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New Kinetic Model that Describes the Reversible Adsorption and Desorption Behavior of CO2 in a Solid Amine Sorbent Anahita Abdollahi Govar, Armin D. Ebner, and James Anthony Ritter Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.5b01119 • Publication Date (Web): 17 Jun 2015 Downloaded from http://pubs.acs.org on July 2, 2015

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New Kinetic Model that Describes the Reversible Adsorption and Desorption Behavior of CO2 in a Solid Amine Sorbent

Anahita Abdollahi Govar, Armin D. Ebner and James A. Ritter Department of Chemical Engineering Swearingen Engineering Center University of South Carolina Columbia, SC 29208

A revised research article submitted to Energy and Fuels for consideration for publication.

June 2015

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Abstract Five, semi-empirical, temperature-dependent, kinetic models were developed and systematically studied to determine which one best described the reversible reaction/adsorption and desorption behavior of CO2 in a solid amine sorbent over a broad range of experimental conditions. Each model varied in the number and type of reaction to account for different CO2-amine site reactions. The solid amine sorbent was composed of polyethyleneimine (PEI) immobilized on a CARiACT® G10 silica support. Four temperatures (40, 60, 80 and 100 °C) and seven concentrations of CO2 in N2 at 1 atm (1.2, 4.8, 14.5, 32.8, 56.1, 69.8 and 88.6 vol%) were studied by carrying out four consecutive adsorption/desorption cycles at each of the 28 conditions using a thermogravimetric analyzer (TGA). Each cycle consisted of 40 minutes of adsorption in CO2/N2 followed by 40 minutes of desorption in N2. The best model consisted of three parallel reactions, which was consistent with PEI having three different amine sites. Considering the wide range of conditions studied, this is a first-of-its-kind, kinetic model that should prove to be very useful in an adsorption process simulator and thus for the development of new pressure and temperature swing adsorption processes utilizing this commercially viable PEI solid amine sorbent for CO2 removal from a variety of gas streams.

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Introduction The CO2 concentration in the atmosphere has been steadily increasing over the last century, primarily due to anthropogenic CO2 emissions, with it being blamed for recent changes in climate.1 In an attempt to rectify this situation, sources that emit large amounts of CO2 into the atmosphere, like fossil fuel burning electric power plants, are being targeted for carbon capture. Consequently, large scale CO2 capture technologies are being developed and evaluated globally. Two promising technologies for CO2 capture and concentration from flue gas are pressure swing adsorption (PSA) and temperature swing adsorption (TSA).2 An essential part of any PSA or TSA process is the adsorbent or sorbent. With respect to capturing CO2 from flue gas, specific characteristics of the sorbent should be taken into consideration. These include a large CO2 working capacity, limited N2 and O2 adsorption, and being able to handle a large amount of water vapor. A recent review on sorbents for CO2 capture has been given by Wang et al.3 Among the numerous commercial and developmental sorbent materials being studied, X and Y type zeolites and activated carbons are indisputably the most promising commercial candidates, and a class of materials referred to as solid amine sorbents (SASs) are perhaps the most promising developmental candidates, all for post combustion CO2 capture. A review on SASs has also been given by Shakerian et al.4 SASs contain amine functional groups chemically attached or physically immobilized on the surface of a porous support like silica.5-15 Several mechanisms have been proposed to describe the reactions between CO2 and alkanolamines,16 including zwitterian, termolecular and base catalyzed mechanisms. The zwitterion mechanism has been used mostly to describe the reaction of CO2 with primary, secondary and sterically hindered amines, whereas the basecatalyzed mechanism has been used to describe the reaction of CO2 with hydrated tertiary


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amines.16 In fact, what makes SASs so important is that they are water vapor tolerant and the adsorption of CO2 is not negatively affected by water vapor.5,17,18,19 Sayari and co-workers7,8 first used a linear driving force (LDF) model and later used Lagergren pseudo-first and pseudo-second order and Avrami kinetic models10 to describe the kinetics of CO2 adsorption on several amine modified silica sorbents. Sayari and co-workers9 also proposed a Toth equilibrium model to describe CO2 adsorption isotherms on amine-grafted mesoporous silica via two independent mechanisms, i.e., chemisorption on amine functional groups and physisorption on the silica support surface. Similarly, Bollini et al14,15 used Toth14 and Langmuirian15 models to describe the equilibrium behavior and single14 and two parameter15 LDF expressions to describe the mass transfer rates on an amine modified silica sorbent. However, none of these models are based on actual reaction mechanisms that describe the kinetics of reaction/adsorption and desorption of CO2 in an SAS; they all assume the rate processes are based on diffusional mechanisms. In addition, none of these studies provided any information on the desorption kinetics of CO2 on a solid amine sorbent. Ebner et al.5 might have been the first to study both the adsorption and desorption behavior of CO2 on a SAS. They proposed a reversible mechanism that described the chemisorption kinetics of CO2 on polyethyleneimine (PEI) immobilized on a CARiACT® G10 silica support. They also developed a Langmuir-type expression to describe the equilibrium loading of CO2 on this SAS; however, they did not develop a kinetic model to describe any of their dynamic adsorption and desorption data. Liu et al.,20 also studied the adsorption and desorption kinetics of CO2 on an amine functionalized carbon nanotube using Avrami kinetic models; however, as mentioned above, the Avrami kinetic models are not mechanistic in nature. In contrast, Suh and Sun21 developed a particle-scale kinetic model to describe the adsorption


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and desorption kinetics of CO2 on an SAS using three reactions that included dry and wet primary amine reactions and the physisorption of water; however, their particle-scale kinetic model is much too complex to be used in an adsorption process simulator. Therefore, the objective of this study was to show how to develop a mechanistic model that clearly describes the reversible reaction/adsorption and especially desorption behavior of CO2 on PEI immobilized on a CARiACT® G10 silica over a broad range of conditions. Starting from a one site-one reaction/adsorption model, five models were formulated and studied to describe the reversible behavior of CO2 on this commercially viable SAS at 28 different conditions. These models included various combinations of one-site and two-site reactions or adsorption taking place in parallel and/or in series with each other. Also, an empirical equation was utilized to capture the temperature dependence of amine site availability caused by rheological changes in PEI with temperature.12,13 The primary outcome of this work is for the resulting model to be used in a dynamic adsorption process simulator to develop new PSA and TSA processes utilizing this commercially viable SAS for CO2 removal from a variety of gas streams, including the capture of CO2 from power plant flue gas. A secondary outcome of this work is for others to adopt this systematic and universal approach to kinetic model development. Kinetic Model Development Five, first principle, kinetic models were developed to predict the reversible reaction/adsorption and desorption behavior of CO2 on PEI immobilized on CARiACT® G10 silica. These models consisted of different combinations of the reactions shown below to account for the possibility of CO2 reacting with the three different amine sites within PEI. PCO 2 + N1 ↔ q1

(R1)

PCO 2 + N 2 ↔ q2

(R2)


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PCO 2 + N 3 ↔ q3

(R3)

PCO 2 + N 4 ↔ q4

(R4)

PCO 2 + q4 ↔ q5

(R5)

PCO 2 is the partial pressure of CO2 in the gas phase. N1, N2, N3 and N4 are different reaction/

adsorption sites available in the sorbent. N1, N2 and N3 each react with or adsorb just one CO2 molecule from the gas phase, thereby respectively forming product sites q1, q2 and q3. N4 reacts with or adsorbs up to two CO2 molecules from the gas phase, thereby forming product site q4 the first time it reacts and product site q5 the second time it reacts through product site q4. Thus, product sites q1, q2, q3 and q4 contain just one CO2 molecule per site, whereas product site q5 contains two CO2 molecules per site. In Model I there is only one reaction taking place (rxn R1), where reaction site N1 reacts with or adsorbs one CO2 molecule. In Model II there are two reactions taking place in parallel (rxns R1 and R2), where reaction sites N1 and N2 each react with or adsorb one CO2 molecule. In Model III there are three reactions taking place in parallel (rxns R1, R2 and R3), where reaction sites N1, N2 and N3 each react with or adsorb one CO2 molecule. In Model IV there are two reactions taking place in series (rxns R4 and R5), where reaction site N4 reacts with or adsorbs two CO2 molecules. A mechanism similar to Model IV was proposed by Planas et al.22 to explain the adsorption of CO2 in an alkylamine-functionalized metal-organic framework using quantum chemical calculations. In Model V there are three reactions taking place in parallel and series (rxns R1, R4 and R5), where reaction site N1 reacts with or adsorbs only one CO2 molecule and reaction site N4 reacts with or adsorbs two CO2 molecules through the series reaction. Each model described above incorporates a certain set of rate expressions, balance equations and equilibrium relationships. Collectively, for all the models, the rate expressions and 6 ACS Paragon Plus Environment

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balance equations are given by eqs 1 to 10.

dq1 = K1, f PCO 2 ( N1 − q1 ) − K1,b q1 dt

(1)

dq2 = K 2, f PCO 2 ( N 2 − q2 ) − K 2,b q2 dt

(2)

dq3 = K3, f PCO 2 ( N3 − q3 ) − K3,b q3 dt

(3)

dq4 dq = K 4, f PCO 2 ( N 4 − q4 − q5 ) − K5,b q5 − 5 dt dt

(4)

dq5 = K5, f q1 PCO 2 − k5,b q5 dt

(5)

q1 + q2 + q3 + q4 + 2q5 = qt

(6)

N1 = αNt

(7)

N2 = βNt

(8)

N3 = γNt

(9)

N4 = ηNt = (1 − α − β − γ ) Nt

(10)

K1,f, K2,f, K3,f, K4,f and K5,f are the forward reaction constants and K1,b, K2,b, K3,b, K4,b and K5,b are

the backward reaction constants for the formation of q1, q2, q3, q4 and q5, respectively. qt is the total CO2 loading. α,β, γ and η are the fractions of Nt that belong to N1, N2, N3 and N4, respectively. These fractions were assumed to be constant. The temperature dependence of each reaction constant was expressed by Arrhenius relationships, according to K i , f = K i , f , 0 exp( Ki ,b = Ki ,b ,0 exp(

− Ei , f RT

− Ei ,b RT

) ; i =1, 2, 3, 4, 5

) ; i =1, 2, 3, 4, 5


(11)

(12)

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Ki,f,0 and Ki,b,0 are the pre-exponential constants. Ei,f and Ei,b are the activation energies in the

Arrhenius expressions for the forward and backward reactions. R is the universal gas constant and T is the absolute temperature. Since PEI in the SAS contains three different amine reaction sites consisting of linear and branched primary, secondary and tertiary amines,5,11 their reactivity, orientation and location within the silica support might result in different reaction/adsorption sites for CO2. Models II, III, IV and V were conceived to account for these different sites. Moreover, the accessibility of these amine sites for CO2 might change with temperature, due to the fluidity of PEI changing with temperature.12,13 Since PEI is more flexible at higher temperatures, more amine sites might be available for reaction/adsorption with CO2 and vice versa at lower temperatures. Eq 23, an empirical expression in the form of a Fermi-Dirac distribution, was incorporated into each model to capture these temperature-dependent, morphological changes associated with PEI by allowing the total number of reaction/adsorption sites to vary with temperature.

Nt =

N max 1 + exp(− kα (T − T0 ))

(13)

Nmax, kα and T0 are constants.

To test the consistency of the kinetic models proposed above, equilibrium relationships were derived from the models as follows. At equilibrium, the forward reaction rate was assumed to be equal to the backward reaction rate, which lead to

dq1 dq 2 dq3 dq4 dq5 = = = = =0 dt dt dt dt dt

(14)

Collectively, for all the models, the corresponding equilibrium relationships, i.e., the CO2 loadings, equilibrium constants and heats of reaction/adsorption are given by eqs 15 to 24.


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q1,e =

K1,e PCO2 N1

(15)

1 + K1,e PCO2

q2,e =

q3,e =

q4,e =

q5,e =

K 2,e PCO2 N 2

(16)

1 + K 2,e PCO2 K 3,e PCO2 N 3

(17)

1 + K 3,e PCO2 K 4,e PCO2 N 4

(18)

2 1 + K 4,e PCO2 + K 5,e K 4,e PCO 2

2 K 5,e K 4,e PCO N4 2

(19)

2 1 + K 4,e PCO2 + K 5,e K 4,e PCO 2

q1,e + q 2 ,e + q3,e + q 4 ,e + 2q5 ,e = qt ,e K i ,e =

K i ,0 =

Ki, f K i ,b

= K i ,0 exp( −

K i , f ,0 K i ,b ,0

(21)

∆H i ) ; i =1, 2, 3, 4, 5 RT

; i =1, 2, 3, 4, 5

(22)

(23)

∆Hi = Ei, f − Ei ,b ; i =1, 2, 3, 4, 5

(24)

q1,e , q2,e , q3,e , q4,e and q5,e are the equilibrium loadings of CO2. qt,e is the total equilibrium loading of CO2. Ki,e is the equilibrium constant for reaction i, and ∆Hi is the effective heat of reaction/adsorption for reaction i. Table 1 summarizes the specific reactions, rate expressions and balance equations used in each model. It is noteworthy that the set of equations unique to each model are also those that would be utilized in a dynamic adsorption process simulator, depending on which model best describes any available dynamic data. Since the equilibrium relationships for each model are not needed in the simulator, they are not listed in Table 1. Recall, they were derived only to check


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the consistency of the kinetic models against any available equilibrium data.

Experimental The SAS, composed of PEI immobilized on a CARiACT® G10 silica support, was obtained from the DOE National Energy Technology Laboratory. It was used as received, except for activation (regeneration). Details about the synthesis method and the physical properties of the silica support are given elsewhere.5,11 UHP grade N2 (Airgas) and Coleman grade CO2 were obtained from Airgas and also used as received. A Perkin-Elmer TGA-7 thermogravimetric analyzer was used to measure the dynamic adsorption and desorption behavior of CO2 on this SAS. A schematic of the experimental apparatus is displayed in Figure 1. First, a sample ( 20 mg) was activated at 100 °C for 80 min in N2 flowing at around 60 cm3/min and 1 atm. At the end of the activation step, the temperature was adjusted to a predetermined value of 40, 60, 80 or 100 °C using a 20 °C/min ramping rate. When the desired temperature was reached, the test gas was switched from N2 to a CO2/N2 gas mixture (also flowing at around 60 cm3/min and 1 atm) to initiate adsorption and begin the first half of an adsorption/desorption cycle. The adsorption step was continued for 40 min, and then the gas was switched back to N2 to initiate the desorption step and finish the second half of the adsorption/desorption cycle. The concentration of CO2 in the CO2/N2 mixture was varied between 1 and 100 vol%, i.e., 1.2, 4.8, 14.5, 32.8, 56.1, 69.8 and 88.6 vol% CO2. At each of the 28 conditions (i.e., seven CO2/N2 concentrations were studied at each of the four temperatures), four adsorption/desorption cycles were carried.

Results and Discussion It is important to stress at the outset that five mechanistic kinetic models were formulated and systematically analyzed against extensive experimental data to account for the various ways


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CO2 may react with the three different amine groups within PEI. The empirical nature of these models stems only from an assumed temperature dependence that allows for the total number of reaction/adsorption sites to increase with increasing temperature due to morphological changes in PEI. The notion was that a combination of statistics and visual inspection would identify which one of the five semi-empirical models best describes the dynamic adsorption and desorption behavior over a broad range of CO2 concentrations and temperatures. The resulting kinetic model would thus identify how the CO2-amine reactions are taking place within PEI. This rigorous kinetic approach is new and in striking contrast to some of the previous studies that assumed some kind of Fickian diffusional process (or processes) was solely responsible for driving the dynamics to an equilibrium state described by Langmuirian expressions.7,8,10,14,15 This diffusional approach does not provide any fundamental information about the CO2-amine reactions, whereas this new kinetic approach does indeed provide this kind of information, as revealed below. Also, during the course of this study it was determined that a gas phase film mass transfer resistance existed in the TGA chamber in the vicinity of the sorbent. This effect was most pronounced at the beginning of both the adsorption and desorption steps because it took a finite amount of time for the new feed gas to replace the gas remaining in the TGA chamber from the previous step. In other words, the partial pressure of CO2 around the sorbent did not immediately reach the feed gas partial pressure of CO2. This TGA effect was accounted for with a mass balance expression over the TGA chamber that included a film mass transfer resistance, i.e., *  V *  dPCO2 KCO2 A  dqt  * = ( PCO2 − PCO ) − ρ V   s s   2 RT  dt   RT  dt

(24)

* where PCO is the partial pressure of CO2 in the gas phase in contact with or in the vicinity of the 2


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sorbent, V* is the volume of the TGA furnace chamber, K CO2 is the film mass transfer coefficient of CO2 in the gas phase, PCO2 is the partial pressure of CO2 in the feed gas, A is the sorbent external surface area, ρs is the sorbent density and Vs is the sorbent volume. Eq 24 was simplified by rearranging it with all the constants combined into two new constants, according to * dPCO 2

dt

 dq  * = K p ( PCO2 − PCO ) − K qT  t  2  dt 

(25)

where KP ≡

KCO2 A

(26)

V*

Kq ≡ ρs R

Vs V*

(27)

* Since Kp and Kq are unknown, they became fitting parameters. Also, PCO2 was replaced by PCO in 2

eqs 1 to 5 and eqs 15 to 19. Figure 2 shows a typical TGA effect on the adsorption behavior of CO2 in the solid amine sorbent. Although the effect existed for both adsorption and desorption, it was more pronounced and thus easier to discern during adsorption. The four experimental TGA traces were obtained during the first adsorption cycle at all four temperatures for 14.5 vol% CO2 in N2. The predictions in this case were obtained from Model III (by the procedure described below) while including and excluding the TGA effect (i.e., eqs 25 to 27) in the formulation. It was clear that a gas phase film mass transfer resistance had to be included in the model equations to more accurately predict the experimental trends during the first two to three minutes of adsorption. Similar trends were observed during desorption and at all the other conditions. Thus, all the model predictions presented and discussed below include this TGA effect. Four temperatures and seven CO2 concentrations in N2 were studied, which corresponds 12 ACS Paragon Plus Environment

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to 28 different conditions. Four cycles were run at each condition. The model parameters associated with each of the five models were obtained by fitting the model to 20 of the conditions and just the first two cycles. The remaining eight conditions and the last two cycles were then predicted to evaluate the interpolation and extrapolation capabilities of each model. The 20 conditions used for fitting the models included the data obtained at 40, 60, 80 and 100 °C and 1.2, 4.8, 14.5, 56.1 and 88.6 vol% CO2 in N2. The 8 conditions used for evaluating predictions from the models included the remaining data obtained at 40, 60, 80 and 100 °C and 32.8 and 69.8 vol% CO2 in N2. The parameters were obtained using the non-linear regression routine in MS Excel Solver. The resulting model parameters for all five models are summarized in Table 2. The corresponding predictions of the heat of reaction/adsorption (∆Hs) from all five models are shown in Table 3. At this point, a brief discussion on the magnitudes and signs of some of these parameters is justified. Notice that the forward reaction activation energies (Ef1, Ef2, Ef3, Ef4 and Ef5) shown in Table 2 were allowed to take on negative values. As in the previous work,5 this was due to the assumption that an equilibrium driven physical or chemical adsorption step preceded the rate limiting forward amine reaction.23,24 In contrast, all the backward reaction activation energies were allowed to take on only positive values. Also, due to the reaction/adsorption processes taking place between CO2 and the amines both being exothermic; the ∆Hs were expected to be negative. However, ∆H5 was positive, as shown in Table 3. Since there was no physical or chemical basis to justify this positive energy, predictions from Model V were not included in the rest of the results. For the other four models, the values shown in Table 3 were reasonably close to the values reported in the literature for adsorption of CO2 on solid amines (42.7,11 50.0,5 63.2,11 6725 and 9426 kJ mol-1) and for reaction of CO2 with liquid amines10,26 (primary amines:


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84 kJ mol-1, secondary amines: 72 kJ mol-1 and tertiary amines: 48 kJ mol-1). However, it should be noted that the numbers reported here are not the same as those reported by Ebner et al5 for the same material. This inconsistency was due mostly to them using equilibrium data at only 80 and 100 oC to determine the heat of adsorption/reaction, and then assuming the total number of sites to be constant, i.e., independent of temperature. The goodness of the fit of each model was judged by considering the following criteria: the coefficient of determination (R2), visual examination of the fitted curves, capability of capturing kinetic features at both low and high temperatures for all four cycles, model predictions of working capacity, and model predictions of equilibrium loadings at 80 and 100 oC. For each condition, R2 was calculated using the following equation: R =1− 2

Σ(qi , exp − qi , mod ) 2

(28)

Σ( qi , exp − q exp ) 2

qi,exp is the experimental CO2 loading at time t. qi,mod is model-predicted loading of CO2 at time t.

q exp is the mean of the experimental CO2 loading over all four cycles. The resulting R2 values are shown in Table 4 for the 20 conditions utilized in the fitting process and in Table 5 for the remaining 8 conditions utilized just for prediction. The model that exhibited the maximum R2 is also tabulated in these tables. Based on the R2 values, all four models captured most of the trends in the experimental cycling data at 80 and 100 oC (R2 ≥ 0.98), except for 1.2 vol% CO2 at 100 oC. Since the R2 values were very similar at those two temperatures, it was not possible to determine the best model from just this information. This was not the case at the other temperatures. At 60 °C, the lowest R2 values were exhibited by Model I. This indicated very clearly that more than one reaction was needed to model the adsorption and desorption behavior of CO2 at that temperature. Moreover, at 14 ACS Paragon Plus Environment

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40 °C Model III exhibited significantly higher R2 values for most of the conditions, indicating three parallel reactions represented the kinetic data better than the models with two reactions in parallel (Model IV) or two reactions in series (Model V). When accounting for all 28 conditions, the R2 values showed Model III provided the best fit of the experimental data for more than 75% of the conditions. This result was consistent with PEI having three different amine sites for reaction with CO2. No significant differences were observed in visual examination of the fitted curves at temperatures of 60 °C and higher. Therefore, to have a better comparison of the models only results at 40 oC are shown, where the differences were more pronounced. Figures 3 to 7 show the results from Models I, II, III and IV for 1.2, 4.8, 14.5, 56.1 and 88.6 vol% CO2 in N2, respectively. At this temperature, there were two steps during the adsorption: a fast uptake of CO2 that occurred at the beginning that was always followed by a much slower uptake. Although less pronounced, these two steps could be observed also during desorption. These trends are indicative of multiple reactions taking place within the PEI. Figure 3 shows the model predictions for 1.2 vol%. Model I did not capture the trends in the experimental data except during the initial period of the adsorption step (t < 10 min). Predictions from Models II and IV were similar, with both appearing to fit better than Model I by visual inspection. However, both models predicted higher loadings and failed to exactly capture the shape of the curves during the slow adsorption step and during the entire desorption step. Model III fitted the data better than all the other models at this partial pressure of CO2, capturing both the adsorption and desorption behaviors quite well. Figures 4 and 5 show the results for 4.8 and 14.5 vol%. As before, Model I did not capture the features of either the adsorption or desorption step. Models II and IV showed similar


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trends, with both over predicting and missing the shape of the experimental curve for the slow adsorption step and for the entire desorption step. This further revealed that two reactions, either in parallel or series, could not represent the adsorption or desorption behavior of CO2 at these conditions. On the other hand, Model III fitted both the fast and slow adsorption steps, while even predicting the curvature of the desorption step. Similar conclusions could be gleaned from the results shown in Figures 6 and 7. As shown in Figures 3 and 4, the results from Model I deviated significantly from the experimental results. This time, however, Models II and IV showed three steps during adsorption (a fast uptake followed by two consecutive slow uptakes) that were not observed experimentally. In contrast, Model III only slightly over predicted the loading during adsorption at 56.1 vol% and it missed only the late stages during desorption at 88.6 vol%. Nevertheless, it was able to capture with very good agreement the shape of the experimental curves. The results at these concentrations kept confirming the previous conclusion that two reactions, either in series or in parallel, did not represent the experimental results at this temperature (40 oC), thus making the mechanism associated with Model III the best so far. Figure 8 shows the model results for 32.8 and 69.8 vol%. The trends were similar to those exhibited by the other concentrations discussed above. Thus, when considering all the concentrations together, Model III was the best of the four models for representing the adsorption and desorption behaviors of CO2 on CARiACT G10 SAS at 40°C. At the other temperatures, since the results from all the models were quite similar, only the results from Model III are shown in Figures 9 to 12. There was always excellent agreement between this model and the experimental results, except at 1.2 vol% at 100 oC (Figure 11a) where the model over predicted the loading but not the working capacity.


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The periodic state working capacity for each condition was calculated by subtracting the loading at the end of the desorption step from the loading at the end of the adsorption step in the 4th cycle; the 4th cycle represented well the periodic state behavior. The resulting experimental working capacities are shown in Figures 13, along with the predictions from Models I to IV. The corresponding R2 for each model at each temperature for all 7 concentrations is shown in Table 6. At 40 °C (Figure 13a) Model I provided the best fit; however, it was shown earlier that this model did not capture the kinetic features at 40 °C. Models II and III fitted the data up to 69.8 vol%; but, at the higher concentrations they both over predicted the working capacities. In contrast, Model IV over predicted the working capacities at concentrations higher than 32.8 vol%. At 60 °C (Figure 13b) Models II, III and IV all predicted the working capacities at concentrations lower than 56.1 vol%; but, they over predicted them at concentrations higher than 56.1 vol%. In contrast, Model I over predicted the working capacities at concentrations lower than 56.1 vol%; but, it predicted them at concentrations higher than 56.1 vol%. At 80 and 100 °C (Figures 13c and 13d) all four models predicted the working capacities equally well, with R2 ≥ 0.9894 in all cases. All the models predicted very well the equilibrium loadings at 80 and 100 oC, i.e., the only temperatures where equilibrium was achieved during the 40 min adsorption step. The corresponding R2 for each model is shown in Table 7. This was not surprising since the equilibrium expressions for each model (given by eqs 15 to 19) all have the same mathematical form. Since the models all overlapped at these conditions, the experimental and predicted equilibrium loadings (from eqs 15 to 17) are shown only for Model III in Figure 14. The agreement between the experimental results and Model III (representing all the models) was excellent.


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Collectively, the results presented in Tables 4 to 7 and Figures 3 to 14 revealed the following: At the two higher temperatures no significant differences were observed between any of the kinetic models. However, at the two lower temperatures Model III captured the kinetic features much better than the other models. Model III also best predicted the working capacities and the equilibrium loadings at the higher temperatures compared to any of the other models. Thus, Model III was considered to be the best model based on all the statistical and visual evidence. From an engineering perspective, Model III was also considered to be the best model to use in PSA or TSA process simulator because it not only accurately predicted the adsorption and desorption dynamics, but it also accurately predicted both the working capacities and the equilibrium loadings over the entire range of conditions. Since Model III was found to be the best model, it is now worth pointing out some of the mechanistic features it reveals about the three parallel reactions taking place between CO2 and the primary, secondary and tertiary amines in the PEI. First, this kinetic modeling approach cannot for certain identify which CO2 reaction (R1, R2 or R3) corresponds to the primary, secondary or tertiary amine simply from the resulting reaction constants listed in Table 2. However, these constants do reveal that the forward reaction activation energies for reactions R1 and R3 are both negative. This result suggests that dominate and favorable adsorption processes precede both reactions R1 and R3. Also, these constants show that the magnitude of the activation energy for reaction R3 is almost forty times greater than that for reaction R1. This result suggests that the two adsorption processes are very different. In contrast, reaction R2 simply exhibits a positive and rather low activation energy. This result indicates that this reaction occurs either rather easily or perhaps with a weaker adsorption process preceding it that reduces the magnitude of its activation energy. The magnitude of the forward reaction R2 activation


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energy is also in stark contrast to the three backward reaction activation energies. They are all three to nine times greater than the reaction R2 activation energy. This result indicates very clearly that the three backward (desorption) reactions proceed at much slower rates compared to the three forward (adsorption) reactions. These relatively slower desorption trends compared to relatively faster adsorption trends, are quite noticeable in Figures 3 to 9, i.e., in the lower temperature TGA cycling curves; these interesting trends have also been pointed out and discussed elsewhere.5 It is noteworthy that none of the Fickian diffusion models7,8,10,14,15 would be able to predict these differences in the adsorption and desorption rates. Not only were the theoretical developments not formulated to account for such behavior, but also the investigators were not aware such behavior may have existed because they did not measure dynamic desorption data. These facts lend considerable credence to this first-of-its-kind kinetic modeling study of both the uptake and release rates of CO2 on a SAS over such a broad range of conditions.

Conclusions Five, semi-empirical, temperature-dependent, kinetic models were developed and systematically studied to determine which one best described the reversible reaction/adsorption and desorption behavior of CO2 in a solid amine sorbent (SAS) over a broad range of experimental conditions. The SAS was composed of polyethyleneimine (PEI) immobilized on a CARiACT® G10 silica support. Four temperatures (40, 60, 80 and 100 °C) and seven concentrations of CO2 in N2 at 1 atm (1.2, 4.8, 14.5, 32.8, 56.1, 69.8 and 88.6 vol%) were studied. Four consecutive adsorption/desorption cycles were carried out at each of the 28 conditions using a thermogravimetric analyzer (TGA). Each cycle consisted of 40 minutes of adsorption in CO2/N2 followed by 40 minutes of desorption in N2. Model parameters were


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determined by fitting just the first two cycles at 20 conditions. The last two cycles and the remaining data were then predicted using the same parameters without any further adjustments. The goodness of the fit of each model was judged using all four cycles at all 28 conditions based on the highest R2 from the TGA curves. The five models varied by the number and type of reaction with each reaction only involving one CO2 molecule: I) one reaction, II) two reactions in parallel, III) three reactions in parallel, IV) two reactions in series, and V) three reactions in parallel and series. The best model was Model III, with its three parallel reactions being consistent with PEI having three different amine sites. Model III not only predicted the kinetic trends in all the TGA curves, but it also predicted both the working capacities at all the conditions and the equilibrium loadings at higher temperatures. Considering the wide range of conditions studied, this is a first-of-its-kind, kinetic model that describes the reversible reaction/adsorption and desorption behavior of CO2 in a SAS. This model should prove to be very useful in an adsorption process simulator for the development of new PSA and TSA processes utilizing this commercially viable PEI SAS for CO2 removal from a variety of gas streams. The systematic approach utilized in determining that Model III was the best kinetic model should also be useful for others to adopt in the study of SASs.

Acknowledgements The authors gratefully acknowledge financial support provided in part by the DOE National Energy Technology Laboratory through DE-FE0007639, in part by the SAGE Center at the University of South Carolina, and in part by the Process Science and Technology Center, a consortium composed of the University of Texas at Austin, the University of South Carolina, and the Texas A&M University. The authors would also like to acknowledge Dr. McMahan L. Gray


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of the National Energy Technology Laboratory for providing the SAS studied in this work.

Supporting Information If applicable, this information is available free of charge via the Internet at http://pubs.acs.org/.

Nomenclature A = area (m2) Ei,f = forward activation energy for the CO2 chemisorption reaction i (kJ mol-1) Ei,b = backward activation energy for the CO2 chemisorption reaction i (kJ mol-1) i = reaction number K1,b = backward reaction rate constant for reaction of CO2 and N1 and CO2 and N3 (min-1) K1,f = forward reaction rate constant for reaction of CO2 and N1 and CO2 and N3 (kPa-1 min-1) K2,b = backward reaction rate constant for reaction of CO2 and N2 (min-1) K2,f = forward reaction rate constant for reaction of CO2 and N2 (kPa-1min-1) K3,b = backward reaction rate constant for reaction of CO2 and N3 (min-1) K3,f = forward reaction rate constant for reaction of CO2 and N3 (kPa-1 min-1) Ki = equilibrium constant for reaction i (kPa-1) Ki,0 = preexponential constant for equilibrium constant of reaction i ki,b,0 = preexponential constant for backward reaction i (min-1) Ki,f,0 = preexponential constant for forward reaction i (min-1) Kp = constant (min-1) Kq = constant (kg kPa K-1 mol-1) N1 = number of reaction sites which react with CO2 and form q1 (mol kg-1)


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N2 = number of reaction sites which react with CO2 and form q2 (mol kg-1) N3 = number of reaction sites which react with q1 and form q3 (mol kg-1) Nt = total number of reaction sites (mol kg-1) Nmax= maximum number of reaction site (mol kg-1) P = partial pressure of CO2 in the feed gas (kPa) P*= partial pressure of CO2 in the gas that is in contact with adsorbent (kPa) qi,exp = experimental value for CO2 loading at time t (mol kg-1) qi ,mod = model value for CO2 loading (mol kg-1)

q exp = mean of experimental CO2 loading over 4 cycles (mol kg-1) q1 = sites taken from N1 by CO2 at time t (mol kg-1) q1,e = sites taken from N1 by CO2 at equilibrium (mol kg-1) q2 = sites taken from N2 by CO2 at time t (mol kg-1) q2,e = sites taken from N2 by CO2 at equilibrium (mol kg-1) q3 = sites taken from N3 by CO2 at time t (mol kg-1) q3,e = sites taken from N3 by CO2 at equilibrium (mol kg-1) q4 = sites taken from N4 by one CO2 at time t (mol kg-1) q4,e = sites taken from N4 by one CO2 at equilibrium (mol kg-1) q5,e = sites taken from N4 by two CO2s at time t (mol kg-1) q5,e = sites taken from N4 by two CO2s at equilibrium (mol kg-1) qt = total CO2 loading at time t (mol kg-1) qt,e = total CO2 loading at equilibrium (mol kg-1) R = universal gas constant (J mol-1 K-1) R2 = coefficient of determination 22 ACS Paragon Plus Environment

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t = time (min) T = temperature (K) T0 = constant in Fermi-Dirac distribution (K) V* = the volume of the TGA chamber (m3) Vs = adsorbent volume (m3)

Greek Symbols kα = constant in Fermi-Dirac distribution

α = fraction of total reaction sites that belongs to N1 β = fraction of total reaction sites that belongs to N2 γ = fraction of total reaction sites that belongs to N3 η =fraction of total reaction sites that belongs to N2 ρs = adsorbent density (kg m-3) ∆Hi = effective heat of adsorption/reaction for reaction i (kJ mol-1)


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Literature Cited (1)

Secretariat of the Commission for Environmental Cooperation. The North American Mosaic:

An

Overview

of

Key

Environmental

Issues,

Climate

Change.

http://www.cec.org/soe/files/en/SOE_Climate_en.pdf. (2)

Ebner, A. D.; Ritter, J. A. State-of-the-Art Adsoprtion and Membrane Separation Processes for Carbon Dioxide Production from Carbon Dioxide Emitting Industries. Sep. Sci. Technol. 2009, 44, 1273.

(3)

Wang, J.; Huang, L.; Yang, R.; Zhang, Z.; Wu, J.; Gao, Y.; Wang, Q.; O'Hare, D.; Zhong, Z. Recent Advances in Solid Sorbents for CO2 Capture and New Development Trends. Energy Environ. Sci. 2014, 7, 3478.

(4)

Shakerian, F.; Kim, K.-H.; Szzulejko, J. E.; Park, J.-W. A Comparative Review Between Amine and Ammonia as Sorptive Media for Post-Combustion CO2 Capture. Applied Energy 2105, 148, 10.

(5)

Ebner, A. D.; Gray, M. L.; Chisholm, N. G.; Black, Q. T.; Mumford, D. D.; Nicholson, M. A.; Ritter, J. A. Suitability of a Solid Amine Sorbent for CO2 Capture by Pressure Swing Adsorption. Ind. Eng. Chem. Res. 2011, 50, 5634.

(6)

Belmabkhout, Y.; Sayari, A. Isothermal versus Non-isothermal Adsorption-Desorption Cycling of Triamine-Grafted Pore-Expanded MCM-41 Mesoporous Silica for CO2 Capture from Flue Gas. Energy Fuels. 2010, 24, 5273.

(7)

Belmabkhout, Y.; Sayari, A. Effect of Pore Expansion and Amine Functionalization of Mesoporous Silica on CO2 Adsorption over a Wide Range of Conditions. Adsorption.

2009, 15, 318. (8)

Belmabkhout, Y.; Serna-Guerrero, R.; Sayari, A. Adsorption of CO2 from Dry Gases on


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MCM-41 Silica at Ambient Temperature and High Pressure. 1: Pure CO2 Adsorption Chem. Eng. Sci. 2009, 64, 3721. (9)

Serna-Guerrero, R.; Belmabkhout, Y.; Sayari, A. Modeling CO2 Adsorption on AmineFunctionalized Mesoporous Silica: 1. A Semi-Empirical Equilibrium Model Chem. Eng. J.

2010, 161, 173. (10) Serna-Guerrero, R.; Sayari, A. Modeling Adsorption of CO2 on Amine-Functionalized Mesoporous Silica. 2: Kinetics and Breakthrough Curves Chem. Eng. J. 2010, 161, 182. (11) Gray, M. L.; Hoffman, J. S.; Hreha, D. C.; Fauth, D. J.; Hedges, S. W.; Champagne, K. J.; Pennline, H. W. Parametric Study of Solid Amine Sorbents for the Capture of Carbon Dioxide. Energy Fuels. 2009, 23, 4840. (12) Wang, X.; Schwartz V.; Clark, J. C.; Ma X.; Overbury, S. H.; Xu, X.; Song, C. Infrared Study of CO2 Sorption over “Molecular Basket” Sorbent Consisting of PolyethylenimineModified Mesoporous Molecular Sieve. J. Phys. Chem. C 2009, 113, 7260. (13) Zhang, Z.; Ma X.; Wang, D.; Song, C.; Wang, Y. Development of Silica-Gel-Supported Polyethylenimine Sorbents for CO2 Capture from Flue Gas. AIChE J. 2012, 58, 2495. (14) Bollini, P.; Brunelli, N. A.; Didas, S. A.; Jones, C. W. Dynamics of CO2 Adsorption on Amine Adsorbents. 1. Impact of Heat Effects. Ind. Eng. Chem. Res. 2012, 51, 15145. (15) Bollini, P.; Brunelli, N. A.; Didas, S. A.; Jones, C. W. Dynamics of CO2 Adsorption on Amine Adsorbents. 2. Insights into Adsorbent Design. Ind. Eng. Chem. Res. 2012, 51, 15153. (16) Vaidya, P. D.; Kenig, E. Y. CO2-Alkanolamine Reaction Kinetics: A Review of Recent Studies, Chem. Eng. Technol. 2007, 30, 1467. (17) Belmabkhout, Y.; Serna-Guerrero, R.; Sayari, A. Amine-Bearing Mesoporous Silica for


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CO2 Removal from Dry and Humid Air. Chem. Eng. Sci. 2010, 65, 3695. (18) Sayari, A.; Belmabkhout, Y. Stabilization of Amine-Containing CO2 Adsorbents: Dramatic Effect of Water Vapor. J. Am. Chem. Soc. 2010, 132, 6312. (19) Serna-Guerrero, R.; Da'na, E.; Sayari, A. New Insights into the Interactions of CO2 with Amine-Functionalized Silica. Ind. Eng. Chem. Res. 2008, 47, 9406. (20) Liu, Q.; Shi, J.; Zheng, S.; Tao, M.; He, Y.; Shi, Y. Kinetic Studies of CO2 Adsorption/ Desorption on Amine Functionalized Multiwalled Carbon Nanotubes. Ind. Eng. Chem. Res. 2014, 53, 11677. (21) Suh, D.-M.; Sun, X. Particle-Scale CO2 Adsorption Kinetics Modeling Considering Three Reaction Mechanisms. Inter. J. Greenhouse Gas Control. 2013, 17, 388. (22) Planas, N.; Dzubak, A. L.; Poloni, R.; Lin, L.; McManus, A.; McDonald, T.; Neaton, J. B.; Long, J. R.; Smit, B.; Gagliardi, L. The Mechanism of CO2 Adsorption in an AlkylamineFunctionalized Metal-Organic Framework. J. Am. Chem. Soc. 2013, 135, 7402. (23) Hicks, J. C.; Dabestani, R.; Buchanan III, A. C.; Jones C. W. Spacing and Site Isolation of Amine Groups in 3-Aminopropyl-Grafted Silica Materials: The Role of Protecting Groups. Chem. Mater. 2006, 18, 5022. (24) Choi, S; Drese, J. H; Jones, C. W. Adsorbent Materials for Carbon Dioxide Capture from Large Anthropogenic Point Sources. Chem. Sus. Chem. 2009, 2, 796. (25) Siriwardane, R.; Robinson, C. Liquid-Impregnated Clay Solid Sorbents for CO2 Removal from Post Combustion Gas Streams, J. Environ. Eng-ASCE 2009, 135, 378. (26) Satyapal, S.; Filburn, T.; Trela, J.; Strange, J. Performance and Properties of a Solid Amine Sorbent for CO2 Removal in Space Life Support Applications. Energy Fuels. 2001, 15, 250.


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Figures Captions Figure 1. Schematic of the experimental reaction/adsorption and desorption apparatus depicting the thermogravimetric analyzer (TGA) flow-through system: SVs: solenoid valves; FMs: variable area flow meters; NVs: needle valves; CRs: cylinder regulators.

Figure 2. Comparison of experimental TGA data (dotted lines) to predictions (solid lines) from Model III with and without the TGA effect (i.e., a gas phase film mass transfer resistance) at a) 100, b) 80, c) 60 and d) 40 oC for 14.5 vol% CO2 in N2 at 1 atm (fitted data).

Figure 3. Comparison of experimental TGA data (dotted lines) to predictions from Models I, II, III and IV (solid lines) at 40 oC for 1.2 vol% CO2 in N2 at 1 atm (fitted data).





Figure 8. Comparison of TGA experimental data (dotted lines) to predictions from Models I, II, III and IV (solid lines) at 40 oC for a) 32.8 and b) 69.8 vol% CO2 in N2 at 1 atm (predicted data).

Figure 9. Comparison of experimental TGA data (dotted lines) to predictions from Models I, II, III and IV (solid lines) at 60 oC for a) 1.2, b) 4.8, c) 14.5, d) 56.1 and e) 88.6 vol% CO2 in N2 at 1 atm (fitted data). 27 ACS Paragon Plus Environment

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Figure 10. Comparison of experimental TGA data (dotted lines) to predictions from Models I, II, III and IV (solid lines) at 80 oC for a) 1.2, b) 4.8, c) 14.5, d) 56.1 and e) 88.6 vol% CO2 in N2 at 1 atm (fitted data).


Figure 12. Comparison of experimental TGA data (dotted lines) to predictions from Model III (solid lines) at 60, 80 and 100 oC for a) 32.8 and b) 69.8 vol% CO2 in N2 at 1 atm (predicted data).

Figure 13. Comparison of experimental working capacities (symbols) to predictions (lines) from Models I, II, III and IV at a) 40, b) 60, c) 80 and d) 100 °C.

Figure 14. Comparison of experimental equilibrium loadings, i.e., adsorption isotherms (symbols) to predictions (lines) from Model III (eqs 15 to 17) at 80 and 100 oC.


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Table 1. Summary of the reaction/adsorption, rate and balance relationships that apply to Models I, II, III, VI and V. For a given model, the set of corresponding equations are the ones that would be used in a dynamic adsorption process simulator. Model I II III IV V

Reactions from Text R1 R1, R2 R1, R2, R3 R4, R5 R1, R4, R5

Rate and Balance Eqs from Text 1, 6, 7, 11 1, 2, 7, 11 1, 2, 3, 7, 11 4, 5, 7, 11 1, 4, 5, 7, 11


Constraints q2=q3=q4=q5=0 q3=q4=q5=0 q4=q5=0 q1=q2=q3=0 q2=q3=0

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Table 2. Model parameters for Models I, II, III, VI and V. Parameter -1

I

II -1

7.92×10

III -1

7.94×10

IV -1

8.35×10-1

Kp (min )

8.68×10

Kq (kg kPa K-1 mol-1)

4.54×10-3

3.39×10-3

2.59×10-3

3.45×10-3

3.58×10-3

K1f0 (kPa-1 min-1)

1.24×10-2

1.18×10-3

1.55×10-2

-

7.42×10-9

E1f (kJ mol-1)

-5.23×100

-1.29×10-1

-3.68×10-1

-

-3.19×101

K1b0 (min-1) E1b (kJ mol-1) K2f0 (kPa-1 min-1) E2f (kJ mol-1) K2b0 (min-1) E2b (kJ mol-1) K3f0 (kPa-1 min-1) E3f (kJ mol-1) K3b0 (min-1) E3b (kJ mol-1) K4f0 (kPa-1 min-1)

1.18×109 6.67×101 -

5.92×109 7.15×101 1.14×10-1 1.19×101 2.48×108 5.92×101 -

7.43×102 2.31×101 1.75×10-2 8.71×100 2.01×1011 7.93×101 9.48×10-4 -1.39×101 5.17×1010 7.80×101 -

8.99×10-4

2.88×108 6.12×101 7.76×10-4

E4f (kJ mol-1)

-

-

-

-1.36×101

-1.42×101

K4b0 (min-1) E4b (kJ mol-1) K5f0 (kPa-1 min-1) E5f (kJ mol-1) K5b0 (min-1) E5b (kJ mol-1) Nmax

Κα

2.80 4.87×10-2

3.98 3.26×10-2

3.79 3.12×10-2

4.04×109 7.05×101 1.53 2.19×101 5.09×107 5.42×101 2.78 2.99×10-2

4.47×109 7.07×101 3.52×10-3 3.87 7.40×10-1 3.59×10-5 3.46 4.40×10-2

Τ0

2.88×102

2.91×102

2.85×102

2.87×102

2.94×102

α β γ η=1−(α+β+γ)

1.00 0.00 0.00 0.00

6.97×10-1 3.03×10-1 0.00 0.00

1.51×10-1 2.05×10-1 6.44×10-1 0.00

0.00 0.00 0.00 1.00

2.52×10-1 0.00 0.00 7.48×10-1


8.45×10

V -1

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Table 3. Heats of reaction/adsorption for Models I, II, III, VI and V. Parameter -1 ∆H CO2 ,1 (kJ mol ) -1

∆H CO2 , 2 (kJ mol ) -1

∆H CO2 ,3 (kJmol ) -1

∆H CO2 , 4 (kJ mol ) -1

∆H CO2 , 5 (kJ mol )

I

II

III

IV

V

-71.90

-84.36

-23.47

-

-93.06

-

-47.34

-70.63

-

-

-

-

-91.92

-

-

-

-

-

-84.09

-84.92

-

-

-

-32.32

3.87


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Table 4. R2 values for Models I, II, III and IV obtained from all for four TGA cycles at 40, 60, 80 and 100 oC and at 1.2, 4.8, 14.5, 56.1 and 88.9 vol% CO2 in N2 at 1 atm (fitted data). Vol% CO2 in N2

I

II

1.2 4.8 14.5 56.1 88.9

0.5188 0.1472 0.9037 0.6493 -0.4996

0.9387 0.9487 0.9493 0.9504 0.7728

1.2 4.8 14.5 56.1 88.9

0.8798 0.9122 0.9267 0.9148 0.9517

0.9157 0.9781 0.9813 0.9285 0.9611

1.2 4.8 14.5 56.1 88.9

0.9499 0.9842 0.9944 0.9946 0.9956

0.9876 0.9836 0.9987 0.9951 0.9981

1.2 4.8 14.5 56.1 88.9

0.4801 0.9884 0.9989 0.9927 0.9952

0.5078 0.9885 0.9968 0.9942 0.9967

III 40 °C 0.9659 0.9835 0.9883 0.9622 0.8792 60 °C 0.8940 0.9839 0.9883 0.9318 0.9681 80 °C 0.9888 0.9887 0.9985 0.9952 0.9981 100 °C 0.5380 0.9892 0.9965 0.9936 0.9972

IV

Max R2

Best Model

0.9183 0.9538 0.8590 0.9234 0.7442

0.9659 0.9835 0.9883 0.9622 0.8792

III III III III III

0.9131 0.9813 0.9814 0.9257 0.9613

0.9157 0.9839 0.9883 0.9318 0.9681

II III III III III

0.9878 0.9845 0.9990 0.9952 0.9983

0.9888 0.9887 0.9990 0.9952 0.9983

III III IV III, IV IV

0.4911 0.9890 0.9969 0.9936 0.9971

0.5380 0.9892 0.9989 0.9942 0.9972

III III I II III


Page 33 of 49

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Table 5. R2 values for Models I, II, III and IV obtained from all four TGA cycles at 40, 60, 80 and 100 oC and at 32.8 and 69.8 vol% CO2 in N2 at 1 atm (predicted data). Vol% CO2 in N2

I

II

32.8 69.8

0.8083 -0.5049

0.9176 0.6594

32.8 69.8

0.9808 0.9834

0.9914 0.9882

32.8 69.8

0.9971 0.9958

0.9966 0.9964

32.8 69.8

0.9950 0.9969

0.9977 0.9973

III 40 °C 0.9671 0.8014 60 °C 0.9915 0.9915 80 °C 0.9963 0.9966 100 °C 0.9970 0.9983

IV

Max R2

Best Model

0.7958 0.6064

0.9671 0.8014

III III

0.9908 0.9910

0.9915 0.9915

III III

0.9956 0.9966

0.9971 0.9966

I III, IV

0.9974 0.9979

0.9977 0.9983

II III


Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 49

Table 6. R2 values for Models I, II, III, VI and V obtained from the working capacities at 40, 60, 80 and 100 oC.

Model

40 oC

60 oC

80 oC

100 oC

I

0.8988

0.8923

0.9900

0.9969

II

0.7301

0.9286

0.9973

0.9974

III

0.7981

0.9673

0.9971

0.9979

IV

0.5012

0.9470

0.9967

0.9981

V

0.8218

0.9383

0.9955

0.9981


Page 35 of 49

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Table 7. R2 values for Models I, II, III, VI and V obtained from the equilibrium loadings at 80 and 100 oC. Model I II III IV V

80 oC 0.9906 0.9964 0.9984 0.9968 0.9957

100 oC 0.9976 0.9979 0.9981 0.9980 0.9977


Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 49

Figure 1. Schematic of the experimental reaction/adsorption and desorption apparatus depicting the thermogravimetric analyzer (TGA) flow-through system: SVs: solenoid valves; FMs: variable area flow meters; NVs: needle valves; CRs: cylinder regulators.


Page 37 of 49

3.0 a)

Loading (mol/kg)

2.5 2.0 1.5 1.0 Experimnetal

0.5

With TGA effect Without TGA effect

0.0 3.0

0

5

10

15

20

5

10 Time (min)

15

20

d)

b) 2.5

Loading (mol/kg)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

2.0 1.5 1.0 0.5 0.0 0

5

10 Time (min)

15

20

0

Figure 2. Comparison of experimental TGA data (dotted lines) to predictions (solid lines) from Model III with and without the TGA effect (i.e., a gas phase film mass transfer resistance) at a) 100, b) 80, c) 60 and d) 40 oC for 14.5 vol% CO2 in N2 at 1 atm (fitted data).


Energy & Fuels

3.0

I

II

III

IV

Loading (mol/kg)

2.5 2.0 1.5 1.0 0.5 0.0 3.0 2.5

Loading (mol/kg)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 49

2.0 1.5 1.0 0.5 0.0 0

40

80

120 160 200 240 280 320 Time (min)

0

40

80

120 160 200 240 280 320 Time (min)



Page 39 of 49

3.0

I

II

III

IV

Loading (mol/kg)

2.5 2.0 1.5 1.0 0.5 0.0 3.0 2.5

Loading (mol/kg)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

2.0 1.5 1.0 0.5 0.0 0

40

80

120 160 200 240 280 320 Time (min)

0

40

80

120 160 200 240 280 320 Time (min)



Energy & Fuels

3.0

I

II

Loading (mol/kg)

2.5 2.0 1.5 1.0 0.5 0.0 3.0 0

40

80

120 160 200 240 280 320

III

IV

2.5

Loading (mol/kg)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 40 of 49

2.0 1.5 1.0 0.5 0.0 0

40

80

120 160 200 240 280 320 0

40

80

Time (min)

120 160 200 240 280 320 Time (min)



Page 41 of 49

3.0

I

II

III

IV

Loading (mol/kg)

2.5 2.0 1.5 1.0 0.5 0.0 3.0 2.5

Loading (mol/kg)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

2.0 1.5 1.0 0.5 0.0 0

40

80

120 160 200 240 280 320 Time (min)

0

40

80

120 160 200 240 280 320 Time (min)



Energy & Fuels

3.0

I

II

III

IV

Loading (mol/kg)

2.5 2.0 1.5 1.0 0.5 0.0 3.0 2.5

Loading (mol/kg)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 42 of 49

2.0 1.5 1.0 0.5 0.0 0

40

80

120 160 200 240 280 320

0

40

80

Time (min)

120 160 200 240 280 320 Time (min)



Page 43 of 49

3.0

a)

b)

I

I

a)

b)

II

II

a)

b)

III

III

a)

b)

IV

IV

Loading(mol/kg)

2.5 2.0 1.5 1.0 0.5 0.0 3.0

Loading (mol/kg)

2.5 2.0 1.5 1.0 0.5 0.0 3.0

Loading (mol/kg)

2.5 2.0 1.5 1.0 0.5 0.0 3.0 2.5

Loading (mol/kg)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

2.0 1.5 1.0 0.5 0.0 0

40

80

120 160 200 240 280 320 Time (min)

0

40

80

120 160 200 240 280 320 Time (min)

Figure 8. Comparison of experimental TGA data (dotted lines) to predictions from Models I, II, III and IV (solid lines) at 40 oC for a) 32.8 and b) 69.8 vol% CO2 in N2 at 1 atm (predicted data). 43 ACS Paragon Plus Environment

Energy & Fuels

3.0

a)

d)

b)

e)

Loading (mol/kg)

2.5 2.0 1.5 1.0 0.5 0.0 3.0

Loading (mol/kg)

2.5 2.0 1.5 1.0 0.5 0.0 3.0

0

40

80

c)

120 160 200 240 280 320 Time (min)

2.5

Loading (mol/kg)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 44 of 49

2.0 1.5 1.0 0.5 0.0 0

40

80

120 160 200 240 280 320 Time (min)



Page 45 of 49

3.0

a)

d)

b)

e)

Loading (mol/kg)

2.5 2.0 1.5 1.0 0.5 0.0 3.0

Loading (mol/kg)

2.5 2.0 1.5 1.0 0.5 0.0 3.0

0

40

80

c)

120 160 200 240 280 320 Time (min)

2.5

Loading (mol/kg)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

2.0 1.5 1.0 0.5 0.0 0

40

80

120 160 200 240 280 320 Time (min)



Energy & Fuels

3.0

a)

d)

b)

e)

Loading (mol/kg)

2.5 2.0 1.5 1.0 0.5 0.0 3.0

Loading (mol/kg)

2.5 2.0 1.5 1.0 0.5 0.0 3.0

0

40

80

c)

120 160 200 240 280 320 Time (min)

2.5

Loading (mol/kg)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 46 of 49

2.0 1.5 1.0 0.5 0.0 0

40

80

120 160 200 240 280 320 Time (min)



Page 47 of 49

3.0

60°C

a)

b)

Loading (mol/kg)

2.5 2.0 1.5 1.0 0.5 60°C

0.0 3.0

a)

b)

80°C

80°C

a)

b)

100°C

100°C

Loading (mol/kg)

2.5 2.0 1.5 1.0 0.5 0.0 3.0 2.5

Loading (mol/kg)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

2.0 1.5 1.0 0.5 0.0 0

40

80

120 160 200 240 280 320

0

40

80

Time (min)

120 160 200 240 280 320 Time (min)

Figure 12. Comparison of experimental TGA data (dotted lines) to predictions from Model III (solid lines) at 60, 80 and 100 oC for a) 32.8 and b) 69.8 vol% CO2 in N2 at 1 atm (predicted data).


Energy & Fuels

Working Capcity (mol/kg)

3.0

Exp. Mod-I Mod-II Mod-III Mod-IV

a)

2.5 2.0

c)

1.5 1.0 0.5 0.0 3.0

Working Capacity (mol/kg)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 48 of 49

d)

b)

2.5 2.0 1.5 1.0 0.5 0.0 0

20

40 60 PCO2 (kPa)

80

100

0

20

40 60 PCO2 (kPa)

80

100

Figure 13. Comparison of experimental working capacities (symbols) to predictions (lines) from Models I, II, III and IV at a) 40, b) 60, c) 80 and d) 100 °C.


Page 49 of 49

3.0

Equilibrium Loading (mol/kg)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

80 °C

2.5

100 οC

2.0 1.5 1.0 0.5 0.0 0

20

40 60 PCO2 (kPa)

80

100

Figure 14. Comparison of experimental equilibrium loadings, i.e., adsorption isotherms (symbols) to predictions (lines) from Model III (eqs 15 to 17) at 80 and 100 oC.


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