Pore-network models are useful for simulating physical processes in geological porous media. Here in this paper, the network theories are used to analyze X-ray computed tomography (CT) images of geological porous media. Results show the traditional mathematical degree which represents the coordination number of pore networks is insufficient to describe the preferential-attachment mechanism of pore networks. Thus a new parameter, physical degree, was proposed, which represents a physical quantity of both a specific pore and its attached throats to facilitate the description of pore networks. By analyzing X-ray CT images of different geological porous media, it was found the mathematical degree follows a Poisson law whereas the physical degree can be fitted by a power law. This indicates the pore network of geological porous media is randomly scale free. But the scale free is volume dependent. When the power law breaks down, the scale-free quantity, such as porosity, becomes scale variant. Based on these findings, a pore-network model was proposed, which reflects the dynamic generating process of the pore network. And the randomness featured in mathematical degrees and volume-dependent scale free featured in physical degrees are contained in this model.

孔隙网络模型可用于模拟地质多孔介质中的物理过程。在本文中，网络理论用于分析地质多孔介质的 X 射线计算机断层扫描 (CT) 图像。结果表明，传统的表示孔隙网络配位数的数学程度不足以描述孔隙网络的优先附着机制。因此，提出了一个新的参数，即物理度，它代表了特定孔隙及其附着喉道的物理量，以方便描述孔隙网络。通过分析不同地质多孔介质的X射线CT图像，发现数学程度遵循泊松定律，而物理程度可以通过幂律拟合。这表明地质多孔介质的孔隙网络是随机无标度的。但无标度取决于体积。当幂律失效时，无标度的量，例如孔隙度，变成标度变量。基于这些发现，提出了反映孔隙网络动态生成过程的孔隙网络模型。并且数学学位中的随机性和物理学位中的体积相关的无标度特征都包含在这个模型中。