Analytical Investigation of Viscous and Non-Viscous Fluid Particles in a Restricted Region using Diffusion Magnetic Resonance Imaging Equation

Abstract

Nuclear Magnetic Resonance (NMR) technology has been applied in several ways to provide vital information about petro-physical properties of reservoirs. However, due to the need to study the molecular behaviours of particles of the fluids in different restricted media, diffusion magnetic resonance equation evolved from Bloch’s fundamental equations of magnetic resonance is hereby applied in spherical coordinates and solved analytically using the method of separation of variables and solution of Legendre equation by Frobenius method. The viscous fluid considered in this research work is unused engine oil while the non-viscous fluid is water. Maple 17 was used in plotting the graphs. The results obtained show that the analytical solution of Diffusion MRI equation adopted in the research work has shown clearly the difference in the behaviours of the particles of unused engine oil (viscous fluid) with magnetization value of 1.466557018x1014 and water (non-viscous fluid) with magnetization value of 2.311919954x1014 as a result of their responses as simulated in the study.