Modeling of CO2 Absorption Kinetics in Aqueous 2

Article pubs.acs.org/IECR

Modeling of CO2 Absorption Kinetics in Aqueous 2‑Methylpiperazine Xi Chen and Gary T. Rochelle* McKetta Department of Chemical Engineering, The University of Texas at Austin, 200 East Dean Keeton Street C0400, Austin, Texas 78712, United States ABSTRACT: CO2 absorption into 8 molal (m) 2-methylpiperazine (2MPZ) is modeled in Aspen Plus using a previously developed rigorous thermodynamic model. With the regression of three reaction rate constants for carbamate and bicarbonate and one parameter for diffusion activation energy, the kinetic model represents CO2 flux measured in a wetted-wall column at 40−100 °C with 0.1−0.4 mol CO2/mol alkalinity with a relative deviation from −20% to 20%. The kinetic reaction rate is interpreted with activity-based termolecular kinetics and the rate constants are correlated with the Bro̷ nsted theory. The liquid film mass transfer coefficient (kg′) is well represented by the model at medium to rich CO2 loading. The power to which kg′ is dependent on the rate constant of 2MPZ carbamate formation (k2MPZ−2MPZ) decreases from ∼0.5 at very lean loading to nearly 0 at rich loading, whereas it is increasingly dependent upon the diffusion coefficient of the reactants and products and the physical liquid film mass transfer coefficient (k0l ) as loading and temperature increases. In the liquid film, 2MPZ and 2MPZCOO− are the major reactants and protonated 2MPZ carbamate and bicarbonate are the major products. The pseudo-first-order region for 2MPZ narrows and shifts to higher value of k0l as temperature increases. Under typical industrial conditions, the gas film resistance contributes less than 25% of the total resistance.

1. INTRODUCTION

concentrated aqueous MEA and piperazine with literature data and analytical equations. Most of the previous kinetic modeling was focused on the traditional amine solvent, MEA. The current study aims to develop a kinetic model for a novel hindered amine solvent, 2methylpiperazine (2MPZ). 2MPZ was patented as hindered amine by Sartori et al. for application in acid gas treating.9,10 2MPZ was also patented by Suzuki et al.11 for application in CO2 capture. The CO2 solubility and liquid film mass transfer coefficient in 8 m 2MPZ were measured by Chen and Rochelle,12 who found that 2MPZ has greater CO2 capacity and greater mass transfer rate than 7 m MEA. In this work, the kinetics and mass transfer for 8 m 2MPZ are investigated by fitting the wetted wall column (WWC) model created in Aspen Plus to the mass transfer data obtained from the WWC experiments at 40−100 °C.12 The kinetic model is built on the basis of a rigorous thermodynamic model for 2MPZ created in the framework of the electrolyte-NRTL model.13 More details on this work are found in the dissertation by Chen.14

Amine scrubbing is an important technology for CO2 capture from flue gases and mitigation of CO2 emissions. In a real amine scrubbing process, thermodynamic equilibrium is rarely encountered, and the assumption of instantaneous reactions is usually not valid except at very high temperature. Most of the reactions proceed at a finite rate at absorber conditions. At stripper conditions, although the reversion of carbamate or bicarbonate to free CO2 occurs at a very fast rate, mass transfer is limited by the diffusion of reactants and products. Therefore, the creation of rigorous rate-based kinetic models for CO2 absorption into amine solvents is of critical importance for design and simulation of CO2 capture process. A number of efforts in developing kinetic models for CO2 absorption into amine solvents have been reported. Freguia et al.1 created a rate model for monoethanolamine (MEA) using the thermodynamic model created by Austgen et al.2 The kinetic constant for carbamate formation was obtained by matching pilot plant test data. Aboudheir et al.3 used termolecular kinetics to interpret the kinetic data from measurements in a laminar jet for CO2-loaded and concentrated MEA solution and obtained rate constants through data regression. These kinetic data were also used by Plaza et al.4 to extract kinetic constants and develop a rigorous model for MEA in Aspen Plus. Kucka et al.5 created a numerical model for reactive absorption of CO2 into MEA, and validated this model by implementing it to Aspen Custom Modeler. Cullinane6 regressed kinetic constants based on the mass transfer data for absorption of CO2 into PZ/K2CO3 in a Wetted Wall Column and developed a rate model. Tobiesen et al.7 developed a rigorous rate model for CO2 absorption into MEA based on literature data and validated it against experimental results from a laboratory pilot plant. Dugas and Rochelle8 quantitatively explained the rate behavior of CO 2 absorption into © 2013 American Chemical Society

2. MODEL DESCRIPTION 2.1. Flow Sheet. A Ratesep model was created in Aspen Plus to simulate the experimental WWC setup used by Chen and Rochelle.12 The gas film mass transfer coefficient (kg) and physical liquid film mass transfer coefficient (k0l ) for the real WWC were experimentally determined by Bishnoi15 and Pacheco,16 respectively. The same correlations were used for the column in the model in this work. The change in the temperature of gas Received: Revised: Accepted: Published: 4239

September 3, 2012 February 14, 2013 February 15, 2013 February 15, 2013 dx.doi.org/10.1021/ie3023737 | Ind. Eng. Chem. Res. 2013, 52, 4239−4248

Industrial & Engineering Chemistry Research

Article

DCO2 (m 2/s) = 2.35 × 10−6 exp(− 2119/T )

and liquid stream is very small because of the excessive liquid flow rate compared to the gas flow rate. As described by Chen and Rochelle,12 for a solvent at each loading and temperature, six inlet gas compositions corresponding to six values of CO2 partial pressure were used to give both absorption and desorption CO2 fluxes between the gas and the solvent. Chemical and physical properties including kinetic constants and diffusion coefficients are adjusted through the “Data Fit” block in Aspen Plus to match the measured CO2 flux data. The difference between the predicted fluxes yi and the experimentally determined fluxes (yim) weighted by the standard deviation (σiy), as well as the deviation between the reconciled inputs (xi) and the measured inputs (xim) weighted by σix are taken into account in the objective function to be minimized, as shown in the following equation: Fobj =

1 {∑ [(xi − xim)/σix]2 + 2

Equations 4 and 5 were adopted in this work for representation of the binary diffusion coefficients of CO2 in any other components. This ensures the effective CO2 diffusivity in the solution equal to the reported experimental value. Dugas18 measured the effective diffusivity of all the species in loaded MEA and PZ aqueous solution at 30 °C with a diaphragm cell. The measured diffusion coefficient was correlated to solution viscosity (η, cP) and temperature (T, K) as shown in eq 6. The measurements were done at only one temperature, and the temperature dependence of the diffusion coefficient in his correlation is taken from the Wilke−Chang correlation for dilute solution.19 ⎛ T ⎞ ⎟ DAm (m 2/s) = 8.2 × 10−10η−0.72⎜ ⎝ 303.15 ⎠

∑ [(yi − yim )/σiy]2 } (1)

2

⎛ A⎛ 1 1 ⎞⎞ ⎟⎟ DAm = 8.2 × 10−10η−0.72 exp⎜ − ⎜ − ⎝ R ⎝T 303.15 ⎠⎠

(2)

⎛ 1587 ⎞⎟ ⎜ − 3.765 + [CO2 ] ⎝ T ⎠ ⎛ 506.1 ⎞ ⎛ 411.0 ⎞⎟ ⎟[Am] + ⎜1.171 − [CO2 ] +⎜ ⎝ ⎝ T ⎠ T ⎠

ln(η /ηH O) = − 4.634 +

[Am]

(3)

where η is the viscosity of the aqueous amine solution and ηH2O is the water viscosity at the experimental temperature. The concentration of the total CO2 and amine are in the unit of mol/kg solution. Detailed results are given in Chen.14 Diffusion Coefficients. A general correlation for the dependence of the CO2 diffusivity in aqueous alkanolamine solutions on the solvent viscosity was derived by Versteeg and Van Swaalj:17 (η0.8DCO2)Am = (η0.8DCO2)water = Const

(7)

The effect of temperature on the diffusivity in loaded amine solution is still not clear because there has been very few data reported in the currently available literature. A is used as an adjustable parameter in this work to take into account the unknown dependence of DAm on temperature. It is similar to but different from diffusion activation energy (ED). The exponent term in eq 7 basically accounts for the additional impact of temperature on diffusivity other than the effect of changing viscosity. Snijder and co-workers20 measured the diffusion coefficient for several aqueous amines and found that the dependence of the diffusivity of amine in water on temperature can be represented well with the exponential function. The same form was used by Chang et al.21 to describe their diffusivity data as a function of temperature for aqueous amine at 30−70 °C. However, both works did not include viscosity in their correlations. These correlations for the physical properties are input to Aspen Plus through user Fortran subroutines. 2.3. Multicomponent Mass Transfer. The average diffusion coefficient of a component in a mixture calculated from certain mixing rule does not have quantitative application in Aspen Plus. Instead, a rigorous multicomponent mass transfer theory22−24 involving the Maxwell−Stephan equation is employed by Aspen Plus rate-based model to evaluate multicomponent mass transfer rates.25 The correlation obtained by Pacheco16 for the physical liquid film mass transfer coefficient of the WWC is used for calculation of the binary mass transfer coefficient κik from the binary diffusion coefficient Dik, as shown in the following equation:

where ρ is the density of the aqueous amine solution, and ρH2O is the water density at the experimental temperature. Detailed results are given in Chen.14 Viscosity. 2-MPZ is a solid at room temperature. The melting point is about 65 °C and the boiling point is 155 °C. Proper representation of viscosity as a function of temperature and CO2 loading is important for kinetic modeling since the diffusion coefficient is strongly dependent on viscosity. The empirical model shown in eq 3 is used to correlate the viscosity of 8 m 2MPZ to the content of CO2 and amine at variable temperature. 2

(6)

The binary diffusivity of all molecular and ionic species other than CO2 (DAm) in any other species in loaded 2MPZ at 30 °C is assumed to have the same value as reported by Dugas for MEA and PZ solution. However, the dependence of the diffusion coefficient on temperature is expressed in a different form as shown in eq 7.

The only input to be adjusted in this work is CO2 loading. The adjustment in CO2 loading is done by varying the flow rate of the CO2 stream going to the mixer and is specified to be no more than 5%. 2.2. Physical Properties. Density. The molar volume or the density is required for conversion of molar flow rate to volume flow rate and, thus, affects the calculation of liquid velocity in the column and liquid−gas contact time. The density of 8 m 2MPZ is correlated to CO2 loading and temperature with the following empirical equation: ρ /ρH O = 1.018 + 0.0408[CO2 ]

(5)

⎛ 31/321/2 ⎞⎛ Q1/3h1/2W 2/3 ⎞⎛ gρ ⎞1/6 ⎟⎜ ⎟ Dik0.5 κik = kj0Dikα = ⎜ 1/2 ⎟⎜ A ⎠⎝ ⎝ π ⎠⎝ η ⎠

(4)

In the same work, the diffusivity of CO2 in water was also given:

(8) 4240

dx.doi.org/10.1021/ie3023737 | Ind. Eng. Chem. Res. 2013, 52, 4239−4248


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Table 1. Molality-Based pKa of the Bases and Ratios of Kinetic Reaction Constants at 40 °C bases pKa bicarbonate formation k2,bc carbamate formation reaction rate kAm−b

a

amine 2MPZd 2MPZH+d 2MPZCOO−e

2MPZ

2MPZCOO−

H2O

OH−

CO32−

9.16a 1

8.87b 0.75

−1.74 1.8 × 10−5

15.74 7.2 × 102

10.33 3.2

1 0.14 1

0.88 0.13 0.88

6.9 × 10−3 9.9 × 10−4 6.9 × 10−3

2.0 2.9 2

1.7 0.25 1.7

Khalili, Henni et al. 2009.27 bEstimated from the pKa of 2MPZ, PZ, and PZCOO−. cRatio to k2,2MPZ. dRatio to k2MPZ−2MPZ. eRatio to k2MPZCOO−2MPZ.

in which Q is the liquid volumetric flow rate in the real WWC, W is the circumference of the column (3.96 cm), d is the hydraulic diameter of the annulus (0.44 cm), h is the height of the WWC (9.1 cm), and A is the gas−liquid contact area (38.52 cm2). 2.4. Reactions. Single-step termolecular reaction kinetics26 are used in this work to model the reaction rate between CO2, amine solvents, and bases (B), as shown in the following reaction: Am + CO2 + B ↔ AmCOO− + BH+

kinetic reactions are included as both forward and reverse reactions: 2MPZ + CO2 + B ↔ 2MPZCOO− + BH+ 2MPZCOO− + CO2 + B ↔ 2MPZ(COO−)2 + BH+ (16)

2MPZH+ + CO2 + B ↔ H2MPZCOO + BH+

The reaction rate is expressed in the form of the product of the kinetic rate constant and the activity of reactants. As an example, the following forward and reverse reaction rates with respect to CO2 can be written for reaction 9: (10)

rr = k raAmCOO−aBH+

(11)

where kf and kr are the forward and reverse rate constant, respectively. They are correlated to each other by the equilibrium constant (Keq): kr =

kf Keq

(12)

ln kAm − b2 = ln kAm − b1 + 0.457(pK a,b2 − pK a,b1)

Keq is obtained from the equilibrium composition and activity coefficients of reactants and products calculated from the thermodynamic model.13 The overall reaction rate is therefore equal to

= −(k f aAmaCO2aB − k raAmCOO−aBH+)

(13)

In Aspen Plus, a power-law kinetic expression is applied to represent the temperature effect on reaction rate constant: ⎛ T ⎞n ⎡ E ⎛ 1 1 ⎞⎤ k = k 0⎜ ⎟ exp⎢ − ⎜ − ⎟⎥ ⎢⎣ R ⎝ T T0 ⎠⎥⎦ ⎝ T0 ⎠

(18)

Based on the correlation above, the natural logarithm value of the reaction rate constant involving PZ species with CO2 is proportionally related to the pKa value of the catalyzing base with a slope of 0.457. Analysis done by Cullinane in the same work also suggested that a similar relationship between base strength and rate constants is applicable for other amines with the Bro̷ nsted slope close to 0.5. Due to the similar ring structure of PZ and 2MPZ, eq 18 is assumed to be applicable as well to the reactions involving 2MPZ species. For the different amines catalyzed by the same base, if the amine structures are very close to each other, the same factor of 0.457 is applied to account for the effect of the basic strength of amine on rate constant, as shown in the following equation:

rCO2 = rf + rr ⎛ ⎞ −a + a = −k f ⎜⎜aAmaCO2aB − AmCOO BH ⎟⎟ Keq ⎝ ⎠

(17)

The bases (B) included in the reaction set above are 2MPZ, 2MPZCOO−, and H2O. The concentration of OH− is very small and has a negligible effect on the total reaction rate; therefore, it is excluded from consideration. The second pKa value of 2MPZ was reported to be around 5 at 25−50 °C.27 The amount of diprotonated 2MPZ is extremely small in normal CO2-loaded solutions; therefore, 2MPZH+ is not included as a base in this work. Because of the large number of possible kinetic reactions, it is not feasible to independently regress each reaction rate constant in a statistically meaningful manner. To simplify the problem, the Bro̷ nsted theory is used in this work to correlate the rate constants to the pKa of the participating amines and bases. Cullinane6 regressed reaction rate constants for aqueous PZ and found the following Bro̷ nsted correlation for carbamate formation reactions with respect to the termolecular kinetics:

(9)

rf = −k f aAmaCO2aB

(15)

ln kAm2 − b = ln kAm1− b + 0.457(pK a,Am2 − pK a,Am1)

(19)

Equation 19 is used to quantify the change in the carbamate formation rate as 2MPZ is protonated and becomes 2MPZH+. 2MPZ and 2MPZCOO− can also catalyze the hydrolysis of CO2 to bicarbonate as shown in the following reactions:

(14)

where k0 is the pre-exponential constant; T0 is the reference temperature; and E is the reaction activation energy. T0 = 313.15 K and n = 0 are used throughout this work. Based on the speciation study and the thermodynamic model by Chen and Rochelle,13 the species in aqueous 2MPZ that are capable of forming carbamate with CO 2 are 2MPZ, 2MPZCOO−, and 2MPZH+. Consequently, the following

2MPZ + CO2 + H 2O ↔ HCO−3 + 2MPZH+ −

2MPZCOO + CO2 + H 2O ↔

HCO−3

(20)

+ H2MPZCOO (21)

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next to the interface of gas and liquid, the liquid film is further divided into multiple segments. The mass balance and energy balance is applied to each segment. The film discretization implemented in this work is presented in Table 2. δ = 0 represents the vapor−liquid interface and δ = 1 represents the edge of the film next to the bulk.

Versteeg et al.28 summarized the kinetic data for the reactions between tertiary amines and CO2, and correlated the reaction rate of hydrolysis of CO2 to the basic strength of the catalyzing base with a linear relationship: ln k 2 = pK a − 14.24

(22)

Equation 22 is adapted in this work to correlate the bicarbonate formation rate catalyzed by different bases, as shown by the following equation: k 2,b1 k 2,b2

= exp(pK a,b1 − pK a,b2)

Table 2. Film Discretization Used in This Worka point 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

(23)

The pKa values for the bases taken into account in this work and the ratio of reaction rate constants according to eqs 18, 19, and 23 are shown in Table 1. The contribution of H2O, OH−, and CO32− to the overall bicarbonate formation reaction is found to be negligible and is thus excluded from the reaction set. The pKa value predicted for 2MPZCOO− from the thermodynamic model is subject to an uncertainty of as high as ±2.5 due to the standard deviation of the obtained standard property values for 2MPZCOO− and H2MPZCOO, so the model predicted value is not used. Instead, the difference in the pKa of 2MPZCOO− and that of 2MPZ is assumed to be equal to the difference between the pKa of PZ29 and PZCOO−30, and the estimated pKa value for 2MPZCOO− is 8.87. Even though the ratio of bicarbonate formation rate constant is calculated from eq 23 for 2MPZCOO−, as listed in Table 1, the rate constant for bicarbonate formation reaction with 2MPZCOO− (reaction 21), k2,2MPZCOO−, is not linked to that for bicarbonate formation with 2MPZ, k2,2MPZ (reaction 20) through the Bro̷ nsted Theory. They will be independently determined. The hypothesis is that, as a hindered amine, 2MPZCOO− could catalyze the formation of bicarbonate with formation of dicarbamate followed by hydrolysis, which would possibly have a much higher rate than simple base catalysis. For each amine, the carbamate formation reactions having 2MPZ as the catalyzing base are used as the reference case. The reaction rate constants are ratioed to that of one of the following two reactions:

2MPZCOO− + CO2 + 2MPZ (25)

The reaction of CO2 with water or hydroxide to produce bicarbonate has been neglected in this work. In addition to the kinetic reactions mentioned above, the following reactions are accounted for in the model as equilibrium reactions since they involve exchange of proton only. (26)

HCO−3 + H 2O ↔ CO32 − + H3O+ +

(27) +

2MPZH + H 2O ↔ 2MPZ + H3O

(28)

H2MPZCOO + H 2O ↔ 2MPZCOO− + H3O+

(29)

1.00 × 10 2.00 × 10−06 4.00 × 10−06 8.00 × 10−06 1.60 × 10−05 3.20 × 10−05 6.40 × 10−05 7.68 × 10−05 9.22 × 10−05 0.000111 1.33 × 10−04 0.000159 1.91 × 10−04 0.000229 2.75 × 10−04 0.00033 3.96 × 10−04

point

δ

point

δ

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

0.000476 0.000571 0.000685 0.000822 0.000986 0.00118 0.00142 0.0017 0.00204 0.00245 0.00294 0.00353 0.00424 0.00509 0.00611 0.00733 0.00879

35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

0.0106 0.0127 0.0152 0.0182 0.0219 0.0263 0.0315 0.0378 0.0454 0.059 0.0826 0.124 0.198 0.317 0.507 0.862 1.0

3. MODEL RESULTS 3.1. Regression Results. The experimental WWC data for 8 m 2MPZ at 0.102 to 0.365 mol CO2/mol alkalinity and 40 to 100 °C were used for data regression.12 The reaction rate constant at 40 °C (k2,2MPZ) for the bicarbonate formation reaction 20 is estimated from the results reported by Ko and co-workers for MDEA,31 since their results are representative of previous kinetic measurements for MDEA. The kinetic rate was further corrected with the Bro̷ nsted theory using eq 23 to be used for 2MPZ. The pKa value for MDEA was taken from Hamborg et al.32 The first pKa for 2MPZ is based on the value reported by Khalili et al.27 Conversion from concentration-based reaction rate to activity-based reaction rate is also necessary. k2,2MPZCOO− for reaction 21 is determined by data regression. The activation energy for reactions 20 and 21 is approximated with the value reported for MDEA, 44.9 kJ/ mol.31 Studies by Bishnoi33 and Cullinane6 showed that the activation energy for the PZ carbamate formation reaction has a value of ∼35 kJ/mol. This value was used by Dugas in the development of a spreadsheet model for absorption of CO2 into PZ.18 The same activation energy (E) of 35 kJ/mol is also used in this work for the carbamate formation with 2MPZ (reaction 24) and the dicarbamate formation reaction (reaction 25). All the other reactions are assumed to have the same activation energy as the corresponding reaction to which they are referenced. The parameters that were included for regression are kf at 40 °C for reactions 21, 24, and 25 and the quasi-diffusion activation energy A in eq 7 for the diffusivity of all the non-CO2 species. The regressed values for different parameters are summarized in Table 3.

(24)

2H 2O ↔ H3O+ + OH−

−06

a δ: the dimensionless distance from the interface of a segmentation point.

2MPZ + CO2 + 2MPZ ↔ 2MPZCOO− + 2MPZH+

↔ 2MPZ(COO−)2 + 2MPZH+

δ

2.5. Film Discretization. Aspen Plus Ratesep represents the boundary layer with film theory. To more accurately calculate the concentration profile across the boundary layer 4242



Article

ing experimental CO2 loading, as shown in Figure 1, are found to be within ±60%, 86% of which is within ±20%. The absolute

Table 3. Parameters Regressed to Represent CO2 Absorption in 8 m 2MPZ at 40−100 °C and 0.102−0.365 mol CO2/mol Alkalinity parameter

estimate

k2MPZ−2MPZ (kmol/m ·s) k2MPZCOO−−2MPZ (kmol/m3·s) k2,2MPZCOO− A (kJ/mol) 3

std. dev.

1.94 × 10 6.19 × 1010 1.65 × 108 2.0

4.0 × 104 1.1 × 109 1.1 × 107 0.1

10

As can be seen from the table, the regression returns estimates for all the regressed parameters with relatively small standard deviations. The calculation of the covariance matrix shows that all the regressed parameters are very weakly correlated to each other. The greatest correlation is −0.65 for k2,2MPZCOO− with k2MPZCOO−−2MPZ. Kinetics for 2MPZ is expected to be slightly slower than that for PZ due to the moderately hindered amino group. Cullinane and Rochelle34 used a concentration-based rate expression and obtained a value of 7.0 × 104 m6/kmol2·s for kPZ−PZ at 25 °C for dilute PZ by data regression. After being converted to an activity-based rate constant, this value turns out to be 2.4 × 1010 kmol/m3·s at 40 °C. Bishnoi15 reported the second-order rate constant for PZ, which is equal to 3.2 × 1010 kmol/m3·s at 40 °C after the amine concentration is taken into account. The values from both the studies compare favorably with the value of k2MPZ−2MPZ from this work (1.94 × 1010 kmol/m3·s). The relative values of k2MPZCOO−−2MPZ and k2MPZ−2MPZ are a reflection of the activity coefficients. The calculated activity coefficient of 2MPZCOO− at rich CO2 loading is about 1 order of magnitude lower than that of 2MPZ13. When these rate constants are adjusted to concentration-based, the rate constant for Reaction 25 is about 50% of that for Reaction 24. The value of k2,2MPZCOO− is about 1 order of magnitude higher than what would be predicted from the rate measured for another hindered amine, 2-piperidine ethanol (2-PE),35 and corrected by the Bro̷ nsted theory. It could be that the hindrance around the hindered amino group on 2MPZCOO− is not as severe as that on 2-PE; therefore, the bicarbonate formation under the catalysis of 2MPZCOO− could be a result of a faster carbamate formation followed by hydrolysis. If the viscosity term in eq 7 is expressed in an exponential function of temperature, the diffusivity activation energy can be calculated for 8 m 2MPZ. The calculated values are compared to literature data for unloaded amine solutions in Table 4.

Figure 1. Relative deviation of the calculated fluxes from the experimental measurements as a function of CO2 loading for 8 m 2MPZ with 0.102−0.365 mol CO2/mol alkalinity at 40 °C (○), 60 °C (□), 80 °C (◊), and 100 °C (Δ).

average relative deviation (AARD) between the calculated fluxes and the measured fluxes, as calculated by the following equation, is 11%. AARD (%) =

molarity

CO2 loading (mol/mol alk)

viscosity at 60 °C (cP)

ED (kJ/mol)

2MPZ

4.5 4.4 1.0 4.0

0 0.35 0 0

4.1 12.6 0.6 2.3

25.6 27.9 17.8 23.1

MDEA

∑ N

|Flux cal − Flux exp| Flux exp

(30)

This is considered as a good fit because the experimental flux values span more than 3 orders of magnitude over the studied loading range. As a comparison, the spreadsheet model developed by Dugas18 fits the WWC data for 2−12 m PZ within ±50%; the relative deviation between the predictions from Cullinane’s model6 and the measured fluxes for PZ/ K2CO3 in the WWC were ±30%. According to Figure 1, there is no obvious systematic error associated with CO2 loading or temperature. 3.1. Liquid Film Mass Transfer Coefficient. Given that the model represents the experimental CO2 fluxes well, it was used to calculate the values for the liquid film mass transfer for 8 m 2MPZ at 40 to 100 °C. Similar to the method used in obtaining the experimental values for kg′, the model value for kg′ is calculated from the modeling results for the difference of CO2 concentration in the inlet and outlet gas stream and the logarithmic mean of partial pressure driving force. The reported value for kg′ calculated at each temperature and CO2 loading is an average of the calculated kg′ at varied driving force, corresponding to the CO2 partial pressure in the gas phase (PCO2) equal to 0, 0.3, 0.6, 1.4, 1.7, and 2 times the equilibrium CO2 partial pressure of the solvent (PCO * 2). In this way, the experimental conditions are approximately matched.12 The model values are compared to the measured values in Figure 2. The model is able to capture the trend of kg′ with both loading and temperature and agrees satisfactorily with the experimental measurements. The deviations between the model and the data are less than 15% except for a few points. At very lean loading at 40 °C, the predictions are somewhat lower, which could be partially attributed to the greater uncertainty in the measurements at very lean loading. At very lean loading, the resistance of liquid film is much less than the gas film resistance, and the latter dominates the overall mass transfer. Hence, a

Table 4. Comparison of the Diffusion Activation Energy for 8 m 2MPZ with Literature Values for Aqueous MDEA amine

100 N

source this work this work Snijder, te Riele et al. 199320

According to the results by Snijder et al.,20 the diffusion activation energy increases with liquid viscosity. The slightly higher value for ED obtained in this work compared to the literature values is presumably due to the higher viscosity of either unloaded or loaded 8 m 2MPZ. The relative deviations between the model prediction at the adjusted CO2 loading and the measurement at the correspond4243



Article 2 2 ′ kg,PFO ≈ {[DCO2(k 2MPZ − 2MPZx 2MPZ γ2MPZ + k 2MPZCOO− − 2MPZ

x 2MPZCOO−γ2MPZCOO−x 2MPZγ2MPZ)/Vm]1/2 0.5 }/{γCO HCO2}

(33)

2

3

where Vm is the molar volume of the amine solution (m /mol), HCO2 is the Henry’s constant of CO2 in water (Pa), k is the kinetic reaction rate constant (mol/m3·s), and DCO2 is the diffusivity of CO2 in the amine solution (m2/s). The contribution of two amines (2MPZ and 2MPZCOO−) is taken into account in the equation above. The calculated kg,PFO ′ according to eq 33 is compared to kg′ calculated by the model at 40 and 100 °C in Figure 3. At 40 °C,

Figure 2. Liquid mass transfer coefficient for 8 m 2MPZ. Solid lines: model calculations. Points: measurements.

small error in the measured overall mass transfer coefficient would be amplified to greater error in kg′ value. The model overestimates k′g at 80 °C at lean loading but agrees well with experimental results for P*CO2 > 100 Pa. The liquid film resistance is comprised of two components, the reaction resistance and the diffusion resistance, as shown in the following equation: * HCO2 ∂PCO 1 1 2 = + 0 0 kg′ Ekl kl,PROD ∂[CO2 ]T

Figure 3. Comparison of the liquid film mass transfer coefficient from the model to that calculated from the pseudo-first-order assumption (eq 33 for 8 m 2MPZ at 40 and 100 °C).

(31)

where HCO2 is the Henry’s constant of CO2 in the solution, k01,PROD is the mass transfer coefficient of reaction products, and ∂P*CO2/∂[CO2]T is the slope of the equilibrium curve. The first term on the right-hand side of eq 31 represents the reaction resistance. At lean loading and low temperature, the free amine concentration is much higher than that of CO2 and remains almost constant across the boundary layer. As a result, the diffusion of reactant from the bulk to the interface and products from the interface to the bulk is fast enough to keep up with the reaction rate. In this case, the pseudo-first-order (PFO) assumption applies and reaction resistance dominates the overall mass transfer. At high CO2 loading, the slope of the CO2 solubility curve increases as amine gets depleted. If this is coupled with increased reaction rate at high temperature, the mass transfer in liquid film becomes diffusion-controlled, and the second term in eq 31 is more significant. When the PFO assumption is applicable and the aminecatalyzed carbamate formation reaction is interpreted with the termolecular kinetics, the liquid film mass transfer coefficient can be approximated by the following equation:18 ′ kg,PFO ≈

the prediction from the Aspen Plus model is in close agreement with the result based on the PFO approximation, which indicates that the PFO is adequately valid to represent the mass transfer at low temperature and even up to the rich loading (PCO * 2 = 5000 Pa). However, at 100 °C the deviation between k′g,PFO and k′g is significant due to the dominance of diffusioncontrolled mass transfer at high temperature. Calculation of (1/ kg,PFO ′ )/(1/kg′) yields a fraction number, which represents the contribution of the mass transfer resistance from reaction to the overall liquid film resistance. It decreases to 10% at the operating CO2 loading range from 43% at very lean loading. Effect of Loading on kg′ . The sensitivity of the liquid film mass transfer coefficient to various parameters as CO2 loading is increased from the lean loading to the rich loading is examined in Table 5. HCO2 and k remain constant at same temperature and are therefore not shown. It can be seen from the table that at either 40 or 100 °C the vast majority of the decrease in kg′ is caused by the decrease in free amine concentration. This conclusion is consistent with the analysis done by Dugas18 for concentrated PZ. 3.2. General Sensitivity Analysis. The sensitivity of the developed model to various parameters at 40 °C is portrayed in Figure 4. The effect of the change in parameter i on the liquid mass transfer coefficient is represented by d ln(k′g)/(d ln i). Over a large portion of the CO2 loading range at 40 °C, the sum of the sensitivities of the rate constants is about 0.5, consistent with the PFO expression (eq 33). As CO2 loading

2 DCO2k[Am]2 γAm 0.5 γCO HCO2 2

(32)

In the expression above, the unit for concentration is molarity and the unit for HCO2 is Pa·m3/mol. However, this work uses activity-based reaction based on mole fraction. Therefore, eq 32 is adapted into the following form to be used in this work: 4244



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throughout the loading range. This is expected since both the PFO flux and the liquid film mass transfer coefficient (eq 33) vary as the square root of a diffusion coefficient. Equation 33 suggests that at low loading kg′ should be independent of DAm and vary as the square root of DCO2. In solving film theory for the diffusion in the boundary layer, Aspen Plus makes an approximation that permits accurate use of a mass transfer coefficient that varies as the square root of diffusivity. However, with fast reaction in the boundary layer, this approximation consistently gives the unexpected sensitivity to the 0.25 power of both DCO2 and DAm. Refer to Chen for details on this issue.14 Because of this systematic result in Aspen Plus, the relationship between the true value and the regressed value for a rate constant such as k2MPZ−2MPZ can be approximated by the following equation:

Table 5. Change in Parameters Calculated by the Model from the Lean Loading (0.265 mol CO2/mol Alkalinity, P*CO2 = 500 Pa) to the Rich Loading (0.356 mol CO2/mol Alkalinity, PCO * 2 = 5000 Pa) for 8 m 2MPZ at 40 and 100 °C @lean loading

@rich loading

factor of change

kg′ (mol/m2·s·Pa) [Am] γAm DCO2 (m2/s)

1.4 × 10−6

3.4 × 10−7

4.1

1.3 × 10−2 1.9 1.7 × 10−10

2.2 × 10−3 2.0 1.3 × 10−10

5.9 0.9 1.3

γCO2

1.9

2.0

1.0

T

parameter

40 °C

100 °C

−7

−7

kg′ (mol/m2·s·Pa) [Am] γAm DCO2 (m2/s)

6.6 × 10

2.5 × 10

2.6

1.9 × 10−2 1.9 1.1 × 10−9

6.5 × 10−3 2.1 7.8 × 10−10

2.9 0.9 1.3

γCO2

1.6

1.8

0.9

k 2MPZ − 2MPZ

⎛ D ⎞0.5 (true) = ⎜⎜ Am ⎟⎟ k 2MPZ − 2MPZ (regressed) ⎝ DCO2 ⎠ (34)

The ratio of the binary diffusion coefficients for non-CO2 species and CO2 used in this work is relatively constant at 0.6 at relevant conditions. The true value is therefore about 80% of the regressed value. 3.4. Bro̷ nsted Theory Revisited. Cullinane et al.34 reinterpreted the literature values for the kinetic rate constants of morpholine (MOR), diethanolamine (DEA), and diisopropanolamine (DIPA) with the termolecular kinetics. These concentration-based constants are compared to the constant for 2MPZ obtained in this work (after correction with eq 34) and that for MEA to validate the Bro̷ nsted theory, as shown in Table 6. A Bro̷ nsted plot for these rate constants is shown in Figure 5. Amine with high pKa enhances the reaction rate both as a base

Figure 4. Sensitivity of kg′ to different parameters for 8 m 2MPZ at 40 °C.

increases and the speciation changes, the dominant rate constant shifts from k2MPZ−2MPZ to k2MPZCOO−−2MPZ then to k2,2MPZCOO−. The bicarbonate formation reactions are only important at rich loading due to the much slower reaction rate compared to carbamate formation at 40 °C. The physical liquid film mass transfer coefficient k0l has little impact on k′g at very lean loading, but affects kg′ with a power of 0.28 at rich loading. This Ratesep model unexpectedly gives the same dependence of k′g on DAm and DCO2 at very lean loading, both close to the power of 0.26. The dependence on DAm increases with CO2 loading and approaches to 0.34 at rich loading, while the dependence on DCO2 decreases to 0.17 at rich loading. The sum of the sensitivities to DAm and DCO2 is approximately 0.5

Figure 5. Relationship between the termolecular reaction rate constants and the base strength of six amines at 25 °C.

catalyst and a carbamate formation agent. It is found that linear correlations can be obtained for the cyclic amines and the acyclic amines, respectively. The slopes of the two lines are

Table 6. Concentration-Based Termolecular Kinetic Rate Constants (kAm−Am) for Different Amines at 25 °C amine

MORa

PZb

2MPZc

MEAd

DEAe

DIPAf

pKa kAm−Am at 25 °C (m6/kmol2·s)

8.49 1715

9.73 70100

9.57 44557

9.5 1713

8.88 315

8.89 147

a

Alper 1990.36 bCullinane and Rochelle 2006.34 cThis work. dAboudheir, Tontiwachwuthikul et al. 2003.3 eDanckwerts 1979.37 fLittel, Versteeg et al. 1992.38 4245



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approximately equal. Cyclic amines are 20−40 times faster than the acyclic amines at the same basic strength, which can be attributed to the open ring structure.33

4. PRACTICAL APPLICATION The model developed in this work can be used to simulate large-scale CO2 absorption/desorption processes. It is useful for column design and packing selection to analyze the performance of 2MPZ at typical industrial conditions involving treatment of flue gas from coal-fired power plants. Figure 6 presents the variation of k′g with k0l at the rich CO2 loading. A small driving force is used for the analysis, since that Figure 7. Contribution of the gas film resistance to the overall mass transfer in 8 m 2MPZ, PCO2,g = 1.1 × P*CO2, k0l = 3.56 × 10−5 m/s, kg = 0.02 m/s.

5. CONCLUSIONS The Wetted Wall Column was modeled in Aspen Plus as a Radfrac column. Activity-based termolecular kinetics was used to describe the kinetic reactions between CO2 and aqueous 2MPZ. The reaction rate constants of related reactions were correlated with the Bro̷ nsted theory. 86% of the measured CO2 fluxes at 40−100 °C and variable CO2 loading were represented by the model within ±20% by the regression of two carbamate formation rate constants, one bicarbonate formation rate constant, and the temperature dependence of the diffusion coefficient of all the non-CO2 species. The regressed kinetic rate constant for carbamate formation between 2MPZ and CO2 catalyzed by 2MPZ is 1.94 × 1010 kmol/m3·s. The diffusion activation energy for the nonCO2 species in 8 m 2MPZ at the rich loading is approximately 28 kJ/mol. The calculated liquid film mass transfer coefficients at 40−100 °C agree well with the measured values except at very lean loading. The pseudo-first-order approximation is valid near 40 °C. k′g varies with the rate constant for carbamate formation to the 0.5 power. Dependence of k′g on the bicarbonate kinetics is negligible over the CO2 loading range in this study. The dependence on liquid film transfer coefficient increases from the lean loading to the rich loading because of the depletion of free amine. The liquid film mass transfer coefficient is most sensitive to the reaction rate of carbamate formation at lean loading at 40 °C, with the overall power close to 0.5, whereas the dependence on bicarbonate formation is only significant at rich CO2 loading. The overall dependence of k′g on carbamate formation rate decreases with CO2 loading. The dependence on diffusivity of CO2 decreases with loading while the diffusivity of all other species increasingly affects the liquid mass transfer coefficient as loading increases. The sum of the powers of DCO2 and DAm is approximately constant at 0.5 throughout the lean and rich loading and approximately equal to the sum of the powers for the dependence of kg′ on k2MPZ−2MPZ and k2MPZCOO−−2MPZ at very lean loading. The dependence of kg′on physical liquid film mass transfer coefficient, k0l is weak at lean loading but gets stronger at rich loading. At 100 °C CO2 mass transfer is represented by instantaneous reactions with diffusion of reactants and products. The dependence of kg′ on carbamate formation rate constant is

Figure 6. Effect of varying k0l on the kg′ at varied temperature, α = 0.356 CO2 mol/mol alkalinity, P*CO2 = 5000 Pa at 40 °C, PCO2,g = 1.1 × PCO * 2.

is normally also the case in a real absorber, where a pinch is sometimes approached. The value of kl0 for the WWC experiments for 2MPZ varies between 10−5 to 10−4 m/s. For an absorber or a stripper with structured packing, k0l is typically in the range from 1 × 10−5 to 5 × 10−5 m/s. In this region, kg′ is not a strong function of k0l at 40 °C and the PFO assumption applies. However, it is more significantly affected by k0l at 60 and 80 °C. The PFO region shifts to higher k0l and becomes narrower as temperature increases. At values of k0l in the WWC or typical contactors, k′g is not a function of k0l and the effective Hatta number or enhancement factor is on the order of 100 to 1000. Only at very high k0l values does the physical absorption of CO2 become important. The ratio of the overall mass transfer coefficient to the gas film mass transfer coefficient represents the contribution of gas film resistance to the overall resistance. This ratio, as a function of CO2 loading, is shown in Figure 7. The values of k0l and kg used in the analysis are representative of industrial conditions. Again, a small driving force is used. The ratio is not available for 100 °C at rich loading due to convergence issues. The gas film resistance is significant for 40 °C at lean loading because of the abundant free amine and fast chemical reactions in the liquid film. As amine concentration decreases at high loading, the percent gas film resistance drops to 10−25% between the lean and the rich loading. At 100 °C, the gas film resistance is even less important. 4246



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much less and diminishes at rich loading. DAm and k0l dominate the mass transfer rate. The region where kg′ is independent of k0l shifts to higher value of k0l and narrows down with increased temperature. Over the operating CO2 loading range, the contribution of the gas film resistance to the overall mass transfer resistance is less than 25% and decreases with CO2 loading and temperature.

■

T u v V Vm W x

temperature velocity volume flow rate volume molar volume circumference mol fraction

Greek Symbols

AUTHOR INFORMATION

α κ δ ρ η γ

Corresponding Author

*Phone: 1-512-471-7230 Fax: 1-512-471-7060. E-mail: gtr@ che.utexas.edu. Notes

The authors declare the following competing financial interest(s): One author of this publication consults for Southern Company and for Neumann Systems Group on the development of amine scrubbing technology. The terms of this arrangement have been reviewed and approved by the University of Texas at Austin in accordance with its policy on objectivity in research.

■

CO2 loading binary mass transfer coefficient film thickness density viscosity activity coefficient

REFERENCES

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ACKNOWLEDGMENTS The authors acknowledge the financial support of the Luminant Carbon Management Program. NOMENCLATURE quasi-activation energy of diffusion activity Molar concentration diameter diffusion coefficient Binary diffusion coefficient of all non-CO2 components in any other component DCO2 Binary diffusion coefficient of CO2 with respect to any other component E enhancement factor or activation energy ED diffusion activation energy g gravity h height Ha Hatta number Hi,H2O Henry’s constant of component i in water k2 second-order reaction rate constant k2,b rate constant for bicarbonate formation catalyzed by base b Kg overall mass transfer coefficient kg gas film mass transfer coefficient k′g liquid film mass transfer coefficient k0l physical liquid film mass transfer coefficient kf forward reaction rate constant kr reverse reaction rate constant kAm−b rate constant for termolecular reaction (Am + CO2 + base) Keq activity-based equilibrium constant N flux NCO2 CO2 flux P pressure PCO * 2 equilibrium CO2 partial pressure of loaded amine solution PCO2,g CO2 partial pressure in gas Q liquid flow rate R gas constant rCO2 reaction rate of CO2 A a c d D DAm

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