The Post-Extrapolation Method (PEM) is a computational approach designed to enhance the accuracy of hydraulic transient simulations, particularly in oil and gas transportation systems where pump startup and gas release dynamics are critical. In petroleum pipeline networks, rapid pressure fluctuations during pump startup can trigger dissolved gas release, altering fluid compressibility, wave speed, and transient pressure surges. These effects contribute to cavitation risks, reduced operational efficiency, and mechanical instabilities in crude oil and natural gas transport infrastructure.

This study presents a comparative analysis of PEM applied to transient flow scenarios in oil and gas pipeline systems, benchmarking its accuracy in modeling gas release and predicting flow instabilities. The method is validated using experimental data from a centrifugal pump startup test replicating operational conditions in midstream oil and gas transportation. Experimental results indicate a peak transient pressure of 5.2 MPa, a flow rate variation of 3.8%, and an efficiency loss of 2.1% under gas release conditions.

PEM achieved only 1.4% deviation in peak transient pressure and 2.2% in flow rate prediction, outperforming conventional methods such as MOC (10% overestimation) and FDM (8% underestimation). Efficiency deviation was only 1.2%, making it the most accurate among the tested methods. Numerical stability analysis confirmed that PEM eliminates oscillatory behavior common in MOC and FDM under dynamic conditions, ensuring smooth transient responses.

PEM also demonstrated high computational efficiency, achieving a CPU time of 1.5 seconds, compared to 3.2 seconds for FVM (53.1% reduction) and 3.0 seconds for FEM (50% reduction). These findings highlight PEM as a robust and efficient approach for transient flow analysis in petroleum pipeline systems, accurately capturing gas entrainment effects and mitigating startup-induced shock waves, optimizing pump operation, ensuring pipeline integrity, and improving upstream and midstream transport efficiency.