The Equilibrium Solubility of Carbon Dioxide in Aqueous Solutions of

Mar 13, 2013 - Center for Applied Energy Research, University of Kentucky, ... Experimental carbon dioxide solubility data in aqueous 34.8 wt .... An ...
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The Equilibrium Solubility of Carbon Dioxide in Aqueous Solutions of Morpholine: Experimental Data and Thermodynamic Modeling Naser S. Matin, Joseph E. Remias, James K. Neathery, and Kunlei Liu* Center for Applied Energy Research, University of Kentucky, Lexington, Kentucky 40511, United States S Supporting Information *

ABSTRACT: Experimental carbon dioxide solubility data in aqueous 34.8 wt % (6.14 m) and 43.5 wt % (8.85 m) morpholine solutions at 40, 60, 100, and 120 °C are presented. The solubility measurements were done in a static vapor liquid equilibrium cell by measuring total pressure. Furthermore, selected data points were confirmed using gas phase GC methodology. The obtained combined solubility data was integrated with speciation data extracted using an established titration method, for thermodynamic modeling of the system. In regression of the model parameters, the liquid phase activity coefficients were determined using the electrolyte-NRTL equations. In addition to binary and pair interaction adjustable parameters included in the electrolyte-NRTL model, the temperature dependent carbamate stability and Henry’s law constants for CO2 in pure morpholine were also calculated. The determined CO2 equilibrium properties are in good agreement with most of the experimental data.

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INTRODUCTION

factor for selection but not necessarily the primary criterion (i.e., not necessarily highest pKa).4 The cyclic amines show a reverse correlation between carbamate bond strength (correlates to heat of absorption) and reaction rate.6 This property makes them potentially valuable for selection as CO2 capture solvents due to the relatively lower heat of regeneration while maintaining fast absorption rates (lower capital cost) in the absorber column. These amines, despite their fast reaction rates, show a low heat of absorption compared to MEA.7 Morpholine and other cyclic secondary amines also provide a thermally stable amine choice. In regard to thermal stability, morpholine has been reported as the most stable amine tested with the other cyclic secondary amines, including piperazine, having similar performance. The thermal degradation of morpholine was almost 3 times lower than piperazine using an accelerated test at 175 °C. It was also more than 2 orders of magnitude lower than the calculated value for MEA at the same temperature.8,9 There has also been one reported case of morpholine thermal degradation as a constituent of blended solvents.10 Blends of tertiary amines with piperazine or morpholine showed that the morpholine blends degraded less rapidly than piperazine blends. The thermal stability of morpholine (MOR) would allow stripper operating temperature above 160 °C, as estimated by a method reported by Freeman and Rochelle.11 This high temperature operation would allow more thermal compression in the stripper, which reduces compressor load and lowers CO2 capture costs. Considering the fast reaction rate, high thermal stability, and favorable enthalpy, morpholine could be considered a potential solvent for CO2 capture. Furthermore, MOR was noted as a

The increase in the atmospheric CO2 level is one of the most important issues related to climate change. This has caused a high level of concern and effort devoted to mitigating the emission of this gas to the atmosphere from fossil fuel combustion. Several different technologies have been developed and designed to reduce CO2 emissions associated with the production of electricity from coal-fired power stations.1 The most mature and applied technology for the capture and release of CO2 is cyclic chemical absorption/desorption using an aqueous amine solution. It is a temperature swing process where CO2 is absorbed at low temperature (e.g., 313 K) and released at high temperature (e.g., 393 K), with regenerated absorbent returned to the absorption process. While monoethanolamine (MEA), typically at 30% w/w, is one of the most commonly discussed, other amine solutions, so-called “advanced amines”, are also available. The development and selection of new solvents and consequently the design of improved capture processes is the primary target for much current research work related to CO2 capture. In order to choose an alkanolamine as a solvent in the CO2 absorption process, it has to meet various criteria, most importantly, high absorption capacity and rate, low solvent regeneration energy requirement, and high thermal stability. Puxty et al. discussed the structural dependency of alkanolamine CO2 absorption capacity and rate.2 They showed that a higher pKa value favors higher CO2 absorption rate and capacity. However, they also mentioned that the heterocyclic structure of certain secondary amines promotes reaction rates (toward carbamate formation). This is due to the lower sterics around the nitrogen heteroatom making the reaction rate faster. It has been shown that the cyclic nature of alkanolamines increases their reactivity compared to other noncyclic amines with similar pKa values.2−5 Therefore, depending on the alkanolamine structure, the basicity needs to be a considered © 2013 American Chemical Society

Received: Revised: Accepted: Published: 5221

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Figure 1. Schematic flow diagram for the VLE setup. CV, one-way check valve; V, needle valve; BV, ball valve (on/off valve); LV, liquid vessel; P, pressure gauge (pressure transducer); GC, gas chromatograph; 3wv, three-way valve (six-port valve); VP, vacuum pump; COMP, compressor or lab pressurized air; MFC, mass flow controller; COB, circulating oil bath; EC, equilibrium cell; TC/RTD, thermocouple/resistance temperature detector.

degradation product of diglycolamine (DGA).12 Therefore, to improve the performance of the DGA treating process in the presence of MOR, the knowledge of CO2 solubility in MOR is required.13,14 At present, the available vapor liquid equilibrium and thermodynamic data for morpholine is very limited. In this work, the experimental solubility data of CO2 in three different concentrations of morpholine is reported. The data from two different data collection methods, total pressure and gas chromatography, were compared to further validate the determined CO2 partial pressure values. The experimental data was then regressed to train a thermodynamic model that best fit the collected data. Using this regression, the molecule− molecule and molecule−electrolyte binary parameters necessary for thermodynamic modeling of the system, the temperature dependent functional form of carbamate stability constants, and the Henry’s law constant for CO2 in morpholine were determined. Using the CO2 solubility data, the CO2 heat of absorption in the solutions tested was also calculated.

carbon in amine solutions to CO2, and CO2 gas is stripped out with a nitrogen carrier gas before being directed to a HORIBA CO 2 Analyzer (VIA-510). The area under the CO 2 concentration curve is integrated, and CO2 concentration is determined using a calibration curve from known standards of potassium carbonate. Approximately 1 mL of sample (mass determined) was injected into the phosphoric acid reactor, yielding CO2 concentration in mol of CO2/kg of solution. The HORIBA CO2 analyzer was calibrated with a certified CO2:N2 gas mixture (PurityPlus, 14.00% CO2) each day. The uncertainty was checked with a known analytical standard (0.5 M Na2CO3, Fisher Scientific) prior to and after each set of unknowns with the allowable discrepancy in CO2 measurement (|(expected − measured)/expected| × 100) set at less than ±2% absolute. The standard deviation for repeated measurements was ±2.7%. The densities of solutions were measured by using a calibrated pipet (in quadruplicate) and determining the mass of solution. For a density near 1 g/mL, this method gives a precision of ±0.002 g/mL. Considering water as the main compound in the solutions in this study, the approximate density change at the extreme conditions (i.e., at working temperatures and total pressure ranges for the same CO2 loading) for a CO2 loaded solution based on the work done by Marshall and Mesmer16 is most likely less than 4%. Therefore, the uncertainty in the liquid phase volume and consequently in the gas phase volume measurements in the EC can be assumed to be less than 4% (i.e., δV/V = δρ/ρ). For CO2 partial pressure measurement, the static (total pressure) and dynamic (gas phase composition analysis by GC) methods were employed to obtain the data points. In the static method, the equilibrium pressure and temperature were used for the gas and liquid phase CO2 concentration determination. A brief description of the static total pressure method is given here. (I) The EC is charged with CO2 and then evacuated. (II) A known amount of CO2 gas is loaded to the fresh solvent in a separate container (prior to CO2 charging, the container is evacuated by a vacuum pump). (III) Approximately 200 mL of the solution provided at the previous step (step II) is fed to the

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EXPERIMENTAL SECTION A stirred equilibrium cell (EC) with a volume of 600 mL (Parr 4563, 12 400 kPa (max), 225 °C (max)) was used in all experiments. Figure 1 shows the schematic diagram of the experimental setup. Pressure was measured using a pressure transducer 0-1379 kPa (SSI Technologies Inc., P51-20-A-A). A liquid bath circulator was employed to maintain the EC temperature within ±0.1 K of the desired temperature measured using a resistance thermometer (RTD) (OMEGA). The pressure transducer accuracy was determined experimentally to be within ±0.6% of the actual value, using a pressure calibrator (OMEGA, DPI 603), and the RTD was calibrated using a three-point calibration curve including deionized water melting and boiling points and ethanol boiling point (pressure corrected). Deionized water and morpholine (Acros Organics, >99%) were used for the solution preparation. The CO2 content of the loaded solutions was analyzed by an acidbased method.15 In this method, phosphoric acid liberates the 5222

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injection of predefined concentrated aqueous morpholine solutions with known amounts of loaded CO2 (solution loadings were measured and confirmed by the HORIBA CO2 analyzer in advance).

EC (at the same time, a sample is taken for CO2 content analysis to calculate the mole fractions of components in the solution). (IV) At each desired temperature, when the system pressure did not change for at least 45 min, the equilibrium is assumed to have been reached. (V) The CO2 partial pressure is calculated by subtracting the partial pressures of fresh unloaded solutions (34.8 and 43.5 wt % MOR) from the total pressure of the system, eq 1,17 PCO2(T , α) = Pt(T , α) − Psoln*(T )α= 0

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THEORETICAL BACKGROUND AND THERMODYNAMIC MODELING Solution Chemistry. The following independent reactions are considered in the solution: Ionization of water:

(1)

where Pt(T, α) and Psoln*(T) are the total pressure and vapor pressure of the fresh (unloaded) solution, respectively. The fresh solvent (34.8 or 43.5 wt % MOR) vapor pressures at different temperatures were measured separately using the same setup. Having partial pressure, the mole number of CO2 in the gas phase can be calculated through nCO2,g =

2H 2O ↔ OH− + H3O+

Dissociation of dissolved CO2 through carbonic acid: CO2 + 2H 2O ↔ HCO3− + H3O+ HCO3− + H 2O ↔ CO32 − + H3O+

(2)

(6)

Carbamate reversion to bicarbonate (hydrolysis reaction):

where Vg, ZCO2, and R are the gas phase volume in EC, CO2 compressibility factor, and gas constant, respectively. The Peng−Robinson equation of state can be used to calculate the CO2 compressibility factor.18 In the dynamic method, the same procedure is used for charging the cell as described above. However, in this method, the gas phase is circulated through an on line gas chromatograph (GC) and so the gas phase composition is directly determined by GC. Having the gas phase composition and total pressure of the system, the partial pressure of each component can be calculated with the following simple relation: Pi(T ) = yi ·Pt

(5)

Dissociation of bicarbonate:

VgPCO2 ZCO2RT

(4)

MOR + HCO3− ↔ MORCOO− + H 2O

(7)

Dissociation of protonated MOR: MORH+ + H 2O ↔ MOR + H3O+

(8)

Considering the nonideality of the electrolyte solutions, the liquid phase chemical reaction equilibriums can be written in terms of species activities Ki =

υj

∏ aj

(9)

j

where aj and νj are the activity of species and the corresponding stoichiometric coefficients of species j, respectively. Equation 9 can be written in terms of activity coefficients, in mole fraction scale,

(3)

where Pi and yi are the partial pressure and mole fraction of component “i” in the gas phase and Pt is total pressure. In this paper, the dynamic method was utilized primarily as a verification tool to confirm the CO2 partial pressures determined using the static pressure method. The reason for this is twofold: (1) The total pressure method was found to be less time-consuming in the current setup. (2) The circulation pump used was limited in applicability to pressures above 480 kPa. Because a wider range of data was obtained using the static method in this work compared to the dynamic method and consistency was established between the two methods (Table A1, Supporting Information), the regression analysis was performed over both dynamic and static methods solubility data. Gas Chromatography Analysis. An Agilent Series 7890A gas chromatograph equipped with a HP-Plot/Q capillary column (30 m × 530 μm) and a thermal conductivity detector (TCD) was employed to analyze the gas phase compositions including water, CO2, and morpholine. Temperature programming was done with an initial temperature of 60 °C for 2 min and a final temperature of 255 °C for 4.5 min, with a rate of 20 °C/min. A 25 μL gas sampling loop was used for injection of a constant amount of sample gas through a high-pressure six port valve. The temperatures of the gas sampling loop and TCD were held at 250 and 270 °C, respectively. Helium was used as the carrier gas with a constant flow rate of 15 mL/min. Each data point is the average value of at least three GC measurements at an equilibrium condition (i.e., constant temperature and pressure). The GC was calibrated through

Ki =

∏ (xjγj)ν

j

(10)

j

where xj and γj are the mole fraction and activity coefficient of species j, respectively. For the Henry’s component, the phase equilibrium equation also can be written as follows: ⎛ υ ∞(P − P o) ⎞ yi φiP = xiγiHi exp⎜ i ⎟ ⎝ ⎠ RT

(11)

And for the solvent (water and alkanolamine), vapor−liquid equilibrium is given by ⎛ υ (P − Pso) ⎞ ys φsP = xsγsPsoφso exp⎜ s ⎟ ⎝ ⎠ RT

(12)

where, in eqs 11 and 12, P, φi, Hi, and υi are the total pressure, fugacity coefficient, Henry’s constant, and partial molar volume at infinite dilution for molecular species “i”, in the mixed solvent of water and alkanolamine at the system temperature and at the vapor pressure of the mixed solvent, and Po, Pso, and υs are the saturation vapor pressure of the mixed solvent, saturation vapor pressure of pure solvent (water or alkanolamine), and molar volume of the pure solvent at the system temperature. The Henry’s constant in mixed solvent is calculated from the built in definition in ASPEN PLUS. In order to calculate the Henry’s constant of molecular solute “i”, 5223

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i.e., CO2, in the mixed solvent from those in the pure solvents, the following equation is used:19 ⎛H ⎞ ⎛H ⎞ ij ln⎜⎜ ∞i ⎟⎟ = ∑ wj ln⎜⎜ ∞ ⎟⎟ γ γ ⎝ i ⎠ ⎝ ij ⎠ j

ln γi =

∑k xk(V ik∞)2/3

T

τij = aij +

T

+ eij ln(T ) + fij ·T

(16-2) (16-3)

Equations 16-2 and 16-3 give the energy parameter (τij) and nonrandomness factor (αij). For the molecule−molecule binary interaction parameters, eq 16-2 is used, while, for molecule−ion pair interaction parameters, the following short forms were applied during the modeling process.24 τca,m = Cca,m + τm,ca = Cm,ca +

Dca,m (17)

T Dm,ca

(18)

T

The parameters in eqs 14−18, i.e., Aij, Bij, Cij, Dij, Eij, A, B, C, D, αij, aij, bij, cij, dij, eij, f ij, Cca,m, Dca,m, Cm,ca, and Dm,ca, can be determined by using the data regression tool of ASPEN PLUS. The maximum likelihood method was chosen for this regression. In this method, the objective function covers all measured variables in the input data set ⎡

N

B ln(Keq) = A + + C ln(T ) + DT T

bij

(16-1)

αij = cij + dij(T − 273.15)

(13-1)

+ Cij ln(T ) + DijT + Eij /T

j

⎛ ∑ x τ G ⎞ ⎜⎜τij − m m mj mj ⎟⎟ ∑k xkGkj ⎠ ∑k xkGkj ⎝ xjGij

Gij = exp( −αijτij)

where xj is the mole fraction of solvent j on a solute-free basis and V∞ ij is the partial molar volume of molecular solute i at infinite dilution in pure solvent j, which can be calculated from the Brelvi−O’Connell model.20 According to eq 13, in order to calculate the CO2 solubility in a mixed solvent of water and morpholine, the Henry’s law constant of CO2 in both water and morpholine in their pure forms are necessary. Equation 14 is the general temperature dependent form which was used for the Henry’s law constant (Pa/mole fraction) of CO2 in pure water and morpholine separately. Equation 15 was also applied for mole fraction based equilibrium constants for reactions 4−8 ln(Hij) = Aij +

∑k xkGki

∑

where

(13)

xj(V ij∞)2/3

Bij

+

(16)

where wj, Hi, Hij, γi∞, and γij∞ are the weighting factor, the Henry’s constant of molecular solute “i” in the mixed solvent, the Henry’s constant of molecular solute “i” in pure solvent “j”, the infinite dilution activity coefficient of molecular solute “i” in the mixed solvent, and the infinite dilution activity coefficient of molecular solute “i” in pure solvent “j”. The detailed form of the weighting factor wj can be given by eq 13-119 wj =

∑j xjτjiGji

OF =

2

(14)

∑ ⎢⎢ i=1

+ (15)

where Aij, Bij, Cij, Dij, Eij, A, B, C, and D are adjustable parameters. Subscripts i and j in eq 14 refer to CO2 and morpholine or CO2 and water, and T is the temperature in Kelvin. In this work, the parameters of eq 14 for CO2 in pure morpholine and the equilibrium constant for reaction 7 were also adjusted with NRTL model parameters. Activity coefficients are required in aqueous phase chemical equilibrium calculations. In this work, the activity coefficient model based on electrolyte nonrandom two-liquid (electrolyteNRTL) theory for aqueous electrolyte systems is used to represent liquid-phase activity coefficients.21−23 The electrolyte-NRTL activity coefficient model is commonly used for the calculation of activity coefficients for different species in electrolyte solutions with high ionic strength over the entire range of electrolyte concentrations. Electrolyte-NRTL has the capability to calculate activity coefficients for ionic species as well as molecular species in aqueous electrolyte systems or in mixed solvent electrolyte systems. This model includes adjustable parameters which can be defined for every specific system. The parameters included in the electrolyte-NRTL model are for molecule−molecule, molecule−electrolyte, and electrolyte−electrolyte pairs.21,24 Nonrandomness factors for alkanolamine−ion pair and acid gas−ion pair interactions can be fixed at constant values.22 The activity coefficient equation for the NRTL model is given by25

⎣

(Pical − Piexp)2 σPi 2

(xical − xiexp)2 σxi 2

+

+

(Tical − Tiexp)2 σTi 2

(yical − yiexp )2 ⎤ ⎥ ⎥⎦ σy 2 i

(19)

where N, Pi, Ti, xi, and yi are the number of experimental data, pressure, temperature, liquid phase, and gas phase mole fractions of data number “i”, respectively. The superscripts “cal” and “exp” display the model calculated and experimental values, respectively. Each term in the summation is normalized by the corresponding estimated experimental standard deviation of the indicated data, “σ”. The objective function is minimized to vapor−liquid equilibrium for acid gases (Henry’s law), chemical reaction equilibrium for all species in the liquid phase, parameter bounds (which are defined as input data), and liquid and gas phase mole fractions summed to 1 as constraints. In this work, the PTxy data type was selected as input data. Employing the procedure introduced by this group for alkanolamine speciation, additional data points, including the morpholine speciation data at 21 °C, were used in the data regression process. 26 Tables A1 and A2 (Supporting Information) display the experimental CO2 solubility and morpholine speciation data used for data regression. Unless reported otherwise, all molecule−ion pair interaction parameters required in eqs 17 and 18 which included the water molecule with at least one of the nondominant ions in solution (i.e., OH−, H3O+, CO32−) were held constant to (8, −4) and for morpholine with the same ions were held constant to (15, −8).14 The nonrandomness factor for water−salt pair and salt pair−water was held constant at 0.2 and for all molecules 5224

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the target is regression of both the equilibrium constant and the interaction parameters.27,28 Therefore, at first, the equilibrium and Henry’s law constants were fitted stepwise over all data points from both methods, while most of the binary interaction parameters were considered at fixed values using the ASPEN PLUS database and/or the literature.14 After this step, based on the equilibrium constant of eq 7 and the CO2 Henry’s constant in pure morpholine, obtained at the previous step, the binary interaction parameters were adjusted over the same data points to achieve the best possible consistency between model correlation and the dynamic and static methods’ data points. The comparison of the experimental values and model values for CO2 solubility in 34.8 and 43.5 wt % morpholine solutions at different temperatures are given in Figure 2. As can be seen, the model correlates with the experimental solubility data with acceptable agreement. It should be noted that the VLE and speciation data presented in this work are the only data used for regression. The need for a variety of data, for developing reliable equilibrium models for complex absorption systems such as CO2:alkanolamine:H2O is obvious. It can be seen that both of the solutions show close isotherms for CO2 solubility. Generally, the higher concentrated morpholine solution shows higher CO2 partial pressures at loadings up to 0.5. This decrease in CO2 solubility with increasing amine concentration is consistent with the literature.14 The deviation of the model correlation for the lower concentrated morpholine solution (34.8 wt %) at low loadings (loading < 0.15) can be attributed to the lack of experimental data points at this range (Table A1, Supporting Information). On the other hand, the partial pressure of CO2 at higher loadings (>0.5) for both solutions comes closer to values which can be related to the physical solubility nature of CO2 in loadings above 0.5. Figure 3 shows the parity plot of model predicted CO2 partial pressure vs experimental values. As can be seen, the model represents the experimental data in the whole range of temperatures fairly consistently. Figure 4 also displays the ratio of the model predicted values of the system total pressure and partial pressure of CO2 over experimental values used in this work. It is apparent from Figure 4 that the data points are well distributed by the model. The model correlation from the total pressure of the system is quite good, and the CO2 partial pressure data are fitted within ±20%. Liquid phase component speciation prediction is valuable for understanding and interpreting solvent properties such as CO2 partial pressure, carbamate stability, and free amine concentration. The model speciation correlation was compared with the experimental speciation obtained in this work, Figure 5. The model results show good agreement with experimental data for the various species in solution. As can be expected, the protonated morpholine and morpholine carbamate are generally consistent at lean loadings but diverge as the bicarbonate builds, due to carbamate reversion, at richer loadings. The figure provides a qualitative indication of the

(other than water)−salt pair and all salt pair−molecules (other than water) was held constant at 0.1 as previously reported.14 In order to promote model simplicity (fewer adjustable parameters) and based on the preliminary regression and sensitivity analysis results, the regression was limited to Aij, Bij, Cij, Dij, A, and B in eqs 14 and 15. The same approach for parameter reduction was applied (i.e., for binary interaction and pair interaction parameters) at each step of regression analysis to minimize the number of parameters as much as possible without losing model accuracy. The calculated NRTL molecule−molecule binary interaction parameters for MOR/ H2O and H2O/MOR and molecule−ion pair interaction parameters for different species in the solution are given in Tables 1 and 2. The employed and estimated parameters for Table 1. The MOR−H2O, NRTL Binary Interaction Parameters Required for eqs 16-2 and 16-3, Obtained in This Work molecule pair

aij

bij

cij

dij

eij

f ij

H2O−MOR MOR−H2O

3.6332 4.0753

1.5872 43.3633

0.3941 0.3941

0.00 0.00

0.00 0.00

0.00 0.00

Table 2. The electrolyte-NRTL Molecule−Ion Pair Interaction Parameters Required for eqs 15 and 16, Obtained in This Work molecule i H2O H2O MOR MOR

electrolyte j

MORH+ MORH+ MORH+ MORH+ electrolyte j HCO3− MORCOO− HCO3− MORCOO−

MORH+ MORH+ MORH+ MORH+

HCO3− MORCOO− HCO3− MORCOO− molecule i H2O H2O MOR MOR

Cm,ca

Dm,ca (K)

18.7319 2.5319 3.4583 1.7851 Cca,m

−7867.46 −4158.3677 819.6009 1727.8891 Dca,m (K)

−3 −8.9666 13.4902 −9.6122

10000 1236.3080 244.1195 540.2502

Henry’s law and equilibrium constants are listed in Tables 3 and 4. Considering the explanation above and Tables 1−4, a total of 28 parameters were adjusted over experimental data given in Tables A1 and A2 (Supporting Information).

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RESULTS AND DISCUSSION Considering the experimental solubility data collected by the two methods mentioned in this work (Table A1, Supporting Information) except at low temperatures and low loadings for the 34.8 wt % morpholine solution, the rest of the data from the static method are within less than ±20% and in most cases within less than ±10% deviation from the dynamic method. In order to obtain parameters as consistent as possible for the two methods’ data sets, the regression was done in multiple stages. This approach prevents overfitting of the data, especially when

Table 3. Temperature Dependence of Equilibrium Constant Parameters for eq 15, in Terms of Mole Fraction reaction no. 4 5 6 7 8

A 1.33 2.31 2.16 −2.01 −4.53

× × × × ×

B 102 102 102 100 100

−1.34 −1.21 −1.24 2.46 −6.30

× × × × ×

C −2.25 −3.68 −3.55 0.00 0.00

104 104 104 103 103 5225

× × × × ×

D 101 101 101 100 100

0.00 0.00 0.00 0.00 0.00

× × × × ×

ref 100 100 100 100 100

14 14 14 this work 14

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Table 4. The Parameters Required to Calculate Henry’s Law Constant (eq 14) Obtained in This Work (Pa/Mole Fraction) CO2−MORa CO2−H2Ob a

Aij

Bij

Cij

Dij

Eij

169.8227 170.7126

−8460.0000 −8477.7110

−22.1979 −21.9574

0.0082 0.0058

0.0 0.0

This work. bAustgen et al.24

Figure 5. The model predicted liquid phase speciation compared to experimental values as a function of loading, in morpholine solution at 34.8 and 43.5 wt % at 21 °C. Mole fractions were normalized to the sum of the total components plotted in the figure to allow overlay.

Figure 2. The experimental and model predicted partial pressure of CO2 as a function of loading at different temperatures for morpholine solutions 34.8 and 43.5 wt %.

morpholine carbamate stability constant. As can be seen, the bicarbonate amount is fairly large, consistent with a low carbamate stability value as discussed further below. According to the regressed parameters for reaction 7, the morpholine carbamate stability constants at different temperatures have been given in molarity scale in Table 5. As found Table 5. Morpholine Carbamate Stability Constant at Different Temperatures (Reaction 7) Kcarba (M−1)

Figure 3. The model predicted partial pressure of CO2 vs experimental values at 40, 60, 100, and 120 °C.

a

T (K)

this work

literature

ref

298 300 313 333

10.3 9.8 6.9 4.3

11.7 8.2 5.4 3.6

27 14 14 14

M: molarity.

elsewhere in the literature, morpholine carbamate stability was found to decrease with increasing temperature.14 The decrease in carbamate stability can be related to a higher amine reaction rate relative to other species with similar pKa.29 Comparison of the carbamate stability constant with that of another secondary amine diethanolamine (DEA) is consistent with this conclusion.30,31 The 313 K value for the equilibrium stability constant for morpholine was found to be 2 M−1. The pKa value for morpholine (8.49) is comparable to DEA (8.96).32 However, the morpholine rate constant is much higher than that of DEA.5 On the other hand, cyclic alkanolamines show more tendencies to form carbamate, rather than their noncyclic counterparts with the same amine order.29,31 This behavior displays the correlation between the carbamate stability constant and the CO2 rate of absorption in alkanolamine solutions.

Figure 4. The ratio of model predicted values over the experimental total and CO2 partial pressure as a function of loading.

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trend for Henry’s constant is seen, which means higher solubility for CO2 with increasing temperature. On the other hand, in the second approach, having the Henry’s constant for CO2 in water from the literature, its value for CO2 in pure morpholine can be estimated. As it was discussed in the paragraph followed by eq 13-1, the second approach was selected in this work to estimate the Henry’s law constant for CO2 in pure morpholine solution. Using the parameters obtained for Henry’s law constant (Table 4) obtained in this work, its values for CO2 in morpholine solution have been calculated and compared with literature data and also with the values for CO2 in MEA solution, Table 8. At the range

Using the Gibbs−Helmholtz equation, the temperature independent heat of absorption of CO2 (ΔHabs) in morpholine solutions was calculated through solubility data (J/molCO2).7,33 ΔHabs = R(a + b·α + c·α 2)

(20)

where R, a, b, c, and α are the universal gas constant (in SI unit), adjustable parameters, and CO2 loading (mol/mol), respectively. Tables 6 and 7 display the required parameters for the calculation of the CO2 heat of absorption and its values at Table 6. The Required Parameters for Calculation of CO2 Heat of Absorption (J/molCO2) in Aqueous Solutions of Morpholine at 34.8 and 43.5 wt % (eq 20) morpholine (34.8 and 43.5 wt %)

a

b

c

−8589.0235

0.0582

11476.7570

Table 8. The Henry’s Constant Values for Carbon Dioxide in Morpholine and MEA at Different Temperatures ln HCO2,solv (Pa/mole fraction)

Table 7. The CO2 Heat of Absorption Calculated in This Work at Various Loadings for Morpholine at 34.8 and 43.5 wt % a

heat of absorption, kJ/molCO2

a

loading (molCO2/molMOR)

this work

literaturea

0.08 0.21 0.32

71 67 62

80 72 82

T (°C)

CO2−MEAa

CO2−MORb

CO2−MORc

40 60 120

18.5 18.6 19.0

17.8 18.2 18.9

18.2 18.6 19.0

Reference 28. bThis work. cReference 14.

of system pressure in this work, it was assumed that the Henry’s law constant is a temperature dependent function only. Table 8 shows the comparative values for the Henry’s law constant of CO2 in morpholine and MEA. Compared to published values, a trend of lower CO2 solubility as a function of temperature is expected to be obtained. The values obtained here are similar to other reported values for morpholine and the commonly used alkanolamine solvent MEA. Having the Henry’s constant as a function of temperature, the temperature dependent heat of physical dissolution of CO2 (ΔHdiss) in the pure morpholine solution can be estimated using eq 21

3.5 m (∼24 wt %) morpholine concentration.14

different loadings, respectively. There is a decreasing trend of heat of absorption values as the CO2 loading increases. The values for the CO2 heat of absorption reported in this work were compared with the only accessible data in the literature at a different concentration of morpholine.14 In this work, the solution with lower morpholine concentration displayed higher absolute heat of absorption especially at low loadings. However, the trend observed in the previously reported data regarding heat of absorption as a function of solution carbon loading is inconsistent with the data obtained here or in other reports.33 Considering piperazine (PZ) as a secondary and cyclic amine with similar structure as morpholine, the heat of absorption obtained in this work is comparable.7,34 For example, at 0.32 carbon loading, piperazine was regressed by Xu and Rochelle to have a value of 70 kJ/mol of CO2. Since the structure is similar to piperazine, the lower heat of absorption for morpholine can be explained by the difference in the base strength for the two molecules. Morpholine is a weaker base (pKa 8.5) compared to piperazine (pKa1 9.8) which correlates to a weaker carbamate bond strength and lower heat of absorption. For a ternary solution in which a gas is dissolved, the rigorous thermodynamics statements reveal that the Henry’s constant depends on the composition of the mixed solvent.35 The composition dependency for the Henry’s constant for a mixed solvent is implemented by the weighting factor in eq 13. However, in a more simple form, the weighting factor for each component can be replaced by its mole fraction.36,37 In the data regression, it was possible to calculate the apparent Henry’s constant for CO2 in the mixed solvent. Following the abovementioned approach gives a maximum point for Henry’s constant vs temperature, so that the CO2 solubility decreases in an acceptable manner up to a temperature around 90 °C (i.e., ln HCO2‑mix = 18.3 Pa/mole fraction), and after that, a decreasing

∂ ln Hij ∂T

=

−ΔHdissij RT 2

(21)

where it gives −19.2, −16.4, and −13.7 kJ/molCO2 for 40, 60, and 80 °C, respectively. No available heat of dissolution data for pure amines or at least for pure morpholine have been published for comparison. Therefore, these values can be compared with temperature independent values of −15, −13, −17, and −16 kJ/molCO2 for MEA, DEA (diethanolamine), MDEA (methyl diethanolamine), and AMP (2-amino-2methyl-1-propanol) aqueous solutions, respectively.38

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CONCLUSION Using both total pressure and a gas chromatography method to determine CO2 partial pressure, data was collected for two MOR concentrations relevant to potential use for postcombustion CO2 capture applications. The electrolyte-NRTL equations along with the needed thermodynamic equations were used to model the experimental CO2 solubility and morpholine speciation data. The regressed parameters from the experimental data yielded good agreement between the experimental and model values. The morpholine carbamate stability constant was introduced in a functional form which decreases with increasing temperature. The calculated morpholine carbamate stability constant is in acceptable agreement with literature reported values for this alkanolamine. In terms of cyclic and noncyclic secondary alkanolamines, morpholine shows a 5227

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τij

stronger carbamate bond, as evidenced by its higher carbamate equilibrium constant compared to that of a linear secondary amine (DEA). This is reflected in the higher rate for CO2 absorption in aqueous solutions of morpholine compared to the linear amine. The heat of absorption for morpholine was determined as a function of temperature and CO2 solution loading. The trend and values obtained for morpholine were consistent with a similar cyclic amine, piperazine. The temperature dependent Henry’s law constant and heat of dissolution (physical solubility) for CO2 in pure morpholine were also introduced.

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νi wj

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

Tables showing the experimental CO2 solubility data in morpholine solutions (34.8 and 43.5 wt %) and the experimental liquid phase speciation data for morpholine solutions (34.8 and 43.5 wt %) at different CO2 loadings at 21 °C. This material is available free of charge via the Internet at http://pubs.acs.org.

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Energy parameter in the electrolyteNRTL activity coefficient model (eq 16-2) Partial molar volume at infinite dilution for molecular species “i” Weighting factor (eqs 13 and 13-1)

AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the Carbon Management Research Group (CMRG) members, including Duke Energy, East Kentucky Power Cooperative (EKPC), Electric Power Research Institute (EPRI), Kentucky Department of Energy Development and Independence (KY-DEDI), Kentucky Power (AEP), and LG&E and KU Energy, for their financial support.

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NOMENCLATURE A, B, C, D Adjustable parameters (eq 15) Aij, Bij, Cij, Dij, Eij Adjustable parameters (eq 14) aij, bij, cij, dij, eij, f ij Adjustable parameters for molecule− molecule binary interaction (eqs 16-2 and 16-3) Cca,m, Dca,m, Cm,ca, Dm,ca Adjustable parameters for molecule− ion pair interaction (eqs 17 and 18) Hij Henry’s constant of molecular solute “i” in pure solvent “j” (eq 14) Hi Henry’s constant of molecular solute “i” in the mixed solvent (eq 13) ΔHabs CO2 heat of absorption (eq 20) ΔHdiss CO2 heat of dissolution (eq 21) Ka Dissociation constant for protonated amine (reaction 8) and, pKa = −log(Ka) Kcarb Carmbamate stability constant (reaction 7) P Pressure xi Liquid phase mole fraction yi Vapor phase mole fraction Nonrandomness factor in the electroαij lyte-NRTL activity coefficient model (eq 16-3) φi Fugacity coefficient of component “i” γi Activity coefficient of species “i” 5228

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