Frequency response diagram for pipeline leak detection: comparing the odd and even harmonics

Pipeline leak detection using hydraulic transient analysis is a relatively new detection technique. For single pipeline systems, recent work has led to two different approaches for determining leak parameters based on leak-induced patterns displayed in a pipeline's frequency response diagram (FRD). The major difference between the two techniques is that one uses the leak-induced pattern within the odd harmonics of an FRD, while the other one uses the leak-induced pattern at the even harmonics. In order to compare and contrast the two approaches, the current research analyses the relationship between the characteristics of the leak-induced patterns and the parameters of the pipeline system. A dimensionless analysis, based on hydraulic impedance, is adopted to simplify the equations. The amplitudes of leak-induced patterns at both the odd and even harmonics in the FRD are found to be dependent on a critical parameter: the dimensionless steady-state valve impedance, Z*V. The value of Z*V is dependent on the steady-state valve opening. As a result, amplitudes of the leak-induced patterns within the FRD for any specific pipeline system can be controlled by the initial valve opening. This research also derives the equations for calculating the dimensionless leak size based on the value of Z*V and the amplitude of either leak-induced pattern. Finally, the two existing FRD-based leak detection methods are compared, and the approach using the odd harmonics is found to be superior.