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This work aims to introduce a gas detection structure based on stacked layers of graphene-spacer-metal. The presented structure consists of three stacked layers. The first layer is the periodic arrays of graphene disks on top of a typical dielectric such as TOPAS or KAPTON with a known refractive index. Then the second layer provides an air gap opening room for a sample environment. Finally, the third layer includes the dielectric and a continuous graphene sheet. All the exploited elements are modeled by circuit element while the equivalent impedance of the whole structure is calculated. The impedance matching concept is also exploited to obtain absorption power based on the calculated impedance. Additionally, full-wave simulation is performed to investigate the circuit modeling accuracy. Achieving a perfect match for absorption versus frequency verifies the developed method's robustness. Furthermore, comprehensive and ample simulation results are reported to highlight the sensitivity and reliability of the proposed gas detector.