Numerical modeling of the non-equilibrium sorption process

Kaliev, I. A.; Mukhambetzhanov, S. T.; Sabitova, G. S.

doi:10.13108/2016-8-2-39

Cited by 4 publications

(8 citation statements)

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“…This contradicts boundary condition (5). Hence, the function ( , ) attains its minimum on the lower boundary of the domain , that is, at initial time and at this time, the function 0 ( ) is non-negative.…”

Section: Proof Of Theoremmentioning

confidence: 94%

“…In work [4], a global unique solvability was proved for the Dirichlet initial-boundary problem for system (1)-(2). In [5], [6] there was formulated a difference approximation of the differential problem by an implicit scheme, a solution to the difference problem was constructed by means of the sweep method and the results of the numerical experiments were presented.…”

Section: Formulation Of Problemmentioning

confidence: 99%

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Neumann boundary value problem for system of equations of non-equilibrium sorption

Kaliev

Sabitova

2019

Ufimsk. Mat. Zh.

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Filtration of liquids and gases containing associated (dissolved, suspended) solids in porous media is accompanied by diffusion of these substances and mass transfer between the liquid (gas) and solid phases. In this work, we study the system of equations modeling the process of a non-equilibrium sorption. We prove an existence and uniqueness theorem for a multi-dimensional Neumann initial-boundary value problem in the Hölder classes of functions. We obtain a maximum principle, which plays an important role in the proof of the theorem. The uniqueness of the solution follows this principle. The existence of a solution to the problem is shown by Schauder fixed point theorem for a completely continuous operator; we describe a corresponding operator. We obtain estimates ensuring the complete continuity of the constructed operator and the mapping of some closed set of functions into itself over a small time interval. Then we obtain the estimates allowing us to continue the solution up to arbitrary finite time.

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Section: Proof Of Theoremmentioning

confidence: 94%

Section: Formulation Of Problemmentioning

confidence: 99%

Neumann boundary value problem for system of equations of non-equilibrium sorption

Kaliev

Sabitova

2019

Ufimsk. Mat. Zh.

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“…The estimate (7) is proved. The uniqueness of the solution of problem (1)-(5) is a consequence of the estimates (6), (7).…”

Section: Introductionmentioning

confidence: 97%

“…In [6] the global unique solvability of the first initial-boundary value problem for system (1)-(2) is proved. In [7,8], a difference approximation of the differential problem was formulated using an implicit scheme, a solution of the difference problem was constructed using the sweep method, and the results of numerical experiments were presented.…”

Section: Introductionmentioning

confidence: 99%

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The third boundary value problem for the system of equations of non-equilibrium sorption

Kaliev¹,

Sabitova²

2018

Sib. Elektron. Mat. Izv.

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All Russian mathematical portal I. A. Kaliev, G. S. Sabitova, The third boundary value problem for the system of equations of non-equilibrium sorption, Sib.Abstract. In this paper, we investigate the system of equations modeling the process of non-equilibrium sorption. In particular, such systems are used in mathematical modeling of the production process of the useful component by the method of borehole underground leaching. The theorem of existence and uniqueness of the solution of the third boundary value problem in the multidimensional case in Hölder classes of functions is proved. The obtained maximum principle plays an important role in the proof of the theorem. The uniqueness of the solution is a consequence of this principle. The existence of a solution to the problem is shown by Schauder's fixed point theorem of a completely continuous operator. The description of the corresponding operator is given. Estimates are obtained to ensure the continuity of the constructed operator, and it is shown that the operator maps the original set of functions into itself at a small period of time. Then the estimates are given, allowing to continue the solution to any finite value of time.Keywords: process of non-equilibrium sorption, third boundary value problem, global single-valued solvability.Kaliev, I.A., Sabitova, G.S., The third boundary value problem for the system of equations of non-equilibrium sorption.c ⃝ 2018 Kaliev I.A., Sabitova G.S.

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Construction and Study of a Model of Oil Displacement by Water from the Reservoir

Mukhambetzhanov¹,

Mussina²,

Aman³

2023

MMEP

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In this paper, we investigated a two-phase model of incompressible fluid filtration. We apply the irregular grid method and the variable direction scheme. This approach gives the effect of solution accuracy near discontinuities (wells) due to the use of an irregular grid. The model is built taking into account the influence of capillary pressure and gravitational forces. The results confirm that the amount of oil that came out of the layer in a certain time is equal to the volume of water injected, except for the amount of water in the outlet stream in the same time. The proposed solutions of the new approach are intended to improve the methods and schemes of numerical investigation of this model. A balanced monotonic finitedifference scheme was developed and an efficient algorithm for its implementation was proposed. From a practical point of view, numerical modeling allows early prediction of performance. Thus, the applied aspect of the use of the obtained scientific result is the possibility of improving the process by taking into account the distribution of water saturation in the layer.

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Numerical modeling of the non-equilibrium sorption process

Cited by 4 publications

References 1 publication

Neumann boundary value problem for system of equations of non-equilibrium sorption

Neumann boundary value problem for system of equations of non-equilibrium sorption

The third boundary value problem for the system of equations of non-equilibrium sorption

Construction and Study of a Model of Oil Displacement by Water from the Reservoir

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