## 1 Introduction  
The natural gas produced from the subterranean gas fields and subsequently transported through pipelines should meet certain specifications such as environmental and safety standards as well as those of sale gas sectors. The products destined for sale should be free of undesirable contaminants, e.g., carbon dioxide (CO\({}_{2}\)) and hydrogen sulfide (H\({}_{2}\)S), which are both toxic and unfriendly from an environmental point of view. For instance, CO\({}_{2}\) is considered the main contributor to global warming and climate change. Several treatments are employed to remove acidic gases from natural gas. The most famous are the alkanolamine-based treatment operations [1; 2; 3]. This technique was firstly introduced for carbon dioxide removal in 1991 [4; 5]. The used alkanolamines are organic compounds, such as monoethanolamine (MEA), diethanolamine (DEA), and triethanolamine (TEA). By far, MEA was the most preferred alkanolamine compared to DEA and TEA because of its reactivity, low molecular weight, and lower required circulation to maintain a given amine to acid-gas mole ratio. The gas-liquid absorption in amine-based solvents is an efficient process in gas sweetening. Nevertheless, some imperfections have been observed, such as the creation of corrosive byproducts due to the amine degradation, water transfer to the gas stream during the desorption stage, and loss of the feedstock (amine), making the treatment operations expensive [6; 7; 8; 9; 10]. As an alternative, a new class of non-aqueous and environmentally friendly innovating fluids, known as ionic liquids (ILs), has emerged. ILs have many industrial applications such as catalysis for clean technology [11] and the removal of contaminants from refinery feedstock [12]. Furthermore, Ion Engineering Company is intended to use the know-how of ionic liquids for industrial-scale sweetening of natural gas and flue gas CO\({}_{2}\) separation [13; 14], as stated by [PERSON] et al. [15]. Ionic liquids are molten salts, which are liquid (non-volatile) at room temperature. They are comprised exclusively of positively and negatively charged ions. Due to their bulky and asymmetrical cation structure, ILs have a low affinity to constitute crystals [16]. Manipulation of the cation and/or anion allows designing ILs adaptable to any particular application requirements [17]. Moreover, ILs are a perfect medium for acid gas solubilization over wide ranges of temperature and pressure. Thus, great attention was paid to evaluate the performance of ILs as a gas-cleaning agent in gas refinery plants [10]. The only and the most discussed disadvantage related to the use of ILs is their high viscosity, but it can be bypassed as the viscosity can be regulated over a reasonable range of about \(<\)50 cP to \(>\)10,000 cP by selecting an adequate mixture of cation and anion [15]. In the past few years, many experimental studies were conducted to estimate the solubility of acid gases in ILs [1; 6; 8; 10; 18; 19], especially the carbon dioxide solubility [20; 21; 22; 23; 24]. The obtained results confirmed the ILs to be very efficient in carbon dioxide removal. Unfortunately, the experimental studies require many laboratory tests, which are expensive, difficult, tedious, and time-consuming. As an alternative strategy, the solubility of acid gases in ILs has been modeled using thermodynamical laws and the equation of state (EoS). The thermodynamic laws used for modeling the solubility of acid gases in ILs can be divided into four groups that include cubic equations, quantum mechanics-based methods, activity coefficient methods, and statistical mechanics-based molecular approaches [25]. The most used models are the Peng-Robinson equation of state (EoS), the generic Van der Waals EoS, the generalized Redlich-Kwong cubic EoS, the law and extended law of Henry, and the equation of Krichevsky-Kasarnovsky [8; 26; 27; 28; 29; 30; 31; 32].