Mathematical analysis of discontinuities in the flow field of gas in a cylindrical pipe using diffusion MRI

Abstract

In this study, Magnetic Resonance Imaging (MRI) is used to detect partial and total blockage of hydrogen gas in a cylindrical pipe. Diffusion Magnetic Resonance (DMR) equation is solved analytically for flow of fluid in a radially symmetric cylindrical pipe. Appropriate boundary conditions were imposed and the radial axis varied to depict partial and total blockage in the pipe. The results show that for free fluid flow, the magnetization is between 0.004 and 0.005. For partial blockage, the magnetization reduces (signal loss) in value to 0.00001 and for total blockage it is zero (0). This method is a viable alternative to other methods of detecting blockage in fluid pipelines in oil and gas industry due to its noninvasive analysis of flow in fluid. The MRI model also registers signal in its first few seconds or microseconds. The analysis can also be useful in process industries where different network of pipes are used or machines use cylindrical pipes or tubes in transporting materials especially when there is a partial or total blockage at any point in the network.

Keywords: Bloch NMR Equations, DMR equation, Cylindrical pipe, Magnetization