Filtration In Porous Media Research Articles

Numerical Study of Suspension Filtration Model in Porous Medium with Modified Deposition Kinetics

Filtration is one of the most used technologies in chemical engineering. Development of computer technology and computational mathematics made it possible to explore such processes by mathematical modeling and computational methods. The article deals with the study of suspension filtration in a porous medium with modified deposition kinetics. It is suggested that deposition is formed in two types, reversible and irreversible. The model of suspension filtration in porous media consists of the mass balance equation and kinetic equations for each type of deposition. The model includes dynamic factors and multi-stage deposition kinetics. By using the symmetricity of porous media, the higher dimensional cases are reduced to the one-dimensional case. To solve the problem, a stable, effective and simple numerical algorithm is proposed based on the finite difference method. Sufficient conditions for stability of schemes are found. Based on numerical results, influences of dynamic factors on solid particle transport and deposition characteristics are analyzed. It is shown that the dynamic factors mainly affect the profiles of changes in the concentration of deposition of the active zone.

Numerical model of mass transfer processes using fractional derivatives

The article describes the scheme of construction and application of finite element method using Grunwald-Letnikov algorithm. Obtained results make it possible to estimate influence of fractional derivative order in terms of time and space on process of gas filtration in porous medium. Numerical ecperification and analysis performed

Groundwater Chemistry Has a Greater Influence on the Mobility of Nanoparticles Used for Remediation than the Chemical Heterogeneity of Aquifer Media

The application of nanoscale zerovalent iron (nano-ZVI) particles for groundwater remediation has spurred research into the influence of the collector heterogeneity on the nano-ZVI mobility. The chemical heterogeneity of surfaces within aquifer media affects their surface charge distribution and their affinity for nano-ZVI. The groundwater chemistry affects the properties of both aquifer surfaces and the nano-ZVI particles. Commercial poly(acrylic acid)-coated nano-ZVI (PAA-nano-ZVI) particles were tested in column experiments using two solution chemistries and silica collectors with different degrees of chemical heterogeneity, achieved by ferrihydrite coating. A porous media filtration model was used to determine the attachment efficiency of PAA-nano-ZVI particles, and the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory was used to describe the interactions between PAA-nano-ZVI particles and the aquifer "collectors". The mobility of PAA-nano-ZVI particles suspended in ultrapure water depended on the extent of ferrihydrite coating on the collector surfaces. The mobility of PAA-nano-ZVI particles under environmentally relevant conditions was independent of the collector chemical heterogeneity. The size of PAA-nano-ZVI aggregates doubled, inducing gravitational sedimentation and possibly straining as mechanisms of particle deposition. There was no repulsive energy barrier between particles and collectors, and the DLVO theory was unable to explain the observed particle attachment. Our results suggest that the groundwater chemistry has a greater influence on the mobility of PAA-nano-ZVI particles than the collector chemical heterogeneity. A better understanding of polymer adsorption to nanoparticles and its conformation under natural groundwater conditions is needed to further elucidate nanoparticle-collector interactions.

Mathematical model and numerical algorithms to analyze gas filtration process in a porous medium

The paper deals with the problem of gas filtration process in a porous medium using a mathematical model of an object; the model is described by a nonlinear partial differential equation and the corresponding boundary and internal conditions. The paper presents the main stages in construction of mathematical model of the process of gas filtration in porous media, taking into account the changes in hydrodynamic parameters of the object of study. To solve the above problem, the following numerical methods have been used: local-one-dimensional schemes and longitudinal-transverse direction schemes. To solve the problem of nonlinear gas filtration in a porous medium, several methods of constructing an iterative process have been checked. To study the responses of the principal parameters of the process, a series of computational experiments on a computer, their analyses and conclusions are given in the paper.

Flow over natural or engineered surfaces: an adjoint homogenization perspective

Natural and engineered surfaces are never smooth, but irregular, rough at different scales, compliant, possibly porous, liquid impregnated or superhydrophobic. The correct numerical modelling of fluid flowing through and around them is important but poses problems. For media characterized by a periodic or quasi-periodic microstructure of characteristic dimensions smaller than the relevant scales of the flow, multiscale homogenization can be used to study the effect of the surface, avoiding the numerical resolution of small details. Here, we revisit the homogenization strategy using adjoint variables to model the interaction between a fluid in motion and regularly micro-textured, permeable or impermeable walls. The approach described allows for the easy derivation of auxiliary/adjoint systems of equations which, after averaging, yield macroscopic tensorial properties, such as permeability, elasticity, slip, transpiration, etc. When the fluid in the neighbourhood of the microstructure is in the Stokes regime, classical results are recovered. Adjoint homogenization, however, permits simple extension of the analysis to the case in which the flow displays nonlinear effects. Then, the properties extracted from the auxiliary systems take the name of effective properties and do not depend only on the geometrical details of the medium, but also on the microscopic characteristics of the fluid motion. Examples are shown to demonstrate the usefulness of adjoint homogenization to extract effective tensor properties without the need forad hocparameters. In particular, notable results reported herein include:(i)an original formulation to describe filtration in porous media in the presence of inertial effects;(ii)the microscopic and macroscopic equations needed to characterize flows through poroelastic media;(iii)an extended Navier’s condition to be employed at the boundary between a fluid and an impermeable rough wall, with roughness elements which can be either rigid or linearly elastic;(iv)the microscopic problems needed to define the relevant parameters for a Saffman-like condition at the interface between a fluid and a porous substrate; and(v)the macroscopic equations which hold at the dividing surface between a free-fluid region and a fluid-saturated poroelastic domain.

MATHEMATICAL AND COMPUTER SIMULATION OF THE PROCESSES OF TWO-PHASE JOINT GAS FILTRATION AND WATER IN A POROUS ENVIRONMENT

A mathematical model, methods and algorithms for the numerical solution of problems of joint gas-water filtration in porous media are considered. The mathematical model of the process of non-stationary joint gas-water filtration in a porous medium is described by a system of nonlinear differential equations of parabolic type. In the numerical solution of the boundary value problem of gas displacement by water in a porous medium, the differential sweeping method is used for systems of differential-difference equations. The system of differential-difference equations with respect to the gas pressure function is nonlinear, therefore, an iterative method is used for it, based on the method of quasilinearization of nonlinear terms. Computational algorithms and software have been developed for conducting computational experiments to study unsteady processes of gas filtration in porous media. The results of the developed software, as well as the results of computational experiments in a graphical form in visual form are given.

Étude de la performance du milieu filtrant constitué d’une couche de chènevotte sur une couche de grignons d'olives dans le traitement des eaux usées domestiques : du pilote à l’échelle industrielle

Deux matériaux, sous-produits agro-industriels, ont été étudiés en biofiltration à l'échelle pilote : la chènevotte en tant que « couche active », sur des grignons d'olives en tant que « couche de support ». L'objectif était d'étudier la capacité de ces deux matériaux travaillant ensemble comme un seul milieu filtrant poreux. L'impact de la hauteur de la couche active sur la performance du biofiltre a été étudié expérimentalement grâce à deux biofiltres, un premier présentant une répartition des matériaux en deux hauteurs égales, l’autre avec 80 % de couche active sur 20 % de hauteur de couche support. Les deux pilotes ont été alimentés à raison de 75 L·j‑1·EH‑1 (EH : équivalent-habitant) avec des eaux usées domestiques synthétiques. Les résultats ont montré une réduction de la demande biochimique en oxygène en cinq jours (DBO5) et des matières en suspension (MES) de plus de 90 % après dix semaines de fonctionnement. Cette performance s'est maintenue après plus de 30 semaines de fonctionnement continu. Par ailleurs, six prototypes de biofiltres ont été installés pour traiter les eaux usées domestiques de résidences unifamiliales dans des conditions réelles. Les objectifs de cette étude sont de caractériser l'efficacité du traitement de ces prototypes sur plusieurs années dans des conditions réelles, de déterminer l'entretien requis par une telle technologie et d'étudier l'influence de paramètres tels que la hauteur du biofiltre, l'aération et le nombre d'habitants. L'efficacité de traitement à long terme de l'un des biofiltres, qui fonctionne depuis près de quatre ans, est remarquable. Les pourcentages moyens de réduction de la demande chimique en oxygène (DCO), de la DBO5 et de MES sont respectivement de plus de 83 %, 97 % et 96 %, laissant espérer des résultats prometteurs pour les cinq autres.

Effect of Ornamental Plants, Seasonality, and Filter Media Material in Fill-and-Drain Constructed Wetlands Treating Rural Community Wastewater

The effects of Canna indica (P1), Pontederia sagittata (P2), and Spathiphyllum wallisii (P3) growing in different filter media materials (12 using porous river rock and 12 using tepezyl) on the seasonal removal of pollutants of wastewater using fill-and-drain constructed wetlands (FD-CWs) were investigated during 12 months. Three units of every media were planted with one plant of P1, P2, and P3, and three were kept unplanted. C. indica was the plant with higher growth than the other species, in both filter media. The species with more flower production were: C. indica > P. sagittate > S. wallisii. Reflecting similarly in the biomass of the plants, C. indica and P. sagittata showed more quantity of aerial and below ground biomass productivity than S. wallisii. With respect to the removal efficiency, both porous media were efficient in terms of pollutant removal performance (p > 0.05). However, removal efficiency showed a dependence on ornamental plants. The higher removal of chemical oxygen demand (COD), biochemical oxygen demand (BOD5), total kjeldahl nitrogen (TKN), nitrates (NO3−-N), ammonium (NH4+-N), and phosphates (PO4−3-P) oscillated between 81% to 83%, 80% to 84%, 61% to 69%, 61% to 68%, 65% to 71%, 62% to 68%, and 66% to 69%, respectively, in P1 and P2, removals 15% to 30% higher than P3. The removal in planted microcosms was significantly higher than the unplanted control units (p = 0.023). Nitrogen and phosphorous compounds were highly removed (60%–80%) because in typical CWs, such pollutant removals are usually smaller, indicating the importance of FD-CWs on wastewater treatments using porous river rock and tepezyl as porous filter media. (BOD5), chemical oxygen demand (COD), (NO3−-N), (NH4+-N), (TKN), and (PO4−3-P).

Global asymptotics of filtration in porous media

Filtration problems are actual for the design of underground structures and foundations, strengthening of loose soil and construction of watertight walls in the porous rock. A liquid grout pumped under pressure penetrates deep into the porous rock. Solid particles of the suspension retained in the pores, strengthen the loose soil and create watertight partitions. The aim of the study is to construct an explicit analytical solution of the filtration problem. A one-dimensional model of deep bed filtration of a monodisperse suspension in a homogeneous porous medium with size-exclusion mechanism of particles retention is considered. Solid particles are freely transferred by the carrier fluid through large pores and get stuck in the throats of small pores. The mathematical model of deep bed filtration includes the mass balance equation for suspended and retained particles and the kinetic equation for the deposit growth. The model describes the movement of concentrations front of suspended and retained particles in an empty porous medium. Behind the concentrations front, solid particles are transported by a carrier fluid, accompanied by the formation of a deposit. The complex model has no explicit exact solution. To construct the asymptotic solution in explicit form, methods of nonlinear asymptotic analysis are used. The new coordinate transformation allows to obtain a parameter that is small at all points of the porous sample at any time. In this paper, a global asymptotic solution of the filtration problem is constructed using a new small parameter. Numerical calculations are performed for a nonlinear filtration coefficient found experimentally. Calculations confirm the closeness of the asymptotics to the solution in the entire filtration domain. For a nonlinear filtration coefficient, the asymptotics is closer to the numerical solution than the exact solution of the problem with a linear coefficient. The analytical solution obtained in the paper can be used to analyze solutions of problems of underground fluid mechanics and fine-tune laboratory experiments.

Low cost drinking water treatment using nonwoven engineered and woven cloth fabrics.

The study investigated two engineered fabrics and five cloth fabrics for low cost drinking water treatment. An optimized fabric filtration method has been developed and tested. Numerical models for predicting particulate removal efficiency have been developed for each fabric as support tools for selecting optimal process configuration. Both engineered fabrics showed better performance and achieved the most effective particulate removal for the highest number of layers used. Sequential filtration was done on eight layers for representative fabrics of each type and recorded higher contaminant removal than one filtration run. Geotextile 1 was better than geotextile 2 in particulate removal and recorded Escherichia coli removals of up to 1.4 log removal value (LRV) for eight-layer normal filtration and 3.0 LRV for four-pot sequential filtration. Brushed cotton was best among the cloth fabrics in particulate removal but performed below expectation in bacterial removal. It recorded E. coli removals of only 0.04 LRV and 0.2 LRV for eight-layer normal filtration and four-pot sequential filtration, respectively. Effluent turbidity decreased exponentially with number of fabric layers, in line with porous media filtration theory. The optimized filtration method produced very clear drinking water of relatively safe quality using geotextile 1. Appropriate disinfection is still recommended to ensure continued water safety.

Development of model equation for estimating the turbidity reduction in sediment-laden stormwater by a synthetic fiber fence

In this paper, a model equation for predicting the reduction efficiency of turbidity matters in a synthetic fiber fence was presented. This model is developed on the assumption that the collection efficiency of a single collector is contributed by three individual transport mechanisms including diffusion, interception and sedimentation. In consideration of the complex internal structure of fiber media, the simulation was also conducted in Happel’s sphere-in-cell porous media model. In the process of modeling work, the dimensionless parameters governing particle deposition were calculated based on the operational and theoretical parameters, and the equation was subsequently obtained by multiple linear regression. The predicted removal efficacy is in a good agreement with the experimental data over a broad range of values using developed equations, indicating that the resulting equation was applicable to the high-speed filtration condition and highly porous filter media. Hence, the developed model may serve as an alternative for the development of turbid runoff treatment technologies.

Network model evaluation of the effects of pore and particle size distributions on dynamic straining-dominant deep bed filtration in porous media

A straining-dominant filtration model based on a 2D square network is proposed. In this model, the colloid particle can be captured in a node only. The effects of network parameters (node size distribution parameters μn and σn and pore throat size distribution parameters μn and σb), particle concentration of influent (C0), and particle size distribution parameters (μr and σr) on straining-dominant deep bed filtration simulation are investigated. Four parameters (C0, μn, μb, and μr) significantly affect the simulated pressure drop and the normalized particle concentrations of effluent (Ce/C0). The increase in parameters μn and μb decreases pressure drop and increases Ce/C0, whereas the increase in parameters μr and C0 increases pressure drop and decreases Ce/C0. With the experimental condition and a 5% variation in parameters, parameters σn, σb, and σr are lowly sensitive to Ce/C0 and pressure drop. When the variation in σr is sufficiently large, the model simulation is significantly affected. The simulated normalized effluent concentrations and pressure drop are consistent with the experimental data under appropriate simulated conditions.

Microgravity Investigation of Capillary Driven Imbibition

The goal of the present paper is to investigate the capillary driven filtration in porous media under microgravity conditions. New mathematical model that allows taking into account the blurring of the front due to the instability of the displacement that is developing at the front is proposed. The constants in the mathematical model were selected on the basis of the experimental data on imbibition into unsaturated porous media under microgravity conditions. The flow under the action of a combination of capillary forces and a constant pressure drop or a constant flux is considered. The effect of capillary forces and the type of wettability of the medium on the displacement process is studied. A criterion in which case the capillary effects are insignificant and can be neglected is established.

Numerical solving of highly viscous fluids filtration in porous media for nonlinear filtration laws with power growth

We study the steady-state filtration process of an incompressible high-viscosity fluid follows the nonlinear filtration law. The generalized statement of this problem is formulated in the form of an operator equation with a monotone operator in a Banach space. To solve this operator equation, we propose an iteration method that does not require the inversion of the original operator. Each step of the iterative process reduces to solving the boundary value problem for the Laplace equation. In the Matlab environment, a software complex was developed, with the help of which numerical calculations were performed for model filtration problems. The analysis of numerical results is carried out.

REVERSIBLE VENTILATION SYSTEM FOR ADMINISTRATIVE BUILDINGS

Objectives To consider the possibility of applying the principle of reversing air flows for a centralised ventilation system; to develop a specific scheme for air exchange reversible ventilation, which will take into account the peculiarities of the microclimate of administrative buildings; to select the type of filling of the air-permeable element and justify this choice; to determine the conditions for changing the direction of air movement in the ventilation system and the area of its application; to form a list of equipment necessary for the operation of such a system; to consider the influence of supply and exhaust devices on the heat and humidity regime of claddings. Methods To achieve this goal, the published thematic material was reviewed and a patent search carried out using Russian and European databases. Data on mathematical modelling of filtration in porous media and experimental results were used. A method for ventilating rooms in administrative building using the reversal of movement of supply and exhaust air streams along the same channels was applied. Results Schemas for reversible ventilation systems are presented and their modes of operation considered. It is established that the idea of reversing ventilation flows has not yet been applied in the development of centralised ventilation systems. Based on these published materials, it was concluded that the proposed design of supply and exhaust devices can be used in practice. An original air exchange scheme for the ventilation of administrative buildings and design of supply and exhaust devices for this system are proposed. The conditions for changing the operating modes of the system and the scope of its application are determined. Conclusion The use of the proposed ventilation system allows normative air exchange to be provided without using a supply unit during the cold season. This application of airflow reversal allows the potential of natural forces to be used to the fullest extent to ensure the air exchange of the rooms.

Mathematical Modeling of Multiphase Filtration in Porous Media with a Chemically Active Skeleton

The authors propose a mathematical model of two-phase filtration that occurs under the conditions of dissolution of a porous medium. The model can be used for joint description of complex chemical-hydrogeomechanical processes that are of frequent occurrence in the oil-and-gas producing and nature conservation practice. As an example, consideration is given to the acidizing of the bottom zone of the injection well of an oil reservoir. Enclosing rocks are represented by carbonates. The phases of the process are an aqueous solution of hydrochloric acid and oil. A software product for computational experiments is developed. For the numerical experiments, use is made of the data on the wells of an actual oil field. Good agreement is obtained between the field data and the calculated data. Numerical experiments with different configurations of the permeability of an oil stratum are conducted.

Study of oil filtration in porous media under the steam-assisted gravity drainage process

This work is devoted to the development and computer realization of a three-dimensional mathematical model describing the processes of flow, filtration and phase transition during the hot steam injection into a rock mass. The specific feature of the developed model is the possibility to take into account the dependence of thermophysical properties of each component in a multicomponent flow on time or spatial coordinates. It is assumed that considered media is a multicomponent system consisting of steam, oil and water filling the pore space. The developed model includes mass balance equation for components characterizing water and steam saturations, the condition of a fully saturated media to define the oil component of the flow, Darcy’s law for the filtration flow of the multicomponent stream and the law of conservation of energy taking into account the convective heat transfer and the source describing the «steam-water» phase transition. Computer realization of the proposed model is based on the transformation of the system of equations in such a way that the values of steam and water saturations as well as pressure act as unknown variables; representation of the resulting system of equations in a weak form and the introduction of additional stabilization terms. The adequacy of the proposed model and the efficiency of the developed approach to its implementation are illustrated by a three-dimensional numerical simulation of oil production process through the steam-assisted gravity drainage method in the oil sand.

To the theory of non-local non-isothermal filtration in porous medium

A new approach to the theory of non-local and non-isothermal filtration based on the mathematical apparatus of fractional order derivatives is developing. A solution of the Cauchy problem for the system of equations of non-local non-isothermal filtration in fractional calculus is obtained. Some applications of the solutions obtained to the problems of underground hydrodynamics (fracturing and explosion) are considered. A computational experiment was carried out to analyze the solutions obtained. Graphs of pressure and temperature dependences are plotted against time.

Optimization of Thermal Insulation Performance for the Porous Materials

ABSTRACTPorous materials are widely used in porous media filtration, membrane separation, catalyst substrates, solid fuel cells, insulation, and other fields. When the porous material used in the field of insulation, heat transfer characteristics become its most important performance parameters. The heat transfer characteristics of porous material is a complex issue affected not only by solid elements and porosity, it is also affected by composite structures. Therefore, how to optimize the heat transfer properties of porous materials is a problem to be urgently solved. In this paper, the numerical method is used to study the effects of pore size, pore shape, pore connectivity, porosity and so on. It is found that pore shape, pore connectivity and gas conductivity have great impacts on the heat transfer of porous materials. The effect of pore arrangement is very little. The design optimization of porosity is affected by porous material mechanical property.

Study of formation damage caused by retention of bi-dispersed particles using combined pore-scale simulations and particle flooding experiments

The infiltration of solid particles (fines) into a reservoir during drilling or water reinjection is a long-standing problem in the petroleum industry because of the associated production decline or injectivity loss. Solid particle infiltration is also an active area of research in other fields such as waste water treatment and fines migration in clay-rich reservoirs.In this work, we perform experiments to study particle infiltration into sintered glass bead core plugs and measure the changes in porosity and permeability using computed tomography (CT) scanning and pressure transducers, respectively. Suspensions of prescribed bimodal particle sizes, concentrations, and flowrates are flooded through the core plugs. Permeability changes are measured continuously over time, and the porosity change is measured after flowing a fixed mass of invaded particles.A dual pore-scale numerical model approach (a combination of a direct pore-scale discrete element method (DEM) and a pore-scale network model) is used to predict permeability reduction by particle filtration in porous media. Large particle deposition is modeled using the DEM in a disordered sphere pack geometry; the result is a prediction of deposition as a function of large particle concentration. Small particle deposition is modeled using the network model; the result is a prediction of deposition as a function of small particle concentration. Crucially, the geometry of the network model depends on the amount of large particles deposited. In this way, the deposition of large and small sized particles is coupled together.The permeability and porosity reduction of the network due to the deposition of small and large particles are then calculated from the functions above. We compare the experimental results with simulation predictions and find that the dual pore-scale model is capable of predicting the permeability of the invaded core in the regions away from the injection face. Permeability prediction in the region adjacent to the injection face is improved by incorporating the influence of the external filter cake.