We compute the porosity and specific surface area of a two-dimensional (2D) pore-scale segmented image of a natural rock sample, add existing relations linking tortuosity to porosity, and then use the Kozeny-Carman equation to obtain estimates of the absolute permeability of the three-dimensional (3D) host sample. These estimates are very close to the true permeability, measured or computed, of the host sample in rocks with well-connected pore space, including high-porosity sand, glass bead packs, low-to-medium porosity sandstones, and some carbonates. They are higher than the true permeability in carbonates with relatively large pores connected by constricted conduits. They fail in impermeable synthetically constructed samples with disconnected pores. Still, this extremely simple method proves to be viable for a large class of natural rocks. Moreover, it can be used to construct a permeability-porosity trend from a microscopic 2D image by selecting subsections of this image and computing their permeability-porosity pairs. Because the measured or computed permeability-porosity pair of the host 3D sample falls upon such a trend, we argue that this trend may be applicable at a spatial scale much coarser that of the pore-scale image.

我们计算天然岩石样品的二维 (2D) 孔隙尺度分段图像的孔隙度和比表面积，添加将曲折度与孔隙度联系起来的现有关系，然后使用 Kozeny-Carman 方程获得绝对渗透率的估计值三维 (3D) 宿主样本。这些估计值非常接近孔隙空间连通性良好的岩石（包括高孔隙度砂、玻璃珠包、中低孔隙度砂岩和一些碳酸盐）中的宿主样品的真实渗透率（测量或计算）。它们高于碳酸盐岩的真实渗透率，具有相对较大的孔隙，由收缩的管道连接。它们在具有断开孔隙的不透水合成样品中失败。尽管如此，这种极其简单的方法被证明对一大类天然岩石是可行的。此外，通过选择该图像的子部分并计算它们的渗透率-孔隙度对，它可以用于从微观二维图像构建渗透率-孔隙度趋势。因为主体 3D 样品的测量或计算的渗透率-孔隙度对属于这种趋势，我们认为这种趋势可能适用于比孔隙尺度图像更粗糙的空间尺度。