Analytical and Asymptotic Modeling of Coupled Transient Gas Redistribution Induced by Simultaneous Injection and Withdrawal in Transmission Pipelines

This study develops an analytical and computational framework for investigating coupled transient gas redistribution induced by simultaneous localized injection and withdrawal in transmission pipelines. Unlike conventional transient-flow approaches that treat inflow and outflow processes independently, the proposed formulation establishes a unified coupled source-sink model capable of describing their dynamic interaction within a single transmission system. Using the Charny regularization approach, the governing equations of one-dimensional non-stationary isothermal compressible gas flow are transformed into a diffusion-type formulation. The pipeline is decomposed into three interacting spatial regions connected through continuity-based pressure and mass-flux interface conditions, and closed-form analytical solutions for the dimensionless pressure field are derived in the Laplace domain. A practical Laplace-domain approximation is introduced for computational evaluation of transient pressure redistribution. The results reveal the existence of a characteristic balancing point separating injection-dominated and withdrawal-dominated behavior and demonstrate rapid convergence toward a quasi-steady redistribution regime. Optimization analysis shows that redistribution-induced hydraulic disturbance is minimized near a balanced source-sink operating condition. The proposed framework provides new mathematical and physical insight into coupled transient redistribution phenomena and extends the analytical theory of non-stationary gas dynamics through coupled redistribution analysis, asymptotic stabilization behavior, and redistribution-oriented optimization within a unified Laplace-domain formulation.