Numerical modeling of pseudo-homogeneous fluid flow in a pipe with leaks

Abstract

This work deals with the numerical modeling of single-phase flow in a pipe with one leak. The mathematical model governing mass, momentum and energy transport was established containing three coupled partial differential equations. These governing equations were numerically solved by discretizing time and space with backward finite differences, leading to one implicit scheme at every time step. The numerical solution was validated with available lab data obtaining good agreement. We present relevant results as the time behavior of upstream and downstream flow and pressure, while varying the leak location. Besides, we also show the temperature, pressure and flow profiles along the pipe when the leak is located near the inlet and outlet of the pipe. The predictive capabilities of the numerical model are remarkable to simulate the transient state of volumetric flow rate and pressure when a single leak is provoked at the pipe. A future application of our numerical scheme is for rapid automatic detection of loss of containment in pipes transporting valuable fluids as, for instance: oil, refined hydrocarbons, fuel, liquid catalysts, etc.