Theory and Applications of Macroscale Models in Porous Media

Flow modeling and structural characterization in fungal pellets

Fungal pellets are hierarchical systems that can be found in an ample variety of applications. Modeling transport phenomena in this type of systems is a challenging but necessary task to provide knowledge-based processes that improve the outcome of their biotechnological applications. In this work, an upscaled model for total mass and momentum transport in fungal pellets is implemented and analyzed, using elements of the volume averaging and adjoint homogenization methods departing from the governing equations at the microscale in the intracellular and extracellular phases. The biomass is assumed to be composed of a non-Newtonian fluid and the organelles impervious to momentum transport are modeled as a rigid solid phase. The upscaled equations contain effective-medium coefficients, which are predicted from the solution of adjoint closure problems in a three-dimensional periodic domains representative of the microstructure. The construction of these domains was performed for Laccaria trichodermophora based on observations of actual biological structures. The upscaled model was validated with direct numerical simulations in homogeneous portions of the pellets core. It is shown that no significant differences are observed when the dolipores are open or closed to fluid flow. By comparing the predictions of the average velocity in the extracellular phase resulting from the upscaled model with those from the classical Darcy equation (i.e., assuming that the biomass is a solid phase) the contribution of the intracellular fluid phase was evidenced. This work sets the foundations for further studies dedicated to transport phenomena in this type of systems.

Porous nanocomposites with enhanced intrinsic piezoresistive sensitivity for bioinspired multimodal tactile sensors

In this work, we propose porous fluororubber/thermoplastic urethane nanocomposites (PFTNs) and explore their intrinsic piezoresistive sensitivity to pressure. Our experiments reveal that the intrinsic sensitivity of the PFTN-based sensor to pressure up to 10 kPa increases up to 900% compared to the porous thermoplastic urethane nanocomposite (PTN) counterpart and up to 275% compared to the porous fluororubber nanocomposite (PFN) counterpart. For pressures exceeding 10 kPa, the resistance-pressure relationship of PFTN follows a logarithmic function, and the sensitivity is 221% and 125% higher than that of PTN and PFN, respectively. With the excellent intrinsic sensitivity of the thick PFTN film, a single sensing unit with integrated electrode design can imitate human skin for touch detection, pressure perception and traction sensation. The sensing range of our multimodal tactile sensor reaches ~150 Pa, and it exhibits a linear fit over 97% for both normal pressure and shear force. We also demonstrate that an electronic skin, made of an array of sensing units, is capable of accurately recognizing complex tactile interactions including pinch, spread, and tweak motions.

Unlocking Efficiency in Radio-Frequency Heating: Eigenfrequency Analysis for Resonance Identification and Propagation Enhancement in Nigerian Tar Sands

Nigerian bituminous tar sands are among the world's largest deposits of bitumen and heavy oil. They are estimated to contain 38-40 billion barrels of heavy oil and bitumen, spanning approximately 120 km in length and 4-6 km in breadth. With global commitments to net zero emissions and various energy transition plans, improvements in the recovery methods for heavy oil and bitumen are being sought. To address this, renewable energy electrothermal enhanced oil recovery is considered an eco-friendly alternative. In our study, we introduce a novel Reservoir-Waveguide-Debye model. This model explores the enhancement of penetration for radio-frequency electromagnetic (EM) waves, which can be generated from renewable energy sources. These waves facilitate the viscosity reduction of heavy oil and bitumen. Through a comprehensive 2D numerical simulation employing the bulk properties of bituminous tar sands, we assess the propagation of EM fields within porous media. We utilize the industrial heating radio-frequency bandwidth of 1-60 MHz to conduct frequency domain investigations. Our analysis delves into propagation modes using eigenfrequency analysis, pinpointing the EM resonance of the tar sands. Furthermore, we investigate the impact of mesh refinement on the EM eigenfrequencies of porous media at both the microscale (400 μm) and macroscale (100 m in radial distance). Our results demonstrate the occurrence of resonance phenomena at complex eigenfrequencies around 27.12 and 54.24 MHz in both the microscale and macroscale models of the bituminous sands. This breakthrough research offers promising insights into harnessing renewable energy-driven EM waves for efficient thermal recovery processes in the Nigerian bituminous tar sands, thus fostering sustainable and eco-friendly energy solutions.

Constitutive Correlations for Mass Transport in Fibrous Media Based on Asymptotic Homogenization

Mass transport in textiles is crucial. Knowledge of effective mass transport properties of textiles can be used to improve processes and applications where textiles are used. Mass transfer in knitted and woven fabrics strongly depends on the yarn used. In particular, the permeability and effective diffusion coefficient of yarns are of interest. Correlations are often used to estimate the mass transfer properties of yarns. These correlations commonly assume an ordered distribution, but here we demonstrate that an ordered distribution leads to an overestimation of mass transfer properties. We therefore address the impact of random ordering on the effective diffusivity and permeability of yarns and show that it is important to account for the random arrangement of fibers in order to predict mass transfer. To do this, Representative Volume Elements are randomly generated to represent the structure of yarns made from continuous filaments of synthetic materials. Furthermore, parallel, randomly arranged fibers with a circular cross-section are assumed. By solving the so-called cell problems on the Representative Volume Elements, transport coefficients can be calculated for given porosities. These transport coefficients, which are based on a digital reconstruction of the yarn and asymptotic homogenization, are then used to derive an improved correlation for the effective diffusivity and permeability as a function of porosity and fiber diameter. At porosities below 0.7, the predicted transport is significantly lower under the assumption of random ordering. The approach is not limited to circular fibers and may be extended to arbitrary fiber geometries.

Chemical and Reactive Transport Processes Associated with Hydraulic Fracturing of Unconventional Oil/Gas Shales

Hydraulic fracturing of unconventional oil/gas shales has changed the energy landscape of the U.S. Recovery of hydrocarbons from tight, hydraulically fractured shales is a highly inefficient process, with estimated recoveries of <25% for natural gas and <5% for oil. This review focuses on the complex chemical interactions of additives in hydraulic fracturing fluid (HFF) with minerals and organic matter in oil/gas shales. These interactions are intended to increase hydrocarbon recovery by increasing porosities and permeabilities of tight shales. However, fluid-shale interactions result in the dissolution of shale minerals and the release and transport of chemical components. They also result in mineral precipitation in the shale matrix, which can reduce permeability, porosity, and hydrocarbon recovery. Competition between mineral dissolution and mineral precipitation processes influences the amounts of oil and gas recovered. We review the temporal/spatial origins and distribution of unconventional oil/gas shales from mudstones and shales, followed by discussion of their global and U.S. distributions and compositional differences from different U.S. sedimentary basins. We discuss the major types of chemical additives in HFF with their intended purposes, including drilling muds. Fracture distribution, porosity, permeability, and the identity and molecular-level speciation of minerals and organic matter in oil/gas shales throughout the hydraulic fracturing process are discussed. Also discussed are analysis methods used in characterizing oil/gas shales before and after hydraulic fracturing, including permeametry and porosimetry measurements, X-ray diffraction/Rietveld refinement, X-ray computed tomography, scanning/transmission electron microscopy, and laboratory- and synchrotron-based imaging/spectroscopic methods. Reactive transport and spatial scaling are discussed in some detail in order to relate fundamental molecular-scale processes to fluid transport. Our review concludes with a discussion of potential environmental impacts of hydraulic fracturing and important knowledge gaps that must be bridged to achieve improved mechanistic understanding of fluid transport in oil/gas shales.

Modeling and visualizing the transport and retention of cationic and oxyanionic metals (Cd and Cr) in saturated soil under various hydrochemical and hydrodynamic conditions

Cationic and oxyanionic metals are widely existed in the aquatic and soil environment with the process of industrialization and they may behave different transport properties in aquifer systems due to the opposite charges. In this study, the comparative transport behaviors of Cd²⁺ and CrO₄^2- in water-saturated soil columns were investigated under a variety of hydrochemical and hydraulic conditions such as pH, ionic strength (IS), and flow rate. The transport mechanisms of Cd(II) and Cr(VI) were explored by fitting the breakthrough curves with a two-site non-equilibrium transport model. Results indicated that high solution pH inhibited the transport of Cd(II) due to the enhanced electrostatic interaction. In contrast, the migration of Cr(VI) was promoted with the least amount of Cr(VI) (1.23 mg) being retained in soil at high pH, ascribing to the stronger electrostatic repulsion between anions and soil surface. Meanwhile, high pH conditions were not favorable for the participation of reduced iron in the reduction process of Cr(VI), resulting in the least amount of Cr(III) detected (22%). The increase in ionic strength decreased the negativity of the potential at the adsorption plane, which enhanced the transport of cationic Cd(II) and the retardation of anionic Cr(VI). In addition, the increase in flow rate facilitated the transport of Cd(II) and Cr(VI), mainly due to the decreasing contacting with porous media and enhanced dispersion effect. These findings demonstrated that the fate and environmental behavior of metal cations and anions differed with the change of hydrochemical and hydrodynamic properties, which should be considered for the risk assessment and remediation of metal contaminated sites.

A continuum mechanical framework for modeling tumor growth and treatment in two- and three-phase systems

The growth and treatment of tumors is an important problem to society that involves the manifestation of cellular phenomena at length scales on the order of centimeters. Continuum mechanical approaches are being increasingly used to model tumors at the largest length scales of concern. The issue of how to best connect such descriptions to smaller-scale descriptions remains open. We formulate a framework to derive macroscale models of tumor behavior using the thermodynamically constrained averaging theory (TCAT), which provides a firm connection with the microscale and constraints on permissible forms of closure relations. We build on developments in the porous medium mechanics literature to formulate fundamental entropy inequality expressions for a general class of three-phase, compositional models at the macroscale. We use the general framework derived to formulate two classes of models, a two-phase model and a three-phase model. The general TCAT framework derived forms the basis for a wide range of potential models of varying sophistication, which can be derived, approximated, and applied to understand not only tumor growth but also the effectiveness of various treatment modalities.

In Silico Prediction of Food Properties: A Multiscale Perspective

Several open software packages have popularized modeling and simulation strategies at the food product scale. Food processing and key digestion steps can be described in 3D using the principles of continuum mechanics. However, compared to other branches of engineering, the necessary transport, mechanical, chemical, and thermodynamic properties have been insufficiently tabulated and documented. Natural variability, accented by food evolution during processing and deconstruction, requires considering composition and structure-dependent properties. This review presents practical approaches where the premises for modeling and simulation start at a so-called “microscopic” scale where constituents or phase properties are known. The concept of microscopic or ground scale is shown to be very flexible from atoms to cellular structures. Zooming in on spatial details tends to increase the overall cost of simulations and the integration over food regions or time scales. The independence of scales facilitates the reuse of calculations and makes multiscale modeling capable of meeting food manufacturing needs. On one hand, new image-modeling strategies without equations or meshes are emerging. On the other hand, complex notions such as compositional effects, multiphase organization, and non-equilibrium thermodynamics are naturally incorporated in models without linearization or simplifications. Multiscale method’s applicability to hierarchically predict food properties is discussed with comprehensive examples relevant to food science, engineering and packaging. Entropy-driven properties such as transport and sorption are emphasized to illustrate how microscopic details bring new degrees of freedom to explore food-specific concepts such as safety, bioavailability, shelf-life and food formulation. Routes for performing spatial and temporal homogenization with and without chemical details are developed. Creating a community sharing computational codes, force fields, and generic food structures is the next step and should be encouraged. This paper provides a framework for the transfer of results from other fields and the development of methods specific to the food domain.

Multiscale Modeling of Uranium Bioreduction in Porous Media by One-Dimensional Biofilms

We formulate a multiscale mathematical model that describes the bioreduction of uranium in porous media. On the mesoscale we describe the bioreduction of uranium [VI] to uranium [IV] using a multispecies one-dimensional biofilm model with suspended bacteria and thermodynamic growth inhibition. We upscale the mesoscopic (colony scale) model to the macroscale (reactor scale) and investigate the behavior of substrate utilization and production, attachment and detachment processes, and thermodynamic effects not usually considered in biofilm growth models. Simulation results of the reactor model indicate that thermodynamic inhibition quantitatively alters the dynamics of the model and neglecting thermodynamic effects may over- or underestimate chemical concentrations in the system. Furthermore, we numerically investigate uncertainties related to the specific choice of attachment and detachment rate coefficients and find that while increasing the attachment rate coefficient or decreasing the detachment rate coefficient leads to thicker biofilms, performance of the reactor remains largely unaffected.

Numerical Simulation of Ammonothermal Crystal Growth of GaN—Current State, Challenges, and Prospects

Numerical simulations are a valuable tool for the design and optimization of crystal growth processes because experimental investigations are expensive and access to internal parameters is limited. These technical limitations are particularly large for ammonothermal growth of bulk GaN, an important semiconductor material. This review presents an overview of the literature on simulations targeting ammonothermal growth of GaN. Approaches for validation are also reviewed, and an overview of available methods and data is given. Fluid flow is likely in the transitional range between laminar and turbulent; however, the time-averaged flow patterns likely tend to be stable. Thermal boundary conditions both in experimental and numerical research deserve more detailed evaluation, especially when designing numerical or physical models of the ammonothermal growth system. A key source of uncertainty for calculations is fluid properties under the specific conditions. This originates from their importance not only in numerical simulations but also in designing similar physical model systems and in guiding the selection of the flow model. Due to the various sources of uncertainty, a closer integration of numerical modeling, physical modeling, and the use of measurements under ammonothermal process conditions appear to be necessary for developing numerical models of defined accuracy.

Transport of Tl(I) in water-saturated porous media: Role of carbonate, phosphate and macromolecular organic matter

Understanding the transport behaviors of thallium (Tl) in porous media is of considerable interest for both natural soils and artificial filtration removal of Tl. In this context, the transport behaviors of Tl(I) in water-saturated sand columns under different conditions were systematically investigated. It was found that, in addition to the effects of pH and ionic strength (IS), the transport of Tl(I) depended on the carbonate, phosphate and macromolecular organic matter as well. Tl(I) broken the columns more difficultly under higher pH and lower IS conditions. Moreover, the adsorption of carbonate and phosphate on sand surfaces may increase the retention of Tl(I) in columns. As for macromolecular organic matter, humic acid (HA) facilitated Tl(I) transport, especially under neutral and alkaline conditions (7.0 and 9.8), which was possibly associated with Tl-complexes formation and competed adsorption between Tl(I) and HA. However, bovine serum albumin (BSA) impeded Tl(I) transport for the reason that deposited BSA might provide more adsorption sites for Tl(I), though Tl(I) had a slight effect on BSA transport. In order to evaluate the mechanisms of transport, a dual-sites non-equilibrium model was applied to fit the breakthrough curves of Tl(I). Retardation factor (R) values of individual Tl(I) transport from model calculations were found to be higher than that of Tl(I) transport with HA and lower than that of Tl(I) transport with BSA. The fraction of instantaneous sorption sites (β) was found to decrease with increasing pH, implying nonequilibrium sorption is a main sorption mechanism of Tl(I) with pH increasing. The fundamental data obtained herein demonstrated that carbonate, phosphate and macromolecular organic matter significantly influenced the Tl(I) migration and could lead to the leaking or bindings of Tl(I) at Tl-occurring sites.

Recent advances in multiscale CFD modelling of cooling processes and systems for the agrifood industry

Spoilage of agrifood produce is a major issue in the industry. Cooling is an effective technique for extending the shelf life of fresh agrifood produce to minimize spoilage. Due to the practical inability of directly solving the wide spatial and temporal scales in large industrial agrifood cooling systems, the porous medium approach is mostly used. However, improvements of current porous medium models and modeling across much wider scales are needed to better understand the multiscale cooling process and system problems. Recently, as a result of increased computational capacity, multiscale computational fluid dynamics (CFD) modeling approaches have been developed to tackle some of these challenges. The associated problems and applications of CFD in the design and process optimization of cooling processes and systems at different scales are considered. CFD solution and scale bridging techniques relevant for handling multiscale cooling processes and systems problems are discussed. Innovative applications of various CFD modeling techniques at different scales in cooling processes and systems are reviewed. CFD modeling techniques can be used to handle multiscale cooling process and system problems. Lattice Boltzmann method (LBM) is a potentially viable discrete modeling technique for complimentary usages alongside current continuum techniques in future multiscale CFD modeling. The multiscale CFD modeling paradigm can overcome the computational resource limitations associated with the direct modeling approach and enhance model extension across wider spatial and temporal scales. Information from multiscale CFD could be used to improve the accuracy of current porous medium models, and thus the design of more efficient cooling systems.

Toward a New Generation of Two-Fluid Flow Models Based on the Thermodynamically-Constrained Averaging Theory

Traditional models of two-fluid flow through porous media at the macroscale have existed for nearly a century. These phenomenological models are not firmly connected to the microscale; thermodynamic constraints are not enforced; empirical closure relations are well known to be hysteretic; fluid pressures are typically assumed to be in a local equilibrium state with fluid saturations; and important quantities such as interfacial and curvilinear geometric extents, tensions, and curvatures, known to be important from microscale studies, do not explicitly appear in traditional macroscale models. Despite these shortcomings, the traditional model for two-fluid flow in porous media has been extensively studied to develop efficient numerical approximation methods, experimental and surrogate measure parameterization approaches, and convenient pre- and post-processing environments; and they have been applied in a large number of applications from a variety of fields. The thermodynamically constrained averaging theory (TCAT) was developed to overcome the limitations associated with traditional approaches, and we consider here issues associated with the closure of this new generation of models. It has been shown that a hysteretic-free state equation exists based upon integral geometry that relates changes in volume fractions, capillary pressure, interfacial areas, and the Euler characteristic. We show an analysis of how this state equation can be parameterized with a relatively small amount of data. We also formulate a state equation for resistance coefficients that we show to be hysteretic free, unlike traditional relative permeability models. Lastly, we comment on the open issues remaining for this new generation of models.