Mass Imbalance Error of Waterhammer Equations and Leak Detection

The waterhammer equations can be used to compute mass inventory changes for pipeline leak detection. In such applications the pipeline is monitored continuously in time and there is no clear demarcation between steady-state and transients. This paper addresses a mass imbalance error of the waterhammer equations. We establish that the net mass influx error for the waterhammer equations at the steady-state with maximum flow-rate bounds the same error during transients. A method to evaluate this bound is presented. Using petroleum products pipelines as an example, we show that the waterhammer equations are not accurate enough for leak detection in some systems.