Equivalent Leak-Area Estimation in Gas Pipelines: Analytical Modeling and Computational Analysis

This study develops an analytical inverse framework for estimating the effective area of a single leak at a known location in a horizontal gas pipeline. A one-dimensional isothermal diffusion model with constant resistance and separately parameterised boundary pressures is coupled with compressible discharge. Modal and Volterra representations describe pressure and leakage under choked conditions. Independent finite-difference verification gives a pressure root-mean-square discrepancy of 0.011 Pa in the finest benchmark comparison. Extended Monte Carlo tests cover four pressure-noise levels and three opening diameters; at 10 Pa noise, relative area root-mean-square errors are 11.61%, 2.90%, and 0.73% for 10, 20, and 40 mm openings, respectively. Location and resistance errors produce additional estimation bias. Across three leak positions, a 10-fold leakage increase requires area increases of 10.076–10.211 times because of local pressure feedback. However, a nonlinear-friction benchmark yields approximately 1.00 kPa pressure discrepancy and drives absolute-pressure inversion to the zero-area bound. The results establish numerical consistency and conditional sensitivity while revealing substantial model discrepancy. Geometric-area recovery requires discharge-coefficient calibration, and operational application requires further model assessment and experimental validation.