# Comparative study of biogas treatment in dry and wet conditions using modified activated carbons of CNR-115 family

Khaled Abou Alfa, Nour Abou Saleh, Camélia Matei Ghimbeu, Bénédicte Réty, Vincent Platel, Cecile Hort

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Khaled Abou Alfa, Nour Abou Saleh, Camélia Matei Ghimbeu, Bénédicte Réty, Vincent Platel, et al.. Comparative study of biogas treatment in dry and wet conditions using modified activated carbons of CNR-115 family. Chemical Engineering Journal Advances, 2025, 23, pp.100797. 10.1016/j.ceja.2025.100797. hal-05150350

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Comparative study of biogas treatment in dry and wet conditions using
modified activated carbons of CNR-115 family

Khaled Abou Alfa<sup>a,D,*</sup>, Nour Abou Saleh<sup>a</sup>, Camélia Matei Ghimbeu<sup>b,c</sup>, Bénédicte Réty<sup>b,c,D</sup>,
Vincent Platel<sup>a</sup>, Cecile Hort<sup>a</sup>

ARTICLE INFO

Keywords:

Biogas

Activated carbon

Adsorption Performance Indicator

Breakthrough curve

Water vapor

A B S T R A C T

This study investigates the effect of water vapor on the adsorption performance of modified activated carbons (ACs) from the CNR-115 family (CNR-115-ox and CNR-115-ox-am), derived from the commercial AC (CNR-115), for CO₂/CH₄ separation. Breakthrough curve analysis at 0.1 MPa and 303 K showed that CO₂ consistently exhibited higher breakthrough and saturation times than CH₄, indicating stronger interactions with adsorbents of the CNR-115 family. The presence of water vapor in experiments with a 39%/59%/2% (vol.) CO₂/CH₄/H₂O mixture significantly impacted CO₂ adsorption, enhancing its retention and selectivity. Under dry conditions, CNR-115-ox demonstrated higher separation efficiency due to its large BET surface area, while CNR-115-ox-am showed increased CO₂ adsorption capacities and selectivity under wet conditions. This improvement in performance under moist conditions is likely due to bicarbonate formation, which promotes CO₂ retention. Moreover, experiments under wet conditions revealed a roll-up effect for CH₄ and a slight roll-up for CO₂, caused by co-adsorption of H₂O. The findings emphasize the importance of considering water vapor in biogas upgrading processes to optimize adsorbent design and improve CO₂ separation efficiency. Furthermore, the increased CO₂ adsorption per unit area under both dry and wet conditions for CNR-115-ox-am, despite its lower BET surface, underscores the dominant influence of surface chemistry over porosity in gas adsorption. This improvement, driven by nitrogen functionalization, enhances both selectivity and adsorption efficiency, making CNR-115-ox-am a promising material for biogas upgrading applications.

1. Introduction

Renewable energy technologies have grown due to concerns about
energy security and efforts to mitigate the environmental impact of
fossil fuels while advancing living standards [1]. Bioenergy, particu-
larly biogas produced via anaerobic digestion of biomass wastes, has
emerged as a key solution to transitioning toward a low-carbon, sus-
tainable energy system [2,3]. Biogas, primarily composed of methane
(CH₄) (40%–75% v/v) and carbon dioxide (CO₂) (25%–55% v/v),
but it also contains traces of other gases such as hydrogen sulfide
(H₂S), ammonia (NH₃), water vapor (H₂O(g)), siloxanes, halogenated
hydrocarbons, etc. [4]. It is a promising fuel with applications in direct
heating, internal combustion engines, and cogeneration for electricity
production [5]. CH₄ is a vital component with a gross calorific value
of 37 MJ m⁻³ at atmospheric pressure and a temperature of 288 K,
compared to about 21 MJ m⁻³ for raw biogas [6]. Thus, contaminants

must be removed from the biogas stream as they decrease calorific
value, increase flammability, and cause corrosion issues [7,8].

The biogas upgrading, which involves separating CO₂ from the
mixture to produce biomethane, contributes to carbon neutrality and
extends its applicability. Physical adsorption has emerged as an effi-
cient and environmentally friendly method for biogas upgrading due to
its low energy consumption [9–11]. This process involves gas capture
onto an adsorbent surface, followed by regeneration for reuse. The
efficiency of adsorption depends on the properties of the adsorbent
and operational conditions [12,13]. It is one of the most widely used
adsorption-based separation techniques, can produce biomethane with
over 97% CH₄ and an energy consumption of 1250 kJ kg⁻¹ [14].
The adsorbent plays a crucial role in the adsorption performance,
requiring high adsorption capacity, selectivity, regeneration efficiency,
and mechanical stability [11,15]. Several studies have investigated the
impact of modified activated carbons (ACs) on CO₂ separation from

<footnote><sup>a</sup> Laboratoire de Thermique, Energetique et Procedes-IPRA, EA1932, Universite Pau, Pays Adour/E2S UPPA, 64000 Pau, France</footnote>

<footnote><sup>b</sup> Institut de Science des Matériaux de Mulhouse (IS2M), CNRS UMR 7361, Université de Haute-Alsace, 68100 Mulhouse, France</footnote>

<footnote><sup>c</sup> Institut de Science des Matériaux de Mulhouse (IS2M) UMR 7361, Université de Strasbourg, 67081 Strasbourg, France</footnote>

<footnote>* Corresponding author.
E-mail address: kaalfa@univ-pau.fr (K. Abou Alfa).</footnote>
CO₂/CH₄ gas mixtures. For instance, fluorination of pitch-based AC at temperatures ranging from 25 to 200 °C has been found to enhance CO₂ adsorption by narrowing micropores, thereby increasing CO₂ capture and selectivity due to its smaller kinetic diameter (0.33 nm) compared to CH₄ (0.38 nm) [16]. Additionally, modified ACs with functional groups (-COOH, -CO, -OH) elucidated the role of electrostatic interactions in CO₂/CH₄ selectivity. Notably, ACs modified with -COOH groups exhibited significantly improved selectivity, attributed to carbonyl and hydroxyl groups facilitating potential hydrogen bonding, particularly at low pressures [17].

The specific surface area exerts an inverse effect on selectivity and adsorption capacity [18,19]. Increasing specific surface area leads to higher adsorption capacities of pure CO₂ and CH₄, but a possible decrease of CO₂/CH₄ selectivity. At low pressures, CO₂ is preferentially adsorbed over CH₄ because it can form weak chemical bonds, such as hydrogen bonds, with functional groups on the surface of ACs. However, at high pressures, CH₄ will be more compressed into the pores, resulting in lower CO₂/CH₄ selectivity [17]. Peredo-Mancilla et al. [20] investigated three ACs' performance in separating CO₂ from CO₂/CH₄ mixtures: a commercial AC (CNR-115) and its chemical modifications via air oxidation (CNR-115-ox) and air oxidation with NH₄OH treatment (CNR-115-ox-am). The surface area and CO₂ adsorption capacity followed the order CNR-115 >CNR-115-ox >CNR-115-ox-am due to pore collapse from chemical modifications on the ACs' surface. However, CNR-115-ox-am exhibited the highest selectivity due to its basic surface, compared to the other ACs. Thus, a combination of physical and chemical characteristics of ACs and gas molecules significantly impacted the separation of CO₂ from the CO₂/CH₄ mixture.

The impact of H₂O(g) content on CO₂/CH₄ separation is a subject of ongoing research and debate [21,22]. Studies have shown that different materials, such as metal organic framework (MOFs), zeolites, and carbon molecular sieve (CMSs), behave differently in humidified environments. For example, the MOF (MIL-100(Fe)) exhibited enhanced CO₂ adsorption and improved CO₂/CH₄ selectivity in the presence of H₂O(g) (relative humidity of 50%), attributed to the formation of alkaline active sites. In contrast, the MOF (MIL-101(Cr)) showed reduced CO₂ adsorption due to competitive adsorption, resulting in lower selectivity value of 3.7, lower than that in dry atmosphere (4.5) [23]. Zeolite 13X and SAPO-34, which have a strong affinity for H₂O(g), exhibited reduced CH₄ concentration and recovery ratio with increasing moisture concentration. In contrast, the separation efficiency using CMS remained unaffected even with high levels of H₂O(g) (relative humidity of 80%) in the biogas due to its low adsorption of H₂O(g) owing to its hydrophobic nature [24]. These findings highlight the diverse impact of H₂O(g) on adsorbent materials and emphasize the need for further research to optimize CO₂/CH₄ separation processes.

Contradictory findings exist regarding the effect of H₂O(g) on CO₂ adsorption onto ACs. Some studies suggest H₂O(g) enhances CO₂ adsorption [25–27]. For instance, enhanced CO₂ adsorption occurs with 10% H₂O(g) due to bicarbonate formation instead of carbamates [25, 26]. However, others have observed a decrease in the CO₂ adsorption [28,29]. For instance, a study revealed that ACs prepared with water loading of 2%, 3%, and 4% respectively, reduce CO₂ adsorption capacity by competing unfavorably with CO₂ and partially blocking pores [30]. On the other hand, some authors have noted that the presence of H₂O(g) (humidity level up to 7.2%) has little effect on CO₂ adsorption [31]. This could be attributed to either the formation of unusual three-dimensional H₂O(g) clusters and networks [32] or to the separation process of ACs following the kinetic effect, as CO₂ can be adsorbed faster than H₂O(g) [33]. Regarding the impact of the H₂O(g) on the CO₂ separation from a biogas stream (CO₂+CH₄) using ACs, a study was investigated on various CO₂/CH₄ ratios using pine sawdust AC at 303 K and atmospheric pressure. Findings revealed that preadsorbed H₂O(g) (saturated bed) reduced the bed's capacity to capture both gases but increased CO₂ selectivity over CH₄. Wet experiments over a saturated bed demonstrated the highest selectivity, albeit with

lower gas adsorption capacities compared to dry feed gas [28]. In another study, simulations predicted an equilibrium CO₂/CH₄ selectivity of 4.7 at 1 bar and 298 K for a 60/40 vol% mixture, which increased in the presence of moisture (3%), reinforcing its effectiveness for humid biogas upgrading [34].

This study aims to explore the adsorption performance of modified ACs from the CNR-115 family (CNR-115-ox and CNR-115-ox-am) for CO₂/CH₄ separation under dynamic conditions, with a particular focus on the influence of water vapor, a key component of biogas. To approach real biogas conditions, experiments were conducted using a 2% vol. water vapor mix in a CO₂/CH₄ (39%/59%) gas mixture at 303 K and 0.1 MPa. This research seeks to provide a comprehensive understanding of adsorption performance in the presence of humidity. The novelty of this study lies in its investigation of CO₂/CH₄ separation under conditions that more closely resemble those found in biogas, an area not extensively explored in the current literature. This work is critical for optimizing biogas upgrading technologies and advancing the design of more efficient industrial adsorption systems.

In this context, the main contributions of the present work are as follows: (i) it provides a dynamic evaluation of CO₂/CH₄ separation using modified activated carbons (CNR-115-ox and CNR-115-ox-am) under both dry and humid conditions that closely simulate real biogas environments; (ii) it identifies the roll-up effect for CH₄ in dry and wet conditions and for CO₂ in wet conditions, offering new insights into competitive adsorption behavior; (iii) it demonstrates that nitrogen functionalization enhances CO₂ selectivity and retention under humid conditions, making CNR-115-ox-am a strong candidate for biogas upgrading; and (iv) it confirms the critical role of surface chemistry — particularly oxygen and nitrogen functional groups — in improving adsorption performance under realistic dynamic conditions.

## 2. Materials and experimental apparatuses

### 2.1. Materials

Two modified ACs from the CNR-115 family (CNR-115-ox and CNR-115-ox-am) were selected for a comparative study to evaluate their performance in biogas upgrading under dry and humid conditions. Both materials were derived from the commercial AC (CNR-115), sourced from Cabot Corporation in France, through a two-step chemical modification process (see Fig. 1). The first step involved oxidizing CNR-115 in air at 400 °C for 2 h, introducing oxygen-containing functional groups and producing CNR-115-ox. In the second step, CNR-115-ox was treated with ammonium vapor (NH₄OH) at 25 °C for 36 h, incorporating nitrogen functionalities to create CNR-115-ox-am [35]. To enhance CO₂/CH₄ separation performance, the surface chemistry of CNR-115-ox was modified using NH₄OH to increase the concentration of basic surface groups. This modification promotes stronger electrostatic interactions with CO₂ molecules — owing to their quadrupolar nature — while minimizing CH₄ adsorption capacity, which relies primarily on weak van der Waals interactions. These surface modifications effectively tune the adsorbent's chemical affinity, thereby improving selectivity and adsorption performance under relevant operating conditions. The textural and chemical characteristics of these samples were already published by Peredo-Mancilla et al. [35].

#### 2.1.1. Physico-chemical characterizations of CNR-115 family

The characterization of the CNR-115 family was carried out using N₂ adsorption/desorption isotherms at 77 K, which revealed Langmuir isotherms, indicating microporous characteristics with a narrow pore size distribution. Ammonia vapor treatment reduced the surface area from 929 to 352 m² g⁻¹ due to pore blockage by nitrogen groups. The higher surface area of CNR-115-ox results from the oxidation process, which enhances pore development and creates more accessible adsorption sites, favoring physisorption. In contrast, the reduction in surface
<figure><img src="image_2.png" /><figcaption>Fig. 1. Production of CNR-115-ox and CNR-115-ox-am through chemical treatments of the commercially activated carbon CNR-115.</figcaption></figure>

<caption>Table 1</caption>

Textural properties and acid/basic oxygenated surface groups content of the CNR-115 family. Standard deviations: dev<sub>pH</sub> = 0.04, dev<sub>acid</sub> = 0.003 mmol g<sup>-1</sup>, dev<sub>base</sub> = 0.003 mmol g<sup>-1</sup> [35].

<table><thead><tr><th>Property type</th><th>Property</th><th>Unit</th><th>CNR-115-ox</th><th>CNR-115-ox-am</th></tr></thead><tbody><tr><td rowspan="5">Textural</td><td>BET surface area (S<sub>BET</sub>)</td><td>m<sup>2</sup> g<sup>-1</sup></td><td>929</td><td>352</td></tr><tr><td>Micropore Area</td><td>m<sup>2</sup> g<sup>-1</sup></td><td>469</td><td>168</td></tr><tr><td>Micropore volume (V<sub>micro</sub>)</td><td>cm<sup>3</sup> g<sup>-1</sup></td><td>0.36</td><td>0.14</td></tr><tr><td>Mesopore volume (V<sub>meso</sub>)</td><td>cm<sup>3</sup> g<sup>-1</sup></td><td>0.09</td><td>0.07</td></tr><tr><td>Average pore size (L<sub>q</sub>)</td><td>nm</td><td>0.96</td><td>0.78</td></tr><tr><td rowspan="3">Chemical</td><td>Point of zero charge (pH<sub>PZC</sub>)</td><td>–</td><td>5.87</td><td>6.48</td></tr><tr><td>Total acid content</td><td>mmol g<sup>-1</sup></td><td>1.39</td><td>1.15</td></tr><tr><td>Total base content</td><td>mmol g<sup>-1</sup></td><td>0.46</td><td>1.20</td></tr></tbody></table>

area observed for CNR-115-ox-am is attributed to the ammonia treatment, which may partially block pores or introduce functional groups that reduce the accessible surface. Both micropore and mesopore volumes decreased with ammonia chemical treatments, with the average pore size narrowing from 0.96 in CNR-115-ox to 0.78 nm (CNR-115-ox-am) (Table 1) [35,36]. The pH at zero charge (pH<sub>PZC</sub>) indicates the electrically neutral state of a material's surface. During the oxidation process, oxygenated functional groups, such as carboxyls and alcohols, were introduced, resulting in a pH<sub>PZC</sub> of 5.87 for CNR-115-ox [37]. Ammonia vapor treatment increased pH<sub>PZC</sub> to 6.48 by forming nitrogen surface functional groups, enhancing basic oxygenated surface groups and creating π-electron-rich zones acting as Lewis bases. This treatment increased the basic character and total basic functionalities from 0.46 mmol g<sup>-1</sup> to 1.20 mmol g<sup>-1</sup> (Table 1).

## 2.2. Experimental apparatuses for investigating adsorption characteristics

### 2.2.1. Breakthrough curves (adsorption under dynamic conditions)

Fixed-bed experiments were conducted to study breakthrough curves, as shown in Fig. 2. The setup included a 22 g mass of modified CNR-115 ACs in a 33 cm high, 1 cm diameter glass column; a 40%/60% (vol.) CO₂/CH₄ gas mixture; K-type thermocouples for temperature monitoring (±1.5 °C); a water reservoir; a controlled evaporator mixer (CEM) delivered from Bronkhorst, to produce a wet biogas stream with specific relative humidity, comprising a mass flow controller for inlet dry gas (EL-FLOW Select F-201CV-100), a liquid flow meter (MUFLOW L01) for feeding liquid H₂O, and a heat exchanger (W-101A); and a gas chromatography (ThermoFisher Scientific) with a thermal conductive detector (TCD) for measuring CO₂/CH₄ concentrations. Bed pressure was controlled using a piezoresistive Keller pressure regulator (type PAA-33X) (0–3.3 MPa range, ± 0.05% accuracy). The system was placed in a furnace set to 303 K to maintain constant temperature. Experiments were performed at 303 K and 0.1 MPa with a flow rate of 30 Nm L min⁻¹. The ACs of the modified CNR-115 family were regenerated at 363 K under vacuum for 24 h, then cooled to 303 K before gas introduction. Wet experiments involved humidification of the gas mixture to 40% relative humidity using a CEM, producing a 39%/59%/2% (vol.) CO₂/CH₄/H₂O mixture. Breakthrough curves were generated by monitoring outlet concentrations with gas chromatography (ThermoFisher Scientific, TCD) until saturation. To ensure the reliability of the results, repeatability was conducted by performing

each measurement two times, and any uncertainty was quantified by calculating the standard deviation from the two repetitions

### 2.3. Breakthrough curve measurements

Breakthrough curve measurements are crucial for optimizing adsorption processes, understanding mass transfer phenomena, and designing efficient adsorption systems. An important parameter was studied, mass transfer zone (MTZ) (see Eq. (1)), which characterizes the region in the adsorbent bed where significant mass transfer occurs between fluid and solid phases, marking the transition from breakthrough to saturation:

$$MTZ = H \left( \frac{t_s - t_b}{t_s} \right) \qquad (1)$$

where H is the length of the adsorbent in the column (cm), t<sub>b</sub> and t<sub>s</sub> are the breakthrough time (min) and saturation time (min), respectively.

At the first point, the adsorption capacity of gas into the adsorbent under dynamic conditions is calculated using the following relation:

$$n_{ads,i} = \frac{t_i 60 Q P_a(y_{g,init} - y_{g,i})}{100 mRT} \qquad (2)$$

Then, an accumulative method was chosen to carry out the adsorption isotherm between each measurement, and the adsorption capacities of gases were determined using the following equation:

$$n_{ads,i} = n_{g,i-1} + \frac{60(t_i - t_{i-1}) Q P_a(y_{g,init} - y_{g,i})}{100 mRT} \qquad (3)$$

where m is the mass of the sample (g), Q is the volumetric flow rate of the inlet gas (m³ s⁻¹), P<sub>a</sub> is the atmospheric pressure of the system (Pa), t<sub>1</sub> and t<sub>i</sub> (min) are the time of the first gas sampling and the latter points, respectively. n<sub>ads,i</sub> and n<sub>ads,i</sub> are the amount of gas adsorbed for the first point and the latter points, respectively, and y<sub>g,init</sub> and y<sub>g,i</sub> are the mole fraction of gas in the bulk phase at the initial conditions and at time t, respectively.

## 2.4. Adsorption performance indicator (API)

API was used to assess the adsorption performance of the CNR-115 family for separating 40%/60% (vol.) CO₂/CH₄ gas mixture under dry conditions. API was proposed by Wiersum et al. [38] and it integrates the true selectivity, CO₂ adsorption capacity in the mixture, and the
<figure><img src="image_3.png" /><figcaption>Fig. 2. Schematic of breakthrough curves setup under dry and wet conditions.</figcaption></figure>

heat of CO₂ adsorption. As the objective is to remove CO₂ molecules from CH₄ molecules. In this regard, we gave higher importance to the parameter “adsorption capacity” with an exponent “B = 2”, but the exponents (A and C, see Eq. (4)) of the two remaining parameters are kept to 1. This indicator was also applied in our previous study to evaluate the adsorption performance of ACs of the CNR-115 family in static conditions for the binary equimolar CO₂/CH₄ mixture [39]. An adsorbent that has a higher selectivity and adsorption capacity together with a lower heat of adsorption is considered the ideal material for biogas separation, but it is rare to find one that combines these three properties at the same time. The following form can present the API relation:

$$API = \frac{(S_{CO_2/CH_4} - 1)^A n_{ads,CO_2}^B}{|\Delta H_{ads,CO_2}|^C} \quad (4)$$

where S<sub>CO₂/CH₄</sub> is the selectivity of CO₂ over CH₄, calculated as follows:

$$S_{CO_2/CH_4} = \frac{y_{CH_4}/y_{CO_2}}{n_{ads,CH_4}/n_{ads,CO_2}} \quad (5)$$

n<sub>ads,CO₂</sub> and n<sub>ads,CH₄</sub> correspond to the adsorption capacities of the stronger adsorbate component (CO₂) and CH₄, respectively. The molar fractions, y<sub>CO₂</sub> and y<sub>CH₄</sub>, represent the molar fractions of CO₂ and CH₄ in the bulk phase, respectively. Additionally, ΔH<sub>ads,CO₂</sub> is the heat of CO₂ adsorption. A, B, and C are the exponents of the selectivity, the adsorption capacity and the heat of CO₂ adsorption, respectively. In this study, selectivity refers to the equilibrium-based selectivity, and the heat of CO₂ adsorption (ΔH<sub>ads,CO₂</sub>) corresponds to the integral heat of adsorption, determined by integrating the adsorption isotherm with the enthalpy change measured using a high-pressure differential scanning calorimeter (micro DSC VII, Setaram).

### 3. Results and discussions

#### 3.1. Upgrading 40%/60% (vol.) CO₂/CH₄ gas mixture under dry conditions

##### 3.1.1. Breakthrough curves for 40%/60% (vol.) CO₂/CH₄ gas mixture under dry conditions

The dynamic behavior of CNR-115-ox and CNR-115-ox-am at 303 K and 0.1 MPa was studied using a dry binary 40%/60% (vol.) CO₂/CH₄

mixture, representative of the typical CO₂ and CH₄ concentrations found in biogas. The breakthrough curves for this dry mixture on CNR-115-ox and CNR-115-ox-am reveal three distinct phases (marked as (1), (2), and (3) in the Fig. 3(a and b)). Initially, in the breakthrough phase (1), CH₄, the weaker adsorbate, quickly breaks through the fixed-bed column, allowing the two gases to separate, as evidenced by the similar trend observed in recent studies [40,41]. The next stage is the competition phase (2), where CH₄ exhibits a roll-up effect (desorption phase) due to CO₂'s preferential adsorption, causing a temporary increase in CH₄ flow rate above the feed flow rate as CH₄ molecules desorb to accommodate advancing CO₂ molecules. CO₂ begins to break through the column precisely when CH₄ reaches the peak of its roll-up, resulting in an increase in CO₂ concentration and a simultaneous decrease in methane concentration at the outlet [41]. In the saturation phase (3), concentrations of both CO₂ and CH₄ stabilize at the outlet, aligning with the feed concentration levels. Recent studies on CO₂/CH₄ separation using ACs report similar trends and observe the roll-up effect [28,42,43].

The comparison between CNR-115-ox and CNR-115-ox-am reveals significant differences in adsorption behavior (Fig. 3(a and b)), reflecting their distinct surface modifications (Table 1). For both adsorbents, CO₂ shows consistently higher breakthrough and saturation times than CH₄, indicating a stronger interaction with CO₂. CNR-115-ox, which was oxidized to increase oxygen-containing functional groups, exhibits longer breakthrough times for both CH₄ (4.2 min) and CO₂ (12.0 min) compared to CNR-115-ox-am (3.5 min for CH₄ and 9.0 min for CO₂). The CO₂ saturation time for CNR-115-ox (29.0 min) is also longer than for CNR-115-ox-am (21.0 min), suggesting higher adsorption capacity and affinity for CO₂ at 0.1 MPa and 303 K (Table 2). This enhanced performance is attributed to CNR-115-ox's higher BET surface area and pore volume (micropores and mesopores) (929 m² g⁻¹ and 0.45 cm³ g⁻¹) compared to CNR-115-ox-am (352 m² g⁻¹ and 0.21 cm³ g⁻¹) [35].

At 303 K and 0.1 MPa, both CH₄ and CO₂ adsorption capacities decreased after treatment with ammonia vapor, with CH₄ dropping from 0.16 ± 0.02 to 0.11 ± 0.01 mol kg⁻¹ and CO₂ from 0.44 ± 0.04 to 0.27 ± 0.03 mol kg⁻¹ (Fig. 4(a and b) and Table 2). This reduction indicates that the ammonium vapor treatment adversely affects the material's ability to adsorb gases. The roll-up width, indicating competition between CO₂ and CH₄, is narrower for CNR-115-ox compared to CNR-115-ox-am, indicating that CNR-115-ox-am displaces more CH₄
<figure><img src="image_4.png" /><figcaption>Fig. 3. Breakthrough curves for CO₂ and CH₄ in 40%/60% (vol.) CO₂/CH₄ gas mixture on (a) CNR-115-ox and (b) CNR-115-ox-am at 0.1 MPa and 303 K. The three phases in the breakthrough process: (1) breakthrough, (2) competition (roll-up effect), and (3) saturation.</figcaption></figure>

with CO₂, resulting in lower CH₄ adsorption at equilibrium due to its basic character (Fig. 3). The longer CO₂ retention time in CNR-115-ox (20.5 min) compared to CNR-115-ox-am (15.0 min) is due to its larger BET surface area and pore volume. However, ammonium vapor treatment introduces nitrogen groups that enhance CO₂ affinity but also block pores, reducing surface area (352 m² g⁻¹) and pore volume (0.21 cm³ g⁻¹) in CNR-115-ox-am (Table 1). This results in lower adsorption capacities for both CO₂ (0.27 ± 0.03 mol kg⁻¹) and CH₄ (0.11 ± 0.01 mol kg⁻¹) in CNR-115-ox-am.

The heat of CO₂ adsorption on CNR-115-ox and CNR-115-ox-am, previously determined in our earlier study [39], are summarized in Table 2. The selectivity of CNR-115-ox and CNR-115-ox-am for CO₂/CH₄ separation was assessed qualitatively and quantitatively. Qualitatively, a greater time difference between CO₂ and CH₄ breakthrough indicates better separation efficiency [28]. Fig. 3 shows that CNR-115-ox has higher selectivity than CNR-115-ox-am, with breakthrough times of 12.0 min for CO₂ and 4.2 min for CH₄, compared to 9.0 min and 3.5 min, respectively, for CNR-115-ox-am. Quantitative analysis confirms this, with selectivity dropping from 4.13 ± 0.05 to 3.68 ± 0.04 after ammonia treatment (Table 2). This is attributed to the higher

CO₂ adsorption capacity of CNR-115-ox (0.44 ± 0.04 mol kg⁻¹), nearly double that of CNR-115-ox-am (0.27 ± 0.03 mol kg⁻¹). The API also decreases significantly after ammonia treatment, from 0.02 ± 0.01 to 0.007 ± 0.004, indicating that while ammonium vapor treatment introduces nitrogen groups, it reduces the overall adsorption capacity and efficiency for both gases.

Selectivity of the dynamic experiments of the ACs CNR-115-ox and CNR-115-ox-am at 303 K and 0.1 MPa aligns well with literature values for CO₂/CH₄ separation (see Table 3). Both adsorbents outperform some commercial ACs such as Desotec (selectivity of 2.89) [43], Calgon BPL (3.57) [42], and Norit C (3.33) [44], despite these having higher CO₂ adsorption capacities of 1.27, 1.18, and 1.50 mol kg⁻¹, respectively, at 298 K for an equimolar CO₂/CH₄ mixture. The superior selectivity of the CNR-115 adsorbents is attributed to surface modifications with oxygen and ammonia. Although these modifications reduce the surface area and, consequently, the overall CO₂ and CH₄ adsorption capacities, they preferentially enhance CO₂ adsorption over CH₄ with selectivities of 4.13 ± 0.05 and 3.68 ± 0.04 for CNR-115-ox and CNR-115-ox-am, respectively. Other adsorbents, such as two carbon molecular sieves from Carbotech and Xintao, demonstrate even higher
<figure><img src="image_5.png" /><figcaption>**Fig. 4.** Variation of CO₂ and CH₄ adsorption capacities versus time of 40%/60% (vol.) CO₂/CH₄ gas mixture on (a) CNR-115-ox and (b) CNR-115-ox-am at 0.1 MPa and 303 K under adsorption in dynamic conditions.</figcaption></figure>

<caption>**Table 2**</caption>

Experimental results obtained from breakthrough curves for 40%/60% (vol.) CO₂/CH₄ gas mixture into CNR-115-ox and CNR-115-ox-am under dry conditions at 0.1 MPa and 303 K.

<table><thead><tr><th>Parameters</th><th>CNR-115-ox</th><th>CNR-115-ox-am</th></tr></thead><tbody><tr><td>CH₄ breakthrough time (min)</td><td>4.2</td><td>3.5</td></tr><tr><td>CH₄ saturation time (min)</td><td>28.5</td><td>23.0</td></tr><tr><td>CO₂ breakthrough time (min)</td><td>12.0</td><td>9.0</td></tr><tr><td>CO₂ saturation time (min)</td><td>29.0</td><td>21.0</td></tr><tr><td>CO₂ mass transfer zone (cm)</td><td>19.3</td><td>18.8</td></tr><tr><td>CO₂ retention Time (t<sub>r</sub>)</td><td>20.5</td><td>15.0</td></tr><tr><td>CH₄ adsorption capacity (mol kg<sup>-1</sup>)</td><td>0.16 ± 0.02</td><td>0.11 ± 0.01</td></tr><tr><td>CO₂ adsorption capacity (mol kg<sup>-1</sup>)</td><td>0.44 ± 0.04</td><td>0.27 ± 0.03</td></tr><tr><td>Selectivity (CO₂/CH₄)</td><td>4.13 ± 0.05</td><td>3.68 ± 0.04</td></tr><tr><td>Heat of CO₂ adsorption (kJ mol<sup>-1</sup>)</td><td>26.8 ± 0.4</td><td>28.0 ± 0.3</td></tr><tr><td>API</td><td>0.02 ± 0.01</td><td>0.007 ± 0.004</td></tr></tbody></table>

selectivity for CO₂ over CH₄, with selectivities of 15.07 and 12.71, respectively (see Table 3). Carbotech exhibits the highest selectivity among the samples studied, attributed to its kinetic sieving characteristics. Its narrower mean pore diameter (around 0.4 nm) effectively prevents the diffusion of larger CH₄ molecules into the pores [43].

### 3.1.2. Comparison between adsorption in dynamic and static conditions for 40%/60% (vol.) CO₂/CH₄ gas mixture under dry conditions

The adsorption performance of CNR-115-ox and CNR-115-ox-am was evaluated under dynamic conditions (breakthrough curves) in this study and compared with static adsorption data from Ho Bich-Ngoc [46] (Table 4). Results show reasonable agreement, with Root Mean Square Error values of 0.05 for CH₄ and 0.14 for CO₂, confirming consistency between the dynamic and static results [46]. The stability of modified ACs (CNR-115-ox and CNR-115-ox-am) was evaluated through 10 cycles of CO₂ adsorption in static conditions at 303K by Peredo-Mancilla et al. [35]. CO₂ was chosen due to its stronger interaction with the adsorbent than CH₄, making it a reliable stability indicator. A consistent adsorption performance with minimal deviations was observed, confirming the high regenerability and stability of these materials for carbon capture [35].

The results provided in Table 4 demonstrate that, despite a notable decrease in micropore area from 469 to 168 m² g⁻¹ as a result of ammonia vapor treatment, CNR-115-ox-am exhibits significantly higher adsorption capacities when normalized by micropore surface area, which is more representative of the active adsorption sites for small gas molecules. Specifically, the CO₂ adsorption per unit micropore area
<caption>**Table 3**</caption>

Comparison of CO₂ and CH₄ adsorption capacities, breakthrough times and selectivities of the dynamic experiments at 0.1 MPa feeding a binary CO₂/CH₄ mixture.

<table><caption>**Table 4**</caption><thead><tr><th>Adsorbents</th><th>S<sub>BET</sub><br>(m² g<sup>-1</sup>)</th><th>T<br>(K)</th><th>Flow rate<br>(Nm l min<sup>-1</sup>)</th><th>CO₂ feed<br>(%)</th><th>t<sub>b</sub> CH₄<br>(min)</th><th>t<sub>b</sub> CO₂<br>(min)</th><th>AdC(CO₂)<br>(mol kg<sup>-1</sup>)</th><th>AdC(CH₄)<br>(mol kg<sup>-1</sup>)</th><th>S</th><th>Ref</th></tr></thead><tbody><tr><td><strong>Activated carbons</strong></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CNR-115-ox</td><td>929</td><td>303</td><td>30</td><td>40</td><td>4.2</td><td>12</td><td>0.44</td><td>0.16</td><td>4.13</td><td>This study</td></tr><tr><td>CNR-115-ox-am</td><td>352</td><td>303</td><td>30</td><td>40</td><td>3.5</td><td>9</td><td>0.27</td><td>0.11</td><td>3.68</td><td>This study</td></tr><tr><td>CS-CO₂</td><td>1045</td><td>303</td><td>30</td><td>50</td><td>5.9</td><td>9.6</td><td>1.63</td><td>0.47</td><td>3.47</td><td>[42]</td></tr><tr><td>CS-H₂O</td><td>998</td><td>303</td><td>30</td><td>50</td><td>6.1</td><td>10.3</td><td>1.49</td><td>0.37</td><td>4.03</td><td>[42]</td></tr><tr><td>Calgon BPL</td><td>1129</td><td>303</td><td>30</td><td>50</td><td>6.9</td><td>10.9</td><td>1.18</td><td>0.33</td><td>3.57</td><td>[42]</td></tr><tr><td>Norit C</td><td>1361</td><td>298</td><td>30</td><td>50</td><td>0.98</td><td>2.09</td><td>1.50</td><td>0.45</td><td>3.33</td><td>[44]</td></tr><tr><td>No1KCl-600</td><td>1091</td><td>298</td><td>30</td><td>50</td><td>3.85</td><td>6.65</td><td>2.03</td><td>0.80</td><td>2.54</td><td>[44]</td></tr><tr><td>No1KClb-1000</td><td>804</td><td>298</td><td>30</td><td>50</td><td>3.61</td><td>6.42</td><td>1.91</td><td>0.71</td><td>2.69</td><td>[44]</td></tr><tr><td>No2OS-1000</td><td>1233</td><td>298</td><td>30</td><td>50</td><td>2.91</td><td>5.52</td><td>1.83</td><td>0.43</td><td>4.26</td><td>[44]</td></tr><tr><td>Pine sawdust</td><td>788</td><td>303</td><td>15</td><td>50</td><td>10.97</td><td>18.00</td><td>2.05</td><td>0.40</td><td>5.12</td><td>[28]</td></tr><tr><td>Pine sawdust</td><td>788</td><td>303</td><td>30</td><td>50</td><td>5.56</td><td>9.57</td><td>2.00</td><td>0.37</td><td>5.40</td><td>[28]</td></tr><tr><td>50CPDA@A-C</td><td>1841</td><td>298</td><td>2</td><td>50</td><td>2.1</td><td>14.8</td><td>2.51</td><td>0.49</td><td>5.1</td><td>[45]</td></tr><tr><td>Desotec</td><td>970</td><td>303</td><td>700</td><td>40</td><td>30</td><td>61</td><td>1.27</td><td>0.66</td><td>2.89</td><td>[43]</td></tr><tr><td><strong>Carbon molecular sieves</strong></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Carbotech</td><td>400</td><td>303</td><td>700</td><td>40</td><td>1</td><td>21</td><td>1.32</td><td>0.13</td><td>15.07</td><td>[43]</td></tr><tr><td>Xintao</td><td>n.a</td><td>303</td><td>700</td><td>40</td><td>0.1</td><td>25</td><td>1.14</td><td>0.13</td><td>12.71</td><td>[43]</td></tr></tbody></table>

Comparison of CH₄ and CO₂ adsorption capacities for CO₂/CH₄ mixture in dynamic (This study) and static [46] conditions at 0.1 MPa, including adsorption capacities normalized by micropore area.

<table><thead><tr><th>Property</th><th>CNR-115-ox</th><th>CNR-115-ox-am</th></tr></thead><tbody><tr><td>BET surface area (m² g<sup>-1</sup>)</td><td>929</td><td>352</td></tr><tr><td>Micropore area (m² g<sup>-1</sup>)</td><td>469</td><td>168</td></tr><tr><td><strong>CH₄ adsorption (mol kg<sup>-1</sup>)</strong></td><td></td><td></td></tr><tr><td>Dynamic (This study)</td><td>0.16 ± 0.02</td><td>0.11 ± 0.01</td></tr><tr><td>Static [46]</td><td>0.14 ± 0.01</td><td>0.08 ± 0.01</td></tr><tr><td><strong>CO₂ adsorption (mol kg<sup>-1</sup>)</strong></td><td></td><td></td></tr><tr><td>Dynamic (This study)</td><td>0.44 ± 0.04</td><td>0.27 ± 0.03</td></tr><tr><td>Static [46]</td><td>0.46 ± 0.01</td><td>0.20 ± 0.01</td></tr><tr><td><strong>Normalized adsorption per micropore area (mol m<sup>-2</sup>, ×10<sup>-7</sup>)</strong></td><td></td><td></td></tr><tr><td>CH₄ (Dynamic)</td><td>3.41</td><td>6.54</td></tr><tr><td>CO₂ (Dynamic)</td><td>9.38</td><td>16.1</td></tr></tbody></table>

under dynamic conditions increased from 9.38 × 10⁻⁷ mol m⁻² for CNR-115-ox to 16.1 × 10⁻⁷ mol m⁻² for CNR-115-ox-am, while CH₄ adsorption rose from 3.41 × 10⁻⁷ to 6.54 × 10⁻⁷ mol m⁻². These results underscore the enhanced adsorption efficiency of CNR-115-ox-am, despite its lower total and micropore surface areas (469 m² g⁻¹ vs. 168 m² g⁻¹). The use of micropore-normalized adsorption is particularly appropriate in this study, as CO₂ and CH₄ are primarily adsorbed in micropores, and BET surface area may include external and mesoporous contributions that are less relevant to adsorption performance. The higher adsorption per micropore area supports the conclusion that nitrogen functionalities introduced during ammonia treatment improve specific interactions with CO₂ and CH₄, likely due to increased basicity, altered surface polarity, and improved pore accessibility. These findings emphasize that surface chemistry modifications can outweigh surface area reduction in determining adsorption behavior, making CNR-115-ox-am a promising candidate for selective CO₂ capture.

## 3.2. Breakthrough curves for the gas mixture 39%/59%/2% (vol.) CO₂/CH₄/H₂O under wet conditions

Biogas typically contains 1%–5% water vapor, necessitating an understanding of how water vapor affects the separation of CO₂/CH₄ mixtures to understand the real behavior of the biogas upgrading. Most of recent studies have predominantly treated biogas as a dry CO₂/CH₄ mixture, with limited exploration of adsorbents’ performance in the presence of water vapor [28,34,47]. To address this gap, a ternary

CO₂/CH₄/H₂O gas mixture was introduced to fresh beds of CNR-115-ox and CNR-115-ox-am at 303 K and 0.1 MPa. The total gas flow rate was 30 Nml min⁻¹, consisting of 2% (vol.) water vapor (H₂O) and a 39%/59% (vol.) CO₂/CH₄ gas mixture. The breakthrough curves for CO₂ and CH₄ in this ternary gas mixture revealed distinct adsorption behaviors influenced by water vapor, evident from the differences observed compared to dry conditions (see Figs. 3 and 5). The CH₄ breakthrough curves show the same characteristic roll-up as in the dry experiments. Nevertheless, CO₂ breakthrough curves showed a slight roll-up pattern attributed to H₂O(g) co-adsorption (see Fig. 5 (a and b)).

For CNR-115-ox, the breakthrough times for CH₄ and CO₂ are 3.7 min and 32.8 min, respectively, as shown in Table 5. Conversely, CNR-115-ox-am exhibits shorter breakthrough times of 3.0 min for CH₄ and longer times of 42.2 min for CO₂, indicating that CH₄ passes through the adsorbent bed more quickly than CO₂. This suggests stronger interactions between CO₂ molecules and the adsorbent surface, likely due to the presence of oxygen and nitrogen groups. Moreover, CNR-115-ox-am shows higher breakthrough and saturation times for CO₂ (42.2 min and 52.2 min, respectively) compared to CNR-115-ox (32.8 min and 42.7 min, respectively), highlighting its enhanced capability to retain CO₂ molecules in the presence of water vapor. This improvement is attributed to the additional NH₄OH treatment, which enhances the adsorption performance of CNR-115-ox-am (Fig. 6). The CO₂ MTZ further reveals insights into adsorption efficiency, CNR-115-ox exhibits a wider MTZ for CO₂ (7.6 cm), while CNR-115-ox-am shows a narrower MTZ (6.3 cm), indicating improved adsorption strength and CO₂ capacity due to the presence of nitrogen surface groups.

By comparing the breakthrough curves for the two modified ACs of CNR-115 family under dry and wet conditions (Figs. 3 and 5), CO₂ exhibits significantly prolonged breakthrough times under wet conditions for both CNR-115-ox (32.8 min) and CNR-115-ox-am (42.2 min), compared to dry conditions (12.0 min and 9.0 min, respectively). This indicates enhanced CO₂ retention in the presence of water vapor. This unexpected enhancement in CO₂ adsorption capacities and CO₂/CH₄ dynamic selectivity for CNR-115-ox and CNR-115-ox-am contrasted with trends observed for other ACs of the CO₂/CH₄ mixture under wet conditions [28,34]. Conversely, CH₄ breakthrough times decrease under wet conditions (3.7 min for CNR-115-ox and 3.0 min for CNR-115-ox-am) compared to dry conditions (4.2 min and 3.5 min, respectively), suggesting reduced interaction between CH₄ and the adsorbent material due to gas competition in the presence of water vapor.

A significant increase in CO₂ adsorption capacity under wet conditions was observed for both CNR-115-ox and CNR-115-ox-am compared
<figure><img src="image_6.png" /><figcaption>Fig. 5. Breakthrough curves for CO₂ and CH₄ in the mixture (39%/59%/2% (vol.) CO₂/CH₄/H₂O on (a) CNR-115-ox and (b) CNR-115-ox-am at 0.1 MPa and 303 K. The three phases in the breakthrough process: (1) breakthrough, (2) competition (roll-up effect), and (3) saturation.</figcaption></figure>

to dry conditions. Specifically, CNR-115-ox exhibited an increase from 0.44 ± 0.04 to 0.76 ± 0.06 mol kg⁻¹, corresponding to a factor of 1.7, while CNR-115-ox-am increased from 0.27 ± 0.03 to 0.96 ± 0.09 mol kg⁻¹, corresponding to a factor of 3.5 (Table 5). The higher CO₂ adsorption capacity of CNR-115-ox-am, especially in the presence of water vapor, can be attributed to the enhanced interaction between nitrogen groups and CO₂ (see reactions (6) and (7)), facilitating the formation of bicarbonates under wet conditions compared to carbamates under dry conditions [48,49]. Although this mechanism has not been directly confirmed in this study due to the unavailability of spectroscopic tools such as FTIR or XPS, it is supported by previous reports. Irani et al. [27] demonstrated that under wet conditions, approximately 1 mol of CO₂ is adsorbed per mole of amine, while under dry conditions, it is approximately 0.5 mol of CO₂ per mole of amine [27,48]. Further investigation using advanced characterization techniques is needed to confirm the formation and role of bicarbonate species in the current system.

In summary, under dry conditions, the superior CO₂ adsorption capacity of CNR-115-ox can be linked to its higher BET surface area (929 m² g⁻¹) and micropore volume (0.36 cm³ g⁻¹), which favor physisorption. In contrast, the dramatic increase in CO₂ adsorption

capacity for CNR-115-ox-am under wet conditions highlights the dominant role of nitrogen functional groups via bicarbonate formation, especially in the presence of water vapor. This contrast underscores the complementary effects of textural and chemical properties, with CNR-115-ox excelling in physical adsorption environments and CNR-115-ox-am showing enhanced performance when chemical interactions are favored. The enhancement of CO₂ adsorption under humid conditions, particularly for CNR-115-ox-am, suggests a synergistic rather than competitive interaction between CO₂ and H₂O. This behavior contrasts with commonly reported trends where water vapor competes with CO₂ for adsorption sites on hydrophilic surfaces. In this study, it is proposed that the introduction of nitrogen functionalities increases the surface hydrophilicity and facilitates cooperative adsorption mechanisms. Although direct measurements such as water adsorption isotherms or contact angle analysis were not conducted, the observed trends align with previous findings on amine-functionalized adsorbents [27,48]. Future investigations will include such characterizations to confirm the proposed co-adsorption behavior and further elucidate the role of surface chemistry.

The possible reactions under wet conditions that lead to the increase of CO₂ adsorption for CNR-115-ox-am include:

$$R_1NH_2 + CO_2 + H_2O \rightleftharpoons (R_1NH_3^+)(HCO_3^-) \quad (6)$$
<table><caption>**Table 5**
Experimental conditions and results obtained for CO₂/CH₄ gas mixture into both CNR-115-ox and CNR-115-ox-am under dry and wet conditions.</caption><thead><tr><th rowspan="2">Parameters</th><th colspan="2">CNR-115-ox</th><th colspan="2">CNR-115-ox-am</th></tr><tr><th>Dry</th><th>Wet</th><th>Dry</th><th>Wet</th></tr></thead><tbody><tr><td>CH₄ breakthrough time (min)</td><td>4.2</td><td><strong>3.7</strong></td><td>3.5</td><td><strong>3.0</strong></td></tr><tr><td>CH₄ saturation time (min)</td><td>28.5</td><td><strong>41.5</strong></td><td>23.0</td><td><strong>53.5</strong></td></tr><tr><td>CO₂ breakthrough time (min)</td><td>12.0</td><td><strong>32.8</strong></td><td>9.0</td><td><strong>42.2</strong></td></tr><tr><td>CO₂ saturation time (min)</td><td>29.0</td><td><strong>42.7</strong></td><td>21.0</td><td><strong>52.2</strong></td></tr><tr><td>CO₂ mass transfer zone (cm)</td><td>19.3</td><td><strong>7.6</strong></td><td>18.8</td><td><strong>6.3</strong></td></tr><tr><td>CH₄ adsorption capacity (mol kg⁻¹)</td><td>0.16 ± 0.02</td><td><strong>0.14 ± 0.01</strong></td><td>0.11 ± 0.01</td><td><strong>0.08 ± 0.01</strong></td></tr><tr><td>CO₂ adsorption capacity (mol kg⁻¹)</td><td>0.44 ± 0.04</td><td><strong>0.76 ± 0.06</strong></td><td>0.27 ± 0.03</td><td><strong>0.96 ± 0.09</strong></td></tr><tr><td>Normalized CH₄ adsorption (mol m⁻²)</td><td>3.41 × 10⁻⁷</td><td><strong>2.98 × 10⁻⁷</strong></td><td>6.54 × 10⁻⁷</td><td><strong>4.76 × 10⁻⁷</strong></td></tr><tr><td>Normalized CO₂ adsorption (mol m⁻²)</td><td>9.38 × 10⁻⁷</td><td><strong>16.2 × 10⁻⁷</strong></td><td>16.1 × 10⁻⁷</td><td><strong>57.1 × 10⁻⁷</strong></td></tr><tr><td>Selectivity (CO₂/CH₄)</td><td>4.13 ± 0.05</td><td><strong>8.14 ± 0.06</strong></td><td>3.68 ± 0.04</td><td><strong>18.0 ± 0.2</strong></td></tr></tbody></table>

$$R_1 R_2 \text{NH} + \text{CO}_2 + \text{H}_2\text{O} \rightleftharpoons (R_1 R_2 \text{NH}_2^+) (\text{HCO}_3^-) \quad (7)$$

Under humid conditions, both CNR-115-ox and CNR-115-ox-am exhibited reduced CH₄ adsorption capacities (0.14 ± 0.01 and 0.08 ± 0.01 mol kg⁻¹, respectively) compared to dry conditions (0.16 ± 0.02 and 0.11 ± 0.01 mol kg⁻¹, respectively) (see Tables 2 and 5). This decrease in CH₄ adsorption is primarily attributed to the competitive adsorption behavior induced by the presence of water vapor and CO₂. Consequently, this leads to greater selectivity for CO₂ adsorption, as evidenced by both the significant difference in breakthrough times between CO₂ and CH₄, and the theoretical selectivity equation, which showed substantial increases for CNR-115-ox-am and CNR-115-ox (18.0 ± 0.2 and 8.14 ± 0.06, respectively) under humid conditions compared to dry conditions (3.68 ± 0.04 and 4.13 ± 0.05, respectively) (Table 5). Thus, CNR-115-ox-am demonstrates enhanced suitability for effectively separating the mixture, with CO₂ being more strongly retained and efficiently separated from CH₄.

Under wet conditions, both materials exhibited a substantial increase in CO₂ adsorption per unit area, suggesting that moisture plays a key role in enhancing CO₂ uptake. Specifically, CNR-115-ox exhibited an increase in normalized CO₂ adsorption from 9.38 × 10⁻⁷ mol m⁻² in dry conditions to 16.2 × 10⁻⁷ mol m⁻² in wet conditions, while CNR-115-ox-am showed an even greater enhancement from 16.1 × 10⁻⁷ mol m⁻² to 57.1 × 10⁻⁷ mol m⁻² (Table 5). This suggests that the nitrogen functionalities in CNR-115-ox-am improve CO₂ adsorption efficiency in the presence of water, likely by facilitating bicarbonate formation. In contrast, normalized CH₄ adsorption capacities decreased slightly under wet conditions for both materials, further supporting the hypothesis that water competes with CH₄ for adsorption sites. This decrease in CH₄ adsorption per unit surface area reinforces the trend observed in total adsorption capacity, where water limits CH₄ uptake while promoting CO₂ selectivity.

### 3.3. Adsorption selectivity of CO₂/CH₄ in wet conditions: comparative performance of various adsorbents

Fig. 7 provides a comparison of adsorption selectivities for CO₂/CH₄ among various adsorbents based on breakthrough curves in wet conditions at 0.1 MPa. CNR-115-ox-am demonstrates the highest selectivity value of 18.0 ± 0.2 for the CO₂/CH₄ mixture in conditions reflecting the real composition of biogas, which typically includes water vapor. This highlights its exceptional efficiency in preferentially adsorbing CO₂ over CH₄, even under conditions where water vapor may compete for adsorption sites and potentially interfere with the process. CNR-115-ox-am also demonstrates significant performance with a selectivity of 8.14 ± 0.06, outperforming numerous other adsorbents. In contrast, MOFs generally exhibit lower selectivity values under wet conditions, with MIL-100(Cr) showing selectivity of 3.70 at 2% water vapor by volume, 303 K, and 1 bar. This is attributed to their hydrophilic nature, which favors the adsorption of water vapor over CO₂ and CH₄, consequently lowering their selectivity. However, modified MOFs like MIL-100(Fe) achieve a high selectivity of 16.3 under the same

conditions (2% water vapor by volume, 303 K, 1 bar), due to the formation of alkaline adsorptive sites, indicating their potential for effective CO₂ capture and separation from biogas even in the presence of water vapor [23]. Similarly, zeolite 13X exhibits a high selectivity value of 14.5, underscoring its effectiveness as an adsorbent under similar conditions despite its hydrophilic nature [34]. However, AC such as pine-sawdust-AC shows a significantly lower selectivity value of 3.4 at 2% water vapor by volume, 303 K, and 1 bar [28], while commercial CAC BX 30 achieves a slightly higher selectivity of 5.4 at 3% water vapor by volume, 298 K, and 1 bar. This suggests they are less effective at separating CO₂ from CH₄ in the presence of water vapor, likely due to competition with water vapor molecules for active adsorption sites, which diminishes their selectivity. It should be noted that all reported comparisons were performed under approximately the same operating conditions (pressure of 1 bar, water vapor content between 2%–3%, and temperatures ranging from 298 to 303 K), allowing for a reasonably fair comparison of performance across materials.

### 4. Conclusions and perspectives

In this study, the adsorption performance of the modified ACs from the CNR-115 family (CNR-115-ox, and CNR-115-ox-am) for CO₂/CH₄ separation was assessed under fry and wet dynamic conditions. The calculated heat of CO₂ adsorption for CNR-115-ox and CNR-115-ox-am fell within the physisorption range (<40 kJ mol⁻¹). Breakthrough curves, plotted at 0.1 MPa and 303 K, revealed three phases: breakthrough, competition between CO₂ and CH₄, and saturation. CO₂ consistently showed higher breakthrough and saturation times than CH₄, indicating stronger interactions with the adsorbents of the CNR-115 family. Adsorption in dry dynamic conditions experiments of a 40%/60% (vol.) CO₂/CH₄ gas mixture showed that CH₄ exhibits a roll-up effect due to the preferential adsorption of CO₂, which was more pronounced in CNR-115-ox. CNR-115-ox demonstrated higher separation efficiency than CNR-115-ox-am, attributed to its high BET surface area (929 m² g⁻¹) and the presence of oxygen groups. The results indicate that the dry dynamic adsorption performance of CNR-115-ox and CNR-115-ox-am showed strong agreement with the static adsorption data, confirming the reliability of the results. The increase in CO₂ adsorption per unit area demonstrates that nitrogen functionalization improves selectivity and adsorption efficiency, making CNR-115-ox-am a promising candidate for biogas upgrading. The CH₄ breakthrough curves for a ternary 39%/59%/2% (vol.) CO₂/CH₄/H₂O gas mixture at 303 K and 0.1 MPa exhibited the same roll-up effect as in the dry experiments, while the CO₂ curves showed a slight roll-up due to H₂O co-adsorption. Water vapor significantly impacted the CO₂ adsorption behavior, enhancing CO₂ retention and selectivity under wet conditions. Notably, CNR-115-ox-am showed higher CO₂ adsorption capacities and selectivity values in the presence of water vapor, likely due to the formation of bicarbonates. This highlights the importance of accounting for water vapor in the biogas upgrading process to optimize adsorption performance. CNR-115-ox-am proves more effective for separating CO₂ from
<figure><img src="image_7.png" /><figcaption>Fig. 6. Variation of CO₂ and CH₄ adsorption capacities in the mixture (39%/59%/2%) (vol.) CO₂/CH₄/H₂O on (a) CNR-115-ox and (b) CNR-115-ox-am at 0.1 MPa and 303 K.</figcaption></figure>

the mixture, with CO₂ being more strongly retained and efficiently separated from CH₄ compared to CNR-115-ox due to the NH₄OH treatment. Future studies should focus on the regeneration and reuse of ACs under wet conditions to assess their long-term performance in industrial applications. Additionally, investigating the physical and chemical properties of adsorbents in humid environments is essential to confirm that surface chemistry modifications play a more dominant role in gas adsorption performance. This is essential to optimize material design and improve adsorption efficiency. Moreover, since biogas contains various impurities, future research should investigate the separation performance of activated carbons using real industrial biogas. These efforts will advance the development of more efficient and durable adsorbents for large-scale biogas upgrading.

### CRediT authorship contribution statement

**Khaled Abou Alfa:** Methodology, Visualization, Investigation, Data curation, Writing – original draft, Software, Validation, Resources, Formal analysis, Conceptualization. **Nour Abou Saleh:** Formal analysis, Investigation, Methodology, Data curation. **Camélia Matei Ghimbeu:** Resources, Methodology. **Bénédicte Réty:** Methodology. **Vincent

**Platel:** Supervision, Validation, Resources. **Cecile Hort:** Supervision, Resources, Writing – review & editing, Funding acquisition, Validation.

### Funding

This research was carried under the framework of E2S UPPA supported by the "Investissements d'Avenir" French programme managed by ANR, France (ANR-16-IDEX-0002).

### Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Cecile Hort reports financial support was provided by E2S UPPA.

### Data availability

Data will be made available on request.
<figure><img src="image_8.png" /><figcaption>Fig. 7. Comparison of adsorption in dynamic conditions Selectivity of the modified CNR-115 family with other adsorbents for CO₂/CH₄ in the presence of water vapor at 0.1 MPa. Data sources; (1): [34], (2): [28], and (3): [23].</figcaption></figure>

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