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1. Reduced Model for Properties of Multiscale Porous Media with Changing Geometry

   https://doi.org/10.3390/computation9030028  

   Peszynska, Malgorzata; Umhoefer, Joseph; Shin, Choah (March 2021, Computation)

   null (Ed.)

   In this paper, we consider an important problem for modeling complex coupled phenomena in porous media at multiple scales. In particular, we consider flow and transport in the void space between the pores when the pore space is altered by new solid obstructions formed by microbial growth or reactive transport, and we are mostly interested in pore-coating and pore-filling type obstructions, observed in applications to biofilm in porous media and hydrate crystal formation, respectively. We consider the impact of these obstructions on the macroscopic properties of the porous medium, such as porosity, permeability and tortuosity, for which we build an experimental probability distribution with reduced models, which involves three steps: (1) generation of independent realizations of obstructions, followed by, (2) flow and transport simulations at pore-scale, and (3) upscaling. For the first step, we consider three approaches: (1A) direct numerical simulations (DNS) of the PDE model of the actual physical process called BN which forms the obstructions, and two non-DNS methods, which we call (1B) CLPS and (1C) LP. LP is a lattice Ising-type model, and CLPS is a constrained version of an Allen–Cahn model for phase separation with a localization term. Both LP and CLPS are model approximations of BN, and they seek local minima of some nonconvex energy functional, which provide plausible realizations of the obstructed geometry and are tuned heuristically to deliver either pore-coating or pore-filling obstructions. Our methods work with rock-void geometries obtained by imaging, but bypass the need for imaging in real-time, are fairly inexpensive, and can be tailored to other applications. The reduced models LP and CLPS are less computationally expensive than DNS, and can be tuned to the desired fidelity of the probability distributions of upscaled quantities. 

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2. Three-dimensional (3D) Simulation of Micro-Void Development within Large Scale Polymer Composite Deposition Beads

   Aigbe Awenlimobor, Zhaogui Wang (October 2022, 2022 International Solid Freeform Fabrication Symposium)

   Structural integrity and quality of short fiber composite parts produced by Big Area Additive Manufacturing (BAAM) are largely affected by inherent bead microstructural features such as voids. Unfortunately, our understanding of void nucleation and evolution during polymer deposition process is lacking. Flow modeling focused on the associated microstructural formation provides a means for better understanding the process-structure-properties relations in large area extrusion deposition additive manufacturing of fiber reinforced composites. Our prior computational effort that investigated mechanisms that may promote micro-void formation was based on 2-dimensional planar models of a single ellipsoidal fiber motion in purely viscous polymer extrusion/deposition flow through a BAAM nozzle. Here we present a 3D finite element modelling approach to simulate single fiber out-of-plane rotations utilizing velocity and velocity gradient values computed along streamlines obtained from a 3D extrusion/deposition simulation of the BAAM polymer deposition process. The pressure distribution on the fiber’s surface along the flow path provides new insight into potential micro-void nucleation mechanism. Results show low pressure regions occur near the fiber’s surface which varies across the printed bead and through its thickness. 

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3. Persistent Homology as a Heterogeneity Metric for Predicting Pore Size Change in Dissolving Carbonates

   https://doi.org/10.1029/2023WR034559  

   Thompson, E. P.; Ellis, B. R. (September 2023, Water Resources Research)

   Abstract Accurate prediction of physical alterations in carbonate reservoirs under dissolution is critical for development of subsurface energy technologies. The impact of mineral dissolution on flow characteristics depends on the connectivity and tortuosity of the pore network. Persistent homology is a tool from algebraic topology that describes the size and connectivity of topological features. When applied to 3D X‐ray computed tomography (XCT) imagery of rock cores, it provides a novel metric of pore network heterogeneity. Prior works have demonstrated the efficacy of persistent homology in predicting flow properties in numerical simulations of flow through porous media. Its ability to combine size, spatial distribution, and connectivity information make it a promising tool for understanding reactive transport in complex pore networks, yet limited work has been done to apply persistence analysis to experimental studies on natural rocks. In this study, three limestone cores were imaged by XCT before and after acid‐driven dissolution flow‐through experiments. Each XCT scan was analyzed using persistent homology. In all three rocks, permeability increase was driven by the growth of large, connected pore bodies. The two most homogenous samples saw an increased effect nearer to the flow inlet, suggesting emerging preferential flow paths as the reaction front progresses. The most heterogeneous sample showed an increase in along‐core homogeneity during reaction. Variability of persistence showed moderate positive correlation with pore body size increase. Persistence heterogeneity analysis could be used to anticipate where greatest pore size evolution may occur in a reservoir targeted for subsurface development, improving confidence in project viability. 

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4. Clustering of inertial particles in turbulent flow through a porous unit cell

   https://doi.org/10.1017/jfm.2022.100  

   Apte, Sourabh V.; Oujia, Thibault; Matsuda, Keigo; Kadoch, Benjamin; He, Xiaoliang; Schneider, Kai (April 2022, Journal of Fluid Mechanics)

   Direct numerical simulation is used to investigate effects of turbulent flow in the confined geometry of a face-centred cubic porous unit cell on the transport, clustering and deposition of fine particles at different Stokes numbers ( $St = 0.01, 0.1, 0.5, 1, 2$ ) and at a pore Reynolds number of 500. Particles are advanced using one-way coupling and the collision of particles with pore walls is modelled as perfectly elastic with specular reflection. Tools for studying inertial particle dynamics and clustering developed for homogeneous flows are adapted to take into account the embedded, curved geometry of the pore walls. The pattern and dynamics of clustering are investigated using the volume change of Voronoi tesselation in time to analyse the divergence and convergence of the particles. Similar to the case of homogeneous, isotropic turbulence, the cluster formation is present at large volumes, while cluster destruction is prominent at small volumes and these effects are amplified with the Stokes number. However, unlike homogeneous, isotropic turbulence, the formation of a large number of very small volumes was observed at all Stokes numbers and attributed to the collision of particles with the pore wall. Multiscale wavelet analysis of the particle number density indicates that the peak of the energy density spectrum, representative of enhanced particle clustering, shifts towards larger scales with an increase in the Stokes number. Scale-dependent skewness and flatness quantify the intermittent void and cluster distribution, with cluster formation observed at small scales for all Stokes numbers, and void regions at large scales for large Stokes numbers. 

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5. Clustering of inertial particles in turbulent flow through a porous unit cell

   Apte, SV; Oujia, T; Matsuda, K; Kadoch, B; He, X; Schneider, K (February 2022, Journal of fluid mechanics)

   Direct numerical simulation is used to investigate effects of turbulent flow in the confined geometry of a face-centred cubic porous unit cell on the transport, clustering and deposition of fine particles at different Stokes numbers ( 𝑆𝑡=0.01,0.1,0.5,1,2 ) and at a pore Reynolds number of 500. Particles are advanced using one-way coupling and the collision of particles with pore walls is modelled as perfectly elastic with specular reflection. Tools for studying inertial particle dynamics and clustering developed for homogeneous flows are adapted to take into account the embedded, curved geometry of the pore walls. The pattern and dynamics of clustering are investigated using the volume change of Voronoi tesselation in time to analyse the divergence and convergence of the particles. Similar to the case of homogeneous, isotropic turbulence, the cluster formation is present at large volumes, while cluster destruction is prominent at small volumes and these effects are amplified with the Stokes number. However, unlike homogeneous, isotropic turbulence, the formation of a large number of very small volumes was observed at all Stokes numbers and attributed to the collision of particles with the pore wall. Multiscale wavelet analysis of the particle number density indicates that the peak of the energy density spectrum, representative of enhanced particle clustering, shifts towards larger scales with an increase in the Stokes number. Scale-dependent skewness and flatness quantify the intermittent void and cluster distribution, with cluster formation observed at small scales for all Stokes numbers, and void regions at large scales for large Stokes numbers. 

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