A Study Of Inverse Method And Application In NMR Logging

The fundamental advantage of nuclear magnetic resonance(NMR) logging technology is that it can provide a wide range of reservoir information, and solves a lot of key questions in the oil exploration and development. This technology obtains the comprehensive interpretation of logging data by studying the inversion of collected original echo strings. The process of inversion is actually to solve the first kind Fredholm integral equation. The difficulty of nuclear magnetic resonance inversion has greatly increased due to the large condition number of the coefficient matrix and the low signal-to-noise ratio of the observation data and the complex geological conditions of the reservoir and so on.In this thesis, the specific implementation process of the inverse algorithms in NMR logging is discussed in detail, and it makes the comparison and evaluation on these algorithms from both the theory and the application. First of all, two kinds of algorithms have been derived for the inversion of one-dimensional NMR relaxation signals on the basis of the mathematical model of nuclear magnetic resonance logging: the modified SVD method and the modified LSQR algorithm. The modified SVD algorithm introduces the regularization method into the basic SVD algorithm, and can be divided into two ways including the damping method and the truncation method. This algorithm uses the L-curve method to choose the regularization parameters. The modified LSQR algorithm fully exploits the standard LSQR algorithm's advantage of suppressing data error and introduces the regularization operator to constrain the flatness of the model and get the smoothest solution.Compared to one-dimensional logging, two-dimensional NMR logging provides more information, but its inversion is more challenging. Based on the data compression, this thesis provides two algorithms that are suitable to two-dimensional NMR: the modified truncation method and regularization inversion algorithm based on BRD method. To deal with the huge amount of data in the two-dimensional inversion, modified truncation method takes advantage of a more efficient compacted singular value depression method, which successfully solve the problem of insufficient memory caused by the basic truncation method. Regularization inversion algorithm based on BRD in the Tikhonov regularized frame transforms the constrained optimization problem into unconstrained optimization problem inversion algorithm, and reduces the dependence on prior information by optimizing, iteration and some other steps. Numerical simulation experiments and practical applications indicate that the algorithms proposed herein are able to effectively characterize pore fluids, thus laying the foundation for accurate calculation of physical property parameters of reservoir fluids.