基于ADI-FDTD模拟的岩石核磁共振横向弛豫特征分析

Analysis of NMR Transversal Relaxation Based on ADI-FDTD Numerical Simulation

将复杂的骨架-孔隙系统抽象成等效双孔介质,根据Bloch方程构建数学模型,用交替隐式时域有限差分(ADI-FDTD)和联合反演迭代法(SIRT)进行横向宏观磁化矢量的数值模拟与核磁共振T2谱的反演,定量研究扩散系数、弛豫速率、孔隙组分比和孔隙宽度对核磁响应的影响.结果表明:横向宏观磁化矢量衰减速率与扩散系数和微孔隙分量成正比,与孔隙宽度成反比,与表面弛豫速率基本无关.当扩散系数较大、孔隙宽度较小时,核磁共振T2谱难以直观反映孔隙组分及孔隙结构.应用核磁共振评价孔隙结构时需特别注意扩散系数和孔隙尺寸的影响.

To study influence of diffusion coefficient, relaxation rates, pore component ratio and pore width on NMR T2 distributions, a complex rock-pore system is simplified to an equivalent dual porosity medium in a mathematical physics model with Bloch＇ s equation. ADI-FDTD and SIRT methods are used in numerical simulations of NMR transversal response and decomposition of NMR T2 spectrum, respectively. It shows that transversal magnetization vector decay rate is proportional to diffusion coefficient and micro porosity, inversely proportional to pore width and nearly irrelevant to surface relaxation rate. NMR T2 spectrum hardly reflects pore components and structure as diffusion coefficient is small and pore width is large. Special attentions should be paid to influence of diffusion coefficient and pore-size as evaluating pore structure by NMR.