基于SVD和BRD的二维核磁共振测井正则化反演算法研究

二维核磁共振能从"弛豫-扩散"两个维度上展现流体性质,在识别稠油储层方面具有理论优势,是当前核磁共振测井技术的研究热点.本文深入研究二维核磁共振测井原理,系统分析CPMG-DE脉冲序列测量扩散系数与弛豫时间的方法,结合核磁共振二维谱数理模型,提出一种基于SVD和BRD的正则化反演算法.该算法通过SVD压缩数据,采用带非负约束的Tikhonov正则化方法求解流体"弛豫-扩散"分布,并基于BRD算法迭代确定最佳正则化因子.模拟实验与数值分析表明,该算法无需先验信息、运算效率高、相对误差小,在原始数据信噪比低至50时,仍可有效获取流体(T₂,D)二维分布.在二维核磁共振测井数据实时解释应用中,该方法较传统反演算法(如TSVD)具有较大优势.同时,在自主研发的核磁共振测井仪测量CuSO₄溶液(T₂,D)分布的实验显示,本文设计算法对弛豫时间和扩散系数的反演误差分别仅为2%和4%,较TSVD算法有较大改善.

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.