## 1 Introduction  
Methane (CH\({}_{4}\)) and carbon dioxide (CO\({}_{2}\)) gases coexist often in nature, forming gas mixtures, such as natural gas, biofuel gas, landfill gas, coal bed methane, etc. [1, 2, 3, 4, 5]. Separation of CO\({}_{2}\) gas from CO\({}_{2}\)/CH\({}_{4}\) mixed binary gas is a core and strategic target in enhancing the gas purity and efficiency. The existence of CO\({}_{2}\) impurity within CH\({}_{4}\) gas reduces its heating value and leads to pipeline corrosion, especially if moisture is found [6]. Furthermore, CO\({}_{2}\) and CH\({}_{4}\) gases are key players in the amassing of greenhouse gases, and subsequently in the augmented global warming crisis [7]. The greenhouse warming impact of CH\({}_{4}\) is 21 times bigger than that of CO\({}_{2}\)[8]. Owing to the strong augmentation in the cost of oil and recent rigorous ecological regulations, there is a noticeable rise in the extraction of natural gas as a strong competent source of energy [9]. Therefore, it is desired to establish efficient techniques for removing CO\({}_{2}\) gas from natural gas. The separation of CO\({}_{2}\) gas from natural gas or biogas mixtures is of a vital importance to their economic value, and is an issue of dire investigations [10, 11]. It is reported that that natural gas is principally formed from CH\({}_{4}\) (95%) and C\({}_{2}\)H\({}_{6}\) (5%) while the biogas mainly includes CH\({}_{4}\) (45% to 65%) and CO\({}_{2}\) (30% to 40%). The higher content of CO\({}_{2}\) (30% to 40%) contributes to the much lower energy of biogas comparing to the natural gas [12]. The separation of CO\({}_{2}\) from gas mixtures is conducted by numerous techniques, such as cryogenic distillation, absorption, membrane technology, and adsorption [13]. The use of adsorption is of strategic importance in industry. Numerous materials (e.g., carbons [14, 15], zeolites [8, 16], metal organic frameworks [17, 18], molecular sieves [19, 20], and clays [21]) have attracted attention as adsorbents to separate mixtures of CO\({}_{2}\) and CH\({}_{4}\) gases. The distinguished selectivity is the most important and unique feature of adsorption processes over other separation techniques. The informative knowledge of pure and multi-component adsorption equilibrium data is necessary for designing and optimizing industrial units, and is very pivotal for determining the selectivity and the adsorption capability of specific adsorbents [6]. Nonetheless, binary or multicomponent adsorption experiments are very difficult and time-expensive. Thus, it would be advantageous if such findings could be forecasted using the traditional adsorption models. For its simplicity, the extended dual site Langmuir (DSL) model is commonly used to forecast the mixed gas adsorption equilibrium data from single component adsorption data [22; 23; 24]. Carbon nanotubes (CNTs) have attracted much attention as a result of their distinct chemical and physical properties [25; 26]. CNTs are one-dimensional nanoscale substances formed of carbon atoms, where each carbon atom is sp\({}^{2}\) hybrid, and is bonded covalently to three adjacent carbon atoms. Upon the number of their wall layer(s), CNTs can be classified as either single-walled carbon nanotubes (SWCNTs) or multiwall carbon nanotubes (MWCNTs) [27]. It is well-known that the activated carbons are featured with disorder and non-uniformity, while MWCNTs are featured with highly uniform and ordered structures. It is expected that the structure uniformity of MWCNTs may be affected when mixing them with activated carbon nanoparticles, which reflects their changing performance in gas adsorption or separation processes. It is well-known that CNTs are very weak in adsorption capacity; therefore, the addition of other carbon materials may enhance their adsorption performance. In addition, according to the authors' knowledge, there is no work available in the literature to address the carbon-carbon interactions effect on adsorption.