Water - Industrial

Article pubs.acs.org/IECR

Thermodynamics of CO2/2-Methylpiperazine/Water Xi Chen and Gary T. Rochelle* McKetta Department of Chemical Engineering, The University of Texas at Austin, 200 E. Dean Keeton St., C0400, Austin, Texas 78712, United States ABSTRACT: Aqueous 2-methylpiperazine (2MPZ) is an attractive solvent for CO2 capture from coal-fired power plants. Quantitative NMR spectroscopy was used to speciate at 40 °C 8 m 2MPZ loaded with CO2. 13C NMR spectra were acquired from 0 to 0.37 mol CO2/mol alkalinity (or per amino group). 13CO2 was used for solution preparation to amplify signals from carbamate and bicarbonate. The NMR spectra show that the unhindered 2MPZ monocarbamate is the dominant carbamate species and accounts for more than 75% of the total dissolved CO2; bicarbonate and 2MPZ dicarbamate each only account for up to 10% of the total absorbed CO2. Hindered 2MPZ was not detected. This speciation and CO2 solubility were represented by an electrolyte nonrandom two liquid thermodynamic model developed through data regression. At a CO2 loading giving 1.5 kPa CO2 partial pressure at 40 °C the heat of CO2 absorption varies from 50 to 75 kJ/mol at 40−140 °C. At 40 °C the equilibrium CO2 partial pressure was 0.5 kPa at 0.265 mol CO2/mol alkalinity and 5 kPa at 0.356 mol CO2/mol alkalinity. These values give an intrinsic CO2 operating capacity of 0.81 mol/kg (2MPZ + water) compared to 0.47 for 7 m MEA and 0.79 for 8 m piperazine. amine (MDEA)11 and calculated equilibrium constants for carbamate formation reactions. Cullinane determined the equilibrium speciation in K2CO3/PZ by 1H NMR.12 Hilliard used 13CO2 for preparation of amine solutions and conducted extensive quantitative speciation of PZ, MEA, and potassiumPZ solvents.13 The thermodynamic properties of a variety of aqueous amine solutions as CO2 absorbents have been successfully modeled with the electrolyte non-random two liquid (e-NRTL) model.14−17,11,12,18,19 Hilliard prepared a comprehensive eNRTL model in Aspen Plus of MEA/PZ/K 2 CO 3 /CO 2 regressing data for CO2 solubility, amine volatility, heat capacity, heat of CO2 absorption, and NMR speciation.13 Frailie et al.20 developed PZ and PZ/MDEA models starting from Hilliard’s model13 to better fit the high temperature VLE and heat capacity data. The present study intends to quantify speciation in concentrated aqueous 2MPZ. The liquid composition data from quantitative NMR spectroscopy were used with CO2 solubility data in the development of a rigorous e-NRTL model for 2MPZ in Aspen Plus. The obtained thermodynamic model was used for calculation of liquid composition, activity coefficient, reaction stoichiometry, and heat of CO2 absorption at variable loading and temperature.

1. INTRODUCTION Acid gas treating with alkanolamine solvents is one of the most important technologies for postcombustion CO2 capture due to the maturity and extensive practical operating experience in the oil and petrochemical industry. However, with traditional amine solvents such as monoethanolamine (MEA), the energy penalty for solvent regeneration and CO2 compression is significant. Other issues such as solvent degradation, corrosiveness, and foaming also lead to considerable operating cost. To solve these problems, many efforts have been focused on development of advanced amine solvents.1−4 Piperazine (PZ) is a better solvent than MEA for CO2 removal from coal-fired power plants in the sense that PZ has faster CO2 absorption rate, greater cyclic CO2 capacity, and greater thermal and oxidative stability.5 In an effort to screen solvents, Chen et al. characterized CO2 solubility and absorption/desorption rates for PZ derivatives or blends in a wetted wall column.6 They showed that 2-methylpiperazine (2MPZ) and a blend of 2MPZ and PZ provide properties similar to PZ with fewer constraints from solid solubility. To predict the performance of an amine solvent, valid thermodynamic and kinetic models need to be developed and incorporated into process simulation tools. Of the various data necessary for model development, speciation in a solvent is crucial since it provides important information about absorption mechanism as well as chemical equilibria. Nuclear magnetic resonance (NMR) has been used to speciate amine−H2O−CO2 systems by a number of researchers. NMR validates and refines VLE models developed solely from phase equilibrium data.7 Suda et al. used 1H and 13C NMR spectra to quantify dissolved species during the course of CO2 absorption into primary, secondary, tertiary, and hindered amines.8 Ermatchkov and co-workers systematically studied speciation in PZ solutions at varied temperature and CO2 loading and determined the equilibrium constants for different reactions based on quantitative 1H NMR data.9 Bishnoi and Rochelle quantified species in PZ10 and PZ/N-methyldiethanol© 2013 American Chemical Society

2. EXPERIMENTAL SECTION 2.1. Material. 2-Methylpiperazine (99%, AK Scientific Inc.), 1,4-Dioxane (99.5%, Acros Organics Inc.), 13C labeled carbon dioxide (13CO2, 99%, Cambridge Isotope Laboratories Inc.), and deuterium oxide (D2O, 99.9%, Cambridge Isotope Laboratories Inc.) were all used as received without further purification. Deionized distilled (DDI) water generated by Received: Revised: Accepted: Published: 4229

September 3, 2012 February 26, 2013 February 26, 2013 February 26, 2013 dx.doi.org/10.1021/ie3023725 | Ind. Eng. Chem. Res. 2013, 52, 4229−4238

Industrial & Engineering Chemistry Research

Article

3. MODEL DESCRIPTION 3.1. Chemical Reactions. Figure 1 shows the reactions and seven 2MPZ compounds associated with 2MPZ−H2O−CO2.

Direct-Q 5 ultrapure water systems (Millipore) was used in this study. 2.2. Preparation of NMR Samples. Amine was slowly added to DDI water and then heated to 60 °C to make a homogeneous unloaded concentrated aqueous solution. About 10 mL of the solution were placed in a specially designed CO2 loader, a slim and long bubbling glass column. 13CO2 was introduced into the solution with a glass frit submerged well below the solution. The flow rate is precisely controlled at 0− 10 mL/min by a mass flow controller to make sure that the flow is slow enough for maximum absorption. Samples at intermediate CO2 loading were prepared by mixing unloaded solution with a highly loaded one. The CO2 loading (α, mol CO2/mol alkalinity) was determined both gravimetrically and by NMR. A small amount of each amine solution (∼1.5 mL) prepared from the procedure described above was transferred to an NMR sample tube (5.0 mm o.d. × 0.77 mm i.d. × 7 in. length, 300 mHz, WILMAD Labglass). Approximately 10 wt % D2O was added to suppress the interference of signals from water, and a known amount of 1,4-dioxane (∼1 wt %) was added as an internal standard. 2.3. Acquisition of NMR Spectra. All the sample tubes were sealed and thermostated at 40 °C before being transferred to an NMR spectrometer (VARIAN INOVA 500, 500 MHz). 13 C NMR spectra were acquired at 40 °C. A relaxation delay of 5 times relaxation time (T1) was applied for acquisitions of quantitative 13C NMR spectra. 2.4. NMR Data Analysis. To quantitatively analyze NMR data, 1,4-dioxane was used as the internal standard because it has a symmetric cyclic molecular structure similar to that of PZ. A sensitivity analysis conducted by Hilliard13 shows that the minimal amount of 1,4-dioxane needed for accurate determination of liquid composition is 1−5 wt %. In this work, the method employed by Hilliard13 was also followed to quantify different species based on the known amount of the standard. In this method, a universal ratio is determined:

Rb =

Figure 1. The species and reaction scheme in 2MPZ−CO2−H2O.

The two amino groups on 2MPZ are not equivalent due to the substitution of the methyl group, which introduces moderate hindrance to the adjacent amino group. Formation of the hindered monocarbamate (−OOC2MPZ) closest to the methyl group is expected to be less favorable than that of the unhindered monocarbamate (2MPZCOO−). However, the electron-donating methyl group is expected to stabilize the positive charge on the neighboring amino group, so the protonation is projected to occur first on the hindered amino group. The 2MPZ monocarbamates can either be protonated and form zwitterions (H2MPZCOO and OOC2MPZH) or react with one more CO2 to form dicarbamate [2MPZ(COO−)2]. The second pKa value of 2MPZ was reported to be around 5 at 25−50 °C,21 and the normal pH value in CO2-loaded amine solution at the rich loading is typically well above 8.22 Therefore, the amount of diprotonated 2MPZ is extremely small in loaded solutions and it is excluded from consideration in this work. To differentiate the carbon nuclei with different electronic environment, they are numbered for different species present in 2MPZ−H2O−CO2, as shown in Table 1. Due to the rapid exchange rate of protons, a protonated species and the unprotonated counterpart cannot be differentiated by the NMR spectroscopy used in this study. Therefore, it is the sum of them that was quantified from the NMR spectra. In addition to the species listed in Table 1, free CO2 is also expected to be present in the liquid. However, the amount of free CO2 in the amine solutions is well below the detection limit of the NMR spectroscopy and will not be accounted for. 3.2. Chemical Equilibrium. The following chemical equilibria are included in the model:

φref Cref A ref

(1)

where Rb is the number of moles of 1,4-dioxane/kg H2O per unit area, φref is the number of active protons or carbons in 1,4dioxane, Cref is the experimental 1,4-dioxane molality based on the batch solution, and Aref is the experimental integrated area for the 1,4-dioxane reference peak. With the Rb calculated, the molality of other species in the same sample can be determined by the following equation: Ci =

Ai R b φi

(2)

where Ai and φi are the experimental integrated peak area for species i and the number of active protons or carbons in species i, respectively. The CO2 loading in the solution can also be determined by dividing the sum of all the CO2-related species concentration with the sum of all the amine-related species concentration. The values of CO2 loading determined from the NMR method, which are reported in the present work, are found to agree well with those determined by the gravimetric method with a deviation less than 5%. 4230

H 2O ↔ H+ + OH−

(3)

CO2 + H 2O ↔ HCO3− + H+

(4)

HCO3− ↔ CO32 − + H+

(5)

2MPZ + HCO3− ↔ 2MPZCOO− + H 2O

(6)

dx.doi.org/10.1021/ie3023725 | Ind. Eng. Chem. Res. 2013, 52, 4229−4238


Article

Table 1. Molecular Structure of the Compounds in CO2Loaded 2MPZ Aqueous Solutions

−ln Kj = =

ΔGj0 RT ΔG0,0 j − ΔH0,0 j RT0 −

∫T

T

0

ΔG00,j,

ΔH0,0 j

1 + + RT T

∫T

T

0

ΔC p0, j R

dT

ΔC p0, j dT R T

ΔH00,j,

(15)

ΔC0p,j

where and are standard free energy change, standard enthalpy change, and heat capacity change, respectively, at reference temperature for reaction j. 3.3. Vapor Phase Model. The Redlich−Kwong−Soave (RKS) equation of state 23 is used in this work for representation of vapor phase. 3.4. e-NRTL Model. The activity coefficients and liquid thermodynamic properties were represented by the e-NRTL model24,25 in Aspen Plus. The temperature dependence of the e-NRTL parameters is expressed in the following relationships: molecule−molecule binary parameters τmm ′ = A mm ′ + 2MPZCOO− + HCO3− ↔ 2MPZ(COO−)2 + H 2O

(7)

2MPZH+ ↔ 2MPZ + H+

(8) −

H2MPZCOO ↔ 2MPZCOO + H

+

(10)

H2MPZCOO ↔ HOOC2MPZ

(11)

τca,m = Cca,m +

∏ i

=

i

τm,ca = Cm,ca +

as

xw → 1

as

xi → 0

T

⎡ (T − T ) ⎛ T ⎞⎤ + Em,ca⎢ ref + ln⎜ ⎟⎥ ⎢⎣ T ⎝ Tref ⎠⎥⎦

where Tref = 298.15K. The default values for A, B, F, G, D, and E are zero. The default values for Cca,m and Cm,ca are set at −8 and 15, respectively, in this work, if not specified otherwise. If the molecule is water, then the default values for Cca,m and Cm,ca are −4 and 8, respectively. The interaction between ion pair− ion pair is neglected (τc′a′,ca = 0). For molecule−molecule interaction, the nonrandomness parameter α = 0.3; for molecule−ion pair interaction or ion pair−ion pair interaction, α = 0.2. 3.5. Data Regression and Parameter Settings. The data regression system (DRS) incorporated into Aspen Plus was used in this study for regression of relevant parameters based on the existing experimental data sets. Standard-state property parameters and binary interaction parameters were determined in Aspen Plus with the Britt−Luecke algorithm to minimize the maximum likelihood objective function, in which errors in all measured variables are taken into account. The thermodynamic model built for 2MPZ in this work is based on the model for PZ (“Fawkes” model) developed by Frailie et al.20 As there are no data available for 2MPZ in the Aspen Plus databank, 2MPZ was added as a new component by providing the molecular structure and boiling point. The standard free energy of formation and the standard enthalpy of formation for 2MPZ share the same values as PZ, since it is the difference of the state properties of reactants and products that matters. All other 2MPZ-related species are then referenced to

(12)

(13)

For other molecular and ionic species, the reference state is infinite dilution in water at the temperature and pressure of the mixture:

γi* → 1

Dm,ca

(18)

where Kj is the equilibrium constant for reaction j, ai is the activity of component i, vij is the stoichiometric coefficient of component i in reaction j, and xi and γi is the mole fraction and the activity coefficient of component i, respectively. The symmetric convention for definition of activity coefficient is applied for water as a solvent: γw → 1

T

⎡ (T − T ) ⎛ T ⎞⎤ + Eca,m⎢ ref + ln⎜ ⎟⎥ ⎢⎣ T ⎝ Tref ⎠⎥⎦

molecule−electrolyte pair parameters

vij

∏ (xiγi)

Dca,m

(17)

The last two reactions account for the mutual transformation of the hindered and unhindered species. The equilibrium constants are activity-based: Kj =

(16)

electrolyte−molecule pair parameters

(9)

2MPZCOO− ↔ −OOC2MPZ

v ai ij

Bmm ′ + Fmm ′ ln(T ) + Gmm ′T T

(14)

2MPZ is modeled as a Henry’s component like CO2. H2MPZCOO and OOC2MPZH are both zwitterion species, so they are treated as nonvolatile Henry’s components in the liquid phase. The chemical equilibrium constant is determined from the standard free energy of formation, heat of formation, and heat capacity of reactants and products: 4231



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The Fawkes model for PZ also fits the measured γCO2 in 8 m PZ at multiple temperatures. To reasonably represent γCO2 in 8 m 2MPZ, it is assumed that γCO2 has the same values as in 8 m PZ, and the binary interaction parameters for CO2 with other molecular and ionic species in aqueous 2MPZ are taken from the Fawkes model for PZ.

2MPZ. The values for the reference state properties are given in Table 2. Table 2. Parameters for the Reference State Properties Used in This Work (unit kJ/mol)a component i

ΔfGigi b

ΔfHigi c

2MPZ 2MPZH+ H2O CO2 HCO3− CO32‑ OH−

170.1139

16.41096

−228.743 −394.648

−241.976 −393.773

d ΔfG∞,aq i

e ΔfH∞,aq i

826.0

−107.0

−586.770 −527.810 −157.244

−587.333 −528.336 −157.403

4. RESULTS AND DISCUSSION 4.1. Quantitative 13C NMR. 4.1.1. NMR Spectra. The 13C NMR spectra for 8 m 2MPZ at varied CO2 loading and 40 °C in the upfield are shown in Figure 2. The peaks at δ = 66.5 ppm

a

All but those for 2MPZ and 2MPZH+ are based on the Aspen Databank. bΔfGigi : ideal gas free energy of formation at 298.15K. c ΔfHigi : ideal gas enthalpy of formation at 298.15K. dΔfG∞,aq : aqueous i phase free energy of formation at infinite dilution and 298.15K. e ΔfH∞,aq : aqueous phase heat of formation at infinite dilution and i 298.15K.

is related to ΔfGigi by For the Henry’s components, ΔfG∞,aq i ⎛ Hi ,H O ⎞ Δf Gi∞ ,aq = Δf Giig + RT ln⎜ ref2 ⎟ ⎝ P ⎠

(19)

where Hi,H2O is the Henry’s constant of solute i in water and Pref is the reference pressure of 1 bar. ΔfH∞,aq is correlated to ΔfHigi i with the following equation: Δf Hi∞ ,aq = Δf Hiig − RT 2

Figure 2. 13C NMR spectra (upfield, δ = 15−70 ppm) for 8 m 2MPZ at 40 °C and varied loading (α = mol CO2/mol alkalinity).

∂(ln Hi ,H2O)

are from 1,4-dioxane. As CO2 was added to the amine solution, additional peaks emerge near the original peaks for 2MPZ. The intensity of the new peaks also increases with CO2 loading, whereas the peaks for C1 through C5 shrink. The position of the peaks also shifted upfield slightly with CO2 loading. Since the most probable products of 2MPZ with CO2 are the unhindered carbamate or its protonated form, the new peaks in

(20)

∂T

The heat capacity parameters for the 2MPZ−CO2−H2O system are not regressed in this work and are assumed to have the same values as the similar species in the Fawkes PZ model. The values for heat capacity model parameters used in this work are summarized in Table 3.

Table 3. Coefficients for Ideal Gas Heat Capacity (Cigp for molecules, kJ/(mol·k)) and Aqueous Infinite Dilution Heat Capacity (C∞,aq for ions, kJ/(mol·k)) p Cpig = C0 + C1T + C2T 2 + C3T 3 + C4T 4 + C5T 5 C p∞ ,aq = C0 + C1T + C2T 2 +

C3 C C + 42 + 5 T T T parametersa

a

compd

C0

C1

C2

C3

C4

C5

2MPZ 2MPZH+ 2MPZCOO− − OOC2MPZ H2MPZCOO OOC2MPZH 2MPZ(COO−)2 CO2 H2O OH− HCO3− CO32‑

−3.60 × 10−2 2.21 × 10−1 1.07 × 10−1 1.07 × 10−1 −2.55 × 10−1 −2.55 × 10−1 −1.41 × 100 1.98 × 10−2 3.37 × 10−2 −1.49 × 10−1 2.11 × 10−1 1.33 × 100

7.25 × 10−4 0 6.04 × 10−4 6.04 × 10−4 0 0 4.07 × 10−3 7.34 × 10−5 −7.02 × 10−6 0 −8.82 × 10−4 −5.56 × 10−3

0 0 0 0 0 0 0 −5.60 × 10−8 2.73 × 10−8 0 8.75 × 10−07 5.19 × 10−06

0 0 0 0 0 0 0 1.72 × 10−11 −1.67 × 10−11 0 −1.88 × 101 −1.19 × 102

0 0 0 0 0 0 0 0 4.30 × 10−15 0 0 0

0 0 0 0 0 0 0 0 −4.17 × 10−19 0 0 0

Values for 2MPZ-related species are from the Fawkes model20 and the others are from the Aspen Plus databank. 4232



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the spectra are assigned to 2MPZCOO−/H2MPZCOO. The peaks for the carbamate are separated more from the peaks for 2MPZ as loading increases. At α = 0.367, it can be clearly seen that there appears one new peak for each original peak. However, there are no separate 13C peaks observed for − OOC2MPZ/OOC2MPZH or 2MPZ(COO−)2, presumably because these species are below the detection limit, or they may be merged into other large peaks. Most of the enriched 13CO2 is converted to carboxyl groups after being absorbed, so the downfield (166 < δ < 160 ppm) spectra (Figure 3) is where all the CO2-related reaction

Figure 4. Expanded 13C NMR spectra (downfield, δ = 160−166 ppm) for 8 m 2MPZ at 40 °C and varied loading.

4.1.2. Species Quantification. Theoretically, the peaks from downfield (∼160 ppm) and from the upfield (∼40−60 ppm) can both be used for quantification of H2MPZCOO/ 2MPZCOO−. However, the peak for the standard, 1,4-dioxane, shows up only in the upfield, and its height and area are only comparable to the peaks in the upfield for H2MPZCOO/ 2MPZCOO−. The peaks in the downfield are from enriched 13 C, so their peak height is much greater than those in the upfield. It is suggested that the ratio of the areas of the peaks with similar size and position yields better accuracy in quantification;29 therefore, the upfield peaks should be used to determine the amount of the unhindered carbamate species. Since the peaks for HCO3−/CO32‑ and 2MPZ(COO−)2 cannot be observed in the upfield, the amount of them has to be determined through the ratio of their peak areas in the downfield to the downfield peak area of H2MPZCOO/ 2MPZCOO−. The amount of 2MPZCOO−/H2MPZCOO determined from C6 through C10 and C21 respectively render a ratio that correlates the amounts determined from natural 13C atoms and enriched 13C atoms. This number is in turn used to determine the amount of the other species observed in the downfield. The concentration of different species was thus determined for 8 m 2MPZ over the loading range of 0−0.367 with the application of eqs 1 and 2. For any species that can be represented by multiple carbon peaks, the average value of the peak areas was used. The distribution of the total absorbed CO2 in different reaction products as a function of CO2 loading is shown in Figure 5. Although 2MPZCOO−/H2MPZCOO is the major sink for CO2 at lean loading, the amount of dissolved CO2 in the form of 2MPZCOO−/H2MPZCOO decreases significantly with increased CO2 loading. The share of HCO3−/CO32‑ and 2MPZ(COO−)2 steadily increases with loading. At the rich loading of 0.367, 12% and 9% of the total absorbed CO2 is converted to HCO3−/CO32‑ and 2MPZ(COO−)2, respectively. 4.2. Thermodynamic Model Results. 4.2.1. Binary System 2MPZ−H2O. Volatility of 2MPZ in Water. Since 2MPZ is modeled as a Henry’s component in this work, Henry’s law is applied to calculate the vapor pressure of 2MPZ. The vapor pressure of 2MPZ above 1 m 2MPZ aqueous solution from 40 to 70 °C measured by Nguyen30 was used for

Figure 3. 13C NMR spectra (downfield, δ = 160−166 ppm) for 8 m 2MPZ at 40 °C and varied loading.

products should be seen. The largest peak is assigned to 2MPZCOO−/H2MPZCOO, which shifts slightly upfield as CO2 loading increases. The shift is attributed to the change in the ratio of the monocarbamate and its protonated form, as the pH of the loaded solution drops with CO2 loading. The second largest peak is deemed to come from HCO3−/CO32‑, the chemical shift of which changes significantly with loading. Previous NMR studies on two hindered amines, 2-amino-2methylpropanol26,22 and 2-piperidine ethanol,27 have shown that there is no or very little carbamate found in CO2 loaded aqueous solutions. The speciation study on another hindered amine, 2-amino-2-hydroxymethyl-1,3-propanediol,28 indicated that there is much less carbamate formed than bicarbonate/ carbonate at relatively high CO2 loading and 25 °C. These studies suggest that hindered carbamate is thermodynamically unstable and much less likely to be formed in a loaded solution than bicarbonate/carbonate. If there was any hindered 2MPZ monocarbamate formed, it should exist in a much smaller amount than HCO3−/CO32‑. The downfield spectra are expanded in Figure 4. The two peaks of similar size correspond to the two carbonyl groups on 2MPZ(COO−)2. The dicarbamate cannot be protonated, so the positions of the two peaks remain almost constant at varied loading. The four tiny peaks on the far left may be the carbamate of impurity amines in the 2MPZ samples, since their peak position and size remains essentially unchanged with loading. There are no separate peaks found for the hindered 2MPZ monocarbamate in the spectra, even at the highest loading. The fact that the dicarbamate is observed but the monocarbamate is not indicates that the formation of carbamate on the unhindered amino group increases the stability of the other carbamate on the hindered amino group. 4233



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Figure 6. 2MPZ vapor pressure predicted by the model compared with experimental data for 1 m 2MPZ, 2 m PZ, and 8 m PZ with no CO2 loading: filled points, measurements for 1 m 2MPZ; open points, measurements for 2 and 8 m PZ;30 solid lines, model prediction from this work.

Figure 5. The distribution of CO2 in different reaction products as a function of loading in 8 m 2MPZ at 40 °C.

data regression. The first two coefficients in the Henry’s constant model are needed to fit the data. The regression results are given in Table 4 along with the parameters in the Henry’s constant model for CO 2 and H2MPZCOO. H2MPZCOO is a zwitterion and thus not volatile, so an extremely small Henry’s constant is assigned to H2MPZCOO. The calculated vapor pressure of 2MPZ in unloaded 2MPZ aqueous solutions is compared to the experimental data in Figure 6. The calculated values from the model agree well with the experimental data for 1 m 2MPZ. Since there are no data available for 2 and 8 m 2MPZ, the prediction for 2MPZ at these two concentrations are compared to 2 and 8 m PZ, respectively. Because of the additional methyl group, 2MPZ is expected to be less hydrophilic and more volatile than PZ at the same concentration, which is what is predicted by the model above 50 °C. pKa Values for Dissociation of 2MPZH+. ΔfG∞,aq and i + ΔfH∞,aq for 2MPZH were manually adjusted to fit the pK data i a reported by Khalili and co-workers.21 Figure 7 shows that experimental pKa data from 25 to 50 °C are represented well by the calculated correlation from the model. 4.2.2. Ternary System 2MPZ−CO2−H2O. The equilibrium partial pressure of CO2 for 8 m 2MPZ has been measured with a wetted wall column at temperatures up to 100 °C,6 and the total pressure was measured from 100 to 160 °C.30 These two sets of data along with the 13C NMR speciation data at 40 °C were used for data regression. On the basis of the NMR speciation study, there is no hindered 2MPZ monocarbamate (−OOC2MPZ and OOC2MPZH) present in the system; therefore, reactions 10 and 11 are excluded from consideration in the chemical equilibria. Table 5 summarizes the regression results for the selected parameters. A total of eight parameters were determined, which include reference state properties for 2MPZ carbamate species and binary interaction parameters. Because 2MPZ(COO−)2 is never a significant species, its parameters have relatively larger uncertainty. CO2 Solubility. As shown in Figure 8, the dependence of CO2 partial pressure (P*CO2) on loading and temperature is

Figure 7. pKa of dissociation of 2MPZH+ as a function of temperature: solid line, model prediction; points, Khalili et al.21 data.

satisfactorily represented by the model. The lean and rich CO2 loading, which correspond to P*CO2 = 500 and 5000 Pa at 40 °C, are 0.265 and 0.356 mol CO2/mol alkalinity, respectively, giving an intrinsic CO2 operating capacity of 0.81 mol/kg (2MPZ + water). NMR and Speciation. The distribution of the total absorbed CO2 in different CO2-related species as a function of loading is shown in Figure 9. The prediction of the model is in good agreement with the experimental NMR measurements, except that the amount of bicarbonate at loading above 0.3 is overpredicted by the model. The fraction of CO2 in the form of monocarbamate decreases from about 95% at very lean loading to 50−60% at rich loading. The initial drop in the contribution of HCO3−/CO32‑ at the lean end is due to the slight increase in the contribution of monocarbamate, which replaces CO32‑ as the major CO2 sink at very lean loading. Due to the depletion of free amine, the bicarbonate production keeps increasing with CO2 loading and accounts for about 40% of the total at the loading of 0.5 mol CO2/mol alkalinity. The share of 2MPZ dicarbamate as a CO2 sink increases with loading until the CO2

Table 4. Coefficients for Henry’s Constant in H2O: ln H = a + b/T + c ln T + dT (unit Pa) solute

a

b

c

d

source

2MPZ CO2 H2MPZCOO

33.1 ± 0.6 170.7 −10

−9180 ± 205 −8478 0

0 −21.96 0

0 5.78 × 10−3 0

this work Aspen databank this work

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Table 5. Parameters and Results for the Simultaneous Regression of the CO2 Solubility and NMR Data for 8 m 2MPZ

a

no.

parameter

1 2 3 4 5 6 7 8

ΔfG∞,aq i ΔfH∞,aq i ΔfG∞,aq i ΔfH∞,aq i ΔfGigi ΔfHigi Cca,ma Cca,ma

component i

component j

2MPZCOO−

−

2MPZ(COO−)2

−

H2MPZCOO

−

(2MPZH+, 2MPZCOO−) (2MPZH+, HCO3−)

H2MPZCOO H2MPZCOO

value (kJ/mol)

SD(kJ/mol)

−219.5 −500.7 −564.9 −928.2 −229.1 −564.4 −10.42 −11.46

3.4 30.3 40.0 808.2 15.2 23.1 5.75 4.90

See eq 17.

Figure 10. Calculated speciation in 8 m 2MPZ at 40 °C.

Figure 8. CO2 solubility in 8 m 2MPZ from 40 to 160 °C: solid line, model prediction; diamond points, measurements in the WWC;6 triangle points, Xu and Rochelle31 data.

to H2MPZCOO and the rest is converted to 2MPZH+. There is little 2MPZ(COO−)2 at lean loading, and at α = 0.33 it reaches its maximum, which is still more than 1 order of magnitude lower than 2MPZH+ and H2MPZCOO concentrations. HCO3− increases with CO2 loading and becomes a significant species at loading greater than 0.3. The concentration of HCO3− is slightly more than 3.5 m at α = 0.5. CO32‑ and free CO2 are not significant species in the solution across the entire CO2 loading range. The temperature dependence of species concentration at the rich condition from 40 to 160 °C is presented in Figure 11. The amount of 2MPZH+ and 2MPZCOO− is found to be relatively stable despite the change in temperature. Free 2MPZ, HCO32‑, and CO2 all increase with temperature while H2MPZCOO, 2MPZ(COO−)2, and CO32‑ are less stable at greater temper-

Figure 9. Distribution of CO2 in difference reaction products at 40 °C: points, quantitative 13C NMR data; lines, model prediction in this work.

loading is above 0.33, presumably because the dicarbamate is not very stable and is converted to bicarbonate at rich loading. Figure 10 shows the detailed calculated speciation for 8 m 2MPZ at 40 °C. Free 2MPZ decreases drastically with CO2 loading and is almost completely depleted at α = 0.4 mol/mol alkalinity. 2MPZH+ and 2MPZCOO− are the two major products in the lean loading range. As CO2 loading increases, the amount of H2MPZCOO is more and more significant. The increase in H2MPZCOO is partially attributed to the protonation of 2MPZCOO− as 2MPZCOO− starts to decrease as loading is above 0.27. At α = 0.5, there is no 2MPZCOO− left and the concentration of H2MPZCOO is close to 5 m, which indicates that about 60% of the total 2MPZ is converted

Figure 11. Temperature dependence of speciation for 8 m 2MPZ at α = 0.37 mol CO2/mol alkalinity, P*CO2 = 5000 Pa at 40 °C. 4235



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ature. An increase of more than 2 orders of magnitude in free CO2 is also observed, which indicates a stronger tendency for CO2 to leave the solution. Activity Coefficient. The calculated activity coefficients for 8 m 2MPZ at 40 °C are shown in Figure 12. The γ of 2MPZ and

Figure 13. Reaction stoichiometry for 8 m 2MPZ at 40 °C.

Heat of Absorption. The heat of absorption (ΔHabs) is an important thermodynamic property that represents the thermal effect as CO2 is absorbed into an amine solvent. It is also equivalent to the minimal heat duty required to reverse the CO2 absorption reactions and desorb CO2 from the solvent. Therefore, ΔHabs is critical for estimation of energy performance for an amine solvent. The calculation of ΔHabs is done by applying the Gibbs− Helmholtz equation to the CO2 fugacity (f *CO2) predicted from the e-NRTL model. A small change (0.1 K) in temperature (T) was introduced and the f *CO2 value is calculated, and the differential of ln f CO * 2 with respect to 1/T is approximated by Δ(ln f *CO2)/Δ(1/T). The heat absorption calculated in this way for 8 m 2MPZ at varied temperature is shown in Figure 14.

Figure 12. Predicted activity coefficients by the e-NRTL model for 8 m 2MPZ at 40 °C.

CO2 are both greater than 1 and increase slightly with loading. The values and the behavior with loading are consistent with the experimental results from the Henry’s constant measurement for PZ13 in CO2-loaded aqueous PZ and that for N2O in CO2-loaded concentrated aqueous monoethanolamine.32 The increase in CO2 loading leads to higher ionic strength of the solution, which salts out the molecular species. The γ of all the ionic species, on the other hand, is found to decrease with loading. The charged species are expected to have a favorable interaction with the more polar liquid phase and thus have lower activity coefficient. The dependence of γ of HCO3−, 2MPZH+, and 2MPZCOO− on CO2 loading is similar, presumably because that they are all singly charged species. The γ of CO32‑ is found to have exactly the same trend as shown for 2MPZ(COO−)2. H2MPZCOO has the smallest γ throughout most of the CO2 loading range. This might be attributed to the zwitterion nature of H2MZPCOO, which makes it favorably interact with both cations and anions in the solution. It is found that ΔfGigi of H2MPZCOO is strongly correlated with the binary interaction parameters for H2MPZCOO in the data regression, so the value of γ is also affected by the final estimates for ΔfGigi of H2MPZCOO. Reaction Stoichiometry. The reaction stoichiometry is calculated for 8 m 2MPZ at 40 °C and shown in Figure 13. The amount of reactant and product is normalized to the amount of CO2 absorbed. At very lean loading the dominant stoichiometry is given by the reaction 2(2MPZ) + CO2 (g) ↔ 2MPZH+ + 2MPZCOO−

Figure 14. Heat of absorption calculated by the e-NRTL model for 8 m 2MPZ.

As CO2 loading increases, bicarbonate formation, which comes with a low heat of reaction, gradually takes over the role of carbamate formation and starts to dominate CO2 absorption due to the depletion of free amine, as shown in the reaction stoichiometry plot (Figure 13). As a result, the apparent ΔHabs decreases dramatically with CO2 loading. However, ΔHabs is decreasingly dependent on CO2 loading as temperature increases. At loading less than 0.25, ΔHabs decreases slightly with temperature. This trend is reversed as loading is above 0.25 and ΔHabs is greater at higher temperature. An analysis of the speciation and the reaction stoichiometry at 140 °C at the rich loading shows that 2MPZ concentration and the stoichiometric number for 2MPZ are higher than at 40 °C;

(21)

At the nominal rich loading the dominant stoichiometry is given by the reaction: 2MPZCOO− + CO2 (g) + H 2O ↔ H2MPZCOO + HCO3−

(22)

These two reactions are both important at the nominal lean loading (P*CO2 = 500 Pa). The reaction stoichiometry from this study resembles that for 1.8 PZ at 25 °C given by Cullinane.12 4236



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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.

thus, bicarbonate reaction is less important. Between the lean and the rich loading, ΔHabs at the CO2 loading corresponding to 1.5 kPa equilibrium CO2 partial pressure varies between 70 and 75 kJ/mol at 120−140 °C, which is expected to be the range of stripper temperature.

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NOMENCLATURE a activity A NMR peak area C molal concentration Cigp ideal gas heat capacity C∞,aq aqueous infinite dilution heat capacity p f fugacity G0i standard free energy of formation of component i H0i standard enthalpy of formation of component i Hi,H2O Henry’s constant of component i in water Keq activity-based equilibrium constant P pressure Pi*,l liquid vapor pressure of component i PCO * 2 equilibrium CO2 partial pressure of loaded amine solution R gas constant T temperature x mol fraction

5. CONCLUSIONS The liquid composition of 8 m 2MPZ at varied loading was determined from quantitative 13C NMR spectra. Over the loading range of 0.10−0.37 mol CO2/mol alkalinity, the unhindered monocarbamate 2MPZCOO−/H2MPZCOO comprises more than 75% of the total CO2-related reaction products, while the amount of HCO3−/CO32‑ and 2MPZ(COO−)2 is relatively small but steadily increases with CO2 loading. The hindered monocarbamate species was not found in the spectra. A thermodynamic model was developed for 8 m 2MPZ in the framework of the e-NRTL model by sequential data regression. 2MPZ is modeled as a Henry’s component instead of a solvent. pKa and volatility of 2MPZ in water are well-represented by the model. The prediction for CO2 solubility and speciation is in good agreement with the experimental data. Speciation calculation from the model shows that 2MPZ is depleted at loading of 0.4 in 8 m 2MPZ at 40 °C. 2MPZCOO− reaches a maximum concentration around loading of 0.25 and diminishes at the rich end. About 40% of the original 2MPZ is in the form of 2MPZH+ and the remainder is H2MPZCOO at 0.5 loading. Bicarbonate is an important species starting at α = 0.3 and reaches 3.6 m at 0.5 loading, accounting for about 40% of the total dissolved CO2. The activity coefficients of 2MPZ and CO2 slightly increase with CO2 loading, while those of the ionic species decrease. H2MPZCOO has the lowest activity coefficient among all the species, which might be related to the property of a zwitterion ion but is more likely a consequence of the strong correlation of its standard Gibbs free energy of formation with the activity coefficient parameters. Calculated reaction stoichiometry shows that 2MPZ is the major reactant at lean loading and is consumed at 2:1 ratio when normalized to CO2, resulting in the formation of an equal mole of carbamate and protonated 2MPZ. This ratio drops as CO2 loading increases, and the bicarbonate formation buffered by 2MPZ and 2MPZCOO− becomes the major reaction above the lean loading. The heat of absorption for 8 m 2MPZ decreases with CO2 loading, but the dependence of it on CO2 loading decreases as temperature increases. ΔHabs is relatively constant at temperature from 120− to 140 °C, ranging from 70 to 75 kJ/mol in the operating CO2 loading range. The dependence of heat of absorption on temperature is reversed at loading of 0.25.

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GreekSymbols

α δ γ τij ΔHabs ϕi φ

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CO2 loading chemical shift in NMR, or film thickness, or dimensionless distance in liquid film activity coefficient binary interaction parameters between component i and j enthalpy of CO2 absorption fugacity coefficient of component i number of active nuclei on a molecule

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 1-512-471-7230. Fax: 1512-471-7060. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the Luminant Carbon Management Program for the financial support and Steve Sorey for the NMR measurements and valuable discussion. One author of 4237



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