Abstract
This study develops an analytical inverse framework for estimating the effective opening area of a single leak at a known location in a horizontal gas pipeline. One-dimensional isothermal flow is approximated by a diffusion-type pressure equation with linearised friction and independently decaying boundary pressures. A compressible discharge rela-tion couples leakage to local pressure, yielding explicit pressure and leakage representa-tions under choked conditions. An independent finite-difference solution verifies numeri-cal consistency, with a pressure root-mean-square discrepancy of 0.011 Pa in the finest benchmark comparison. Noise-free inversion recovers the prescribed area with a relative error of −0.0059%; independent pressure noise with a standard deviation of 10 Pa pro-duces a relative area root-mean-square error of 2.69% across 200 realisations. Five leakage fractions are examined at locations of 1, 4, and 9 km in a 10 km pipeline. A tenfold in-crease in leakage requires area increases of 10.076, 10.211, and 10.082 times, respectively, reflecting location-dependent pressure feedback. The framework provides conditional hy-draulic-size estimates; geometric-area recovery requires a calibrated discharge coefficient, and operational application requires experimental validation.