Phenol-Formaldehyde Resin-Based Carbons for CO₂ Separation at Sub-Atmospheric Pressures

Abstract

The challenge of developing effective separation and purification technologies that leave much smaller energy footprints is greater for carbon dioxide (CO₂) than for other gases. In addition to its involvement in climate change, CO₂ is present as an impurity in biogas and bio-hydrogen (biological production by dark fermentation), in post-combustion processes (flue gas, CO₂-N₂) and many other gas streams. Selected phenol-formaldehyde resin-based activated carbons prepared in our laboratory have been evaluated under static conditions (adsorption isotherms) as potential adsorbents for CO₂ separation at sub-atmospheric pressures, i.e., in post-combustion processes or from biogas and bio-hydrogen streams. CO₂, H₂, N₂, and CH₄ adsorption isotherms at 25 °C and up to 100 kPa were obtained using a volumetric equipment and were correlated by applying the Sips model. Adsorption equilibrium was then predicted for multicomponent gas mixtures by extending the multicomponent Sips model and the Ideal Adsorbed Solution Theory (IAST) in conjunction with the Sips model. The CO₂ uptakes of the resin-derived carbons from CO₂-CH₄, CO₂-H₂, and CO₂-N₂ at atmospheric pressure were greater than those of the reference commercial carbon (Calgon BPL). The performance of the resin-derived carbons in terms of equilibrium of adsorption seems therefore relevant to CO₂ separation in post-combustion (flue gas, CO₂-N₂) and in hydrogen fermentation (CO₂-H₂, CO₂-CH₄).

1. Introduction

The sustainable production of energy is currently a topic of extensive research with the aim of producing low carbon footprint processes and mitigating the CO₂ impact [1]. As a sustainable and clean energy source with minimal or zero use of hydrocarbons, hydrogen is a promising alternative to fossil fuels [2]. Hydrogen can be generated by thermochemical, electrochemical or microbial fermentation processes. Biological methods are preferable to chemical methods because they offer the possibility of using sunlight, CO₂ and organic wastes as substrates for environmentally benign conversions under moderate conditions [3]. The biological methods for generating H₂ include light-dependent methods, such as direct and indirect biophotolysis and photo fermentation; and methods not dependent on light, such as the dark fermentation process and bioelectrochemical systems (BES). Hydrogen production through dark fermentation has advantages over the other processes because it does not require the input of external energy and it offers the possibility of rapid scalability owing to its similarity to the well-known anaerobic digestion process [4]. In addition, bio-hydrogen production from anaerobic fermentation is linked to bio-methane generation since the process develops in two main stages. In the first stage acidogenic bacteria break down substrates into primarily H₂, acetic acid, and CO₂, and in the second stage methanogenic bacteria convert acetic acid, H₂, and CO₂ to methane gas. The two reactions can be separated, at least partially, in distinct bioreactors placed in series. Both streams must be further purified to obtain bio-hydrogen and bio-methane with a high calorific value, appropriate for industrial applications [5]. Concentrations of H₂ of up to 30–70 vol% on average and of up to 45–80 vol% in the case of CH₄ on average can be achieved but the presence of CO₂ in both streams (20–70 vol%) is a nuisance and needs to be removed for further utilization of H₂ and CH₄ [6].

On the other hand, conventional energy production from fossil fuels is one of the main sources of anthropogenic CO₂. The separation of CO₂ from flue gas (post-combustion CO₂ capture), is very challenging given that it is at near atmospheric pressure and CO₂ only represents between 4 to 15 vol%, depending on the fuel used, and if dry or wet basis conditions are considered. However, the conditions required for CO₂ transport, storage or subsequent use as a chemical make a concentration step necessary to reach the set target of ca. 95 vol%.

Different technologies have been evaluated to separate CO₂ under sub-atmospheric pressure and particular emphasis has been paid in recent years to post-combustion CO₂ capture due to increasing concerns about global warming and climate change. Adsorption with low temperature solid sorbents has the potential to reduce the energy penalty associated with the separation of CO₂ at sub-atmospheric pressures, not only under post-combustion capture conditions (CO₂/N₂ separation) but also for bio-hydrogen (CO₂/H₂ separation) and bio-methane production (CO₂/CH₄ separation) [7,8]. However, the success of these approaches depends on the development of adsorbents with a high selectivity, sufficient adsorption capacity and easy regeneration. Carbon adsorbents fulfil all these requirements: they have a significant adsorption capacity at atmospheric pressure and the necessary characteristics for the separation of CO₂ at sub-atmospheric pressures including hydrophobicity, low cost and low intensity in terms of the amount of energy required for regeneration.

The distinction between activated or porous carbons and carbon molecular sieves has not been clearly defined. Whereas most of the pores in carbon molecular sieves are in the molecular size range, activated carbons may also have very small pores. The main difference is that activated carbons separate molecules through differences in their adsorption equilibrium whereas carbon molecular sieves provide molecular separations based on rate of adsorption, allowing the separation of molecules on the basis of their size, rather than on the differences in adsorption capacity [9,10].

The use of polymeric precursors to produce activated carbons allows the incorporation of custom tailored features (e.g., pore size, conformation, etc.) along with other material properties to meet the required specifications. Phenol-formaldehyde resin-derived microporous activated carbons have been previously studied in our laboratory [6,11,12]. They can be produced in a wide variety of physical forms, at a low cost and with a close control of porosity. More importantly, all these features are accompanied by a very low level of impurities and good physical strength, key parameter in the design of an adsorption process [13,14].

In this work, the performance of phenol-formaldehyde resin-based activated carbons prepared in our laboratory to separate CO₂ at sub-atmospheric pressures has been evaluated in a fundamental study of the equilibrium of adsorption of CO₂, N₂, H₂ and CH₄. A preliminary CO₂ uptake screening test has been carried out to discard the samples with less than 2 mol·kg⁻¹ of CO₂ adsorbed at atmospheric pressure. Adsorption models are very useful as they can predict the behaviour of the equilibrium of adsorption over a wide range of temperatures and pressures. In order to predict multicomponent adsorption from binary CO₂-CH₄, CO₂-H₂, and CO₂-N₂ mixtures, the extended multicomponent Sips equation and the Ideal Adsorbed Solution Theory (IAST) in conjunction with the Sips model have been used and the results have been compared. Both equations deliver different conclusions regarding the heterogeneity of the adsorbate-adsorbent system. Additionally, a commercial activated carbon (Calgon BPL) was evaluated under the same operating conditions as a reference carbon adsorbent.

2. Materials and Method

Porous carbons can be prepared from a wide range of carbon-containing materials including coal, lignin, wood, peat and synthetic and natural polymers. Carbonisation and activation of these materials under appropriate conditions yield carbons with a rather uniform pore structure consisting of micropores whose size is similar to that of the adsorbed molecules. For instance, low-density materials can be prepared by carbonisation of polymeric compounds pretreated by various procedures, including modification with inorganic additives [15]. In particular, carbon sorbents with exactly the prescribed structure have been prepared using NaCl [16] and silicon [17] additives.

2.1. Synthesis of Carbon Precursors

Phenol-formaldehyde (PF) resins were used in this work to produce carbon-based microporous materials. Synthesis was conducted following two different routes, acid (hydrochloric acid, 37 wt% HCl solution) and basic (sodium hydroxide, NaOH) catalysis for the Novolac and the Resol resins, respectively. Details on the synthesis of the PF resins can be found elsewhere [18]. Carbon precursors were prepared from the aforementioned resins, and potassium chloride (KCl) was incorporated as inorganic additive. One set of materials was impregnated with a saturated KCl solution at ambient temperature (set a) while another was boiled in a saturated KCl solution (set b). Another carbon precursor was prepared by mixing PF resin with an agricultural by-product, olive stones (OS), at a proportion of 20:80 wt% of PF to OS. A curing agent, hexamethylenetetramine (hexa) was added to PF at a hexa ratio of 7:2 wt%.

Table 1. Departing materials and conditions for the production of PF resin-derived carbon precursors.

Precursor	Type of PF Resin	F/P *	Curing (Tmax, °C)	Additive Incorporation	K/R **
ReKCla	Basic catalysis (Re)	2.5:1	80	Ambient KCl	1.7
ReKClb	Basic catalysis (Re)	2.5:1	80	Boiling KCl	1.9
No1KCla	Acid catalysis (No1)	1:1.2	100	Ambient KCl	2.1
No1KClb	Acid catalysis (No1)	1:1.2	100	Boiling KCl	1.7
No2OS	Acid catalysis (No2)	1:1	170	OS (20:80) and hexa (7:2)	—

* F/P: formaldehyde to phenol molar ratio; ** K/R: potassium chloride to resin weight ratio.

summarizes the materials and conditions for the production of the PF resin-derived carbon precursors.

2.2. Production of Microporous Carbons

The prepared carbon precursors were first carbonised and then activated with CO₂ to develop their microporous structure, preferably in the narrow microporosity domain (pore sizes of less than 1 nm) since CO₂ adsorption at sub-atmospheric pressures is known to focus on the narrow micropores [15,19,20].

Carbonisation was conducted in a tubular furnace under an inert atmosphere (50 mL·min⁻¹ of N₂). Two different temperature programs were selected for PF-KCl; the two precursors of set a were subjected to a one-step carbonisation procedure at 600 °C for 1.5 h while for set b, a three-step slow carbonisation treatment at 200 (1 h), 600 (0.5 h) and 1000 °C (0.5 h) was carried out. The PF-OS composite was carbonised at 1000 °C (0.2 h) by slowly heating from ambient temperature at 4 °C·min^‒1.

Activation with carbon dioxide favours the development of microporosity [21]. The largest increase in porosity is produced in the early stages of the activation process. Burn off (i.e., degree of activation) increases the widening of existing micropores but external burning of the particle outweighs the creation of new porosity, resulting in a net destruction of porosity, especially above 40%–50% burn off [22]. Control of the activation parameters (temperature and burn off degree) is crucial for tailoring the micropore size distribution. Previous works carried out in our research group have demonstrated the relationship between the volume of narrow micropores of less than 0.7 nm and CO₂ uptake at atmospheric pressure [20]. Response surface methodology was performed to obtain the optimum conditions of activation with CO₂ that maximise CO₂ adsorption at atmospheric pressure for each precursor (details can be found in [18]). Activation with CO₂ was conducted in a tubular furnace with a CO₂ flowrate of 10 mL·min⁻¹.

Table 2. Conditions of carbonisation and activation with CO₂ for each precursor.

Activated Material	Precursor	Carbonisation		Activation
		Temp. (°C)	Yield (%) *	Temp. (°C)	Burn off (%) **
RKa-A71	ReKCla	600	40	694	10
RKb-A75	ReKClb	1000	39	722	50
NKa-A82	No1KCla	600	37	810	22
NKb-A82	No1KClb	1000	40	800	20
NOS-A94	No2OS	1000	32	940	38

* Char yield has been estimated as yield (%) = (m_c/m_i) × 100, where m_c is the mass of char produced and m_i is the mass of raw precursor; ** Burn off or degree of activation is estimated as burn off (%) = (m_c − m_a) × 100/m_c, where m_c is the mass of char and m_a is the mass of activated sample produced.

summarises the conditions of the carbonisation and activation with CO₂ steps. Yields of char production during carbonisation were around 40% for PF-KCl precursors independently of the carbonisation temperature selected or type of PF resin (acid, No, or basic, Re), and slightly lower for PF-OS due to the high volatile matter content of the biomass: olive stones. Higher activation temperatures were required for the No1KCl than for the ReKCl precursors and even higher ones for No2OS. The burn off degrees ranged between 10 and 50%, the two limits of the experimental region tested, for the ReKCl precursors while intermediate values were found to be optimal for the No1KCl and No2OS precursors. It should be noted that for precursors No1KClb and No2OS the burn off was not statistically significant, according to the response surface methodology. Consequently, the lowest burn off to yield the highest experimental CO₂ uptake was selected. For the sense of clarity and simplicity the activated samples will be denoted hereafter as follows: RKa-A71 (ReKCla activated carbon), RKb-A75 (ReKClb activated carbon), NKa-A82 (No1KCla activated carbon), NKb-A82 (No1KClb activated carbon) and NOS-A94 (No2OS activated carbon).

3. Results and Discussion

3.1. Chemical and Textural Characterisation

The elemental composition (carbon, hydrogen and oxygen contents) of the PF resins, the PF-KCl and PF-OS precursors and the corresponding chars and activated materials were determined using a LECO CHN-2000 analyzer. The acid/basic character of the carbon surfaces was evaluated by means of the Point of Zero Charge (pH_PZC), as determined by mass titration. The data are presented in

Table 3. Chemical characteristics of the materials.

Sample	Elemental Composition (wt%, daf)			pHPZC
	C	H	O *
Resol-based series
Re	74.7	5.9	19.4	7.2
ReKCla char	94.7	2.2	3.1	8.5
RKa-A71	96.2	1.3	2.5	9.5
ReKClb char	91.0	0.8	8.2	9.4
RKb-A75	92.7	1.1	6.2	9.6
Novolac-based series
No1	82.6	6.0	11.4	5.2
No1KCla char	96.5	0.5	3.0	4.6
NKa-A82	99.0	0.4	0.6	8.7
No1KClb char	97.0	0.4	2.6	7.6
NKb-A82	99.0	0.6	0.4	8.5
No2	78.1	5.8	16.1	4.8
No2OS char	96.3	0.8	2.9	7.4
NOS-A94	98.0	0.4	1.6	8.4

daf: dry ash free basis; * calculated by difference.

.

The synthesised resins, Re, No1 and No2, do not contain nitrogen and so it has not been included in the table. As expected for a carbon precursor the C contents in the initial resins are high (>70 wt%) and are enhanced during the subsequent steps of carbonisation and activation. The resultant activated materials present C contents well above 90 wt% at the expense of a reduction in the volatile matter content, here represented by the O and H contents.

There is a basification effect on the carbon surfaces as a consequence of the activation with CO₂. This effect is particularly significant in the case of the activated carbons produced from the acid catalyzed resins (No1 and No2). Basicity might be ascribed to basic oxygen functionalities incorporated from the activating gas (CO₂) or to Lewis type basic sites associated to the carbon structure [11].

Textural characterisation of the samples mainly involved the evaluation of the microporosity (pore sizes < 2 nm), given the critical role of these pore sizes on the CO₂ adsorption capacity of the samples. The N₂ and CO₂ adsorption isotherms at −196 and 0 °C, respectively (Figure 1a,b), were determined in a Micromeritics TriStar 3000 volumetric apparatus. Prior to any measurements, the samples were outgassed overnight at 100 °C under vacuum.

The five tested activated carbons exhibited distinctive textural features, as can be observed in Figure 1a. RKa-A71 is the least developed in terms of total porosity but shows a type I isotherm, according to the IUPAC classification, characteristic of strictly microporous materials. RKb-A75 presents a wider microporosity, characterised by a more open knee at low relative pressures, and it also shows a hysteresis loop at relative pressures above 0.4, which suggests the presence of some mesoporosity in the sample. On the other hand, NKa-A82 and NKb-A82 display similar type I isotherms but with different volumes of adsorbed N₂ along the evaluated pressures. NOS-A94 is the sample that has the most extended textural development, particularly in the domain of microporosity. Regarding CO₂ adsorption at 0 °C (Figure 1b), the uptake of the activated carbons follows the order: NKa > NKb ≈ NOS > RKa > RKb. RKa-A71 is the sample with the narrowest microporosity as reflected by the more pronounced curvature of the CO₂ isotherm.

The micropore volumes (W₀) and average micropore widths (L₀) were determined by applying the Dubinin–Radushkevich (DR) relation [23] and the Stoeckli-Ballerini relation [24] to these isotherms, respectively. This allowed the total microporosity and the narrow microporosity (pore sizes <1 nm) to be assessed. The textural parameters estimated from the experimental N₂ and CO₂ isotherms are collected in

Table 4. Textural parameters evaluated from the N₂ and CO₂ adsorption isotherms at −196 and 0 °C, respectively.

Parameter	RKa-A71	RKb-A75	NKa-A82	NKb-A82	NOS-A94
Vp (cm3·g−1)	0.08	0.46	0.45	0.32	0.53
W0,N2 (cm3·g−1)	-	0.35	0.44	0.32	0.50
L0,N2 (nm)	-	1.80	1.00	1.23	0.82
W0,CO2 (cm3·g−1)	0.21	0.18	0.38	0.31	0.27
L0,CO2 (nm)	0.58	0.70	0.71	0.64	0.64

.

As expected, in agreement with the shape of the corresponding isotherms, most of the porosity in NKa-A82, NKb-A82 and NOS-A94 lies in the microporosity domain. To be more precise, NKb-A82 concentrates its microporosity in the narrow microporosity range, whereas NKa-A82 and, particularly, NOS-A94 have a wider microporosity. Samples RKa-A71 and RKb-A75 show similar narrow micropore volumes (W_0,CO2). The textural development of RKa-A71 is restricted to this narrow microporosity, whereas RKb-A75 also presents supermicropores (1–2 nm) and mesopores (2–50 nm) as can be inferred from the differences between V_p, W_0,N2 and W_0,CO2. Average micropore widths (L_0,N2) of around 1 nm for the NK and NOS based ACs and ca. 2 nm for the RKb-A75 sample were assessed. The narrow microporosity (L_0,CO2) fell within the 0.6–0.7 nm range. The route selected to synthesise the PF precursor compromised the textural development that could have been achieved for the activated carbon. In order to gain a better insight into the narrow microporosity, the pore size distributions in the range of 0.3–1 nm were estimated by means of the Density Functional Theory (DFT) for CO₂ adsorption onto slit pore carbons using Micromeritics’ software (method: non-negative regularization, little smoothing). The plots are shown in Figure 2.

The narrow micropore size distributions of the studied materials can be described as bimodal as they present two main peaks with characteristic pore sizes in the range of 0.55–0.65 and 0.8–0.9 nm, respectively. The bimodal shape of the pore size distributions is a characteristic feature for many adsorbents possessing even a small amount of micropores. It is shown that this feature results from the similarity of the local adsorption isotherm in the range of the pore widths for which the gap between peaks (related to the primary and secondary micropore filling mechanism) exists [25].

Generally, the tested carbons show striking similarities in the pore size distributions. Sample RKa-A71 seems the exception as it shows a narrower micropore size distribution. The sizes of the narrow micropores in the materials are highly suitable for the separation of CO₂ at sub-atmospheric pressures [15,20].

3.2. CO₂ Uptake Screening

The CO₂ adsorption capacity of the produced carbons was first evaluated at sub-atmospheric pressures and room temperature. CO₂ adsorption isotherms at 25 °C and up to 101 kPa were determined in a Quantachrome Nova 4000 volumetric device. The samples were previously outgassed overnight at 100 °C under vacuum. A commercial activated carbon, Calgon BPL, was also tested for reference purposes [26]. This is a Calgon Carbon granular activated carbon specifically designed for use in gas phase applications. The measured isotherms are plotted in Figure 3.

The NK and NOS carbons showed substantial CO₂ uptakes over the sub-atmospheric pressure range tested, with isotherms characterised by more pronounced slopes at pressures below 20 kPa. Maximum CO₂ uptakes of 2.9, 2.4 and 2.3 mol·kg⁻¹ were achieved at 101 kPa for samples NKa-A82, NKb-A82 and NOS-A94, respectively. The isotherms of the two NK samples nearly overlapped in the pressure range below 20 kPa, as might be expected from the similarities in the narrower microporosity of both samples. When the pressure approaches the atmospheric value, differences in the CO₂ adsorption capacity appeared revealing the different microporosity features of the two NK activated carbons. The performance of carbon NOS shows striking similarities to that of NKb in agreement with the similarities in the narrow microporosity of both samples. The RK carbons showed similar performances to that of the commercial activated carbon over the tested pressure range with maximum CO₂ uptakes of less than 2 mol·kg⁻¹ at 101 kPa. Taking 2 mol·kg⁻¹ as the screening value for selecting optimum CO₂ adsorbents, RK carbons were discarded for further study.

3.3. Binary Adsorption from Mixtures of CO₂-H₂, CO₂-CH₄, and CO₂-N₂

3.3.1. Single-Component Adsorption Isotherms

H₂, CH_4, and N₂ adsorption isotherms at 25 °C and sub-atmospheric pressures (up to 100.3 kPa) for the NK and NOS carbons were obtained using a Micromeritics TriStar 3000 volumetric equipment. BPL was also tested for comparison purposes. Detailed textural characteristics of this activated carbon can be found elsewhere [27]. Prior to analysis the samples were outgassed overnight at 100 °C under vacuum.

Experimental data of the single component CO₂, H₂, CH₄, and N₂ adsorption isotherms were fitted to the Sips equation, as follows:

$$\text{Sips equation}: q=q_s\frac{{\left(bP\right)}^{1/n}}{1+{\left(bP\right)}^{1/n}}$$

(1)

where q represents the concentration of the adsorbed species, q_s the saturation capacity and P the pressure of the adsorptive. The parameters b, n and q_s are temperature dependent; b usually takes the form of the adsorption affinity. The parameter n shows the heterogeneity of the system and its value is usually greater than unity; therefore, the larger the value of n, the more heterogeneous the system is.

This empirical three-parameter equation has been widely used for fitting the isotherm data of different hydrocarbons on activated carbon. The Sips equation is believed to give a more accurate fit over a larger pressure regime than the standard Langmuir or Freundlich equations, and provides more accurate prediction of the quantity adsorbed at saturation than the Langmuir equation for heterogeneous adsorbents. However, it suffers from the same disadvantage as the Freundlich equation: it does not reduce to Henry’s Law at low surface coverage [28].

Fitting of the model to the experimental data was conducted by means of the Solver Excel tool (Microsoft Office Excel 2010) departing from values of q_s and n of 1 and b of 0. The goodness of the fit was evaluated on the basis of the minimum squared relative error (SRE) as given by the following expression:

$$SRE(\%)=\sqrt{\frac{{\displaystyle \sum _i{\left[\left(q_{\exp ,i}-q_{\mathrm{mod},i}\right)/q_{\exp ,i}\right]}^2}}{N-1}}\times 100$$

(2)

where q_exp,i and q_mod,i are the experimental and Sips-predicted adsorbed amounts of component i, respectively, and N is the number of experimental data points. The optimal parameters and squared relative errors from fitting the Sips model to the single-component data of CO₂, H₂, CH₄, and N₂ at 25 °C are summarized in

Table 5. Optimal parameters of the single-component CO₂, CH₄, H₂, and N₂ adsorption data fitting to the Sips model.

Sample	CO2			SRE (%)	CH4			SRE (%)
	qs	b	n		qs	b	n
NKa-A82	7.37	5.77 × 10−3	1.17	1.1	3.76	5.69 × 10−3	1.10	1.5
NKb-A82	5.38	7.46 × 10−3	1.24	1.0	3.37	3.13 × 10−3	1.15	1.9
NOS-A94	6.29	4.77 × 10−3	1.28	0.6	4.20	2.62 × 10−3	1.30	3.3
BPL	4.72	6.02 × 10−3	1.17	3.0	2.63	4.03 × 10−3	1.07	2.6
Sample	H2			SRE (%)	N2			SRE (%)
	qs	b	n		qs	b	n
NKa-A82	0.39	1.50 × 10−3	1.00	8.8	2.18	2.55 × 10−3	1.00	1.7
NKb-A82	2.46	1.29 × 10−4	1.00	8.2	2.87	1.17 × 10−3	1.00	2.1
NOS-A94	1.44	4.06 × 10−5	1.65	11.0	2.36	1.81 × 10−3	1.00	2.1
BPL	0.41	1.98 × 10−4	1.19	5.1	2.90	9.89 × 10−4	1.00	2.0

q_s: mol·kg⁻¹, b: kPa⁻¹.

. Isotherm experimental data and fittings to the Sips model are shown in Figure 4.

The experimental adsorption data show that much more CO₂ is adsorbed than CH₄ and more significantly than N₂ and H₂ on the tested carbons. The differences in CO₂, CH₄ and N₂ uptake may be explained by the larger quadrupole moment of CO₂ that produces a strong attraction towards the adsorbent surface resulting in a greater uptake. The high level of polarizability of CO₂ and CH₄ can create a momentary shift in its neutral electrostatic field but this attraction force is much weaker than the quadrupole moment [29]. In contrast, N₂ molecules are nonpolar and smaller, compared with CH₄ molecules. For this reason, the differences in CO₂ and N₂ uptake are greater than the differences in CO₂ and CH₄ uptake. Since the narrow micropores allow the strongest interaction between the carbonaceous solid and the hydrogen molecule, it is to be expected that this fraction of the porous volume will make a major contribution to the hydrogen adsorption capacity of the materials. Although hydrogen should only interact through induced polarization, surface chemistry may influence hydrogen adsorption on carbonaceous surfaces, particularly at sub-atmospheric pressures [30,31].

By comparing the quantities adsorbed by the phenol-formaldehyde carbons in Figure 4 it can be seen that NKa-A82 is the sample with the greatest CO₂, CH₄, N₂ and H₂ uptakes over the sub-atmospheric pressure range tested. Moreover, the adsorption capacities of the three PF carbons are greater than that of the reference carbon, BPL. In terms of CO₂ adsorption, the performance at pressures below 20 kPa is quite similar for the NK and NOS carbons and it is only at higher pressures where NKa-A82 stands out. CH₄ adsorption isotherms show differentiated uptakes for the three PF carbons that follow the order NKa > NOS > NKb. All three samples present relevant microporosity; in sample NKb narrow micropores (<1 nm) are mainly encountered, whereas for NKa and NOS microporosity >1 nm is also present, in agreement with the textural parameters estimated from the DR relation (see Table 4). In this scenario selectivity effects related to the kinetic diameters of the two gas molecules (3.30 Å for CO₂ and 3.80 Å for CH₄) [29] may play a role in the change in the CO₂ and CH₄ adsorption trends of the three PF carbons. N₂ and H₂ adsorption is characterised by linear isotherms that reveal the unspecific nature of the adsorbate-adsorbent interaction [32].

The pure component CO₂, H₂, CH₄, and N₂ adsorption isotherms fitted to the Sips model (Equation (1)) are represented by the continuous lines in Figure 4. The saturation capacities (q_s) and the parameter n have been fitted to the adsorption data for the four gas species independently (Table 5).

The Sips model reproduces the adsorption of CO₂, CH₄, and N₂ with good accuracy, with substantial deviations for the adsorption of H₂. It should be noted that the experimental H₂ adsorption data at sub-atmospheric pressures and ambient temperature are subject to greater uncertainty due to the significantly lower uptakes of H₂ under these conditions. The values of q_s and b follow the trend CO₂ > CH₄ > N₂ >> H₂, as might be expected from the experimental data where the capacity and, consequently, the affinity of the carbons to adsorb CO₂ and CH₄ is one and two orders of magnitude greater than that of N₂ and H₂, respectively. The parameter n takes values close to unity for CO₂ and CH₄ while for N₂ takes values of unity, suggesting that heterogeneity plays a minor role in these systems. The uneven fitting of the H₂ isotherms for the studied carbons can be mainly ascribed to uncertainty of the experimental data. Sample NOS is where greatest deviation from unity in the values of n is found for the adsorption of CO₂, CH₄ and H₂.

3.3.2. Multicomponent Adsorption Prediction

In order to predict multicomponent adsorption from binary CO₂-H₂, CO₂-CH₄, and CO₂-N₂ mixtures, the fitting of the single component adsorption data to the Sips model represented by Equation (1) was rerun to account for the interaction between components in each binary mixture. Given that CO₂ is the strongest adsorbate, the fitting was conducted keeping q_s constant (the value of q_s estimated from the fitting of single component CO₂ adsorption isotherm for each sample) and adjusting the b and n values to minimize the relative error for the pairs CO₂-H₂, CO₂-CH₄, and CO₂-N₂, respectively. The values of the parameters estimated from these fittings are collected in

Table 6. Optimal parameters of the single-component CO₂, H₂, CH₄, and N₂ adsorption data fitting to the Sips model for multicomponent prediction.

Sample	CO2-CH4
	bCO2	bCH4	n	SRE (%)
NKa-A82	5.83 × 10−3	2.01 × 10−3	1.16	3.0
NKb-A82	7.99 × 10−3	1.52 × 10−3	1.19	2.7
NOS-A94	4.43 × 10−3	1.36 × 10−3	1.32	2.3
BPL	6.33 × 10−3	1.60 × 10−3	1.14	3.7
Sample	CO2-H2
	bCO2	bH2	n	SRE (%)
NKa-A82	6.55 × 10−3	4.27 × 10−5	1.10	7.9
NKb-A82	1.03 × 10−2	5.33 × 10−5	1.01	15.4
NOS-A94	4.18 × 10−3	1.69 × 10−5	1.35	9.6
BPL	6.08 × 10−3	1.31 × 10−5	1.16	4.3
Sample	CO2-N2
	bCO2	bN2	n	SRE (%)
NKa-A82	6.93 × 10−3	5.36 × 10−4	1.06	6.6
NKb-A82	9.63 × 10−3	6.98 × 10−4	1.06	9.6
NOS-A94	6.90 × 10−3	5.12 × 10−4	1.05	11.9
BPL	7.00 × 10−3	3.75 × 10−4	1.10	10.7

b: kPa⁻¹.

.

The fitted parameters follow the same trend observed in the previous independent Sips fittings: the n values are close to unity and the b values follow the order CO₂ > CH₄ > N₂ >> H₂. When mixed the affinity, as represented by the parameter b, increases for the strong adsorbate (CO₂) when compared to the pure component CO₂ adsorption data independent fitting. Likewise, the weaker adsorbate shows a substantial decrease in affinity particularly in the CO₂-H₂ and CO₂-N₂ systems.

In this way, use of the parameters from the fitting of pure component data pairs guarantees the thermodynamic consistency of the resulting analytical expression of the multicomponent Sips model. Using the same analogy for extending the single-component Langmuir equation to that for multicomponent adsorption, the following equation is obtained for the multicomponent Sips model [33]:

$$q_i=\frac{q_s{\left(b_i{y}_{i}P\right)}^{1/n}}{1+{\displaystyle \sum _{j=1}^N{\left(b_j{y}_{j}P\right)}^{1/n}}}$$

(3)

where i and j stand for the components in the binary mixture, y is the mole fraction of the corresponding component in the gas phase, and N is the number of components in the gas mixture, i.e., 2. However, this equation only corresponds to a specific case of surface energetic heterogeneity. For normal activated carbons in which the energy sites are highly correlated, the Ideal Adsorbed Solution Theory (IAST) should be used. Application of the IAST with the concept of hypothetical pure-component pressure results in the following equation [34]:

$$q_i=\frac{q_s{b}_i{y}_{i}P{\left({\displaystyle \sum _{j=1}^N{b}_j{y}_{j}P}\right)}^{(1/n)-1}}{1+{\left({\displaystyle \sum _{j=1}^N{b}_j{y}_{j}P}\right)}^{1/n}}$$

(4)

It can be seen that Equations (3) and (4) deliver different expressions to reproduce the multicomponent Sips model on the basis of different assumptions regarding the heterogeneity of the adsorbate-adsorbent system. Nevertheless, both equations were used in the present study to predict the binary adsorption equilibrium for CO₂-H₂, CO₂-CH₄, and CO₂-N₂ systems and the results are discussed and compared. The parameter values used for such multicomponent adsorption predictions were those previously obtained from the combined fitting of the pure component adsorption data of the pairs of gases in each mixture as shown in Table 6.

The predictions of the binary gas adsorption equilibria from the multicomponent Sips model represented by Equations (3) and (4) and from the parameters included in Table 6 are depicted in Figure 5, Figure 6 and Figure 7. Multicomponent predictions were assessed under the following temperature and pressure conditions: 25 °C and 100 kPa.

Globally, the predicted multicomponent adsorption isotherms show a reduction in the uptakes of the four components when mixed in binary CO₂-H₂, CO₂-CH₄ or CO₂-N₂ mixtures. However, while the CO₂ uptake when mixed in a 1:1 molar ratio is reduced to 60%, 70% and 75% (average values for the four evaluated carbons in the CO₂-CH₄, CO₂-N₂ and CO₂-H₂ binary mixtures, respectively) of the pure gas CO₂ adsorption at 25 °C and 100 kPa, the H₂, N₂ and CH₄ uptakes drastically drop down to around 30–35% of those corresponding to pure gas adsorption. This suggests that the presence of another component in the mixture influences the adsorption of CO₂ to a lesser extent.

It is apparent that when n (Table 6) approaches unity the values of the numerator and the denominator of Equations (3) and (4) tend to match each other and both Equations (3) and (4) give similar predictions. This suggests that there is little heterogeneity in the systems that could influence the adsorption of the binary mixtures onto the evaluated carbons. The CO₂-H₂ system is where greater deviations between the two predictions are observed, particularly for the H₂ uptake. It should be noted that at sub-atmospheric pressures and room temperature experimental H₂ adsorption is characterised by extremely low uptakes. In addition, the affinity of the carbons towards H₂ adsorption is significantly lower than that to CO₂. Consequently, binary adsorption prediction for the CO₂-H₂ system is subject to greater uncertainty. Moreover, predicted CO₂ adsorption in the CO₂-H₂ binary mixtures nearly matches pure component CO₂ adsorption at similar partial pressures suggesting that H₂ adsorption in these mixtures can be considered as negligible. This is in agreement with previous results from the research team [6,35].

The CO₂ uptake at y_j = 0 (where j stands for H₂, N₂ and CH₄, respectively) is slightly overestimated for the CO₂-H₂ and CO₂-N₂ systems compared to the pure component CO₂ adsorption data. This may be attributed to the different affinity of the adsorbent towards CO₂ and H₂ or N₂.

In the case of CO₂-CH₄ (Figure 6) and CO₂-N₂ (Figure 7) the predictions of the two Equations (3) and (4) seem consistent. The values of n (Table 6) are close to unity for the CO₂-N₂ system and thus Equations 3 and 4 deliver similar predictions. For the phenolic resin-biomass composite derived carbon, NOS-A94, Equation (3) predicts slightly greater CH₄ uptakes (+0.15 mol·kg⁻¹) than Equation (4) for molar fractions of methane (y_CH4) in the binary mixture between 0.3 and 0.6. Both CO₂ and CH₄ show specific interaction with the carbon surface, as reflected by the shape of the isotherms (type I, according to the IUPAC classification). However, despite the preferential adsorption of CO₂ over CH₄, competition between both adsorbates exists. The significantly higher critical temperature of CO₂ in comparison with CH₄ makes carbon dioxide more likely to behave as a condensable steam than as a supercritical gas, making it less volatile and increasing its chances of adsorption. Moreover, CO₂ presents a higher polarizability which may enhance attractive forces with the surface and a permanent quadrupole, leading to stronger interactions with any solid surface.

The simplified extended Sips model (Equation (3)) shows limitations bearing in mind the assumptions needed to extend the single component Sips equation to the multicomponent one. However, the observed deviations between the multicomponent predictions represented by Equations (3) and (4) are small and therefore, both could be applied to predict the adsorption of CO₂, CH₄, and N₂ on the evaluated carbons in binary CO₂-CH₄, and CO₂-N₂ mixtures. The H₂ uptakes predicted for the CO₂-H₂ systems should be handled with care given the uncertainty of the experimental H₂ adsorption data under sub-atmospheric pressures and room temperature. H₂ adsorption can be regarded as negligible in the CO₂-H₂ systems. Moreover, data on the performance of the phenolic resin-derived carbon for CO₂-CH₄ adsorption were also experimentally obtained in a lab scale fixed-bed adsorption unit. Details can be found elsewhere [6]. The CO₂ and CH₄ uptakes assessed at 120 kPa and 25 °C for a 1:1 CO₂:CH₄ binary mixture are in good agreement with the multicomponent predictions at 100 kPa and 25 °C presented herein; for instance, the predicted CO₂ uptake on carbon NKa-A82 for a 1:1 CO₂:CH₄ mixture at 120 kPa is 1.90 mol·kg⁻¹ in agreement with 2.03 mol·kg⁻¹ estimated experimentally.

3.4. Selectivity to CO₂ Separation

The selectivity of the prepared carbons to separate CO₂ from CO₂-H₂, CO₂-N₂ and CO₂-CH₄ mixtures at ambient temperature and sub-atmospheric pressures was evaluated on the basis of the multicomponent adsorption predictions. The following expression was used:

$$S_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}= \frac{q_1/q_2}{y_1/y_2}$$

(5)

where q₁ stands for the CO₂ uptake of the carbon from the binary mixture and q₂ represents the H₂, N₂ and CH₄ uptakes, respectively. y₁ and y₂ are the corresponding molar fractions of the gas component in the binary mixtures. From the IAST-Sips multicomponent adsorption model represented by Equation (4), the following equation can be inferred to account for the selectivity to separate CO₂ from binary mixtures:

$$S_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}= \frac{b_1}{b_2}$$

(6)

where b₁ and b₂ stand for the affinity constants of CO₂ and H₂, N₂ and CH₄, respectively. According to Equation (6) the selectivity to separate CO₂ from binary mixtures is independent of the partial pressures of the components in the binary mixture.

Table 7. Selectivities of the carbons to separate CO₂ from CO₂-H₂, CO₂-N₂ and CO₂-CH₄ binary mixtures.

S1/2	CO2-H2	CO2-N2	CO2-CH4
NKa-A82	153	12.9	2.9
NKb-A82	193	13.8	5.3
NOS-A94	247	13.5	3.3
BPL	464	18.7	3.9

summarizes the selectivities of the carbons as estimated from Equation (6) (b₁:b_CO2 and b₂:b_H2, b_N2 or b_CH4).

The selectivity values follow the order CO₂-H₂ >> CO₂-N₂ > CO₂-CH₄ indicating that the separation of CO₂ from CO₂-H₂ mixtures at sub-atmospheric pressures and ambient temperature is favoured. BPL shows the greatest selectivity values to separate CO₂ from CO₂-H₂ and CO₂-N₂ binary mixtures whereas the phenolic resin-derived carbon NKb-A82 presents the highest selectivity for CO₂ to be separated from CO₂-CH₄ mixtures. Nevertheless, selectivity values for the four evaluated carbons are in the same order of magnitude for each mixture and the values are particularly close in the case of CO₂-N₂ and CO₂-CH₄ separation.

The selectivity value, as estimated from Equation (6), could serve as a rough sorbent selection parameter. However, for a more precise evaluation the working capacities (differences between the gas uptakes of both components under adsorption and regeneration conditions) and the heat required for the regeneration of the adsorbent would also need to be taken into account [36].

4. Conclusions

Phenolic resin-derived carbons were prepared and evaluated for CO₂ adsorption at sub-atmospheric pressures. Single component adsorption isotherms of CO₂, H₂, N₂ and CH₄ were measured at 25 °C and up to 100 kPa and fitted to the Sips model. Binary adsorption from CO₂-H₂, CO₂-N₂ and CO₂-CH₄ mixtures was then predicted by applying the extended multicomponent Sips model and the Ideal Adsorbed Solution Theory (IAST) in conjunction with the Sips model. Both equations showed similar predictions for the adsorption of CO₂, CH₄ and N₂ on the evaluated carbons in the binary mixtures. The adsorption of H₂ at the conditions evaluated can be considered negligible. Both Sips multicomponent equations might predict binary adsorption in the studied systems. This is a significant advantage from the viewpoint of computational modelling requirements in adsorption process design.

In terms of CO₂ uptake, the performance of the acid resin-derived carbons in separating CO₂ from CO₂-CH₄, CO₂-H₂, and CO₂-N₂ at atmospheric pressure was superior to that of a reference commercial carbon (Calgon BPL) and an even higher selectivity towards CO₂ was found in the separation of CO₂-CH₄.