Self-similar solutions of one-dimensional gas-motion problems in a porous medium with a two-term drag law

1984 ◽  
Vol 47 (5) ◽  
pp. 1360-1365
Author(s):  
Yu. N. Gordeev ◽  
N. A. Kudryashov ◽  
V. V. Murzenko
Keyword(s):  
Porous Medium ◽  
One Dimensional ◽  
Self Similar ◽  
Motion Problems ◽  
Similar Solutions ◽  
Drag Law

A similarity problem of a porous material drying

2008 ◽  
Vol 6 ◽  
pp. 75-81
Author(s):  
D.Ye. Igoshin
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Gas Mixture ◽  
Dimensional Problem ◽  
Vapor Mixture ◽  
Initial State ◽  
One Dimensional ◽  
Similarity Problem ◽  
Self Similar ◽  
Similar Solutions

The plano-one-dimensional problem of heat and mass transfer is considered when a porous semi-infinite material layer dries. At the boundary, which is permeable for the gas-vapor mixture, the temperature and composition of the gas are kept constant. Self-similar solutions are set describing the propagation of the temperature field and the moisture content field arising when heat is supplied. The intensity of dry flows is studied, depending on the initial state of the wet-porous medium, as well as the temperature and concentration composition of the vapor-gas mixture at the boundary of the porous medium.

Gas Injection into Porous Reservoir Partly Saturated by Water

2015 ◽  
Vol 756 ◽  
pp. 336-341 ◽  
Author(s):  
М.K. Khasanov
Keyword(s):  
Porous Medium ◽  
Gas Injection ◽  
Hydrate Formation ◽  
Critical Conditions ◽  
Frontal Surface ◽  
One Dimensional ◽  
Gas Hydrate Formation ◽  
Porous Reservoir ◽  
Self Similar ◽  
Similar Solutions

Specific features of formation of gas hydrates due to injection of a gas into a porous medium initially filled by a gas and water are considered. Self-similar solutions to the planar one-dimensional problem are constructed, which give the distribution of main bed characteristics. The influence of the initial parameters of the porous medium and the intensity of the gas injection on the dynamics of the processes of hydrate formation is studied. The existence of solutions is demonstrated, which predict gas hydrate formation both on the frontal surface and in the volume zone. The critical conditions that separate the different modes of hydrate formation are found.

A self-similar solution for expansion into a vacuum of a collisionless plasma bunch

1998 ◽  
Vol 59 (1) ◽  
pp. 83-90 ◽  
Author(s):  
A. V. BAITIN ◽  
K. M. KUZANYAN
Keyword(s):  
Electron Distribution Function ◽  
Collisionless Plasma ◽  
Electron Component ◽  
One Dimensional ◽  
Ultrarelativistic Electron ◽  
Plasma Bunch ◽  
Self Similar Solution ◽  
Self Similar ◽  
The One ◽  
Similar Solutions

The process of expansion into a vacuum of a collisionless plasma bunch with relativistic electron temperature is investigated for the one-dimensional case. Self-similar solutions for the evolution of the electron distribution function and ion acceleration are obtained, taking account of cooling of the electron component of plasma for the cases of non-relativistic and ultrarelativistic electron energies.

Self-similar solutions of the second kind for the modified porous medium equation

1994 ◽  
Vol 5 (3) ◽  
pp. 391-403 ◽  
Author(s):  
Josephus Hulshof ◽  
Juan Luis Vazquez
Keyword(s):  
Porous Medium ◽  
Porous Medium Equation ◽  
Self Similarity ◽  
Compactly Supported ◽  
Medium Equation ◽  
Self Similar ◽  
Image Position ◽  
Similar Solutions

We construct compactly supported self-similar solutions of the modified porous medium equation (MPME)They have the formwhere the similarity exponents α and β depend on ε, m and the dimension N. This corresponds to what is known in the literature as anomalous exponents or self-similarity of the second kind, a not completely understood phenomenon. This paper performs a detailed study of the properties of the anomalous exponents of the MPME.

scholarly journals The problem of melting ice in a porous medium saturated with ice and gas

2019 ◽  
Vol 14 (1) ◽  
pp. 59-62
Author(s):  
M.N. Zapivakhina ◽  
D.A Umerov
Keyword(s):  
Porous Medium ◽  
Warm Water ◽  
Water Ice ◽  
Higher Temperature ◽  
Self Similar ◽  
Porous Soil ◽  
Temperature And Pressure ◽  
Lower Temperature ◽  
Similar Solutions ◽  
Constructed Self

The problem of ice formation in a dry, cold, porous medium saturated with ice and gas (air) when pumping warm water is considered in a flat one-dimensional self-similar formulation. The task was considered in volume area. During the injection of warm water from the beginning deep into the reservoir, it spread in a volume region that will divide the reservoir into 3 zones. The first zone was filled with water, the second zone was filled with ice and water, and the third zone was filled with ice and gas. To describe the process of heat and mass transfer, the following hypotheses were used: the temperature of the saturated substance (water, ice or gas) is equal to the temperature of the porous medium; ice and skeleton still; water, ice and skeleton of the reservoir are incompressible; skeletal porosity is constant. On the basis of constructed self-similar solutions, a numerical analysis was performed illustrating the effect of the initial parameters of a dry porous medium saturated with ice and gas, as well as the temperature of the injected water on the temperature and pressure distribution in the porous medium. It has been established that an increase in the temperature of the injected water does not lead to a significant increase in the area of ice decomposition. It is also established that if the pressure of the injected water is increased, this will not lead to a large increase in the area of ice decomposition. However, based on the results obtained, it can be seen that the speed of movement of the melting boundary increases, in particular, as the pressure increases by <i>p<sub>e</sub></i>=0.05 MPa, the intermediate region increases by one and a half times. It was found that it is economically more profitable to pump water with a lower temperature, because water with a higher temperature slightly increases the freezing area of the porous soil.

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