Ind. Eng. Chem. Res. 2006, 45, 2531-2545
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Kinetics of Carbon Dioxide Absorption into Aqueous Potassium Carbonate and Piperazine J. Tim Cullinane and Gary T. Rochelle* Department of Chemical Engineering, The UniVersity of Texas at Austin, Austin, Texas 78712
The absorption rate of CO2 was measured in a wetted-wall column in 0.45-3.6 m piperazine (PZ) and 0.03.1 m potassium carbonate (K2CO3) at 25-110 °C. A rigorous kinetic model was used to model the data and interpret diffusivities and rate constants. The rate approaches second-order behavior with PZ and is highly dependent on other strong bases. In 1 M PZ, the overall rate constant is 102 000 s-1, 20 times higher than in monoethanolamine. The activation energy is 35 kJ/mol, similar to other amine-CO2 reactions. Rate constants for contributions of carbonate, PZ carbamate, and water to the rate were determined according to base catalysis theory. The addition of neutral salts to aqueous PZ increases the apparent rate constant. In 2.7 M NaCl/0.6 M PZ, the overall rate constant is increased by a factor of 7. Ionic strength effects were accounted for within the rigorous model of K+/PZ mixtures. The absorption rate in concentrated K+/PZ mixtures is up to 3 times faster than in 30 wt % monoethanolamine. At low temperatures and low CO2 loadings, a pseudo-first-order approximation adequately represents the absorption rate. At high loadings, the reaction approaches instantaneous behavior but is still influenced by reaction kinetics. Under industrial conditions, gas film resistance may account for >80% of the total mass transfer resistance at low loadings. Introduction The removal of carbon dioxide from gas streams by aqueous absorption is important in both natural gas treating and ammonia production. Aqueous potassium carbonate (K2CO3) promoted by amines are sometimes used as the solvent in these processes. One potential application of the aqueous absorption technology is CO2 capture from combustion flue gas, particularly coal-fired power plants. Though solvents are generally effective in removing CO2, performance is often limited by the absorption rate of CO2 into the solvent. An understanding of the fundamental mechanisms dictating the rate of absorption is critical to the development of more efficient capture processes. Several amines have been developed for application to CO2 removal. Primary amines, such as monoethanolamine (MEA) or diglycolamine (DGA), are known to have fast absorption rates.1-3 Secondary amines, including diethanolamine (DEA) and diisopropanolamine (DIPA), are limited in application due to slower absorption rates but often used to promote absorption rates in K2CO3-based solvents based on favorable thermodynamic characteristics.4-7 Other researchers have identified numerous amine blends possessing favorable absorption properties.8,9 Previous work has also identified piperazine (PZ) as an effective promoter of CO2 absorption rates in methyldiethanolamine (MDEA) and K2CO3.9-11 This work focuses the development of a concentrated K+/ PZ mixture for CO2 capture from flue gas. The rate of CO2 absorption is reported for 0-6.2 m K+ and 0.45-3.6 m PZ at 25-110 °C. The rate of absorption is also quantified in the presence of neutral salts. A rigorous kinetic model was developed to determine rate constants and diffusion coefficients as regressed from experimental data. The completed model describes the absorption rate of CO2 into K+/PZ mixtures over a comprehensive range of conditions. Approximations to the rigorous solution have been developed, and the application of this solvent to industrial conditions has been investigated. * Corresponding author. Phone: (512)471-7230. Fax: (512)4757824. E-mail:
[email protected].
Figure 1. Schematic of the wetted-wall column.
Experimental Methods The rate of CO2 absorption was measured in a wetted-wall column constructed by Mshewa12 and used in previous investigations of amine solutions.9-11,13 The gas-liquid contactor, shown in Figure 1, was constructed from a stainless steel tube 9.1 cm long and 1.26 cm o.d., giving a total contact area of 38.5 cm2. The column was surrounded by a thick-walled glass cylinder, giving a hydraulic diameter of 0.44 cm. A second glass cylinder enclosed the chamber, containing an insulating layer of heat transfer fluid. A flowsheet of the apparatus is shown in Figure 2. The amine solvent was stored in a 1400 cm3 reservoir. After contacting the gas phase, the solvent was collected and pumped back to the reservoir. A liquid rotameter indicated the volumetric flow rate of the liquid, typically 2-3 cm3/s. The inlet and outlet liquid temperatures were measured by Type-J thermocouples.
10.1021/ie050230s CCC: $33.50 © 2006 American Chemical Society Published on Web 09/16/2005
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Ind. Eng. Chem. Res., Vol. 45, No. 8, 2006
in terms of a normalized flux, or kg′, a mass transfer coefficient for the partial pressure driving force across the liquid film:
Ekol NCO2 ) (P - PCO2/) ) k′g(PCO2,i - PCO2/) HCO2 CO2,i
(3)
The normalized flux is essentially the liquid-phase mass transfer coefficient with a gas-phase driving force and can be directly related to the kinetics of the absorption process. The normalized flux was calculated from the following expression:
k′g )
Figure 2. Flowsheet of the wetted-wall column experiment.
Nitrogen and CO2 were mixed and fed to the column through mass flow controllers. The CO2 content was varied between 0.01 and 10% of the total flowrate. The gases were saturated with water at the operating temperature of the column prior to entering the wetted-wall column. The gas then entered the column, counter-currently contacting the liquid film. The gas exited the column and was dried by a condenser and a drying column containing magnesium perchlorate to protect downstream gas analyzers. Total pressure in the column was controlled between 340 and 480 kPa by a needle valve on the gas outlet. The CO2 concentration in the outlet gas was measured by Horiba 2000 infrared CO2 gas analyzers. The analyzers were calibrated prior to each experiment by bypassing the wettedwall column and adjusting the CO2 partial pressure to give known concentrations. During each experiment, liquid samples were taken from the wetted-wall column. A liquid CO2 concentration was determined by total inorganic carbon analysis.14 Bishnoi15 correlated the gas film mass transfer coefficient (kg) in the wetted-wall column using SO2 absorption into 0.1 M NaOH. The coefficient was corrected to represent CO2 by accounting for changes in gas diffusivity. Experiments in this work were run with 5-7 L/min of gas. Values for kg were on the order of 3 × 10-9 kmol/m2‚Pa‚s, giving 25-45% gas film resistance for typical experiments. Pacheco13 correlated the liquid film mass transfer coefficient o (kl ) of the wetted-wall column using CO2 desorption from water and ethylene glycol. Most experiments in this work had values of kol between 0.007 and 0.014 cm/s. During each experiment, several data points were collected at a steady-state flux with various bulk gas partial pressures. The flux of CO2 was calculated and characterized by the overall gas-phase mass transfer coefficient (KG). Because the rate of CO2 absorption is small relative to the total CO2 concentration of the liquid, PCO2* may be assumed constant for each experiment:
NCO2 ) KG(PCO2,b - PCO2*)
(1)
The bulk gas partial pressure was represented as the log mean average of the inlet and outlet partial pressures:13
PCO2,b )
PCO2,in - PCO2,out ln(PCO2,in/PCO2,out)
(2)
An expression of the liquid film resistance, including the kinetics of CO2 absorption, is commonly written in terms of an enhancement factor (E). In systems much faster than physical absorption, it becomes more convenient to express enhancement
(
)
1 1 KG kg
(4)
Modeling Modeling Mass Transfer. Bishnoi and Rochelle9 created a model to calculate the rate of CO2 absorption into an amine solvent from a given solution composition and gas-phase partial pressure of CO2. The model corrects for gas film resistance and uses the eddy diffusivity theory16,17 to describe mass transfer with chemical reaction in the liquid boundary layer. The concentration profile of CO2 through the liquid is given by
[
]
∂[CO2] ∂ (DCO2 + x2) - rCO2 ) 0 ∂x ∂x
(5)
where rCO2 is the rate of reaction of CO2. The proportionality constant () is calculated from the liquid film mass transfer coefficient:
( )
π ) 2
2
kol
xDCO
(6)
2
Glasscock and Rochelle18 have shown that this theory adequately describes absorption by amines and gives a solution equivalent to surface renewal and penetration theory under most conditions. A numerical solution to the problem is obtained using an equation transformed into a dimensionless spatial variable (r). The transformation, as proposed by Versteeg,19 is
(x )
2 r ) arctan x π
Di
(7)
Details of the solution by finite difference methods can be found in Bishnoi15 and Bishnoi and Rochelle.9 Given a gas-phase CO2 partial pressure, the solution requires knowledge of equilibrium conditions in the bulk solution, diffusive properties of transported species, and rates of contributing reactions. Modeling Solution Equilibrium. Cullinane and Rochelle20 developed a thermodynamic model based on the electrolyte NRTL model21 to describe the behavior of aqueous K+/PZ mixtures. This system can be represented with seven equilibrium reactions:
CO2(aq) + 2H2O a HCO3- + H3O+
(8)
HCO3- + H2O a CO32- + H3O+
(9)
2H2O a H3O+ + OH-
(10)
PZH+ + H2O a PZ(l) + H3O+
(11)
PZ(l) + CO2(aq) + H2O a PZCOO- + H3O+
(12)
Ind. Eng. Chem. Res., Vol. 45, No. 8, 2006 2533
H+PZCOO- + H2O a PZCOO- + H3O+
(13)
PZCOO- + CO2(aq) + H2O a PZ(COO-)2 + H3O+ (14) A rigorous model of CO2 absorption into a solvent requires specific knowledge of the equilibrium behavior in the bulk solution to calculate the proper driving force for reaction. In this work, the activity-based equilibrium constants for these reactions are used with activity coefficients to determine the equilibrium speciation of the bulk solution.20 Four concentrationbased equilibrium constants, defined below, are calculated from bulk solution properties and used to describe the reversible reactions within the boundary layer. The implicit assumption is that activity coefficients and water concentration do not change from the gas-liquid interface to the bulk solution:
KHCO3- )
[HCO3-] [CO2][OH-]
Kw ) [H3O+][OH-] KPZCOO- ) KPZ(COO-)2 )
[PZCOO-][H3O+] [PZ][CO2] [PZ(COO-)2][H3O+] [PZCOO-][CO2]
(15) (16) (17)
(18)
Modeling Reaction Kinetics. Carbamate Formation. Caplow22 proposed a mechanism of the CO2 reaction with primary and secondary amines. Researchers often interpret this as a twostep, “zwitterion” mechanism in which CO2 reacts with the amine to form a net-neutral, locally charged intermediate (eq 19), followed by the extraction of the proton by a base, such as water (eq 20).
where kAm-b represents the combination of kf, kr, and kb. For example, if PZ is the amine and water is the base, the nomenclature is
kPZ-H2O )
kfkH2O . kr
(24)
This interpretation is equivalent to a single-step, termolecular mechanism,24,25 which has also been proposed for amine reactions with CO2. While difficult to make conclusions concerning the physical mechanism, the termolecular equation is attractive in its simplicity and has been chosen to represent the data in this work. Several investigations of amine systems utilize the zwitterion mechanism in its entirety to describe amine kinetics (eq 21), but the values of kf often have questionable significance or little impact on the reaction rate.26-29 With eq 23, a termolecular interpretation, varying orders of reaction are obtained depending on bases included. Regardless of the chosen mechanism, an equally effective representation of the reaction rate is possible. The reaction of CO2 with the amine to form carbamate species accounts for a majority of the absorption rate. The following amine reactions, considered relevant from the chosen mechanistic framework, are included in the model:
[
PZ + CO2 + kPZ-OH-
OH- {\} PZCOO- + H2O
[
kPZ-H
2O
H2O {\} PZCOO- + H3O+ kPZ-PZ
PZ {\} PZCOO- + PZH+ kPZ-CO
2-
CO32- {\} PZCOO- + HCO33
kPZ-PZCOO-
PZCOO- {\} PZCOO- + H+PZCOO-
PZCOO- + CO2 +
]
kPZCOO--H
2O
H2O {\} PZ(COO-)2 + H3O+
The rate of reaction can be written as the following expression: 23
[Am][CO2] rCO2 ) kr 1 + kf kf kb[b]
(21)
∑
The reaction order obtained by this expression is variable. If kb f ∞, the reaction rate is first-order with respect to the amine:
rCO2 ) kf[Am][CO2]
(22)
The mechanism also describes secondary amine kinetics, which frequently approach second-order behavior with respect to the amine. Assuming Σkb[b] , kr, the zwitterion mechanism can be simplified to
rCO2 )
∑b kAm-b[Am][b][CO2]
(23)
kPZCOO--PZ
PZ {\} PZ(COO-)2 + PZH+ kPZCOO--CO
2-
CO32- {\} PZ(COO-)2 + HCO33
kPZCOO--PZCOO-
PZCOO- {\} PZ(COO-)2 + H+PZCOO-
(25)
]
(26)
Because the concentration of hydroxide is small when PZCOOis present, hydroxide was not considered to be a contributing base in eq 26. All proton exchange reactions were considered to be at equilibrium at all times. The resulting expressions for the reversible reactions of CO2 with PZ and PZCOO- to produce PZCOO- and PZ(COO-)2 respectively are
r)
(
∑b kPZ-b[b] [PZ][CO2] - K
Kw
)
[PZCOO-]
PZCOO-
[OH-]
(27)
2534
r)
Ind. Eng. Chem. Res., Vol. 45, No. 8, 2006
(
∑b kPZCOO -b[b] [PZCOO -
-
][CO2] -
)
The rate constants for amine-catalyzed bicarbonate formation were assumed equal to that of the MDEA-catalyzed reaction given by Littel:32
[PZ(COO-)2]
Kw
-
KPZ(COO-)2
[OH ]
(28)
The temperature dependence of these rate constants is given by
k∞ ) ko exp
( (
-∆Ha 1 1 R T (K) 298.15
))
kOH-
CO2 + OH- {\} HCO3-
(30)
+
-
PZ + CO2 + H2O {\} PZH + HCO3 kPZCOO-
-
+
-
-
The formation of bicarbonate in this manner is typically much slower than the reaction of CO2 with amines and has little effect on the absorption rate under most conditions but must be included to properly model equilibrium in the boundary layer. A generalized, second-order rate expression for these reactions can be written:
r)
(
∑b kb[b] [CO2] - K
)
[HCO3-]
HCO3-
-
[OH ]
(33)
where b, in this case, represents the active catalyst OH-, PZ, or PZCOO-. The rate constant for CO2 reacting with OH- is well-defined in the literature and is given as a function of ionic strength:31
∑i κiIi
(34)
2382.0 T (K)
(35)
∞ log kOH- ) log kOH - +
where ∞ log kOH - ) 11.916 -
and κi is an ion specific parameter and Ii is ionic strength calculated as
1 Ii ) (Cizi2) 2
)
(
(36)
where Ci is the molar concentration and zi is the charge or species i.
)
m3 -5771.0 ) 1.34 × 109 exp kmol‚s T (K)
(37)
An ionic strength correction is made to all amine rate constants (eqs 25, 26, and 37) according to the theory of salt effects, presented later. The correction is
k ) k∞ exp(0.3I)
(38)
where I is the summation of ionic strength. Physical Property Estimation. The N2O analogy33-35 was used to estimate the physical solubility of CO2. The solubility of N2O in K+/PZ mixtures was measured in an apparatus built by Al-Jauied36 and is similar to that used by Al-Ghawas et al.37 Results of these experiments14 were included in the regression of significant parameters in the thermodynamic representation of the solution20 and are implicit in thermodynamic calculations. Values are calculated and reported with the experimental data. Similarly, the diffusion coefficient of CO2 in solution was estimated by the N2O analogy. This method has been used previously in several studies on CO2 absorption.33,34,38 Data from Versteeg and van Swaaij39 were correlated by Pacheco,13 giving expressions for the diffusivity of CO2 and N2O in water:
( (
) )
DCO2,w (cm2/s) ) 0.02397 exp
-2122.2 T (K)
(39)
DN2O,w (cm2/s) ) 0.04041 exp
-2288.4 T (K)
(40)
(31)
PZCOO + CO2 + H2O {\} H PZCOO + HCO3 (32)
1
(
(29)
where k∞ represents the rate constant in the absence of significant ionic strength, ko is the specific rate constant at 298 K, and ∆Ha is the activation energy for the specific reaction. The values of all regressed model parameters from this work are presented in Table 1. Parameters include the above rate constants, an activation energy (assumed constant for all aminebase reactions), and a correction for the diffusivity of ions. Bicarbonate Formation. On the basis of work with tertiary amines and experience with base-catalyzed reactions, amines and hydroxide are expected to catalyze the formation of bicarbonate ion.15,30 Three parallel reactions are included in the model to account for this effect:
kPZ
kAm
Pacheco also correlated DN2O in amine solutions to viscosity and temperature by
T (K) DN2O,s (cm2/s) ) 5.533 × 10-8 µs (cP)0.545
(41)
The diffusivity of CO2 in amine solutions was estimated by
DCO2,w DCO2,s ) DN2O,s DN2O,w
(42)
For fast kinetics, the diffusion of the amine and products in the gas-liquid interface may limit the overall reaction rate. The Wilke-Chang correlation40 was used to estimate the diffusion coefficient of the amine and products as a function of solvent viscosity (µsol), temperature, and solvent specific parameters:
D∞Am )
1.17 × 10-13(ξsolMsol)0.5T V0.6 Amµsol
(43)
where ∞ denotes the diffusion coefficient of the amine at infinite dilution in water, VAm indicates molar volume, Msol is the molecular weight of the solvent, and ξsol represents a solvent specific parameter (2.6 for water). This equation predicts the diffusivity of amines and organic electrolytes to within 10%.41-43 The diffusion coefficients of all ions in this model were considered equal to that of PZCOO-. The molar volume of PZCOO- was estimated to be 0.1311 m3/kmol by the group contribution method of Le Bas.44 The extrapolation of D∞ to higher concentrations has been determined to be dependent on the specific solute-solvent
Ind. Eng. Chem. Res., Vol. 45, No. 8, 2006 2535 Table 1. Regressed Constants for Modeling CO2 Absorption into K+/PZ i
pKa a
i × 10-3 b
σ × 10-3 c
relation
o d kPZ-H 2O o kPZ-PZCOOo kPZ-PZ o kPZ-CO 23 o kPZ-OH o d kPZCOO --H O 2 o kPZCOO--PZCOOo kPZCOO --PZ o kPZCOO --CO 23
-1.74 9.51 10.30 10.33 15.74 -1.74 9.51 10.30 10.33
0.6 48.9 70.1 145.1 1857 0.4 66.3 95.1 96.7 35.02 0.00151
0.09
regressed from aqueous PZ o + 0.457(pKa,PZCOO- - pKa,PZ) ) ln kPZ-PZ regressed from aqueous PZ regressed from K+/PZ regressed from aqueous PZ o 2) ln kPZCOO --CO 2- + 0.457(pKa,H2O - pKa,CO3 ) 3 o 2) ln kPZCOO --CO 2- + 0.457(pKa,PZCOO - pKa,CO3 ) 3 o 2) ln kPZCOO --CO 2- + 0.457(pKa,PZ - pKa,CO3 ) 3 regressed from K+/PZ regressed from aqueous PZ regressed from K+/PZ
∆Ha βe
9.6 486
2.0
a pK of the extracting base. b Rate constants given as m6/kmol2‚s. ∆H given as kJ/kmol. c Standard deviation of the regressed value. d Regressed as a a pseudo-first-order rate constant with [H2O] ) 55.55 kmol/m3. e Parameter for diffusivity correction.
interaction. In general, the diffusion coefficient of amines can be related to D∞ by a ratio of viscosity in water and in the amine solvent, µw and µs, respectively:39,45,46
DAm )
D∞Am
() µw µs
0.6
xDCO k2[Am]b(P 2
HCO2
CO2,i
- PCO2/)
(45)
where [Am]b is the concentration of the amine in the bulk liquid. The resulting expression for the normalized flux is
k′g,PFO )
xDCO k2[Am]b. 2
HCO2
(46)
The PFO approximation will apply with a fast, but not instantaneous, reaction and a low flux of CO2 that does not deplete the amine or accumulate reaction products at the gasliquid interface. Another limiting case suitable for simplification is when all reactions can be considered instantaneous with the application of a small driving force, so that the diffusion of reactants and products dictates the absorption rate. This condition will be referred to as the global instantaneous case, designated by GBL,INST. An approximate solution to this condition is given by
NCO2,GBL,INST ) kol
x
NCO2,PZ,INST )
lim
∑Am∑b(kAm-bf∞)
NCO2
(48)
(44)
The viscosity of K+/PZ solutions was measured and correlated in Cullinane.14 Approximations. It is often useful, and appropriate, to consider simplified solutions to the rigorous mass transfer equation that are valid over limited conditions. One common approximation for CO2 absorption by amines is a pseudo-firstorder (PFO) simplification where the concentration of all species except CO2 is assumed constant across the liquid boundary layer. Solving eq 5 for flux and writing in terms of gas-phase concentrations gives
NCO2 )
reaction rate. An instantaneous flux for the formation of amine carbamates can be defined:
DProd∂[CO2]T (P - PCO2/) DCO2 ∂P / CO2,i
(47)
CO2
where DProd represents the diffusion coefficients of the reaction products and [CO2]T is the concentration of all CO2 species.47 Other instantaneous reactions can be considered to determine the contribution of a particular class of reactions to the overall
A comparison to the global instantaneous case reveals the potential limiting reactions under given conditions. Results and Discussion CO2 Absorption into Aqueous Piperazine. Bishnoi and Rochelle48 measured the rate of CO2 absorption into 0.2 and 0.6 M PZ at 25 to 60 °C and zero loading and reported a rate constant assuming first-order rate dependence on PZ. The reported rate constant is 53 700 m3/kmol‚s at 25 °C with an activation energy of 33 600 kJ/kmol. In this work, the absorption rate was measured in 0.45-1.5 m PZ at 25 and 60 °C and zero loading. Data were also obtained in 0.6 m PZ containing 0.15 m KOH. Table 2 provides a summary of the experiments. All data on aqueous PZ is represented as an apparent secondorder rate constant (k2,app) in Figure 3. This is equivalent to a PFO simplification in which the rate is first-order with PZ as given by eq 45. The dependence of k2,app on PZ concentration shows that the reaction is not first-order with PZ as had been previously assumed. As PZ concentration is increased above a concentration of 0.5 M, the reaction order approaches 2. The curvature at low PZ concentrations is due to contributions of water as the dominant catalyzing base at low PZ concentrations. In addition to the second-order dependence on the amine, a significant rate enhancement is observed with hydroxide in solution. With 0.15 m KOH, the flux increases by a factor of 2 in 0.6 m PZ solution. This suggests that strong bases contribute to the overall reaction rate and must be included in the rate expression, consistent with the mechanism given by eq 23. Data on aqueous PZ from Bishnoi and Rochelle48 and this work were combined in a regression of PZ rate constants for CO2 absorption into aqueous PZ. The regressed parameters, reported in Table 1, are kPZ-PZ, kPZ-H2O, kPZ-OH, and ∆Ha. Values of the flux calculated (Table 2) were within approximately 20% of the measured values. The rate constant found for PZ is consistent with previous work at similar concentrations. In 0.6 M PZ, the overall rate constant is 61 320 s-1 compared to 53 700 s-1 as given by Bishnoi and Rochelle.48 The activation energies were assumed equal for all rate constants, with a regressed value of 35 kJ/mol, comparable to Bishnoi and Rochelle.48 The curves in Figure 3 represent a model correlation under typical experimental conditions. The model correlation of the
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Ind. Eng. Chem. Res., Vol. 45, No. 8, 2006
Table 2. Absorption Rate of CO2 into Aqueous PZ T (°C)
[PZ] (m)
25
0.45 0.68 1.20
1.50
0.60b
60
a
1.20
loading (mol of CO2/mol of PZ)
PCO2,b (Pa)a
kg × 109 (kmol/ Pa‚m2‚s)
kol × 105 (m/s)
KG/kg (%)
CO2 removal (%)
HCO2 × 10-6 (m3‚Pa/ kmol)
DCO2 × 109 (m2/s)
0.008 0.008 0.008 0.012 0.012 0.012 0.008 0.010 0.013 0.016 0.019 0.007 0.007 0.007 0.005 0.000 0.000 0.000 0.000 0.009 0.010 0.012 0.015 0.017
51 98 167 448 65 356 34 64 287 93 247 50 302 93 422 55 287 181 87 32 58 215 334 238
2.99 3.01 2.98 2.61 2.58 2.59 2.54 2.70 2.89 2.53 2.71 2.53 2.59 2.48 2.61 2.23 2.21 2.22 2.23 2.73 2.73 3.04 3.45 3.40
7.9 8.0 8.0 9.0 9.0 8.9 8.7 8.7 8.7 8.9 8.7 8.2 8.2 8.2 8.2 9.5 9.5 9.5 9.6 11.7 11.8 12.0 11.8 11.9
50.8 44.5 40.1 51.0 58.5 53.1 58.0 61.3 58.0 60.4 59.5 66.6 67.0 69.9 64.3 80.8 72.4 75.2 79.4 60.3 73.0 66.9 62.1 65.3
40.1 36.1 32.8 38.9 39.3 40.3 43.6 46.4 44.3 46.2 45.5 49.4 48.8 50.2 46.9 54.4 51.7 53.5 54.8 47.5 54.0 50.9 47.3 48.9
3.01 3.03 3.04 3.35 3.35 3.35 3.12 3.14 3.18 3.25 3.25 3.49 3.49 3.49 3.49 3.22 3.22 3.24 3.25 6.40 6.51 6.65 6.62 6.72
1.83 1.84 1.85 1.85 1.85 1.85 1.43 1.44 1.46 1.49 1.50 1.46 1.46 1.46 1.46 1.82 1.82 1.83 1.84 3.28 3.36 3.45 3.43 3.50
NCO2 × 107 (kmol/m2‚s) measured predicted 0.78 1.31 2.00 5.86 0.82 4.78 0.47 1.06 4.78 1.39 3.95 0.84 5.24 1.60 7.09 0.90 4.52 2.95 1.45 0.53 1.16 4.38 7.14 5.29
0.66 1.26 2.14 6.15 0.89 4.87 0.53 1.02 4.76 1.43 3.93 0.82 4.98 1.49 7.02 0.88 4.57 2.90 1.40 0.61 1.10 4.36 7.28 5.16
Log mean average of bulk partial pressure of CO2. b Solution also contains 0.15 m KOH. Table 3. Overall Rate Constants for 1.0 M Amines at 25 °C
amine piperazine monoethanolamine diethanolamine diglycolamine ethylenediamine piperidine morpholine
source (rate/pKa) this work 3, 49 3, 50 51, 52 36, 52 53, 50 54, 50 55, 50 51, 50 54, 50 36, 50
pKa 9.73 9.55 8.88 9.46 9.91 11.12 8.49
rate constanta (s-1) 102.2 × 103 5.9 × 103 1.3 × 103 4.52 × 103 6.7 × 103 15.1 × 103 93.3 × 103 60.3 × 103 20.6 × 103 20.0 × 103 22.3 × 103
∆Ha (kJ/mol) 35.0 41.2 53.1 39.4 40.1
23.3
Overall rate constant calculated as k ) kAm or kAm-Am[Am] + k′Am-H2O assuming 25 °C (i.e., r/[CO2]), negligible loading, and negligible hydroxide contributions. a
Figure 3. Apparent second-order rate constant for CO2 absorption into aqueous PZ. Lines: model (PCO2,i ) 100 Pa, kl° ) 1 × 10-4 m/s); open points: Bishnoi and Rochelle;48 filled points: this work.
experimental data deviates by less than 25% on average. The model captures the non-first-order behavior displayed by the experimental data and the addition of kPZ-OH effectively compensates for the accelerated rate in the presence of excess hydroxide. The activation energy provides an adequate fit between 25 and 60 °C. A comparison between overall rate constants of several amines at 1.0 M and 25 °C is shown in Table 3. The fact that piperazine has the highest rate constant may be attributed to the moderately high pKa. Also the cyclic diamine structure yields rates faster than would be expected from simple chemical classifications or pKa correlations. These characteristics are also observable in diamines such as ethylenediamine (EDA) and heterocycles such as piperidine and morpholine. Ionic Strength Effects. The potential for ionic strength to alter reaction rates through primary and secondary salt effects has been recognized in many types of reactions.56-59 To quantify the influence of salt on CO2 absorption into aqueous PZ, the
absorption rate has been measured in 0.6 m PZ with various salts at 25 and 60 °C. The data are presented in Table 4. For modeling neutral salts, the Henry’s constant of CO2 was estimated by the model of Weisenberger and Schumpe.60 The salt effect is commonly represented by a logarithmic function56,61 so that
ln k ) ln k∞ + bI
(49)
where b is a constant and I is the ionic strength. The rigorous rate model has been run with rate constants of the form shown in eq 49 to interpret the effect of neutral salts. The average value of b was found to be 0.45 ( 0.10. The constant b can be specific to both the ion and the reaction involved; the limited data presented here prevents a rigorous interpretation of its value for individual species. Other studies on ionic strength effects show similar acceleration of reaction rates. French57 studied the iodine-catalyzed decomposition of hydrogen peroxide. The influence of up to 2 M of several neutral salts increased reaction rates by as much as factor of 2. As interpreted through eq 49, reported values of b include 0.32 for LiCl, 0.13 for NaCl, and 0.08 for KCl. Grube
Ind. Eng. Chem. Res., Vol. 45, No. 8, 2006 2537 Table 4. Absorption Rate of CO2 into 0.6 m PZ at High Ionic Strength, Zero Loading T (°C) 25
60
salt
[salt] (M)
PCO2,b (Pa)
kg × 109 (kmol/ Pa‚m2‚s)
kol × 105 (m/s)
KG/kg (%)
CO2 removal (%)
NCO2 × 107 measured (kmol/m2‚s)
KHCO2
1.81
NaCl
2.81
KCl
3.04
K2SO4
1.38
KCl
1.78
KHCO2
1.75
57 103 59 38 117 157 90 68 43 66 311 195 80 219 113 155 203 66 36 87 54 15 28 111 167 187 283 299 31 67 248 183 131 101
2.85 2.81 2.80 2.82 2.54 2.53 2.50 2.51 2.46 2.27 2.25 2.71 2.73 2.92 3.31 3.32 3.06 2.97 2.98 3.01 2.38 2.37 2.33 2.37 2.41 2.39 2.38 2.41 2.79 2.79 2.84 2.82 2.84 2.79
9.01 8.97 8.97 8.97 6.78 6.80 6.83 6.84 6.84 10.2 10.2 10.3 10.3 10.3 10.8 10.8 10.7 10.8 10.8 10.8 12.6 12.5 12.6 12.9 12.7 12.8 12.8 12.9 11.0 11.0 11.0 11.0 11.0 11.0
47.6 44.3 44.1 43.4 52.6 51.1 53.6 53.5 52.2 76.0 68.9 68.0 72.0 62.6 49.9 47.8 50.5 49.5 54.4 50.5 72.3 71.8 74.8 68.8 59.6 59.7 60.1 59.4 55.1 54.9 54.6 54.7 54.7 56.1
42.7 39.8 40.3 40.4 37.7 37.0 38.2 38.2 37.7 54.2 54.4 52.3 52.9 49.4 43.0 41.5 43.3 43.1 46.5 43.6 55.1 55.4 56.3 52.9 51.5 51.1 49.7 49.1 51.1 48.5 46.3 46.7 47.1 48.4
0.80 1.31 0.75 0.49 1.57 2.03 1.20 0.91 0.56 1.02 4.70 3.48 1.44 3.87 1.88 2.47 3.14 0.98 0.59 1.33 0.93 0.28 0.49 1.82 2.68 2.96 4.34 4.57 0.55 1.10 3.91 2.90 2.11 1.66
average γCO2 a
estd k2 × 10-3 (m3/kmol‚s)b
1.93
236
2.06
348
1.92
814
1.55
684
1.33
983
1.75
1323
a Estimated from the model of Weisenberger and Schumpe.60 KHCO assumed to be the same as KHCO . b Estimated from pseudo-first-order analysis, 2 3 eq 45.
and Schmid59 determined the effect of concentrated neutral salts on the hydrolysis of cyanamide. The authors conclude that the value of b ranges from 0.16 in KNO3 to 0.40 in Mg(NO3)2. Again, the reaction rates in 2 M ionic strength increase by a factor of 2. Neutral salts have also been shown to positively influence the absorption rate of CO2 into amines. Data from Danckwerts and Sharma62 give a value of b of approximately 0.4 for CO2 absorption into ammonia with NaCl. Laddha and Danckwerts63 suggest values of 0.4 and 0.6 for Na2SO4 and K2SO4 in DEA, respectively. Pohorecki et al.64 quantified the effect of KCl addition on CO2 absorption into K2CO3-promoted ethylaminoethanol. Interpreting the results in terms of eq 49, a value of 0.31 is obtained for b. Because K2CO3 constitutes a significant portion of the ionic strength and similar results for KCl have been found in other studies, the contribution to ionic strength effects by K2CO3 must be similar to that of the neutral salts. Given the general applicability of the salt effect to promote acid or basic catalyzed reactions, a comparable effect is expected to apply to CO2 absorption by concentrated K+/PZ. Assigning a definitive value in this instance is difficult due to the reactive nature of the carbonate, its contribution to the reaction mechanism, and complications arising from speciation of the amine, though some effort has been made to reconcile the ionic strength effect with kinetics. From the conclusions of previous studies, a value of 0.3 was chosen for b for use in this work. This value is the most consistent, and moderate, choice based on the wide range of b values presented in the literature.
Figure 4. Effect of ionic strength on the apparent rate constant and physical parameters in 0.6 m PZ. Closed points: 25 °C experiments; open points: 60 °C experiments; lines: model for K2CO3/PZ at 25 °C (k2,app excludes CO32- catalysis).
Figure 4 illustrates the influence of neutral salts in 0.6 m PZ on the apparent rate constant and important physical parameters, represented as xDCO2/HCO2. Experiments show that the apparent rate constant is elevated by ionic strength. The addition of 1.8 M ionic strength increases the k2,app by a factor of 2.5 at 25 and 60 °C. With 3 M KCl the apparent rate constant increases by a factor of 15. The rate model for K+/PZ shows similar results and suggests that the value of 0.3 for b is a reasonable estimate for the ionic strength contribution to PZ reactions.
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Ind. Eng. Chem. Res., Vol. 45, No. 8, 2006
necessary parameters proved to be statistically unachievable. Figure 5 illustrates the relationship of base strength with rate. A representation of the pKa of H2O and OH- was calculated from assuming
Kw ) [H+][OH-] ) 10-14
(51)
[H+][OH-] 10-14 ) [H2O] [H2O]
(52)
Thus
Ka )
Figure 5. Fit of specific rate constants to Brønsted theory of acid-base catalysis. Circles: regressed values; squares: correlated values.
It is important to recognize that ionic strength also changes the effective diffusion coefficient and physical solubility of CO2; therefore, the interpretation of a rate constant strongly depends on the ability to estimate xDCO2/HCO2. In 3 M K2CO3, the parameter decreases by 70%. The normalized flux (kg′) is only a weak function of ionic strength; however, the competing effects of kinetics and changes in DCO2 and HCO2 result in a diminishing value of absorption rate. CO2 Absorption into Aqueous K2CO3/PZ Mixtures. Parameter Regression and Correlation. The absorption rate of CO2 into K2CO3/PZ mixtures was measured in the wetted-wall column. This study includes 2.5-6.2 m K+, 0.6-3.6 m PZ, and 40-110 °C. Selected results spanning the most typical conditions are shown in Table 5. The complete set of data is presented in Cullinane.14 The data were used to regress rate constants (kPZ-CO32-, kPZCOO--CO32-) and a correction to the diffusion coefficient of ions (β). Other rate constants were found by correlation to base strength. The heats of activation were assumed to be the same as in aqueous PZ. Table 1 shows the values of the regressed rate constants and the value obtained by correlation, if applicable. Brønsted and co-workers61,65 concluded that the catalytic effect of acids and bases on reaction rates is given by a linear function of the acid or base strength (i.e., dissociation constant). Thus, for a given reaction involving catalysis by multiple bases, unknown rate constants may be correlated to known values according to
ln kb2 ) ln kb1 + χ‚(pKa,b2 - pKa,b1)
(50)
Base catalysis has been widely recognized as a contributing factor in the reaction of some amines with CO2, as reflected in eq 23. Sharma54 summarized the rate constants of numerous amines and demonstrated their correlation with base strength. Other researchers in the area have shown similar correlating behavior.26,28,66 From the previous efforts in this field and the proven validity of Brønsted theory as applied to the capture of CO2, the kinetic mechanism proposed in this work can justifiably rely in a large part on the correlation of kinetics to base strength. From the previous regression of rate constants in the aqueous PZ solution, the slope of the Brønsted relationship was found to be 0.457. This value was used to correlate several of the rate constants for the K+/PZ data; independent regression of all the
This type of approximation is supported by previous work on other amines. Published data on CO2 absorption into aqueous morpholine (MOR), diethanolamine (DEA), and diisopropanolamine (DIPA) have been re-analyzed in terms of a termolecular mechanism to give rate constants for comparison to PZ in this work. The rate constants are presented in Figure 6 and Table 6. As the analysis shows, the effect of base strength on the rate is nearly proportional for the given amines (i.e., χ ∼ 0.5). It is also striking that the effect does not depend on the type of molecule, only the pKa; thus, water and hydroxide can be represented by the same correlation used for amines. Deviations from the correlation, as observed for TEA, can be explained in terms of steric effects. The vertical displacement is also a function of base strength and steric effects. DEA and DIPA are of approximately the same pKa but are differentiated by structure. In constrast, MOR and PZ have similar structures, but the PZ has a higher pKa and, consequently, a larger rate constant. As previously mentioned, a correction to the diffusion coefficient representing ions in solution was regressed in addition to the kinetic parameters. The correction was added to eq 44 so that
DAm ) βD∞Am
() µw µs
(53)
β was correlated to be 1.51, suggesting that the Wilke-Chang correlation used for ions under-predicts diffusion coefficients. The incorporation of the above parameters into the model results in a good representation of the experimental data. Of the predictions of flux, 91% fall within (30% of the experimental data and 79% fall within (20%. Figure 7 illustrates the ability of the model to correlate the flux of CO2 into K+/PZ mixtures under the given conditions. Model SensitiVity. Figure 8 shows the sensitivity of the model to variations in parameter i (d ln k′g/d ln i) in 5.0 m K+/2.5 m PZ at 60 °C. The conditions represent values typical of experiments in this work. Parameters with sensitivities under 0.05 have been omitted. In the region of low PCO2* (
