Leakage-Induced Transient Pressure Responses in Hydrogen-Enriched Gas Pipelines: Analytical Sensor-Response Modeling and Numerical Verification

This study develops and verifies an analytical framework for investigating leakage-induced transient pressure responses in hydrogen-enriched natural gas pipelines. A one-dimensional linearized diffusion model is formulated with a localized leakage interface, where pressure continuity and a derivative-jump condition describe the leakage disturbance. An eigenfunction expansion provides an analytical pressure solution, from which a convolution-based sensor-response kernel is derived. A representative 100 km pipeline with a leak at 20 km and sensors at 30, 40, and 60 km is investigated under three prescribed leakage intensities. The analytical solution is independently verified using the finite-difference method, with a maximum absolute pressure difference of approximately 0.108 Pa for a 250 m spatial grid. At 900 s, the intermediate leakage scenario produces additional pressure reductions of 20.007, 15.054, and 7.850 kPa at the respective sensors. The results demonstrate proportional sensitivity to prescribed leakage intensity and decreasing pressure-response amplitude with increasing sensor distance. A consistency assessment further reveals that a previously proposed exponential sensor-gradient condition is incompatible with the adopted initial and boundary conditions. The derived sensor-response kernel provides a mathematically consistent basis for interpreting transient pressure measurements and developing future inverse leakage-estimation methods.