Kinetic Behavior of Solid K2CO3 under Postcombustion CO2 Capture

Article pubs.acs.org/IECR

Kinetic Behavior of Solid K2CO3 under Postcombustion CO2 Capture Conditions Abhimanyu Jayakumar,† Arturo Gomez,† and Nader Mahinpey* Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, Calgary, AB T2N 1N4, Canada ABSTRACT: Trends in CO2 and H2O uptakes by solid K2CO3 were studied at different carbonation temperatures and flue gas compositions over 50 consecutive regeneration− carbonation cycles. Differences in carbonation behavior between the initial and final cycles evidence changes in the phase composition of K2CO3 during cycling, which stabilize in accordance with the operating conditions. Rates of carbonation and hydration were observed to decrease at higher temperatures, indicating that the forward reactions are limited by adsorption, not chemical reaction. Multiple regression analysis of the uptake data yielded negative apparent activation energies for both forward reactions modeled as simple chemical reactions, thus proving the assumption invalid. A proposed Langmuir−Hinshelwood model yielded consistent apparent activation energies for the forward reactions, showing that adsorption limitations are significant in this chemisorption process. Important process design considerations, for realizing high carbonation rates and selecting promising support materials to enhance the CO2 capture capacity of K2CO3, are also discussed. reaction with H2O in the flue gas, as shown by the hydration reaction (reaction 2). The formation of K4H2(CO3)3·(1.5 H2O) can be represented as a simple combination of reactions 1 and 2.

1. INTRODUCTION Emissions of CO2 into the atmosphere, from fossil fuel combustion processes for thermal power generation, need to be controlled to help mitigate the effects of anthropogenic CO2 on global climate change.1 A low-cost, retrofittable postcombustion capture process for CO2, a greenhouse gas, could provide a feasible solution for controlling its emissions from fossil fuel combustion processes. At this point, CO2 capture using aqueous amine solutions is the only postcombustion technology that has been developed to a mature stage. However, this technology has many shortcomings, with its main drawback being its high regeneration energy requirements due to the presence of significant quantities of water.2,3 To potentially avoid such a regeneration energy penalty, solid CO2 sorbents provide an interesting range of materials for further investigation. Solid alkali metal carbonates, such as K2CO3, are promising chemisorbents of CO2 with high maximum possible CO2 uptake capacities. K2CO3 captures CO2 from combustion flue gases, around 40−80 °C, by reacting with H2O and CO2 to form KHCO3 via the overall carbonation reaction (reaction 1). K2CO3 can be regenerated from KHCO3 by calcination of the spent sorbent above 120 °C.4 K 2CO3(s) + H 2O(g) + CO2 (g) ⇋ 2KHCO3(s)

K 2CO3(s) + 1.5H 2O(g) ⇋ K 2CO3·(1.5H 2O)(s)

Most previous studies on the use of solid K2CO3 for postcombustion applications are of the view that CO2 capture, i.e., KHCO3 formation, occurs through a sequential reaction mechanism.7−11 In this two-step mechanism, K2CO3 is supposedly hydrated first via reaction 2 to form K2CO3·(1.5 H 2O) as the intermediate, which is then claimed to subsequently react with CO2 in the flue gas to produce the bicarbonate by reaction 3. K 2CO3·(1.5H 2O)(s) + CO2 (g) ⇋ 2KHCO3(s) + 0.5H 2O(g) (3)

Further examination of these works,7−11 however, discovered several shortcomings in the experimental approaches used, as explained in detail previously.12,13 These limitations led to a lack of information on the amounts of KHCO3 and K2CO3·(1.5 H2O) present in the K2CO3 samples being carbonated and resulted in the inability to explain why prehydrated K2CO3 samples showed negligible weight changes when exposed to CO2 to prove the occurrence of reaction 3.14 Therefore, the

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Carbonated K2CO3 has also been shown to contain hydration products such as K 2 CO 3 ·(1.5 H 2 O) and K4H2(CO3)3·(1.5 H2O), based on X-ray diffractometry (XRD) analysis of the spent sorbent in the literature.5,6 K2CO3·(1.5 H2O) is the hydrated salt of K2CO3, formed by its © 2017 American Chemical Society

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Received: Revised: Accepted: Published: 853

November 18, 2016 January 2, 2017 January 5, 2017 January 5, 2017 DOI: 10.1021/acs.iecr.6b04498 Ind. Eng. Chem. Res. 2017, 56, 853−863

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Industrial & Engineering Chemistry Research sequential reaction mechanism was not clearly proven, and there were still significant doubts regarding its validity. In our recent studies on this topic, the aforementioned experimental limitations were addressed by the use of a coupled thermogravimetric analysis-mass spectrometry (TGA-MS) analysis system.12,13 The results demonstrated and verified that the carbonation and hydration of solid K2CO3 are both reversible reactions which proceed in parallel to one another, via direct reaction with the flue gas components, and compete for the sorbent active sites, without the occurrence of reaction 3. Hence, it was confirmed that the global reaction mechanism for KHCO3 and K2CO3·(1.5 H2O) formation is a parallel reaction mechanism involving reactions 1 and 2 only. Prior studies also found that the carbonation reactivity and bicarbonate yield of K2CO3 derived from KHCO3 (phase I) are much higher than those of K2CO3 derived from previously hydrated samples (phase II).6,12−15 These two K2CO3 phases have slightly different monoclinic structures, but upon sufficient cycling, the carbonation performance of K2CO3 was shown to stabilize at almost the same intermediate level, independent of the precursor and related to the carbonation conditions used, because of a stabilization in the phase composition of the sorbent being produced by regeneration.12 In this study, the kinetic behavior of unsupported solid K2CO3 is assessed by subjecting the sorbent sample to 50 consecutive regeneration−carbonation cycles in the coupled TGA-MS analysis setup, using three different carbonation temperatures and three different model flue gas compositions. Multiple regression analysis of the time-based bicarbonate and hydrate conversion data during carbonation is performed to determine the apparent rate constants for the chemical reaction model and a proposed Langmuir−Hinshelwood (L-H) kinetic model. The L-H kinetic model proposed for this gas−solid reaction system is based on a possible initial rate-limiting step involving H2O adsorption, for both the forward carbonation and hydration reactions. Using theoretical estimates of the equilibrium constant for H2O adsorption on K2CO3,16 the apparent rate constants obtained for the chemical reaction model can be adjusted to evaluate the apparent rate constants for forward carbonation and hydration, according to the L-H model. Model validation is achieved by testing the consistency of the apparent activation energies estimated from the apparent rate constants for each particular model.17 Takeaways for process design include determining the optimum carbonation conditions, where adsorption rates and kinetic rates are in synergy or a high stabilized CO2 equilibrium capacity is ensured by the use of a flue gas mixture containing above equimolar levels of CO2 with respect to H2O at lower temperatures, and choosing a suitable support material that improves the phase I composition of active K2CO3 under stabilized operation.

The crucible was loaded into the TGA while maintaining the reactor in dry N2. The K2CO3 sample was then subjected to 50 consecutive cycles, each consisting of a sample regeneration step followed by a sample carbonation step. Full descriptions of the TGA-MS setup, the sorbent cycling procedure, and the sorbent uptake quantification method are presented in a previous study.12 Sorbent regeneration was carried out at 150 °C in an atmosphere of dry N2. Carbonation of the regenerated K2CO3 sample was performed using a different model flue gas composition and reactor temperature for each multicycle test in order to evaluate the kinetic behavior of solid K2CO3 under postcombustion CO2 capture conditions. The different model flue gas compositions and reactor temperatures used for K2CO3 carbonation in this kinetic study are shown in Table 1. The Table 1. Different Model Flue Gas Compositions and Reactor Temperatures Used for the Carbonation Steps of Each Multicycle Test Performed Using Solid K2CO3 in This Kinetic Study model flue gas compositions (std. vol %) no.

CO2

H2O

N2

carbonation temperatures (°C)

1 2 3

1.42 2.34 4.14

2.15 2.13 2.09

96.43 95.48 93.77

40, 50, 60 40, 50, 60 40, 50, 60

model flue gas compositions are mentioned in standard volume % with respect to the reference temperature and pressure of 25 °C and 1 atm, respectively. The experiments were carried out in Calgary, Alberta, where the atmospheric pressure is around 0.87 atm. Flue gas compositions used ranged from containing below equimolar to above equimolar ratios of CO2/H2O. The flow rates of N2 (152.85 std ml min−1) and H2O (3.4 std ml min−1) were kept fixed, while the flow rate of CO2 was varied from 2.25 to 3.75 to 6.75 std ml min−1 for gas compositions 1, 2, and 3 in Table 1, respectively. The total flow rates for gas compositions 1, 2, and 3 were 158.5, 160, and 163 std ml min−1, respectively. For this kinetic study, the variation of just the CO2 flow rate was considered sufficient because it enabled the study of carbonation and hydration behavior at different relative concentrations of CO2 and H2O. A similar study can also be conducted by varying only the H2O flow rate instead, but this procedure will impact the rates of both the carbonation and hydration reactions and might result in greater differences in the times required to reach equilibrium at a given temperature. These results may be more difficult to accurately compare but will be qualitatively no different to the current study because the CO2/H2O ratio is of importance. Also, higher concentrations of CO2 and H2O will decrease the fraction of unreacted K2CO3 at equilibrium.12 Another important parameter is the relative humidity of the flue gas, which was maintained almost constant here, because H2O and CO2 were the minor components in the flue gas mixtures, and only the CO2 flow rate was slightly varied. Higher relative humidities can favor hydration, but if high enough, they can also result in H2O condensation on the sample, leaving the sample waterlogged and suppressing carbonation by introducing mass-transfer limitations.13 The operating temperature range of 40−60 °C was chosen because undesirable H2O condensation is more favored at temperatures below 40 °C,

2. EXPERIMENTAL SECTION A coupled TGA-MS analysis system was used to characterize sorbent performance during carbonation over multiple (50) regeneration−carbonation cycles. The TGA-MS experimental setup provides the capability to separately track the quantities of CO2 and H2O adsorbed by the sample in time, thus enabling the quantification of both bicarbonate and hydrate conversions of the K2CO3 sample in each carbonation step. The multicycle tests were started by adding around 120−125 mg of the K2CO3 analytical reagent (Sigma-Aldrich, ACS reagent, ≥99.0%) into a wide stainless steel crucible, designed to reduce mass-transfer limitations as explained elsewhere.12,18 854

DOI: 10.1021/acs.iecr.6b04498 Ind. Eng. Chem. Res. 2017, 56, 853−863

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Industrial & Engineering Chemistry Research while the CO2 uptake capacity of the sorbent is more limited at temperatures above 60 °C. It is important to note that the K2CO3 sample quantities of 120−125 mg used in this TGA-based study are larger than the typical sample quantities used in TGA studies. Larger sample quantities are required to affect a large enough weight change in the TGA, and a more significant CO2 signal change in the MS, compared to the baseline noise levels in the respective instrument readings. This approach enhances the accuracy of the sorbent uptakes calculated. Furthermore, in this study, the mass-transfer resistances in the K2CO3 samples were kept to a minimum by customizing the TGA reactor system employed to allow for the use of a 1.5 in. i.d. circular stainless steel crucible to hold the sample.12 This wide crucible permitted the larger K2CO3 sample quantity to be spread in a predominantly monolayer particle distribution as in typical TGA studies, using the methodology previously developed in our laboratory to reduce the effects of interparticle diffusion limitations in TGA samples.18 Intraparticle diffusion cannot be reduced because there is agglomeration of K2CO3 during cycling, which is one of the limitations to be considered for process scale-up.

It is important to note that partial pressures (PCO2 and PH2O) have been used in formulating the above rate equations (eqs 4 and 5) and will be used in place of concentrations (CCO2 and CH2O) for model development in this work. For the purpose of analyzing the experimental results here, the use of partial pressures is sufficient because CO2 and H2O are present in low concentrations and the results have been obtained over a narrow temperature range (40−60 °C). However, for higher concentrations and/or wider temperature ranges, only the use of concentrations (CCO2 and CH2O) will be appropriate. Also note that rate equations 4 and 5 can be divided throughout by C0 (concentration of active sites per kilogram of the regenerated K2CO3 sample at t = 0) to express the reaction rate as a conversion rate r′ (units, time−1), which is common practice for gas−solid reaction systems. Rate equations 4 and 5 can be rewritten with constant coefficients for the independent conversion-based variables of the forward and backward reactions as shown below by eqs 6 and 7, respectively.

3. KINETIC MODEL DEVELOPMENT Recent work in the literature has demonstrated that the global reaction mechanism of solid K2CO3 under postcombustion conditions consists of only reversible reactions 1 and 2, which occur in parallel to each other and compete for the active sites.12,13 The direct conversion of K2CO3·(1.5 H2O) to KHCO3, i.e., the sequential carbonation reaction 3, was not detected. 3.1. Simple Chemical Reaction Model (CRM). Given that only reversible reactions 1 and 2 are occurring via the direct reaction of K2CO3 with the flue gas components, the first approach to modeling the kinetics of this gas−solid reaction system would be to treat reactions 1 and 2 as two parallel, simple chemical reactions in progress. Analytically, such a kinetic model for this system of reactions can be represented as follows. Rate of formation of KHCO3 by reaction 1 at time t r1, t =

C0dX1, t dt

(8)

2 or 1 wrt C KHCO3 , respectively)

(9)

a 2 = k 2PHq 2OC0

(10)

a−2 = k −2C0

(11)

These constant coefficients can be determined by performing a multiple regression using least-squares with the time-based conversion data from the TGA-MS for the carbonation step. Forcing any constant intercept in the model eqs 6 and 7 to be zero, as shown above, yields a coefficient of determination (R2) that is higher than that when eqs 6 and 7 are allowed to include a nonzero constant intercept. A higher resulting R2 when fewer degrees of freedom are allowed proves that this model is consistent and qualitatively follows the variations in the experimental data. Determining the constant regression coefficients during carbonation at different temperatures for a given flue gas composition enables the determination of the apparent activation energies (EappCRM) of the forward and backward reactions of carbonation and hydration. EappCRM for a particular half reaction is found from the slope of the plot of the natural logarithm of its associated regression coefficients determined at different temperatures against reciprocal temperature. The kinetic model can be validated if the estimated apparent activation energy consistently follows the Arrhenius equation as presented elsewhere.17 3.2. Langmuir−Hinshelwood Model. With the carbonation of solid K2CO3 being carried out at low temperatures (40−60 °C), involving reactions with the flue gas components of CO2 and subcritical H2O, it is very likely that the rates of reactions 1 and 2 may be limited by the rates of adsorption of at least one of the gaseous species. In previous studies, it has been evidenced that hydration and carbonation rates have a similar order of magnitude,12,13 but the equilibrium constant for CO2

n 2 = k1CtPCO P m − k −1(C KHCO or C KHCO3, t ) 2 H2O 3, t

where X1,t is the K2CO3 conversion into KHCO3 obtained from the CO2 uptake detected by the MS and Xt is the overall K2CO3 conversion. The rate of formation of K2CO3·(1.5 H2O) by reaction 2 at time t is = k 2CtPHq 2O − k −2C K 2CO3·(1.5H 2O), t

= k 2PHq 2OC0(1 − X t ) − k −2C0X 2, t

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a−1 = k −1C02 or k −1C0 (if backward carbonation is order

(4)

dt

r2, t = a 2(1 − X t ) − a−2X 2, t n a1 = k1PCO Pm C 2 H 2O 0

n = k1PCO P m C (1 − X t ) − k −1(C02X1,2 t or C0X1, t ) 2 H2O 0

C0dX 2, t

(6)

where the constant coefficients

n = k1C0(1 − X t )PCO P m − k −1((C0X1, t )2 or C0X1, t ) 2 H2O

r2, t =

r1, t = a1(1 − X t ) − a−1(X1,2 t or X1, t )

(5)

where X2,t is the K2CO3 conversion into K2CO3·(1.5 H2O) obtained from the difference between the total weight change in the TGA and the total weight gain due to KHCO3 formation determined by the CO2 uptake data from the MS. Note that Xt = X1,t + X2,t. 855


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negative apparent activation energies, then the proposed model is not a valid representation of the real reaction mechanism.

adsorption on K2CO3 is significantly smaller than the equilibrium constant for H2O adsorption on K2CO3;16 therefore, the adsorption of water vapor may be the limiting step because it is the only component in the gas phase involved in both carbonation and hydration reactions. Even though the global reaction mechanism for K2CO3 carbonation proceeds via the occurrence of reactions 1 and 2 in parallel to each other, the detailed or stepwise mechanism for each reaction may include an initial rate-limiting adsorption step. The process of chemisorption of H2O and CO2 by K2CO3 is expected to include initial adsorption step(s) in addition to chemical reaction steps. One possible stepwise reaction scheme for the carbonation and hydration reactions may involve an initial ratelimiting H2O adsorption step, as described below by eqs 12−14. K 2CO3(s) + H 2O(g) ⇋ K 2CO3 ·[H 2O]ads K 2CO3 ·[H 2O]ads + CO2 (g) ⇋ 2KHCO3(s)

4. RESULTS AND DISCUSSION 4.1. Observed Conversion Trends. Conversions of the K2CO3 sample to KHCO3 (X1), K2CO3·(1.5 H2O) (X2), and their total (X), were calculated from the TGA-MS data during every carbonation step. The sample conversions observed during cycles 1 and 50 of each multicycle test, after 3000 s and at the end (7800 s) of carbonation, are presented in Tables 2 Table 2. Bicarbonate (X1), Hydrate (X2), and Total (X) Conversions Calculated after 3000 S of Carbonation during (a) Cycle 1 and (b) Cycle 50 at the Different Temperatures and Model Flue Gas Compositions Used

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(a) cycle 1 (at t = 3000 s)

(13)

K 2CO3 · [H 2O]ads + 0.5H 2O(g) ⇋ K 2CO3·(1.5H 2O)(s) (14)

Based on this mechanism, the rates of formation of KHCO3 and K2CO3·(1.5 H2O), at time t, are given below by eqs 15 and 16, respectively. r1, t =

k1K H2OPH2OPCO2C0(1 − X t ) 1 + K H2OPH2O

− k −1C02X1,2 t

(15)

T (°C)

CO2 (std. vol %)

X1

X2

X

40 50 60 40 50 60 40 50 60

1.42 1.42 1.42 2.34 2.34 2.34 4.14 4.14 4.14

0.19 0.22 0.21 0.14 0.20 0.18 0.08 0.16 0.12

0.61 0.38 0.02 0.71 0.30 0.10 0.94 0.38 0.07

0.81 0.60 0.23 0.85 0.50 0.28 1.02 0.54 0.19

(b)

r2, t =

k 2K H2OPH2 2OC0(1 − X t ) 1 + K H2OPH2O

− k −2C0X 2, t

cycle 50 (at t = 3000 s)

(16)

Equations 15 and 16 can also be expressed with constant coefficients for the independent conversion variables in the same form as eqs 6 and 7, where the regression coefficients are a1 =

k1K H2OPH2OPCO2C0 1 + K H2OPH2O

a−1 = k −1C02 a2 =

(17) (18)

k 2K H2OPH2 2OC0 1 + K H2OPH2O

a−2 = k −2C0

T (°C)

CO2 (std. vol %)

X1

X2

X

40 50 60 40 50 60 40 50 60

1.42 1.42 1.42 2.34 2.34 2.34 4.14 4.14 4.14

0.49 0.52 0.45 0.57 0.57 0.42 0.69 0.56 0.28

0.22 0.13 0.09 0.30 0.07 0.08 0.31 0.13 0.06

0.70 0.65 0.54 0.87 0.64 0.50 1.00 0.69 0.34

and 3, respectively. In the first 3000 s, the bulk of the sample conversion occurs for most of the flue gas and temperature conditions studied, and equilibrium is assumed at 7800 s, after allowing the reactions to progress toward equilibrium, with mass-transfer limitations, for the remaining 4800 s. Before the observed bicarbonate and hydrate conversion trends in this kinetic study are analyzed, it is important for the readers to keep in mind that the K2CO3 phase derived from previously hydrated samples, called phase II, has a much lower reactivity and yield for bicarbonate formation (reaction 1) than the K2CO3 phase derived from KHCO3, called phase I, from results in the literature.6,12−15 Previous studies have also concluded that phase II may favor the hydration reaction 2 more than phase I.6,14,15 The regenerated K2CO3 starting sample, carbonated in cycle 1 of the multicycle tests in this study, was mostly composed of phase II.12 Over the course of 50 consecutive regeneration− carbonation cycles, the phase I content of the sample increases significantly and stabilizes after a sufficient number of cycles. The stabilized amount of phase I contained in the sample by

(19) (20)

The constant regression coefficients in eqs 6 and 7 are determined from the time-based TGA-MS conversion data during carbonation in the first and last (50th) cycle of each multicycle test. The regression coefficients for the forward carbonation and hydration rate terms at different temperatures for a given flue gas composition are used to determine the apparent activation energies for the forward carbonation and hydration reactions according to the simple chemical reaction model (EappCRM) and the suggested possible H2O adsorption limited L-H model (EappL‑H). The theoretical consistency of the models, related to the resulting apparent activation energies of the forward reactions, is tested to determine the underlying nature of the kinetic behavior of K2CO3. If a kinetic model follows the Arrhenius equation consistently, it could be a possible representation of the reaction mechanism, but if a kinetic model contradicts the Arrhenius equation, by yielding 856


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equimolar level (2.34 std vol %). Further increase in CO2 concentration to above the equimolar level does not result in any significant change in X1 at equilibrium compared to that observed at the equimolar level. At 40 °C, hydrate conversion (X2) increases along with an increase in CO2 concentration at 3000 s, and this trend is still maintained at equilibrium. In the first cycles at 50 °C, X2 exhibits a minimum at the equimolar level at 3000 s as the CO2 concentration is increased. However, at equilibrium at 50 °C, X2 is observed to be increasing along with the CO2 concentration. At 60 °C, on the other hand, X2 is observed to be maximum for the equimolar CO2/H2O flue gas feed. Total conversions (X) greater than 1 may be observed at temperatures of 40 °C or lower. At these lower temperatures, it is possible for the K2CO3 samples to capture more H2O than that corresponding to K2CO3·(1.5 H2O) because of hydrogen bonding and condensation. This phenomenon is more pronounced in cycle 1 because of the high content of phase II in the K2CO3 sample which favors the hydration reaction 2. During cycle 1, increasing the CO2 concentration at any of the given temperatures suppresses the rate and extent of bicarbonate formation (X1), unexpectedly, while resulting in increasing hydration extents at 40 and 50 °C at equilibrium. It is possible that the carbonation rates and final extents of phase II of K2CO3 in cycle 1 might be very sensitive to the minor suppression in H2O concentrations caused by the addition of more CO2 in the flue gas (see Table 1). This observation is an important reason why the L-H model proposed here is based on H2O adsorption, instead of CO2 adsorption, as the ratelimiting step. In Table 2b for cycle 50, the bicarbonate conversion (X1) at 3000 s is again seen to be at a maximum at 50 °C upon increasing the carbonation temperature from 40 to 60 °C, for the flue gas compositions with CO2 concentrations at the equimolar level or below with respect to H2O. This trend is not observed for the flue gas containing above equimolar CO2, because the reaction rate for bicarbonate formation (reaction 1) and equilibrium extent for X1 are much higher for this flue gas mixture at 40 °C. At equilibrium, as shown in Table 3b, X1 decreases as the temperature is raised from 40 to 60 °C for all of the flue gas mixtures tested. The bicarbonate conversions observed in cycle 50 are significantly higher than those observed in cycle 1 because of the increased contents of phase I present in the K2CO3 samples. The hydrate conversions (X2) shown in Tables 2b and 3b exhibit decreasing trends with increasing temperature under the various gas compositions used. The extents of hydration in cycle 50 are significantly lower than their corresponding first cycles, except for the case where the K2CO3 sample is carbonated at 60 °C by the flue gas mixture containing less than equimolar CO2 with respect to H2O. From Tables 2b and 3b for cycle 50, the trends in X1 and X2 are now assessed with respect to a given temperature and increasing CO2 concentrations in the flue gas. At 40 °C, an increase in the CO2 concentration results in an increased X1 at 3000 and 7800 s. However, after 3000 s of carbonation at 50 °C, a maximum in X1 is observed for the flue gas mixture containing equimolar CO2/H2O, along with very low hydrate formation (X2). The observations of maxima occurring for X1 after 3000 s at 50 °C compared to 40 and 60 °C, along with the observed maximum for X1 at 3000 s for the equimolar CO2/ H2O gas mixture, likely indicate that an optimum carbonation rate is observed at 50 °C under equimolar CO2/H2O

Table 3. Bicarbonate (X1), Hydrate (X2), and Total (X) Conversions Calculated at the End (7800 s) of Carbonation for (a) Cycle 1 and (b) Cycle 50 at the Different Temperatures and Model Flue Gas Compositions Used (a) cycle 1 (at t = 7800 s) T (°C)

CO2 (std. vol %)

X1

X2

X

40 50 60 40 50 60 40 50 60

1.42 1.42 1.42 2.34 2.34 2.34 4.14 4.14 4.14

0.28 0.24 0.26 0.18 0.21 0.18 0.19 0.21 0.17

0.72 0.58 0.10 0.93 0.63 0.27 1.00 0.65 0.19

1.00 0.81 0.37 1.10 0.84 0.44 1.19 0.85 0.36

(b) cycle 50 (at t = 7800 s) T (°C)

CO2 (std. vol %)

X1

X2

X

40 50 60 40 50 60 40 50 60

1.42 1.42 1.42 2.34 2.34 2.34 4.14 4.14 4.14

0.59 0.52 0.49 0.68 0.60 0.44 0.76 0.66 0.28

0.41 0.31 0.19 0.28 0.24 0.16 0.37 0.27 0.14

1.00 0.82 0.68 0.96 0.84 0.60 1.13 0.93 0.42

cycle 50 is related to the carbonation temperature and flue gas composition used for that particular multicycle test. From Table 2a for cycle 1, it is observed that the bicarbonate conversion (X1) is at a maximum at 50 °C when the temperature is increased from 40 to 60 °C, for all flue gas compositions at 3000 s. At 7800 s in Table 3a, maxima in X1 at 50 °C are still observed at equilibrium for the flue gas compositions containing equimolar or greater concentrations of CO2 with respect to H2O. For the flue gas containing less than equimolar (1.42 std vol %) CO2, X1 is seen to be minimum at 50 °C once the system is considered to be at equilibrium after 7800 s, likely due to hydration being more favored between 3000 and 7800 s. However, it is important to note that the uncertainties in determining X1 and X2 by the TGA-MS system are ±1.06% and ±2.06% as conversion percentages, or ±0.01 and ±0.02, respectively.12 Hence, the uncertainty in X1 is comparable to the differences between the X1 extrema at 50 °C and the corresponding X1 data at 40 and 60 °C for the different gas compositions. Reaction 1 is exothermic; therefore, by Le Chatelier’s principle, X1 at equilibrium would be expected to decrease with an increase in temperature. In the case of hydration conversion (X2) in cycle 1, both Tables 2a and 3a show that X2 decreases with an increase in temperature from 40 to 60 °C for all flue gas compositions tested. The hydration reaction 2 is also an exothermic reaction. The trends for X1 and X2, in Tables 2a and 3a for cycle 1, are now viewed with respect to a given temperature and changing gas compositions. At 40, 50, and 60 °C, X1 decreases when the CO2 concentration is increased from below equimolar to above the equimolar level (4.14 std vol %) at 3000 s. At the end of the carbonation, however, X1 decreases significantly only when the CO2 concentration is increased from below equimolar to the 857


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Industrial & Engineering Chemistry Research conditions; however, the maximum carbonation rate is observed for the above equimolar CO2/H2O gas mixture at 40 °C. After 7800 s at 50 °C, the trend in X1 changes to one which increases with the flue gas CO2 concentration. Unlike in cycle 1, X1 in cycle 50 can increase along with the CO2 concentration because the large quantities of phase I present in the K2CO3 samples make them more amenable to carbonation and capable of effectively reacting with higher CO 2 concentrations. Hydrate conversions (X2) in Table 2b, at 3000 s, increase with an increase in CO2 concentration at 40 °C, while at 50 °C, hydration is seen to be at a minimum in the case of the equimolar CO2/H2O gas mixture. At equilibrium, in Table 3b, hydration conversions (X2) are seen to be at a minimum for the equimolar CO2/H2O gas mixture at both 40 and 50 °C. On the other hand, at 60 °C in cycle 50, both bicarbonate (X1) and hydrate (X2) conversions are observed to decrease when the CO2 concentration in the flue gas is increased. It is very likely that at the higher temperature of 60 °C, this observation is due to the reaction system becoming very sensitive to the suppression in H2O concentration which results when the amount of CO2 fed to the gas mixture is increased. The resulting lower H2O concentrations along with higher backward reaction rates negatively impact both the carbonation and hydration reactions. Also, the corresponding X1 values at 60 °C after 3000 and 7800 s of carbonation, in Tables 2b and 3b, respectively, are almost the same, thus indicating that the system reaches carbonation equilibrium faster. The increase in temperature to 60 °C moves the equilibrium level of X1 lower, which decreases the difference between the speeds of the forward and backward carbonation reactions. Also, diffusion limitations do not play a huge role in the progress of carbonation because the hydrate conversion and total sample conversion remain low under these conditions, thereby allowing for equilibrium to be approached more promptly. Information about the accuracy, precision and uncertainty of the bicarbonate and hydrate conversion data obtained from the TGA-MS analysis system has been presented previously.12 4.2. Kinetics during Carbonation. Multiple regression analysis was performed to determine the regression coefficients (a1, a−1, a2, and a−2) for the forward and backward reactions in rate equations 6 and 7 using the time-based bicarbonate (X1,t) and hydrate (X2,t) conversion data from the TGA-MS analysis system. The regression coefficients were determined from the TGA-MS data in cycle 1 and cycle 50 of all the multicycle tests carried out under different carbonation conditions in this kinetic study. In this type of gas−solid reaction system, the uptake of CO2 and H2O by the K2CO3 sample introduces masstransfer limitations in the carbonation and hydration reaction rates due to pore blockage. At greater times (t > 1000−5000 s), the reaction rates become primarily mass-transfer-limited because of intrapore diffusion, which is characterized by a linear drift in X1 and/or X2 over time, as presented in Figure 1. The time ranges for the regression analysis were carefully selected, from 96 s after the beginning of carbonation until the time when X1 and X2 begin to stabilize, so as to exclude the initial times of gas concentration development in the reactor due to dispersion effects19 and the greater times when the reactions are mainly mass-transfer-controlled. The upper time limit for regression analysis varies for each of the cycles analyzed, and the conversion ranges are also different, as the main focus was on isolating and analyzing the kinetically controlled times of the reactions.

Figure 1. Bicarbonate (X1,t) and hydrate (X2,t) conversions versus carbonation time t for the flue gas mixture containing 1.42 std. vol % CO2 in cycle 50 at 60 °C.

As a first attempt, both the carbonation and hydration forward reaction rates are assumed to proceed with a first-order dependence on the concentration of the active K2CO3 sites in eqs 4 and 5. The backward carbonation rate term is considered to have a second-order dependence on the concentration of KHCO3 sites in eq 4 (equivalent to the reaction order for overall carbonation as an elementary reaction), because the coefficient of determination (R2) for the regression analysis is higher with this consideration compared to the first-order assumption. The backward hydration rate term is assumed to be first-order with respect to the concentration of K2CO3·(1.5 H2O) sites. Reaction order assumptions are being made because the real reaction orders are unknown. 4.3. Chemical Reaction Model Evaluation. The regression coefficients determined for eqs 6 and 7 are initially considered to have only a temperature dependence due to rate constants that follow the Arrhenius equation (eqs 8−11). The validity of this simple chemical reaction model in section 3.1 is tested by determining the apparent activation energies (EappCRM) for the forward carbonation and hydration reactions. These apparent activation energies are calculated from the forward reaction rate regression coefficients using the slopes of the ln(ai) versus 1/T plots for a given flue gas composition. The EappCRM results have been determined for cycles 1 and 50. The plots of the forward reaction rate regression coefficients (a1 and a2) determined at different temperatures for the flue gas mixture containing 1.42 std vol % CO2 (below equimolar with respect to H2O) are presented in Figure 2, for cycles 1 and 50. Linear fits to the regression data are also included in these plots to test the linearity of the ln(ai) data and help calculate the EappCRM from its slope. The discussion in this paper requires the presentation of regression data for only one of the flue gas compositions used because the trends in the regression data are similar for the other gas compositions utilized in our experiments. The regression data in Figure 2a for forward carbonation in cycle 1 shows the forward reaction rate increasing from 40 to 50 °C, but the rate goes through a maximum around 50 °C and is slightly lower at 60 °C. If the regression coefficients were dependent only on Arrhenius-type kinetic rate constants, as described by the simple chemical reaction model in section 3.1, the forward reaction rates would be expected to be increasing with an increase in temperature and yield a linear ln(a1) versus 1/T plot. In the results, however, the linear fit is in poor agreement with the data, which indicates that the forward carbonation reaction rate is not purely controlled by the 858


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Figure 2. Plots of the regression coefficients for the forward carbonation and hydration reaction rate terms from the simple chemical reaction model at different temperatures for the flue gas mixture containing 1.42 std. vol % CO2: (a) forward carbonation, cycle 1; (b) forward carbonation, cycle 50; (c) forward hydration, cycle 1; and (d) forward hydration, cycle 50.

kinetics of simple chemical reactions. The forward carbonation rate coefficients might include other temperature-dependent terms besides the Arrhenius rate constant, which might be decreasing the reaction rate as the temperature increases. For cycle 50, the regression coefficients for forward carbonation, shown in Figure 2b, are much higher compared to cycle 1 because of higher contents of the more reactive phase I in the K2CO3 samples. Increasing the temperature from 40 to 50 °C results in a slight increase in the rate of forward carbonation; however, a further increase in temperature to 60 °C results in a drastic decrease in the forward reaction rate. The linear fit is again in poor agreement with the data for cycle 50 and, in fact, yields a negative apparent activation energy, EappCRM = −15.5 kJ mol−1. A negative activation energy in the Arrhenius equation is not possible because it contradicts the concepts of reaction energetics, and most likely points to a significant temperature dependence of the reaction rate on the rate of a process which decreases at higher temperatures. Therefore, the simple chemical reaction model is incorrect for modeling the forward carbonation reaction, and this reaction is likely limited by an initial adsorption step. The estimated rate coefficients for the forward hydration reaction in cycle 1, shown in Figure 2c, decrease drastically with an increase in temperature. The decrease in the hydration rate with temperature is so dominant in this case that the linear fit matches the regression data very well, while yielding a large negative apparent activation energy, EappCRM = −79.1 kJ mol−1. This result reveals that the forward hydration reaction rate is indeed significantly dependent or limited by the process of H2O adsorption on the K2CO3 sample, because negative activation energies are invalid results which imply that the single elementary reaction model does not model the forward hydration reaction. The adsorption of H2O on K2CO3 is an exothermic process (ΔHadsH2O < 0), and the overall rate of H2O adsorption decreases with an increase in temperature based on

its equilibrium constant (KH2O) for this process. Rate coefficients for the forward hydration reaction in cycle 50, in Figure 2d, also exhibit a decreasing trend with increasing temperature, thus yielding inconsistent activation energies. Therefore, the chemical reaction model is invalid for describing this chemisorption process involving K2CO3. A discussion on the backward carbonation and hydration reaction rate coefficients is beyond the scope of this work because focusing on understanding the underlying kinetic nature of the forward reactions is more important for the development of this CO2 capture technology, at present. The backward reactions are probably more impacted by the masstransfer limitations in this gas−solid reaction system, which become more prominent as sample conversion increases, thus increasing uncertainties in the estimated backward rate coefficients. Moreover, the backward rate coefficients (a−1 and a−2) determined at 40 °C were negligibly small or even negative (because of uncertainty), indicating that the reverse reactions for carbonation and hydration are very slow at 40 °C. These results likely explain why K2CO3 hydration can proceed beyond K2CO3·(1.5 H2O) formation at low temperatures, possibly via condensation. Consequently, the meaningful determination of the apparent activation energies of the backward reactions is not possible using the insufficient number of data points at 50 and 60 °C. The backward reaction rates for carbonation and hydration are observed to increase with an increase in temperature and may also include endothermic desorption limitations which are not considered here. 4.4. L-H Reaction Model Evaluation. Based on the theoretical invalidity of the negative EappCRM results in Figure 2 for the simple chemical reaction model, it is quite clear that both the carbonation and hydration forward reaction rates are significantly limited by at least one initial exothermic adsorption step. Figure 2c,d suggests that the forward hydration reaction 859


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Figure 3. Plots of the adjusted regression coefficients for the forward carbonation and hydration reaction rate terms in the H2O adsorption limited kinetic model at different temperatures for the flue gas mixture containing 1.42 std. vol % CO2: (a) forward carbonation, cycle 1; (b) forward carbonation, cycle 50; (c) forward hydration, cycle 1; and (d) forward hydration, cycle 50.

carbonation and hydration according to this model are shown by eqs 15 and 16. These rate equations have been derived assuming a first-order dependence on the concentration of K2CO3 active sites for the H2O adsorption step (eq 12). H2O desorption and the forward carbonation reaction are assumed to be first-order with respect to the concentration of the K2CO3·[H2O]ads intermediate or activated species. The forward and backward hydration reactions (eq 14) have been assumed to proceed with a first-order dependence on the concentrations of K2CO3·[H2O]ads and K2CO3·(1.5 H2O) sites, respectively, because the real reaction orders are unknown. Only the backward carbonation reaction is considered to be secondorder with respect to the concentration of KHCO3 sites, which assumes carbonation to be an elementary reaction, as explained earlier. The resulting rate equations for carbonation and hydration for regression analysis purposes are of the same form as eqs 6 and 7 for the chemical reaction model. The expressions for the regression coefficients of the forward carbonation and hydration rate terms, showing their dependence on the equilibrium constant of H2O (KH2O), are given by eqs 17 and 19, respectively. Because both models have the same form of rate equations, the values of the regression coefficients for the chemical reaction model can be directly adjusted to find the apparent activation energies (E appL‑H ) for the forward carbonation and hydration reactions according to the H2O adsorption limited L-H kinetic model. Carbonation and hydration rate constants of the L-H kinetic model are calculated by dividing their respective chemical reaction model regression coefficients by KH2O. These adjusted coefficients are then used in the Arrhenius equation to determine EappL‑H, where KH2O ∝

rate is H2O adsorption limited because H2O is the only component of the flue gas involved in this reaction. Forward carbonation, on the other hand, could be limited by only H2O adsorption, only CO2 adsorption, or a more complex coadsorption/multistep adsorption mechanism involving both H2O and CO2. Theoretical computational estimates of the equilibrium constants for H2O (KH2O) and CO2 (KCO2) adsorption on K2CO3 have been provided in the recent literature.16 Using these equilibrium constant estimates for H2O and CO2 adsorption at 0 and 100 °C, the possible equilibrium constant values at 40, 50, and 60 °C have been determined for this study. The values of KH2O are 10 orders of magnitude higher than the corresponding KCO2 values at 40, 50, and 60 °C. The rates of bicarbonate and hydrate formation, from Tables 2 and 3, however, are comparable to each other (within the same order of magnitude) and are likely governed by reaction steps with similar overall rates. Therefore, the adsorption of subcritical H2O on K2CO3 is a more likely initial reaction step for forward carbonation, as it is already known to be limiting the rate of forward hydration. Moreover, the observations of decreasing bicarbonate conversions upon increasing the CO2 concentration in the flue gas in cycle 1 and also at 60 °C in cycle 50 cannot be explained if CO2 adsorption is the initial rate-limiting step for forward carbonation. The possibility of both forward carbonation and hydration reactions only being limited by an initial H2O adsorption step is evaluated to showcase the validity of considering adsorption limitations in the rate equations and the impact it has on the resulting apparent activation energies (EappL‑H). The reactions involved in this L-H kinetic model are given by eqs 12−14 in section 3.2. An initial rate-limiting H2O adsorption step is a likely reaction scenario because the activated K2CO3·[H2O]ads basic site might have a much greater affinity for interacting with acidic CO2 than the neutral K2CO3 salt. The rates for

(

exp −

ΔHadsH2O RT

);

ΔHadsH2O < 0, and EappL‑H = EappCRM −

ΔHadsH2O. However, the accuracy of this model in determining 860


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Industrial & Engineering Chemistry Research EappL‑H will be higher if the term KH2O·PH2O ≪ 1 in the denominators of a1 and a2. The ΔHads values for H2O and CO2 adsorption on K2CO3 from the theoretical estimates of the equilibrium constants in the literature are similar, −54.6 and −63.9 kJ mol−1, respectively.16 The plots of the natural logarithms of a1/KH2O and a2/KH2O against reciprocal temperature to determine the EappL‑H values for forward carbonation and hydration in cycles 1 and 50 are presented in Figure 3, for the flue gas mixture containing 1.42 std vol % CO2. The KH2O-adjusted regression coefficients for forward carbonation in cycle 1 are plotted in Figure 3a. After considering the H2O adsorption limitation, the plot is in much better agreement with its linear fit than the corresponding plot for the simple chemical reaction model. The apparent activation energy for the forward carbonation rate constant in cycle 1 according to this model is a valid positive number, EappL‑H = 76.9 kJ mol−1. The adjusted regression coefficients for forward carbonation in cycle 50, shown in Figure 3b, are higher than for cycle 1, representing higher carbonation rates due to the presence of larger quantities of phase I in the K2CO3 sample in cycle 50. Higher carbonation rates are mainly due to the higher phase I content of the sample and not due to an improved morphology.12 The plotted regression coefficients are in good agreement with their linear fit and now result in a positive EappL‑H of 39.1 kJ mol−1, which is a theoretically consistent result. The apparent activation energy for forward carbonation in cycle 1 is greater than that for cycle 50, thus validating previous experimental results that phase I of K2CO3 has a better carbonation reactivity and bicarbonate yield. More specifically, according to this model, the activated intermediate species, K2CO3·[H2O]ads, of phase I favors bicarbonate formation more than its phase II counterpart. For forward hydration in cycle 1, however, the adjusted regression coefficients in Figure 3c, still result in an invalid negative apparent activation energy. Therefore, the kinetic model assumed is still incorrect or inadequate in its current form; however, the forward hydration reaction can still only be limited by initial H2O adsorption step(s). Furthermore, this inconsistent result could be due to the error introduced into the adsorption limited model by the magnitude of the KH2O·PH2O term in the denominator of a2 being comparable to or greater than 1. This result could also mean that the forward hydration reaction might have a different, likely higher, real reaction order dependence on the concentration of the activated K2CO3· [H2O]ads species. In cycle 50, the plot of the adjusted regression coefficients for forward hydration in Figure 3d is in good agreement with its linear fit and evidences a valid positive apparent activation energy, EappL‑H = 42.6 kJ mol−1. Considering that the reasons for observing a negative EappL‑H for forward hydration in cycle 1 are also applicable to the results of cycle 50, it is quite likely that the EappL‑H for forward hydration in cycle 1 is lower than that for cycle 50. Previous conclusions that phase II of K2CO3 favors hydrate formation more than phase I may, therefore, be in consensus with the results for this model. Specifically, according to this model, the activated K2CO3· [H2O]ads species produced from phase II of K2CO3 in cycle 1 is more likely to form the hydrate than the activated species produced from phase I of K2CO3. Similar apparent activation energy (EappL‑H) trends were found for the other flue gas compositions used as well. Uncertainties in the determination of the EappL‑H values come

from the uncertainties in measuring the bicarbonate (X1) and hydrate (X2) conversions of the sample by the TGA-MS system, presented previously,12 and the variable mass-transfer limitations in the sample, depending upon the sample morphology, extent of conversion, and the carbonation conditions used, which are not considered here. Further uncertainty in the EappL‑H results for cycle 50 may be present because the stabilized phase compositions of the samples are different for the different flue gas compositions and temperatures used. Using the EappL‑H values determined for forward carbonation in cycles 1 and 50 for all the flue gas compositions, the mean EappL‑H and the uncertainties in estimating the EappL‑H values have been calculated. For forward carbonation, in cycle 1, EappL‑H = 63.0 ± 12.4 kJ mol−1, and in cycle 50, EappL‑H = 34.5 ± 4.0 kJ mol−1. For forward hydration, however, in cycle 1, the EappL‑H values are still inconsistent because of the reasons mentioned above, which also apply to cycle 50; therefore, discussion of their EappL‑H values is omitted. The mean EappL‑H values and uncertainties mentioned for forward carbonation are only meant to give the reader an idea of the relative values and their variance based on the reaction mechanism assumptions made here. The true EappL‑H values and uncertainties cannot be determined until further information about the real stepwise mechanisms and real reaction orders for carbonation and hydration can be established using more reliable estimates of the equilibrium constants for the gaseous species. The H2O adsorption limited model presented here is to be considered only as one of the likely reaction schemes for this gas−solid reaction system. It is important for the reader to note that the equilibrium constants for H2O and CO2 adsorption on K2CO3 used in this study are theoretical estimates and could be very different in magnitude and temperature dependence (ΔHads) in reality. Therefore, the EappL‑H estimates above cannot be considered as realistic values and are merely part of a proof-of-concept exercise to show the validity of including adsorption rate limitations for modeling the kinetics of this reaction system. Also, because the ΔHads values for H2O and CO2 adsorption on K2CO3 from the theoretical estimates are similar in magnitude, it is not possible to tell whether H2O or CO2 adsorption is limiting the rate of forward carbonation simply based on the validity of the EappL‑H results for the kinetic models considering their respective adsorptions to be ratelimiting. Moreover, the different phases of K2CO3 might have their own unique values for KH2O and KCO2, along with differing values for the Arrhenius rate constants for forward carbonation and hydration, k1 and k2. Therefore, until experimental values for KH2O and KCO2 are available for each of the phases I and II of K2CO3, an accurate reaction scheme and representative kinetic model cannot be confirmed. Forward carbonation could still be limited by the adsorption of H2O or CO2 or involve a more complex mechanism. Future work might include fundamental experimental studies to determine intrinsic parameters, such as the equilibrium constants for H2O and CO2 adsorptions on the different K2CO3 phases, as well as the energetics and reaction orders of the carbonation and hydration reactions involved. These findings may be useful in developing more accurate predictive theoretical models and simulations for understanding the feasible or dominant reaction pathways in this system, in order to explain the real detailed reaction mechanism observed in practice. In terms of takeaways for process design from this study, it would be important to find the optimum carbonation 861


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activation energies (EappCRM) for the forward carbonation and hydration reactions. Negative EappCRM values are theoretically inconsistent with the concepts of reaction energetics, indicating that the simple chemical reaction model is incorrect, and implied that the forward reaction rates were significantly limited by at least one initial exothermic adsorption step. A L-H kinetic model based on a possible reaction scenario involving an initial rate-limiting H2O adsorption step common to both forward carbonation and hydration was proposed for this reaction system. This H2O adsorption limited model yielded adjusted regression coefficient plots in good agreement with their corresponding linear fits and/or more consistent apparent activation energies (EappL‑H) for the forward carbonation and hydration reactions. The improved theoretical consistency of the EappL‑H results for the H2O adsorption limited model shows that the consideration of adsorption rate limitations in modeling the kinetics of K2CO3 carbonation and hydration are valid. Moreover, the EappL‑H results show that the apparent activation energy for carbonation in cycle 1 is higher than in cycle 50, while the apparent activation energy for hydration in cycle 1 is likely lower than in cycle 50. These results are in agreement with previous experimental findings, which state that phase I of K2CO3 favors bicarbonate formation (cycle 50), while phase II favors hydrate formation (cycle 1). Important implications for future process design are also discussed. An optimal carbonation rate was observed at 50 °C for the flue gas mixture containing equimolar CO2 with respect to H2O. However, the maximum carbonation rate was realized during the stabilized operation of K2CO3 (cycle 50) in the flue gas mixture containing above equimolar levels of CO2 with respect to H2O, at the adsorption-favoring lower temperature of 40 °C. Higher CO2 concentrations relative to H2O lead to higher quantities of phase I to be present in the sorbent during stabilized operation, thus resulting in higher carbonation rates and higher realized CO2 capacities. On the basis of these results, hydrophobic or CO2 adsorptive support materials for K2CO3 might be the most promising candidates to maximize the carbonation performance of K2CO3-based solid sorbents in practice.

temperature for the process in order to realize the best possible carbonation rate based on the concentrations of CO2 and H2O in the flue gas. A low temperature might inhibit the carbonation rate kinetically (40 °C in this study), while a high temperature may result in low carbonation rates due to adsorption limitations (60 °C in this study). In this work, the optimal rates for carbonation were observed at 50 °C for the flue gas mixture containing equimolar CO2 with respect to H2O. More importantly, the feasibility of a process using a flue gas mixture with an above equimolar level of CO2 must be evaluated, because it could have better carbonation rates and a higher stabilized CO2 capacity at lower temperatures which favor adsorption. An above equimolar CO2-containing flue gas may be produced by the integration of a flue gas water and energy recovery step prior to the carbonation unit. However, care must be taken to ensure the presence of adequate amounts of H2O in the flue gas, so as to not suppress the carbonation rates, while still trying to keep hydration levels as low as possible. Sample dehydration is an energy penalty during regeneration. Mass-transfer effects are present over a wide range of conversions in this gas−solid reaction system; however, they will vary greatly based on sorbent morphology, system geometry, and process configurations. Therefore, the analysis of mass-transfer effects on reaction rates has been excluded from the kinetic models in this study because the mass-transfer effects in the laboratory scale fixed bed system here would be drastically different than those in a large-scale process, which may include a fluidized bed configuration and a supported K2CO3 sorbent. For selecting a potential support material for K2CO3, the impacts of choosing a hydrophilic, neutral, hydrophobic, or a CO2-adsorptive support on the carbonation performance of K2CO3 must be evaluated. It is likely that a hydrophilic support will promote hydrate formation, due to a higher apparent H2O concentration locally at the active sites, and suppress bicarbonate formation, thus maintaining a high proportion of the less reactive phase II in the sorbent, which will result in a lower stabilized CO2 capacity. However, a hydrophobic or CO2-adsorptive support may promote bicarbonate formation over hydration because of a lower apparent H2O concentration or a higher apparent CO2 concentration at the active sites, respectively, and maintain a high proportion of phase I in the sorbent, which will result in a higher stabilized CO2 capacity. K 2 CO 3 -based solid sorbents show promise for future applications in postcombustion CO2 capture processes because of their high CO2 capture capacities. In this study, the maximum realized bicarbonate conversion (X1) was 76% of the theoretical limit (7.24 mmol CO2·g−1 K2CO3) at equilibrium for the 4.14 std vol % CO2 (above equimolar with respect to H2O) containing flue gas at 40 °C. This performance translates to a capacity of 5.5 mmol CO2·g−1 K2CO3.

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AUTHOR INFORMATION

Corresponding Author

*Dept. of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada. Phone: (403) 2106503. Fax: (403) 284-4852. E-mail: nader.mahinpey@ucalgary. ca. ORCID

Abhimanyu Jayakumar: 0000-0002-4018-7362 Arturo Gomez: 0000-0003-2923-2991 Nader Mahinpey: 0000-0001-8477-7228

5. CONCLUSION The bicarbonate (X1) and hydrate (X2) conversion trends of the K2CO3 analytical reagent show that the rates of carbonation and hydration, in most instances, decrease with an increase in carbonation temperature and that increases in flue gas CO2 concentrations result in higher bicarbonate conversions only after the sorbent has been cycled a sufficient number of times and contains adequate quantities of phase I of K2CO3. The simple chemical reaction kinetic model yielded regression coefficient plots in poor agreement with their corresponding linear fits and/or predicted negative apparent

Author Contributions †

A.J. and A.G. are considered as first authors of this work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are thankful to the Natural Sciences and Engineering Research Council (NSERC) of Canada for funding this study, through its Industrial Research Chairs (IRC) program. 862



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phase I = K2CO3 phase derived from the KHCO3 precursor phase II = K2CO3 phase derived from K2CO3·(1.5 H2O) or aqueous solution precursors t = time elapsed since the beginning (t = 0) of the carbonation step r1,t = rate of formation of KHCO3 at time t r2,t = rate of formation of K2CO3·(1.5 H2O) at time t X1,t = bicarbonate conversion of the K2CO3 sample at time t X2,t = hydrate conversion of the K2CO3 sample at time t Xt = total conversion of the K2CO3 sample at time t, given by X1,t + X2,t k1 = Arrhenius rate constant for the forward carbonation reaction k−1 = Arrhenius rate constant for the backward carbonation reaction k2 = Arrhenius rate constant for the forward hydration reaction k−2 = Arrhenius rate constant for the backward hydration reaction C0 = concentration of active sites per kilogram of the regenerated K2CO3 sample at t = 0 Ct = concentration of available active sites per kilogram of the K2CO3 sample at time t CKHCO3,t = concentration of sites converted to KHCO3 per kg of the K2CO3 sample at time t CK2CO3·(1.5 H2O),t = concentration of sites converted to K2CO3· (1.5 H2O) per kilogram of the K2CO3 sample at time t PCO2 = partial pressure of CO2 in the model flue gas mixture used PH2O = partial pressure of H2O in the model flue gas mixture used n = order of carbonation reaction with respect to PCO2 m = order of carbonation reaction with respect to PH2O q = order of hydration reaction with respect to PH2O CCO2 = concentration of CO2 in the model flue gas mixture used CH2O = concentration of H2O in the model flue gas mixture used a1 = regression coefficient for the forward carbonation rate term a−1 = regression coefficient for the backward carbonation rate term a2 = regression coefficient for the forward hydration rate term a−2 = regression coefficient for the backward hydration rate term R2 = coefficient of determination of multiple regression analysis or linear fit EappCRM = apparent activation energy based on the simple chemical reaction kinetic model KH2O = equilibrium constant for H2O adsorption on K2CO3 KCO2 = equilibrium constant for CO2 adsorption on K2CO3 ΔHads = enthalpy/heat of adsorption of H2O or CO2 on K2CO3 ΔHadsH2O = enthalpy/heat of adsorption of H2O on K2CO3 ΔHadsCO2 = enthalpy/heat of adsorption of CO2 on K2CO3 R = universal gas constant T = TGA reactor temperature during carbonation E appL‑H = apparent activation energy based on the Langmuir−Hinshelwood kinetic model 863


Kinetic Behavior of Solid K2CO3 under Postcombustion CO2 Capture

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