We propose various optical ring gas sensors. These gas sensors are promising candidates for integrated on-chip sensing. The sensing operation depends on the change in the effective index. We show a detailed study of different sensors utilizing the absorption wavelength of both methane and carbon dioxide gases. These sensors mainly operate at the range of mid-infrared wavelengths because it contains the vibrational resonance of the gases of interest. We provide the details about the dimensions and the material used in our different structures. Moreover, we report sensitivity up to 5938  nm  /  RIU, and the full-width-half maximum (FWHM) and figure of merit (FoM) for all designs are also calculated. We succeeded in squeezing the FWHM to 4.76 nm and increasing the FoM to 1744.72.