Solubility of Carbon Dioxide in Activated Potash ... - ACS Publications

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Solubility of Carbon Dioxide in Activated Potash Solutions in the Low and High Gas Loading Regions Michael Imle, Jacek Kumelan, Dirk Speyer, Nichola McCann, Gerd Maurer, and Hans Hasse* Laboratory of Engineering Thermodynamics, University of Kaiserslautern, P.O. Box 30 49, D-67653 Kaiserslautern, Germany ABSTRACT: In the Hot Potassium Carbonate Process, carbon dioxide (CO2) is removed from gaseous streams by chemical absorption in an aqueous solution of potassium carbonate (K2CO3). It is common to activate the solvent by adding borates and vanadates as promoters. In the present investigation, we investigate the influence of borates and vanadates on the equilibrium solubility of CO2 in aqueous solutions of K2CO3. The solubility of CO2 in four activated aqueous solutions of K2CO3 was determined experimentally at two temperatures that are typical for CO2 absorption (343 K) and solvent regeneration (383 K) in the Hot Potassium Carbonate Process. The mass fraction of K2CO3 in the solvent was 0.26 g/g, and the mass fractions of boron (vanadium) was varied between 0.006 g/g and 0.013 g/g (0.01 g/g and 0.02 g/g). Two experimental setups were used: A headspace gas chromatography technique was applied to determine the solubility of CO2 at partial pressures of CO2 between 1 kPa and 140 kPa, and the synthetic gas solubility technique was applied for total pressures between 0.4 MPa and 10 MPa. The new experimental results are compared to predictions from a physicochemical thermodynamic model for the solubility of CO2 in aqueous solutions of K2CO3 that is based on the extended Pitzer equation for describing the nonidealities of the electrolyte solution. The results reveal that both the borate and the vanadate reduce the solubility of CO2 in such solutions. The new model provides a physicochemically sound basis for process simulation of the Hot Potassium Carbonate Process.

■

INTRODUCTION In many chemical processes, carbon dioxide (CO2) must be removed from gaseous streams (e.g., in ammonia synthesis, in natural gas purification, in hydrogen purification).1 A wellknown process for this task is the Hot Potassium Carbonate Process that was developed in the 1950s by Benson and Field,2−4 in which a hot aqueous solution of potassium carbonate (K2CO3) is used for carbon dioxide absorption. In such a solution, CO2 is dissolved chemically, i.e., it is converted to hydrogen carbonate. Aqueous solutions of K2CO3 have a high capacity for CO2 as one mole of K2CO3 can absorb one mole of CO2. The absorption media can be regenerated by desorption of CO2 at increased temperatures. Thus, a closed process for CO2 removal is possible. However, there are also some disadvantages. For example, the temperature must be sufficiently high to avoid the precipitation of solid potassium hydrogen carbonate, the aqueous solutions of potassium carbonate are corrosive, and the conversion of CO2 to hydrogen carbonate is a rather slow chemical reaction. There are several proposals in the literature to overcome such disadvantages by adding so-called “promoters” and/or “inhibitors” to the aqueous solution of K2CO3. An overview is given in Table 1. Organic promoters are used in ammonia synthesis and natural gas purification (the absorption with an amine-promoted potash solution was modeled e.g., by Sanyal et al.5 and Hilliard6). The use of arsenious acid (formerly used in the Giammarco−Vetrocoke arsenite-based process)7 is less important nowadays. Because of its high toxicity, arsenite was replaced by glycine or secondary amines.4,8 In the case of ethylene oxide plants, inorganic catalysts are required.4 Eickmeyer9,10 suggested adding a mixture of borate and vanadate to the aqueous solution of K2CO3. Although it is commonly acknowledged that adding a mixture of borates and vanadates to the solvent improves the performance of a Hot © 2013 American Chemical Society

Table 1. Some Additives Used in the Hot Potassium Carbonate Process additive

intended effect

reference

Inorganic Compounds NaVO3 (vanadate) inhibitor Field and Bienstock52 K2Cr2O7 (dichromate)a inhibitor KBO2 and V2O5 (borate and promoter Eickmeyer,10 Field37 vanadate) As2O3 (arsenate) promoter Giammarco7 Organic Compounds DEA (diethanolamine) promoter Killeffer,53 Mahajani and Danckwerts54 MEA (monoethanolamine) promoter DIPA (diisopropanolamine) promoter Mahajani and Danckwerts54 2A2MP (2-amino-2promoter Mahajani and Danckwerts,54 methylpropanol) Tang et al.55 PIP (piperazine) promoter Tang et al.,55 Cullinane and Rochelle56 b amino derivates promoter Tang et al.55 various alcohols promoter Killeffer53 glycine promoter Giammarco,8 Portugal et al.57 a Potassium dichromate is ineffective when H2S is present in the raw gas.52 bFor example, piperidine, morpholine, imidazole.

Potassium Carbonate Process, a detailed investigation of the reasons (influence on the phase equilibrium and/or the chemical reaction kinetics) for the improvements is not yet available. There are some measurements from Endo et al.11 for Received: Revised: Accepted: Published: 13477

June 10, 2013 July 19, 2013 July 31, 2013 July 31, 2013 dx.doi.org/10.1021/ie401835x | Ind. Eng. Chem. Res. 2013, 52, 13477−13489

Industrial & Engineering Chemistry Research

Article

a mixture of borate and potassium carbonate at 323 K and 343 K. Schäfer et al.12 measured the solubility of CO2 in a mixture of KOH and B(OH)3 and Schäfer et al.13 measured the solubility of CO2 in a mixture of KOH and KVO3. But neither vapor−liquid equilibrium data nor kinetic data for the solubility of CO2 in the “full” activated solvents (i.e., in aqueous solutions of K2CO3 activated by borates and vanadates) are available in the open literature. The aim of the present research is to investigate the influence of two simultaneously dissolved promoters (B(OH)3 and KVO3) on the equilibrium solubility of CO2 in aqueous solutions of K2CO3 and to develop a physicochemical model for describing their influence on the vapor−liquid equilibrium. The influence of the single components (B(OH)3 and KVO3) and mixtures of these components on the solubility of CO2 in aqueous solutions of K2CO3 is experimentally studied at two temperatures (343 and 383 K). The experiments are performed with two different types of experimental equipment that enable investigations at partial pressures of CO2 between 1 kPa and 140 kPa on one side and at total pressures of 0.4−10 MPa on the other side. The experiments in the low-pressure range cover typical conditions for absorption/desorption in the Hot Potassium Carbonate Process. However, for the development of a reliable thermodynamic model, gas solubility measurements at elevated pressures (i.e., at elevated concentrations of CO2 and its reaction products) are important (see refs 14−20). Because CO2 is predominantly dissolved chemically (i.e., as hydrogen carbonate and carbonate) and borate and vanadate is present in a variety of ionic species, interactions between the solute species are important in the liquid phase. Experimental results in the high-pressure region enable a more reliable determination of the corresponding interaction parameters since, there, the concentration of the reaction products is high. Therefore, one can expect that a sound physicochemical thermodynamic model for the solubility of CO2 based on experimental data in the high-pressure region also gives good predictions for the low-partial-pressure region. Experimental data in the low-pressure region can be used to test the extrapolation capability of the model and to additionally determine some model parameters that are not accessible from high-pressure gas solubility data. The experimental data obtained in the present study are used to extend a previously developed physicochemical thermodynamic model for the solubility of CO2 in aqueous solutions of K2CO3.19 The nonidelatity of the aqueous electrolyte solution is described by the extended Pitzer equation for the excess Gibbs energy of aqueous electrolyte solutions.21−23 The model is based on the molality scale. The complex reaction network in the aqueous solution between CO2, borates, vanadates, and K2CO3 is explicitly taken into account.

chemical equilibrium between hydrogen carbonate and carbonate: HCO3− ⇌ CO32 − + H+

autoprotolysis of water:

H 2O ⇌ H+ + OH−

(III)

These three reactions determine the speciation in the liquid phase when no other solutes are present. However, the presence of the additives (B(OH)3 and KVO3) results in many additional chemical reactions in the liquid phase. The presence of B(OH)3 in (basic) aqueous solutions (of KOH and CO2) results in the formation of a large number of ionic species (cf. Ingri,24 Spessard,25 Botello et al.26). However, in the pH range of interest to an activated Hot Potassium Carbonate Process, it is sufficient to consider the following additional anions: B(OH)4−, B3O3(OH)4−, B3O3(OH)52−, and B4O5(OH)42−. Their presence is taken into consideration using four additional chemical equilibrium reactions: B(OH)3 + H 2O ⇌ B(OH)4 − + H+ −

+

(IV)

3B(OH)3 ⇌ B3O3(OH)4 + H + 2H 2O

(V)

3B(OH)3 ⇌ B3O3(OH)52 − + 2H+ + H 2O

(VI)

4B(OH)3 ⇌ B4 O5(OH)4 2 − +2H+ + 3H 2O

(VII)

Ingri,24 Spessard,25 and Botello et al.26 mention that a boron pentamer B5O6(OH)4− exists in acid solutions. Guo et al.27 propose a reaction mechanism resulting in a complex (B(OH)4CO2−). However, as the solvent of a Hot Potassium Carbonate Process is a basic solution and as our NMRspectroscopic investigations provided no indication for a stable complex of boron and carbon dioxide, these species are not considered here. In basic aqueous solution, vanadate exists in several forms. We assume that KVO3 dissociates in water completely to H2VO4− and K+: KVO3 + H 2O → H 2VO4 − + K+

(VIII)

28

McCann et al. showed that, in the basic solution, at concentrations relevant to this work, H2VO4− undergoes further reactions that result in nine vanadium-containing ionic species: H 2VO4 − ⇌ HVO4 2 − + H+

■

(IX)

2H 2VO4 − ⇌ V2O7 4 − + 2H+ + H 2O

(X)

2H 2VO4 − ⇌ HV2O7 3 − + H+ + H 2O

(XI)

2H 2VO4 − ⇌ H 2V2O7 2 − + H 2O

CHEMICAL REACTIONS An aqueous solution of K2CO3 is a chemical solvent for CO2, i.e., it dissolves CO2 predominantly as hydrogen carbonate (at the same time, carbonate is converted to hydrogen carbonate). Therefore, the chemical reaction equilibrium for the formation of hydrogen carbonate from CO2, the chemical reaction equilibrium between hydrogen carbonate and carbonate, and the autoprotolysis of water must be considered: formation of hydrogen carbonate from CO2: CO2 + H 2O ⇌ HCO3− + H+

(II)

(XII)

3H 2VO4 − ⇌ HV3O10 4 − + H+ + 2H 2O

(XIII)

4H 2VO4 − ⇌ V4O136 − + 2H+ + 3H 2O

(XIV)

4H 2VO4 − ⇌ V4O12 4 − + 4H 2O

(XV)

5H 2VO−4 ⇌ V5O155 − + 5H 2O

(XVI)

Furthermore, based on the results of a recent NMRspectroscopic investigation, two carbonato-vanadate complexes must be taken into account:29

(I) 13478

dx.doi.org/10.1021/ie401835x | Ind. Eng. Chem. Res. 2013, 52, 13477−13489


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H 2VO4 − + CO32 − + H+ ⇌ HVO4 CO2 2 − + H 2O

CO2 before it is charged with a known amount of the solvent. The solvent is added via a calibrated spindle press. The density of the aqueous solvent (c.f. Table 2) is determined using a vibrating tube densimeter (Anton Paar GmbH, Model DMA 4500 M). The amount of solvent filled into the cell is always slightly above the minimum amount that is required to fill the cell completely with a liquid phase, i.e., after equilibration the pressure in the cell is above the solubility pressure. After equilibration, very small amounts of the solvent are withdrawn step by step from the cell until the first (very tiny) gas bubbles appear, i.e., starting from a single phase liquid mixture, the pressure is reduced until the phase boundary to the vapor− liquid region is crossed. The mass of CO2 charged to the cell (4.16−5.30 g) is determined with an uncertainty of 0.008 g. The uncertainty of the mass of the solvent in the view cell (typically 31 g) is 0.09 g. The accuracy of the temperature measurement is ±0.1 K. The typical uncertainty in determining the solubility pressure is 0.015 MPa in the pressure range of 0.4−10 MPa. More details have been given in previous publications.20,34−36 Headspace Gas Chromatography. Figure 2 shows a schematic of the headspace gas chromatographic arrangement. The main components are eight thermostatted sample cells (only one sample cell is shown in Figure 2), a vapor-phase expansion system, a sampling system, and a gas chromatograph. In an experiment, the sample cells (stainless steel vials, volume = 30 cm3) are filled with 25 cm3 of the loaded solvent. After equilibration, the sample cell is pressurized with nitrogen from buffer tank A to a constant pressure. Immediately afterward, the vapor phase is expanded to a larger volume by connecting the vapor phase of the cell to buffer tank B, which is pressurized to a slightly lower pressure than that of buffer tank A. The sampling system including the sample loop (SL; internal volume = 20 μL) is filled in that step. The sample is then transferred to the gas chromatograph. After each measurement, the sampling system is purged with nitrogen. A multiposition valve (Valco Instruments Co. Inc., Type 2CSD16MWE) allows the connection of each of the eight sample cells to the sample loop (positions S1−S8). The other eight positions (P1−P8) are used for purging. The gas chromatograph (Agilent, Type 6890) is equipped with a capillary column (Alltech, Type Heliflex ATQ, 30 m, 0.32 mm inner diameter) and a thermal conductivity detector. The peak area resulting from CO2 in the sample is used to determine the partial pressure of CO2 above the liquid solution in the sample cell via a calibration curve. The calibration curves are determined by filling pure CO2 into the vial and measuring the pressure in the vial with a high-precision pressure transducer (MKS, Andover, MA, USA, Type 690A13TRA) with an accuracy of 0.05%. In a gas chromatographic experiment, 4−6 sample cells were filled with the same loaded liquid mixture. The standard deviation of the peak areas of CO2 from samples taken from the different cells that were filled with the same loaded solvent was typically T1); A, nitrogen tank (higher pressure); B, nitrogen tank (lower pressure); GC, gas chromatograph; He, helium (carrier gas); SC, sample cell; MV, multiposition valve; S1−S8, sample positions; P1−P8, purge positions; SV, sample valve; and SL, sample loop.]

(a) KOH + B(OH)3

(b) KOH + KVO3

(c)

loaded liquid mixture and mounted in the cell holder, where they were thermostatted to the experimental temperature for at least 12 h. Small corrections to the overall molalities of the solutes were considered to account for the transfer of CO2 and water to the vapor phases in both the storage tank and the sample cells. Since all vapor-phase volumes are small and the partial pressures of CO2 and water are low, the corrections to the overall molality of all solutes are small. The temperature is measured with a calibrated platinum resistance thermometer in the liquid that is used for thermostatting the sample cell holder. The estimated uncertainty of the temperature measurement is 0.1 K.

KOH + B(OH)3 + KVO3

The concentration of potassium in the solvent was 0.16 g/g (i.e., when the potassium content is expressed by the mass fraction of K2CO3, that mass fraction is ∼0.26 g/g), which is a typical concentration in a Hot Potassium Carbonate Process (cf. Eickmeyer10 and Field37). In the experiments with the single promoters, their concentration in the solvent was xB = 0.01 g/g for boron (solvent B) and xV = 0.02 g/g for vanadium (solvent V). When both promoters were dissolved in the solvent, their mass ratio mV/mB was 2 and the mass fraction of vanadium was either 0.013 g/g (solvent BV1) or 0.02 g/g (solvent BV2) (cf. Table 3 and Figure 3). The experimental results for the solubility of CO2 are given here using the molality scale with water being the solvent. Therefore, in the following, rather then specifying the mass fractions of single ions as above, overall molalities of KOH, B(OH)3, and KVO3 are used to characterize the overall solution

■

MATERIALS Carbon dioxide (volume fraction ≥99.995%) was purchased from Messer Griesheim GmbH, Krefeld, Germany. Boric acid (B(OH)3; mass fraction ≥99.8%) was purchased from Merck, Darmstadt, Germany. Potassium metavanadate (KVO3; mass fraction ≥98%) was purchased from Sigma−Aldrich, Munich, Germany; potassium carbonate (K2CO3; mass fraction ≥99%) and an aqueous potassium hydoxide solution (mass fraction = 50%) were purchased from Fluka, Munich, Germany. For all evaluations, the impurities were assumed to be nonreactive. Water was prepared by a water purification system (TWF/EIIon UV Plus, Siemens AG, Water Technologies). The liquid components were degassed before they were used for the preparation of the solvent mixtures. The real amount of a solute was calculated taking the impurity of the materials into account.

Table 3. Overview of Solute Composition Used in the Present Study

13480

identifier

xK (g/g)

xB (g/g)

xV (g/g)

B V BV1 BV2

0.16 0.16 0.16 ± 0.01 0.16 ± 0.01

0.011 0 0.006 ± 0.001 0.01 ± 0.001

0 0.021 0.013 ± 0.001 0.020 ± 0.001



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Table 4. Solubility of Carbon Dioxide in Aqueous Solutions of CO2, KOH, B(OH)3, and KVO3 in the High-Pressure Rangea Overall Molalities (mol (kg H2O)−1) identifier

T (K)

BV1

Figure 3. Overview of composition of solvents considered in the present study. [Legend: (■) this work, xK = 0.16 ± 0.01 g/g; (○) Pérez-Salado Kamps et al.,19 xK = 0.03, 0.07, 0.1, 0.12 g/g.]

composition. Overall molalities are marked with an overbar (m̅ i), in contrast to true molalities (mi). The overall molality of, for example, B(OH)3 is calculated from the amount of boric acid added to the solution, whereas the true molality of a species (for example, that of HCO3−) is calculated from the number of moles of that species in the mixture, taking all occurring chemical reactions into account. The solubility of CO2 in aqueous solutions of KOH + B(OH)3 and/or KVO3 was measured at 343 and 383 K. The experimental results from the investigations by the synthetic method (headspace gas chromatographic technique) are given in Table 4 (Tables 5 and 6) as the total pressure (partial pressure of carbon dioxide) above an aqueous solution. Figure 4 shows, as a typical example, a comparison between some new experimental results for the solubility of CO2 in aqueous solutions of (KOH + B(OH)3 + KVO3) from the present study and the correlation of Pérez-Salado Kamps et al.19 for the solubility of CO2 in aqueous solutions of KOH, i.e., without any promoters. The comparison reveals that adding the promoters results in a lower solubility (higher partial pressure) of CO2. Therefore, adding a mixture of those promoters does not improve the equilibrium solubility of CO2 in aqueous solutions of K2CO3.

■

a

THERMODYNAMIC MODEL The new experimental data are used to extend the model of Pérez-Salado Kamps et al.19 for the solubility of CO2 in aqueous solutions of K2CO3. Since similar models were also used in related work on the solubility of acid gases in aqueous solutions,14−16,20,31−34,38,39 here, only an outline of the model is given with the focus on the extension to the systems investigated in the present work. Vapor−Liquid Equilibrium. The model describes the vapor−liquid equilibrium via the extended Henry’s law for CO2: ∞ s ⎤ ⎡ νCO (p − pW ) (m) (m) 2 ⎥aCO2 = pyCO φCO ⎢ exp kH,CO 2 2 2 ⎢⎣ ⎥⎦ RT (1)

m̅ KVO3 0.351

m̅ CO2 4.687 4.815 4.889 5.017 5.115 5.235 5.324 5.378

BV2

343.2

4.954

1.326

0.565

4.4718 4.599 4.646 4.774 4.840 4.950 5.060 5.140 5.297

0.403 0.797 1.058 1.889 2.299 3.21 4.56 5.42 7.78

BV1

383.2

4.908

0.770

0.351

4.484 4.594 4.741 4.809 4.918 5.060 5.226 5.252

0.747 1.138 2.069 2.71 4.1 5.88 9.17 9.43

BV2

383.2

4.954

1.326

0.565

4.335 4.456 4.724 4.780 4.836 4.941 5.043 5.072 5.167

0.638 0.914 2.426 3.19 3.53 5.05 6.54 6.88 8.57

0.755 1.556 2.304 3.44 4.54 6.09 7.72 8.41

ΔT = ±0.1 K; Δm̅ i/m̅ i = ±0.002; Δptot = ±0.015 MPa.

k(m) H,CO2 is Henry’s constant of CO2 in pure water (based on the molality scale) at the vapor pressure of water psw; ν∞ CO2 and νW are the partial molar volume of CO2 at infinite dilution in water and the molar volume of pure liquid water, respectively. The (m) influence of pressure on ν(m) CO2 and vW is neglected. yCO2, yW, aCO2, and aW are the vapor-phase mole fractions and the liquid-phase activities of CO2 and water, respectively. R is the universal gas constant. φsw and φi are the fugacity coefficients of pure water at saturation and the fugacity coefficients of component i (i = CO2 or H2O) in the vapor phase, respectively. The chemical potentials of all solute species are normalized according to Henry’s law on the molality scale. The activity of CO2 is mCO2 (m) (m) aCO = γ 2 (3) m◦ CO2

and the extended Raoult’s law for water: ⎡ ν W (p − p s ) ⎤ s W ⎥aW = pyW φW φWs exp⎢ pW RT ⎣ ⎦

m̅ B(OH)3 0.770

ptot (MPa)

343.2

m̅ KOH 4.908

(2) 13481



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Table 5. Solubility of Carbon Dioxide in Aqueous Solutions of KOH, B(OH)3, and KVO3 in the Low-Pressure Range at T = 343.1 Ka

Table 6. Solubility of Carbon Dioxide in Aqueous Solutions of KOH, B(OH)3, and KVO3 in the Low-Pressure Range at T = 382.5 Ka ()

Overall Molalities (mol (kg H2O)−1) m̅ KVO3 0.574 0.574 0.580 0.574 0.580 0.580 0.580 0.574 0.580 0.580

m̅ CO2 3.142 3.270 3.414 3.612 3.643 3.748 3.881 3.890 4.048 4.199

pCO2 (kPa)

ΔpCO2,repr (kPa)

1.74 2.47 3.31 5.32 5.58 7.00 9.40 9.80 13.5 18.0

0.01 0.02 0.01 0.08 0.03 0.09 0.05 0.08 0.1 0.1

V

1.385 1.384 1.385 1.384 1.385 1.385 1.382 1.382 1.384 1.382 1.382

0 0 0 0 0 0 0 0 0 0 0

3.022 3.255 3.377 3.401 3.468 3.612 3.749 3.887 3.910 4.073 4.227

1.063 2.36 3.37 3.51 4.41 6.04 10.0 13.5 13.8 19.9 30.6

0.001 0.01 0.06 0.02 0.06 0.01 0.1 0.4 0.2 0.4 0.7

5.942 5.942 5.952 5.952 5.942 5.952 5.952 5.952 5.952

0.849 0.849 0.817 0.817 0.849 0.817 0.817 0.817 0.817

0.385 0.385 0.383 0.383 0.385 0.383 0.383 0.383 0.383

3.167 3.585 3.863 3.995 4.151 4.295 4.688 4.822 4.989

0.837 2.64 4.57 6.01 9.09 11.9 27.9 36.4 54.3

0.004 0.03 0.08 0.08 0.05 0.2 0.2 0.6 0.6

5.450 5.755 5.450 5.450 5.253 5.755 5.253 5.450 5.755 5.450

1.364 1.399 1.364 1.364 1.341 1.399 1.341 1.364 1.399 1.364

0.632 0.626 0.632 0.632 0.604 0.626 0.604 0.632 0.626 0.632

2.574 2.956 3.069 3.359 3.422 3.897 3.599 4.075 4.471 4.565

0.645 1.12 2.58 4.87 6.80 8.67 10.3 23.8 30.8 80.9

0.006 0.01 0.01 0.05 0.09 0.05 0.1 0.4 0.3 1.8

m̅ KOH 5.059 5.059 5.103 5.059 5.103 5.103 5.103 5.059 5.103 5.103

m̅ B(OH)3 0 0 0 0 0 0 0 0 0 0

B

5.739 5.734 5.739 5.734 5.739 5.739 5.723 5.723 5.734 5.723 5.723

BV1

identifier V

BV2

Overall Molalities (mol (kg H2O)−1) pCO2 (kPa)

ΔpCO2,repr (kPa)

1.36 2.27 2.86 4.96 6.23 6.88 12.3 16.1 27.4 43.9

0.07 0.09 0.08 0.09 0.19 0.23 0.4 0.7 0.8 1.0

2.770 2.920 3.005 3.195 3.261 3.493 3.674 4.020 4.220 4.408

1.15 2.66 3.76 7.11 8.55 16.6 25.8 52.9 93.7 135

0.03 0.12 0.05 0.12 0.10 0.4 0.4 1.0 2.9 5

0.401 0.386 0.386 0.386 0.386 0.386 0.401 0.386

2.869 3.234 3.392 3.521 3.745 4.028 4.561 4.470

1.02 5.51 8.27 10.9 18.1 31.6 63.7 79.7

0.03 0.17 0.25 0.4 0.3 1.0 0.8 3.1

0.623 0.623 0.623 0.607 0.607 0.623 0.607 0.623

2.666 2.711 2.944 2.898 3.148 3.879 3.771 4.444

1.91 2.21 4.56 8.20 14.0 33.2 51.2 105

0.04 0.08 0.16 0.11 0.2 1.3 0.6 1

m̅ KOH 5.050 5.050 5.004 5.050 5.050 5.004 5.004 5.050 5.050 5.050

m̅ B(OH)3 0 0 0 0 0 0 0 0 0 0

m̅ KVO3 0.573 0.573 0.571 0.573 0.573 0.571 0.571 0.573 0.573 0.573

m̅ CO2 2.685 2.806 2.846 3.028 3.113 3.153 3.354 3.515 3.770 3.988

B

5.695 5.695 5.695 5.695 5.736 5.695 5.695 5.695 5.695 5.695

1.376 1.376 1.376 1.376 1.385 1.376 1.376 1.376 1.376 1.376

0 0 0 0 0 0 0 0 0 0

BV1

5.964 5.741 5.741 5.741 5.741 5.741 5.964 5.741

0.876 0.858 0.858 0.858 0.858 0.858 0.876 0.858

BV2

5.724 5.724 5.724 5.283 5.283 5.724 5.283 5.724

1.391 1.391 1.391 1.349 1.349 1.391 1.349 1.391

identifier

ΔT = ±0.1 K; Δm̅ i/m̅ i = ±0.002; ΔpCO2/pCO2 = ±0.02 or 0.8 kPa (whichever is larger).

a

well as the activity of water. Details were given in a recent publication.34 It is given as21−23

ΔT = ±0.1 K; Δm̅ i/m̅ i = ±0.002; ΔpCO2/pCO2 = ±0.02 or 0.8 kPa (whichever is larger).

a

GE = f (I ) + nW RTM W ∗

where γ(m) CO2 is the activity coefficient (on the molality scale) of the neutral solute CO2 and mCO2 is the true molality of CO2 in water, m° = 1 mol (kg H2O)−1. Details on the calculation of the acitivity coefficient of CO2 and the activity of water are given below. Pitzer’s Molality Scale Based Equation for the Excess Gibbs Energy. Pitzer’s molality scale based equation for the excess Gibbs energy (GE) of aqueous electrolyte solutions is used to calculate the activity coefficients of all solute species, as

+

⎛ mi ⎞⎛ mj ⎞ ⎟⎜ ⎟B (I ) ij m◦ ⎠⎝ m◦ ⎠

∑ ∑ ⎜⎝

i≠W j≠W

∑ ∑ ∑ i≠W j≠W k≠W

⎛ mi ⎞⎛ mj ⎞⎛ mk ⎞ ⎜ ⎟⎜ ⎟⎜ ⎟μ ⎝ m◦ ⎠⎝ m◦ ⎠⎝ m◦ ⎠ ijk

(4)

MW* is the relative molar mass of water divided by 1000 and mi the concentration of component i expressed in molality. Bij and μijk are second and third osmotic virial coefficients for interactions between solute species in water. These osmotic virial coefficients depend on temperature. The second osmotic 13482



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The molality-based activity coefficient γ (m) is calculated from i eq 8: ⎡ ⎤ ⎛2⎞ I + ⎜ ⎟ ln(1 + b I )⎥ ln γi(m) = − Aϕzi 2⎢ ⎝b⎠ ⎣1 + b I ⎦ mj + 2 ∑ ◦ Bij (I ) j≠W m ⎤ ⎛ 2zi 2 ⎡ α2 ⎞ ⎢1 − ⎜1 + α1 I + 1 I ⎟ exp(− α1 I )⎥ 2 2 2 ⎠ α1 I ⎣⎢ ⎝ ⎦⎥ mj mk (1) mj mk ∑ ∑ ◦ ◦ βjk + 3 ∑ ∑ ◦ ◦ μijk j≠W k≠W m m j≠W k≠W m m

−

(8)

40

b is an adjustable parameter and usually set to 1.2. This is done here as well. The second osmotic virial coefficient Bij is calculated according to Pitzer, as shown in eq 9: Bij (I ) =

βi(0) ,j

2βi(1) ,j

+

α12I

[1 − (1 + α1 I ) exp( −α1 I )] (9)

α1 is an adjustable parameter and set to 2.0. “Symmetrical and unsymmetrical mixing terms”,23 as well as all parameters describing interactions between ionic species carrying charges of the same sign, are neglected. The binary (βi,j(0) and β(1) i,j ) and ternary (μi,j,k) interactions parameters are treated as symmetric (0) (1) (1) (i.e., β(0) i,j = βi,j ; βi,j = βi,j , μi,j,k = μi,k,j = μj,i,k = μj,k,i = μk,i,j = μk,j,i). The activity of water is calculated from the Gibbs−Duhem equation:

Figure 4. Partial pressure of CO2 above liquid mixtures of CO2 + B(OH)3 + KVO3 + H2O vs loading αCO2 = m̅ CO2/m̅ K+ Top panel shows the experimental results, using the synthetic method at 343 K ((●) BV1 and (■) BV2); solid line represents the prediction19 (m̅ KOH = 4.92 mol (kg H2O)−1). Bottom panel shows the experimental results, using headspace gas chromatography at 383 K ((△) BV1 and (◇) BV2); dashed line represents the prediction19 (m̅ KOH = 5.73 mol (kg H2O)−1).

⎧ ⎛ I1.5 ⎞ ⎪ ln aW = MW *⎨2Aϕ⎜ ⎟ ⎪ ⎝1 + b I ⎠ ⎩ ⎛ m ⎞⎛ mj ⎞ − ∑ ∑ ⎜ ◦i ⎟⎜ ◦ ⎟[βi(0) + βi(1) (− α1 I )] ,j ⎝ m ⎠⎝ m ⎠ , j i≠W j≠W −2

i≠W j≠W k≠W

virial coefficient Bij also depends on the ionic strength I, which is expressed on the molality scale. The ionic strength I is calculated using the charge zi (i.e., the electronic charge of ionic species i). 1 I = ∑ mizi 2 2 i (5)

⎛ ⎞1.5 1 e2 2πNAρW ⎜ ⎟ 3 ⎝ 4πε0εW kT ⎠

∑ i≠W

⎫ mi ⎪ ⎬ ◦⎪ m ⎭

Chemical Reaction Equilibrium in the Liquid Phase. The chemical equilibrium condition for a chemical reaction r (= I − XVIII) is given by eq 11: K r (T ) =

∏ aiν

i ,r

i

(11)

where Kr is the chemical reaction equilibrium constant for reaction r and νi,r is the stoichiometric factor of reactant i in reaction r (νi,r > 0 for a product and νi,r < 0 for a reactant). Kr is assumed to be dependent only on temperature, i.e., the influence of pressure is neglected. Water is treated as the solvent while CO2, B(OH)3, and all ionic species are treated as solutes on the molality scale, with water being the solvent. The equations for thermodynamic equilibrium are combined with the balance equations for each stoichiometric component i (i = CO2, H2O, B(OH)3, and KVO3) to calculate the speciation of the liquid phase (i.e., the true molalities mi of all solute species i and the true amount of water) for given temperature T and overall molalities of CO2 (m̅ CO2), B(OH)3 (m̅ B(OH)3), and KVO3 (m̅ KVO3) in the liquid phase.

(6)

Aϕ is the Debye−Hückel constant for the osmotic coefficient: Aϕ =

⎛ mi ⎞⎛ mj ⎞⎛ mk ⎞ ⎟⎜ ⎟⎜ ⎟μ − ⎝ m◦ ⎠⎝ m◦ ⎠⎝ m◦ ⎠ ijk

⎜

(10)

The function f(I) represents long-range electrostatic forces. It is based on the Debye−Hückel limiting law.40 ⎛ 4I ⎞ f (I ) = −Aϕ⎜ ⎟ ln(1 + b I ) ⎝b⎠

∑ ∑ ∑

(7)

The relative permittivity (εW) as well as the density (ρW) of pure liquid water are required for the calculation of Pitzer’s modification of the Debye−Hückel term f(I). They were approximated by the properties of pure, saturated liquid water.41,42 NA is the Avogadro constant, e the electronic charge, ε0 the vacuum permittivity, and k the Boltzmann constant. 13483



Article

Table 7. Chemical Reaction Equilibrium Constants (on the Molality Scale)a ln K r = A +

B T

+ C ln(T ) + DT +

E T2

reaction

A

B

C

D

E

T (K)

source

I II III IV V VI VII IX X XI XII XIII XIV XV XVI XVII XVIII

−1203.01 175.36 140.932 176.231 −15.539 −39.47 −34.1 −14.999 −47.720 −18.130 0.8778 −21.485 −42.167 −12.058 −25.685 13.342 26.474

68359.6 −7230.6 −13445.9 −9118.00 219.36 −122.04 0 −1738.06 1083.93 251.94 1200.18 2193.35 1484.18 8369.00 12783.68 3863.57 6452.61

188.444 −30.6509 −22.4773 −30.221 0 0 0 0 0 0 0 0 0 0 0 0 0

−0.206424 0.01315 0 0.01768 0 0 0 0 0 0 0 0 0 0 0 0 0

−4712910 −372805 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

273−673 273−523 298−573 273−428 298−383 298−383 298 274−357 274−357 274−357 274−357 274−357 274−357 274−357 274−357 274−329 274−357

Patterson et al.44 Patterson et et al.45 Fisher and Barnes43 this workb this workc this workc Ingri24 McCann et al.28 McCann et al.28 McCann et al.28 McCann et al.28 McCann et al.28 McCann et al.28 McCann et al.28 McCann et al.28 McCann29 McCann29

a

All temperatures shown in Kelvin. bBased on experimental data by Manov et al.46 (273−333 K), Owen and King47 (278−328 K), and Mesmer et al.48 (373−573 K). cBased on experimental data by Ingri24 (293 K) and VLE data from this work.

Model Parameters. Chemical Reaction Equilibrium Constants. The equilibrium constants for chemical reactions I−XVIII are given in Table 7. The chemical reaction equilibrium constants for reactions I−III, V, and IX−XVIII were adopted from the literature.24,28,43−45 The influence of temperature on the equilibrium constant for the formation of B(OH)4− (reaction IV) was determined from the experimental data by Manovet al.46 (273−333 K), Owen and King47 (278− 328 K), and Mesmer et al.48 (373−573 K). Based on the results from Ingri,24 the chemical reaction equilibrium constants for reactions VI and VII were slightly adjusted to the new experimental gas solubility data, to cover the range of temperature of interest here. The chemical reaction equilibrium constants for the various reactions with vanadate species were all taken from recent investigations by McCann et al.28 (reactions IX−XVI) and McCann29 (reactions XVII and XVIII). The correlation equations for reactions IX−XVIII are based on experimental data for temperatures in the range of 274−357 K, but the correlations were also used for 383 K. Henry’s Constant for the Solubility of CO2 in Water and Partial Molar Volumes at Infinite Dilution of CO2 in Water. Henry’s constant of CO2 in water was taken from Rumpf and Maurer.36 It is given in Table 8. The partial molar volume of CO2 dissolved in water at infinite dilution (n∞ CO2) was calculated as recommended by Brelvi and O’Connell.49 The numerical values are given in Table 9. Properties of Pure Water. The vapor pressure of pure water (psW) was calculated from the equation by Saul and Wagner.41

Table 9. Partial Molar Volume of CO2 in Water at Infinite 49 Dilution v∞ CO2

A T

B

C

D

T (K)

source

−9624.4

−28.749

0.01441

192.876

273−473

Rumpf and Maurer36

a (m) kH,CO2

343 383

35.4 39.5

Table 10. Second Virial Coefficientsa T (K)

BCO2,CO2 (cm3/mol)

BCO2,H2O (cm3/mol)

BH2O,H2O (cm3/mol)

343 383

−91.2 −69.3

−136 −110

−647 −424

a

Data taken from refs 50 and 51.

Interaction Parameters in Pitzer’s Equation. Pitzer’s equation for the excess Gibbs energy of aqueous electrolyte solutions considers temperature-dependent parameters, binary and ternary, for interactions between species that carry electric charges of different signs. The extension used here also requires such parameters between neutral solutes and ionic species. Therefore, there is an enormous number of binary and ternary interaction parameters in the expression for the excess Gibbs energy of an aqueous solution of CO2, KOH, B(OH)3, and KVO3. Some of those parameters are already available from previous studies on the solubility of CO2 in aqueous solutions of K2CO3 (see the work of Pérez-Salado Kamps et al.19). The

+ B ln(T ) + CT + D

A

3 v∞ co2 (cm /mol)

The relative permittivity (εW), which is required in Pitzer’s equation for the excess Gibbs energy, was adopted from Bradley and Pitzer.42 Vapor-Phase Fugacity Coefficients. The virial equation of state, which was truncated after the second virial coefficient, was used to calculate the vapor-phase fugacity coefficients. Pure-component second virial coefficients were calculated from a correlation based on data recommended by Dymond.50 The mixed second virial coefficient for CO2 and H2O was calculated as recommended by Hayden and O’Connell.51 All required second virial coefficients are given in Table 10.

Table 8. Henry’s Constant of CO2 in Water (on the Molality Scale)a (m) ln kH,CO = 2

T (K)

is given in MPa. All temperatures are given in Kelvin. 13484



Article

Table 11. Interaction Parameters in Pitzer’s GE Equationa Par = A par +

Bpar T

C par

+

T2

Apar

Bpar

βK(0) + ,OH−

1.298 × 10−1

0

0

Pitzer and Mayorga58

βK(0) + ,CO2 −

3.8621 × 10−1

−82.857

0

Pérez-Salado Kamps et al.19

parameter

Cpar

source

3

4.9547 × 10−1

(0) βCO ,K+

−292.86

49047.9


2

1.0662 × 10−1

−40.439

0


1.788 × 10−1

0

0

this work

−2.397 × 10−1

0

0

this work

−1.796 × 10−1

0

0

this work

βK(0) + ,B O (OH)−

−7.038 × 10−2

0

0

this work

βK(0) + ,VO (CO

−2.479 × 10−1

0

0

this work

3.20 × 10−1

0

0


βK(0) + ,HCO− 3

(0) βCO ,B(OH) 2

3

(0) βCO ,B O (OH)2 − 2 4 5

4

(0) βCO ,VO (CO 2

3− 2 )2

4

3 3

4

3− 2 )2

4

βK(1) + ,OH− βK(1) + ,HCO−

8.19

−2648

0


βK(1) + ,CO2 −

2.1975 × 101

−6974.6

0


3

3

μK+,K+,CO2 −

−8.72 × 10−3

2.69

0


μK+,K+,HCO−

−3.48 × 10−4

0.215

0


0

0


0


3

3

1.367 × 10−3

μK+,K+,OH− μCO

+ 2 ,CO2 ,K

−3.9588 × 10

12.008

μCO2 −,HCO−,K+

−1.18 × 10−5

0.2181

0


μCO

−1.931 × 10−2

0

0

this work

3

3

+ 3− 2 ,K ,VO4 (CO2 )2

a

−2

All temperatures are given in Kelvin.

Comparison of New Experimental Data with Literature Data and Model Results. Comparisons between the new experimental data and the model results are shown in Figures 5 and 6, where the partial pressure of CO2 is plotted versus the loading αCO2 (αCO2 = m̅ CO2/m̅ K+). In Figure 5, the results for solvents BV1 and BV2 are given. The prediction for solvents BV1 and BV2 is based on the composition of the measurements in the synthetic method. In the low-pressure range, the influence of the different compositions of BV1 (BV2) − see Tables 4−6 − on the partial pressure of CO2 over the solution is negligible and, hence, is not discussed here. Figure 6 shows the experimental data for the solvents B and V in the low-pressure range. The average relative deviation between the experimental data for the total pressure (partial pressure of CO2) and the correlation is given in Table 12. These deviations are larger than the experimental uncertainty (between 5% and 19%). We assume that this can be attributed to different causes. For example, the equilibrium constants for the oligomers of boric acid were only known at 298 K. Good measurements of these equilibrium constants might give a better fit for the borate subsystem. Also the equilibrium constants for the reactions that involve vanadates are only available up to 357 K. Furthermore, the VLE data was only measured at two concentrations for borates and vanadates and at one concentration of potassium hydroxide, at only two temperatures.

number of remaining, unknown interaction parameters is still too high to be reasonably adjusted to the new experimental data for the solubility of CO2 in activated solutions of K2CO3. However, only some of the unknown interaction parameters are really important. Therefore, the most important, still-missing interaction parameters were selected in sensitivity studies and, finally, five binary parameters and one ternary parameter were adjusted to the new experimental results for the solubility of CO2 in aqueous solutions of K2CO3 + B(OH)3 and/or KVO3: three binary parameters for interactions between molecular CO2 on one side and either boric acid or a boron-containing anion or a carbonato-vanadate complex on the other side, two binary parameters between potassium on one side and either a boron-containing anion or a carbonato-vanadate complex on the other side, and a ternary parameter for interactions between CO2, potassium, and a carbonato-vanadate complex. Since the new experiments were performed only at two temperatures (343 and 383 K), the influence of temperature on the newly adjusted interaction parameters had to be neglected. Therefore, the set of parameters is considered to be preliminary. It should be revised as soon as new experimental datain particular, data for other temperaturesbecome available. All non-neglected interaction parameters (i.e., those taken from the literature and the newly adjusted ones) are given in Table 11. 13485



Article

Figure 6. Partial pressure of CO2 above liquid mixtures of CO2 + B(OH)3 + KVO3 + H2O vs loading αCO2 (αCO2 = m̅ CO2/m̅ K+). Top panel shows experimental results for B, using headspace gas chromatography ((⬡) 343 K and (⊞) 383 K); data for the model is represented as a solid line. Bottom panel shows experimental results for V, using headspace gas chromatography ((▽) 343 K and (⊕) 383 K); data from the model is represented as a solid line.

Figure 5. Partial pressure of CO2 above liquid mixtures of CO2 + B(OH)3 + KVO3 + H2O vs loading αCO2 (αCO2 = m̅ CO2/m̅ K+). Top panel shows experimental results for BV1 using headspace gas chromatography ((○) 343 K and (△) 383 K) and using the synthetic method ((●) 343 K and (▲) 383 K); data from the model is represented as a solid line). Bottom panel shows experimental results for BV2 using headspace gas chromatography ((□) 343 K and (◇) 383 K) and using the synthetic method ((■) 343 K and (◆) 383 K); data from the model is represented as a solid line).

Table 12. Summary of Deviations (dev.) between Experimental Data and Model Results for the Total Pressure p (Synthetic Method) and the Partial Pressure of CO2 pCO2 (Headspace Gas Chromatography Method)a.

Figure 7 shows a comparison of the experimental results for the solubility of CO2 in an aqueous solution of K2CO3 (m̅ K2CO3 = 3.1 mol (kg H2O)−1) and B(OH)3 (m̅ B(OH)3 = 0.5 and 0.85 mol (kg H2O)−1) by Endo et al.11 and predictions from the model. The partial pressure over the solution is plotted versus the “shifted loading”, as given by Endo et al.11 The calculation results agree with the experimental data within the scattering of these experimental results. This is not self-evident as the model parameters were neither fit to these data, nor do the range of concentrations and temperatures of the investigation by Endo et al.11 agree with the investigations of the present work. The experimental results by Schäfer et al.12 for the solubility of CO2 in an aqueous solution of KOH (m̅ KOH = 3.05 mol (kg H2O)−1) and B(OH)3 (m̅ B(OH)3 = 0.238 mol(kg H2O)−1) are shown and compared to model predictions in Figure 8. The error bars are only shown when the experimental uncertainty exceeds the size of the symbol. The model overestimates the partial pressure of CO2 by a factor of up to 2 in the highpressure region. Figure 9 shows a comparison between the experimental results by Schäfer et al.13 for the solubility of CO2 in an

Synthetic Method T (K)

identifier

343

B V BV1 BV2

383

averageb

B V BV1 BV2

Headspace GC

mean rel. dev. (%)

max. abs. dev. (kPa)

mean rel. dev. (%)

5.3 5.4

0.9 0.8 0.2 0.5

8 10 19 16

7.5 10.5

0.4 0.7 0.5 0.4

7 19 10 12

7.2

12

a

For partial pressures of

Solubility of Carbon Dioxide in Activated Potash ... - ACS Publications

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