Microscopic (pore-scale) properties of porous media affect and often determine their macroscopic (continuum-or Darcy-scale) counterparts. Understanding the relationship between processes on these two scales is essential to both the derivation of macroscopic models of, e.g., transport phenomena in natural porous media, and the design of novel materials, e.g., for energy storage. Most microscopic properties exhibit complex statistical correlations and geometric constraints, which presents challenges for the estimation of macroscopic quantities of interest (QoIs), e.g., in the context of global sensitivity analysis (GSA) of macroscopic QoIs with respect to microscopic material properties. We present a systematic way of building correlations into stochastic multiscale models through Bayesian networks. This allows us to construct the joint probability density function (PDF) of model parameters through causal relationships that emulate engineering processes, e.g., the design of hierarchical nanoporous materials. Such PDFs also serve as input for the forward propagation of parametric uncertainty; our findings indicate that the inclusion of causal relationships impacts predictions of macroscopic QoIs. To assess the impact of correlations and causal relationships between microscopic parameters on macroscopic material properties, we use a momentindependent GSA based on the differential mutual information. Our GSA accounts for the correlated inputs and complex non-Gaussian QoIs. The global sensitivity indices are used to rank the effect of uncertainty in microscopic parameters on macroscopic QoIs, to quantify the impact of causality on the multiscale model's predictions, and to provide physical interpretations of these results for hierarchical nanoporous materials.
Ubiquitous uncertainty about pore geometry inevitably undermines the veracity of pore-and multiscale simulations of transport phenomena in porous media. It raises two fundamental issues: sensitivity of effective material properties to pore-scale parameters and statistical parameterization of Darcy-scale models that accounts for pore-scale uncertainty. Homogenization-based maps of porescale parameters onto their Darcy-scale counterparts facilitate both sensitivity analysis (SA) and uncertainty quantification. We treat uncertain geometric characteristics of a hierarchical porous medium as random variables to conduct global SA and to derive probabilistic descriptors of effective diffusion coefficients and effective sorption rate. Our analysis is formulated in terms of solute transport diffusing through a fluid-filled pore space, while sorbing to the solid matrix. Yet it is sufficiently general to be applied to other multiscale porous media phenomena that are amenable to homogenization.
Pseudo-2-dimensional models are routinely used to predict the lithiation curves for energy storage devices, including lithium-metal batteries. The performance of such models is as good as their parameterization, which remains a challenge especially in the presence of carbon binder domain (CBD). We propose two alternative parameterization strategies, which explicitly account for the CBD volume fraction and physical properties. The first aggregates CBD with the electrolyte-filled pore space and expresses the Bruggeman exponent in terms of a solution of microstructure-specific closure problem. The second treats CBD and active particles as a composite solid phase, whose effective properties are computed (semi-)analytically via homogenization. We show that the latter strategy used to parameterize the Doyle-Fuller-Newman model provides an attractive middle ground between the model complexity and the prediction accuracy. Our modeling results suggest that the battery discharge time decreases as either the CBD volume fraction increases or the CBD ionic diffusivity decreases, and is insensitive to the CBD ionic conductivity. The quantitative nature of these observations can be used in the optimal design of porous cathodes.
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