Unsteady gas dynamics modeling for leakage detection in parallel pipelines

Abstract: This study presents a novel analytical framework for modeling unsteady gas dynamics in parallel pipeline systems under leakage conditions. The proposed method introduces a time-dependent leakage mass flow rate function, which dynamically captures the temporal decay of leakage based on real-time inlet pressure measurements. This functional form allows for a more physically consistent and mathematically tractable representation of gas loss compared to conventional constant-rate or stepwise models. The pipeline system is partitioned into three regions relative to the leakage point, and closed-form pressure solutions are derived using Laplace transform techniques. These expressions enable direct estimation of the leakage location through inverse pressure profiles, eliminating the need for computationally intensive iterative schemes. The analytical model is further validated against representative benchmark scenarios, demonstrating good agreement with literature-based results. A comparative analysis underscores the model's ability to localize leakage using minimal sensor data while preserving interpretability - an essential feature for deployment in industrial environments. The approach provides a lightweight yet robust alternative to purely numerical or machine learning-based solutions and offers potential integration into real-time monitoring systems. This work contributes to the field by unifying gas dynamic principles, sensor-assisted modeling, and analytical solution strategies to enhance the reliability and speed of leak detection in modern gas transport infrastructures.