Mathematical modelling and simulation of leak detection system in crude oil pipeline

A first-order differential leak detection model that accurately detects leaks in a crude oil pipeline is presented. This model incorporates a leak factor K(L) in the axial direction, which is simulated by applying the finite element method of numerical solution using COMSOL multi-physics software. Additionally, the model includes the transport equation for turbulent kinetic energy and the rate of kinetic energy model. Eigenvalues for velocities and pressures were determined and plotted against time for various pipe segments. The system is stable when the Eigenvalue is zero, but a leak is declared when the Eigenvalue for pressure or velocity is less than one. The study shows that pressure measurements are more sensitive parameters for detecting leaks than velocity measurements, and the sinusoidal waveform characterizes leak behaviours for velocity.