A study of regulation inversion method in 2D NMR logging based on SVD and BRD

The 2D NMR logging describes fluid property both in diffusion and relaxation and thus has great superiority in evaluating crude oil formation. Nowadays, 2D NMR logging has become a research focus in reservoir exploration. In this paper, we studied deeply the principle of 2D NMR logging, discussed systematically the mechanism of CPMG-DE pulse sequence, which measures diffusion coefficient and relaxation time simultaneously. Based on the model of 2D NMR spectrum, a regulation inversion algorithm based on SVD and BRD was proposed to get the (T₂, D) distribution map. In this algorithm, the raw data was compressed through SVD method and then interpreted into (T₂, D) distribution by Tikhonov regulation algorithm with non-negative constraint, in which the best normalizing factor was chosen through BRD method. Simulation and numerical analysis have shown that the inversion designed in this paper is of high efficiency, small error and little reliance on prior information. Even when the SNR of raw data is as low as 50, the (T₂, D) distribution map can be effectively interpreted. Compared to the traditional method-TSVD, it is expected to perform better in real-time 2D NMR logging interpretation. Furthermore, experiments with our own designed NMR logging tool were conducted to measure CuSO4 solution's (T₂, D) distribution. The results have shown that with the inversion algorithm devised in this paper, the interpretation error of relaxation time and diffusion coefficient are only 2% and 4% respectively, which exhibited a great improvement compared to TSVD.