Non-Field Analytical Method for Filtration of Slightly Compressible Fluid through Porous Media with Stagnation Areas

In this study the method of Kulish has been used to derive a non-field solution of the equation, which models the process of unsteady filtration of a slightly compressible fluid within a domain consisting of both flow and stagnation areas under the influence of some pressure distribution at the boundary. The solution relates the local values of pressure and the corresponding pressure gradient and is valid everywhere within the domain including the boundary. The solution thus obtained is in the form of a series with respect to generalised differ-integral operators of fractional orders. The solution has been compared with the know solution of the filtration problem with no stagnation areas. Finally, an integral equation to estimate the pressure evolution at the boundary for a given filtration speed has been proposed.

Numerical Study of the Process of Unsteady Filtration of a Fluid in Interacting Porous Pressure Layers

A review of the fundamental studies conducted in 2010 - 2020 is given in the article to develop a mathematical model related to the fluid and gas filtration processes in porous media. To conduct a comprehensive study of the process of unsteady filtration of fluid in multi-layer porous pressure media and to make a management decision, a mathematical model described by a system of partial differential equations with corresponding initial and boundary conditions and a conservative numerical algorithm were developed. On the basis of the developed software of the problem posed, computational experiments were conducted on a computer; the calculation results were presented in the form of tables and graphical objects. The schemes of location and capacity of vertical drainage wells to protect irrigated and non-irrigated areas from flooding were proposed on the basis of the developed software. Using the proposed mathematical tool, it is possible to obtain the prognostic groundwater levels for any area for the required period of time, considering a number of factors, for example, the formation heterogeneity in plan, the gradient of the permeability barrier, and other hydrogeological, hydro-technical, and natural conditions; to calculate the capacity and optimal drilling pattern of vertical drainage wells to protect the territory and to develop oil and gas fields.

Unsteady filtration under maximal draw-off velocities of Tupolang water reservoir

The article presents the results of field studies to determine unsteady filtration in Tupolang dam core. Calculations are carried out for phreatic line curve in the core of Tupolang dam under unsteady filtration for various velocities of reservoir draw-off and water yield coefficient. At the same time it has been established that the increase of velocity and time of water reservoir draw-off leads to the increase of filtration pressure, and the decrease of water yield factor leads to the decrease of filtration pressure. The increase of filtration pressure, in turn, contributes to the increase of the intensity of unsteady filtration of Tupolang dam core.

Influence of speed of filling and draw-off to the filtration regime of Earth-fill dam

To use and manage water resources and carry out protection measures from the destructive effect of water flow, water reservoir hydrosystem construction has greatly developed. The article presents the results of field studies to determine unsteady filtration in the Earth-fill dam core. In the research process, static data from literature review, field study data, and theoretical processing of research results were used. Numerical data processing was carried out with methods of mathematical statistics, and the graphical part was done using Microsoft Excel. Calculations were carried out for phreatic line curve in the core of Earth-fill dam under unsteady filtration for various velocities of reservoir draw-off and water yield coefficient. At the same time, it has been established that the increase of velocity and time of water reservoir draw-off leads to the increase of filtration pressure, and the decrease of water yield factor leads to the decrease of filtration pressure. The increase of filtration pressure, in turn, contributes to the increase of the intensity of unsteady filtration of the Earth-fill dam core.

Methodology for determining water losses from irrigation canals

The aim of the article is to develop a method for calculating water losses from irrigation channels in determining the permeability of rock in the zone of filtration flow on the basis of the law of infiltration A.N. Kostyakov using the results of studies of free filtration from pits and foundation pits in loess loams. Pressure movement of water in irrigation canals is subject to the laws of two-phase flow, in which – in contrast to the Darcy law for the zone of saturation plays an important role, the volume and its change in time. The filtration rate (VF) increases with increasing rock moisture (θ) along the S-curve, while the pressure gradient (I = dh/dz) decreases. The dependences of these parameters on the pressure are represented by power functions, and their product CDP = VFI does not change in time and can serve as a characteristic of the filtration flow under the channel. When installing paired piezometers near the water chore line in the channel and determining the graph I(t) by the value of the twophase flow constant CDP, it is possible to calculate the filtration rate at a number of times and the water losses during unsteady filtration. Water losses from the channels at equilibrium humidity increases with increasing head according to the formula A.N. Kostyakova, in which the water permeability of rocks is characterized by a steady filtration rate at a head of 1.0 m, and the gradient is the function of pressure. The application of the proposed method of calculating losses in the design of irrigation systems will increase the reliability of the justification of the volume of anti-filtration measures and the forecast of the groundwater level.

MODEL OF UNSTEADY FILTRATION OF TWO-COMPONENTS MEDIUM

The article examines the aspects of building the geological model of oilfield, it suggests a number of methods of distribution of geometric and porosity-permeability properties of reservoir formations on the basis of geophysical and hydrodynamic studies of data. In this article also is described the mathematical model of oilfield, which characterizes the unsteady filtration of two-component (water+oil) medium. This model is linked to the model of transport hydraulic system (THS) and allows to specify the interaction of technical hydrosystem and formation hydrosystem in the conditions of changing of porosity-permeability properties of multihorizont field and technical characteristics of the elements of aboveground system.