RISE Research Institutes of Sweden, 41276, Göteborg, Sweden.
Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, 41296, Göteborg, Sweden.
Sci Rep. 2020 Sep 17;10(1):15239. doi: 10.1038/s41598-020-72085-5.
Quantitative structure-property relationships are crucial for the understanding and prediction of the physical properties of complex materials. For fluid flow in porous materials, characterizing the geometry of the pore microstructure facilitates prediction of permeability, a key property that has been extensively studied in material science, geophysics and chemical engineering. In this work, we study the predictability of different structural descriptors via both linear regressions and neural networks. A large data set of 30,000 virtual, porous microstructures of different types, including both granular and continuous solid phases, is created for this end. We compute permeabilities of these structures using the lattice Boltzmann method, and characterize the pore space geometry using one-point correlation functions (porosity, specific surface), two-point surface-surface, surface-void, and void-void correlation functions, as well as the geodesic tortuosity as an implicit descriptor. Then, we study the prediction of the permeability using different combinations of these descriptors. We obtain significant improvements of performance when compared to a Kozeny-Carman regression with only lowest-order descriptors (porosity and specific surface). We find that combining all three two-point correlation functions and tortuosity provides the best prediction of permeability, with the void-void correlation function being the most informative individual descriptor. Moreover, the combination of porosity, specific surface, and geodesic tortuosity provides very good predictive performance. This shows that higher-order correlation functions are extremely useful for forming a general model for predicting physical properties of complex materials. Additionally, our results suggest that artificial neural networks are superior to the more conventional regression methods for establishing quantitative structure-property relationships. We make the data and code used publicly available to facilitate further development of permeability prediction methods.
定量结构-性质关系对于理解和预测复杂材料的物理性质至关重要。对于多孔材料中的流体流动，描述孔隙微结构的几何形状有助于预测渗透率，渗透率是材料科学、地球物理学和化学工程中广泛研究的关键性质。在这项工作中，我们通过线性回归和神经网络研究了不同结构描述符的可预测性。为此目的，创建了一个包含 30000 个不同类型的虚拟多孔微结构的大型数据集，包括颗粒状和连续固相。我们使用晶格玻尔兹曼方法计算这些结构的渗透率，并使用单点相关函数（孔隙率、比表面积）、两点表面-表面、表面-空隙和空隙-空隙相关函数以及测地迂曲度作为隐式描述符来描述孔隙空间的几何形状。然后，我们研究了使用这些描述符的不同组合对渗透率的预测。与仅使用最低阶描述符（孔隙率和比表面积）的 Kozeny-Carman 回归相比，我们获得了显著的性能提升。我们发现，结合所有三个两点相关函数和迂曲度可以提供渗透率的最佳预测，其中空隙-空隙相关函数是最具信息量的单个描述符。此外，孔隙率、比表面积和测地迂曲度的组合提供了非常好的预测性能。这表明高阶相关函数对于形成预测复杂材料物理性质的通用模型非常有用。此外，我们的结果表明，人工神经网络在建立定量结构-性质关系方面优于更传统的回归方法。我们公开了所使用的数据和代码，以促进渗透率预测方法的进一步发展。
