油水双相饱和孔隙模型核磁特性理论研究

利用特征函数展开方法，给出了基于扩散效应的核磁共振Bloch控制方程的弛豫模式解表达式, 在此基础上分别给出了水饱和与油水双相饱和孔隙模型的核磁共振特性模拟结果. 结果表明，孔隙流体的核磁弛豫与孔隙大小、孔隙表面弛豫率、孔隙流体的扩散能力以及含油饱和度等有密切的关系. 对于水饱和孔隙，弛豫时间主要由孔隙大小控制. 当孔隙较大时，即使均匀大小孔隙，孔隙流体的弛豫也会表现为多指数弛豫. 而且最小模式弛豫时间与孔隙大小为非线性关系. 对于油水双相饱和孔隙，在孔隙较小时，含油饱和度对弛豫的影响主要表现在弛豫时间随含油饱和度的增加而线性减小；但在孔隙较大时，含油饱和度的增加对弛豫影响表现在两个方面，其一，孔隙水弛豫由多个弛豫模式控制逐渐转变为由最小弛豫模式控制；其二，孔隙水弛豫时间与含油饱和度表现为非线性关系. 对由实际岩芯抽象出的孔隙模型，采用本文获得的理论公式，在油水双相饱和时进行了正反演模拟. 计算结果与已有的实验结果较为一致.

A THEORETICAL STUDY ON NUCLEAR MAGNETIC RESONANCE OF PORE SPACE SATURATED WITH OIL AND WATER

We study the basic characteristics of the model spin-spin relaxation. By the series expansion method, the Bloch equations controlled by diffusion effect are solved for double-phase pore space of slab and sphere saturated with oil and water. The result shows that the Nuclear Magnetic Resonance (NMR) relaxation is controlled by multi relaxation modes and associated with pore size, surface relaxation ability, diffusion coefficient of pore fluid and oil saturation. Numerical results indicate that for water saturated pore space, relaxation is mainly related to pore size. For small water saturated pore, the relaxation is dominated by the smallest relaxation mode and the corresponding relaxation time is proportional to pore size. But for large pore space, multi-mode relaxation composes the pore water relaxation process, even when the pore size is uniform. And under this situation, it is no longer a linear function between relaxation time and pore size. For water-oil double-phase saturated pore space, when pore size is small and as oil saturation increases, the water relaxation time decreases linearly. However, when pore size is relative large, the multi relaxation mode turns to be single mode with the increasing of oil saturation. And at the same time, the variation of relaxation time with oil saturation is non-linearity. Using the formulae in the paper, the responses for the pore space model obtained from real rock core have been calculated. There is a fine agreement between the theoretical and experimental results.