Analytical Solution to Fundamental Bloch NMR Flow Equations for Non-Zero Porosity Transformation Parameter

摘要

The Bloch NMR flow equation was transformed into a porous media based on the condition that with transformation constant ‘a’ which must be positive. Furthermore, an emerging differential equation along the line was also solved for a physical case where using the method of partial integration. It assumed that the parameter ‘A’ that was a consequence of transforming the fundamental Bloch NMR flow equation into a porous media is not trivial, and thus cannot be ignored. It’s been decades since analysis has been done using the porosity derived on an assumption of triviality of this parameter. The interesting thing about our solution is that it encompasses the solution for a trivial ‘A’ which we believe to be a special case. The solution to this equation is useful in describing physical phenomenon such as permeability and for modelling various other intrinsic factors that affect or influence pore dynamics. The result obtained in this study can have applications in functional magnetic resonance imaging (fMRI), petroleum well design and geological engineering.