Filtration Problems Research Articles

An Online Generalized Multiscale Finite Element Method for Dual-continuum Unsaturated Filtration Problem in Domains with Rough Boundaries

An Online Generalized Multiscale Finite Element Method for Dual-continuum Unsaturated Filtration Problem in Domains with Rough Boundaries

CHARACTERISTIC METHOD FOR SOLVING FILTRATION PROBLEM

During construction, a liquid solution of a grout or waterproof filler is pumped into porous rock to improve its properties. The filtration of a suspension moving at a variable speed in a porous medium is simulated. A one-dimensional problem of filtration in a homogeneous porous medium with a curvilinear concentration front of suspended and retained particles is considered. For the numerical solution of the problem by the method of finite differences, the method of characteristics is used. The transition to characteristic variables allows one to straighten the front and construct a discrete grid with a constant step. When calculating the solution using an explicit difference scheme, additional points are used that do not coincide with the grid nodes. A detailed description of the algorithm for calculating a solution at the grid nodes and an example of a numerical solution of the problem are given.

COUPLED HEAT AND MASS TRANSFER PROBLEM WITH DEPENDENT HEAT CONDUCTIVITY PROPERTIES AND ITS SEMI-ANALYTICAL SOLUTION

Present paper proposes a computation method for a coupled heat and mass transfer problem within the porous media where the heat conductivity properties of the media undergo changes caused by the mass transfer. Heat and mass transfer processes are coupled through the inclusion of evaporation and condensation phenomena which in turn require the solution to an another the vapour transfer problem. This complex coupled problem re-sults in a system of both linear and non-linear second order partial differential equations that are spatially discre-tized by Finite Element Method. Temporal integration is carried out analytically. Thus, the proposed system of equations covering linear vapor transfer problem, linear filtration problem and non-linear heat transfer problem is transformed into a system of both linear and non-linear first order ordinary differential equations being solved by semi-analytical method. Picard approach of successive iterations is used for linearization of the equations. Convergent solution is achieved which is demonstrated on a sample problem herein below. Proposed method gives good insight on the processes taking place within the structures being subjected to temperature and vapor pressure gradients, including the residual effects of moisture accumulation, and assesses its impact on heat con-ductivity of materials that the structures consist of. Present study is a part of more extensive research on the ap-plication of semi-analytical methods in heat transfer problems, therefore it is not exhaustive and complete. Shortcomings of the method and its possible work-arounds as well as the topics for further studies are discussed in Conclusions and Further Studies section.

Numerical Solution of Inverse Problems in Filtration of a Viscoplastic Fluid

Numerical Solution of Inverse Problems in Filtration of a Viscoplastic Fluid

Solution of filtration problems of construction geotechnology in thin water layers

Filtration problems of construction geotechnics during water movement in thin permeable layers of soils and artificial materials are considered. Under such conditions, traditional approaches borrowed from classical hydrogeology give errors. This is due to the fact that under normal conditions of underground aquifers of a sufficiently large depth, in hydrogeological practice, the hydraulic theory of filtration is used, in which the velocities of filtration currents are averaged along the vertical coordinate. The original nonlinear differential equations of filtration flows are subjected to forced linearization by one or another known method. In this case, the method of linearization by introducing the average power (depth) of the filtration flow is widely used. This method was originally developed for aquifers of great depth. In the presented work, an attempt was made to abandon such a linearization and solve some of the problems of unsteady filtration flows in thin aquifers, which are characteristic of building geotechnics, with obtaining analytical solutions of the final form without introducing artificial simplifications. A methodology is proposed for combining analytical and numerical methods in the process of finding solutions to filtration problems of construction geotechnics with obtaining self-similar dependencies. This approach will make it possible to avoid linearization errors and carry out filtration calculations in thin permeable layers of soils and artificial materials more accurately. A review of domestic and foreign scientific publications on the topic of research has shown some stagnation in this direction. The comparison revealed that in thin permeable layers of soils and artificial materials, preference can be given to filtration calculations using the presented method, since it more accurately describes the non-stationary movement of water in construction geotechnics.

Electrochemical Disposable Biosensor to Monitor Dabigatran in Point-of-Care Anticoagulation Therapy.

Dabigatran etexilate, an oral prodrug, is often used to treat complications linked to thrombosis. Dabigatran (DAB, active form) does not need to be monitored. However, there are several conditions, such as reduced renal function, traumatic bleeding, emergency surgery, the need for thrombolytic therapy in acute stroke, or the requirement to use other forms of anticoagulation, where knowing the concentration of DAB in the blood is indispensable. Unfortunately, there are no convenient DAB-specific point-of-care tests available. To solve this problem, two disposable sensors were constructed and optimised in this work to detect the anticoagulant drug DAB using novel co-facing disposable electrodes, which allows a calibration-free quantitation of the electroactive mediator concentration. A trypsin-based sensor was evaluated. This sensor performed well in a 10 mM Tris buffer (pH 8.8) solution. However, trypsin was inhibited by alpha-1 antitrypsin when a plasma sample was introduced into the sensor. This problem was overcome by plasma filtration. This sensor showed a detection limit of 50.7 ng mL-1 DAB in plasma and a quantification range of 177-500 ng mL-1. A thrombin-based sensor was also constructed. This sensor performed well in ten-fold diluted plasma, overcoming the filtration problem observed with the trypsin-based sensor. This sensor showed a detection limit of 9.6 ng mL-1 DAB in plasma and a quantification range of 11.5-140 ng mL-1. Its extensive pH stability range, the possibility of working at physiological pH, low volume, low cost, and fast turnaround response (less than 20 s) make the calibration-free thrombin-based sensor a suitable point-of-care test to measure DAB concentration in the blood.

Influence of factors on filtration regime of an earth dam under headwater drawdown

Introduction. As the statistics of observations of groundwater retaining structures shows, one of the most significant factors of emergencies in these structures is the occurrence of filtration deformations in the dam body. This often results in the appearance of moves of concentrated filtration. The occurrence of these phenomena can be provoked by a rapid decrease of the headwater level known as reservoir drawdown. It can be caused either by the technological requirements of the operation of the hydraulic unit or by the occurrence of an emergency situation. Modern design standards require mandatory consideration of the case of rapid drawdown with an assessment of the filtration regime and stability of the structure.
 
 Materials and methods. The results of numerical studies of unsteady filtration in a homogeneous earth dam under reservoir drawdown are considered. Numerical studies were carried out on the basis of the finite element method using the PRAXIS software package. Test calculations were carried out, which showed the reliability of the results obtained. The influence of the soil filtration coefficient of the dam, the rate of drawdown and the slope of the structure on the change in the position of the depression curve and the value of the maximum pressure gradient is analyzed.
 
 Results. For the considered variants of earth dams with different characteristics, the parameters of the filtration flow are obtained when the headwater level changes: the position of the depression curve and the values of the maximum pressure gradients. An assessment of the possibility of occurrence of filtration deformations of soils of the upper prism of the dam is given.
 
 Conclusions. The use of the PLAXIS software package for solving problems of unsteady filtration under reservoir level changes allows to obtain reliable results that are well comparable with the results of other proven methods. At certain rates of runoff for soils of different permeability in the upper prism of an earth dam, large values of pressure gradients exceeding critical values may occur. This indicates the necessity to control the process of drawdown and the use of antifiltration measures.

High-Accuracy Numerical Schemes for Solving Plane Boundary Problem for a Polyharmonic Equation and Their Application to Problems of Hydrodynamics

Boundary value problems are considered for harmonic, biharmonic equations, as well as the general polyharmonic equation for multiply connected domains on the plane. The problems are reduced to solving linear integral equations on boundary contours, which are assumed to be smooth. An algorithm for deriving an approximation of integral equations by a linear system is presented, taking into account the logarithmic singularities of the kernels of integral operators, through which integral equations are expressed. The algorithm uses the periodicity of functions defined on closed boundary contours. As the number of grid points increases, the approximation error decreases faster than the grid spacing to any fixed degree. Applications to solving problems of hydrodynamics, filtration and other problems of theoretical physics are considered.

Hydrodynamic Permeability in Axisymmetric Flows of Viscous Fluids through an Annular Domains with Porous Layer

Mass, energy, and momentum transfer processes between fluid-saturated porous media and the adjacent free flow occur in many natural and technical systems. The flow dynamics in the porous region and the adjacent free flow is strongly controlled by the mechanisms at the common interface and conditions on the outer surface of the free-flow. The present paper considers unsteady axisymmetric flows of viscous fluids through an annular domain with a porous layer covering a cylindrical solid core. Fluid flow in the domain filled with porous material and in transparent domain is described by Brinkman model and Navier Stokes equations, respectively. Analytical solutions for the dimensionless velocity fields in the Laplace domain are determined using Bessel functions, Laplace transform, and the appropriate interface and boundary conditions. The inversion of the Laplace transforms is done with the help of a numerical algorithm. In addition, the hydrodynamic permeability is determined. The dependence of the dimensionless velocity fields and of hydrodynamic permeability on characteristic parameters of the porous layer is numerically and graphically discussed. Since the velocity on the outer surface is given by an arbitrary function of time, the results in this paper could be used to study various filtration problems.

On the properties of solutions of a nonlinear filtration problem with a source and multiple nonlinearities

In this work, we studied the conditions for global solvability and unsolvability of a nonlinear filtration problem with a source and with a nonlinear boundary flow. The critical exponent of the global existence of the solution and the critical exponent of the Fujita type of the problem of nonlinear filtration in an inhomogeneous medium are established. An asymptotic representation of a compactly supported solution is obtained, which makes it possible to carry out a numerical experiment.

On the properties of solutions of a nonlinear filtration problem with a source and multiple nonlinearities

In this work, we studied the conditions for global solvability and unsolvability of a nonlinear filtration problem with a source and with a nonlinear boundary flow. The critical exponent of the global existence of the solution and the critical exponent of the Fujita type of the problem of nonlinear filtration in an inhomogeneous medium are established. An asymptotic representation of a compactly supported solution is obtained, which makes it possible to carry out a numerical experiment.

Application of genetic algorithms to optimize solution of filtering and prediction problems in dynamic program testing systems

Subject of research: probabilistic time models of testing created to form complex stochastic connections between individual test elements and developed to detect certain groups of the web applications program errors.
 The purpose of research: substantiate the possibility of using genetic algorithms in the process of solving probabilistic testing problems based on a multi-particle filter and evaluate their effectiveness. The study provides fundamental methods to improve the accuracy of the posterior distribution of probabilistic testing models and the total number of matched with evidences samples.
 Methods and objects of research: object of the research is to solve filtering and smoothing problems for a probabilistic test model based on a multi-particle filter. Methods and algorithms based on the Monte Carlo method are presented, allowing, in combination with genetic algorithms, to increase the accuracy of obtaining posterior estimates of samples. This approach allows you to narrow the range of samples, as well as increase their consistency. The formation of each next sample will be carried out taking into account the previous ones through the use of crossover and mutation operations.
 The main results of research: as a result, the validity of the proposed approaches to solving filtration and prediction problems in the process of implementing testing procedures based on multi-particle filter algorithms and genetic algorithms was proved. The given practical results prove the constructiveness and scientific validity of the proposed methods and algorithms for solving web applications testing problems.

On non-uniqueness of pressures in problems of fluid filtration in fractured-porous media

The paper proposes a new approach to the numerical solution of the singular Neumann problem for a system of elliptic equations, in which, for example, the problem of filtration of a two-phase incompressible fluid in a fractured-porous medium is reduced within the framework of the dual porosity model. The one-dimensionality of the kernel of the corresponding operator is established, after which an extended generalized mixed formulation is considered in which the singularity is eliminated by introducing some additional bilinear form. The extended formulation is approximated by the mixed finite element method, and the properties of the resulting system of linear algebraic equations with a saddle point matrix are established. Moreover, some numerical examples illustrate the theoretical results.

Применение методов Монте-Карло для решения регулярной и вырожденной задачи двухфазной фильтрации

One of popular mathematical models of filtration is the classical elastic regime model describing the nonstationary equilibrium filtration. It is also called the Muskat-Leverett model. Solving filtration problems by Monte Carlo methods makes it possible to find the solution of the problem at an individual point of the domain and to estimate derivatives of the solution. This paper is devoted to applying algorithms of the Monte Carlo method to problems of filtration. The Monte Carlo algorithms of random walk by spheres and on boundaries are used for solving the stationary problem of filtration of two immiscible inhomogeneous incompressible fluids in a porous medium and for estimating the solution and the derivatives of the solution of this problem.

Исследование фильтрации из оросительного канала методом электрогидродинамических аналогий

Purpose: simulation of the filtration process from an irrigation canal made in an earthen channel. Materials and methods. One of the most common methods in the waterworks construction and operation is the filtration process modeling. In practice, the use of mathematical modeling based on the use of mathematical analogies of various physical processes, which are described by the same differential equations, is widespread. The electric analogy method (EGDA) is based on the analogy between the groundwater velocity and the electrical current flow and allows solving various filtration problems on models of electrically conductive materials. The purpose of modeling the groundwater velocity using the EGDA method is to develop a model similar to a full-scale object, for studying the ongoing filtration processes with its help. Results. A flow net and a filtration velocity profile which were used to study free filtration from a canal in an earthen channel were constructed. As a result of the study, the specific filtration flow rate, filtration rate were determined and a comparison with the values obtained by calculation was made. Comparison of the results obtained from the flow net with the calculation formula showed that their values coincide with an error of 1.26 %. The specific flow rate determined by the calculation method coincides with the flow net value for the selected belt of equal pressure with an error of 2.8 %. Conclusions: the EGDA method allows determine effectively the seepage water losses from the canal, however, when quantifying the seepage flow, it gives more significant errors due to the complexity of complete recording when modeling the real conditions of the object under consideration.

ОБҐРУНТУВАННЯ ПАРАМЕТРІВ АНКЕРНОГО КРІПЛЕННЯ ПІДГОТОВЧИХ ВИРОБОК В УМОВАХ ІНТЕНСИВНИХ ВОДОПРИПЛИВІВ

Purpose. Improvement of the method of reducing water inflows into mine workings with using com-bined frame-roof bolting to ensure the stability of the mine workings, waterproofing and protection against the collapse of wet contour rocks inside the mine workings. Methods. When solving the problem of water filtration in deformed rock, the method of studying the state of a layered rock massif with a mine working in the presence of water-saturated layers in its vicinity, which was developed by the authors, as well as the finite element method, were used. Research results. As a result of the calculations, the stress values, the zones of inelastic defor-mations, the values of permeability coefficients, water pressure and water inflows have been obtained for the roadways supported with different number of roof bolts. It is shown that the number of roof bolts af-fects all these parameters around the roadway in the rock mass and in the water-saturated seam. If a larg-er number of roof bolts are installed, the processes of crack formation and, accordingly, rock fracturing are slower. After mining, if 3 or more roof bolts installed, intensity of water filtration process is minimal, but after 2-3 days water from the water-saturated seam begins to penetrate deep into the surrounding rocks. Roof bolting significantly reduces these processes, the using of a scheme with 5-9 roof bolts re-strains the movement of water and, most importantly, practically isolates the roadway from water-saturated rocks. Scientific novelty. For the first time, a numerical model has been created and the calculations have been completed for roadways supported with 1-9 roof bolts in conditions of intensive inflows over time from the moment of its building. Practical significance. Research and calculations make it possible to obtain a significant economic effect due to the setting of the optimal number of roof bolts and the reduction of the use of materials for supporting the roadway and, at the same time, to prevent water inflows and increase the stability of road-ways.

Analysis of changes in moisture transport parameters in soils under waterlogged conditions

The article considers changes in natural patterns of moisture transport parameters under waterlogging and lowering of groundwater table, in conditions of filtration-anisotropic strata. The nature of anisotropy characteristic of river sediments (alluvial, pluvial, deltaic and their combinations) is the most widespread in the surface zone of the earth’s crust. Impact factors: external and artificial, in the process of waterlogging and drainage, affect both positively and negatively the thickness of the active zone, capacity and water permeability values. The research method is based on the generalization of different approaches, causes and factors of moisture movement and on the results of field experiments to determine the nature to reveal the essence of “gravity moisture discharge”. In more exact statement the problem of stationary filtration is solved by Laplace equation. The state of moisture in the aeration zone has been studied: unsteady, transient and gravitational. By investigating the nature of this process, it is established that the evaporation process takes place not from the surface of groundwater table, but from aeration zone located between air (above ground surface) and water space (lower boundary of aeration zone).

Construction of a numerical model and algorithm for solving two-dimensional problems of filtration of multicomponent liquids, taking into account the moving “oil-water” interface

The paper considers a two-dimensional mathematical model of the filtration of a viscous, incompressible fluid in a deformable porous medium. The article describes a mathematical model of the problem at the “oil-water” interface with a system of parabolic differential equations. The problem posed is solved numerically using the differential-difference method based on the longitudinal-transverse scheme and the differential sweep method to determine the unknown boundary. To obtain a differential-difference problem, an algorithmic representation of a hidden scheme of alternating directions (longitudinal-transverse scheme) is used. The resulting system of differential-difference equations with initial conditions is known for each time layer along straight lines along the x axis, and then along each y axis it is solved by a differential sweep along a straight line, where the values just found correspond to time, i.e., the layer is taken as initial conditions. By approximating the differential equations in time, the position of the interface is determined for each time layer.

Numerical model of oil, water and gas flow in oil pools

During the oil well usage its flow rate inevitably lessens. As a result the oil production enterprises must solve the most important problem of the oil extraction intensification. When solving filtration problems (there is a great set of problems; here we will deal with one of them including physical processes, difficulties and problem setting-up) ordinarily use well-known problems. However, in many cases, for example, when describing thermogas-chemica modification (TGCM) there capacity is insufficient. For example, one needs describing of more than two phases, taking into account chemical reactions and so on. We produced a program which clears this trouble. This program can model main features of the TGCM case: many-phase and non-isothermal process, non-one-dimensional flow. As a result we can better tune calculation programs for specific deposits by taking into consideration of geologic peculiarities and near-well zone defects occurred as a result of previous usage.

Optimization of High Temperature-Resistant Modified Starch Polyamine Anti-Collapse Water-Based Drilling Fluid System for Deep Shale Reservoir.

During drilling in deep shale gas reservoirs, drilling fluid losses, hole wall collapses, and additional problems occur frequently due to the development of natural fractures in the shale formation, resulting in a high number of engineering accidents such as drilling fluid leaks, sticking, mud packings, and buried drilling tools. Moreover, the horizontal section of horizontal well is long (about 1500 m), and the problems of friction, rock carrying, and reservoir pollution are extremely prominent. The performance of drilling fluids directly affects drilling efficiency, the rate of engineering accidents, and the reservoir protection effect. In order to overcome the problems of high filtration in deep shale formations, collapse of borehole walls, sticking of pipes, mud inclusions, etc., optimization studies of water-based drilling fluid systems have been conducted with the primary purpose of controlling the rheology and water loss of drilling fluid. The experimental evaluation of the adsorption characteristics of "KCl + polyamine" anti-collapse inhibitor on the surface of clay particles and its influence on the morphology of bentonite was carried out, and the mechanism of inhibiting clay mineral hydration expansion was discussed. The idea of controlling the rheology and water loss of drilling fluid with high temperature resistant modified starch and strengthening the inhibition performance of drilling fluid with "KCl + polyamine" was put forward, and a high temperature-resistant modified starch polyamine anti-sloughing drilling fluid system with stable performance and strong plugging and strong inhibition was optimized. The temperature resistance of the optimized water-based drilling fluid system can reach 180 °C. Applied to on-site drilling of deep shale gas horizontal wells, it effectively reduces the rate of complex accidents such as sticking, mud bagging, and reaming that occur when resistance is encountered during shale formation drilling. The time for a single well to trip when encountering resistance decreases from 2-3 d in the early stages to 3-10 h. The re-use rate of the second spudded slurry is 100 percent, significantly reducing the rate of complex drilling accidents and saving drilling costs. It firmly supports the optimal and rapid construction of deep shale gas horizontal wells.