Transient Pressure Redistribution and Hydraulic-Junction Localization in Ring Gas Pipelines: Analytical Modeling and Numerical Verification

Transient pressure redistribution in ring gas pipelines is governed by both withdrawal intensity and spatial configuration, which determine circumferential flow redistribution and the location of the hydraulic junction. This study develops an analytical framework for transient pressure dynamics and hydraulic-junction localization in ring pipelines with multiple discrete withdrawals. A closed-form Fourier-series solution is derived and numerically verified against an independently implemented finite-difference model, demonstrating close analytical–numerical agreement. The hydraulic-junction coordinate is identified from the transient pressure-extremum condition, while a dimensionless localization factor is introduced to characterize its position relative to the geometric midpoint. Two contrasting ring configurations reveal distinct behaviors: For the investigated 30 km configuration, the hydraulic junction remains localized near the geometric midpoint under the considered proportional-withdrawal scenarios. In the second, increasing withdrawal loading causes progressive upstream migration toward a withdrawal-controlled limiting location. A steady balanced flow-reversal criterion provides a physical interpretation of the limiting junction position without being extended to globally unbalanced transient states. The results further show that efficient distributed withdrawal requires consideration of both pressure retention and hydraulic-junction behavior. The proposed framework provides a mathematically interpretable basis for assessing transient hydraulic states and withdrawal strategies in ring gas pipelines.