MAGNET: Medial Axis Guided Network Extraction Tool

Minimum requirements for predictive pore-network modeling of solute transport in micromodels

One of the factors leading to a decrease in the efficiency of polymer electrolyte membrane (PEM) electrolyzers is the blockage of water transport pathways through the porous transport layer (PTL). The oxygen bubbles generated from the electrochemical reaction at the catalyst layer accumulate in the PTL, impeding the transport pathways and reaction sites for the reactant water (1). An improved understanding of oxygen bubble accumulation and water transport behaviour in porous transport layers is essential to reduce mass transport losses in PEM electrolyzers. This study presents a method to stochastically generate a PTL composed of sintered titanium (Ti) powders and investigate the transport properties using pore network modeling. A microscale X-ray computed tomography (µ-CT) was performed for a sintered Ti powder PTL sample to obtain a 2D density map. The density map contains material content information, providing higher intensity at the positions with higher material content. With the density map as an input, a stochastic model of the PTL was generated by placing Ti powder particles at positions decided by the density map and a probability function until the model reached the target volume (2). Two critical parameters are considered in this model: the seeding parameter, α, and a filling radius, β. The seeding parameter controls the number of Ti powder “seeds” that act as nucleation sites. The second parameter, the filling radius, allows the model to mimic the morphology of the sintered regions. The structural properties of the stochastic model are investigated by comparing the pore size distribution, throat size distribution, and the porosity profile to the µ-CT reconstruction. Pore network modeling is an alternative to continuum modeling for simulating transport in porous media. Pore network modeling simplifies the solution of differential equations for mass transport by treating the pore space as a network of pores and narrow throats (3). Using pore network modeling as the analysis tool, the in-plane permeabilities of the µ-CT reconstruction and the stochastic model were compared. The stochastic modeling of PTLs will facilitate the detailed parametric studies of PTL structural property impacts on transport and provide novel insights into mass transport behavior in PEM electrolyzers.References H. Ito, T. Maeda, A. Nakano, Y. Hasegawa, N. Yokoi, C. M. Hwang, M. Ishida, A. Kato, and T. Yoshida, International journal of hydrogen energy 35(18), 9550-9560 (2010). A. Ebrahimi Khabbazi, J. Hinebaugh, A. Bazylak, Science Bulletin, 61(8), 601-611(2016).A. Putz, J. Hinebaugh, M. Aghighi, H. Day, A. Bazylak, and J. T. Gostick, ECS Transactions, 58(1), 79-86 (2013).

Predicting the petrophysical properties of rock samples using micro-CT images has gained significant attention recently. However, an accurate and an efficient numerical tool is still lacking. After investigating three numerical techniques, (i) pore network modeling (PNM), (ii) the finite volume method (FVM), and (iii) the lattice Boltzmann method (LBM), a workflow based on machine learning is established for fast and accurate prediction of permeability directly from 3D micro-CT images. We use more than 1100 samples scanned at high resolution and extract the relevant features from these samples for use in a supervised learning algorithm. The approach takes advantage of the efficient computation provided by PNM and the accuracy of the LBM to quickly and accurately estimate rock permeability. The relevant features derived from PNM and image analysis are fed into a supervised machine learning model and a deep neural network to compute the permeability in an end-to-end regression scheme. Within a supervised learning framework, machine and deep learning algorithms based on linear regression, gradient boosting, and physics-informed convolutional neural networks (CNNs) are applied to predict the petrophysical properties of porous rock from 3D micro-CT images. We have performed the sensitivity analysis on the feature importance, hyperparameters, and different learning algorithms to make a prediction. Values of R2 scores up to 88% and 91% are achieved using machine learning regression models and the deep learning approach, respectively. Remarkably, a significant gain in computation time—approximately 3 orders of magnitude—is achieved by applied machine learning compared with the LBM. Finally, the study highlights the critical role played by feature engineering in predicting petrophysical properties using deep learning.

Mathematical modelling of evaporation process in capillary porous media is commonly addressed using two approaches: Continuum models (CMs) derived within the framework of the volume averaging technique and pore network models (PNMs) developed on the basis of invasion percolation concepts. Though widely used, CMs are unable to adequately describe the microstructure of porous media and the relevant physics such as fractal behaviour. PNMs however overcome such limitations by approximating the pore structure of porous media and by formulating conservative transport equations for individual phases at the pore scale. Despite these advantages, PNMs cannot truly resolve the details of the void space geometry and they also bypass individual pore-scale effects. These shortcomings can be overcome by using the lattice Boltzmann method (LBM) which has recently become a popular technique for simulating multiphase flow in porous media. In LBM the void space is precisely described and the averaged intermolecular forces are accommodated. In this chapter, we present a multiphase lattice Boltzmann method called Shan Chen LBM for simulating pore-scale physics and micro-macro interactions during evaporation process in capillary porous media.

Pore network modeling is a widely used technique for simulating multiphase transport in porous materials, but there are very few software options available. This work outlines the OpenPNM package that was jointly developed by several porous media research groups to help address this gap. OpenPNM is written in Python using NumPy and SciPy for most mathematical operations, thus combining Python's ease of use with the performance necessary to perform large simulations. The package assists the user with managing and interacting with all the topological, geometrical, and thermophysical data. It also includes a suite of commonly used algorithms for simulating percolation and performing transport calculations on pore networks. Most importantly, it was designed to be highly flexible to suit any application and be easily customized to include user-specified pore-scale physics models. The framework is fast, powerful, and concise. An illustrative example is included that determines the effective diffusivity through a partially water-saturated porous material with just 29 lines of code.

The medial axis can be viewed as a compact representation for an arbitrary model; it is an essential geometric structure in many applications. A number of practical algorithms for its computation have been aimed at speeding up its computation and at addressing its instabilities. In this paper we propose a new algorithm to compute the medial axis with arbitrary precision. It exhibits several desirable properties not previously combined in a practical and efficient algorithm. First, it allows for a tradeoff between computation time and accuracy, making it well-suited for applications in which an approximation of the medial axis suffices, but computational efficiency is of particular concern. Second, it is output sensitive: the computation complexity of the algorithm does not depend on the size of the representation of a model, but on the size of the representation of the resulting medial axis. Third, the densities of the approximated medial axis points in different areas are adaptive to local free space volumes, based on the assumption that a coarser approximation in wide open area can still suffice the requirements of the applications. We present theoretical results, bounding the error introduced by the approximation process. The algorithm has been implemented and experimental results are presented that illustrate its computational efficiency and robustness.

Chapter 19 - The Medial Axis Transform

Numerical studies of interfacial phenomena in liquid water transport in polymer electrolyte membrane fuel cells using the lattice Boltzmann method

A greyscale volumetric lattice Boltzmann method for upscaling pore-scale two-phase flow

Pore network simulations of thin porous medium characterization by evapoporometry

Enhanced permeability prediction in porous media using particle swarm optimization with multi-source integration

Lattice Boltzmann simulations for micro-macro interactions during isothermal drying of bundle of capillaries

Machine and deep learning for estimating the permeability of complex carbonate rock from X-ray micro-computed tomography

A methodology is suggested for the explicit computation of the absolute permeability and Knudsen diffusion coefficient of tight rocks (shales) from pore structure properties. The pore space is regarded as a pore-and-throat network quantified by the statistical moments of bimodal pore and throat size distributions, pore shape factors, and pore accessibility function. With the aid of percolation theory, analytic equations are developed to express the nitrogen (N2) adsorption/desorption isotherms and mercury (Hg) intrusion curve as functions of all pertinent pore structure parameters. A multistep procedure is adopted for the successive estimation of each set of parameters by the inverse modeling of N2 adsorption–desorption isotherms, and Hg intrusion curve. With the aid of critical path analysis of percolation theory, the absolute permeability and Knudsen diffusion coefficient are computed as functions of estimated pore network properties. Application of the methodology to the datasets of several shale samples enables us to evaluate the predictability of the approach.

A method for the numerical determination of the steady-state response of complex charged porous media to pressure, salt concentration, and electric potential gradients is presented here. The Pore Network Model (PNM), describing the porosity as a network of pores connected by channels, is extended to capture electrokinetic couplings which arise at charged solid−liquid interfaces and allows us to compute the macroscopic fluxes of solvent, salt, and charge across a numerical sample submitted to macroscopic gradients. On the channel scale, the microscopic transport coefficients are obtained by solving analytically (in simple cases) or numerically the Poisson-Nernst-Planck and Stokes equations. The PNM approach then allows us to upscale these transport properties to the sample scale, accounting for the complex pore structure of the material viathe distribution of channel diameters. The Onsager relations between macroscopic transport coefficients are preserved, as expected. Electrokinetic couplings, combined with the sample heterogeneity, result in qualitative differences with respect to their microscopic counterparts for some macroscopic transport coefficients, however ( e.g.permeability or electro-osmotic coefficient). This underlines the care that should be taken when accounting for transport properties based on a single channel of average diameter.