Kinetic Behavior of Solid K2CO3 under Postcombustion CO2 Capture

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Study of the kinetic behavior of solid K2CO3 under post-combustion CO2 capture conditions Abhimanyu Jayakumar, Arturo Gomez, and Nader Mahinpey Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b04498 • Publication Date (Web): 05 Jan 2017 Downloaded from http://pubs.acs.org on January 14, 2017

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Industrial & Engineering Chemistry Research

Study of the kinetic behavior of solid K2CO3 under post-combustion 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.

*Author for correspondence: Dr. Nader Mahinpey Dept. of Chemical and Petroleum Engineering Schulich School of Engineering University of Calgary 2500 University Drive NW Calgary, AB T2N 1N4, Canada. Phone: (403) 210-6503 Fax: (403) 284-4852 E-mail: [email protected] †

Both, A. Jayakumar and A. Gomez, are considered as first authors of this work.

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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.

1. Introduction Emissions of CO2 into the atmosphere, from fossil fuel combustion processes for thermal power generation, need to be controlled in order to help mitigate the effects of anthropogenic CO2 on global climate change.1 A low-cost, retrofittable post-combustion 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 post-combustion 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 In order 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 K2CO3(s) + H2O(g) + CO2(g) ⇋ 2KHCO3(s)

(1)

K2CO3(s) + 1.5 H2O(g) ⇋ K2CO3•(1.5 H2O) (s)

(2)

Carbonated K2CO3 has also been shown to contain hydration products such as K2CO3•(1.5 H2O) 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 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.

Most previous studies on the use of solid K2CO3 for post-combustion applications are of the view that CO2 capture, i.e. KHCO3 formation, occurs through a sequential reaction mechanism.7 – 11 In this two-step 2 ACS Paragon Plus Environment

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mechanism, K2CO3 is supposedly hydrated first via reaction (2) to form K2CO3•(1.5 H2O) as the intermediate, which is then claimed to subsequently react with CO2 in the flue gas to produce the bicarbonate by reaction (3). K2CO3•(1.5 H2O) (s) + CO2(g) ⇋ 2KHCO3(s) + 0.5 H2O(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 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 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, due to 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 3 different carbonation temperatures and 3 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 LangmuirHinshelwood (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.

2. Experimental 3 ACS Paragon Plus Environment


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A coupled thermogravimetric analyzer-mass spectrometer (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 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 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 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. 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.

Carbonation temperatures (°C) CO2

H2O

N2

1

1.42

2.15

96.43

40, 50, 60

2

2.34

2.13

95.48

40, 50, 60

3

4.14

2.09

93.77

40, 50, 60

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 since 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 only varying 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 since the CO2/H2O ratio is of importance. Also, higher concentrations of CO2 and H2O will decrease the fraction of 4 ACS Paragon Plus Environment

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unreacted K2CO3 at equilibrium.12 Another important parameter is the relative humidity of the flue gas, which was maintained almost constant here, since 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, can also result in H2O condensation on the sample, leaving the sample waterlogged and supressing carbonation by introducing mass transfer limitations.13 The operating temperature range of 40-60 °C was chosen since undesirable H2O condensation is more favored at temperatures below 40 °C, 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. Further, 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” 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 since there is agglomeration of K2CO3 during cycling, which is one of the limitations to be considered for process scale-up.

3. Kinetic model development Recent work in the literature has demonstrated that the global reaction mechanism of solid K2CO3 under post-combustion conditions only consists of 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’, 𝑟𝑟1,𝑡𝑡 =

𝐶𝐶0 𝑑𝑑𝑋𝑋1,𝑡𝑡 2 𝑛𝑛 𝑚𝑚 = 𝑘𝑘1 𝐶𝐶𝑡𝑡 𝑃𝑃𝐶𝐶𝐶𝐶2 𝑃𝑃𝐻𝐻2𝑂𝑂 − 𝑘𝑘−1 (𝐶𝐶𝐾𝐾𝐾𝐾𝐾𝐾𝐾𝐾3,𝑡𝑡 𝑜𝑜𝑜𝑜 𝐶𝐶𝐾𝐾𝐾𝐾𝐾𝐾𝐾𝐾3,𝑡𝑡 ) 𝑑𝑑𝑑𝑑 2

𝑛𝑛 𝑚𝑚 𝑃𝑃𝐻𝐻2𝑂𝑂 − 𝑘𝑘−1 (�𝐶𝐶0 𝑋𝑋1,𝑡𝑡 � 𝑜𝑜𝑜𝑜 𝐶𝐶0 𝑋𝑋1,𝑡𝑡 ) = 𝑘𝑘1 𝐶𝐶0 (1 − 𝑋𝑋𝑡𝑡 )𝑃𝑃𝐶𝐶𝐶𝐶2

𝑛𝑛 𝑚𝑚 2 = 𝑘𝑘1 𝑃𝑃𝐶𝐶𝐶𝐶2 𝑃𝑃𝐻𝐻2𝑂𝑂 𝐶𝐶0 (1 − 𝑋𝑋𝑡𝑡 ) − 𝑘𝑘−1 (𝐶𝐶02 𝑋𝑋1,𝑡𝑡 𝑜𝑜𝑜𝑜 𝐶𝐶0 𝑋𝑋1,𝑡𝑡 )

(4)

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. 5 ACS Paragon Plus Environment


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And, the rate of formation of K2CO3•(1.5 H2O) by reaction 2 at time ‘t’, 𝑟𝑟2,𝑡𝑡 =

𝐶𝐶0 𝑑𝑑𝑋𝑋2,𝑡𝑡 𝑞𝑞 = 𝑘𝑘2 𝐶𝐶𝑡𝑡 𝑃𝑃𝐻𝐻2𝑂𝑂 − 𝑘𝑘−2 𝐶𝐶K2CO3•(1.5 H2O),𝑡𝑡 𝑑𝑑𝑑𝑑 𝑞𝑞

= 𝑘𝑘2 𝑃𝑃𝐻𝐻2𝑂𝑂 𝐶𝐶0 (1 − 𝑋𝑋𝑡𝑡 ) − 𝑘𝑘−2 𝐶𝐶0 𝑋𝑋2,𝑡𝑡

(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. It is important to note that partial pressures (PCO2 and PH2O) have been used in formulating the above rate equations 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 since 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 kg 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 equations 6 and 7, respectively. 2 𝑜𝑜𝑜𝑜 𝑋𝑋1,𝑡𝑡 ) 𝑟𝑟1,𝑡𝑡 = 𝑎𝑎1 (1 − 𝑋𝑋𝑡𝑡 ) − 𝑎𝑎−1 (𝑋𝑋1,𝑡𝑡

(6)

𝑟𝑟2,𝑡𝑡 = 𝑎𝑎2 (1 − 𝑋𝑋𝑡𝑡 ) − 𝑎𝑎−2 𝑋𝑋2,𝑡𝑡

(7)

where, the constant coefficients 𝑛𝑛 𝑚𝑚 𝑎𝑎1 = 𝑘𝑘1 𝑃𝑃𝐶𝐶𝐶𝐶2 𝑃𝑃𝐻𝐻2𝑂𝑂 𝐶𝐶0

(8)

𝑎𝑎−1 = 𝑘𝑘−1 𝐶𝐶02 𝑜𝑜𝑜𝑜 𝑘𝑘−1 𝐶𝐶0 (if backward carbonation is order 2 or 1 wrt CKHCO3, respectively.)

(9)

𝑎𝑎−2 = 𝑘𝑘−2 𝐶𝐶0

(11)

𝑞𝑞

𝑎𝑎2 = 𝑘𝑘2 𝑃𝑃𝐻𝐻2𝑂𝑂 𝐶𝐶0

(10)

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 equations 6 and 7 to be zero, as shown above, yields a higher coefficient of determination (R2) than when equations 6 and 7 are allowed to include a non-zero 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 6 ACS Paragon Plus Environment

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3.2 Langmuir – Hinshelwood (L-H) 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 sub-critical 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 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 since 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 rate-limiting H2O adsorption step, as described below by equations 12-14. K2CO3(s) + H2O(g) ⇋ K2CO3.[H2O]ads

(12)

K2CO3.[H2O]ads + 0.5 H2O(g) ⇋ K2CO3•(1.5 H2O) (s)

(14)

K2CO3.[H2O]ads + CO2(g) ⇋ 2KHCO3(s)

(13)

Based on this mechanism, the rates of formation of KHCO3 and K2CO3•(1.5 H2O), at time ‘t’, are given below by equations 15 and 16, respectively. 𝑟𝑟1,𝑡𝑡 =

𝑟𝑟2,𝑡𝑡 =

𝑘𝑘1 𝐾𝐾𝐻𝐻2𝑂𝑂 𝑃𝑃𝐻𝐻2𝑂𝑂 𝑃𝑃𝐶𝐶𝐶𝐶2 𝐶𝐶0 (1−𝑋𝑋𝑡𝑡 ) 1+𝐾𝐾𝐻𝐻2𝑂𝑂 𝑃𝑃𝐻𝐻2𝑂𝑂

2 𝑘𝑘2 𝐾𝐾𝐻𝐻2𝑂𝑂 𝑃𝑃𝐻𝐻2𝑂𝑂 𝐶𝐶0 (1−𝑋𝑋𝑡𝑡 )

1+𝐾𝐾𝐻𝐻2𝑂𝑂 𝑃𝑃𝐻𝐻2𝑂𝑂

2 − 𝑘𝑘−1 𝐶𝐶02 𝑋𝑋1,𝑡𝑡

(15)

− 𝑘𝑘−2 𝐶𝐶0 𝑋𝑋2,𝑡𝑡

(16)

Equations 15 and 16 can also be expressed with constant coefficients for the independent conversion variables in the same form as equations 6 and 7, where the regression coefficients, 𝑎𝑎1 =

𝑘𝑘1 𝐾𝐾𝐻𝐻2𝑂𝑂 𝑃𝑃𝐻𝐻2𝑂𝑂 𝑃𝑃𝐶𝐶𝐶𝐶2 𝐶𝐶0

(17)


𝑎𝑎−1 = 𝑘𝑘−1 𝐶𝐶02

(18)

𝑎𝑎−2 = 𝑘𝑘−2 𝐶𝐶0

(20)

𝑎𝑎2 =

2 𝑘𝑘2 𝐾𝐾𝐻𝐻2𝑂𝑂 𝑃𝑃𝐻𝐻2𝑂𝑂 𝐶𝐶0

(19)


The constant regression coefficients in equations 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 7 ACS Paragon Plus Environment


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

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 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 towards equilibrium, with mass-transfer limitations, for the remaining 4800 s. 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. (a) Cycle 1 (at t = 3000 s) T CO2 X1 X2 (°C) (std. vol%) 40 1.42 0.19 0.61 50 1.42 0.22 0.38 60 1.42 0.21 0.02 40 2.34 0.14 0.71 50 2.34 0.20 0.30 60 2.34 0.18 0.10 40 4.14 0.08 0.94 50 4.14 0.16 0.38 60 4.14 0.12 0.07

X 0.81 0.60 0.23 0.85 0.50 0.28 1.02 0.54 0.19

(b) Cycle 50 (at t = 3000 s) T CO2 X1 X2 X (°C) (std. vol%) 40 1.42 0.49 0.22 0.70 50 1.42 0.52 0.13 0.65 60 1.42 0.45 0.09 0.54 8 ACS Paragon Plus Environment

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40 50 60 40 50 60

2.34 2.34 2.34 4.14 4.14 4.14

0.57 0.57 0.42 0.69 0.56 0.28

0.30 0.07 0.08 0.31 0.13 0.06

0.87 0.64 0.50 1.00 0.69 0.34

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 CO2 X1 X2 (°C) (std. vol%) 40 1.42 0.28 0.72 50 1.42 0.24 0.58 60 1.42 0.26 0.10 40 2.34 0.18 0.93 50 2.34 0.21 0.63 60 2.34 0.18 0.27 40 4.14 0.19 1.00 50 4.14 0.21 0.65 60 4.14 0.17 0.19

X 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 CO2 X1 X2 (°C) (std. vol%) 40 1.42 0.59 0.41 50 1.42 0.52 0.31 60 1.42 0.49 0.19 40 2.34 0.68 0.28 50 2.34 0.60 0.24 60 2.34 0.44 0.16 40 4.14 0.76 0.37 50 4.14 0.66 0.27 60 4.14 0.28 0.14

X 1.00 0.82 0.68 0.96 0.84 0.60 1.13 0.93 0.42



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Before analyzing the observed bicarbonate and hydrate conversion trends in this kinetic study, 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 cycle 50 is related to the carbonation temperature and flue gas composition used for that particular multicycle test. From Table 2(a) 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 3(a), 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 – 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 2(a) and 3(a) 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 2(a) and 3(a) 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 only decreases significantly when the CO2 concentration is increased from below equimolar to the 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. Although, 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) due to 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 10 ACS Paragon Plus Environment

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40 °C 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 rate-limiting step. In Table 2(b) 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, since 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 3(b), 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 due to the increased contents of phase I present in the K2CO3 samples. The hydrate conversions (X2) shown in Tables 2(b) and 3(b) 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 2(b) and 3(b) 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 s 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 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 CO2 concentrations. Hydrate conversions (X2) in Table 2(b), 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 3(b), 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 2(b) and 3(b), 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 since 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 mass transfer 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 due to 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 till 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.

Conversion X1,t or X2,t

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1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

X1,t X2,t

0

2000

4000

Time 't' (s)

6000

8000

Figure 1: Bicarbonate (X1,t) and hydrate (X2,t) conversions vs 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 equations 4 and 5. The backward carbonation rate term is considered to have a second-order dependence on the concentration of KHCO3 sites in equation 4 (equivalent to the reaction order for overall carbonation as an elementary reaction), since 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


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first-order with respect to the concentration of K2CO3•(1.5 H2O) sites. Reaction order assumptions are being made since the real reaction orders are unknown. 4.3 Chemical reaction model evaluation The regression coefficients determined for equations 6 and 7 are initially considered to only have a temperature dependence due to rate constants that follow the Arrhenius equation (equations 8 – 11). The validity of this simple chemical reaction model (CRM) 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) vs 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 only requires the presentation of regression data for one of the flue gas compositions used, since the trends in the regression data are similar for the other gas compositions utilized in our experiments.



0.0028 -8

Cycle 1

Cycle 50

1/T (K-1)

1/T (K-1)

0.003

0.0032

EappCRM = 22.3 kJ.mol-1

0.0028 -7 -7.2

ln (a1)

ln (a1)

0.0034

(a)

-8.2 -8.4 -8.6

EappCRM = -15.5 kJ.mol-1

-8.6

y = 9508.9x - 38.376 R² = 0.9918

0.0032

1/T (K-1) 0.0034

0.0028 -7.8

(c) ln (a2)

-8.2 -9 -9.4 -9.8 -10.2

0.0034

(b)

y = 1860.6x - 13.145 R² = 0.6993

1/T (K-1) 0.003

0.0032

-7.4

-7.8

0.0028 -7.8

0.003

-7.6

y = -2676.8x - 0.086 R² = 0.733

-8.8

ln (a2)

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-8

0.003

0.0032

y = 1446.8x - 12.604 R² = 0.9366

0.0034

(d)

-8.2 -8.4


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. The regression data in Figure 2(a) 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 only dependent 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) vs 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 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 2(b), are much higher compared to cycle 1 due to 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 14 ACS Paragon Plus Environment

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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 and 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 2(c), 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, since 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 2(d), 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 out of 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 mass transfer 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 (due to 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. Figures 2(c) and 2(d) suggest that the forward hydration reaction rate is H2O adsorption limited since H2O is the only component of the flue gas involved in this reaction. Forward carbonation, on the other hand, could be either limited by only H2O adsorption, only CO2 adsorption or a more complex co-adsorption/multi-step 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 15 ACS Paragon Plus Environment


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estimates for H2O and CO2 adsorption at 0 °C 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 sub-critical 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 equations 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 carbonation and hydration according to this model are shown by equations 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 (equation 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 (equation 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, since the real reaction orders are unknown. Only the backward carbonation reaction is considered to be second-order 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 equations 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 equations 17 and 19, respectively. Since 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 (EappL-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 𝐾𝐾𝐻𝐻2𝑂𝑂 ∝ exp �−

∆𝐻𝐻𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎2𝑂𝑂 𝑅𝑅𝑅𝑅

� ; ∆𝐻𝐻𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎2𝑂𝑂 < 0,

and 𝐸𝐸𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎−𝐻𝐻 = 𝐸𝐸𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 − ∆𝐻𝐻𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎2𝑂𝑂 . However, the accuracy of this model in determining EappL-H will be higher if the term KH2O.PH2O

Kinetic Behavior of Solid K2CO3 under Postcombustion CO2 Capture

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