Photonic crystals demonstrate photonic band-gaps in their optical spectra, due to the periodic contrast of refractive index. The periodic nature characteristic of photonic crystals exhibits the Bragg scattering phenomena, which only captures the targeted wavelengths to create resonance effect within the cavity structure. Using this phenomena, we present the model of High-Q 1D photonic crystal waveguide resonator for wavelengths centered at 2.4 µm in silicon-on-insulator (SOI). Moreover, silicon proves to be a low-loss material for mid-IR range of up to 4 µm. The modelling and optimization of the silicon photonic crystal is achieved by performing 3D FDTD simulations using a commercial software. A well-known L3 cavity is designed in 400 nm thick SOI layer by removing three holes from the center. Due to fabrication tolerance circular holes are used to achieve photonic crystal effect. The cavity is optimized in two stages by placing a magnetic dipole source at the center. In first stage, a two-step optimization was performed by optimizing the air hole period followed by the radius. In second stage, the period and radius optimization of the inner most air holes of the cavity were carried out to achieve the maximum High-Q factor of 77,538 at wavelength of 2.4 µm. Our proposed design is consistent with the available lithography for achieving the mid-IR sensors in SOI. Also, Multi-Project-Wafer (MPW) monolithic integration can be achieved using single etch process reducing the effective cost. These sensors can widely be used for gas sensing applications for example environmental monitoring of public areas to monitor the concentrations of carbon dioxide gas.