Jin Guodong, Torres-Verdín Carlos, Toumelin Emmanuel
Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, TX 78712, USA.
J Magn Reson. 2009 Oct;200(2):313-20. doi: 10.1016/j.jmr.2009.07.021. Epub 2009 Jul 22.
We develop and compare two formulations of the random-walk method, grain-based and voxel-based, to simulate the nuclear-magnetic-resonance (NMR) response of fluids contained in various models of porous media. The grain-based approach uses a spherical grain pack as input, where the solid surface is analytically defined without an approximation. In the voxel-based approach, the input is a computer-tomography or computer-generated image of reconstructed porous media. Implementation of the two approaches is largely the same, except for the representation of porous media. For comparison, both approaches are applied to various analytical and digitized models of porous media: isolated spherical pore, simple cubic packing of spheres, and random packings of monodisperse and polydisperse spheres. We find that spin magnetization decays much faster in the digitized models than in their analytical counterparts. The difference in decay rate relates to the overestimation of surface area due to the discretization of the sample; it cannot be eliminated even if the voxel size decreases. However, once considering the effect of surface-area increase in the simulation of surface relaxation, good quantitative agreement is found between the two approaches. Different grain or pore shapes entail different rates of increase of surface area, whereupon we emphasize that the value of the "surface-area-corrected" coefficient may not be universal. Using an example of X-ray-CT image of Fontainebleau rock sample, we show that voxel size has a significant effect on the calculated surface area and, therefore, on the numerically simulated magnetization response.
我们开发并比较了随机游走方法的两种形式，即基于颗粒和基于体素的形式，以模拟包含在各种多孔介质模型中的流体的核磁共振（NMR）响应。基于颗粒的方法使用球形颗粒堆积作为输入，其中固体表面通过解析定义，无需近似。在基于体素的方法中，输入是重建多孔介质的计算机断层扫描或计算机生成图像。除了多孔介质的表示方式外，两种方法的实现大致相同。为了进行比较，两种方法都应用于各种多孔介质的解析模型和数字化模型：孤立球形孔隙、球体的简单立方堆积以及单分散和多分散球体的随机堆积。我们发现，数字化模型中的自旋磁化衰减比其解析对应模型快得多。衰减率的差异与由于样品离散化导致的表面积高估有关；即使体素尺寸减小，这种差异也无法消除。然而，一旦在表面弛豫模拟中考虑表面积增加的影响，两种方法之间就会发现良好的定量一致性。不同的颗粒或孔隙形状导致表面积增加的速率不同，因此我们强调“表面积校正”系数的值可能不具有普遍性。以枫丹白露岩样的X射线计算机断层扫描图像为例，我们表明体素尺寸对计算出的表面积有显著影响，因此对数值模拟的磁化响应也有显著影响。
