Heat-dependent processes, such as distillation and absorption, account for more than 10 % of the world's energy consumption, increasing greenhouse gas emissions and global pollution [1]. Membrane-based separation processes are newer than traditional and common separation methods and do not require heat and are therefore a competitive approach for gas separation [2]. Gas separation with membrane technology is gorgeous due to its high productivity, little energy consumption, and simple action. Membranes with high penetrability and high selectivity are urgently needed [3].

The division of membranes based on the type of materials used in them includes inorganic, polymeric, mixed matrix, and liquid membranes. Mineral membranes include silicate, metal, glass, metal oxide, and zeolite materials, etc. which have many advantages compared to polymeric membranes: such as chemical stability, high thermal stability, and mechanical stability, as well as reduced plasticization and improved regulation of pore size and distribution, enable enhanced control over selectivity and permeability [4].

Zeolite membranes are examined among the various types of membranes. In recent times, the potential of zeolite membranes as separation membrane materials has been recognized due to their chemical and thermal stability, rigid pore structure, and outstanding support for molecular sieving [5]. Zeolite membrane separation technology involved the selection of zeolite materials. Thus far, many zeolites have been reported for the preparation of gas separation membranes [6]. Zeolites are microporous crystalline aluminosilicates with high thermal and chemical stability, composed of a three-dimensional framework, which are broadly used as catalysts in a diversity of reactions, as adsorbents for separation processes, and in environmental remediation [7].

RHO zeolites were first reported and named by Harry E. Robeson et al., in 1973 [8]. RHO-type zeolite is an artificial zeolite with a cubic structure with narrow pores of 8 rings. Typical Si/Al proportions are around 4 or 5:1. These membranes have holes with a size of 3.6 × 3.6 Å2 [9]. The reversible operating mechanism of Zeolite RHO can be regulated to gradually transition from one stable configuration to another through the application of dehydration, vacuum, and alterations in temperature. This zeolite exhibits significant potential for utilization in molecular sieving applications of small molecules, rendering it a highly promising subject of investigation for materials that are both heat-resistant and highly flexible [10].

Computer simulations can deliver insight into the separation ability of molecular sieve materials [[11], [12], [13], [14]]. The molecular dynamics (MD) technique presents a robust approach to investigating gas separation systems. Membrane distillation is a viable method for studying the gas mixture separation mechanism. MD simulations are a precise and dependable method for tracking the movement of particles at the atomic scale, thereby enabling the attainment of macroscopic properties through structural analysis. Molecular simulations offer a valuable means of characterizing the static and dynamic attributes of fluids confined within microporous environments [15]. MD is one of the simulation methods to study the temporal motion of constituent molecules by combining Newton's equations of motion for a system of interacting molecules [7].

Natural gas (methane as the main component) has been broadly used in daily life [6]. Methane, which is represented by the chemical formula CH4, is the primary combustible substance found in natural gas, alongside various other hydrocarbons. Additional constituents encompass carbon dioxide (CO2), nitrogen (N2), oxygen (O2), hydrogen sulfide (H2S), helium (He), water (H2O), and other similar elements [16]. Significant quantities of gases that are rich in N2 and are generated at the wellhead and cannot be transported through pipelines are frequently released into the atmosphere through venting or flaring processes that can last for several days. The presence of nitrogen in natural gas is a prevalent impurity that poses a significant challenge in its elimination. The devaluation of natural gas is observed. Broadly speaking, the primary drawbacks associated with the presence of nitrogen in natural gas are as follows [17,18].

Reducing the calorific value of fuel.

Reducing the temperature of the combustion flame and increasing the energy loss through combustion gases.

Increasing the cost of construction of transmission pipelines and related pressure-boosting facilities.

Increasing the number of nitrogen oxides in combustion products with pure oxygen.

The quest for a financially feasible technique for the elimination of N2 has presented a noteworthy challenge to the natural gas sector. Various methodologies have been explored by scholars to segregate nitrogen (N2) from natural gas (NG). Currently, the prevailing technology employed is cryogenic distillation, which is associated with substantial capital and operational expenditures [19]. One separation technology that has been successfully tested is pressure swing adsorption (PSA), which uses molecular sieves to preferentially absorb N2. This separation process can be done at room temperature. However, the commercialization of PSA processes for N2 removal is slow because it is difficult to find a satisfactory adsorbent with adequate N2/CH4 selectivity. Membranes and membrane processes are another option [[20], [21], [22], [23], [24]].

To address this critical challenge, it is essential to consider the potential of advanced materials, such as zeolites, in gas separation applications. In 2014, Cheng and Hedin [9] made significant strides in the field of gas separation by focusing on CO2 removal from factory flue gas using RHO-type zeolite. Different forms of this zeolite have demonstrated a remarkable capacity for CO2 absorption, primarily owing to its unique structure. Notably, RHO-type zeolites exhibit high CO2 selectivity when compared to other gases like CH4 or N2. This selectivity can be attributed to their small pore diameter and the high surface polarity of RHO zeolites. These promising characteristics open the door to the development of materials that could enhance the selectivity and efficiency of N2 separation processes, addressing the challenges faced by the natural gas sector in a cost-effective manner.

In 2015, Sun et al. [25] investigated O2, N2, SO2, and H2S emission data in 4A and MFI zeolites obtained from MD simulations, specifically its dependence on concentration and temperature. Self-diffusion coefficients of all gases in two zeolites increase with increasing temperature at high concentrations. But due to the dissimilar topological structures of cages (4A) and straight channels (MFI), the order of diffusion in the two zeolites is different at lesser concentrations.

In 2022, Azizi et al. [26] examined how well the MFI zeolite membrane separated CH4 and N2 gases. Systems with MFI zeolite membranes and gas mixtures of varying CH4 and N2 concentrations were examined. The effects of hydrostatic pressure application and temperature increase on the separation process were studied in this study. Density mapping, density profiling, the potential of the mean force of gas molecules, permeability, and van der Waals interaction energy were all carefully analyzed. Methane molecules are purified on the feed side whereas nitrogen molecules are able to pass through the MFI zeolite channels. MFI GPU zeolite showed a maximum N2 penetration of 3.43 105 at 298 K and 0.5 MPa pressure, demonstrating its excellent performance in separating CH4/N2 gas combination. This zeolite membrane can potentially be an effective option for separating gas mixtures.

Deep Neural Networks (DNNs) and generally Artificial Neural Networks (ANNs) have been extensively employed in the modeling and data prediction of chemical processes and membrane separation processes. One notable application of DNNs in this context is the modeling of chemical transfer processes through poly-parameter linear free energy relationships (pp-LFERs) for organic chemicals [27]. These relationships are crucial for understanding and predicting the behavior of solutes in various chemical systems. By utilizing DNNs, researchers aim to accurately and quickly obtain solute descriptors, which are essential for constructing pp-LFER models.

In the field of membrane separation processes, DNNs have also found utility. The Donnan membrane principle, which relies on the immobility of ions between different phases, can be effectively modeled and understood using DNNs [28,29]. The physical existence of a semipermeable membrane is not always necessary in processes that operate based on this principle. DNNs enable the simulation and prediction of ion behavior and diffusion across different phases, thereby aiding in the optimization and design of membrane separation systems. Furthermore, DNNs have contributed to the modeling and prediction of various membrane processes used in desalination and water treatment. These processes include reverse osmosis, forward osmosis, and others. DNN-based models have been employed to enhance the understanding of the underlying mechanisms and to optimize the performance of these membrane processes [30]. By utilizing DNNs, researchers can analyze complex datasets, predict system behavior, and develop more efficient and sustainable water treatment technologies.

In summary, the purpose of this research is to investigate the CH4/N2 separation by RHO zeolite membrane using the molecular dynamics simulation method and the process modeling by DNN and data prediction for other operating conditions. The permeability and selectivity of zeolite membrane in gas separation were investigated. The effect of pressure and mixture concentration on the separation rate was also studied.