Storage of Natural Gas by CNTs

Abstract

Carbon nanotubes (CNTs) have gained considerable attention over the past decade as up-to-date materials for storing renewable energy. The properties of CNTs, e.g., exceptionally high surface area, thermal conductivity, and electron mobility can be advantageous for applications toward energy storage. Conventional methods in natural gas storage include liquefaction (LNG) and compression (CNG) in the compression range of 2×104 – 3×104 kPa in steel cylinders. But nanotubes carbon (CNT), which includes two models, is used for higher pressures (about 4×104kPa). Single-walled carbon nanotubes (SWCNTs) and multiwalled carbon nanotubes (MWCNTs) are the two models in which the gas storage mechanism is superficial. Studies have also shown that the capacity of MWCNT to store natural gas can be enhanced by treating the nanotubes with acid. In the case of CO2, however, positive CNT charging always enhances the adsorption while negative CNT charging always suppresses it. By doubling the nanotube diameter, the amount of the gas adsorption capacity increased by 45%.

1. Introduction

Natural gas is one of the cleanest and most useful forms of energy, with almost 90% of it being methane. In addition, natural gas contains a small amount of gases, such as ethane, propane, hydrogen, helium, carbon dioxide, nitrogen, hydrogen sulfide, and water vapor. The composition of natural gas varies depending on exploration wells and seasons. Due to the dissimilar distribution pattern of natural gas fields in the world and the increase in its use as a fuel, its transmission and storage are highly important [1]. The vast potential application of nanotechnology has propelled numerous research studies in various fields including the oil and gas sector. There are several challenges in the oil and gas industry that nanotechnology could address if articulately harnessed through research, and one of such challenges is natural gas storage and transportation. Several types of porous media for gas storage have been proposed, developed, and studied, and these include molecular sieve, activated carbon, zeolite, and carbon nanotubes (CNTs) [2]. Since the discovery of CNTs in the 1990s, they have been studied and used as adsorbents for various natural gases, alkanes, and noble gases. Due to the tubular shape, uneven structure with well-defined adsorption strategies and their exceptional specific surface area (up to 1550 m²/g), carbon nanotubes are a better candidate for natural gas storage and separation especially compared with other porous adsorbents in the industry materials such as carbon and zeolite [3]. In general, the nanostructures with high surface-to-volume ratio envisage a diversity of applications against the bulk materials. Particularly, one-dimensional carbon nanotubes (CNTs) exhibit the interesting features in nanotechnolo [4]. Research has shown that carbon nanotube (CNT), products of nanotechnology have the capacity to store natural gas through a comparatively cheap and efficient method, though investigations are still ongoing in solving the challenges facing this method. This chapter is thus aimed at reviewing the prospects of storing and transporting natural gas in CNT, and it highlights some factors that can enhance the gas storing capacity of methane in nanotubes [2].

2. Methods of gas storage

Natural gas storage and transport methods include underground gas storage (UGS) and adsorbed natural gas (ANG) [1]. Compression (compressed natural gas – CNG) and liquefaction (liquefied natural gas – LNG), but these methods are complex and expensive. In compression, the gas is stored as a supercritical fluid at room temperature but at high pressures of about $2\times {10}^4$ – $3\times {10}^4$ kPa, reaching a density that is about 230 times higher (230 v/v) than the density of natural gas at standard temperature and pressure (STP) conditions [2]. In this case, the energy density is approximately 25% of that of gasoline. The disadvantages associated with this storage method include the risk of carrying highly pressurized tank in transit, high energy requirement for raising the pressure to $2\times {10}^4$ – $3\times {10}^4$ kPa, the costs associated with acquiring the heavy thick-walled steel cylinders that can withstand such pressure, safety valves requirements, and the cost of transporting these heavy cylinders containing highly pressurized gas [2]. In the liquefied natural gas storage method, the gas is stored at a temperature of 112 K in a tank with a pressure of $1\times {10}^3$ kPa, in which case the gas has 72% of the total energy density of gasoline. Natural gas can be stored in CNTs, which are lightweight containers stuffed in a pressure vessel of about $2\times {10}^4$ – $4\times {10}^4$ kPa. This method reduces cost; it reduces the risks associated with other storage methods and is a possible alternative for large-scale transportation of natural gas. A comparison between the natural gas storing capacity of CNT and CNG has shown that although CNT stores less amount of natural gas, it however does this at 83% storage pressure lower than CNG, which is a huge advantage that can be exploited to efficiently and economically store and transport natural gas [2]. Due to the problems of CNG, adsorbed natural gas (ANG) storage was introduced as a good alternative to CNG. In the ANG process, gas storage is done at a lower pressure than CNG. To be used on cheaper ships, work safety must be increased. Natural gas is absorbed through the embedded pores of the adsorbents. This adsorption process is performed at room temperature. The adsorption that an adsorbent performs depends primarily on the properties of the adsorbent. Materials that can be used to adsorb natural gas include highly porous materials such as activated carbon, zeolite, silica gel, activated alumina, carbon nanotubes, and a variety of material artificial adsorbents [1]. Activated carbon is usually used in ANG vessels. The maximum capacity of gas storage of activated carbon at 1500 psi and 298 K is reported to be 160 v/v, which compared with CNG has a lower storage volume. The amount of the pure methane adsorbed is more than when natural gas is used [1]. Studies show that under the same conditions, adsorption on carbon nanotubes is often greater than adsorption on activated carbon. It is also agreed that the nanoparticles used in nanotubes are the best option for absorbing and storing natural gas [1]. As already mentioned, the efficiency of ANG is lower than that of CNG. To solve this problem, natural gas storage can be considered in nanostructures. Another disadvantage of the adsorption process on activated carbon, which has made these materials less popular, is their isothermal heat. Adsorption is a thermal phenomenon, and the high conductivity of activated carbon makes it act as an insulating material. Researchers try to use nanoscale adsorbents to adsorb more gas [1].

3. Natural gas as a clean energy source

Natural gas is a homogeneous mixture, having variable proportions of hydrocarbons. The general composition of natural gas includes methane (CH₄) constituting the major part, and it generally ranges from 55 to 98% in volume, ethane (C₂H₆), propane (C₃H₈), and other heavy constituents. There is a growing interest in the use of natural gases as an alternative source of energy especially because it is clean. Its thermal efficiency is higher than that of other fuels, and it produces mainly CO₂ and water vapor. The emissions of CO₂ are 25–30% lower than that generated from fuel-oil and 40–50% lower than coal per unit of produced energy [2]. As regards its use as a fuel, natural gas has many advantages. These include reduction in post combustion contaminants, reduction in maintenance costs compared with other fuels, reduction in suspended solid particles, which are associated with combustion of gasoline, absence of sulfur and sulfur dioxide (SO₂) emissions, which are typical contaminants from transportation vehicles. Compared with liquid fuels, the emissions from natural gas vehicle combustion are 76% less in carbon monoxide, 75% less in nitrogen compounds, 88% less in hydrocarbons, and 30% less in carbon dioxide [2]. Furthermore, the physiochemical properties of natural gas enable the use of catalysts for the combustion of gases, obtaining excellent results and minimizing emissions. In spite of the numerous advantages associated with the use of natural gas as a fuel over other forms of hydrocarbon fuels, its efficiency and economics in storage and transportation have constituted a major barrier to its usage. This could be attributed to its low energy density (heat of combustion/volume) at standard temperature and pressure conditions [2].

4. Types and characteristics of carbon nanotubes (CNTs)

Elemental carbon in sp² hybridization can form a variety of amazing structures, such as graphite, graphene, CNTs, and fullerene [5]. Carbon nanotubes are allotropes of carbon with a concentric cylindrical shape of diameter in the order of nanometer and length of micrometer [2]. In particular, CNTs with very high length-to-diameter ratios ($\sim$132,000,000:1) have been constructed [6]. The carbon network of the shells is closely related to the honeycomb arrangement of the carbon atoms in the graphite sheets [5]. The structural shape of SWNTs is a tube several nanometers in diameter and several microns in length. They are also made of perforated graphene sheets. They are placed in one direction and next to each other to form the pipes. A MWNT is an arrangement of several to tens of hundreds of concentric tubes of graphite plates with adjacent $\sim$0.34 nm shells separated (Figure 1) [5].

Figure 1.

Scheme of MWNT [5].

They are tubular cylinders of carbon atoms with extraordinary mechanical, electrical, thermal, optical, and chemical properties. CNTs were first discovered by Iijima in 1991; however, the first microscopic production of CNT was made by two researchers at Nippon Electric company limited fundamental research laboratory, and since then, there have been several developments of CNT [2]. Carbon nanotubes can be classified into chair-shaped and zigzag (Figure 2). Among them, only nanotubes have metal sex seats, chiral semiconductor tubes and zigzag tubes have 1–3 narrow slits and 2–3 large slits, respectively [5].

Figure 2.

Scheme of different SWNTs: armchair (a); zigzag (b); and chiral (c) [5].

Methods of producing CNTs include arc evacuation, chemical vapor deposition (CVD), laser ablation, electrolysis, pyrolysis, flame synthesis, electron or ion beam irradiation, and solar approaches. Laser abrasion and arc discharge are common methods for producing CNTs from carbon vapor. Carbon nanotubes made by these two methods can maintain good quality with less structural defects due to the presence of impurities in their constituents. In both methods, the growth process is performed at high temperatures, and re-firing properly ensures that the defects in the shape of the tubular graphene are reduced. In these techniques, it is difficult to control growth on patterned substrates at a reasonable rate. It should be noted that these production methods are expensive due to the need for high temperatures. To solve such problems, CVD production methods have been considered and used to allow the growth of various CNT structures. CVD seems to be a practical process due to its low required temperature range (∼500–1200 °C). In addition, because CVD provides better control over the diameter, length, and number of CNT walls, their application can be extended to nanoelectronics, field diffusion, and more. However, researchers continue to emphasize the development of more efficient, cost-effective, and environmentally friendly alternatives to large-scale CNTs. Recycling waste or disposable materials into higher-value products (such as ceramics and steel) has encouraged researchers to synthesize CNTs from waste sources for a variety of applications. The use of waste as a source for the synthesis of carbon nanotubes can simultaneously reduce solid waste and construction costs [6]. But the most popular and most widely used method of synthesis is the chemical vapor deposition method [2]. Today, many advances have been made to obtain carbon materials with very fine porous pores that have very high adsorption properties for most gases. Pores at the molecular scale can absorb large amounts of gas, the adsorption potential of porous walls increases the density of the adsorbed material inside the pores. The major advantage of CNTs is related to the fact that the carbon structure is practically known. This aspect has permitted the correlation of experimental data with theoretical predictions [5]. Since the discovery of CNTs to date, scientists have made great efforts to design, synthesize, and characterize CNT layouts, including single-walled, double-walled, and multiwalled CNTs (SWCNTs, DWCNTs, and MWCNTs). Due to the strong van der Waals (VDW) forces between the carbon atoms of adjacent pipes, CNTs tend to form in stable molds on their own. This geometric shape creates different adsorption sites that differ in the amount of energy required to absorb the gas. Most scientists agree that the so-called groove area (g) between the two CNTs is the best absorption region (see Figure 3). The best CNT geometry for maximum adsorption depends strongly on the applied pressure. Thus it can happen that the adsorption strength does not change monotonically as a function of the nanotube diameter D and the inter-tube distanced [7].

Figure 3.

Schematic arrangement of a parallel aligned three dimensionally SWCNT array in a simulation box (i.e. the black framework) of volume L_x × L_y × L_z nm³. D is the nanotube diameter. The parameter d is the surface to surface intertube distance beyond VDW diameter σ_C-C = 0.34 nm of carbon atoms. It is defined as d = d_CNT - σ_C-C with d_CNT denoting the shortest separation between carbon atoms of adjacent tubes. Interstitial and groove regions are represented by i and g, respectively. Note that there is some ambiguity on how to discriminate between i and g [7].

Undoubtedly, yeast fermentation plays a critical role in the formation of CNTs. Therefore, an in-depth understanding of the CNT formation mechanism is required [8]. Molecular surface engineering is based on the construction of CNTs through the chemical route. This is related to the adjustable structure of CNTs, for example, crystallinity, number of walls, cavities, and length with the help of variables such as proper growth control, use of suitable catalysts and carbon sources. The cost of manufacturing CNTs can be easily calculated with the help of the selected chemical route and process control [6]. There are two types of carbon nanotube based on the number of layers or walls: the single-wall carbon nanotubes (SWCNTs) and the multi-wall carbon nanotubes (MWCNTs). The SWCNT can be described as a graphene sheet rolled into single cylindrical shape so that the structure is one-dimensional with axial symmetry. Most SWCNTs typically have diameters in the range of 1–1.3 nm and a few micrometers long. SWNT can be formed in three different designs: armchair, chiral, and Zig-Zag. The design of nanotubes depends on the complexity of the graphene in a tube, which can be represented by an index pair (n, m). The integers n and m represent the number of unit vectors in two directions in the graphene crystal lattice. If m = 0, this type of nanotube is called zigzag; if n = m, those nanotubes produced are called chair nanotubes, and in the third case, if m ≠ n, it is called chiral nanotube. The values of the integers n and m greatly affect the property of SWNT. The MWCNT is a multilayer of graphene sheets rolled and superimposed on each other. The outer diameters are typically in the range of 2–100 nm while the inner diameters are in the range of 1–3 nm, and the length is one to several micrometers. SWCNTs are more flexible than MWCNTs. They can be twisted, flattened, and bent into small circles or around a sharp bend without breaking, thereby increasing its applicability. SWCNTs have the unique electronic and mechanical properties, which can be used in applications such as field emission displays, nanocomposite material, nanosensors, and logical elements. MWCNTs exhibit some advantages over SWCNTs such as higher surface-to-volume ratio, they are easier to produce in high volume quantities, the product cost per unit is low, and its thermal stability and chemical stability are enhanced. However, MWCNTs have regions of structural imperfection, which may reduce its desirability for application. CNTs are light in weight and have the strongest tensile strength as compared with any synthetic fiber. This strength results from the covalent Sp² bonds formed between the individual carbon atoms. A standard SWCNT can withstand a pressure of 25 GPa without deformation. In terms of thermal conductivity, nanotubes are good conductors along the tube axis but good insulators lateral to the tube axis. Measurements carried out show that SWCNTs have better thermal conductivity compared with copper under the same conditions. MWCNTs exhibit a striking telescoping property whereby an inner nanotube core can slide almost without friction within its outer nanotube shell, thus creating an atomically perfect linear or rotational bearing. The symmetry and unique electronic structure of graphene strongly affect its electrical properties. All CNTs have a large surface area and a high level of adsorption [2]. The type of adsorption in CNTs can be easily divided into three modes: (1) internal adsorption in which only the CNT interior space can be used, (2) external adsorption where adsorption can only be done in the space between CNTs (e.g., areas intermediate and groove; see Figure 1 and (3) unlimited absorption in which both sides of the CNT, i.e., inside and outside, can be used. Among them, unlimited recruitment is the only thing that matters in the industry [7].

5. Storage mechanism of gas in carbon nanotubes

CNTs store gas through the process of adsorption. Adsorption of a gas is a process that gains one or more constituents of the gas in the region of the gas-solid interface where the molecules of the gas are bounded to the surface of the adsorbent as illustrated in Figure 4. Gas absorption in CNT is superficial, and this phenomenon involves increasing the density of the gas near the contact surface, and because the process is spontaneous, Gibbs free energy changes are negative. And because the entropy change is also negative (decreasing the degree of release of gas molecules during the process), the enthalpy changes are less than zero, so the process is hot. There are two types of absorption: physical adsorption and chemical adsorption. In physisorption, the bounding of the gas molecules is superficial because the gaseous molecules are not chemically bounded to the walls of the adsorbent. Weak van der Waals forces are responsible for holding the molecules of the gas to the adsorbent. The adsorption of methane on CNT is most likely through the process of physisorption where the adsorbents require an elevated exposed surface per gram of material called specific surface area, and it is expressed in cubical centimeters of adsorbate per gram of adsorbent. When the elemental constituents of the solid get smaller, the specific surface area gets larger. CNTs that have diameters in the order of nanometers and with hollow cylindrical surfaces present good specific surface areas and are an excellent adsorbent for adsorption of gases. As the pores of a CNT surface decrease, the gas storage capacity increases [2]. The doping of CNTs with metal atoms (such as Li or K) or functional groups (such as COO or NH³⁺) is a possible way to enhance their adsorption capability [7].

Figure 4.

Representation of the adsorption process of a gas on a solid surface [2].

6. Factors that affect the storage capacity of natural gas in CNT

In general, carbon nanotubes (SWCNT with a diameter of 2040 nm and MWCNT with a diameter of 3060 nm) are stable in the temperature range of 25–600°C. Also, an increase in the thermal capacity of carbon nanotubes has been reported by shortening the length of CNT diameter nanotubes in the range of 60–100 nm. While thermal stability increases with increasing nanotube length [6]. In a conducted simulation work to study the storage capacity of SWCNT at different temperatures and pressures, it was observed that methane is weakly adsorbed in SWCNT. Results showed that as pressure increases, the amount of methane adsorbed on SWCNT increased but as temperature increased, the amount of methane adsorbed on SWCNT decreased. It was reported that the binding energies for methane on the defected SWCNT increased by about 56% over the defect-free SWCNT showing that the presence of defects on the structure of nanotubes increases its methane adsorption capacity. Furthermore, for the encapsulated methane molecules inside the defected nanotubes, results showed about 68% increase in binding energy compared with the confined molecules in the defect-free nanotubes. It was pointed out that introducing surface curvatures in the nanotubes could reduce the binding energy between the methane molecules and the substrate. Thus, some factors that affect methane adsorption in SWCNT are pressure, temperature, structural defects, and curvatures. The methane storage capacity of MWCNT has been studied by several researchers. One set of results showed that a type of MWCNT strongly adsorbed methane at a maximum value of 5.44 mmol/g at a temperature of 283.15 K and a pressure of 40 bars. It was also reported that increasing pressure increased the amount of methane adsorbed, while increasing temperature decreased the amount of adsorbed methane. Another report has it that treating MWCNT with acids such as HCl and HNO₃ improves its methane adsorption capacity. The results of experiments conducted using acid-treated MWCNT and untreated MWCNT at the same pressures revealed that acid treatment of nanotubes enhances methane adsorption capacity especially at low pressures. In another work, the methane adsorptions on MWCNT treated with sulfuric and nitric acids, nitric acid, and alkaline were compared with the methane adsorption capacity of untreated MWCNT. Reported results showed that sulfuric and nitric acid–treated MWCNT adsorbed more methane than all other treated and untreated nanotubes. This was followed by nitric acid–treated case before the alkaline-treated nanotubes. The methane adsorption capacity on all the treated nanotubes was higher than the untreated cases showing that treating MWCNT with acids enhances its methane adsorption capacity. This work also showed that increase in pressure increases methane adsorption while increase in temperature decreases methane adsorption on MWCNT [2]. A group of scientists found in their research that the initial slopes of isotherms increased sharply, which indicates that active sites are created on the adsorbent during the functionalization step. Existence of functional groups on MWCNTs causes the adsorption capacity to increase gas at low pressures. At low pressures, adsorption on MWCNTs is affected by the fluid adsorbent interaction; therefore, functional groups led to increased fluid adsorbent interactions. But at higher pressures, fluid interactions become more important than fluid adsorbent interactions, and the role of functional groups is reduced [9].

7. Neutral and charged CNTs

Scientists considered the absorption of gas by loaded nanotubes to absorb CO₂-N₂ gas in a hexagonal CNT pipeline. They found that positive charges on CNTs increased both CO₂ uptake and N₂-CO₂ uptake. Negative charges in a neutral CNT lead to weaker CO₂-N₂ uptake. Undoubtedly, charge distribution, both on CNTs and on adsorbent molecules, plays an important role in the uptake of gases into pregnant CNTs. In this work, they performed a large Monte Carlo simulation to evaluate the absorption and separation of dual gas mixtures of CO₂, SO₂, and H₂S in neutralized and charged. Carbon nanotubes at low pressure and 303 K at SWCNT with a diameter of 2.17, 2.71, and 3.26 nm and inter-tube distance of 1.0 nm were modeled. Certain loads from -0.04 q to +0.04 q were placed on each nanotube to investigate the effect of the load. It has been shown that the behavior of mixed gases in pregnant SWCNTs follows the same rules as pure gases. Due to the additional strong coulomb force between the adsorbent and the charged SWCNTs, the amount of polar molecule adsorption increases significantly when mixed with CO₂, while CO₂ adsorption is usually suppressed as a result of adsorption competition [3]. In addition to the general change in local charge distribution by doping or cavitation, electric oscillation absorption (ESA) provides another way to increase gas absorption by carbon-based adsorbents. Therefore, non-fading electric charges on the absorber can be generated and removed by charging and discharging and enable the rapid absorption and disposal of gases. For example, using GCMC simulations, some scientists have studied H2 uptake on charged SWCNTs. At temperatures 77 K and 298 K, they observed that charging of SWCNTs leads to a significantly better hydrogen storage than accessible in uncharged SWCNT systems. For positively charged CNTs, they observed a larger CO₂ adsorption than in neutral samples, while the opposite has been detected for CNT systems with a negative charge. Negative charges lead to a weaker adsorption and to a reduced CO₂/N₂ selectivity than a neutral CNT bundle [7]. With the criterion of unloaded CNT samples, it is easy to understand that the absorption in a positively charged pregnant CNT is always greater than that in a negatively charged pregnant CNT. Compared with the neutral CNT mode, negative overloads increase adsorption in areas with low pressure and suppress adsorption in areas with high pressure, while positive overloads always increase adsorption [7].

8. Prospects of CNT as a natural gas storage device

Carbon nanotubes have many industrial applications, but more attention is currently given to it as a material for natural gas storage. Several research studies have been conducted to investigate the adsorption behavior of methane, which is a major component of natural gas on SWCNT and MWCNT. The key to successful commercialization of CNT for gas storage is the adsorption capacity of the nanotubes at standard conditions, that is, the ratio of the volume of adsorbed natural gas to the volume of storage container (Vg/Vs). There are indications that substantial volume of methane can be stored in activated carbon pellets at atmospheric conditions, in fact an adsorption capacity of 126 Vg/Vs has been reported. Commercial development of CNT for adsorption of natural gas requires high storage gas capacity greater than 150 Vg/Vs. There are other advances in gas storage on CNT that can be leveraged on to improve the natural gas storage capacity on nanotubes. It should however be noted that a volumetric capacity of about 160 Vg/Vs for methane adsorption on SWCNT has been reported. One of the challenges facing the wide use of CNT as a major adsorbent for natural gas storage is achieving consistency in storage densities and replicable manufacturing capacity. The methods used to manufacture the carbon nanotubes that give the required capacity are quite rigorous, and research in its reproducibility is still ongoing. There is need to control the pressure, temperature, and the flow rate at which gas is efficiently filled and released from the CNT tanks for automotive application. These conditions affect the performance of the storage system since the adsorption process is exothermic. The cost of producing, purifying, and tuning the CNT to obtain the required diameter in large quantity makes the existing methods economically viable [2].

9. Mathematical modeling

9.1 Geometry creation

As mentioned, natural gas adsorption on nanotubes depends on its varied features, including the diameter of nanotubes, construction method, gas arrangement in the nanotube structure, pressure, and temperature. The free spaces of nanotubes have the highest potential for natural gas adsorption. With an increase in the loading pressure, adsorption increases, but as the temperature of the adsorption medium enhances, adsorption decreases. A model was developed for natural gas storage in a vessel containing nanotubes. In fact, the adsorption phenomenon and gas storage of natural gas were modeled here. It was seemed that multi-wall nanotube could be a best choice for adsorbent, and so, multiwall carbon nanotube was used as adsorbent in this chapter. A container with a volume of about 100 ml and has inlet and outlet diameters of 6.35 mm, which we see in Figure 5. This container has an inner diameter of 35.85 mm and a height of 25.3 mm. It also has a porosity of 98.4%. Multiwalled nanotubes are uniformly placed inside the container, which can be considered as a porous medium [1].

Figure 5.

Schematic of the geometry used here [1].

The hypotheses that must be considered before solving the problem are:

• The porous environment is the same in all areas.

• The properties of the nanotubes do not change during the process.

• Convective heat transfer is established in the wall of the vessel and the surrounding fluid is in the experimental reference of the bath water.

• Radial heat transfer occurs inside the vessel.

• No chemical reaction occurs between the nanotubes and natural gas.

In addition, the properties and composition are listed. According to the assumptions mentioned above, the governing equations are obtained [1]. To simulate natural gas storage in carbon adsorbents, the equations must be solved simultaneously. Several equations are calculated and obtained, and other equations are collected from other sources. To answer the equations of adsorption and storage of natural gas in nanoparticles, the equations of adsorption isotherm, adsorption heat, kinetics, energy, and mass must be used. To obtain the mass and energy equations, it is first necessary to write the equilibrium equations and then, using the conditions and assumptions governing the problem, the final equation is obtained. Due to the small physical dimensions, especially the thickness, it is not necessary to solve the problem in all dimensions. After examining this issue with Comsol software, it was proved that considering multidimensional or one-dimensional problem does not cause a difference in the results obtained, which is another reason for not solving the problem in all dimensions. To solve the existing equations, a radial system was considered to study temperature changes along the radius and other volumetric and mass values were calculated. Because the pressure gradient in ANG storage tanks is less than 700 kPa, there is no need to solve the Navier-Stokes equation [1].

9.2 Adsorption isotherm

Since the process of adsorption of natural gas on carbon nanotubes is similar to the adsorption of gas by ANG method, it was considered as a possible type of interaction between nanotubes and natural gas. The adsorption equilibrium depends on the pressure, temperature, and geometry of the adsorbent, which makes adsorption isotherms to be used to obtain the adsorption equilibrium. The Sips equation has the highest consistency with the experimental data to explain the adsorption of natural gas in nanotubes; thus, it can be used to describe the behavior of the adsorption process. The equation of the Sips adsorption isotherm is shown below:

$${\mathrm{q}}_{\mathrm{e}}=\frac{{\mathrm{q}}_{\mathrm{m}}{\left(\mathrm{b\rho }\right)}^{\frac{1}{\mathrm{n}}}}{1+{\left(\mathrm{b\rho }\right)}^{\frac{1}{\mathrm{n}}}}$$E1

$$\frac{1}{\mathrm{n}}=\frac{1}{{\mathrm{n}}_{\mathrm{o}}}+\mathrm{\alpha }\left(1-\frac{\mathrm{T}}{{\mathrm{T}}_{\mathrm{o}}}\right)$$E2

where b is adsorption/desorption constant (Pa⁻¹), n is adsorbate/adsorbent interaction parameter, p is pressure (Pa), q_e is adsorption equilibrium(mmol/gr), q_m is maximum adsorption (mmol/gr), T is temperature (K), T_o is reference temperature (K), and b_o,n_o, and α are constant parameters of adsorption isotherm. Eq. (2) proves that the amount of equilibrium adsorption in the original equation is pressure-dependent, and the dependence of the Sips model on parameters b and n on temperature is proved. In addition, the reference temperature is 283.15 K. The other parameters are different depending on the type and structure of the adsorbent, which are shown in Table 1.

Parameter	Unit	Nanotube type	Value
qm	mmol/gr	C	80.92
		Si	65.83
bo	Pa^−1	C	0.0143e−5
		Si	0.262e−5
no	_	C	0.884
		Si	1.164
Q	Kj/mol	C	7.595
		Si	12.5
$\alpha$	_	C	0.726
		Si	0.5909

Table 1.

Constant parameters of equations [1].

$$\mathrm{b}={\mathrm{b}}_{\mathrm{o}}exp\left[\frac{\mathrm{Q}}{{\mathrm{RT}}_{\mathrm{O}}}\left(\frac{\mathrm{T}}{{\mathrm{T}}_{\mathrm{o}}}-1\right)\right]$$E3

where Q is isosteric heat adsorption during the half-life of adsorption (kJ/mol), R is universal gas constant (j/mol K), T is temperature (K), and T_o is reference temperature (K). Absorption is heat, and when the temperature of the adsorption medium increases, isothermal heat has a negative effect on the process and reduces the adsorption capacity. The Clausius-Clapeyron equation is used to calculate isothermal heat. Each of the adsorption equations can be used to calculate the adsorption heat:

$$Q_{\mathit{st}}=R{T}^2{\left(\frac{\mathit{\delta ln\rho }}{\mathit{\delta T}}\right)}_q$$E4

$$Q_{\mathit{st}}=Q-\mathit{anR}{T}_o\mathit{ln}\left(b_p\right)$$E5

where Q_st is isosteric heat adsorption. Simultaneously with environmental conditions, equilibrium time has a great impact on the process. The kinetic equation (6) is used to obtain the absorption capacity at a given time. This is because after reaching the equilibrium point, the process of gas adsorption by nanoparticles stops, and this time is called the end time of the process:

$$\frac{t}{q_t}=\frac{1}{k^2{q}_e^2}+\frac{t}{q_e}$$E6

where q_e is adsorption equilibrium (mmol/gr), q_t is adsorption capacity (mmol/gr), t is time (min), and k² is the experimental parameter that varies upon a change in the pressure, and its relationship is obtained by the interpretation of experimental data [1].

9.3 Mass equation

Natural gas can be stored on carbon nanotubes in the following two ways:

• Absorbed gas on the adsorbent.

• Gas storage in the open space of the ship as compressed natural gas (CNG).

After writing the mass balance according to the hypotheses, the following equation was obtained:

$$\frac{{\mathit{dm}}_g}{\mathit{dt}}=\pm m{̇}_g-m_s\frac{\mathit{da}}{\mathit{dt}}$$E7

$$a=M_g\times q_t$$E8

$$\frac{\mathit{da}}{\mathit{dt}}=M_g\times \frac{{\mathit{dq}}_t}{\mathit{dt}}$$E9

$$\frac{\mathit{da}}{\mathit{dt}}=M_g\frac{{\mathit{dq}}_t}{\mathit{dt}}=M_g\left[\frac{q_t}{t}-\frac{q_t^2}{q_e^t}\right]$$E10

where ṁ_g is inlet (outlet) gas flow (gr/s), m_g is the amount of gas stored in the vessel as gas phase (gr), m_s is loaded mass of nanoparticles in the vessel (gr), a is adsorbed gas relative to adsorbent mass (gr gas/gr adsorbent), and M_g is molecular weight (gr/mol) [1].

9.4 Energy equation

To investigate the thermal behavior of the vessel, the energy equation in one dimension and the radial direction were used based on Eq. (11):

$$r\left(\epsilon {\rho }_g{C}_g+\mathit{\rho C}+{\rho }_a{\mathit{aC}}_a\right)\frac{\mathit{\delta T}}{\mathit{\delta t}}+{\mathit{r\rho }}_g{\mathit{\vartheta C}}_g\frac{\mathit{\delta T}}{\mathit{\delta r}}=\frac{\delta }{\mathit{\delta r}}\left(\mathit{r\lambda }\frac{\mathit{\delta T}}{\mathit{\delta r}}\right)+{\mathit{\vartheta Q}}_{\mathit{st}}\rho \frac{\mathit{\delta a}}{\mathit{\delta t}}$$E11

where C is the specific heat kJ/kg. K, r is radius (m), $v$ is velocity of fluid (m/s), α is the relationship between viscosity and permeability, ε is overall porosity, λ is overall thermal conductivity (W/mK), and ρ is density (kg/m³). Using the Darcy equation, the mass velocity of the fluid inside the porous medium can be obtained. Because the Reynolds range was small during the process, the Darcy equation is used:

$$\vartheta =-\frac{1}{\alpha }∆$$E12

$$\alpha =\frac{150\mu }{4}\frac{{\left(1-{\epsilon }_b\right)}^2}{{\epsilon }_b^3{R}_p^2}$$E13

where Δ$\mathrm{\rho }$ is pressure difference (Pa), ε_b is bed porosity. These laboratory-obtained equations correspond to the experimental results in the main fields for spherical nanoparticles, and their equivalent diameter must be used for nonspherical nanoparticles. Eq. (14) can be used to obtain the equivalent radius of the nanotubes:

$$R_p=\frac{1}{2}\left(\frac{L}{\mathit{ln}\left(\frac{2L}{d}\right)}\right)$$E14

where R_p is the radius of the particle (m), d is external diameter of nanotubes (nm), and L is nanotube length (nm) [1].

9.5 Initial and boundary conditions

To answer the energy equation, we must first determine the boundary values. For this purpose, the boundary conditions of the system, in the initial network and based on the Eq. (15), was calculated:

$$\frac{\mathit{\delta T}}{\mathit{\delta r}}\left(r_i,t\right)=0$$E15

Two thermal resistors named R1 and R2, which show the conductivity and convection resistance, respectively, are used between the end points (vessel wall) and the fluid. The resistors are closed in series, and the resistance of each of them can be obtained by merging with each other. As Figure 6 shows, the heat conduction and convection in the wall are balanced, and the thermal equilibrium is applied to the Eq. (16):

Figure 6.

Thermal boundary conditions in external environment of vessel [1].

$${\mathrm{\lambda }}_{\mathrm{eff}}\frac{\mathrm{\delta T}}{\mathrm{\delta r}}\left({\mathrm{r}}_{\mathrm{o}},\mathrm{t}\right)=\mathrm{U}\left({\mathrm{T}}_{{\mathrm{r}}_{\mathrm{o}}}-{\mathrm{T}}_{\mathrm{f}}\right)$$E16

$$\mathrm{U}=\frac{1}{{\mathrm{R}}_{\mathrm{s}}}$$E17

$${\mathrm{R}}_{\mathrm{s}}={\mathrm{R}}_1+{\mathrm{R}}_2$$E18

$${\mathrm{R}}_1=\frac{{\mathrm{r}}_{\mathrm{o}}ln\left(\frac{{\mathrm{r}}_{\mathrm{w}}}{{\mathrm{r}}_{\mathrm{o}}}\right)}{{\mathrm{\lambda }}_{\mathrm{w}}}$$E19

$${\mathrm{R}}_2=\frac{1}{{\mathrm{h}}_{\mathrm{o}}}$$E20

where h_o is convection heat transfer coefficient of surrounding fluid of vessel (w/m.K). r_o is external radius of the vessel (m), Rs is equivalent resistance, r_w is inner radius of vessel (m), T_f is bath temperature of vessel (K), U is the overall heat transfer coefficient (W/m².k), λ_eff is effective heat transfer conduction coefficient (W/m.K), and λ_w is the thermal conductivity of the vessel’s wall (W/m.K) [1].

9.6 Nanotube’s properties

The smallest inner diameter of the nanotube has been reported to be 0.4 nm, and the distance between the nanotubes is equal to 0.34 nm. Hence, to obtain the number of the nanotube wall, Eq. (21) is used. As the nanotube diameter increases, the number of wall increases:

$$N_{\mathit{\text{wall}}}=\frac{1}{d_d}\left(d_{\mathit{ext}}-d_{\mathit{int}}\right)+1$$E21

where N_Wall is the number of nanotubes wall, d_d is the distance between the walls (nm).

$$\rho =\frac{4000}{1315}\left[\frac{N_{\mathit{\text{wall}}}}{d_{\mathit{ext}}}-\frac{2d{\sum }_{i=0}^{N_{\mathit{\text{wall}}}^{-1}}i}{d_{\mathit{ext}}^2}\right]$$E22

d_ext is external diameter of the nanotube (nm), and d_int is internal diameter of the nanotube (nm). The weight and density of nanotubes depend on the internal and external diameter of nanotubes and the number of walls.

The properties of methane, natural gas, and carbon nanotubes are given in Tables 2 and 3. Nanotubes made of silicon can be called a competitor to carbon nanotubes, because there are many similarities between carbon and silicon. In this experiment, which is performed in a laboratory environment, pure methane gas is used, but on a large and industrial scale, natural gas must be used. By looking at Table 4, the natural gas composition used in this experiment can be obtained [1].

Parameter	Unit	Gas type	Value
Conduction heat transfer coefficient	W/(m.K)	Methane	0.035
		Natural gas	0.0335
Specific heat capacity	j/(Kg.K)	Methane	2265
		Natural gas	2340
Dynamic viscosity	Pa.s	Methane	1.5e−5
		Natural gas	1.04e−5
Specific heat ratio	_	Methane	1.32
		Natural gas	1.32
Density	Kg/m^3	Methane	0.656
		Natural gas	0.668–0.717
Molecular weight	gr/mol	Methane	16.04
		Natural gas	19
Critical temperature	°C	Methane	−82.3
		Natural gas	−62.7
Critical pressure	psi	Methane	4.64e+6
		Natural gas	4.564e+6

Table 2.

Natural gas and methane properties [1].

Parameter	Unit	Type	Value
Density	Kg/m^3	C	60–2200
		Si	232.9
Conduction heat transfer coefficient	W/(m.K)	C	12–600
		Si	159
Specific heat capacity	j/(Kg.K)	C	0.75–0.85
		Si	0.7
External diameter	nm	-	4–25
The distance between the nanotubes	nm	-	0.34

Table 3.

Specification of nanotubes [1].

Component	Composition
Methane	95
Ethane	3.2
Propane	0.2
i-Butane	0.03
n-Butane	0.03
i-Pentane	0.01
n-Pentane	0.01
Hexane and heavier	0.01
Nitrogen	1
Carbon dioxide	0.5
Oxygen	0.02
Hydrogen	Nil

Table 4.

Composition of natural gas [1].

10. Influence of different factors on absorption in CNT

10.1 Nanotube’s diameter effect on the process

The diameter of the nanotubes with sizes of 5, 10, 15, and 30 nm was considered to investigate the effect of the outer diameter of the nanotubes on the process, and the other parameters listed in Table 5 were selected. As the diameter of the nanotubes increases, the walls of the nanotubes increase, and thus, the active surface area of the nanotubes for adsorption increases. As the outer diameter of carbon nanotubes increases, their adsorption capacity increases (Figure 7). It has been proven that by doubling the diameter of the nanotube, the absorption of natural gas in the pipes will increase by 45%. With an increase in the diameter of the nanotube, nanotube walls increase, and due to its density per unit mass, the adsorption capacity increases.

Parameter	First series	Second series	Third series	Fourth series
External diameter (nm)	Changeable	20	20	20
Bed porosity (%)	90	Changeable	90	90
Loading pressure (Pa)	5.2e+6	5.2e+6	Changeable	5.2e+6
Temperature of water bath (K)	310	310	310	Changeable

Table 5.

Input data [1].

Figure 7.

Adsorption capacity at different diameters of the nanotubes [1].

To prove that less porosity causes more gas to be absorbed, the porosity values of 70, 80, 90, and 98 were considered. The other parameters are listed in Table 5. Based on this, the mass loaded in the container increases if the porosity decreases, resulting in an increase in the total amount of gas adsorbed in the nanotube. The adsorption capacity of the tubes will not change continuously with changes in porosity (Figure 8) [1].

Figure 8.

Adsorption capacity at different porosity [1].

10.2 Loading pressure effect on the process

To evaluate the effect of the applied pressure, pressures of 5, 20, 35, and 50 were applied. The rest of the parameters are listed in Table 5. As the applied pressure increases, the amount of gas introduced and the nanotube adsorption capacity increase (Figure 9). But increasing pressure has limitations in terms of safety, manufacturing costs, and more. During emptying, the container pressure should be reduced to the ambient pressure. A pressure of 5 Pa was chosen for the ambient pressure. The adsorption capacity tripled when the applied pressure increased from 20 Pa to 35 Pa. This increase in pressure increases the molecular density of the gas in the container space. As the pressure increases, the gas molecules penetrate the inner layers of the adsorbent and the amount of gas absorbed increases [1].

Figure 9.

Adsorption capacity at different pressure [1].

10.3 Surrounding condition effect on the process

To investigate the effect of temperature (water bath temperature) on the process, environmental conditions (water bath temperature) 298 K, 305 K, 320 K, 335 K, and 350 K were considered. The other parameters are based on Table 5. Figure 10 shows that the natural gas adsorption capacity of nanotubes that are exposed to temperature decreases. Because the temperature of the container is low at the beginning of the process, the maximum gas absorption capacity is obtained. Therefore, it is better to keep the temperature low and increase the discharge time to get better results during the charging process. For example, the adsorption capacity at 298 K is 0.4945 g/g. By increasing the temperature to 320, by reducing the adsorption capacity by 22%, 0.3826 g/g is obtained. Optimal conditions for this work include the maximum diameter of the carbon nanotubes and the applied pressure and the minimum amount of porosity (Table 6).

Figure 10.

Adsorption capacity at different temperature [1].

Numerical adsorption capacity (gr/gr)	Material	Study type	Adsorption capacity (gr/gr)
0.83	SWCNT	Numerical	0.35
	KOH activated	Experimental	0.1
	BPL	Experimental	0.06
	Pre-oxidized		0.065
	Notpre-oxidized		0.05
	Chemical activation	Experimental	0.09

Table 6.

Comparison of gas adsorption capacity in the presence of different adsorbents [1].

The absorbed gas in the CNG tank is 11.2 grams, which is 25.9 grams using multiwalled nanotubes. By comparing the results, it can be seen that nanotubes have the highest and best percentage of storage and use to absorb and store natural gas in tanks [1].

11. Conclusion

Natural gas is a clean source of energy, but an efficient and economical means of storing and transporting it is a challenge that is a growing research area of interest. CNTs have the potential to store natural gas at low pressures and are an economical and efficient candidate for storing and transporting natural gas. Structural defect in SWCNT improves its methane adsorption capacity. Purification of MWCNT with acids increases its methane adsorption capacity. Increasing pressure increases CNT methane adsorption capacity while increasing temperature decreases CNT methane adsorption capacity. Adsorption capacity and adsorbed gas increase with increasing MWCNT diameter. Increasing the diameter of the nanotube reduces its density. Natural gas is more absorbed in carbon nanotubes than in silicon nanotubes. The porosity of the tanks has a significant effect on the adsorption capacity (gr/gr), but affects the total adsorbed mass of the gas (gr). By reducing the porosity of the tank, the loaded mass of the adsorbent in the container increases, and as a result, natural gas storage becomes more. Adsorption capacity is a function of adsorbent, temperature, and pressure. As the loading pressure increases, the inlet and gas absorption capacity improves. The adsorption capacity of the bed decreases with increasing bed temperature. Optimal conditions are a combination of maximum nanotube diameter, loading pressure, minimum possible porosity, and water bath temperature in the presence of carbon nanotubes.