Modeling of Three-Phase Non-isothermal Flow in Porous Media Using the Approach of Reduced Pressure

Temirbekov, Nurlan; Baigereyev, Dossan

doi:10.1007/978-3-319-25058-8_17

Cited by 3 publications

(1 citation statement)

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“…The model with various assumptions about physical data was studied, for example, in [1,2,3]. In [4], a new "global" formulation of the threephase non-isothermal flow problem was proposed, which is based on the introduction of a change of variables for the pressure, called "global" pressure, to eliminate the gradients of capillary pressures from the equations for pressure and temperature. As a result, the initial equations were reduced to a system of five partial differential equations with respect to pressure, temperature, velocity, and two saturations.…”

Section: Introductionmentioning

confidence: 99%

Efficient difference schemes for the three-phase non-isothermal flow problem

Zhumagulov

Temirbekov

Baigereyev

2017

AIP Conference Proceedings

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The paper focuses on constructing and investigation of cost-effective difference schemes for the numerical solution of the two-dimensional three-phase non-isothermal flow problem without capillary and gravitational forces. In this paper, the finite difference method is used to solve the problem numerically. The method of energy inequalities is applied to examine the stability of the finite difference scheme with respect to the initial data and the right-hand sides of the equations. Three cost-effective difference schemes are constructed on the base of the studied scheme. The efficiency of the proposed algorithms is analyzed on the basis of comparing the average time spent on the numerical implementation of one time layer.

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Section: Introductionmentioning

confidence: 99%