Semi-empirical closed-form model for methane leakage monitoring and sensor placement

Due to the significant hazard posed by gas leaks in enclosed spaces and the current lack of mature research in this area, the present paper proposes a methane-leak dispersion prediction method based on a semi-empirical closed-form model. It is tailored to small-orifice, high-speed leak scenarios in semi-enclosed spaces such as commercial kitchens, and optimizes both gas concentration forecasting and sensor-placement design. A laboratory platform was used to simulate the methane leakage process, and a two-stage parameter calibration strategy combining particle swarm optimization (PSO) with the L-BFGS-B algorithm improved model accuracy and computational efficiency. Experimental results show that the conventional Gaussian plume model yields substantial prediction errors in the near-source and ceiling-reflection regions, with an average RMSE of 0.49. By introducing momentum jet, buoyancy coupling, and a temporal correction factor, the semi-empirical closed-form model reduces RMSE to 0.27 and raises R2 to 0.91, confirming high fidelity across all spatial and temporal scales. Through optimized sensor placement, the final scheme achieves full deployment within 5 min and attains over 90 % leakage-detection accuracy, demonstrating clear advantages over traditional computational fluid dynamics (CFD) approaches in engineering practice. The method's short computation time and low hardware requirements make it well suited for on-site deployment.