Developing nuclear magnetic resonance imaging for engineering applications

Abstract

Nuclear magnetic resonance (NMR) is a powerful, noninvasive measurement method which can be used to obtain spatially resolved information about fluid distributions within media. In the present work, an approach for quantitatively analyzing magnetic resonance imaging (MRI) data is extended for use with multiple spatial dimensions. A relaxation model is introduced and then used in an inverse problem to obtain local estimates of relaxation distributions. These distributions are then used to obtain spatial distributions of the intrinsic magnetization, the key quantity for quantification of NMR images. The inverse problem utilizes B-spline basis functions to represent the unknown relaxation distribution and a regularization term to stabilize the solution. The impact of the regularization is controlled through the use of a regularization parameter which is chosen using a data driven, computerized method based on nonparametric regression. The approach is demonstrated on laboratory data obtained from a Bentheimer sandstone sample to obtain one-and two-dimensional porosity distributions.