Experimental Study on the Kinetics of CO₂ and H₂O Adsorption on Honeycomb Carbon Monoliths under Cement Flue Gas Conditions

Abstract

The main challenge of adsorption consists in the production of materials that can be used in real situations. This study comprehensively describes the CO₂ and H₂O adsorption behavior of honeycomb-shaped sorbents commonly used in rapid pressure swing adsorption cycles (RPSA). With this purpose, the kinetics and equilibrium of adsorption of CO₂/H₂O/N₂ mixtures on three honeycomb carbon monoliths (793, 932, and AM03) were assessed in a thermogravimetric analyzer (TGA) under different postcombustion capture scenarios (temperature of 50 °C and several concentrations of CO₂). The kinetics study exhibited that the single adsorption of CO₂ and H₂O can be adequately described by the Avrami and exponential decay-2 models, respectively. As expected, the three carbon monoliths presented fast adsorption of CO₂ from a CO₂/H₂O mixture. Furthermore, when humid flue gas was considered, overall adsorption kinetics were governed by CO₂. Besides, the experimental data fitting to the intraparticle diffusion model showed that gradual CO₂ and H₂O diffusion toward the micropores was the rate-limiting stage. The obtained results give a better insight into the selective adsorption of CO₂ and the potential of honeycomb carbon monoliths to separate CO₂ from humid flue gas in the context of the cement industry. Carbon monolith 793 is the best carbon monolith candidate to capture CO₂ under the evaluated conditions: a capacity of adsorption of 1 mmol of CO₂ g^–1 and favorable kinetics in 32 vol % CO₂ and 4 vol % H₂O_(v), at 50 °C and 101.3 kPa.

Short abstract

Adsorption equilibrium and kinetics of CO₂/H₂O/N₂ mixtures on three honeycomb carbon monoliths were assessed in a thermogravimetric analyzer under different scenarios representative of postcombustion capture.

Introduction

Among the industrial sources, cement plants constitute a major CO₂ emitter.¹ The CO₂ emissions from the cement industry are in the order of 1306 Mt year^–1, around 27% of the carbon emissions from industry. It implies that for every tonne of cement produced, 0.6–1.0 t of CO₂ are emitted.² Half of the emitted CO₂ results from the calcination of limestone; the combustion of different fuels in the kiln such as coal, petroleum coke, tires, waste oil, sewage sludge, etc., account for an additional 40%; and transportation and electricity used in manufacturing operations contribute 5% each.³

CO₂ capture, utilization, and sequestration (CCUS) technologies will be crucial to reduce CO₂ emissions from the cement sector, specifically process emissions associated with limestone calcination.⁴ Postcombustion CO₂ capture technologies similar to those applied in the power sector are the starting options and can easily be retrofitted to the existing facilities, therefore reducing the time frame for large-scale deployment.⁵

Solid-based technologies to capture CO₂ entail an alternative to the benchmark chemical absorption relying on their capability to be more energy-efficient. Gas purification and impurity removal can be carried out by adsorption, which is a well-implemented process in the chemical and petrochemical industries. In any low-temperature adsorption-based process, the sorbent selectively separates the adsorbate molecules from a gas mixture in which the pair adsorbate–sorbent establishes the nature of the type of bonding involved.^6,7 Under postcombustion CO₂ capture conditions, the presence of water vapor is a nuisance to the selective capture of CO₂ by a physical adsorbent. The competition of H₂O against CO₂ for the adsorption sites in the solid leads to a loss of adsorption capacity. The extent of the impact of water vapor on CO₂ uptake depends on both the relative humidity (RH %), the concentration levels of CO₂ in the gas streams,⁶ and the relative kinetics of CO₂ and H₂O adsorption.⁸

Accurate knowledge of multicomponent adsorption equilibria and kinetics is essential to comprehend the effects of moisture content on the CO₂ adsorption from flue gases. It requires a comprehensive understanding of single and multicomponent adsorption thermodynamics to describe the equilibria of gas components and water vapor. In addition, kinetics provides knowledge about the adsorption rate under established conditions. Thus, both kinetic and equilibrium data constitute very useful information to ensure the successful removal of CO₂ from industrial gases through the utilization of a suitable adsorbent.^9,10

Several studies have been published in the literature dealing with CO₂ and H₂O single-component adsorption kinetics. For instance, Wei et al.^11,12 studied the kinetics of the adsorption of CO₂ using activated carbon produced from waste ion-exchange resin. After employing a broad interval of temperatures and pressures, they concluded that the models that most appropriately described the CO₂ adsorption kinetics were those of Avrami and fractional order. Likewise, Zhang et al.¹³ investigated the H₂O_(v) kinetics of adsorption at different temperatures and under different relative humidity conditions on the inner surface of silica-based nanoporous materials. The exponential-decay-2 model was found to satisfactorily fit the kinetic data for water vapor adsorption. In terms of binary CO₂/H₂O adsorption, authors such as Li et al.^14,15 performed breakthrough experiments using activated alumina F-200 and CDX (a special BASF mixture made of alumina and NaY) to explore the impact of CO₂ and H₂O on each other over a wide range of concentrations of saturated water vapor and at different temperatures. These authors found that at increasing humidity, the inhibitory effect of CO₂ on H₂O diminished and the H₂O adsorption quickly recovered the single-component adsorption values. For alumina CDX, the CO₂ loading under dry conditions strongly decreased from 2.3 to 0.3 mmol g^–1 at a relative humidity of 2.79% (0.12 kPa of water vapor). Conversely, the amount of CO₂ adsorbed in the H₂O_(v)/CO₂ system remained the same; however, a mild decrease was observed for higher humidity levels. Likewise, Xu et al.,¹⁶ using activated carbon GC1200, observed, at the same partial pressure, that both CO₂ and H₂O slightly diminished their loadings when mixed with regard to their pure component loadings.

The above-mentioned research has provided a better insight into the mechanism of adsorption and an effective way to predict the CO₂–H₂O adsorption behavior. More recently, in previous work,⁶ we evaluated the effect of relative humidity (RH %) on the CO₂ uptake of a potassium-based sorbent under simulated flue gas conditions and concluded that a relative humidity of around 20% in the K₂CO₃-doped biocarbon bed benefited the carbonation reaction and increased the CO₂ uptake, which showed a value of 1.9 mmol g^–1 at 50 °C and 14 kPa CO₂. This was achieved regardless of the H₂O flue gas concentration. Furthermore, at higher temperatures between 300 and 500 °C, Coenen et al.¹⁷ developed a kinetic model, based on an extensive thermogravimetric analysis (TGA) study, that was able to represent the CO₂ and H₂O adsorption and desorption kinetics on a potassium-promoted hydrotalcite-based sorbent. The model took also into account their complex interactions. However, as far as we know, a comprehensive kinetic study of the adsorption behavior of CO₂, H₂O, and their interactions on activated carbons has not been reported as yet.

Flue gas from the cement industry usually contains a higher CO₂ concentration of ca. 14–33%, compared to the 12–14% and 4% CO₂ for pulverized fuel (pf) coal and gas power plants, respectively.^3,18

The main challenge of adsorption, when applied at an industrial scale, consists in the production of materials that can successfully handle real process conditions. The adsorption capacity should not be the sole criteria for decision-making and process costing. The efficiency of the process and the technological feasibility should be balanced as indicated by Sun et al.¹⁹ For instance, adsorption/desorption kinetics impact the effectiveness of the process and the associated expenses. Better design and integration of the adsorption and desorption units can increase the speed of the cycles, but this can induce some problems in process engineering and, eventually, give rise to limitations in the selection of adsorbents. As indicated by Querejeta et al., carbon-based adsorbents are selective to CO₂, can be regenerated without difficulty, and contrarily to other adsorbents (i.e., zeolites or metal–organic frameworks (MOFs)), they are hydrophobic and present high stability under humid environments.²⁰ Besides, the use of monolith-structured carbon-based solid sorbents with flow-through channels, such as the honeycomb-shaped sorbents selected in this study, is very suited for rapid pressure swing adsorption cycles (RPSA). The monolith-structured sorbents allow high flow rates of gases carrying dust without experiencing the associated pressure drop of packed beds, avoid the fluidization of adsorbents in fluidized beds, offer a larger geometric surface area that enhances the contact between gas and solid, and are easily scalable. Nevertheless, the open structure of honeycomb monoliths may result in poor adsorption performance.^21,22

With this regard, the equilibrium and kinetics of adsorption of CO₂/H₂O/N₂ mixtures on three honeycomb carbon monoliths were studied in a thermogravimetric analyzer (TGA). The findings of this research give a better comprehension of the selective adsorption of CO₂ and the potential of honeycomb carbon monoliths to separate CO₂ from humid flue gas in the context of the cement industry.

Characterization of Adsorbents

In this study, three honeycomb carbon monoliths, denoted as 793, 932, and AM03, were evaluated in CO₂ adsorption experiments. These monoliths were produced by MAST Carbon International Ltd. avoiding the addition of a binder. The process entailed the carbonization of extruded phenolic resins and their ulterior activation. This method of fabrication gives rise to a singular and precise control of the monoliths structure at the micro and macropore levels.²²

Textural Properties

Characterization of the porosity of the activated carbon monoliths was accomplished by N₂ adsorption isotherms at −196 °C (Micromeritics ASAP 2010), and CO₂ adsorption isotherms at 0 °C (Micromeritics TriStar 3000). Before the measurements, the samples were degassed at 100 °C overnight under vacuum.

The porous texture of the samples is well described by N₂ and CO₂ adsorbates. N₂ adsorption isotherms include relative pressures that span from p/p⁰ = 0 to 0.98 and cover a wide range of pore sizes, but N₂ suffers diffusion limitations in ultramicropores (<0.7 nm) due to the low temperature. Likewise, CO₂ adsorption at 0 °C and subatmospheric pressures (which correspond to a maximum relative pressure of p/p⁰ < 0.03) is linked to the ultramicroporosity and complements the information given by the N₂ isotherms. Table 1 depicts the methodology used to determine the textural parameters of the samples.

Table 1. Textural Parameters Determined from the N₂ (−196 °C) and CO₂ (0 °C) Adsorption Isotherms.

Textural parameters
Total pore volume (PV)	Vp	Amount of N2 adsorbed at a relative pressure of 0.99
Surface area	BET	Brunauer–Emmett–Teller equation23
Micropore volume	W0	N2 isotherms: Dubinin–Radushkevich (DR) equation assuming a density of the adsorbed phase of 0.808 cm3 g–1 and a cross-sectional area of 0.162 nm2;24 CO2 isotherms: Dubinin–Radushkevich (DR) equation assuming a density of the adsorbed phase of 1.023 cm3 g–1 and a cross-sectional area of 0.187 nm2 2525
Micropore surface area	SDR
Average micropore width	L0	Stoeckli–Ballerini equation26
Pore size distribution	PSD	Quenched solid state (QSDFT) for N2 isotherms, assuming cylindrical pore geometry and both nonlocal density functional theory (NLDFT) and grand canonical Monte Carlo (GCMC) model for CO2 isotherms, assuming slit pore geometry27

Surface Chemistry

The surface chemistry, in general, and the oxygen surface functionalities of carbon materials, in particular, play a crucial role in the adsorption of H₂O_(v) at low relative pressures. Thus, to determine the effect of the carbon samples’ surface chemistry on the adsorption of H₂O_(v), temperature-programmed desorption (TPD) tests were carried out (the experimental protocol is described in the Supporting Information).

Adsorption studies

The equilibrium of adsorption and the uptake rates of CO₂ and H₂O on the selected carbon adsorbents was determined from adsorption tests carried out under different experimental conditions typical of CO₂ postcombustion capture (temperature of 50 °C and several CO₂ partial pressures). The equipment and the experimental methodology are described below.

Volumetric experiments

Adsorption isotherms of CO₂ and H₂O were collected at 50 °C. Single-component CO₂ adsorption isotherms were collected in a volumetric device, TriStar 3000 from Micromeritics, where the temperature was controlled by a Thermo Haake thermostatic bath. H₂O_(v) adsorption isotherms were determined in a volumetric device, VSTAR, from Anton Paar QuantaTec by the company Gas to Material Technologies S.L. Before each measurement, samples were outgassed at 100 °C under vacuum overnight.

Gravimetric tests

The nature of adsorbents and the selected operating conditions can substantially affect the CO₂ adsorption capacity.²⁸ Despite the hydrophobic character of activated carbons, the gas separation efficiency decreases under moisture conditions. Herein, a simple thermogravimetric analysis (TGA) apparatus was adapted to render a screening methodology to evaluate the influence of water vapor on CO₂ adsorption performances using a minimal amount of sample (∼70 mg).²⁹

The CO₂ and H₂O capture capacities of the carbon monoliths were studied under dynamic conditions in a thermogravimetric analyzer Setaram TAG24, following the procedure of Singh et al. and Plaza et al.^28,30 but self-adapted to assess humid conditions. Dynamic measurements were performed following the conditions listed in Table 2 for both adsorbates, H₂O and CO₂, at 50 °C and 101.3 kPa total pressure.

Table 2. Conditions of the TGA experiments to determine kinetic parameters.

	Adsorption stage
Description	T (°C)	Ptot (kPa)	Flow rate (cm3 min–1)	PCO2 (kPa)	PH2O (kPa)	PN2 (kPa)	Ads time (min)
CO2 adsorption	50	101.3	50.0	101.3			60
N2/H2O adsorption	50	101.3	104.2		4.0	97.3	30
CO2/H2O adsorption	50	101.3	104.2	97.3	4.0		30

Single and binary experiments (CO₂, N₂/H₂O, and CO₂/H₂O)

CO₂ capture capacity experiments were performed as schematized in Figure 1: after an initial conditioning step (50 cm³ min^–1 N₂, at 100 °C for 1 h) to remove any moisture and unwanted gases, and subsequent cooling down to 50 °C in N₂ flow and mass stabilization, the sample was exposed to a gas stream with 100 vol % CO₂. Finally, the samples were regenerated by switching the feed gas back to 100 vol % N₂ at a constant temperature of 50 °C.

Figure 1.

Total mass uptake vs time (full experiment) for single-component adsorption measurements on the three honeycomb carbon monoliths.

Likewise, binary adsorption experiments in the presence of water vapor were performed as shown in Figure 2: after an initial conditioning step (100 cm³ min^–1 N₂, at 200 °C for 2 h), and subsequent cooling down to 50 °C in N₂ flow and mass stabilization, the sample was exposed to a mixture consisting of 96 vol % (N₂ or CO₂) and 4 vol % H₂O for half an hour. Finally, the samples were regenerated by switching the composition of the feed gas to 100 vol % N₂ and elevating the temperature to 200 °C.

Figure 2.

Total mass uptake vs time (full experiment) for binary adsorption measurements on the three honeycomb carbon monoliths.

During the cooling step, the mass uptake increases due to the N₂ adsorption. Once the temperature of the sample stabilizes, so does the mass of the sample as it reaches thermal and adsorption equilibrium with the gas phase. By running blank experiments, buoyancy and dragging effects were appropriately corrected.

During the adsorption step, the composition of the feed switched from 100% N₂ to 100% CO₂ in the case of the single-component adsorption experiments and to 96% (CO₂ or N₂) and 4% H₂O_(v) for the binary experiments. The temperature kept constant at 50 °C. The mass of the sample increases due to the H₂O_(v) and/or CO₂ adsorption. The total mass uptake q_i is expressed in weight percentage (see Table 3) taking as a reference the mass of the sample at the end of the stabilization stage (i.e., N₂ adsorption step), where m_50,N2 is the N₂ mass uptake at 50 °C and m_50,i is the mass of the sample in the flow (CO₂ and/or H₂O_(v)) at the end of the adsorption step at 50 °C.

Table 3. Adsorption Capacities from Single and Binary Experiments.

Adsorption capacity	Equation
CO2, H2O, CO2 + H2O

It has been confirmed that the adsorption of N₂ at 50 °C is negligible.³¹ Therefore, the total mass uptake during the binary N₂/H₂O experiments, represented with q_i (see Table 3), corresponds to the H₂O adsorption capacities as determined from the H₂O adsorption isotherms (at 50 °C and 4.0 kPa), respectively. For the binary CO₂/H₂O experiments, the individual contributions of both components cannot be isolated and q_i accounts for the joint CO₂ + H₂O uptake.

Ternary experiments (CO₂/N₂/H₂O)

Flue gas from cement industry contains higher CO₂ concentrations of approximately 14–33 vol %, compared to 12–14 vol % CO₂ for coal-fired power plants and around 4 vol % CO₂ for gas-fired power plants.^3,18 Furthermore, those gas streams are saturated with water vapor concentrations ranging from 5 to 10 vol % (i.e., 100% relative humidity (RH) ≈ 12.3 vol % H₂O at 50 °C) and the temperature of the feed is never below 40 °C.¹⁸ For this reason, multicomponent experiments are critical to evaluate the adsorbent performance under more realistic flue gas conditions. To that end, CO₂ capture capacities of the honeycomb carbon monoliths were estimated in the thermogravimetric analyzer under humid postcombustion capture conditions representative of cement flue gas following the aforementioned procedure. After the initial conditioning step, a simulated flue gas stream (total flow rate of 104.2 cm³ min^–1) composed of 32 vol % CO₂, 4 vol % H₂O, and N₂ balance, at 50 °C and atmospheric pressure fed the thermogravimetric analyzer during the adsorption stage.

Results and Discussion

The results reported herein point at two main research areas: (i) the study of the equilibrium of CO₂ and H₂O adsorption that leads to the maximum capacity of each adsorbent material in the selected scenario, (ii) the study of the kinetics of CO₂ and H₂O adsorption analyzing the adsorption rate. The effect that the CO₂ concentration in the feed has on the adsorption performance will also be discussed in this section.

Textural Characterization

The nitrogen adsorption isotherms at −196 °C and the corresponding QSDFT pore size distributions (PSD) of the three carbon monoliths are displayed in Figure 3a,b. As it can be observed, carbon monoliths present type I adsorption isotherms (IUPAC classification), characteristic of microporous structures. It has to be noticed that AM03 presents the highest adsorption of N₂, owing to its higher microporosity development (cf. BET surface areas and pore volumes from the N₂ adsorption isotherms shown in Table 4).

Figure 3.

(a) N₂ adsorption isotherms at −196 °C and (b) N₂ adsorption QSDFT-PSD of the carbon monoliths.

Table 4. Textural Parameters Estimated from the N₂ and CO₂ Adsorption Isotherms.

	N2 adsorption (−196 °C)				CO2 adsorption (0 °C)
Sample	Vpa	SBETb	W0a	L0c	W0a	L0c	Smib
793	0.33	835	0.32	0.56	0.32	0.60	1059
932	0.32	824	0.31	0.61	0.32	0.62	1024
AM03	0.42	1085	0.42	0.74	0.41	0.71	1155

^aV, W in cm³ g^–1.

^bS in m² g^–1.

^cL₀ in nm.

The sharp knee alongside a horizontal plateau in Figure 3a shows that monoliths have narrow micropore size distributions with a limited volume of N₂ adsorbed and the monolayer formation at low relative pressures (p/p⁰ < 0.1).³² It is in good concordance with the QSDFT-PSD in Figure 3b, calculated by assuming cylindrical pore geometry and adsorption branch kernel that shows single peaks centered at pore sizes <0.7 nm. This is the reason why the diffusion of N₂ into these narrow micropores is hindered and leads to an underestimation of the micropore width (L₀). It is worth noting that carbon monoliths 793 and 932 show very similar narrow PSD, while AM03 presents larger pores.

The CO₂ adsorption isotherms of the samples at 0 °C and the NLDFT-PSD are represented in Figure 4a,b. The micropore ratio on each sample can be evaluated by comparing the volumes adsorbed of N₂ and CO₂.³¹ Likewise, Table 4 includes the CO₂ narrow micropore volume calculated through the DR equation.

Figure 4.

(a) CO₂ adsorption isotherms at 0 °C, (b) CO₂ adsorption NLDFT-PSD, (c) comparison of CO₂ adsorption GCMC and NLDFT pore volume (PV) of the carbon monoliths, and (d) goodness of the GCMC and NLDFT model fittings.

NLDFT-PSD characteristics of the carbon monoliths are alike; however, AM03 has a greater pore volume (Figure 4b). Pore sizes from 0.35 to 0.5 nm can contain one layer of CO₂ molecules, whereas for those from 0.65 and 0.8 nm, the adsorbate experiences a change to a two-layer structure. It is interesting to note that differential NLDFT-PSD exhibits a minimum at ca. 0.2 nm. The appearance of this minimum could be a consequence of the limitations of the model, which derive from the strong packing effects displayed by the parallel wall model along with the assumption of homogeneity of the surface. Figure 4c shows the application of the grand canonical Monte Carlo (GCMC) method to the CO₂ adsorption isotherms to get further insights into the pore size distributions. This model has been customarily employed to characterize carbons assuming a simplified physical structure of microporous carbons.³³ The combined use of these models is very useful to improve the outcome and complement the results. However, the main drawback of both sets of equations in the models is the assumption of a structureless, chemical, and geometrically smooth surface model.^34,35 The assumption of slit-shaped pores and the associated shortcomings frequently pose disagreements in the pore size distributions extracted from adsorption isotherms. It becomes more evident in the networking and molecular sieving effects, as well as in the specific interactions between adsorbate and carbon.^33,34,36

Contrary to the trend observed for other activated carbons in which both distributions (NLDFT and GCMC) in the ultramicroporous region (width <0.7 nm) were very comparable,³⁷ for the carbon monoliths under study, the GCMC CO₂ isotherms generated at subatmospheric pressures (Figure 4c) provide more reliable information about the PSD of the samples than the NLDFT model (Figure 4b). The better fitting of GCMC is illustrated in Figure 4d for monolith 793.

The fit of the GCMC model is particularly good for the narrower pore widths where the NLDFT presents the aforementioned gap or artifact. Deviations between both models are particularly significant in pore sizes between 0.65 and 0.8 nm where the adsorbate experiences a change from a one- to two-layer structure. In this pore range, spherical molecules form dense packing but the three-center CO₂ molecules form a less-dense structure due to a trade-off between the tendency to lie flat to the wall and the tendency to form T-like configurations due to the quadrupole.³⁸ Overall, GCMC deduced that most pore volume concentrates at sizes below 0.525 nm, therefore in the narrow micropores. Besides, about 43–48% of the total narrow micropore volume is between 0.325 and 0.425 nm. As we have explained elsewhere,³⁹ a tailored porous network with ca. 40–46% of ultramicropores of less than 0.5 nm and an irrelevant presence of pores >0.7 nm allows a 40% increase in the CO₂ retention capability for materials with similar micropore volume.

It is interesting to note that a key factor of the carbon dioxide adsorption is the average micropore width (L₀): lower values of L₀ give stronger adsorption potentials that can enhance the filling of the narrower microporosity with the CO₂ molecules. Therefore, activated carbons with small average micropore widths alongside good microporosity development may be great candidates to CO₂ capture.^21,39

As can be appreciated in Table 4, AM03 displays the largest volume of narrow microporosity. The textural characteristics from CO₂ adsorption follow the same pattern observed in N₂ adsorption. From the CO₂ adsorption isotherms, the values obtained for W₀ and L₀ are within the typical ranges described for activated carbons and point out a good development of the narrow microporosity in the carbon monoliths.^20,40

The microporosity features have a strong influence on the CO₂ uptake but also influence water vapor adsorption. The surface oxygen functional groups content promotes water vapor uptake at low pressures, but from medium to high pressures, the micropore filling is responsible for the adsorption capacity of the activated carbon. Moreover, the size of the formed water clusters is dependent on the micropore width.^41,42

Hence, the narrow range of microporosity present on the carbon monoliths allows us to selectively adsorb CO₂ at low partial pressures.^31,43 Among the evaluated monoliths, the more developed micropore network in AM03 suggests that this carbon monolith may exhibit both the highest CO₂ and H₂O adsorption capacities.

Surface Oxygen Functional Groups

The monitoring of labile surface oxygen groups in the carbons in the form of CO and CO₂ as a function of temperature was followed through TPD tests (cf. Figure S1 in the Supporting Information). Integration and deconvolution of these curves rendered the concentration of oxygen surface functionalities, which are shown in Table 5. It can be seen in this table that the number of oxygen functionalities that evolve as CO is much higher than those that give CO₂. The total amount of oxygen functionalities on the surface of carbons is given by the sum of CO + CO₂, as indicated in Table 5.

Table 5. Amount of CO and CO₂ Evolved during the TPD Experiments.

Sample	CO (μmol g–1)	CO2 (μmol g–1)	CO/CO2	CO + CO2 (μmol g–1)
793	1515	567	2.7	2082
932	1775	665	2.7	2440
AM03	2402	796	3.0	3198

Overall, honeycomb carbon monoliths present a basic surface as explained by the higher content of surface functionalities that decompose into CO. Moreover, all samples show similar oxygen functionality ratios on their surfaces, as can be inferred from the values of CO/CO₂. Only carbon monolith AM03 shows a slightly acidic surface. Besides, the surface oxygen functionalities amount (CO + CO₂) is analogous to other ACs.²⁰

Tables 6 and 7 display the distribution of the main oxygen functionalities (i.e., carbonyl and quinone, pyrone and chromene, together with carboxylic, peroxide, and lactone), which were estimated from the deconvolution of the CO and CO₂ profiles.

Table 6. Distribution of Oxygen SurfaceComplexes Estimated from CO-TPD Profiles.

Sample	Carbonyl and quinone (μmol g–1)	Pyrone and chromene (μmol g–1)
793	1083	373
932	1389	335
AM03	2349	337

Table 7. Distribution of Oxygen Surface Complexes Estimated from CO₂-TPD Profiles.

Sample	Carboxylic (μmol g–1)	Peroxide (μmol g–1)	Lactone (μmol g–1)
793	272	131	165
932	289	200	177
AM03	292	232	273

The deconvolution of the TPD profiles clearly shows the similarities of the honeycomb carbon monoliths surfaces in terms of oxygen surface functionalities development, the slight differences ascribed to the intensity of the activation conditions. As can be observed in Table 6 and 7, all of the samples present similar contents of pyrone and chromene while sample AM03 doubles the content of carbonyl and quinone and also exceeds in peroxide and lactone.

Volumetric CO₂ and H₂O_(v) Adsorption

Water vapor is an unavoidable flue gas component and competes with CO₂ for the adsorption on a solid sorbent surface.^18,20 Therefore, it is important to evaluate the capacity of carbon to adsorb CO₂ and H₂O_(v), when addressing CO₂ capture from industrial flue gases. The CO₂ and H₂O adsorption isotherms of the three carbon monoliths at 50 °C are presented in Figure 5. At a given pressure, all of the carbons adsorb a greater amount of H₂O_(v) than CO₂. Temperature limits the pressure range for water vapor adsorption due to condensation (see Figure 5b) given that the vapor pressure (p⁰) of water at 50 °C is 12.3 kPa. Differences in adsorption uptakes between the three monoliths are however more relevant for H₂O_(v).

Figure 5.

Equilibrium adsorption isotherms of (a) CO₂ and (b) H₂O_(v) at 50 °C on the honeycomb carbon monoliths 793, 932, and AM03.

Globally, the CO₂ adsorption isotherms belong to type I (IUPAC classification), representative of stronger adsorbate–adsorbent interactions. CO₂ uptakes are similar for the three monoliths in the lower-pressure range that corresponds to CO₂ postcombustion capture conditions (i.e., up to ∼40 kPa) and slightly differ at higher pressures. This is due to the similarities observed in the textural development of the three carbon monoliths in the narrow microporosity range where CO₂ adsorption is likely to occur by a micropore filling mechanism.

Likewise, water vapor adsorption on the carbon monoliths displays the typical type V topology (IUPAC classification). It is characterized by small uptakes at low pressures (absolute pressures below 4 kPa in Figure 5b) and a hysteresis loop that covers most of the pressure range. All of the carbon monoliths, 793, 932, and AM03, exhibit similar water vapor adsorption capacities at low pressures (∼3 kPa), wherein the amount of H₂O_(v) adsorbed on the carbon correlates with the number of oxygen groups present on the activated carbon surface. At higher pressures, from around 3.8 kPa for 793 and AM03 up to 4.0 kPa for 932, water–water interactions predominate and a sharp rise of the isotherm occurs due to the water cluster growth around primary adsorption centers and the micropore volume filling.⁴⁴ In the third region of the H₂O_(v) isotherm of the carbon monoliths, at pressures above 8.5 kPa (cf. Figure 5b), a wide micropore filling takes place. Significantly higher uptakes are attained at saturation for samples 793 and AM03 compared to 932.

The characteristics of the carbon material such as pore shape and connectivity and the surface chemistry affect the position, extension, and width of the water hysteresis loop.^45,46 Carbon monolith AM03, with a wider micropore size distribution, shows pronounced hysteresis because the water molecules adsorb in large clusters that then enter the micropore volume and finally desorb through uniform molecular evaporation.³²

The differences observed in the adsorption performance of the honeycomb carbon monoliths were analyzed in terms of the equilibrium separation factor, assuming simulated cement flue gas after desulphurization, at 50 °C and 101.3 kPa, with two compositions (vol %): 32% CO₂ and 4% H₂O_(v), that will be evaluated hereafter experimentally, and other composition with a higher water vapor content (10% H₂O_(v)) (see Table 8). Since the small pores are the preferred adsorption sites for the molecules of CO₂ and H₂O, both adsorbates show strong competition for the adsorption on these sites at such low partial pressures.⁴⁷

Table 8. H₂O/CO₂ Separation Factor for a Simulated Cement Flue Gas Previously Desulfurized (32% CO₂ and 4 and 10% H₂O) at 50 °C and 101.3 kPa.

	aSeparation factor
Sample	4% H2O	10% H2O
793	7	22
932	7	15
AM03	7	24

^a

There is a prevalence of H₂O adsorption over CO₂, as estimated by the separation factor, as defined in Table 8. However, the values in Table 8 are significantly lower than those previously reported in the literature for carbon monoliths, 34 and 89, under postcombustion capture conditions in a coal-fired power plant.²²

CO₂ Adsorption Measurements: Thermogravimetric Tests

CO₂ and H₂O Adsorption

Figure 6a,b shows TGA results using small pieces of honeycomb carbon monoliths and operating the adsorption step at 50 °C in 100% CO₂ flow. The three samples exhibited very fast adsorption in the first few minutes where the major CO₂ uptake takes place (ca. 1.7 mmol CO₂ g^–1 after 2 min that corresponds to approximately 86% of the equilibrium capacity). Then, the uptake continued to increase at a slower pace and reached a plateau within 6 min (see Figure 6a). The amount adsorbed at equilibrium represents the maximum adsorptive sample capacity. We have verified that the CO₂ mass uptake in this type of single-component gas adsorption measurements is in good concordance with the CO₂ adsorption capacities determined from the adsorption isotherms of CO₂ at 50 °C up to 101.3 kPa.^6,31 It is evidenced comparing the data reported in Figures 5a and 6b.

Figure 6.

CO₂, H₂O, and CO₂ + H₂O uptakes of the honeycomb carbon monoliths at 50 °C under (a, b) pure CO₂ flow; (c, d) 4.0 vol % H₂O_(v), N₂ balance; and (e, f) 4.0 vol % H₂O_(v), CO₂ balance. Plots on the left-hand side show the uptake evolution with time. Plots on the right-hand side show the maximum uptake at equilibrium.

Analyzing the textural characteristics of the carbon monoliths (Table 4) and the CO₂ adsorption capacities (Figure 6a,b), it follows that the differences in adsorption uptake between the carbon monoliths are in agreement with their microporosity developments.

The CO₂ adsorption capacities of the carbon monoliths evaluated in this study surpass the values reported in the literature for carbon monoliths at 50 °C and 100% CO₂ and even those achieved at more favorable conditions (25–35 °C, 100% CO₂).^{21,28,43,48,49} Among the three carbon monoliths, the maximum CO₂ adsorption capacity was observed for AM03 (2.04 mmol CO₂ g^–1) due to the greater textural development, as described above. Samples 793 and 932 reached capacities slightly below 2 mmol CO₂ g^–1 that are still significant. The CO₂ adsorption capacities follow the order: AM03 > 793 > 932.

To evaluate the effect of H₂O_(v) on the CO₂ capture performances of the carbon monoliths, two sets of binary adsorption experiments feeding water vapor to the system were conducted in the TGA at 50 °C and atmospheric pressure: (i) feeding 4.0 vol % H₂O_(v), N₂ balance, and (ii) feeding 4.0 vol % H₂O_(v), CO₂ balance. The H₂O_(v) uptakes during the binary N₂/H₂O_(v) adsorption experiments are summarized in Figure 6c,d, while the global uptakes during the binary CO₂/H₂O_(v) adsorption experiments are presented in Figure 6e,f.

As can be observed in Figure 6c, the H₂O profiles took longer times to attain the equilibrium capacity compared to the single-component CO₂ adsorption experiments. This difference in time is due to significantly slower kinetics of adsorption of H₂O that require approximately 25 min to reach the plateau characteristic of the equilibrium (H₂O uptake within ∼9 min reached 0.7–0.8 mmol g^–1, 87% of the maximum uptake). The amount of water adsorbed at equilibrium represents the maximum capacity of adsorption of the sample. We have verified that the H₂O mass uptakes during the binary N₂/H₂O adsorption experiments (Figure 6d) correspond to the H₂O adsorption capacities as determined from the adsorption isotherms of H₂O_(v) at 50°C and 4.0 kPa. Therefore, the adsorption of N₂ under these conditions is negligible.

In Figure 6d, it is observed that carbon monoliths 932 and AM03 displayed comparable H₂O profiles. Sample 932 reached a maximum uptake of approximately 1.0 mmol g^–1. Despite the similarities in the narrow microporosity of these samples, 793 showed a much lower H₂O adsorption capacity. The aforementioned surface oxygen functional groups content on each sample would account for the differences in water vapor uptake at low pressures.²⁰ Regarding the H₂O adsorption capacity, the adsorbents follow the order: 932 > AM03 > 793.

When a binary mixture of CO₂/H₂O fed the TGA, the combined CO₂ + H₂O (Figure 6f) capacity of the adsorbents increased for samples 932 and AM03 compared to the CO₂ uptake during the single-component experiments. The profiles show a steep uptake in the first few minutes, similar to the single-component experiments in pure CO₂, which indicate fast adsorption kinetics. Most of the maximum uptake (86%) is reached within ∼2 min, but the presence of water vapor seems to slow down the achievement of the plateau to 10 min (see Figure 6e). We have demonstrated in previous work that low-humidity conditions, like those studied in this work, do not alter the CO₂ capture performance of the adsorbents.⁵⁰ Additional shreds of evidence are presented in the Supporting Information. Thus, assuming that the slower adsorption kinetics of H₂O do not hinder the faster adsorption of CO₂ at the beginning of the experiment, the carbon monoliths may reach the equilibrium CO₂ uptakes at the evaluated conditions (50 °C and 97.3 kPa CO₂). These maximum CO₂ uptakes were obtained from the adsorption isotherms of CO₂ at 50 °C (see Figure 5a). Therefore, the excess uptake, once the plateau is reached, might be attributed to H₂O adsorption. Table 9 summarizes the CO₂ and H₂O adsorption capacities during the binary CO₂/H₂O adsorption experiments.

Table 9. CO₂ and H₂O Adsorption Capacities of the Carbon Monoliths Assessed from the Binary CO₂/H₂O Adsorption Experiments at 50 °C under 4.0 vol % H₂O_(v), CO₂ Balance.

Sample	CO2 adsorption capacity (mmol g–1)	H2O adsorption capacity (mmol g–1)
793	1.9	0.2
932	1.8	0.6
AM03	2.0	0.7

During the two sets of binary experiments, the H₂O_(v) concentration in the feed gas remained unchanged (4 vol % ), but it must be noted that the water vapor uptake significantly reduced in the presence of CO₂. In the binary CO₂/H₂O experiments, there is competitive adsorption between the two strong adsorbates. However, the faster kinetics of CO₂ alongside the surface oxygen functional groups content and microporosity development characteristic of each sample might limit the water vapor adsorption in the presence of CO₂. Given that the relative pressure of water vapor in the isotherms correlates to the relative humidity (RH), it is expected that the equilibrium water vapor uptake under the experiment conditions matches the theoretical 33% RH of the feed. However, the relative humidity corresponding to the calculated H₂O uptakes from the H₂O adsorption isotherms at 50 °C render values below the theoretical one: 8, 29, and 31% for 793, 932, and AM03, respectively. It would confirm that the adsorption of H₂O does not reach equilibrium in the presence of CO₂ under the evaluated conditions and the characteristics of sample 793 substantiate the effect. Consequently, in terms of CO₂ + H₂O adsorption capacity, the adsorbents follow the order: AM03 > 932 > 793. The H₂O adsorption capacity of each sample is the key factor defining the final combined uptake and relegates sample 793 to the last position (see Table 9).

CO₂ Adsorption under Flue Gas Conditions

The performance of carbon monoliths was evaluated at partial pressures relevant to flue gas emissions from the cement industry. Therefore, multicomponent adsorption experiments were carried out to evaluate the performance in a simulated flue gas stream (total flow rate of 104.2 cm³ min^–1) composed of 32 vol % CO₂, 4 vol % H₂O, and N₂ balance, at 50 °C and atmospheric pressure.

As can be deduced from Figure 7a, the profiles of the CO₂ + H₂O uptake (N₂ adsorption is considered negligible under these conditions, as confirmed in a previous study²²) for the carbon monoliths in the presence of 32 vol % CO₂ show similarities to those of the binary experiments in 96 vol % CO₂, although the amounts adsorbed in absolute terms significantly reduced given the lower CO₂ partial pressure. The total mass uptake (Figure 7b) was calculated following the criteria discussed for the CO₂/H₂O binary experiments. The excess with regard to the equilibrium CO₂ uptake under the evaluated conditions was attributed to H₂O adsorption. It has to be noticed that the relative contribution of the water uptake to the combined CO₂ + H₂O uptake under simulated flue gas conditions of the cement industry is more relevant than in the CO₂/H₂O binary experiments (see Figure 8a,b). For instance, the H₂O uptake for sample AM03 in binary experiments accounted for 27% of the total uptake, while this percentage increased to 36% in ternary experiments.

Figure 7.

CO₂ + H₂O uptakes of the honeycomb carbon monoliths under simulated cement flue gas conditions at 50 °C: (a) evolution of the uptake with time and (b) maximum uptake at equilibrium.

Figure 8.

Comparison of the experimental values of the CO₂ and H₂O uptakes at two CO₂ partial pressures (filled bars: 97.3 kPa CO₂ and 4.0 kPa H₂O; dotted bars: 32.1 kPa CO₂, 4.0 kPa H₂O, balanceN₂ balance).

Table 10 summarizes the isolated CO₂ and H₂O contributions determined from the multicomponent adsorption experiments in simulated flue gas. Compared to the binary experiments, the CO₂ uptake experienced a substantial reduction (see Figure 8a), in agreement with the reduced CO₂ partial pressure in the feed that decreases the driving force for CO₂ adsorption.²⁸ Thus, a stronger competition in adsorption between CO₂ and H₂O is observed (see Figure 8b) that in turn reduces the combined adsorption capacity below the values obtained in pure CO₂ and binary CO₂/H₂O adsorption experiments.

Table 10. CO₂ and H₂O Adsorption Capacities of the Carbon Monoliths Assessed from the Experiments in Simulated Cement-Industry Flue Gas (32 vol % CO₂, 4 vol % H₂O, andN₂ Balance, at 50 °C and Atmospheric Pressure).

Sample	CO2 adsorption capacity (mmol g–1)	H2O adsorption capacity (mmol g–1)	CO2/H2O ratio
793	1.0	0.1	10
932	0.9	0.4	2
AM03	0.9	0.5	2

Thus, in terms of CO₂ + H₂O adsorption capacity in the flue gas stream, the adsorbents follow the order: AM03 > 932 > 793. However, besides the combined uptake, it is important to highlight the ability of the adsorbents to selectively separate CO₂ from the other components in the flue gas. Under conditions relevant to cement-industry flue gas, sample 793 showed the highest CO₂ uptake in conjunction with the lowest H₂O uptake, which translates into the highest ratio CO₂/H₂O. Thus, sample 793 seems the best carbon monolith candidate for capturing CO₂ from cement-industry flue gas streams under the evaluated conditions.

Adsorption Kinetics

In porous adsorbents, mass or heat transfer resistances mostly control the overall rate of the adsorption/desorption process because physical adsorption at the active surface takes place very rapidly, and thus the intrinsic rate of sorption is not the rate-controlling step.⁵¹ High-capacity CO₂ adsorbents present extended narrow microporosity. Transport through these pores takes place principally by diffusion that could also control the process overall rate. The development of adsorption processes together with their proper design and optimization needs a comprehensive understanding of the intricacies of diffusion behavior in porous materials.

For practical applications, it is crucial to comprehend the dynamic behavior of the adsorption system.⁵² The adsorption kinetics analysis determines the residence time and the rate-controlling mechanism of the process. It is a requirement to define the fixed-bed performance or any other flow-through process. High capacity and slow kinetics of adsorption or the combination of low capacity and fast adsorption kinetics might not be suitable for the selected application.^53,54 Therefore, in any adsorption application, it is essential to establish the diffusional behavior and the macroscopic adsorption/desorption kinetics relationship through mathematical models. The adsorption data obtained during the thermogravimetric tests were fitted to the four models summarized in Table 11. The use of detailed mechanistic models in industrial-plant simulations is not appropriate due to their intrinsic computational load. More simplistic relations, such as those in Table 11, that can be readily solved are preferred.⁵² Thus, the four kinetic models may contribute to gaining more insights into the water vapor effects on the CO₂ adsorption kinetics on the carbon monoliths.

Table 11. Adsorption Kinetics Empirical Models.

Kinetic model	Equation	Ref.
Pseudo-first-order	qt = qe(1 – e–kft)	(6)
Avrami	qt = qe(1 – e(−(kAt)nA))	(6)
Fractional-order		(55)
Exponential decay-2	qt = qe + a1 e–t/b1 + a2 e–t/b2	(13)

Table 11 lists the equations associated with these kinetic models, where t is the time elapsed from the beginning of the adsorption stage, q_t (mmol g^–1) is the amount adsorbed at a given time, q_e (mmol g^–1) represents the amount adsorbed at equilibrium, k_f (min^–1) is the pseudo-first-order rate constant, k_A (min^–1) and n_A are the Avrami kinetic constant and exponent, respectively, k_n (min^–1) is the fractional-order kinetic constant, n and m are the fractional-order model constants, and a₁ (mmol g^–1), a₂ (mmol g^–1), b₁ (min), and b₂ (min) are fitting parameters.

Based on the standard deviation to quantify the measured data and the predictions discrepancy from the model, the sum of squared errors (SSE) and the coefficient of determination (R²) were estimated. And the equations are shown in Table 12, where q_t,exp and q_t,pred are the experimentally measured and model-predicted adsorption capacities, respectively; N is the number of experimental data points for each sample; and p is the number of parameters of the model.

Table 12. Goodness of Fitting of the Kinetic Models.

Sum of squared errors (SSE)		(6)
Coefficient of determination (R2)		(6)

Hereafter, the fittings of the honeycomb monolith 793 data will be shown in the figures for illustrative purposes.

Adsorption Rate

First, the kinetics of CO₂ adsorption in pure CO₂ atmosphere were evaluated by the pseudo-first-order, Avrami, and fractional-order models (see Figure 9). Carbon monoliths show two-stage adsorption that corresponds to mass transfer resistance^56,57 and to proper surface adsorption, which is generally very quick.^57,58 It can be seen that the pseudo-first-order model does not suitably fit the experimental data. It underestimates the CO₂ uptakes at the initial stages of the adsorption step but overestimates the uptakes when approaching the maximum capacity (equilibrium). This model better suits adsorption processes controlled by surface diffusion.

Figure 9.

Fittings for the adsorption of pure CO₂ at 50 °C on carbon monolith 793 (open symbols, experimental data; solid lines, pseudo-first-order model; dashed lines, Avrami’s model; and dotted lines, fractional-order model).

Avrami and fractional-order models better describe the experimental data over the entire adsorption step, indicating that CO₂ adsorption on carbon monoliths is a complex multipath process.^59,60 On the one hand, Avrami’s model has described the kinetics of crystallization, and it accounts for the random nucleation and subsequent growth, whereas the fractional-order model can explain different adsorption pathways, including surface and intraparticle diffusion, and interaction with active sites on the adsorbent surface (physical and chemical). Thus, the parameter k_n lumps adsorption-related factors in an overall parameter.^61,62

The kinetic parameters values determined for the three models, the corresponding correlation coefficients (R²), and the associated sum of squared errors (SSE (%)) are presented in Table 13.

Table 13. Values of the Kinetic Model Parameters for the Adsorption Experiments in Pure CO₂ at 50 °C and Atmospheric Pressure.

	Pseudo-first-order			Avrami				Fractional-order
Sample	kf (min–1)	SSE (%)	R2	kA (min–1)	nA	SSE (%)	R2	kn (min–1)	n	m	SSE (%)	R2
793	1.36	0.05	0.966	1.51	0.71	0.01	0.998	1.36	2.65	1.30	0.03	0.989
932	0.91	0.02	0.995	0.93	0.93	0.02	0.996	0.81	2.84	1.62	0.04	0.981
AM03	1.26	0.06	0.964	1.39	0.70	0.01	0.998	1.20	2.58	1.28	0.03	0.990

The CO₂ adsorption approximates the crystal nucleation and growth, which begins from a point and then extends to the surroundings. The values of Avrami’s exponent (n_A), as can be seen from Table 13, are around 2/3 for samples 793 and AM03, and around 1 for sample 932. These reaction orders respond to the different performances observed for 932 in the first minutes of adsorption (see Figure 6a). The fractional-order model parameter n reflects the strong effect of the adsorption driving force (values larger than 2). Besides, m refers to diffusion resistance, attaining a higher value for 932 that suggests slightly fast adsorption for this carbon monolith.

Among the two models, Avrami provides the best description of the CO₂ adsorption behavior on the honeycomb carbon monoliths, according to the values of R² and SSE. This is in accordance with other studies on the CO₂ adsorption kinetics on biomass-based activated carbons.^6,63

The adsorption of water vapor on carbon monoliths has inherent complexity. It entails the water molecules and clusters diffusion in the micropore network. This diffusion occurs into those micropores that present a width smaller than the free path of the gas molecules. The kinetics of H₂O adsorption have been evaluated with the pseudo-first-order model alongside the exponential decay-2 model. The latter have proved feasible when other kinetic models failed to represent the water vapor adsorption kinetics along the whole adsorption step.¹³ The fittings of the experimental data of sample 793 by the two models are shown in Figure 10. The exponential decay-2 model fits the adsorption data of the complete experiment and displays a correlation coefficient higher than the pseudo-first-order model. Conversely, the pseudo-first-order model again underestimates or overestimates the H₂O uptake depending on the time interval.

Figure 10.

Fittings for the H₂O adsorption at 50 °C on the carbon monolith 793 when feeding a binary mixture of N₂/H₂O (open symbols, experimental data; solid lines, pseudo-first-order model; and red dashed lines exponential decay-2 model).

The kinetic parameters values calculated for the two models, the corresponding correlation coefficients (R²), and the sum of squared errors (SSE (%)) are presented in Table 14. Overall, the exponential decay-2 model gives better fitting with values of the correlation coefficient close to 1 and significantly lower values of SSE.

Table 14. Values of the Kinetic Model Parameters for the Adsorption Experiments in 4 vol % H₂O and Balance N₂ at 50 °C and Atmospheric Pressure.

	Pseudo-first-order			Exponential decay-2
Sample	kf (min–1)	SSE (%)	R2	a1 (mmol g–1)	a2 (mmol g–1)	1/b1 (min–1)	1/b2 (min–1)	SSE (%)	R2
793	0.27	0.02	0.985	–0.48	–0.32	0.51	0.14	0.003	0.999
932	0.23	0.03	0.985	–0.64	–0.41	0.42	0.12	0.007	0.999
AM03	0.27	0.03	0.977	–0.57	–0.40	0.53	0.14	0.003	1.000

Water vapor adsorbs rapidly from the outset of the adsorption step, but the adsorption rate decreases with time because of the continuous reduction in the driving force⁶⁴ as illustrated, for instance, in the exponential decay-2 model with the kinetic parameters 1/b₁ and 1/b₂. The empirical decay-2 model has four-fitting parameters that increase the chances of a better fit of the water vapor adsorption data on the carbon monoliths compared to the single-parameter pseudo-first-order model.¹³

Comparing the adsorption rate profiles of CO₂ and H₂O in Figures 9 and 10, it turns apparent that the adsorption of CO₂ proceeds faster even though H₂O is the strongest adsorbate. Thus, it is of utmost interest to elucidate the kinetic performance of both adsorbates when mixed in a gas stream.

The dynamic behavior during multicomponent adsorption was split into the CO₂ and H₂O contributions, to gain an insight into the performance of adsorbents in the presence of humid CO₂ streams. To do so, the Avrami and exponential decay-2 model parameters obtained for the individual adsorption of CO₂ and H₂O and the corresponding uptakes at each partial pressure were used. It has to be borne in mind that Avrami’s kinetic constant k_A, expressed in min^–1, is not related to the initial concentration of the adsorbate and H₂O exponential decay-2 model parameters depend on the relative humidity (RH).^13,60,65Figure 11 shows the q_t vs t plots for the monolith 793 during multicomponent adsorption at two concentrations of CO₂ in the feed (32 and 96 vol %) and the corresponding predictions of the monocomponent Avrami and exponential decay-2 models. Even though the water concentration in the feed gas kept constant (∼4 vol %) during both multicomponent adsorption experiments, the presence of CO₂ hindered the uptake of H₂O_(v).

Figure 11.

CO₂ and H₂O contributions to the adsorption kinetics in 4 vol % H₂O and 32 or 96 vol % CO₂ at 50 °C for the carbon monolith 793 (open symbols, experimental data for the total uptake (CO₂ + H₂O); dashed blue lines, Avrami’s model predictions for CO₂; and dashed red lines, exponential decay-2 model predictions for H₂O).

As shown in Figure 11, the evolution of the CO₂ + H₂O uptakes in the presence of 32 and 96 vol % CO₂ exhibits two-stage adsorption associated with mass transfer resistances and proper surface adsorption. Adsorption proceeds rapidly at the beginning of the experiment and then slows down with the decreasing of the driving force.⁶⁴ As expected, the uptake is smaller at the lower CO₂ partial pressure in the feed. The prevalence of CO₂ adsorption with regard to H₂O_(v) co-adsorption is highlighted in the individual contributions estimated with the models, wherein H₂O adsorption takes longer times (up to 7.67 min in the experiment with a 32 vol % CO₂) to initiate compared to CO₂ adsorption, which occurs instantaneously. The analysis of the CO₂ + H₂O uptake has then considered two scenarios: (1) both CO₂ and H₂O contribute to the overall kinetics and (2) the CO₂ uptake controls the overall kinetics. The former implies the addition of the CO₂ and H₂O estimated uptakes (see Figure 11), while the latter assumes that the overall kinetics relies on the CO₂-Avrami model parameters. The values of the experimental uptake considered in the calculations and the associated sum of squared errors (SSE (%)) are listed in Table 15. Figure 12 shows the q_t vs t plots for the monolith 793 at two concentrations of CO₂ in the feed (32 and 96 vol %) for the two scenarios under analysis.

Table 15. Values of the Kinetic Model Parameters for the Adsorption Experiments in 4 vol % H₂O and at Two CO₂ Partial Pressures at 50 °C.

		CO2 and H2O addition			CO2 control
CO2 (vol %)	Sample	qCO2 (mmol g–1)	qH2O (mmol g–1)	SSE (%)	qt (mmol g–1)	SSE (%)
32	793	1.0	0.1	0.14	1.1	0.03
	932	0.9	0.4	0.21	1.3	0.04
	AM03	0.9	0.5	0.16	1.4	0.05
96	793	1.9	0.2	0.15	2.1	0.04
	932	1.8	0.6	0.20	2.4	0.07
	AM03	2.0	0.7	0.13	2.7	0.07

Figure 12.

CO₂ + H₂O adsorption kinetics analysis for the carbon monolith 793 in 4 vol % H₂O and 32 or 96 vol % CO₂ at 50 °C (open symbols, experimental data; dashed blue lines, CO₂ kinetics control; and dashed purple lines, CO₂ and H₂O summed contributions).

It can be observed that the first scenario (CO₂ and H₂O summed contributions) shows limitations to fit the CO₂ + H₂O uptake data during the first half of the experiment in which the adsorption of CO₂ prevails over H₂O. On the other hand, when considering the CO₂ control of the kinetics, the goodness of the fitting significantly enhances as evidenced in Table 15 with the lowest values of SSE (maximum of 0.05 and 0.07% for the experiments feeding 32 and 96 vol % CO₂, respectively).

As we can infer from Table 15, the goodness of the fittings is consistent for both scenarios with the lowest error values attained for the experiments at the lower CO₂ concentration. The CO₂ control scenario better describes the overall kinetics and sample 793 shows the best fittings.

Hence, it can be concluded that the overall adsorption kinetics of humid CO₂ streams on the carbon monoliths are mainly controlled by the adsorption of CO₂.

Adsorption Mechanism

Mass transfer phenomena impair adsorbate adsorption rate onto porous materials. Kinetic models do not often distinguish the adsorption mechanism, so it is important to explore models that account for the diffusion mechanism involved during the adsorption process and determine the rate-limiting step. Usually, film diffusion, intraparticle diffusion, or both, are the controlling steps of the adsorption rate.^28,63 Intraparticle diffusion is related to pore volume diffusion (i.e., diffusion takes place in the pores filled with fluid) and surface diffusion (migration through the pore surface, i.e., an adsorbate moves from one available adsorption site to another in various reactions of adsorption and desorption), or both can occur simultaneously.^66,67

For this purpose, the intraparticle diffusion model sounded on the theory proposed by Weber and Morris was selected to fit the experimental data. This single-resistance model details the process that takes place in the internal pores of the solid. It assumes that intraparticle diffusion is the sole rate-limiting step. The expression in Table 16 derives from Fick’s second law considering the intraparticle diffusivity constant and a small uptake of adsorbate by the adsorbent compared to the concentration in the bulk of the fluid.^68,69

Table 16. Intraparticle Diffusion Model Proposed by Weber and Morris.

Kinetic model	Equation
Intraparticle diffusion	qt = ki,dt1/2 + C	(68)

Table 16 shows the equation associated with this model, where t (min) is the time elapsed from the starting of the adsorption process, q_t (mmol g^–1) is the amount adsorbed at a given time, k_i,d (mmol g^–1 min^–1/2) is the intraparticle diffusion rate constant, and C (mmol g^–1) refers to the boundary layer thickness.

Despite the appearing easiness, the model implementation is not always straightforward to interpret. It is a consequence of the multilinearity of the plots (q_t vs t^1/2), which indicates that more than one stage takes place in the adsorption process. The first linear region corresponds to boundary layer diffusion or external diffusion, the second region is related to the intraparticle diffusion, and the third region is ascribed to the final equilibrium stage. The uncertainty in determining the linear segments translates to the calculation of the slopes and intercepts and, consequently, leads to a loss of accuracy in the estimation of the diffusion coefficients. Besides, valuable information would be lost if the elapsed time from film to intraparticle diffusion, and the transitions that occur between successive intraparticle diffusion regimes were not properly identified.

For this reason, we have used a statistical method called piecewise linear regression (PLR), previously reported by Malash et al.,⁵² to establish the start and end of each linear segment and to identify the number of linear segments. It avoids subjective decisions and the associated errors.

If intraparticle diffusion is the only rate-limiting step, the plot should afford a straight line that passes through the origin; meanwhile, in our study, we have identified three main regions in the CO₂ and H₂O uptake plots (see Figure 13). These curve-shaped plots account for the following mechanism: the adsorption process starts with the diffusion of the adsorbate (CO₂ or H₂O) across the bulk gas/vapor phase to the outer surface of the carbon monoliths along with, in the case of H₂O, the formation of water vapor clusters around oxygen surface functionalities present on the carbon surfaces. This first segment correlates with the boundary layer diffusion of the adsorbate (CO₂ or H₂O). The second corresponds to the gradual CO₂ or H₂O adsorption due to intraparticle diffusion toward inner sites (i.e., micropores), where intraparticle diffusion is the rate-limiting step. The last one is assigned to the final equilibrium stage wherein intraparticle diffusion starts to slow down due to saturation of active sites.^70,71

Figure 13.

Fittings of the intraparticle diffusion model to the single adsorption of CO₂ and H₂O on carbon monolith 793.

As expected, the CO₂ and H₂O adsorption kinetics on the carbon monoliths depicted completely different plots for both adsorbates and the steepest curves correspond to CO₂.⁶ In Figure 13, it is observed that the linear fittings of the second and third stages do not pass through the origin and this divergence might be because of the difference in the mass transfer rate between the initial and final adsorption stages as indicated by other authors.^54,72 Therefore, intraparticle diffusion is not the single rate-limiting mechanism in the adsorption process and film diffusion likewise contributes to the CO₂ and H₂O adsorption kinetics on the honeycomb carbon monoliths.^28,73

The values of the intraparticle diffusion model parameters, the corresponding correlation coefficients (R²), and the associated sum of squared errors (SSE (%)) are listed in Table 17. These parameters were determined from the fittings of the model to the linear intervals of the uptake profiles identified with the PLR method.

Table 17. Intraparticle Diffusion Model Parameters from the Fittings of the Single CO₂ and H₂O_(v) Adsorption on the Carbon Monoliths^a.

	Sample	Intraparticle diffusion model parameters
		ki,1	ki,2	C2	ki,3	C3	SSE (%)	R2
CO2	793	1.94	0.61	0.83	0.03	1.85	0.02	0.992
	932	1.29	0.43	1.03	0.03	1.80	0.01	0.998
	AM03	2.03	0.61	0.87	0.04	1.91	0.02	0.997
H2O	793	0.34	0.12	0.32	0.03	0.64	0.01	0.998
	932	0.41	0.16	0.37	0.04	0.78	0.01	0.997
	AM03	0.39	0.15	0.40	0.03	0.78	0.01	0.997

^ak_i,d in mmol g^–1 min^–1/2; C in mmol g^–1.

Analyzing the parameters of the first and second linear regions, the intraparticle diffusion rate constant values of the second linear region k_i.2 are inferior for both adsorbates and all of the carbon monoliths.^63,70 Thus, the diffusion of the adsorbate from the outer surface of the carbon monoliths into the micropores governs the rate of the adsorption.

Extrapolation of the linear fittings back to the y-axis gives the intercepts (C), which account for the boundary layer thickness, i.e., the larger the intercept, the greater the boundary layer effect on retarding intraparticle diffusion.^74,75

Attending to the fittings of CO₂, the samples with the larger surface areas, 793 and AM03, exhibited higher overall external mass transfer k_i,1 and pore diffusion k_i,2 rates. Slower diffusion may be ascribed to oxygen functional groups concentrated at the entrance of the pores that hinder the diffusion of CO₂ into the pores.⁶⁷ As expected, the lower external mass transfer rate is a consequence of a wider boundary layer (i.e., sample 932).

As can be seen in Table 17, the diffusion rates for H₂O_(v) are lower due to the reduced water vapor partial pressure in the feed compared to the experiments in pure CO₂ streams. For H₂O diffusion, the external mass transfer is also influenced by cluster formation related to the oxygen functional groups content on the surface of the carbon monoliths; this phenomenon allows us to stabilize H₂O_(v) inside the pores and attain faster intraparticle diffusion.^20,76

An adequate description of intraparticle diffusion of multicomponent mixtures results critical in the simulation and design of PSA processes.^43,77 Nevertheless, the individual contribution of each species in a mixture may vary substantially from the single-component behavior.⁷⁸ For this reason, CO₂ + H₂O intraparticle diffusion parameters have been estimated considering that the overall diffusion is a sum of the CO₂ and H₂O contributions. Thus, intraparticle diffusion parameters were calculated for each adsorbate separately. The values of the CO₂ and H₂O intraparticle diffusion parameters and the associated sum of squared errors (SSE (%)) are listed in Table 18 and Table 19, respectively.

Table 18. CO₂ Intraparticle Diffusion Model Parameters for the Adsorption Experiments in 4 vol % H₂O and at Two CO₂ Partial Pressures on the Carbon Monoliths^a.

		Intraparticle diffusion model parameters
CO2 (vol %)	Sample	ki,1	ki,2	C2	ki,3	C3	SSE (%)	R2
32	793	1.08	0.17	0.59	0.01	0.94	0.012	0.995
	932	0.97	0.16	0.52	0.01	0.85	0.008	1.000
	AM03	0.80	0.11	0.56	0.01	0.81	0.014	0.999
96	793	2.05	0.36	1.14	0.02	1.84	0.016	0.996
	932	1.87	0.31	1.10	0.03	1.70	0.014	0.999
	AM03	1.60	0.28	1.27	0.03	1.84	0.017	0.999

^ak_i,d in mmol g^–1 min^–1/2; C in mmol g^–1.

Table 19. H₂O Intraparticle Diffusion Model Parameters for the Adsorption Experiments in 4 vol % H₂O and at Two CO₂ Partial Pressures on the Carbon Monoliths^a.

		Intraparticle diffusion model parameters
CO2 (vol %)	Sample	ki,1	ki,2	C2	ki,3	C3	SSE (%)	R2
32	793	0.12	0.02	0.06	1.35 × 10–3	0.10	0.001	1.000
	932	0.41	0.16	0.52	5.91 × 10–3	0.01	0.004	1.000
	AM03	0.44	0.06	0.31	7.66 × 10–3	0.45	0.008	1.000
96	793	0.19	0.05	0.08	2.41 × 10–3	0.17	0.002	1.000
	932	0.64	0.11	0.35	8.99 × 10–3	0.56	0.005	1.000
	AM03	0.58	0.10	0.47	9.23 × 10–3	0.67	0.006	1.000

^ak_i,d in mmol g^–1 min^–1/2; C in mmol g^–1.

Among the linear intervals attributed to the first and second regions, where adsorption is kinetically driven, it can be observed that at any CO₂ partial pressure, the intraparticle diffusion rate constant k_i,2 is again inferior.^63,70 This means that joint CO₂ and H₂O diffusion through the microporosity of the carbon monoliths is the rate-controlling step.

The CO₂k_i,1 and k_i,2 values increased with the CO₂ partial pressure in the feed that enhances the driving force of the CO₂ to move from the bulk onto the surface and then into the porosity of the carbon monolith.^79,80 With regard to the water vapor effect on the CO₂ diffusion, the lower values of CO₂k_i,2 compared to those of pure CO₂ (see Table 17) indicate that the presence of water vapor hinders to some extent the transport of CO₂ through the narrow microporosity.⁷⁸ It is important to highlight that at the two CO₂ concentrations, the trends are similar for the three carbon monoliths: carbon monolith 793 shows the highest intraparticle diffusion rate, while AM03 seems the most affected by the presence of humidity.

This scenario also leads to significantly lower H₂O k_i,2 values compared to the pure component (see Table 17) for a similar concentration of water vapor in the feed (4 vol %), demonstrating the predominant role of CO₂ diffusion in the intraparticle diffusion stage at the two CO₂ partial pressures considered. This is particularly remarkable for the carbon monolith 793 and highlights its suitability for capturing CO₂ at the evaluated conditions, representative of cement flue gas.

Conclusions

The potential of three honeycomb carbon monoliths for their application to humid postcombustion CO₂ capture from cement-industry flue gases has been explored. Adsorption experiments were conducted to assess the adsorption equilibrium and the kinetics of CO₂ and H₂O on the selected carbon adsorbents, under different scenarios representative of postcombustion capture (50 °C and two CO₂ partial pressures).

The narrow microporosity present on the carbon monoliths allows us to selectively adsorb CO₂ at partial pressures representative of cement flue gas. From the three carbon monoliths, AM03 showed a more developed micropore network that translated into the highest adsorption capacity of pure CO₂ and H₂O.

From the point of view of the kinetics study, the three carbon monoliths present fast adsorption of CO₂ from a CO₂/H₂O stream. The dynamic adsorption of single CO₂ and H₂O can be adequately described by the Avrami’s and the exponential decay-2 models, respectively. When a flue gas with 4 vol % H₂O_(v) is considered, overall adsorption kinetics are, however, governed by CO₂. The fittings of the experimental data to the intraparticle diffusion model revealed that gradual CO₂ and H₂O diffusion toward the inner sites (i.e., micropores) was the rate-limiting step. Regarding the effect of water vapor on CO₂ diffusion, it is important to highlight that at the two CO₂ concentrations evaluated, the trends were similar for the three carbon monoliths. Carbon monolith 793 showed the highest intraparticle diffusion rate while AM03 seemed the most affected by the presence of humidity.

Under the flue gas conditions evaluated, there exists competitive CO₂ and H₂O adsorption; however, in the case of carbon monolith 793, due to its intrinsic characteristics, the adsorption of CO₂ is little affected (thermodynamically and kinetically) by H₂O. Therefore, it is a suitable carbon monolith for capturing CO₂ from cement-industry flue gas streams under the evaluated conditions (∼1 mmol CO₂ g^–1 of adsorption capacity and favorable kinetics in 32 vol % CO₂ and 4 vol % H₂O_(v), at 50 °C and 101.3 kPa).

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acssuschemeng.1c07213.

• CO₂ and H₂O TPD profiles; desorption profiles of CO₂ (m/z 44), H₂O (m/z 18), and N₂ (m/z 28); total mass uptake vs time (desorption step) for multicomponent adsorption; and CO₂m/z signal normalized (PDF)

The authors declare no competing financial interest.