Simple graphical method for detection of a partial blockage or leak in a single pipeline

Transient-based methods in the frequency domain are used for fault detection in pipes. However, the required measurements are performed with a large number of valve frequencies. Sometimes the number of frequencies in traditional frequency-domain methods can be in the hundreds. More runs are required with higher harmonics when the required number of frequencies is more. The current study aims to overcome this difficulty of requirement of higher number of frequencies. The location and the size of a single leak or a single discrete blockage are proposed to be predicted using two appropriately chosen low frequencies. isopressure frequency responses (IPFRs) are generated by performing numerical experiments with these two low frequencies enabling determination of the fault. The methodology is demonstrated through various numerical examples. The results show that the procedure is quite accurate, with a high level of agreement between the actual and the predicted fault parameters. The error in the result is of the order of the chosen discretization. An uncertainty analysis is performed to illustrate that the prediction error caused by the error in the measurements of the pressure frequency responses (PFRs) depends on the location and the size of the fault itself. The error in prediction results is analyzed in uncertainty analysis with 0.10%, 0.15%, and 0.20% error in the peak head measurement. For the same error in the PFR measurement, the fault lying in a thin density of the contours would lead to a higher error in the final solution.