Article pubs.acs.org/IECR
Thermodynamic and Mass-Transfer Modeling of Carbon Dioxide Absorption into Aqueous 2‑Amino-2-Methyl-1-Propanol Brent J. Sherman and Gary T. Rochelle* The McKetta Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712-1589, United States S Supporting Information *
ABSTRACT: Explanations for the mass-transfer behavior of 2-amino-2-methyl-1-propanol (AMP) are conflicting, despite extensive study of the amine for CO2 capture. At equilibrium, aqueous AMP reacts with CO2 to give bicarbonate in a 1:1 ratio. Although this is the same stoichiometry as a tertiary amine, the reaction rate of AMP is 100 times faster. This work aims to explain the mass-transfer behavior of AMP, specifically the stoichiometry and kinetics. An eNRTL thermodynamic model was used to regress wetted-wall column mass-transfer data with two activitybased reactions: formation of carbamate and formation of bicarbonate. Data spanned 40−100 °C and 0.15−0.60 mol CO2/mol alk. The fitted carbamate rate constant is 3 orders of magnitude greater than the bicarbonate rate constant. Rapid carbamate formation explains the kinetics, while the stoichiometry is explained by the carbamate reverting in the bulk liquid to allow CO2 to form bicarbonate. Understanding the role of carbamate formation and diffusion in hindered amines enables optimization of the solvent amine concentration by balancing viscosity and free amine concentration. This improves absorber design for CO2 capture.
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INTRODUCTION Amine scrubbing has long been used to treat acid gas and now is being used to treat flue gas from power plants. The largest operating scrubber captures 90% of the CO2 from a 139 MW coal-fired unit, and startup is set for early 2017 for a scrubber on a 240 MW slip stream from a coal-fired power plant.1 The new largest scrubber will use KS-1, which is a hindered amine solvent,2,3 showing that hindered amines are displacing the standard monoethanolamine (MEA). This displacement is due to the advantages of sterically hindered amines, namely, high CO2 absorption capacity coupled with acceptable rates. The capacity is from a 1:1 reaction stoichiometry of amine:CO2, such as tertiary amines. Unlike tertiary amines, the rates for sterically hindered amines are 100 times faster.4 (They are still slower than primary or secondary amines.) This mass-transfer performance and good stability makes hindered amines a promising solvent candidate, whether alone or in a blend.5 The reason for this combination of stoichiometry and kinetic rate in hindered amines has not been satisfactorily explained. As a step toward understanding the mass-transfer behavior for all sterically hindered amines, 2-amino-2-methylpropan-1-ol (AMP) is examined in this work. AMP is chosen because it is the sterically hindered analog of monoethanolamine (MEA), the most widely used amine, and, as such, AMP has been studied extensively, both alone and in blends. This work builds off of prior NMR and thermodynamic modeling work that is unavailable for other hindered amines.6,7 AMP is a commercially significant amine, because of its high capacity, acceptable rates, and good thermodynamic and oxidative stability. A deeper © XXXX American Chemical Society
understanding of the fundamental behavior of AMP aids in optimizing the amine concentration, whether alone or in a blend. Prior work has proposed three different mechanisms. Chakraborty et al.8 did not observe any carbamate in NMR spectra, and therefore proposed that AMP reacts like a tertiary amine to form bicarbonate. Knowing this reaction was too slow, they postulated that AMP reacted directly with CO2 to form an unidentified intermediate. Yih and Shen9 also believed that carbamate formation did not occur, and so they proposed that AMP formed a zwitterion (+HAMPCOO−) that then formed bicarbonate. Most researchers10−16 interpret the kinetics using the zwitterion mechanism to form carbamate, which explains the kinetics. The stoichiometry is then explained by some combination of the carbamate hydrolyzing to bicarbonate, the zwitterion forming bicarbonate, or base-catalyzed hydration of CO2. These theories seek to answer the following question. If AMP forms carbamate, then why is it not as fast as a primary amine? To explain why AMP is faster than a tertiary amine and yet not as fast as an unhindered amine, researchers hypothesize that AMP carbamate acts as an unstable intermediate to accelerate absorption.9,12 This work examines the mass transfer in concentrated, CO2 loaded AMP systems, such as that which would be used in the amine scrubbing process. The AMP rates are explained by the formation of carbamate through a single, termolecular Received: Revised: Accepted: Published: A
September 9, 2016 December 14, 2016 December 16, 2016 December 16, 2016 DOI: 10.1021/acs.iecr.6b03009 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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aq ΔG∞, f, AMPCOO−. The effect on the VLE at 313 K was calculated relative to the basis thermodynamic model. This temperature was chosen because it is the operating temperature of the absorber and is used to characterize solvent properties, such as capacity, loading range, and mass transfer. Three different amines were modeled: monoethanolamine (MEA),24 2-piperadineethanol (2PE),25 and AMP (this work). These amines span the range of carbamate stability and have robust thermodynamic models. Mass-Transfer Model. Hydraulics. Viscosity and density are necessary to model mass transfer. The viscosity plays an important role in both the diffusion rate of species as well as the liquid film physical mass-transfer coefficient (k0l ), which factors into the thickness of the liquid boundary layer. Table 1 lists the
mechanism,17 rather than the two-step zwitterion mechanism. The termolecular mechanism has been used to explain the masstransfer performance of many amine solvents,18,19 and recent computational chemistry work shows that a trimolecular reaction is possible.20,21 This work shows that AMP forms carbamate using a different mechanism than that of an unhindered primary amine. The stoichiometry is explained by reversion of the carbamate to free amine and CO2 in the bulk liquid accompanied by base-catalyzed hydration of CO2 to form bicarbonate, as in tertiary amine systems. In addition to studying the mass-transfer phenomena, the effect of the equilibrium carbamate concentration on the CO2 vapor−liquid equilibrium (VLE) was examined to explain why a prior thermodynamic model6 could represent AMP without carbamate. This allows for an estimate of the degree to which such errors in speciation affect the VLE as a function of carbamate concentration.
Table 1. Viscosity Fit of Aqueous AMP
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[AMP] (m)
METHODS Thermodynamic Model. The model used was a derivative of the Aspen Plus model of Li et al.,6 which used the asymmetric electrolyte nonrandom two-liquid (eNRTL) activity-coefficient thermodynamic model for the liquid phase (ELECNRTL) and the Redlich−Kwong equation of state for the vapor phase (ESRK). This model was modified to include carbamate, whose molecular structure is shown in Figure 1. Since the carbamate was
4.8 0.26−3.2 2.4, 4.1
temperature, loading number of ARD T (°C) (mol CO2/mol alk) data points (%) source 40 25 24−77
0.15−0.56 0 0
4 12 12
2.5 2.5 8.8
18 11 26
available data. As the operating amine scrubber will always be loaded with CO2, the unloaded data is only useful to set the asymptotic behavior at zero loading and the change with temperature. These data were fit along with the loaded data by regressing parameters a, b, and g with f set to zero in eq 4.
{
μAMP = μH O exp [(awAMP + b)T + cwAMP + d] 2
× [(ewAMP + fT + g )α + 1]
−
Figure 1. Molecular structure of AMPCOO .
wAMP T2
}
(4)
27
This equation was used by Frailie to describe piperazine (PZ). Not all parameters could be regressed, because of limited data. The nonregressed parameters were left at values representative of methyldiethanolamine (MDEA);27 the minor implications of this decision are discussed later. The regression was done using the nonlinear regression algorithm of fitnlm in MATLAB to minimize the ARD. For density, no loaded data were available. Parameters a and b of eq 5 were regressed with the unloaded data of Table 2 by minimizing the ARD with the Excel add-in Solver.
not available in the Aspen Plus databank, the parameters needed to define it were set, such as charge and molecular weight. All parameters related to the carbamate were left at default values, with the exception of those listed in the Supporting Information. Equation 1 was added to the model chemistry. 2 AMP + CO2 ⇔ AMPCOO− + AMPH+
(1)
The equilibrium of eq 1 was regressed to fit speciation data.7 The earlier data from Ciftja et al.22 were excluded because of inconsistency with the later, more-comprehensive dataset by the same author.7 The dataset contained 61 data points at 25, 35, and 45 °C.7 The goodness of fit was quantified by the average relative deviation (ARD) defined by eq 2, 100 ARD = n
∑ n
|Nî − Ni| Ni
ρAMP = x H2OρH O + xAMP(aT + b) + xCO2(cT + d) 2
Table 2. Density Fit of Aqueous, Unloaded AMP
(2)
where n is the number of data points. aq ΔG∞, f, AMPCOO− (DGAQFM) was regressed to fit the 25 °C data, ∞, aq and ΔHf,AMPCOO− (DHAQFM) was regressed to fit the temperature dependence by minimizing the ARD. Carbamate Sensitivity. The sensitivity of the VLE to the equilibrium carbamate concentration was quantified using the carbamate stability constant (Kc), as defined by eq 3. Kc =
[AmCOO− ] [Am][HCO−3 ]
(5)
xAMP
temperature, T (°C)
data points
ARD (%)
source
0.02−1.0 0.01−1.0
20−91 25−80
41 99
0.45 0.36
26 28
The behavior with loading was represented by using the same c and d values as MDEA,27 the minor implications of which are discussed later. Diffusivity. There were two different effective liquid diffusion coefficients modeled: one for CO2 and N2, DCO2, and one for all other species, DAm. DCO2 used the correlation developed by Versteeg and van Swaaij,29 while DAm was set to half of DCO2, as done by Sherman et al.25 Reaction Set. The kinetics were activity-based and used the termolecular mechanism, where three molecules react in one
(3)
This Kc is given on a concentration basis, to allow for comparison to the literature values.23 Kc was varied by changing B
DOI: 10.1021/acs.iecr.6b03009 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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correlation of Li19 was made from concentrated, loaded amines measured in a wetted-wall column (WWC) and interpreted using third-order kinetics. The other correlations use data from a variety of apparatuses operating under dilute, unloaded conditions at widely varying amine concentrations. These variations complicate interpretation of the data. In addition, as the data are unloaded, the mass-transfer behavior is much different than mass-transfer behavior in a loaded system. Therefore, the primary amine correlation of Li19 was used in this work and is shown in eq 15.
single reaction step. The activity basis is necessary because the electrolytes make the liquid highly nonideal. Two kinetic reactions were modeled: the formation of carbamate (eq 6) and the formation of bicarbonate (eq 7). kAMP−AMP
2 AMP + CO2 HooooooooI AMPCOO− + AMPH+
(6)
kAMP
AMP + H 2O + CO2 HoooI HCO−3 + AMPH+
(7)
kAMP−AMP is the rate constant for AMP catalyzed by AMP, and kAMP is the rate constant of AMP serving as a base. The proton exchange reaction of eq 8 was assumed to be at equilibrium, i.e., it is instantaneous. AMP + HCO−3 ⇔ AMPH+ + CO32 −
* −AMP,c = 0.706pKa − 7.918 log10 kAMP
Equation 15 was developed at 40 °C, so the corresponding pKa was used. kAMP−AMP,c * is defined by eq 16.
(8)
The base-catalysis of water was neglected because (i) water is a much weaker base than AMP and (ii) AMP was concentrated (30 wt %). The hydroxide ion was not modeled, because of its low concentration and, thus, negligible role as a base. The reaction rates were calculated by eqs 9 and 10. 2 −rCO2 = kAMP−AMPaCO2aAMP
−rCO2 = kAMPaCO2aAMP
* −AMP,c = kAMP
kf Keq
(10)
kAMP−AMP =
(11)
(13)
Aspen Plus uses a mole fraction basis. Thus, it was necessary to convert the concentration-based, ideal eq 13 to a mole-fraction, activity basis, using eq 14. kAMP
AMP CO2
(17)
Flowsheet. The specific WWC used to collect the data was simulated in Aspen Plus, using a custom flowsheet, as described by Sherman et al.25 The physical liquid-film resistance, gas-film resistance, and boundary-layer discretization are as detailed by Sherman et al.25 Kinetic Parameter Regression. To regress the masstransfer data,18 the greatest desorption and absorption CO2 flux (NCO2) values for each loading and temperature were fit, since these have the least experimental error. NCO2 ranged from −1.61 × 10−2 mol/(s m2) to 7.68 × 10−3 mol/(s m2). Prior to regression, the loading for each point was adjusted to give zero flux at zero driving force, as described by Sherman et al.25 This loading adjustment compensates for both experimental error and model fit error (i.e., error in the vapor−liquid equilibrium (VLE) fit). The adjusted dataset was fit using response surface methodology (RSM), which was developed from the work of Frailie.27 The RSM method created a simplified model from the rigorous Aspen Plus model, and then regressed the parameters in the simplified model using a response surface. The regressed parameters from the response surface were checked in the Aspen Plus model. By creating a simplified, algebraic model, any regression algorithm may be applied to the data, rather than only those available in Aspen Plus. This results in a better, morecontrolled regression with more statistics with the added benefit of reduced computational time. The method started with running the Aspen Plus model for all of the data points to establish a basis (basis). Next, each parameter was individually increased by 10%, and the data set run again (+10%). This determined the response surface by setting the sensitivity αji to each parameter i for each data point j. α was calculated by eq 18.
Brønsted Correlations. As the reactions of amine with CO2 are base-catalyzed, they should obey Brønsted theory, which correlates the rate constant of reaction with the strength of the catalyzing base.30 A different Brønsted correlation was used for each reaction. For the bicarbonate reaction, it was assumed that the reaction mechanism is the same as that of tertiary amines. The tertiary amine correlation (eq 13) was used to estimate the concentrationbased rate constant kAMP,c (m3/(mol s)) at 20 °C.31
kAMP,c ρ ̅ 2 = γ γ*
kAMP−AMP,c ρ ̅ 3 γ 2 γ* AMP CO2
(12)
ln kAMP,c = pK a − 14.24
(16)
First, the activity of CO2 was used to convert k*AMP−AMP, c to kAMP−AMP, c, which is concentration-based, ideal. Then, kAMP−AMP,c was converted to a mole-fraction, activity basis with eq 17.
(9)
The kinetic reaction equilibrium (Keq) was equated to the thermodynamic equilibrium by calculating the reverse reaction rate constant kr from the forward rate constant kf using eq 12. (This is necessary as the Aspen Plus model separates the thermodynamic equilibrium chemistry reactions from the kinetic reactions.) kr =
kAMP−AMP,c (γ * )2 CO2
Both rate constants were calculated using the Arrhenius equation (eq 11) with Tref = 313.15 K. ⎡ E ⎛1 1 ⎞⎤ ki = k 0 exp⎢ − A ⎜ − ⎟⎥ ⎢⎣ R ⎝ T Tref ⎠⎥⎦
(15)
(14)
This conversion was done at 0.397 mol CO2/mol alk and 20 °C, and then the rate was brought to the reference temperature using an activation energy of EA = 44.9 kJ/mol.32 For the carbamate reaction, there were multiple Brønsted correlations available in the literature.19,33,34 The Brønsted C
DOI: 10.1021/acs.iecr.6b03009 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research ln αji =
ln
̂ +Δ NCO | 2
ln
NCO2|basis k 0, i+Δ |
=
Δ= 10%
̂ +| 10% NCO 2
condition was simulated with instantaneous reactions. Reactioncontrolled mass transfer is pseudo-first-order (PFO), where the amine species concentation at the interface is the same as in the bulk liquid. The PFO mass-transfer coefficient kg,PFO ′ can be generally calculated by eq 21.33
NCO2|basis
ln 1.1
(18)
k 0, i|basis
The response surface took the form of eq 19. ̂ NCO 2 NCO2
=
i
̂ NCO 2 NCO2
basis
⎛ k 0, i ⎞αj ⎟⎟ ∏ ⎜⎜ k | i ⎝ 0, i basis ⎠
′ kg,PFO =
DCO2
′ kg,PFO =
kAMP
kAMP−AMP
ARD (%)
Brønsted regress regress Brønsted no carbamate
45 6.9 15 39 11
1 1 Kg
−
1 kg
=
* (PCO 2,i
NCO2 * )LM − PCO 2,b
(kAMP−AMPaAMP 2 + kAMPaAMPa H2O) * HCO − H O γCO 2 2
(22)
where HCO2−H2O (Pa) is from the work of Carroll et al.35 Vm converts HCO2−H2O to a concentration basis. The boundary layer speciation profile was calculated to determine (i) where carbamate and bicarbonate formed, (ii) what product was most responsible for transporting CO2, and (iii) if the carbamate was hydrolyzed or reverted in the boundary layer. The correlation of diffusion to viscosity was quantified because, at fast reaction rates, the mass transfer is diffusion-controlled and the rate of diffusion is a strong function of viscosity. This is demonstrated in the improved performance of lower viscosity. To correlate the viscosity and the temperature dependence of the diffusion of amine and products (DAm (m2/s)), the diffusion activation energy (ED) was calculated using eq 23: ⎛ ln DAm ⎞ ⎟ ED = −R ⎜ ⎝ 1/T ⎠
basis was redone for each case. These different cases tested the predictive capability of the Brønsted correlations and determined if the most significant reactions had been accounted for, which allowed for model discrimination. Mass-Transfer Analysis. The mass-transfer behavior was examined to determine the sensitivities of the liquid-film mass-transfer coefficient, the approach to pseudo-first-order and instantaneous conditions, and the applicability of Brønsted correlations for both reactions. Since case 1 was the best mass-transfer fit, it was used to study mass transfer in AMP by examining the liquid-film mass-transfer coefficient (k′g) and diffusion effects. k′g is defined by eq 20, kg′ =
Vm
2
Table 3. 4.8 m AMP Mass-Transfer Regression Cases and Resulting ARD Brønsted regress Brønsted regress regress
(21)
Applying eq 21 to AMP, by accounting for the carbamate and bicarbonate reactions, yields eq 22,
A nonlinear regression was done with the fitnlm command of MATLAB called using eq 19 as the model equation. The parameters were k0 and EA for both reactions, as defined by eq 11. Once the parameters were regressed, the fit was checked with the Aspen Plus model. No discrepancies were observed. Since fitnlm did not allow for parameter constraints, if a parameter went beyond a bound in unconstrained regression, that parameter was fixed at the bound, and the regression was run again with the remaining parameters. Further details and a flowchart are available.45 The four cases listed in Table 3 were regressed. As the response surface assumes linearity in the sensitivities, the
case
* HCO − H O γCO 2 2 2
(19)
Brønsted 1 2 3 4
2 DCO2kaAMP
(23)
This was done by taking the slope of a line fit to ln DAm vs 1/T for the experimental data.
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RESULTS Thermodynamic Model. The addition of carbamate to the model of Li et al.6 did not change any aspect of the thermodynamic model beyond the speciation. Figure 2 shows that the VLE of the present model has no systematic bias.
(20)
where (P*CO2,i − P*CO2, b)LM is the logarithmic mean average driving force from the interface i to the bulk liquid b. The sensitivity of k′g to individual variables was calculated using a ±5% central difference to approximate the analytical derivative. The variables were the rate constants for both reactions, the viscosity, the diffusivity of CO2 and carbamate, and the physical mass-transfer coefficient. For the study of the carbamate diffusivity, the diffusion coefficient of the carbamate alone was varied, leading to three diffusion coefficients: DCO2, as previously defined; DAm for all other species without carbamate; and DAMPCOO− for the carbamate. The asymptotes of reaction-controlled mass transfer and diffusioncontrolled mass transfer were simulated. The diffusion-controlled
Figure 2. 4.8 m AMP VLE at 20 °C intervals with loading adjusted data for case 1. D
DOI: 10.1021/acs.iecr.6b03009 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Figure 3. Speciation prediction for 4.8 m AMP at 35 °C (lines) compared to data taken from ref 7.
Figure 4. Viscosity prediction for 4.8 m AMP (lines), compared to data taken from ref 18.
The speciation data were fit with two parameters: ΔG°aq,AMPCOO− = −4.574 × 10 8 J/kmol and ΔH aq,AMPCOO ° = −7.500 × − 108 J/kmol for an ARD of 13%. Figure 3 shows the fit of the 35 °C data. This fit is consistent with prior work8,36 and shows that Sartori et al.37 over-reported the amount of carbamate by a factor of 5. CO2 VLE Sensitivity to Carbamate. Table 4 shows that, as expected, systems with less carbamate are less sensitive to
is reported in Table 1, with the overall ARD being 5.2%. The parameter correlation matrix shows that a and b are highly correlated (corr(b, a) = −0.97), while g is moderately correlated (corr(g, a) = −0.57; corr(g, b) = −0.43). Viscosity is used to calculate k0l and diffusion coefficients, both of which become more important at greater loading and at greater temperature. The diffusion coefficient is dependent on viscosity (to the −0.8 power),29 meaning that viscosity can have a significant impact on mass-transfer performance. The predicted temperature dependence of viscosity is approximated by that of MDEA.27 This approximation does not impact the conclusions but could alter the predicted bicarbonate reaction rate. Density affects mass transfer in a few ways: in the calculation of the liquid film thickness at the one-sixth power,18 in the conversion of the measured volumetric flow rate to a mass flow rate for simulation (see eqs 14 and 17), and in the conversion from mole fraction to concentration and vice versa. Of these, the largest effect is observed on the conversions of eqs 14 and 17. The density predictions were made using eq 5 with the parameters of Table 6 and yielded an overall ARD of 0.38% for
Table 4. Necessary Increase in log Kc at 40 °C for a 5% ARD Change in VLE system
pKa
log Kc
Δ log Kc
model
pKa source
7 m MEA 8 m 2PE 4.8 m AMP
9.0 9.7 9.3
3.20 0.89 0.44
0.03 0.09 0.36
24 25 this work
38 25 39
changes in Kc. The log Kc value listed is an average of the rich and lean loadings, defined by P*CO2 = 5 and 0.5 kPa, respectively, calculated at 40 °C. These loadings are typical of capture from coal-fired power plant flue gas:27 0.27 and 0.56 mol CO2/mol alk for 4.8 m AMP. Table 4 shows that a large change in the equilibrium concentration of carbamate is necessary to affect the VLE, which explains why the model of Li6 was able to fit the VLE without carbamate. Table 4 shows that, for amines of similar hindrance, namely, 2PE and AMP, the pKa is proportional to Kc. This observation agrees with the works of McCann et al.40 and Li.19 Studies of the underlying molecular and solvent forces that explain this trend are available.41,42 Mass-Transfer Model. Hydraulics. The viscosity was predicted using eq 4 with the parameters of Table 5. Figure 4 shows the loaded viscosity predictions. The ARD for each dataset
Table 6. AMP Density Parameters of eq 5
value
a b c d e f g
1010 899 1.34 3.69 2.22 0 0.752
SE 464 107
fixed 0.149
value
source
a b c d
−1.03 1240 3.82 −12.1
this work this work 27 27
the unloaded data26,28 with the individual fits given in Table 2. The fit for unloaded data ensures that ρ is well-behaved at low loading, but the loaded predictions of Figure 5 are more important for the mass-transfer data and the CO2 capture process. The estimation of loaded ρ does not affect the conclusions drawn here. Kinetic Parameters. Table 7 reports the kinetic parameters for the four regression cases. The Brønsted case is not a regression but illustrates the fit achieved using the Brønsted estimates. For each regressed reaction, two parameters were regressed. In case 1, four parameters were regressed, while in the other three cases, two parameters were regressed. To test if the fit of case 1 is better solely because of more parameters, an F-test comparing
Table 5. AMP Viscosity Parameters of eq 4 parameter
parameter
source this work this work 27 27 27 this work this work E
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Table 8. Case 1 Loading Adjustment, Compared to Data Taken from Ref 18 Loading (mol CO2/mol alk) temperature, T (°C)
experimental
adjusted
relative difference (%)
40 60 80 100 40 60 80 100 40 60 80 40 60
0.15 0.15 0.15 0.15 0.29 0.29 0.30 0.30 0.45 0.45 0.45 0.56 0.60
0.13 0.15 0.17 0.16 0.25 0.29 0.31 0.30 0.43 0.44 0.45 0.55 0.58
−14 3.3 11 7.6 −13 −1.4 2.9 0.02 −3.6 −1.6 −0.18 −1.6 −4.1
Figure 5. 4.8 m AMP density prediction.
case 1 to case 4 was performed at α = 0.01. The fit of case 1 is statistically better (F = 17.5 for case 1, which is greater than F = 5.66 for case 4), even after discounting the two additional parameters. Examining correlation matrices shows that the parameters of kAMP are highly correlated (|corr(k0, Ea)| > 0.94), while those for kAMP−AMP are not (|corr(k0, Ea) | < 0.27). There is also a strong correlation between the prefactor of kAMP and the activation energy of kAMP−AMP (|corr(k0,AMP, Ea,AMP−AMP)| = 0.81). The loading adjustment for case 1 is shown in Figure 2 and listed in Table 8. The adjustment is greatest for the two leanest loadings, because these loadings fall at or outside the lean loading for which the original model was developed.6 Thus, the adjustment is mostly for model error, rather than experimental error. The mass-transfer fit of case 1 is shown in Figure 6. The dashed lines represent the estimated ±8.5% reproducibility of the experimental flux measurements.19 The fit is tight and shows no bias with temperature. There appears to be a bias toward underprediction at greater loading; however, this is within the margin of reproducibility. The underprediction of the two greatest loading points is likely due to depletion of free amine at the interface associated with the greater driving force. This combination of conditions results in a more diffusion-limited regime. Since the activation energy for the bicarbonate reaction is at the bound in cases 1 and 4, the sensitivity to this bound was quantified by changing the bound by ±10%. Table 9 shows that the kinetic parameters of kAMP−AMP vary by
