Filtration Problems Research Articles

Applications of Spectral Analysis Methods of Differential Operators and Fourier Analysis to Solving Filtration Problems

Applications of Spectral Analysis Methods of Differential Operators and Fourier Analysis to Solving Filtration Problems

Neural operators for hydrodynamic modeling of underground gas storage facilities

Objectives. Much of the research in deep learning has focused on studying mappings between finite-dimensional spaces. While hydrodynamic processes of gas filtration in underground storage facilities can be described by partial differential equations (PDE), the requirement to study the mappings between functional spaces of infinite dimension distinguishes this problem from those solved using traditional mapping approaches. One of the most promising approaches involves the construction of neural operators, i.e., a generalization of neural networks to approximate mappings between functional spaces. The purpose of the work is to develop a neural operator to speed up calculations involved in hydrodynamic modeling of underground gas storages (UGS) to an acceptable degree of accuracy.Methods. In this work, a modified Fourier neural operator was built and trained for hydrodynamic modeling of gas filtration processes in underground gas storages.Results. The described method is shown to be capable of successful application to problems of three-dimensional gas filtration in a Cartesian coordinate system at objects with many wells. Despite the use of the fast Fourier transform algorithm in the architecture, the developed model is also effective for modeling objects having a nonuniform grid and complex geometry. As demonstrated not only on the test set, but also on artificially generated scenarios with significant changes made to the structure of the modeled object, the neural operator does not require a large training dataset size to achieve high accuracy of approximation of PDE solutions. A trained neural operator can simulate a given scenario in a fraction of a second, which is at least 106 times faster than a traditional numerical simulator.Conclusions. The constructed and trained neural operator demonstrated efficient hydrodynamic modeling of underground gas storages. The resulting algorithm reproduces adequate solutions even in the case of significant changes in the modeled object that had not occurred during the training process. The model can be recommended for use in planning and decision-making purposes regarding various aspects of UGS operation, such as optimal control of gas wells, pressure control, and management of gas reserves.

Application of Digital Technology for Oil and Gas Fields

The paper investigates the problem of isothermal filtration using an approximate method for solving the theory of partial differential equations. The mathematical model under consideration is nonlinear and does not lend itself to analytical methods of solution. The results obtained indicate the need for wide application in the development of oil and gas fields in the Republic of Kazakhstan. In particular, the results of the study make it possible to solve the problems of adapting mathematical models and evaluating changes in technological indicators, which are necessary attributes in the digital technology ""Information System for the Analysis of oil and Gas Field Development"" (ISAR). Many problems and mathematical problems of filtration theory arose while working on specific oil and gas fields in the western region of the Republic of Kazakhstan. The above approximate solution methods have found applications not only in filtration theory, but also in other problems (geophysics, ecology, etc.)"

Numerical Method for the Variable-Order Fractional Filtration Equation in Heterogeneous Media

This paper presents a study of the application of the finite element method for solving a fractional differential filtration problem in heterogeneous fractured porous media with variable orders of fractional derivatives. A numerical method for the initial-boundary value problem was constructed, and a theoretical study of the stability and convergence of the method was carried out using the method of a priori estimates. The results were confirmed through a comparative analysis of the empirical and theoretical orders of convergence based on computational experiments. Furthermore, we analyzed the effect of variable-order functions of fractional derivatives on the process of fluid flow in a heterogeneous medium, presenting new practical results in the field of modeling the fluid flow in complex media. This work is an important contribution to the numerical modeling of filtration in porous media with variable orders of fractional derivatives and may be useful for specialists in the field of hydrogeology, the oil and gas industry, and other related fields.

SURVEY OF THE DAM «GEGHARKUNIK 2»

In many hydraulic structures, including dam bodies, it is not possible to effectively solve the problem of filtration. The Gegharkunik 2 reservoir is located within the land boundaries of the settlement of the same name, 900 m southeast of the village cemetery, on the elevation of the northeastern slope of the Geghama ridge, at an altitude of about 2220 m. The water in the bowl doesn't stay for long. Studies have shown that most of the water loss happens at the lower part of the dam, where there are many washouts. This means the reservoir not only fails to serve its main purpose but also poses a significant threat to the Gegharkunik community if the dam were to fail. The paper presents the results of a survey of the «Gegharkunik 2» dam.

ANALYSIS OF CONTENT RECOMMENDATION METHODS IN INFORMATION SERVICES

The object of the research is the process of selecting a content recommendation method in information services. The study's relevance stems from the rapid development of informational and entertainment resources and the increasing volume of data they operate on, thus prompting the utilisation of recommendation systems to maintain user engagement. Considering the different types of content, it is necessary to address the problem of data filtration based on their characteristics and user preferences. To solve this task, we analysed content-based and collaborative filtering methods using various techniques (model-based, memory-based, and hybrid collaborative filtering techniques), knowledge-based filtering, and hybrid filtering methods. Considering each method's advantages and disadvantages, we chose a hybrid method using model-based collaborative filtering and content-based filtering for the future development of our universal recommendation system.

Microscale insights into deep bed membrane filtration: Influence of internal surface roughness

Deep bed filtration is widely applied in bioprocessing, virus filtration, and water purification to remove small impurities, such as particles or virus fragments. However, more needs to be understood about the parameters that influence particle capture and deposition. Detailed simulations and microfluidic filtration experiments with straight pores have been widely investigated, yet realistic membrane porosity features such as pore gradients and roughness have not been addressed in detail. The internal membrane morphology is assumed to have a strong effect on filtration performance. Therefore, this study introduces a new microfluidic membrane mimicking device (MMD) and methodology that analyzes spatio-temporal particle collections in a deep bed filtration MMD with gradually decreasing pore size toward the retentate side. The design allows us to systematically tailor an internal filter surface roughness to investigate its influence on differently sized soft particles and the consequences for filtration performance, in particular, particle capture. Optical investigation and quantitative evaluation show enhanced particle–pillar interactions for increased roughness. This results in a reduced penetration depth and reduced particle breakthrough. The modes of capture or filtration phenomena, such as pore blocking, bridging, or dendrite formation, differ significantly between smooth and rough membrane filter structures. In the case of rough inner filter surfaces, those phenomena lead to a less distinct decrease in volumetric flow, allowing a longer filtration process. The microfluidic study offers a detailed investigation of how microscale phenomena influence the filtration process. The results provide a fundamental understanding of microscale filtration effects based on roughness and, hence, motivate a tailoring of the internal membrane filter surface according to the filtration problem at hand.

Non-linear filtration model with splitting front

We consider filtration of a suspension in a homogeneous porous medium which is described by a macroscopic 1-D model including the mass exchange equation and the kinetic equation for deposit growth. The standard model assumes that suspended particles move at the same speed as the carrier fluid. However, in some experiments, a lag between the front boundary of suspended particles and the front of the carrier fluid was observed. This article proposes a modification of the standard model that provides a description of the separation between the fluid front and the particle front. For this purpose, a non-smooth non-linear function depending on the concentration of the suspension is introduced into the deposit growth equation. In case of a non-smooth suspension function, the concentration of suspended particles at the front decreases to zero in a finite time. At this moment the united front splits into the front of pure injected water and the front of suspended and retained particles. The particle front moves slower than the pure water front. In case of a linear filtration function (Langmuir coefficient), an exact solution is constructed in a closed form. For the filtration problem with a suspension function in the form of a square root, explicit analytical formulae are obtained. In case of a non-smooth filtration function, the filtration time is finite. The curvilinear boundary separates the filtration domain, where concentrations increase with time, from the stabilization domain, where the concentrations of suspended and retained particles have reached their limits. The limit speeds of the stabilization border and of the particle front coincide.

STUDY OF TEMPERATURE FIELDS NEAR A WELL DURING FILTRATION OF VISCOPLASTIC OIL

The work examines the time variation of fluid temperature during non-isothermal filtration of viscoplastic oil near a well. It is known that a characteristic feature of modern oil production is an increase in the share of hard-to-recover oil reserves, which include viscoplastic oils. According to their rheological characteristics, such oils are non-Newtonian liquids and, therefore, their filtration process is not described by Darcy’s linear law. When filtering fluids that are not described by Darcy's law, it is necessary to use nonlinear filtration laws, which make it possible to more adequately describe the processes occurring in productive formations when hydrocarbons are displaced from them. To describe the nonlinear filtration law, empirical formulas obtained by approximating data from laboratory experiments are usually used.In the works of V.V. Devlikamov and his co-authors provide experimental data on the dependence of viscosity on shear stress for high-viscosity oils. They have been shown to be approximated quite well by a sigmoid function. However, the problem then becomes significantly nonlinear. Subsequently, in order to simplify finding a solution to the problem of filtration of high-viscosity oil, experimental data were obtained by V.V. Devlikamov and his co-authors were approximated by broken lines.In this work, the experimental data are approximated by a sigmoid function, which allows for more accurate calculations. Assuming that the viscosity and density of oil do not depend on temperature, which is typical for natural development modes, the results of calculations of temperature changes over time near the well are presented. It is shown that the temperature of viscoplastic oil in the first hours after starting a well differs significantly from the temperature of Newtonian oil (oil with constant viscosity). Thus, if the temperature of Newtonian oil continuously increases, then the temperature of viscoplastic oil immediately after starting a well increases and coincides with the temperature of oil with constant viscosity, then drops and after some time begins to increase again. The work shows that such an unusual change in the temperature of viscoplastic oil over time is associated with a change in the zone of destruction of the formation structure.

Моделирование течения воздуха в упруго-деформируемой пористой среде, аппроксимирующей легкие человека: структура модели, ее основные уравнения и разрешающие соотношения

This paper is devoted to refining the mathematical model of the human respiratory system designed to predict the occurrence of respiratory pathologies caused by the negative effects of atmospheric air pollution. It is difficult to identify individual air channels in the human lungs, consisting of small respiratory tracts, called alveoli, through which oxygen from the air passes into blood. Therefore, the human lungs are modeled as a two-phase elastically deformable saturated porous medium, in which one phase is the deformable skeleton of the medium (lung tissue) described by the model of deformable solid body, and the other phase is gas filling the porous space. We construct the model of air flow in the human lungs, which consists of the sub-model of elastic deformation of the porous lung medium, experiencing large displacement gradients, and the sub-model of air filtration through the deformable porous medium. The model takes into account the relationships between sub-models of the respiratory system, i.e. we consider the coupled problems of deformation and filtration in differential form. Since at present the analytical solution of the stated essentially nonlinear problem is unfeasible, the problem is formulated in a generalized weak form to allow subsequent application of numerical methods using the Galerkin method. For the numerical solution of the nonlinear problem of deformation of the two-phase lung medium, it is suggested to use the finite element method, for the filtration problem - the finite volume method. The resolving relations needed to solve the formulated sub-problems are derived. To solve the nonlinear problem, we developed algorithms and a set of programs. The description of these computational tools, as well as analysis of the results obtained will be presented in our the next paper.

MESHFREE MULTISCALE METHOD WITH PARTIALLY EXPLICIT TIME DISCRETIZATION

In this paper, a multiscale approach with partially explicit time discretization is proposed. The idea is to use a partially explicit time scheme, considering a filtration problem in a fractured medium, where the implicit scheme is used for nodes whose subdomains contain fractures, and the explicit scheme is used for all others. In this way, it is possible to use a time step that is independent of the diffusion coefficient for fractures. Numerical results demonstrating high accuracy of calculations are presented.

Numerical Solution of the Inverse Problem of Non-stationary Filtration of Bingham Non-Newtonian Fluid to a Horizontal Well

Numerical Solution of the Inverse Problem of Non-stationary Filtration of Bingham Non-Newtonian Fluid to a Horizontal Well

Superhydrophobic Materials for Self-cleaning Applications: A Review

Abstract: Since the discovery of the “lotus effect,” the superhydrophobic structure of the research is more and more profound. When the droplets fall on the surface, it will not occur as a wetting phenomenon. Making full use of this feature will achieve the self-cleaning effect of the object surface. In the dust filtration problem, it is possible to spray superhydrophobic materials on the surface of the equipment using superhydrophobic self-cleaning characteristics to change the filtering method and to improve the self-cleaning efficiency. This paper describes the methods of preparing superhydrophobic materials, self-cleaning methods, and the application of superhydrophobic materials in the field of self-cleaning. Based on the summary of patents and papers, this paper focuses on the filtration and self-cleaning effect of superhydrophobic materials on dust particles in humid environments. With a simple structure, high filtration efficiency, and long service life, the super sparse/hydrophilic hybrid mesh can work continuously without manual operation. It can effectively filter dust particles and improve air quality in humid environments. Coal powder condensation experiments in this paper proved that the application of superhydrophobic materials in the field of self-cleaning yielded significant results. When superhydrophobic materials are sprayed on copper-based filters, the hydrophilic line mixes with the hydrophobic region, greatly improving the self-cleaning efficiency.

A physics-informed deep learning approach for solving strongly degenerate parabolic problems

AbstractIn recent years, Scientific Machine Learning (SciML) methods for solving Partial Differential Equations (PDEs) have gained increasing popularity. Within such a paradigm, Physics-Informed Neural Networks (PINNs) are novel deep learning frameworks for solving initial-boundary value problems involving nonlinear PDEs. Recently, PINNs have shown promising results in several application fields. Motivated by applications to gas filtration problems, here we present and evaluate a PINN-based approach to predict solutions to strongly degenerate parabolic problems with asymptotic structure of Laplacian type. To the best of our knowledge, this is one of the first papers demonstrating the efficacy of the PINN framework for solving such kind of problems. In particular, we estimate an appropriate approximation error for some test problems whose analytical solutions are fortunately known. The numerical experiments discussed include two and three-dimensional spatial domains, emphasizing the effectiveness of this approach in predicting accurate solutions.

ФИЛЬТРАЦИОННО-ТЕМПЕРАТУРНЫЙ РЕЖИМ ГРУНТОВОЙ ПЛОТИНЫ МЕРЗЛОГО ТИПА В КРИОЛИТОЗОНЕ

In this paper, the solution of a joint temperature filtration problem is considered in relation to a soil dam in a cryolithozone. The dam is designed according to one of the principles adopted for the design and construction of structures in such climatic conditions. A description of the methodology used is given. Using the PLAXIS software package, a numerical solution to the problem was obtained, taking into account the phased construction of the structure, repair and reconstruction of the structure caused by the occurrence of an emergency situation after rapid filling of the reservoir. The obtained results of solving the temperature filtration problem revealed problems with ensuring the "frozen" regime of the structure and the need to take additional measures for this.

Numerical homogenization of the gas filtration problem

The non-stationary gas flow equation in homogeneous and heterogeneous media is considered. Areas of this type are often encountered when considering gas production processes from a gas-bearing reservoir. The heterogeneous structure of the reservoir can strongly affect the extraction processes. For the numerical solution of the problem under consideration, we construct an approximation of the equations on a coarse grid using the numerical averaging method. The method allows us to solve the problem using less computational power and in a shorter time. A numerical comparison of the results of solving the model problem is carried out in a two-dimensional domain for the cases of linear and nonlinear variants of the equations, as well as in a homogeneous and heterogeneous medium. The finite element solution on a fine mesh was taken as a reference solution. The computational realization was performed using the FEniCS library. The construction of the geometric computational domain was performed in the program Gmsh. Paraview and the Matplotlib library in Python were used for data visualization.

Donors with repeated blood product discards for filtration problems, clots or hemolysis: Causes and follow-up.

Sanquin donor medicine department is informed when donations or their components are rejected. This can occur isolated or frequently. It is undesirable because the donations cannot be used and there may be an underlying medical cause. Based on regional approaches, a uniform procedure was developed. Information about whole blood, plasma- plateletpheresis donations from which one or more components were rejected for filtration time (>2 h), hemolysis or clots were extracted from blood bank information system. After rejection of two successive components or donations or total ≥3 the donor is contacted. Depending on the medical history and investigation by the family doctor, the donor carrier is re-evaluated. We looked for the causes of the discarded products and performed a survey among blood services regarding polices with discarded products. One or more components from 1742 of about 2.2 million successful donations (0.08%) were rejected. The highest percentage of rejection was seen in plateletpheresis (1.5%), all for clots. No underlying medical causes were found. 24 whole blood donors were found to have sickle cell trait (SCT) and were permanently deferred. The policies for follow-up after discarded products or acceptance of SCT donors vary between the 16 blood banks. Six organizations do not follow-up donors and seven accept SCT for blood or plasma donation. Informing donors with repeated discarded products avoids the non-use of donations. Causes of repeated discarded products can be found by follow-up of donors. The results of the survey indicate a large discrepancy in policies applied worldwide.

Characterization of molar mass and conformation of relevant (non-)starch polysaccharides in cereal-based beverages

Arabinoxylans, β-glucans, and dextrins influence the brewing industry's filtration process and product quality. Despite their relevance, only a maximum concentration of β-glucans is recommended. Nevertheless, filtration problems are still present, indicating that although the chemical concentration is essential, other parameters should be investigated. Molar mass and conformation are important polymer physical characteristics often neglected in this industry. Therefore, this research proposes an approach to physically characterize enzymatically isolated beer polysaccharides by asymmetrical flow field-flow fractionation coupled to multi-angle light scattering and differential refractive index detector. Based on the obtained molar masses, root-mean-square radius (rrms from MALS), and hydrodynamic radius (rhyd), conformational properties such as apparent density (ρapp) and rrms/rhyd can be calculated based on their molar mass and size. Consequently, the ρapp and rrms/rhyd behavior hints at the different structures within each polysaccharide. The rrms/rhyd 1.2 and high ρapp values on low molar mass dextrins (1–2·105 g/mol) indicate branches, while aggregated structures at high molar masses on arabinoxylans and β-glucans (2·105 –6·106 g/mol) are due to an increase of ρapp and a rrms/rhyd (0.6–1). This methodology provides a new perspective to analyze starch and non-starch polysaccharides in cereal-based beverages since different physical characteristics could influence beer's filtration and sensory characteristics.

A multiparameter mathematical model for the problem of nonlinear filtration of fluids in two-layer media

In the realm of fluid dynamics and porous media, the nonlinear filtration of fluids in two-layer media presents a complex and intriguing challenge that demands a comprehensive mathematical framework for accurate representation and analysis. This paper introduces a multiparameter mathematical model designed to elucidate the intricacies of fluid filtration in heterogeneous environments, specifically focusing on two-layer media. The authors research the construction of a multiparameter mathematical model and numerical solution of nonlinear problems of the theory of filtration of unstructured and structured fluids in hydrodynamically connected multilayer formations with different characteristics. The developed models and solution algorithms were tested on hypothetical data.

ДЕЯКІ КРАЙОВІ ЗАДАЧІ, ВІДПОВІДНІ МОДЕЛІ ДРОБОВО-ДИФЕРЕНЦІЙНОЇ ФІЛЬТРАЦІЙНОЇ ДИНАМІКИ В ТРІЩИНУВАТО-ПОРИСТОМУ СЕРЕДОВИЩІ ЗА УМОВ ЧАСОВОЇ НЕЛОКАЛЬНОСТІ

Closed-form solutions of some boundary-value problems of fractional-differential geofiltration dynamics in a fractured-porous medium are obtained for a model with weakly permeable porous blocks. In particular, the direct and inverse boundary-value problems of filtration for the finite thickness layer are solved, the conditions for the existence of their regular solutions are given, and the solution of the problem of filtration dynamics with nonlocal boundary conditions is found. For a particular case of the filtration model, the problem of modeling the anomalous dynamics of filtration pressure fields on a star-shaped graph is considered. Keywords: mathematical modeling, fractional-differential dynamics of filtration processes, fractured-porous medium, non-classical models, boundary-value problems, inverse problems, problems with non-local conditions, closed-form solutions.