An Efficient, Robust, and Data-Oriented Inversion Method for Noisy T2 Echo Trains

Abstract

Abstract For NMR logging of hydrocarbon bearing formations, the inversion of T2 echo trains is a critical pre-processing step to compute porosity, permeability, and fluid saturations of formations. To accurately and efficiently invert NMR measurement data, a new inversion method is presented to compute the optimal solution of T2 distribution with a unique optimal regularization factor for NMR logging data processing. This inversion method has no assumption about the white noise of a T2 echo train. A new supplementary nonlinear equality constraint was introduced to optimize the solution of T2 distribution by explicitly taking into account the measured noise of a measured T2 echo train. An efficient iterative algorithm has been developed to solve the nonlinear optimization problem defined in the new inversion method. An initial-guess solution of the regularization factor was proposed for accelerating the searching process of the regularization factor. The new inversion method has been verified with synthetic T2 echo train data and applied to process T2 echo train data of core samples of carbonate and Berea sandstone formations that are saturated with different fluids. This method has also been compared with conventional methods. The testing and comparison results show that: The optimal solution of T2 distribution from the new inversion method has a unique solution that is independent of the pre-selected values of regularization factor, so does the regularization factor. The optimal solutions T2 distribution and regularization factor will be convergent to their true solutions when the SNR of echo train data becomes sufficiently high.The computation cost for searching the optimal solutions of T2 distribution and regularization factor using the new nonlinear optimization algorithm is only a few iterations.The initial-guess solution of the regularization factor is more close to the solution determined from the S-curve method, which could be higher than the optimal solution of the regularization factor searched in the new inversion method.