Experimental Studies of Methane Adsorption on Activated Carbon and 3D Graphene Materials

Abstract

Two kinds of slit pore carbon materials, namely activated carbon (AC) and 3D graphene materials (3D-GS), were purchased to examine their methane storage capabilities. The structural analysis and characterization of AC and 3D-GS were carried out using X-ray diffraction (XRD), scanning electron microscopy (SEM), the X-ray energy dispersive spectrum (EDS), and N₂ adsorption/desorption isotherms. Additionally, a thermodynamic framework was employed in the Henry’s law region to evaluate the potential well between the adsorbed fluid and adsorbent. The adsorption behavior of methane on two materials at room temperature and high pressure was also investigated. The results show that the Toth equation is the most suitable model for predicting adsorption isotherms than the Langmuir and L-F equations and determines that the absolute uptake of methane storage on AC and 3D-GS are, respectively, 7.86 mmol·g⁻¹ and 8.9 mmol·g⁻¹ at 298 K and 35 bar. In the Henry’s law region, the isosteric heat of methane adsorption on 3D-GS is larger than that of AC. Meanwhile, the potential well between methane and carbon-based materials decreases as the temperature increases. This indicates that the capacity of methane uptake is enhanced at lower temperatures, which is consistent with the measurements of adsorption isotherms. The research concludes that the 3D-GS is more suitable as a material storage medium than AC. This study provides valuable theoretical guidance for exploring the potential of methane storage on slit pore carbon-based material.

1. Introduction

Methane is one of the most important energy sources in natural gas and biogas [1], but the low volumetric and gravimetric storage capacities of methane at room temperature still restrict its application as fuel in mobile vehicles [2,3]. It is still a challenge to safely and effectively improve the capacity of methane storage [4]. Traditional methane storage includes liquefied natural gas (LNG) and compressed natural gas (CNG). Although LNG can store methane with commendable energy density, the additional energy must be consumed for cooling at 112 K [5]. CNG consumes a lot of energy to pressurize over 20 MPa for compressing natural gas since methane is a supercritical gas at room temperature [6]. Adsorbed natural gas (ANG) is considered an alternative method of natural gas storage because it can store natural gas at room temperature and medium pressure (3–4 MPa) [7,8].

Methane adsorption on sorbents with high surface areas, such as carbon materials [4,9], MOFs [10,11,12] and other porous materials, has been extensively researched due to its lightness, fast kinetics, and full reversibility. Developing suitable and excellent adsorbent materials remains a bottleneck issue for the large-scale use of ANG as an energy carrier. Compared with MOFs, the outstanding advantages of carbon materials such as ease of preparation, low cost, chemical and mechanical stability and controllable porosity are important features of their wide availability [13]. According to the pore structure classification, carbon-based materials can be divided into graphite plates (e.g., graphite, carbon black and graphene sheets [14,15]), slit pores (e.g., coal and activated carbon [1,15,16,17,18]), and cylindrical pores (e.g., CMS, nanotubes [19] and nanofibers [20,21,22,23]). Considering the low price, ultra-high specific surface area and easy preparation of activated carbon, it has been widely studied for ANG since the 1980s [24]. However, most activated carbons exhibit a methane adsorption capacity of 50–160 v/v under standard conditions [25,26], which does not meet the goals set by the U.S. Department of Energy (DOE) [27]. In order to maximize the storage capacity of methane, it is still feasible to adjust the pore size distribution and increase the specific surface area of activated carbon [9,28]. Recent research showed that the premix of polypyrrole (PPY) and biomass-derived air-carbonized date seed carbon has been successfully used to adjust the porosity of activated carbon, which achieved higher gravimetric and volumetric methane uptake than MOFs [29]. However, the preparation process is relatively complex compared to commercial activated carbon.

Recently, the family of nanostructured carbons has been expanded to include graphene-related materials as an adsorbent, which have been reported to adsorb methane [30,31]. In general, graphene sheets (GS) have smaller surface areas and micro-pore volumes than activated carbon, and it is often assumed that they have a maximal surface area of about 2630 m²/g, which is many times greater than those in previously published studies performed only on reduced graphene oxide (r-GO) samples [14,30,31]. In a previous study [15], we found that GS and activated carbon have similar isosteric heat of methane adsorption and interaction energy between adsorbates. Therefore, the development of GS-related adsorbents should focus on expanding their specific surface area and pore volume. Activation of graphene promotes the creation of a 3D structure made up of linked (i.e., 3D graphene materials), highly imperfect graphene sheets with a greater surface area required for increased methane adsorption [32]. Due to the ultra-high specific surface area and excellent conductivity, 3D graphene materials are widely studied in energy storage [33]. But the capacity of methane adsorption for 3D graphene materials has not been investigated. Therefore, for this study, we purchased commercial activated carbon and 3D graphene materials to investigate their capacity for methane storage for ANG.

In this paper, the behavior of methane adsorption on activated carbon and 3D graphene materials was studied for the development of a storage medium for ANG. Firstly, the structures of AC and 3D-GS were analyzed and characterized by XRD, SEM, EDS and N₂ adsorption/desorption isotherms. Secondly, the thermodynamic framework was used to evaluate the potential well between adsorbents and slit pore adsorbents in the Henry’s law region. Finally, the absolute capacity of methane adsorption on carbon-based materials at room temperature and high pressure ~8 MPa was studied based on engineering applications. This work provides a useful effort to explore the potential of methane storage on carbon-based materials.

2. Materials and Methods

2.1. Materials

Considering engineering applications, carbon materials are all commercial products. The activated carbon and 3D graphene materials used in this paper were, respectively, purchased from Ningde Xinsen Activated Carbon Ltd. (Ningde, China) and ENN Group (Langfang, China) instead of being synthesized. The activated carbon was a kind of coconut shell activated carbon, which was named AC. The 3D graphene materials were named 3D-GS. The three gases that were employed were ultra-high quality (methane, nitrogen, and helium 99.999%). The used gases, LN and LAR, were acquired from Xiamen Linde Gas Co., Ltd. (Xiamen, China).

2.2. Characterization

Both carbon materials were, respectively, studied for their microstructure and composition by SEM and EDS, as shown in Figure 1.

The SEM image in Figure 1 reveals that 3D-GS is composed of a multilayer graphite plate, and its structure is quite different from that of activated carbon. The elemental analysis results of desiccant material from the EDS image are listed in

Table 1. Elemental analysis results of carbon materials by the EDS.

AC		3D-GS
Element	Atom Concentration/%	Element	Atom Concentration/%
C	95.91	C	67.00
O	4.09	O	32.24
--	--	Cl	0.31
--	--	K	0.15
--	--	Cr	0.30
Total	100	Total	100

.

As shown in Table 1, the content of carbon atoms in the 3D-GS is only 67%, and that of the AC is 95.91%. The above results are similar to our previous studies on graphene sheets and carbon black [14].

In order to evaluate the structure of carbon-based materials, a Rigaku MiniFlex 600 X-ray diffraction instrument was used to analyze the crystal structure of carbon-based materials with a scanning step size of 0.02° in the 2θ range of 5–90°. Figure 2 shows the XRD spectra of activated carbon AC and porous graphene material 3D-GS. The characteristic peaks of activated carbon and 3D-GS obtained indicate that the two peaks observed on activated carbon are at 26.2° (002) and 44.3° (101), while the most obvious peak of GS is at 24° (002). A peak of 44.3° (101) also exists but is not obvious. The results indicate that both carbon-based materials have amorphous characteristics with a slight crystal structure [34,35].

In this work, the distance of interlayer $d$ in carbon materials is determined utilizing Bragg’s law, $d=\raisebox{1ex}{$\lambda $}\!\left/ \!\raisebox{-1ex}{$2\mathrm{Sin}\theta $}\right.$. Here, $\lambda =0.15406 \mathrm{n}\mathrm{m}$. The calculation results show that the distance of the activated carbon interlayer is 0.34 nm, which is consistent with the theoretical distance of the graphite interlayer [36]. Therefore, it is assumed to be a slit pore composed of two graphite plates.

The distance of the 3D-GS interlayer is 0.37 nm, which indicates that during the preparation process, the interlayer distance of graphene increases. This implies some characteristics of nano-carbon materials, such as graphene sheets and carbon nanotubes [37].

2.3. Gas Adsorption Measurements

Micromeritics 3Flex was used to measure N₂ adsorption isotherms at 77 K, from which the BET specific surface area, pore size distribution, and pore volume were determined. Before each test, the samples were subjected to vacuum at 393 K for 24 h to remove any moisture. The specific surface area has been calculated from isothermal data using the BET method. The pore size distribution (PSD) of both carbon-based materials was determined by the 2D-NLDFT method. The detailed process can be found in our previous work [38].

Approximately 0.0338 g AC and 0.0287 g 3D-GS were selected for methane adsorption measurements at low pressure and 283–303 K. Equilibrium data were also volumetrically obtained by Micromeritics 3Flex.

About 0.2581 g AC and 0.2283 g 3D-GS were selected for methane adsorption measurements at high pressure. The adsorption equilibrium data under high pressure were volumetrically measured by Setaram PCTPro E & E, an instrument for accurately measuring gas adsorption equilibrium within a temperature–pressure range, respectively, from 77–673 K and 0–20 MPa, and more testing details can be found in our previous research [39].

Prior to each adsorption test using Micromeritics 3Flex and PCTPro E & E, the sample was placed in a vacuum at 393 K for 12 h to degas any moisture from it. To ensure the accuracy of the experimental data, the test was repeated twice in a bath of liquid nitrogen or oil.

3. Results and Discussion

3.1. Pore Structures

The N₂ adsorption data at 77 K were measured by Micromeritics 3Flex; the adsorption isotherms of both carbon-based materials were as shown in Figure 3. The adsorption isotherms of N₂ on both carbon materials are typical type I adsorption isotherms according to the IUPAC classification [40]. The adsorption amounts of AC samples are close to saturation after P/P₀ = 0.2. It is possible to see that the AC is a typical microporous material. But the desorption isotherm on 3D-GS has an obvious ‘hysteresis loop’ phenomenon, and the desorption isotherm on AC is inconspicuous. It implies that the 3D-GS sample has some mesopores and micropores, and AC can be considered a typical microporous material.

Table 2. Textural parameters of the as-prepared HKUST-1 samples.

Simple	3D-GS	AC
BET specific surface area SBET$/{\mathrm{m}}^2·{\mathrm{g}}^{-1}$	2045	1637
Micropore volume $\left(\text{≤}2 \mathrm{n}\mathrm{m}\right)/{\mathrm{cm}}^3·{\mathrm{g}}^{-1}$	0.544	0.65
Mesopore volume $\left(\text{>}2 \mathrm{n}\mathrm{m}\right)/{\mathrm{cm}}^3·{\mathrm{g}}^{-1}$	0.838	0.142

shows the results of calculating the S_BET of both carbon-based materials using the relative pressure P/P₀ = 0.05–0.3; detailed information can be found in the Supplementary Materials.

As listed in Table 2, the S_BET of 3D-GS is around 2045 m²·g⁻¹, which is larger than that of AC (1629 m²·g⁻¹). It can be found from Figure 3 that the capacity of N₂ adsorption on 3D-GS is also larger than that of AC, which indicates that it has a larger specific surface area and pore volume. For supercritical adsorption, the adsorption capacity is positively correlated with the specific surface area [4]. Therefore, 3D-GS may have a better adsorption potential than AC.

For the characterization of PSD of carbon materials, its pore structure is often approximated as a 1D pore structure. For example, the slit pores of activated carbon are only related to the pore width [41]. When NLDFT was used to solve the PSD of activated carbon in the early stage, it was considered that the fluid was distributed on the graphite plate with a uniform energy distribution, but the surface energy distribution of activated carbon and other porous materials was in fact heterogeneous, which would lead to the deviation between the predicted results and the experimental values. For this reason, Ustinov and Do further consider the surface energy heterogeneous term of a 1D energy distribution in the solution process of NLDFT [42]. Ravikovich et al. regard the rough carbon crystal surface as the carbon atom in the quenched phase state, proposed the QSDFT theory [43,44], solved the contribution of the binary hard sphere fluid repulsion term by using the FMT theory, and predicted the adsorption–desorption equilibrium of nitrogen and argon on the ordered porous silica gel MCM-41 [45]. However, the above research based on NLDFT or QSDFT with a 1D function still cannot accurately describe the surface energy heterogeneous distribution on the adsorbent, so it is necessary to further establish a 2D or 3D surface energy distribution model.

As early as 2013, Jagiello and others studied the 2D-NLDFT [46]. They consider two 2D-NLDFT models: energetically heterogeneous and geometrically corrugated of the graphite plane [47], and the results show that the PSD results of the two hypotheses are similar. This indicates that for activated carbon, the 2D gas–solid surface model can be used to analyze the two basic characteristics of the sample’s micropore geometry and heterogenous surface energy. The quantitative improvement of the original slit pore model can significantly improve the analysis results of the PSD of activated carbon. Subsequently, they used 2D-NLDFT to characterize cylindrical pores such as silica gel and carbon nanotubes. The characterization gases used were nitrogen, oxygen, argon and hydrogen. The model was widely verified [48].

Therefore, considering the heterogeneous surface energy of carbon-based materials, the 2D-NLDFT method was employed to determine the PSD and cumulative micropore volume as shown in Figure 4. The mean pore width of two carbon materials was calculated and is listed in Table 2.

It can be found from Figure 4 and Table 2 that the PSD of activated carbon is concentrated in micropores, and its characteristic pores are concentrated at 0.64 nm, 0.91 nm, 1.3 nm and 2 nm, respectively. However, the micropore volume of 3D-GS is smaller than that of mesopores, and the micropores are mainly concentrated at about 0.91 nm. According to the research [9], methane is suitable for storage in pores 2–3 times the molecular diameter (i.e., between 0.76 and 1.15 nm), while the pore volume of 3D-GS in this region is 0.338 ${\mathrm{cm}}^3·{\mathrm{g}}^{-1}$ and that of activated carbon is only 0.185 ${\mathrm{cm}}^3·{\mathrm{g}}^{-1}$. Combined with the S_BET value in Table 2, 3D-GS is 1.25 times that of AC, which shows that 3D-GS seems to be more suitable for methane storage. In addition, the mesopores of 3D-GS are concentrated in the range of 2–6 nm, while the activated carbon is concentrated in the range of 2–4 nm.

3.2. Adsorption Equilibrium at Low Surface Coverage Region

The adsorption isotherms for methane at 283–303 K, which were measured using Micromeritics 3Flex within the low-pressure range of 0–100 kPa, are plotted in Figure 5.

Figure 5 shows that all isotherms of methane adsorption on carbon materials appear to be characteristic of the type I isotherm of adsorption, and $n_{exc}$ of methane adsorption on the AC is smaller than that on the 3D-GS at 100 kPa and all test temperatures (283–303 K). According to Table 2, the S_BET of 3D-GS is larger than that of AC, which means that an adsorbent with a larger S_BET has a larger methane uptake. In addition, it also indicates the same interaction mechanism between methane and the aforementioned carbon-based adsorbents, with their specific surface area and microporous volume being important contributors to methane adsorption.

3.2.1. Adsorption Equilibrium

According to Gibbs’ definition of adsorption, excess adsorption $n_{exc}$ and absolute adsorption $n_{abs}$ can be correlated as follows:

$$n_{exc}=n_{abs}-{\rho }_{bulk}{v}_a$$

(1)

where $v_a$ is the volume of adsorbed phase for carbon-based materials and ${\rho }_{bulk}$ is the density of the bulk gas phase. Here, the density of the bulk gas phase can be found in the NIST data [49].

3.2.2. Isosteric Heat of Adsorption

Aimed at more accurately comparing the adsorption behavior of methane on carbon-based materials AC and 3D-GS, the isosteric heat of adsorption at zero surface coverage $q_{st}^0$ was determined by experimental data as shown in Figure 4.

In the region of Henry’s law, the excess adsorption is proportional to the equilibrium pressure of adsorption [50],

$$n_{exc}\cong H_{P}P$$

(2)

where $H_P$ is the Henry’s law constant. The process to determine the $H_P$ by the equilibrium data at 0–1.5 kPa is shown in Figure 6.

$q_{st}^0$ is determined by $H_p$ as [51],

$$q_{\mathrm{s}t}^0=R\frac{d\ln \left(H_P\right)}{d\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$T$}\right.\right)}$$

(3)

Results are also listed in

Table 3. Parameters calculated by methane uptake on the AC and 3D-GS in Henry’s law region.

T/K	${\mathit{H}}_{\mathit{p}}/\mathbf{mmol}·{\mathbf{g}}^{-1}·{\mathbf{kPa}}^{-1}$		${\mathbf{B}}_{2\mathit{s}}\mathbf{E}+6/{\mathbf{m}}^3·{\mathbf{g}}^{-1}$
	AC	3D-GS	AC	3D-GS
283	0.01758	0.01706	41.3633	40.1398
293	0.01362	0.01327	33.1783	32.3257
303	0.01004	0.00887	25.2921	22.3448

. The $q_{st}^0$ of methane adsorption on AC and 3D-GS is about 19.93 kJ·mol⁻¹ and 23.23 kJ·mol⁻¹, respectively. It implies that, in addition to a contribution from a larger S_BET of the 3D-GS, the more activation sites of 3D-GS adsorbing methane may be another important reason for its larger adsorption capacity.

As listed in Table 3, the parameters of $H_p$ were determined using Equation (2) using the experiment data as shown in Figure 6, which decrease as the temperature increases. Since activated carbon has more ultra-micropores (<0.7 nm) as shown in Figure 4, the parameters of $H_p$ for AC are slightly higher than those of 3D-GS at all test temperatures.

3.2.3. Thermodynamic Framework for Potential Well between Methane-Adsorbent

For a slit pore model of activated carbon and 3D-GS, it cannot be directly solved as a graphite plane as in previous work [14]. In this paper, we introduce 2D-NLDFT to solve the integral adsorption isotherm equation (IAE) of PSD [41],

$$n_{exc}={\displaystyle {\int }_{w_{\min }}^{w_{\max }}{n}_{exc}^w}f\left(w\right)dw={\displaystyle \sum _i^N{n}_{exc}^{w_i}}f\left(w_i\right)\mathsf{\Delta }w$$

(4)

where $w$ is the pore width, $f\left(w\right)$ is a function about pore size distribution as shown in Figure 3, and $n_{exc}^w$ is excess adsorption capacity with pore width $w$.

At very low coverage, the adsorbate molecules can be regarded as the Boltzmann distribution relative to the slit pore with the pore width of $w$.

$$n_{abs}={\rho }_{bulk}{\displaystyle {\int }_{v_a}\exp \left[\frac{-V_{ext}(z)}{kT}\right]}dv$$

(5)

The bulk density of fluid under low pressure can be approximated to an ideal state, ${\rho }_{bulk}=\frac{P}{RT}$, and according to Gibbs’ definition of adsorption as listed in Equation (1),

$$n_{exc}^{w_i}=\frac{P}{RT}{\displaystyle {\int }_{v_a}\left\{\exp \left[\frac{-V_{ext}(z)}{kT}\right]-1\right\}}dv=\frac{P}{RT}{\displaystyle {\int }_0^H\left\{\exp \left[\frac{-V_{ext}(z)}{kT}\right]-1\right\}dz}$$

(6)

where $V_{ext}(z)$ is the interaction between fluid and adsorbent in the slit pore with a pore width of $w$. The 10-4-3 potential [52] was selected to determine the $V_{ext}(z)$, which defines the pore width $H$ measured between the centers of carbon atoms composing the surface planes of the opposite walls, $H=\mathrm{w}+{\sigma }_{\mathrm{ss}}$.

$$V_{ext}(z)=A{\epsilon }_{sf}\left\{\left[\frac{2}{5}{\left(\frac{{\sigma }_{sf}}{z}\right)}^{10}-{\left(\frac{{\sigma }_{sf}}{z}\right)}^4-\frac{{\sigma }_{sf}^4}{3\mathsf{\Delta }{\left(z+0.61\mathsf{\Delta }\right)}^3}\right]+\left[\frac{2}{5}{\left(\frac{{\sigma }_{sf}}{H-z}\right)}^{10}-{\left(\frac{{\sigma }_{sf}}{H-z}\right)}^4-\frac{{\sigma }_{sf}^4}{3\mathsf{\Delta }{\left(H-z+0.61\mathsf{\Delta }\right)}^3}\right]\right\}$$

(7)

where $A=2\pi {\sigma }_{sf}^2{\rho }_s\mathsf{\Delta }$, ${\rho }_s$ and $\mathsf{\Delta }$ are the density and interlayer distance of graphite. For methane adsorption on carbon materials, we set the solid–fluid interaction parameters as ${\sigma }_{sf}=0.3605 \mathrm{n}\mathrm{m}$. But the potential well between adsorbate–adsorbent ${\epsilon }_{sf}$ is considered as a variable to be determined as follows.

The excess adsorption $n_{exc}$ can also be associated with the Virial equation [53]

$$n_{exc}\cong B_{2S}\left(\frac{P}{RT}\right)$$

(8)

where $B_{2S}$ is the second Virial constant. In the very low surface concentration region, one can obtain the following expression from Equations (4), (6), and (8) as

$$B_{2S}={\displaystyle \sum _i^N\left({\displaystyle {\int }_0^{H_i}\left\{\exp \left[\frac{-V_{ext}(z)}{\mathrm{k}T}\right]-1\right\}dz}\right)}f\left(w_i\right)\mathsf{\Delta }w$$

(9)

The variation in ${\epsilon }_{sf}$ has a function relationship between $\frac{{\epsilon }_{sf}}{kT}$ with $B_{2S}$ as shown in Figure 7.

As shown in Figure 7, $\ln (B_{2S})$ and ${\epsilon }_{sf}$ have a satisfactory linear relationship. Then, the adsorbate–adsorbent well depth potential ${\epsilon }_{sf}$ could easily be determined by linear interpolation via linear plot [54]; the results are listed in

Table 4. The potential well between methane and carbon-based materials.

T/K	$\frac{{\mathit{\epsilon }}_{\mathit{s}\mathit{f}}}{\mathit{k}}/\mathit{K}$
	AC	3D-GS
283	68.67	65.64
293	68.14	64.73
303	66.66	62.11

.

As listed in Table 4, the well depth potential ${\epsilon }_{sf}/k$ is around 62.11–68.67 K, which is close to that of using the Lorentz–Berthelot combining rules [55], ${\epsilon }_{sf}=\sqrt{{\epsilon }_{ss}{\epsilon }_{ff}}$ (${\epsilon }_{sf}/k=64.4 \mathrm{K}$). This indicates that 2D-NLDFT is accurate in characterizing the PSD of carbon-based materials.

Meanwhile, the well depth potential ${\epsilon }_{sf}/k$ between fluid and AC as well as between the 3D-GS is, respectively, about 68.14 K and 64.73 K at 298 K. This suggests that the interaction energy between methane molecules and the AC is likely stronger than that between 3D-GS. This may be due to the fact that activated carbon has more micropores and provides more adsorption sites at very low pressure. AC has a greater number of methane adsorption activation sites compared to 3D-GS, resulting in a higher well depth potential ${\epsilon }_{sf}/k$ for AC at zero surface coverage. Another significant factor contributing to higher adsorption energy is the smaller mean pore width of AC compared to 3D-GS, as indicated in Table 2.

Meanwhile, the potential well ${\epsilon }_{sf}/k$ between methane and carbon-based materials decreases as the temperature increases. This indicates that the capacity of methane uptake is enhanced at lower temperatures, which is consistent with the measurements of adsorption isotherms as shown in Figure 5.

However, 3D-GS will show a stronger adsorption capacity for methane with the increase in equilibrium pressure. The isosteric heat of adsorption at 0–100 kPa was determined by the Clausius–Clapeyron equation:

$$q_{st}=-R{\left[\frac{d\ln \left(P\right)}{d\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$T$}\right.\right)}\right]}_n$$

(10)

As shown in Figure 8, the isosteric heat of methane adsorption on AC is approximately 17.9–19.93 kJ·mol⁻¹, while that of 3D-GS is around 19.3–23.23 kJ·mol⁻¹. According to Figure 8, the change trend in adsorption heat $q_{st}$ with the adsorption uptake also suggests the adsorption of methane on the carbon materials with a heterogeneous energy surface, wherein $q_{st}$ decreases with the increase in adsorption uptake. At higher pressure, the energy heterogeneity on the surface of 3D-GS is stronger than that on the AC surface. This may be due to the fact that the main component of AC is carbon atoms, then the adsorbent surface is uniform. Meanwhile, the carbon atom content of 3D-GS accounts for about two-thirds and the oxygen content accounts for 32.24%, as listed in Table 1, indicating that it has a large number of functional groups, enhancing the energy heterogeneous of the surface.

3.3. Adsorption Equilibrium at High Pressure

According to DOE storage requirements for ang commercial applications, the storage temperature is room temperature and the storage pressure is 35–80 bar [27]. The experimental data measured by PCTPro E & E were set as the test condition with high pressure 0–8 MPa and 298 K, and the results are shown in Figure 9.

Considering that the absolute adsorption capacity must be determined in engineering applications, the static volumetric measurement determines the excess adsorption capacity. Therefore, we selected the Langmuir, L-F and Toth equations for monolayer adsorption, determined the absolute adsorption capacity from the experimental data, and determined the appropriate model from their accuracy.

$n_{exc}$ can be determined by the Langmuir, L-F and Toth equations [56], which are:

$$n_{exc}=n_0\frac{bf}{1+bf}\left(1-\frac{{\rho }_{bulk}}{{\rho }_a}\right)$$

(11)

$$n_{exc}=n_0\frac{{\left(bf\right)}^t}{1+{\left(bf\right)}^t}\left(1-\frac{{\rho }_{bulk}}{{\rho }_a}\right)$$

(12)

$$n_{exc}=n_0\frac{bf}{{\left[1+{\left(bf\right)}^t\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$t$}\right.}}\left(1-\frac{{\rho }_{bulk}}{{\rho }_a}\right)$$

(13)

where $n_0$ is the saturation adsorption capacity, ${\rho }_{\mathrm{a}}$ is the density of adsorbed phase, $f$ is the bulk gas fugacity, and $b$ and $t$ parameters that can be nonlinearly determined by fitting the experimental data via Equations (11)–(13).

The accuracy of fitting was evaluated by the mean deviation δ:

$$\delta =\frac{1}{N}{\displaystyle \sum _i^N\frac{\left|n_{exc}^i-n_{cal}^i\right|}{n_{exc}^i}}\times 100\%$$

(14)

The results are shown in

Table 5. Parameters of Langmuir, L-F and Toth equation determined by non-linear fit of the experimental data of methane adsorption on the carbon materials.

Parameters	Langmuir Equation		L-F Equation		Toth Equation
	AC	3D-GS	AC	3D-GS	AC	3D-GS
$n_0$/mmol g−1	9.9161	12.292	12.758	17.875	16.498	24.1
$b$/mmol g−1 MPa−1	0.8907	0.6365	0.5086	0.2918	0.8682	0.5227
$t$	--	--	0.8191	0.8052	0.5832	0.554
${\rho }_a$/mol·L−1	45,230	113.86	36.252	22.8248	25.31	19.513
δ/%	0.8191	0.7835	0.1648	0.2657	0.1622	0.2342

and Figure 10.

As shown in Table 5, the δ of the Toth equation is the smallest of the three equations, which verifies the accuracy of the fitting equation. The values of parameter $t$ determined by L-F and the Toth equation for AC and 3D-GS are similar. This shows that the structural parameters of the two materials are similar because they are both carbon materials. The adsorption of methane on the carbon-based materials at supercritical temperature is similar to that of compressed gas. After calculating the absolute adsorption capacity and determining the density of the adsorption phase of methane, it is found that the adsorption phase density of methane on the test sample is smaller than that of liquid methane using the Toth equation. This indicates that methane molecules gather in a state similar to compressed gas. However, the parameters of ${\rho }_a$ determined by Langmuir and L-F equations may be larger than 26.5 mol/L of the liquid methane. The results also verify the rationality of the Toth equation. Therefore, when selecting the adsorption model, we should consider whether the assumptions made by the model on the adsorption phase of supercritical methane are reasonable.

As shown in Figure 10, the methane storage capacities of the carbon-based materials AC and 3D-GS are 7.86 mmol·g⁻¹ and 8.9 mmol·g⁻¹ at 298 K and 35 bar. This indicates that under high-pressure adsorption conditions, the S_BET is still the main factor determining the adsorption amount.

4. Conclusions

This study comparatively investigated the behavior of methane adsorption on carbon-based materials, with the aim of developing a storage medium for adsorbed natural gas (ANG), and the conclusions reached can be summarized as follows:

(1)

The 3D-GS is a more promising storage medium for ANG than AC in terms of the specific surface area and pore volume. The limit isosteric heat of methane adsorption on the AC and 3D-GS is about 19.93 kJ/mol and 23.23 kJ/mol, respectively. The methane storage capacities of both carbon-based materials AC and 3D-GS are, respectively, 7.86 mmol·g⁻¹ and 8.9 mmol·g⁻¹ at 298 K and 35 bar. Meanwhile, the S_BET of 3D-GS is around 2045 m²·g⁻¹, which is larger than that of AC (1629 m²·g⁻¹). It can therefore be concluded that under high pressure, the S_BET is still the main factor determining the adsorption amount.

(2)

The potential well between methane molecules and the AC is larger than that in the 3D-GS. Considering the heterogeneous surface of carbon-based materials, the framework to determine the potential well between adsorbate–adsorbent is built by PSD determined by 2D-NLDFT. Using Boltzmann distribution approximation for the fluid density on the heterogeneous surface, the adsorption potential well between methane molecules and the AC and 3D-GS was shown to be, respectively, about 68.14 K and 64.73 K. Both values are close to that of using the Lorentz–Berthelot combining rules (64.4 K); this indicates that 2D-NLDFT is accurate in characterizing the PSD of carbon-based materials. Meanwhile, the potential well between methane and carbon-based materials decreases as the temperature increases. This indicates that the capacity of methane uptake is enhanced at lower temperatures.

(3)

The Toth equation is the most suitable model for predicting methane adsorption on carbon-based materials than that of the Langmuir and L-F equation. After determining the values of the parameters by nonlinearly fitting on the experimental data covering the pressure range from 0 to 8 MPa at 298 K, the Toth equation can predict the experimental data of hydrogen adsorption on the carbon-based materials AC and 3D-GS with mean relative deviations of less than 0.25% and can determine that the density of the adsorbed phase is less than 26.5 mol/L of the liquid methane. This indicates that methane molecules gather in a state similar to compressed gas. The results also verify the rationality of the Toth equation.