Abstract This paper studies various approaches of hydrogen-, boron-, nitrogen, and fluorine-doped graphene structures as selective membranes for helium gas diffusion in the presence of natural gas. Due to the study of the doping effect onto the diffusion process, the helium gas atoms pass through the created cavities in the doped nanoporous graphene membranes of C90H27, C87H27B3, C84H27N3, and C87H27F3. All calculations performed using GAMESS program. Results analysis by the quantum theory of Atoms In Molecules (AIM) and Natural Bond Orbital (NBO) showed that C87H27B3 has the highest probability of passing He through the natural gas. To investigate the temperature effect, the selectivity of helium atoms over natural gas calculated over the temperature range 300 K–1000 K. The results show that helium gas separation from other natural gas in 300 K reaches to a maximum amount. We believed that our result could give a good insight into extracting the He from natural gas in oil wells.

中文翻译：

---

H-、B-、N- 和 F- 掺杂纳米多孔石墨烯膜在天然气存在下的氦选择性：密度泛函理论研究

摘要 本文研究了氢、硼、氮和氟掺杂的石墨烯结构作为天然气存在下氦气扩散选择性膜的各种方法。由于对扩散过程的掺杂效应的研究，氦气原子穿过 C90H27、C87H27B3、C84H27N3 和 C87H27F3 掺杂纳米多孔石墨烯膜中产生的空腔。所有计算均使用 GAMESS 程序执行。分子中原子（AIM）和自然键轨道（NBO）的量子理论结果分析表明，C87H27B3通过天然气的He概率最高。为了研究温度效应，在 300 K-1000 K 的温度范围内计算了氦原子对天然气的选择性。结果表明，300K中氦气与其他天然气的分离量达到了最大值。我们相信我们的结果可以很好地了解从油井中的天然气中提取 He。