Types Of Porous Media Research Articles

Removal of Nitrogen, Phosphates, and Chemical Oxygen Demand from Community Wastewater by Using Treatment Wetlands Planted with Ornamental Plants in Different Mineral Filter Media

This study aimed to explore the impact of various ornamental plants (Heliconia psittacorum, Etlingera elatior, Spatyphilum walisii) grown in different filter media (porous river rock (PR) and tepezyl (TZ)) on the removal of pollutants in vertical-subsurface-microcosm treatment wetlands (TWs). This study also sought to assess the adaptability of these plant species to TW conditions. Twenty-four microcosm systems were utilized, with twelve containing PR and twelve containing TZ as the filter media. Each porous media type had three units planted with each species, and three were left unplanted. Rural community wastewater was treated in the TWs. The results showed no significant differences in the effects of the porous media on pollutant removal performance (p > 0.05). However, it was noted that while both porous media were efficient, TZ, a residue of construction materials, is recommended for sites facing economic constraints. Additionally, the removal efficiency was found to be independent of the type of ornamental plant used (p > 0.05); however, the measured parameters varied with plant spp. The adaptation of the plants varied depending on the species. H. psittacorum grew faster and produced a larger number of flowers compared to the other species (20–22 cm). S. wallisii typically produced 7–8 flowers. E. elatior did not produce flowers, and some plants showed signs of slight disease and pests, with the leaves turning yellow. In terms of plant biomass, the type of porous media used did not have a significant effect on the production of above (p = 0.111) or below-ground biomass (p = 0.092). The removal percentages for COD in the presence and absence of plants were in the ranges of 64–77% and 27–27.7%, respectively. For TN, the numbers were 52–65% and 30–31.8%, and for N-NO3, they were 54–60% and 12–18%. N-NH4 saw removal rates of 67–71% and 28–33%, while P-PO4 saw removal rates of 60–72% and 22–25%. The difference in removal percentages between microcosms with and without plants ranged from 30 to 50%, underscoring the importance of plants in the bio-removal processes (phytoremediation). These results reveal that incorporating ornamental plants in TWs with TZ for wastewater in rural areas holds great promise for enhancing the visual appeal of these systems and ultimately gaining public approval. Our findings also enable us to offer recommendations for selecting suitable plants and substrates, as well as designing combinations for TWs.

Tempered fractional differential equations on hyperbolic space

Abstract In this paper we study linear fractional differential equations involving tempered Caputo-type derivatives in the hyperbolic space. We consider in detail the three-dimensional case for its simple and useful structure. We also discuss the probabilistic meaning of our results in relation to the distribution of an hyperbolic Brownian motion time-changed with the inverse of a tempered stable subordinator. The generalization to an arbitrary dimension n can be easily obtained. We also show that it is possible to construct a particular solution for the non-linear porous-medium type tempered equation by using elementary functions.

A numerical investigation to assess changes to displacement front and by-passed zones employing kinetic interface-sensitive tracer

An important aspect in groundwater remediation is to understand changes of multiphase fluid front morphology and stagnant regions on macro scale. However, the prediction of those changes during two-phase flow remains a challenging task due to the interplay of various physical factors. Recent laboratory experiments have demonstrated tracers' ability to predict deformation in the front of a two-phase flow system by utilizing a new reactive tracer known as, the kinetic interface sensitive tracer (KIS). This research employs a reactive transport model coupled with a macro-scale two-phase flow model to numerically analyse how viscosity ratio, capillary number, and heterogeneities on the tracer's signal and its impact the frontal deformation. One homogeneous and two heterogeneous types of porous media are considered. The background porous medium is a fine-grained, low-permeability medium, with a coarser, high-permeability lenses, generating heterogeneous material properties. The high-permeability lenses account for 25 % of the total model area and are arranged in either periodic or random patterns. The findings are evaluated using four parameters (effective front length, swept area, front roughness, and transition zone length). The flow patterns dominating the shape of the front are characterized by the viscous and capillary forces i.e. capillary number and the viscosity ratio between the two fluids. The results show that changes in flow regimes can be quantified using effective front length, thus employing the effective front length the viscous fingering regions can be quantified. Furthermore, front roughness and transition zone length are extracted and their relevance to the by-passed zones is presented. The slope of the reactive KIS tracer breakthrough curve, plotted on a phase diagram, can also be used to predict the existence of the by-passed zones for a low viscosity ratio. Finally, changes in front roughness and transition zone length induced by the inclusions are correlated to the slope of the KIS tracer BTC. The findings of this study can contribute to a better understanding of the impact of different flow regimes on the KIS tracer breakthrough signals and the linkages between the tracer signals and the front sizes.

Porous medium type reaction-diffusion equation: Large time behaviors and regularity of free boundary

We consider the Cauchy problem of the porous medium type reaction-diffusion equation∂tρ=Δρm+ρg(ρ),(x,t)∈Rn×R+,n≥2,m>1, where g is the given monotonic decreasing function with the density critical threshold ρM>0 satisfying g(ρM)=0. We prove that the pressure P:=mm−1ρm−1 in Lloc∞(Rn) tends to the pressure critical threshold PM:=mm−1(ρM)m−1 at the time decay rate (1+t)−1. If the initial density ρ(x,0) is compactly supported, we justify that the support {x:ρ(x,t)>0} of the density ρ expands exponentially in time. Furthermore, we show that there exists a time T0>0 such that the pressure P is Lipschitz continuous for t>T0, which is the optimal (sharp) regularity of the pressure, and the free surface ∂{(x,t):ρ(x,t)>0}∩{t>T0} is locally Lipschitz continuous. In addition, under the same initial assumptions of compact support, we verify that the free boundary ∂{(x,t):ρ(x,t)>0}∩{t>T0} is a local C1,α surface.

Biological invasion with a porous medium type diffusion in a heterogeneous space

The knowledge of traveling wave solutions is the main tool in the study of wave propagation. However, in a spatially heterogeneous environment, traveling wave solutions do not exist, and a different approach is needed. In this paper, we study the generation and the propagation of hyperbolic scale singular limits of a KPP-type reaction–diffusion equation when the carrying capacity is spatially heterogeneous and the diffusion is of a porous medium equation type. We show that the interface propagation speed varies according to the carrying capacity.

Knowledge Extraction via Machine Learning Guides a Topology‐Based Permeability Prediction Model

AbstractThe complexity and heterogeneity of pore structure present significant challenges in accurate permeability estimation. Commonly used empirical formulas neglect its microscopic and topological characteristics, thus lacking accuracy and adaptability. While machine learning (ML) and deep learning (DL) models demonstrate promising performance, but encounter challenges of data availability, computational cost, and model interpretability. The present study aims to develop a more robust and accurate permeability prediction model via knowledge extraction from ML model. We first establish an ML model between permeability and the geometry‐topology characteristics of porous media using Extreme Gradient Boosting (XGBoost) algorithm. The data set used to fit ML model is prepared from 458 samples of different types of porous media. Using the SHapley Additive exPlanations (SHAP) value, the influence of each feature on permeability prediction is quantified. It is found that the closeness centrality (topology feature), tortuosity, porosity (macroscopic features) and throat diameter, throat length, pore diameter (pore network features) are vital for permeability prediction. Guided by partial dependence calculation, the unknown function relationship between permeability and the top six important features is established. The novel permeability prediction model incorporating topology feature improves the prediction accuracy and demonstrates strong applicability across diverse data sets. This new model presents an optimal balance between simplicity and performance, rendering it a compelling alternative for permeability prediction in porous media. The research provides a novel referable framework of knowledge extraction via ML to reveal the important features and establish the potential relationship that can be extended and applied in other research fields.

Entropy solutions for time-fractional porous medium type equations

Entropy solutions for time-fractional porous medium type equations

Transport and retention of positively charged zinc oxide nanoparticles in saturated porous media: Effects of metal oxides and clays

The effects of metal oxides and clays on the transport of zinc oxide nanoparticles (ZnO-NPs) in saturated porous media were investigated under different ionic strength (IS) conditions. We studied the transport and retention behavior of ZnO-NPs for different types of porous media (untreated, acid treated, and acid–salt treated sand). The selected untreated sand was used as a representative sand, coated with both metal oxide and clay. The acid treated and acid–salt-treated sands were used and compared to investigate the effects of clays on the surface of the sand. In addition, the effects of clay particles in bulk solutions on the mobility and retention of ZnO-NPs were observed using bentonite as a representative clay particle. We found that the increased mobility of positively charged ZnO-NPs can be attributed to increasing charge heterogeneity of silica sand with metal oxides (mainly, iron oxide) and clays in untreated sand. No breakthrough of ZnO-NP was observed for acid-treated (presence of clays and absence of metal oxides) and acid–salt-treated sand (absence of both metal oxide and clays). Most of the injected ZnO-NPs were deposited on the surface of the sand near the column inlet. The transport of bentonite-facilitated ZnO-NPs was improved at the lowest IS (0.1 mM) (∼20%), whereas there was no difference in the mobility of ZnO-NPs at high IS solutions (1 mM and 10 mM). In particular, the breakthrough amount improved with increasing bentonite concentration. Classical Derjaguin–Landau–Verwey–Overbeek interactions help explain observed interactions between ZnO-NPs and sand as well as bentonite and sand.

Nonlinear aggregation-diffusion equations with Riesz potentials

We consider an aggregation-diffusion model, where the diffusion is nonlinear of porous medium type and the aggregation is governed by the Riesz potential of order s. The addition of a quadratic diffusion term produces a more precise competition with the aggregation term for small s, as they have the same scaling if s=0. We prove existence and uniqueness of stationary states and we characterize their asymptotic behavior as s goes to zero. Moreover, we prove existence of gradient flow solutions to the evolution problem by applying the JKO scheme.

Experimental Study of Hydrogen Synthesis under Conditions of a Natural Gas Reservoir

This research discusses issues related to hydrogen production, a promising source of “green” energy. Various methods of hydrogen production are considered, along with a new technology for hydrogen synthesis in natural gas reservoirs that has never been implemented before. At the same time, existing published experimental studies indicate a high probability of hydrogen synthesis when steam is injected into oil reservoirs. However, considering that oil is the primary raw material for hydrogen generation, there is high uncertainty about the success of the process in natural gas fields in the absence of residual oil. The experimental study presented in this work aims to justify the possibility of hydrogen synthesis under conditions of a natural gas reservoir. Specially designed reactors filled with different models of porous media, including the rock of a real gas field, are used for the physical modeling of the process. The process simulates injecting steam into a preheated porous medium mixed with hydrocarbon gas, specifically methane, at a reservoir pressure of 80 atm. The main variable parameters, aside from the type of porous medium, are the temperature and the steam-to-methane ratio in the system. The article presents the results of a series of nine experiments. The gas products were analyzed using a gas chromatograph. At the same time, the properties of rock samples were investigated after each experiment. The results of the experiments reveal patterns of concentration of hydrogen produced depending on the parameters, indicating the high potential of hydrogen synthesis technology under reservoir conditions in natural gas fields.

A unified Bayesian inversion approach for a class of tumor growth models with different pressure laws

Abstract. In this paper, we use the Bayesian inversion approach to study the data assimilation problem for a family of tumor growth models described by porous-medium type equations. The models contain uncertain parameters and are indexed by a physical parameter m, which characterizes the constitutive relation between density and pressure. Based on these models, we employ the Bayesian inversion framework to infer parametric and nonparametric unknowns that affect tumor growth from noisy observations of tumor cell density. We establish the well-posedness and the stability theories for the Bayesian inversion problem and further prove the convergence of the posterior distribution in the so-called incompressible limit, m →∞. Since the posterior distribution across the index regime m ∈ [2,∞) can thus be treated in a unified manner, such theoretical results also guide the design of the numerical inference for the unknown. We propose a generic computational framework for such inverse problems, which consists of a typical sampling algorithm and an asymptotic preserving solver for the forward problem. With extensive numerical tests, we demonstrate that the proposed method achieves satisfactory accuracy in the Bayesian inference of the tumor growth models, which is uniform with respect to the constitutive relation.

Reynolds number dependence of turbulent flows over a highly permeable wall

Direct numerical simulations of turbulent flows over highly permeable porous walls were performed at various Reynolds numbers to examine the effects of the Reynolds number on permeable wall turbulence. The porous medium consisted of Kelvin cell arrays with porosity $0.95$ , and the permeability Reynolds number $Re_K$ ranged from approximately 7 to 50. Simulations with thin and thick porous walls were performed to investigate the effects of spanwise roller vortices associated with the Kelvin–Helmholtz instability. The results show that the effect of the Kelvin–Helmholtz instability becomes more significant with increasing the permeability Reynolds number, and spanwise rollers, for which length scale is an order of channel height, dominate turbulence when $Re_K \gtrsim 30$ . Spanwise rollers reinforce the negative correlation between the wall-normal and streamwise velocity fluctuations close to the porous/fluid interface, and intensify the turbulent velocity fluctuations away from the porous walls, leading to increased frictional resistance. An investigation of the Reynolds number dependence of the modified logarithmic law indicates that the zero-plane displacement and equivalent roughness height are proportional to the square root of permeability, whereas the von Kármán constant increases with the permeability Reynolds number because of the increased mixing length resulting from the relatively large-scale velocity fluctuations induced by spanwise rollers. We developed a model for the modified log law for permeable wall turbulence based on permeability, and confirmed that the skin friction coefficient obtained from the model reasonably predicts the skin friction coefficient for several types of high-porosity porous media. Hence, permeability is a key parameter that characterizes the logarithmic mean velocity profiles over a variety of porous media with high porosity.

Study of the Thermal and Hydraulic Performance of Porous Block versus Gyroid Structure: Experimental and Numerical Approaches

Various researchers in the field of engineering have used porous media for many years. The present paper studies heat enhancement using two different types of porous media. In the first type, porous metal foam media was used experimentally and numerically for heat extraction. The porous medium was replaced with a porous structure using the Gyroid model and the triply periodic minimum surfaces technique in the second type. The Darcy–Brinkman model combined with the energy equation was used for the first type, whereas Navier–Stokes equations with the energy equation were implemented for the second type. The uniqueness of this approach was that it treated the Gyroid as a solid structure in the model. The two types were tested for different heat fluxes and different flow rates. A comparison between the experimental measurements and the numerical solution provided a good agreement. By comparing the performance of the two types of structure, the Gyroid structure outperformed the metal foam for heat extraction and uniformity of the temperature distribution. Despite an 18% increase in the pressure drop in the presence of the Gyroid structure, the performance evaluation criteria for the Gyroid are more significant when compared to metal foam.

Effective interface conditions for a porous medium type problem

Motivated by biological applications on tumour invasion through thin membranes, we study a porous medium type equation where the density of the cell population evolves under Darcy’s law, assuming continuity of both the density and flux velocity on the thin membrane which separates two domains. The drastically different scales and mobility rates between the membrane and the adjacent tissues lead to consider the limit as the thickness of the membrane approaches zero. We are interested in recovering the effective interface problem and the transmission conditions on the limiting zero-thickness surface, formally derived by Chaplain et al. (2019), which are compatible with nonlinear generalized Kedem–Katchalsky ones. Our analysis relies on a priori estimates and compactness arguments as well as on the construction of a suitable extension operator, which allows us to deal with the degeneracy of the mobility rate in the membrane, as its thickness tends to zero.

Non-intrusive, transferable model for coupled turbulent channel-porous media flow based upon neural networks

Turbulent flow over permeable interfaces is omnipresent featuring complex flow topology. In this work, a data-driven, end-to-end machine learning model has been developed to model the turbulent flow in porous media. For the same, we have derived a non-linear reduced order model (ROM) with a deep convolution autoencoder. This model can reduce highly resolved spatial dimensions, which is a prerequisite for direct numerical simulation, by 99%. A downstream recurrent neural network has been trained to capture the temporal trend of reduced modes; thus, it is able to provide future evolution of modes. We further evaluate the trained model's capability on a newer dataset with a different porosity. In such cases, fine-tuning could reduce the efforts (up to two-order of magnitude) to train a model with limited dataset (10%) and knowledge and still show a good agreement on the mean velocity profile. Especially, the fine-tuned model shows a better agreement in the porous domain than the channel and interface areas indicating the topological feature is less challenging for training than the multi-scale nature of the turbulent flows. Leveraging the current model, we find that even quick fine-tuning achieves an impressive order-of-magnitude reduction in training time by approximately O(102) and still results in effective flow predictions. This promising discovery encourages the fast development of a substantial amount of data-driven models tailored for various types of porous media. The diminished training time substantially lowers the computational cost when dealing with changing porous topologies, making it feasible to systematically explore interface engineering with different types of porous media.

Assessment of hydrogen storage capacity in porous media at the European scale

A first assessment of the storage resource at European scale for underground hydrogen storage in porous media is presented for the European Union and some neighboring countries (Norway, Türkiye, Ukraine, United Kingdom). The study includes different types of porous media: existing underground gas storages, depleted oil and gas fields, deep saline formations. The storage resources are computed based upon a volumetric analytical approach which accounts for hydrogen physical characteristics (density, viscosity, sweep efficiency and capillary trapping). The computed storage resource is in good agreement with published dynamic storage capacity of deep saline formations in Poland.The extension to the continental scale enables a consistent estimate of the various storage resources. The working storage resources at the European scale are about 8000 TWh among which 37 % are onshore which covers the expected storage requirements. The agreement with previously published working storage capacities for depleted gas fields in the UK continental shelf is quite good at about 2662 TWh. However, at the field level, there might be significant differences linked with the consistency requirements at European scale of this study which estimates the production of oil and gas fields without using the actual field production.Despite its restriction of publicly available data, these results show significant storage resources. The working capacities are not evenly distributed over the continent. However, assuming no competitive usage, the working storage resource would be extremely significant when accounting for onshore and offshore potential. Amongst the different porous media, the underground gas storages present the most interest for conversion to hydrogen underground storage despite their smaller storage resource, 460 TWh, than for depleted gas fields, 5440 TWh for the onshore and offshore. The estimate of working storage resource in deep saline formation is quite low, only 46 TWh as it relies upon traps that were previously characterized.

A machine learning based-method to generate random circle-packed porous media with the desired porosity and permeability

The generation of digital porous media facilitates the fabrication of artificial porous media and the analysis of their properties. The past random digital porous medium generation methods are unable to generate a porous medium with a specified permeability. In this work, a new method is proposed to generate a random circle-packed digital porous medium with a specified porosity and permeability. Firstly, the process of generating the random circle-packed digital porous medium with a specified porosity is detailed. Secondly, the permeability of the digital porous medium is calculated by the multi-relaxation time lattice Boltzmann method. A total of 3,000 digital porous medium samples are generated, and their microstructure data and permeabilities are prepared for the training of a convolutional neural network (CNN) model, which is then applied to effectively predict the permeability of a digital porous medium. Finally, our method is elaborated and the choice of target permeability in this method is discussed. Our approach has the potential to be applied to the generation of other types of porous media.

EXPERIMENTAL STUDY AND THERMODYNAMIC SIMULATION OF CO2 HYDRATE PHASE EQUILIBRIUM CONDITIONS IN POROUS MEDIA

The phase equilibrium of CO<sub>2</sub> hydrates on various types of porous media is studied by experiment and model. The experiments are conducted under controlled conditions to measure the hydrate equilibrium conditions. The proposed model is based on the Chen-Guo theory and incorporates the surface property parameters for each type of porous media. The predictions of model are validated by comparing them to experimental data, and the predicted temperature deviation is within 0.25 K. Furthermore, the accuracy of model is compared with other existing models, and the calculation accuracy of this model in glass beads with weak water absorption is 0.05 K higher than that of the existing model, and 0.09 K higher in sand with strong water absorption. The study contributes to a better understanding of CO<sub>2</sub> hydrate formation on different porous media and provides a reliable model for predicting phase equilibrium conditions in such systems.

PoroFluidics: deterministic fluid control in porous microfluidics.

Microfluidic devices with open lattice structures, equivalent to a type of porous media, allow for the manipulation of fluid transport processes while having distinct structural, mechanical, and thermal properties. However, a fundamental understanding of the design principles for the solid structure in order to achieve consistent and desired flow patterns remains a challenge, preventing its further development and wider applications. Here, through quantitative and mechanistic analyses of the behavior of multi-phase phenomena that involve gas-liquid-solid interfaces, we present a design framework for microfluidic devices containing porous architectures (referred to as poroFluidics) for deterministic control of multi-phase fluid transport processes. We show that the essential properties of the fluids and solid, including viscosity, interfacial tension, wettability, as well as solid manufacture resolution, can be incorporated into the design to achieve consistent flow in porous media, where the desired spatial and temporal fluid invasion sequence can be realized. Experiments and numerical simulations reveal that different preferential flow pathways can be controlled by solid geometry, flow conditions, or fluid/solid properties. Our design framework enables precise, multifunctional, and dynamic control of multi-phase transport within engineered porous media.

Classification of nonnegative traveling wave solutions for certain 1D degenerate parabolic equation and porous medium type equation

Classification of nonnegative traveling wave solutions for certain 1D degenerate parabolic equation and porous medium type equation