scholarly journals On the correctness of one model of the Stefan-Type filtration theory

In this paper a mathematical model of filtration theory with phase transitions is investigated. When using surface-active substances (surfactants) for the development of oil and gas fields in the reservoir occur sorption processes at the interfaces of individual phases (surfactants and oil, or surfactants and soil). In real processes, a finite time is required for achievement equilibrium. Therefore considering the mathematical model was called the mathematical model with phase relaxation. The solvability of the mathematical model, the limiting transition in relaxation time are investigated. It is proved that in the limiting case, the original problem is a problem of Stefan type.

2016 ◽  
pp. 110-113
Author(s):  
T. V. Maltseva ◽  
T. V. Saltanova ◽  
A. N. Kraev ◽  
V. V. Mironov

The influence of facilities on the foundation made of water saturated ground is studied in view of the impact of various external forces on the foundation. The developed mathematical model of the stress-strained state of the system «facility - foundation» enables to determine maximal stresses and strains occurred in the foundation. The numerical solutions were obtained using the modified finite-element method which took into account the impact of the pore water on the strain characteristics of the ground mineral particles.


2021 ◽  
Vol 19 (1) ◽  
pp. 98-108
Author(s):  
Nurgul Shazhdekeyeva ◽  
Beket Kenzhegulov ◽  
Aigul Myrzasheva ◽  
Galymzhan Kabylkhamitov ◽  
Raigul Tuleuova

This paper is devoted to the development and investigation of methods of mathematical and computer simulation of the process of fluid filtration in a porous medium. The methods of numerical solution of the problems of the filtration theory of build-up of conditions in the catchment and discharge areas boundaries, identification of filtration-capacitive parameters of the effective formation and determination of free (unknown) boundaries and creation of computational algorithms for analysis and forecast of technological indicators of oil and gas fields are considered. Methods and models of continuum mechanics, filtration theories, and methods for solving ill-defined problems, numerical modeling and computer programming were used. Approximate Numerical methods for solving direct and inverse problems of filtration theory, mathematical models for single-phase isothermal filtration of a gas mixture in a horizontal formation at small concentration gradients of components, studying the properties of self-similar solutions, as well as numerical solving the problem of identifying the capacitive parameters of the water-bearing stratum.


CIM Journal ◽  
2018 ◽  
Vol 9 (4) ◽  
pp. 195-214
Author(s):  
G. J. Simandl ◽  
C. Akam ◽  
M. Yakimoski ◽  
D. Richardson ◽  
A. Teucher ◽  
...  

Author(s):  
A.V. Antonov ◽  
◽  
Yu.V. Maksimov ◽  
A.N. Korkishko ◽  
◽  
...  

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