approximately 7.2–8.7 at high temperature (383.15 K). The estimated heat of adsorption of CO2 was in the range 30–100 kJ/mol CO2, whereas that of H2S was in the range 10–65 kJ/mol H2S in the CO2/H2S mixture.

Acknowledgements This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (No. 2011951010001A & 20152020201130).


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References

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Energy & Fuels

Industrial & Engineering Chemistry Research 1991, 30, (3), 543-555. 11. Posey, M. L.; Rochelle, G. T., A thermodynamic model of Methyldiethanolamine− CO2− H2S− Water. Industrial & engineering chemistry research 1997, 36, (9), 3944-3953. 12. Zong, L.; Chen, C.-C., Thermodynamic modeling of CO2 and H2S solubilities in aqueous DIPA solution, aqueous sulfolane–DIPA solution, and aqueous sulfolane–MDEA solution with electrolyte NRTL model. Fluid Phase Equilibria 2011, 306, (2), 190-203. 13. Huttenhuis, P. J. G.; Agrawal, N.; Hogendoorn, J.; Versteeg, G., Gas solubility of H2S and CO2 in aqueous solutions of N-methyldiethanolamine. Journal of Petroleum Science and Engineering 2007, 55, (1-2), 122-134. 14. Kaewsichan, L.; Al-Bofersen, O.; Yesavage, V. F.; Selim, M. S., Predictions of the solubility of acid gases in monoethanolamine (MEA) and methyldiethanolamine (MDEA) solutions using the electrolyte-UNIQUAC model. Fluid Phase Equilibria 2001, 183, 159-171. 15. Kent, R., L. and Eisenberg, B. Paper E, Gas conditioning Conference, University of Oklahoma, 1975. Also. Hydrocarbon Processing 1976, 55, (2), 87. 16. Haji-Sulaiman, M.; Aroua, M.; Benamor, A., Analysis of equilibrium data of CO2 in aqueous solutions of diethanolamine (DEA), methyldiethanolamine (MDEA) and their mixtures using the modified Kent Eisenberg model. Chemical Engineering Research and Design 1998, 76, (8), 961-968. 17. Aroua, M.; Mohd Salleh, R., Solubility of CO2 in aqueous piperazine and its modeling using the Kent‐Eisenberg approach. Chemical Engineering & Technology: Industrial Chemistry‐Plant Equipment‐Process Engineering‐Biotechnology 2004, 27, (1), 65-70. 18. Benamor, A.; Aroua, M., Modeling of CO2 solubility and carbamate concentration in DEA, MDEA and their mixtures using the Deshmukh–Mather model. Fluid Phase Equilibria 2005, 231, (2), 150-162. 19. Ma'mun, S.; Jakobsen, J. P.; Svendsen, H. F.; Juliussen, O., Experimental and modeling study of the solubility of carbon dioxide in aqueous 30 mass% 2-((2-aminoethyl) amino) ethanol solution. Industrial & engineering chemistry research 2006, 45, (8), 2505-2512. 20. Kim, I.; Hoff, K. A.; Hessen, E. T.; Haug-Warberg, T.; Svendsen, H. F., Enthalpy of absorption of CO2 with alkanolamine solutions predicted from reaction equilibrium constants. Chemical Engineering


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Science 2009, 64, (9), 2027-2038. 21. Chen, C. C.; Britt, H. I.; Boston, J.; Evans, L., Local composition model for excess Gibbs energy of electrolyte systems. Part I: Single solvent, single completely dissociated electrolyte systems. AIChE Journal 1982, 28, (4), 588-596. 22. Chen, C. C.; Evans, L. B., A local composition model for the excess Gibbs energy of aqueous electrolyte systems. AIChE Journal 1986, 32, (3), 444-454. 23. Chen, C. C.; Song, Y., Generalized electrolyte‐NRTL model for mixed‐solvent electrolyte systems. AIChE Journal 2004, 50, (8), 1928-1941. 24. Hessen, E. T.; Haug-Warberg, T.; Svendsen, H. F., The refined e-NRTL model applied to CO 2–H 2 O–alkanolamine systems. Chemical Engineering Science 2010, 65, (11), 3638-3648. 25. Mondal, B. K.; Bandyopadhyay, S. S.; Samanta, A. N., Vapor–liquid equilibrium measurement and ENRTL modeling of CO 2 absorption in aqueous hexamethylenediamine. Fluid Phase Equilibria 2015, 402, 102-112. 26. Guggenheim, E., L. The specific thermodynamic properties of aqueous solutions of strong electrolytes. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 1935, 19, (127), 588-643. 27. Zhang, G.; Zeng, Y.; Guo, X.; Jiang, F.; Shi, D.; Chen, Z., Electrochemical corrosion behavior of carbon steel under dynamic high pressure H2S/CO2 environment. Corrosion Science 2012, 65, 37-47. 28. Zhang, Y.; Que, H.; Chen, C.-C., Thermodynamic modeling for CO2 absorption in aqueous MEA solution with electrolyte NRTL model. Fluid Phase Equilibria 2011, 311, 67-75. 29. Al-Rashed, O. A.; Ali, S. H., Modeling the solubility of CO2 and H2S in DEA–MDEA alkanolamine solutions using the electrolyte–UNIQUAC model. Separation and purification technology 2012, 94, 71-83. 30. NIST, The NIST Reference on Constants, Units, and Uncertainty. 31. Kim, S. H.; Kang, J. W.; Kroenlein, K.; Magee, J. W.; Diky, V.; Muzny, C. D.; Kazakov, A. F.; Chirico, R. D.; Frenkel, M., Online data resources in chemical engineering education: Impact of the uncertainty concept for thermophysical properties. Chemical Engineering Education (CEE) 2013, 47,


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(1), 48-57. 32. Prausnitz, J. M.; Lichtenthaler, R. N.; de Azevedo, E. G., Molecular thermodynamics of fluid-phase equilibria. 2nd ed.; Pearson Education: 1998. 33. Schwabe, K.; Graichen, W.; Spiethoff, D., Physicochemical investigations on alkanolamines. Z. Phys. Chem.(Munich) 1959, 20, 68-82. 34. Edwards, T.; Maurer, G.; Newman, J.; Prausnitz, J., Vapor‐liquid equilibria in multicomponent aqueous solutions of volatile weak electrolytes. AIChE Journal 1978, 24, (6), 966-976. 35. Meyer, B.; Ward, K.; Koshlap, K.; Peter, L., Second dissociation constant of hydrogen sulfide. Inorganic Chemistry 1983, 22, (16), 2345-2346. 36. Giggenbach, W., Optical spectra of highly alkaline sulfide solutions and the second dissociation constant of hydrogen sulfide. Inorganic chemistry 1971, 10, (7), 1333-1338. 37. Pakzad, P.; Mofarahi, M.; Izadpanah, A. A.; Afkhamipour, M.; Lee, C.-H., An experimental and modeling study of CO2 solubility in a 2-amino-2-methyl-1-propanol (AMP)+ N-methyl-2-pyrrolidone (NMP) solution. Chemical Engineering Science 2018, 175, 365-376.


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Figures (a)

Model 4

313.15K 323.15K 333.15K 363.15K 383.15K 403.15K

CO2 partial pressure (kPa)

300 g

250

f

200 e

150

d

5

c

100

4 3

b

50

350

1

0.0

0.1

0.2

0.3

0.5

0.6

150

0.7

d

250

f

a

350

2

b

1

0.1

d

150

5 c

100 50 0

4

b 1

0.1

150 100

0.2

0.3

0.4

0.5

0.6

0.7

e

5

c

3 1

0.0

0.1

0.2

0.3

2

0.4

0.5

0.6

0.7

(f)

300 H2S partial pressure (kPa)

e

d 7 c

6

100

5

b

4

50 a

1

0.1

0.2

0.3

250 200 150 f

100

2

0.4

0.5

0.6

0.7

6

d

0

CO2 loading ratio (mol CO2/mol MDEA)

7

e 5

c

50

3

0.0

0.7

4

b

a

350

200

0

0.6

H2S loading ratio (mol H2S/mol MDEA)

f

150

h g f

d

0

(e)

250

0.5

200

50

3

300

0.4

250

CO2 loading ratio (mol CO2/mol MDEA) 350

0.3

(d)

2

a

0.0

0.2

300

e

200

4 3


H2S partial pressure (kPa)


h g

e

f

c

0.0

(c)

300

5

g

100


350

313.15K 323.15K 333.15K 363.15K 383.15K 403.15K

200

0

0.4

Model 4

250

50

2 a

0

(b)

300 H2S partial pressure (kPa)

350


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 32

4

b a

0.0

1

0.1

0.2

0.3

2

3

0.4

0.5

0.6

0.7


Figure 1. Partial pressures of CO2/H2S mixtures in MDEA aqueous solutions in the temperature range 313.15–403.15 K: (a) CO2 solubility in 30 wt% MDEA, (b) H2S solubility in 30 wt% MDEA, (c) CO2 solubility in 40 wt%, MDEA (d) H2S solubility in 40 wt% MDEA, (e) CO2 solubility in 50 wt% MDEA, (f) H2S solubility in 50 wt% MDEA (solid lines: model 4)


(a)

100 CO2 H2S 0 % error 10% error 20% error 30% error

10 SMAPE = 92.88% 10

100

Predicted partial pressure of CO2 and H2S (kPa)

1000

(c)

100

10 SMAPE = 50.05% 10

100

SMAPE = 55.01%

10 SMAPE = 54.33% 1000

Experimental partial pressure of CO2 and H2S (kPa)

100

1000

1000

(d)

100

10 SMAPE = 45.00% 10

100

1000



100

100

10

1000

(e)

10

100

10


1000

(b)




1000

1000

1000



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels


Page 27 of 32

1000

(f)

100

10 SMAPE = 52.16% 10

100

1000


Figure 2. Model correlation with experimental data for the partial pressures of CO2 and H2S in MDEA aqueous solutions (30, 40, and 50 wt%) over the entire temperature range: (a) model 1, (b) model 2, (c) model 3, (d) model 4, (e) model 5, and (f) model 6


Energy & Fuels

0.10

(a) H2S = 0.2

MDEAH+

0.08

MDEA

HCO3

Liquid phase mole fraction (xi)

0.06

-

CO2

0.04 HS-

0.02 CO3 0.00 1e-4 1e-5 1e-6 1e-7 1e-8 1e-9 1e-10 1e-11 1e-12

H2S

2-

-

OH

H3O 0.0

0.2

2-

+

S

0.4

0.6

0.8

1.0

1.2

1.4


0.10

(b) CO2 = 0.2

MDEAH+

0.08

HS-

MDEA

0.06

Liquid phase mole fraction (xi)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 32

H2S

0.04 0.02

HCO3-

CO2

0.00 1e-4 1e-5 1e-6 1e-7 1e-8 1e-9 1e-10 1e-11 1e-12

CO32-

CO2 -

OH

H3O 0.0

0.2

0.4

+

2-

S

0.6

0.8

1.0

1.2

1.4


Figure 3. Model-predicted liquid-phase concentrations of a CO2–H2S-loaded 30 wt% MDEA aqueous solutions at 323.15 K (model 4): (a) constant H2S concentration (αH2S = 0.2), (b) constant CO2 concentration (αCO2 = 0.2)


Page 29 of 32

(a) CO2

sure, kPa

800

CO2 partial pres

600

400

323.15 K 200

H S0 2 loa 0.5 din g, 0.4 mo l H 0.3 2 S/ mo 0.2 lM DE A) 0.1

0.6 0.5 0.4 EA MD 0.3 ol m / 0.2 l CO 2 o m , 0.1 ing d PCO2 (Exp.) loa O C 2

(b) H2S

re, kPa

800

su H 2S partial pres

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

600

400

200


0.6 0.5 A 0.4 DE lM 0.3 o /m 0.2 l CO 2 o m 0.1 ing, d loa PH2S (Exp.) 2 O C

Figure 4. Solubilities of CO2/H2S mixtures in 30 wt% MDEA aqueous solutions at 323.15 K: (a) CO2 solubility and (b) H2S solubility (red circles: CO2 partial pressure (Exp.), blue squares: H2S partial pressure (Exp.), solid line mesh: model 4)


Energy & Fuels

(a) CO2

sure, kPa

800

CO2 partial pres

600

400

200


383.15 K

0.6 0.5 0.4 EA MD 0.3 ol m / 0.2 l CO 2 o m 0.1 ing, d PCO2 (Exp.) loa 2 O C

(b) H2S

sure, kPa

800

H 2S partial pres

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 32

600

400

200


0.6 0.5 0.4 EA MD 0.3 ol m / 0.2 l CO 2 o m 0.1 ing, d loa PH2S (Exp.) CO 2

Figure 5. Solubilities of CO2/H2S mixtures in 30 wt% MDEA aqueous solutions at 383.15 K: (a) CO2 solubility and (b) H2S solubility (red circles: CO2 partial pressure (Exp.), blue squares: H2S partial pressure (Exp.), solid line mesh: model 4)


Page 31 of 32

323.15 K 10.0 9.5 9.0

pH

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

8.5 8.0 7.5 7.0

383.15 K

CO0.0 2 m 0.2 ola 0.4 rity 0.6 (m ol 0.8 CO 1.0 2 /L so 1.2 lut ion 1.4 ) 1.6

1.4 1.2 ) 1.0 ion t u l 0.8 so L / 0.6 S 0.4 l H2 o 0.2 ity (m r 0.0 ola m S H2

1.6

Figure 6. pH changes in 30 wt% MDEA aqueous solutions at 323.15 and 383.15 K (solid line mesh: model 4)


Energy & Fuels

(a) CO2

] -H abs [kJ/mol CO 2

120 100 80 60 40 CO20 0.1 2 lo ad 0.2 ing ,m ol 0.3 CO 2 /m 0.4 ol MD 0.5 EA

0.6

0.6 H

0.5 0.4 EA) MD 0.3 ol /m S 0.2 H2 ol 0.1 ng, m di oa Sl 2

(b) H2S 70

-H abs [kJ/mol H 2S]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 32

60 50 40 30 20

CO10 0.1 2 lo ad 0.2 ing ,m ol 0.3 CO 2 /m 0.4 ol MD 0.5 EA

0.6

0.6

H

0.5 0.4 EA) MD 0.3 ol m / S 0.2 H2 ol 0.1 ng, m di loa S 2

Figure 7. Heats of absorption in 30 wt% MDEA aqueous solutions at 323.15 K: (a) CO2 and (b) H2S (solid line mesh: model 4)


Experimental and Modeling Study of Vapor Liquid Equilibrium for a

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