Liquids In Porous Media Research Articles

Effect of a uniform magnetic field on the nonlinear instability of double cylindrical interfaces concerning three magnetic liquids

The present manuscript relates to the movement of three immersed viscous magnetic liquids in porous media that are positioned between three concentric cylindrical interfaces. Every cylindrical layer has an axial extension that extends in both vertical directions to infinity. Moreover, the pressure gradients are the driving force behind the uniform motion of all fluids in a similar upward motion at varying velocities. Permanent magnetic fields are tangentially oriented exert stress on the system. The computations are rendered simpler by applying the viscous potential theory. The Maxwell equations are utilized for the magnetic field, while the Brinkman-Darcy equations define the fluid mobility. Moreover, the rise of the disturbance and the subsequent extraction of fuel from the tiny cracks of the reservoir stone can be managed through the implementation of engineering techniques such as electromagnetic field impacts and oil extraction engineering. Typically, the nonlinear strategy involves incorporating the applicable nonlinear boundary conditions and analyzing the linearized equations of motion. This research offers a framework for verifying theoretical models and simulations based on experimental observations. The inclusion of a homogeneous magnetic field introduces complexity to the system, rendering it a suitable candidate for validating and improving models in the field Magneto hydrodynamics. The originality of the problem lies in the dual nonlinear stability of cylindrical interfaces when subjected to uniform magnetic field. Accordingly, two nonlinear characteristic differential equations controlling the surface displacements are produced. The nonlinear stability prerequisite is met by applying the matrix concept and the multiple scale technique in conjunction with a theoretical analysis of stability. Additionally, the Routh-Hrutwitz criterion is encompassed to judge the stability cofiguration. A detailed examination of the associated nonlinear stability requirements is showed. Meanwhile, the estimated limited solutions of perturbed surfaces are achieved. For the cylindrical middle layer, it is found that the outer cylindrical interface has a more stabilizing effect than the inner one. The approximate solutions for displacements at the interface are calculated. The influence of Weber numeral of the problem on the stability profile is investigated.

In-situ emulsification in low-tension surfactant/polymer systems: Impacts on enhanced oil recovery

The flow of two immiscible liquids in porous media can lead to fluid mixing, resulting in emulsions—where one phase is dispersed as droplets in the other. In reservoir rocks, natural surfactants and polar molecules, like asphaltenes, can promote oil–water emulsion formation. During chemically enhanced oil recovery processes (CEOR) such as surfactant, alkali, or surfactant-alkali flooding, in-situ emulsification is often seen as key to enhancing frontal stability and facilitating the piston-like displacement of oil by water. However, this work reports a minimal effect of in-situ emulsification on oil production during surfactant-polymer (SP) flooding. Experimental studies show this by injecting prepared emulsions into a multi pressure-tap core holder and examining emulsion formation in one reservoir core before moving it into a second core for oil displacement. This helps us understand the specific role of emulsions in oil mobilization. Factors like surfactant concentration, interfacial tension, and the timing of introducing the surfactant-polymer solution do influence the intensity of in-situ emulsification. Yet, the incremental oil recoveries show no significant differences. Through similar experiments, it is observed that ultra-low interfacial tension (IFT) in our surfactant-polymer system is the primary mechanism for oil mobilization. The slight increase in pressures suggests that in-situ emulsification has a limited role in increasing flow resistance during the ultra-low IFT SP flood process, potentially not improving the swept volume. This research can guide the development of systematic approaches to analyze the effects of in-situ emulsification on oil mobilization and evaluate chemical flooding processes.

FLUID FLOW CONTROL IN POROUS MEDIA WITH CONSIDERATION OF ELECTROKINETIC EFFECTS

The paper presents results of the research on the influence of electrokinetic characteristics of fluids on its flow in porous media. Experimental studies have shown the effect of fluid slippage in the channels of porous media due to the electrically charged boundary "liquid-porous medium". It is shown that the change of flow velocity profile and pressure gradient is caused by the display of electrokinetic effects in the filtration of polar liquids.The investigation has shown that the process of the electrolyte solutions filtration in a porous medium is accompanied by the change in the liquid flow rate and the electro-potential of the flow. The periodic nature of changes in flow characteristics is explained by continuous charge formation and charge interaction in the diffuse layer. Periodic charge accumulation and subsequent charge transfer across the channel cross section depending on the charge sign acquired, as well as compression of the diffuse layer with increasing NaCl electrolyte concentration in aqueous solution may be the cause of fluid flow variations. The observed effects may serve as a tool for controlling fluid flow in water-oil-saturated formations and, in particular, injectivity of injection wells by controlling electrical conductivity of water injected into the formation.

Dynamics of Pollution in the Hyporheic Zone during Industrial Processing Brine Discharge

The industrial production of chemicals, including the manufacture of mineral fertilizers, is often associated with the need for the disposal of highly mineralized brines through their discharge into surface water bodies or an underground water-bearing layer. When dealing with surface water bodies, the problem of the hyporheic zone effect could substantially influence the process and, thus, must be examined. We consider a two-layer system (liquid–porous medium) for a detailed assessment of the importance of considering the hyporheic zone during the modeling of brine discharge. A three-dimensional numerical simulation of brine transport is performed for parameters close to the characteristics of the media and flows typical for natural water bodies. The dynamics of a saturated brine in a two-layer system are studied for the period of brine discharging and after the cessation of the disposal, and the accumulation of salts in the bottom porous layer is assessed. Calculations show that a significant amount of impurities is observed not only near the water body bottom but also throughout the entire thickness of the porous layer. Moreover, the obtained data reveal that the effect of vertical stratification dramatically influences the brine discharge process and leads to propagation of the brine into the porous medium with a velocity that is three orders of magnitude higher than the filtration rate in the horizontal direction. As a result, the heterogeneity in the depth distribution of the impurity concentration is significant. In particular, the maximum concentration of salt in the hyporheic zone exceeds those near the river surface by hundreds of times. Impurities accumulated in the water-bearing layer of the river bottom are nonhazardous at low- and medium-flow rates. However, with an increase in the river flow intensity—for example, during the flood period or caused by operating regime of a hydroelectric power plant—the accumulated contamination may become an intensive source of pollution, which significantly limits the water use regime.

Phase separation and aging dynamics of binary liquids in porous media

We employ the state-of-the-art molecular dynamics simulations to study the kinetics of phase separation and aging phenomena of segregating binary fluid mixtures imbibed in porous materials. Different random porous structures are considered to understand the effect of pore morphology on coarsening dynamics. We find the effect of complex geometrical confinement resulting in the dramatic slowing down in the phase separation dynamics. The domain growth follows the power law with an exponent dependent on the porous host structure. After the transient period, a crossover to a slower domain growth is observed when the domain size becomes comparable to the pore size. Due to the geometric confinement, the correlation function and structure factor modify to a non-Porod behavior and violate the superuniversality hypothesis. The role of porous host structure on the nonequilibrium aging dynamics is studied qualitatively by computing the two-time order-parameter autocorrelation function. This quantity exhibits scaling laws with respect to the ratio of the domain length at the observation time and the age of the system. We find the scaling laws hold well for such confined segregating fluid mixtures.

Removal of pollution accumulated in the process of wastewater discharge from the bottom layer of river systems

Three-dimensional numerical simulation has been performed to investigate the transport of impurities in a two-layer system “liquid-porous medium” for different hydrodynamic regimes of river systems. The dynamics of waste water containing heavy impurities in areas of industrial activity is modeled. The parameters of the numerical experiment correspond to the data of full-scale flow experiments in natural water bodies, part of the reservoir where the Solikamsk-Berezniki industrial hub is located. Due to the influx of brines, pollution accumulates in the hyporheic zone of the river, the fluid flow carries this pollution away through the porous medium, thus the problem is solved of washing out the brine distributed in the porous medium. The computational domain consists of a fluid mass (river) propagating over a porous medium (river bottom, hyporheic zone). It is shown that the concentration of polluting ingredients in the soil of the river bottom near the discharge points increases in the presence of "heavy" impurities. Such problems arise acutely when excess highly mineralized brines are discharged into water bodies located in the industrial areas with “heavy” wastewater, for which, due to significant intra-annual fluctuations in the water level and ice cover, the option with near-bottom wastewater disposal is considered preferable.

Ingularly perturbed equations in critical cases

Singularly perturbed partial differential equations with small parameters with higher derivatives deserve special attention, which often arise in a variety of applied problems and are used in describing mathematical models of diffusion processes, absorption taking into account small diffusion, filtration of liquids in porous media, chemical kinetics, chromatography, heat and mass transfer, hydrodynamics and many other fields. It is necessary to consider the creation of an asymptotic classification of solutions of singularly perturbed equations using a well-known approach to solving the boundary value problem. In this case, the singular problem is understood as the problem of constructing the asymptotics of the solution of the Cauchy problem for a system of ordinary differential equations with a small parameter with a large derivative. The asymptotics of the solution in all cases is based on the last time interval or the construction of a boundary value problem for a system with a weak clot in an asymptotically large time interval. Purpose - to construct and substantiate the asymptotics of solving a singular initial problem for a system of two nonlinear ordinary differential equations with a small parameter; To date, a number of methods have been developed for constructing asymptotic expansions of solutions to various problems. This is the method of boundary functions developed in the works of A.B. Vasilyeva, M.I. Vishik, L.A. Lusternik, V.F. Butuzov; the regularization method of S. A. Lomov, methods of averaging, VKB, splicing of asymptotic decompositions of A.M. Ilyin and others. All the above methods allow us to obtain asymptotic expansions of solutions for wide classes of equations. At the same time, such singularly perturbed problems often arise, to which ready-made methods are not applicable or do not allow to obtain an effective result. Therefore, the development of methods for solving equations remains a very urgent problem. As a result of the study, an algorithm for constructing an asymptotic classification of the initial solution of the problem with a singular perturbation is given, and approaches to estimating the residual term are also shown.

Modeling of filtration processes in periodic porous media

Modeling of dynamic processes of diffusion and filtration of liquids in porous media are discussed. The media are formed by a large number of blocks with low permeability, and separated by a connected system of faults with high permeability. The modeling is based on solving initial boundary value problems for parabolic equations of diffusion and filtration in porous media. The structure of the media leads to the dependence of the equations on a small parameter. Assertions on the solvability and regularity of such problems and the corresponding homogenized convolution problems are considered. The statements are actual for the numerical solution of this problem with guaranteed accuracy that is necessary to model the considered processes.

ОБ ОСНОВНЫХ МАТЕМАТИЧЕСКИХ МОДЕЛЯХ И ПРИБЛИЖЕННОМ МЕТОДЕ ТЕОРИИ ФИЛЬТРАЦИИ

The article defines the basic concepts of filtration theory and provides an overview of the existing mathematical models of inhomogeneous liquids in porous media. The paper considers the Stefan problem. The number of scientific papers devoted to the study of porous structures has recently increased. This is primarily due to the fact that the prob-lems of oil and uranium production have been identified, and the solution of environmental problems is overdue. Therefore, a new device is needed to develop models of liquid filtration. With the advent and development of computer technology, it has become easier to solve problems that require numerical methods for their solution. Understanding the movement of fluids and the mechanism of dissolution of rocks under the action of acids in heterogeneous porous media is of great importance for the extraction and production of oil and the effective management of these processes. The article examines the mathematical model of the theory of isothermal filtration. Possible variants of the solva-bility of the model are shown. The research scheme consists of the output of a mathematical model, the formulation of the problem, one variant of the solution of the problem, the algorithm of the numerical method of solving the problem.

Development of adsorption ratio equation and state equation of liquid and their geological significance

There have been many theories to describe adsorbed or free gas. However, quantitative description of the occurrence characteristics of liquids in porous media has always been a great challenge due to a lack of basic theory. Through years of research, two theoretical equations, i.e., adsorption ratio equation and state equation of liquid, have been proposed to describe the characteristics of liquids in porous media, and revealed the mechanism of liquid occurrence. Further, a quantitative evaluation technology for the microscopic distribution of liquids was established by combining nuclear magnetic resonance theory. This research will be of great significance for studying the microscopic distribution of liquids in tight reservoirs, such as shale, coal, and tight sandstone. Cited as: Li, J. Development of adsorption ratio equation and state equation of liquid and their geological significance. Capillarity, 2021, 4(4): 63-65, doi: 10.46690/capi.2021.04.01

Liquid Wicking in a Paper Strip: An Experimental and Numerical Study.

In this decade, paper-based microfluidics has gained more interest in the research due to the vast applications in medical diagnosis, environmental monitoring, food safety analysis, etc. In this work, we presented a set of experiments to understand the physics of the capillary flow phenomenon through paper strips. Here, using the wicking phenomenon of the liquid in porous media, experimentally, we find out the capillary height of the liquid in filter paper at different time intervals. It was found that the Lucas–Washburn (L–W) model, as well as the evaporation model, fails to predict the capillary rise accurately. However, the detailed numerical solution shows a better similarity with the experimental results. We have also shown the different regimes of the wicking phenomenon using scaling analysis of the modified L–W model. The capillary rise method was applied to detect the added water content in milk. We used milk as a liquid food and found the added water content from the change in the capillary height at different concentrations of milk. Finally, results obtained from the paper-based device were verified with the commercially available lactometer data.

СONCEPT AND CALCULATION OF THE LIMIT TRANSVERSE SIZE OF CAPILLARIES

Porous medium are products of processing in food, agricultural, chemical and many other industries. Calculations of processes with wet porous medium are based on capillary properties of the liquid in a pore space. The capillary properties of liquids in porous media are established in pore models in the form of thin tubes of circular or slit transverse sections. The intensity of the processes occurring in it depends on the nature of the filling of the pore space with liquid. Filling with liquid and the formation of a capillary layer is possible only in small pores. However, there is no analytical justification for the transverse pore size, more than which it cannot be filled with liquid by capillary forces. With this in mind, the concept of the limiting transverse size of a capillary for a liquid under conditions of complete wetting is introduced. The limiting size calculation is based on two conditions: the shape of the axial section of the meniscus surface has the appearance of a semicircle and its extremum point is located at the level of the free surface of the fluid supplying the capillary. A capillary column cannot form in larger pores. The absence of formulas for calculating capillaries of the limiting sizes can introduce a significant error into the analytical calculation of the moisture content in the capillary layer of a liquid in porous media and moisture transfer processes. The aim of the study was to obtain formulas for calculating the limiting (largest) sizes of capillaries of a circular, flat slit section and annular transverse sections with complete wetting of their walls. For the conditions above, it was identified that the limiting distance between the walls was independent from annular capillary diameter. The formulas for the limiting transverse sizes of the flat slit and annular capillaries turned out to be the same under the assumptions above. This indicates a weak dependence of the limiting size of a slit capillary on the curvature of its transverse section. Examples of calculations of capillaries of the limiting sizes are performed.

The Growth of Healthy and Cancerous Tissues

The structure of the tissues is formed in a self-similar manner, forming fractal structures in their transport networks. The structure exhibits allometric forming and so-called scaling behavior. This is a basic growth model fine-tuned by various connections of the cells (junctions and adherent connections), intended to direct material and energy transports between them. This secondary control of cell metabolism decreases primary metabolic transport through the free surfaces of the cells. The cellular network is formed by triggering the endogenous electric fields, which are dominantly governed by cell membrane potential. Proliferation exhibits a different electric pattern due to the low cell-membrane potential and resulting negativity relative to its environment. This potential change characterizes cells in normal proliferation and a cluster of cells (a tumor) in the case of cancerous development. This latter has certain similarities to the leakage transport of liquid in porous media, substituting the pressure with endogenous tumor potential. The average survival of a tumor depends on the kind of available metabolic transport and the fractal dimensions of the newly built angiogenic network.

Synergistic effects of surfactant mixtures on the displacement of nonaqueous phase liquids in porous media

Binary surfactant mixtures have often been used to enhance the recovery or cleanup of nonaqueous phase liquids (NAPLs) such as crude oil from subsurface formations. Through synergistic effects, these mixtures further promoted NAPL mobilization and solubilization by lowing NAPL/brine interfacial tension (IFT) and desorbing NAPL from mineral surfaces, thereby altering their wettability. While the impact of mixing synergy on IFT has been well documented, its effect on wettability alteration in rocks under different test conditions (i.e., mineralogy and pore topology) is still unclear. The objective of this study was to establish structure-function relationships in these systems and identify the test conditions under which binary mixtures outperform single surfactants. Four different nonionic surfactants (alkyl glucosides, linear/branched alcohol ethoxylates) were selected with a hydrophile-lipophile balance number of ˜13. We used IFT, contact angle (CA), and spontaneous imbibition tests with NAPL-aged cores to understand the mechanisms of interaction and examine the efficiency of surfactants and their mixtures in promoting NAPL displacement in three sedimentary rocks with different mineralogy and pore topology. Synergistic effects were investigated by calculating cross-sectional areas and interaction parameters of surfactant mixtures and relating them to IFT and CA. Alkylphenol ethoxylates with relatively short aliphatic tails could fill the gaps between the large sugar-based heads of alkyl glucosides and enhance their geometrical packing at NAPL/brine interfaces. The denser interfacial layer formed by these mixtures led to the largest decrease in IFT and promoted the highest NAPL mobilization in low permeability sandstone and carbonate samples. The ability of nonionic surfactants to restore the wettability of oil-wet mineral surfaces was a function of their molecular structure and rock topology. In homogeneous sandstones, alkyl glucosides with their strong hydrogen bonding ability with silanol groups of quartz, could restore the wettability to a greater extent and consequently exhibited the highest NAPL removal. However, they were ineffective in altering the wettability of carbonates due to their strong self-association tendency into large micelles which prevented them from penetrating rough and nanoporous regions. The synergistic mixing of alkyl glucosides with alkylphenol ethoxylates could overcome these limitations as they exhibited a complementary mechanism of action with respect to IFT reduction and wettability alteration, recovering the largest amounts of NAPL in carbonate-bearing rocks.

“Raincoat for explosives”: Surface chemistry approach to control wetting of nitrocellulose with nitroglycerin

HypothesisWicking and percolation of a liquid in porous media is, among other factors, strongly affected by wettability of the pores. Nitrocellulose (NC) fibrous matrix impregnated with nitroglycerin (NG) is a main component of propellant formulations. Over time, NG, being a wetting liquid, leaks out from the matrix causing fires and explosions resulting from the storage. Here, we propose a chemical functionalization approach aimed at preparation of lyophobic coatings of NC to control wetting and to inhibit leakage of NG. ExperimentalNC was functionalized by a two-step process using the reaction of 3-(triethoxysilyl-propyl) isocyanate followed by reactions with either alkyl-, fluoroalkyl-, or phenyl-silane producing NC surfaces ranging in lyophobicity. The wettability of the NC pellets was characterized using water, hexadecane, and NG as probe fluids. FindingsFTIR and chemical analysis supported the covalent attachment of organosilanes to NC via robust carbamate and siloxane bonds. SEM and DSC of the modified NC materials suggested that the bulk properties of NC were not affected by the reactions with silanes. The contact angles of the modified NC changed over a wide range demonstrating surfaces with “tunable” wetting. NC grafted with fluoroalkyl-groups showed the most NG-repelling properties (θAdv/θRec ∼ 90°/50°): NG beaded up and did not penetrate these surfaces.

ОСРЕДНЕННЫЕ МОДЕЛИ МНОГОФАЗНОЙ ДИФФУЗИИ ВПОРИСТЫХ СРЕДАХ

Non-stationary processes of mutual diffusion for multiphase flows of immiscible liquids in porous media with a periodic structure are considered. The mathematical model for such processes is initial-boundary diffusion problem for media formed by a large number of «blocks» having low permeability and separated by a connected system of «cracks» with high permeability. Taking into account such a structure of porous media during modeling leads to the dependence of the equations of the problem on two small parameters of the porous medium microscale and the block permeability. Homogenized initial-boundary value problems will be obtained. Solutions of the problems are approximated for the solutions of the initial-boundary value problem under consideration.

Tuning capillary penetration in porous media: Combining geometrical and evaporation effects

Capillary penetration of liquids in porous media is of great importance in many applications and the ability to tune such penetration processes is increasingly sought after. In general, liquid penetration can be retarded or restricted by the evaporation of volatile liquid at the surface of the porous media. Moreover, when capillary penetration occurs in a porous layer with non-uniform cross section, the penetration process can be accelerated or impeded by adjusting the section geometry. In this work, on the basis of Darcy’s Law and mass conservation, a theoretical model of capillary penetration combining evaporation effects in two-dimensional homogeneous porous media of varying cross-section is developed and further examined by numerical simulations. The effects of sample geometry and liquid evaporation on capillary penetration are quantitatively analyzed. Results show that the penetration velocity is sensitive to the geometry of the porous layer, and can be tuned by varying the evaporation rate for a given geometry. Under given evaporation conditions, penetration is restricted to a limited region with a predictable boundary. Furthermore, we find that the inhibition of liquid penetration by evaporation can be offset by varying the geometry of the porous layer. The theoretical model is further extended to model the capillary flow in three-dimensional porous media. The interplay of geometry and evaporation during the capillary flow process in 3D conditions is also investigated. The results obtained can be used to facilitate the design of porous structures to achieve tunable capillary penetration for practical applications in various fields.

Study on Wettability Variation for Removing Liquid Block in Condensate Gas Reservoir

AbstractCondensate liquid in porous media can prevent gas from exiting when the pressure is lower than the dew point pressure in the condensate gas reservoir. This can lead to liquid block and sharp decreases in gas yield. In this work, super‐amphiphobic materials were used to remove the liquid block and recover the product. The experiments indicated that this method can effectively remove the damage of liquid block and improve the productivity of the gas well.

A Heat Transfer Problem of Viscous Liquid in Porous Media

A Heat Transfer Problem of Viscous Liquid in Porous Media

Chemical potential of a two-component liquid in porous media: The case of unsaturated soil

The aim of this paper is to propose a method to determine the chemical potential of two miscible components of a solution in porous media, particularly in the case of an unsaturated soil. It is limited to the capillary state; the equilibrium of the liquid phase in the soil is determined by gas–liquid interfaces whose geometry obeys Laplace’s law. Deduction of the chemical potential of the two components from the chemical potential of pure water is based on the assumption that, for the same volume occupied by the fluid phase in the porous medium, the geometry of the fluid phase is independent of the composition of the solution.The expressions of the chemical potentials of the two components were established. They show the superposition of two effects: the effect of interfacial forces and the effect of the presence of the other component. A study of the water–alcohol solution in a clayey silty sand soil was then conducted to alcohol mole fractions between 0 and 0.15 and water content in the 5%–15% range. In this field, the chemical potential of the water was seen to be affected by the capillary effects below a water content of 10%. Above that, its variation as a function of the mole fraction of alcohol differed little from that of the potential of the water in a free solution. The chemical potential of the alcohol was little affected by the capillary effects.