However, the remarkably simple form comes with great limitations. Where k is the permeability and c is the Kozeny-Carman constant. The Kozeny-Carman equation 17, 18 is the most notable example, usually written as ![]() These two characteristics are the most frequently used in empirical expressions for the permeability. The porosity \(\phi \) (volume fraction of the pore phase) and specific surface s (pore-solid interface area per unit volume) are perhaps the most basic geometrical characteristics. Numerous efforts in determining the physical properties of complex materials have been made since the early work of Maxwell 1, 8, 9, 10, 11, and such investigations have been enhanced due to the availability of high-resolution 3D images of various types of materials microstructures using X-ray nanotomography 12, 13 or focused ion beam scanning electron microscopy 14, and nuclear magnetic geological events 2, polymeric composites for packaging materials 3, catalysis, filtration and separation 4, energy, fuels, and electrochemistry 5, fiber and textile materials for health care and hygiene 6, and porous, biodegradable polymer films for controlled release of medical compounds 7. Specifically, understanding how fluid transport properties are related to the microstructure of a porous medium is crucial in a wide range of areas e.g. The study of how the microstructural morphology of random, heterogeneous, porous materials affects their effective properties, i.e., determining quantitative structure–property relationships, is key for the understanding and prediction of the physical properties of complex materials 1. We make the data and code used publicly available to facilitate further development of permeability prediction methods. Additionally, our results suggest that artificial neural networks are superior to the more conventional regression methods for establishing quantitative structure–property relationships. This shows that higher-order correlation functions are extremely useful for forming a general model for predicting physical properties of complex materials. ![]() Moreover, the combination of porosity, specific surface, and geodesic tortuosity provides very good predictive performance. ![]() 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. We obtain significant improvements of performance when compared to a Kozeny-Carman regression with only lowest-order descriptors (porosity and specific surface). Then, we study the prediction of the permeability using different combinations of these descriptors. 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. ![]() 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. In this work, we study the predictability of different structural descriptors via both linear regressions and neural networks. 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. Quantitative structure–property relationships are crucial for the understanding and prediction of the physical properties of complex materials.
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