scholarly journals THE DYNAMIC DEFORMATION OF THREE-COMPONENT POROUS MEDIA

2020 ◽  
Vol 6 (1) ◽  
pp. 130
Author(s):  
Victor S. Polenov ◽  
Lyubov A. Kukarskikh ◽  
Dmitry A. Nitsak
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Propagation Velocity ◽  
Elastic Moduli ◽  
Dynamic Deformation ◽  
Velocity Ratio ◽  
Elastic Media ◽  
Longitudinal Waves ◽  
Cubic Equation ◽  
Monochromatic Waves

A mathematical model of the dynamic deformation of three-component elastic media saturated with liquid and gas, given by elastic moduli and coefficients characterizing the porosity and compressibility of the liquid and gas, is considered. Formulas for determining the propagation velocity of monochromatic waves in ternary porous media are obtained. The existence of three longitudinal waves depends on the discriminant of a cubic equation and the velocity ratio.

Features of wave propagation in the sand of different saturation

2011 ◽  
Vol 8 (1) ◽  
pp. 25-38
Author(s):  
A.T. Akhmetov ◽  
S.V. Lukin ◽  
D.M. Balapanov ◽  
S.F. Urmancheev ◽  
N.M. Gumerov ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Porous Medium ◽  
Porous Media ◽  
Wave Propagation ◽  
Water Saturation ◽  
Weak Shock ◽  
Capillary Forces ◽  
Theoretical Studies ◽  
Longitudinal Waves ◽  
Experimental And Theoretical Studies

There are the results of experimental and theoretical studies on the propagation of weak shock waves in the wet sand at different water saturation. There are mathematical model and numerical analysis of propagation of pressure pulses in porous media, taking into account capillary forces. Non-monotonic dependence of the amplitude of the wave resulting in a wet porous medium vs. the degree of water saturation is installed. The evolution of the fast, slow and filtration waves depends on the saturation of the system with water is analyzed. The influence of capillary forces on the propagation of longitudinal waves is evaluated.

A MATHEMATICAL MODEL OF MICROBIAL ENHANCED OIL RECOVERY IN POROUS MEDIA

2017 ◽  
Vol 8 (4) ◽  
pp. 263-272
Author(s):  
Jianlong Xiu ◽  
Tianyuan Wang ◽  
Ying Guo ◽  
Qingfeng Cui ◽  
Lixin Huang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Enhanced Oil Recovery ◽  
Oil Recovery ◽  
Microbial Enhanced Oil Recovery

scholarly journals About Two-dimensional Mathematical Model of Contaminant Migration in Unsaturated Catalytic Porous Media with Traps

2020 ◽  
pp. 25-28
Author(s):  
Anatolyy Vlasyuk ◽  
Viktor Zhukovskyy ◽  
Nataliia Zhukovska ◽  
Serhiy Kraychuk
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Moisture Transfer ◽  
Physical Problem ◽  
Two Dimensional ◽  
Contaminant Migration ◽  
Nonlinear Case ◽  
The Finite Difference Method ◽  
Saline Solutions ◽  
Assessment Strategies

This paper proposes an approach for the computer simulation of complex physical problem of contaminant migration through unsaturated catalytic porous media to the filter-trap. The corresponding mathematical model in the two-dimensional nonlinear case is presented. The model includes detailed considerations of the moisture transfer of saline solutions under the generalized Darcy’s and Cluta’s laws in different subregions of soil. The numerical solution of the boundary value problem was found by the finite difference method and proposed the algorithm for computer implementation. The proposed algorithm may be used for creating software with effective risk assessment strategies and predicting the cleaning and further useful use of the soil massifs.

BASIC MATHEMATICAL MODELS AND AN APPROXIMATE METHOD OF FILTRATION THEORY

2021 ◽  
pp. 25-31
Author(s):  
Alla A. Mussina
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Mathematical Models ◽  
Heterogeneous Porous Media ◽  
Effective Management ◽  
Filtration Theory ◽  
New Device ◽  
Scientific Papers ◽  
The Mathematical Model ◽  
Inhomogeneous Liquids

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.

Asymptotic Model of Free Convection Flow on a Vertical Surface in Porous Media with Newtonian Heating

2015 ◽  
Vol 756 ◽  
pp. 469-475
Author(s):  
Anna A. Bocharova ◽  
Irina V. Plaksina ◽  
Andrey A. Obushnyy
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Free Convection ◽  
Vertical Surface ◽  
Momentum Equation ◽  
Convection Flow ◽  
Asymptotic Model ◽  
Free Convection Flow ◽  
Energy Equations ◽  
The Mathematical Model

The mathematical model based on system of momentum and energy equations for free convection flow along a vertical surface in porous media under boundary conditions of the third sort is solved analytically using the method of matched asymptotic expansions. The region of validity for boundary layer model and expansions for stream function and temperature with parameter of perturbations were defined. The dependence of characteristic flow from governing dimensionless parameters and was analyzed numerically. The influence of viscous and convective terms of momentum equation in the proposed mathematical model significantly increases the rate of heat transfer on plate in porous media in comparison with Darsy flow model.

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