Predicting permeability via statistical learning on higher-order microstructural information

Virtualization and digital twins of the food supply chain for enhanced food safety

Meeting food safety requirements without jeopardizing quality attributes or sustainability involves adopting a holistic perspective of food products, their manufacturing processes and their storage and distribution practices. The virtualization of the food supply chain offers opportunities to evaluate, simulate, and predict challenges and mishaps potentially contributing to present and future food safety risks. Food systems virtualization poses several requirements: (1) a comprehensive framework composed of instrumental, digital, and computational methods to evaluate internal and external factors that impact food safety; (2) nondestructive and real-time sensing methods, such as spectroscopic-based techniques, to facilitate mapping and tracking food safety and quality indicators; (3) a dynamic platform supported by the Internet of Things (IoT) interconnectivity to integrate information, perform online data analysis and exchange information on product history, outbreaks, exposure to risky situations, etc.; and (4) comprehensive and complementary mathematical modeling techniques (including but not limited to chemical reactions and microbial inactivation and growth kinetics) based on extensive data sets to make realistic simulations and predictions possible. Despite current limitations in data integration and technical skills for virtualization to reach its full potential, its increasing adoption as an interactive and dynamic tool for food systems evaluation can improve resource utilization and rational design of products, processes and logistics for enhanced food safety. Virtualization offers affordable and reliable options to assist stakeholders in decision-making and personnel training. This chapter focuses on definitions and requirements for developing and applying virtual food systems, including digital twins, and their role and future trends in enhancing food safety.

Measuring structural nonstationarity: The use of imaging information to quantify homogeneity and inhomogeneity

Heterogeneity is the concept we encounter in numerous research areas and everyday life. While "not mixing apples and oranges" is easy to grasp, a more quantitative approach to such segregation is not always readily available. Consider the problem from a different angle: To what extent does one have to make apples more orange and oranges more "apple-shaped" to put them into the same basket (according to their appearance alone)? This question highlights the central problem of the blurred interface between heterogeneous and homogeneous, which also depends on the metrics used for its identification. This work uncovers the physics of structural stationarity quantification, based on correlation functions (CFs) and clustering based on CFs different between image subregions. By applying the methodology to a wide variety of synthetic and real images of binary porous media, we confirmed computationally that only periodically unit-celled structures and images produced by stationary processes with resolutions close to infinity are strictly stationary. Natural structures without recurring unit cells are only weakly stationary. We established a physically meaningful definition for these stationarity types and their distinction from nonstationarity. In addition, the importance of information content of the chosen metrics is highlighted and discussed. We believe the methodology as proposed in this contribution will find its way into numerous research areas dealing with materials, structures, and measurements and modeling based on structural imaging information.

Robust surface-correlation-function evaluation from experimental discrete digital images

Correlation functions (CFs) are universal structural descriptors; surface-surface F_{ss} and surface-void F_{sv} CFs are a subset containing additional information about the interface between the phases. The description of the interface between pores and solids in porous media is of particular importance and recently Ma and Torquato [Phys. Rev. E 98, 013307 (2018)2470-004510.1103/PhysRevE.98.013307] proposed an elegant way to compute these functions for a wide variety of cases. However, their "continuous" approach is not always applicable to digital experimental 2D and 3D images of porous media as obtained using x-ray tomography or scanning electron microscopy due to nonsingularities in chemical composition or local solid material's density and partial volume effects. In this paper we propose to use edge-detecting filters to compute surface CFs in the "digital" fashion directly in the images. Computed this way, surface correlation functions are the same as analytically known for Poisson disks in case the resolution of the image is adequate. Based on the multiscale image analysis we developed a C_{0.5} criterion that can predict if the imaging resolution is enough to make an accurate evaluation of the surface CFs. We also showed that in cases when the input image contains all major features, but do not pass the C_{0.5} criterion, it is possible with the help of image magnification to sample CFs almost similar to those obtained for high-resolution image of the same structure with high C_{0.5}. The computational framework as developed here is open source and available within the CorrelationFunctions.jl package developed by our group. Our "digital" approach was applied to a wide variety of real porous media images of different quality. We discuss critical aspects of surface correlation functions computations as related to different applications. The developed methodology allows applying surface CFs to describe the structure of porous materials based on their experimental images and enhance stochastic reconstructions or super-resolution procedures, or serve as an efficient metrics in machine learning applications due to computationally effective GPU implementation.

A data-driven framework for permeability prediction of natural porous rocks via microstructural characterization and pore-scale simulation

Understanding the microstructure-property relationships of porous media is of great practical significance, based on which macroscopic physical properties can be directly derived from measurable microstructural informatics. However, establishing reliable microstructure-property mappings in an explicit manner is difficult, due to the intricacy, stochasticity, and heterogeneity of porous microstructures. In this paper, a data-driven computational framework is presented to investigate the inherent microstructure-permeability linkage for natural porous rocks, where multiple techniques are integrated together, including microscopy imaging, stochastic reconstruction, microstructural characterization, pore-scale simulation, feature selection, and data-driven modeling. A large number of 3D digital rocks with a wide porosity range are acquired from microscopy imaging and stochastic reconstruction techniques. A broad variety of morphological descriptors are used to quantitatively characterize pore microstructures from different perspectives, and they compose the raw feature pool for feature selection. High-fidelity lattice Boltzmann simulations are conducted to resolve fluid flow passing through porous media, from which reliable permeability references are obtained. The optimal feature set that best represents permeability is identified through a performance-oriented feature selection process, upon which a cost-effective surrogate model is rapidly fitted to approximate the microstructure-permeability mapping via data-driven modeling. This surrogate model exhibits great advantages over empirical/analytical formulas in terms of prediction accuracy and generalization capacity, which can predict reliable permeability values spanning four orders of magnitude. Besides, feature selection also greatly enhances the interpretability of the data-driven prediction model, from which new insights into the mechanism of how microstructural characteristics determine intrinsic permeability are obtained.

Inverse design of anisotropic spinodoid materials with prescribed diffusivity

The three-dimensional microstructure of functional materials determines its effective properties, like the mass transport properties of a porous material. Hence, it is desirable to be able to tune the properties by tuning the microstructure accordingly. In this work, we study a class of spinodoid i.e. spinodal decomposition-like structures with tunable anisotropy, based on Gaussian random fields. These are realistic yet computationally efficient models for bicontinuous porous materials. We use a convolutional neural network for predicting effective diffusivity in all three directions. We demonstrate that by incorporating the predictions of the neural network in an approximate Bayesian computation framework for inverse problems, we can in a computationally efficient manner design microstructures with prescribed diffusivity in all three directions.

Permeability Models of Hydrate-Bearing Sediments: A Comprehensive Review with Focus on Normalized Permeability

Natural gas hydrates (NGHs) are regarded as a new energy resource with great potential and wide application prospects due to their tremendous reserves and low CO2 emission. Permeability, which governs the fluid flow and transport through hydrate-bearing sediments (HBSs), directly affects the fluid production from hydrate deposits. Therefore, permeability models play a significant role in the prediction and optimization of gas production from NGH reservoirs via numerical simulators. To quantitatively analyze and predict the long-term gas production performance of hydrate deposits under distinct hydrate phase behavior and saturation, it is essential to well-establish the permeability model, which can accurately capture the characteristics of permeability change during production. Recently, a wide variety of permeability models for single-phase fluid flowing sediment have been established. They typically consider the influences of hydrate saturation, hydrate pore habits, sediment pore structure, and other related factors on the hydraulic properties of hydrate sediments. However, the choice of permeability prediction models leads to substantially different predictions of gas production in numerical modeling. In this work, the most available and widely used permeability models proposed by researchers worldwide were firstly reviewed in detail. We divide them into four categories, namely the classical permeability models, reservoir simulator used models, modified permeability models, and novel permeability models, based on their theoretical basis and derivation method. In addition, the advantages and limitations of each model were discussed with suggestions provided. Finally, the challenges existing in the current research were discussed and the potential future investigation directions were proposed. This review can provide insightful guidance for understanding the modeling of fluid flow in HBSs and can be useful for developing more advanced models for accurately predicting the permeability change during hydrate resources exploitation.

Universal scaling for the permeability of random packs of overlapping and nonoverlapping particles

Constraining fluid permeability in porous media is central to a wide range of theoretical, industrial, and natural processes. In this Letter, we validate a scaling for fluid permeability in random and lattice packs of spheres and show that the permeability of packs of both hard and overlapping spheres of any sphere size or size distribution collapse to a universal curve across all porosity ϕ in the range of ϕ_{c}<ϕ<1, where ϕ_{c} is the percolation threshold. We use this universality to demonstrate that permeability can be predicted using percolation theory at ϕ_{c}<ϕ≲0.30, Kozeny-Carman models at 0.30≲ϕ≲0.40, and dilute expansions of Stokes theory for lattice models at ϕ≳0.40. This result leads us to conclude that the inverse specific surface area, rather than an effective sphere size or pore size is a universal controlling length scale for hydraulic properties of packs of spheres. Finally, we extend this result to predict the permeability for some packs of concave nonspherical particles.

Permeability of packs of polydisperse hard spheres

The permeability of packs of spheres is important in a wide range of physical scenarios. Here, we create numerically generated random periodic domains of spheres that are polydisperse in size and use lattice-Boltzmann simulations of fluid flow to determine the permeability of the pore phase interstitial to the spheres. We control the polydispersivity of the sphere size distribution and the porosity across the full range from high porosity to a close packing of spheres. We find that all results scale with a Stokes permeability adapted for polydisperse sphere sizes. We show that our determination of the permeability of random distributions of spheres is well approximated by models for cubic arrays of spheres at porosities greater than ∼0.38, without any fitting parameters. Below this value, the Kozeny-Carman relationship provides a good approximation for dense, closely packed sphere packs across all polydispersivity.

Prediction and Optimization of Ion Transport Characteristics in Nanoparticle-Based Electrolytes Using Convolutional Neural Networks

We develop a convolutional neural network (CNN) model to predict the diffusivity of cations in nanoparticle-based electrolytes and use it to identify the characteristics of morphologies that exhibit optimal transport properties. The ground truth data are obtained from kinetic Monte Carlo (kMC) simulations of cation transport parametrized using a multiscale modeling strategy. We implement deep learning approaches to quantitatively link the diffusivity of cations to the spatial arrangement of the nanoparticles. We then integrate the trained CNN model with a topology optimization algorithm for accelerated discovery of nanoparticle morphologies that exhibit optimal cation diffusivities at a specified nanoparticle loading, and we investigate the ability of the CNN model to quantitatively account for the influence of interparticle spatial correlations on cation diffusivity. Finally, by using data-driven approaches, we explore how simple descriptors of nanoparticle morphology correlate with cation diffusivity, thus providing a physical rationale for the observed optimal microstructures. The results of this study highlight the capability of CNNs to serve as surrogate models for structure-property relationships in composites with monodisperse spherical particles, which can in turn be used with inverse methods to discover morphologies that produce optimal target properties.