Flow Balancing in FEM Modelling of Multi-Phase Flow in Porous Media

Persova, Marina G.; Soloveichik, Yuri G.; Grif, Alexander M.; Patrushev, Ilya I.

doi:10.1109/apeie.2018.8545457

Cited by 6 publications

(3 citation statements)

References 5 publications

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“…1) расчет поля давления методом конечных элементов [7][8][9]; 2) расчет численных потоков смеси i V    , перетекающих через грани i  конечных элементов e  ; 3) использование метода балансировки [10,11]…”

Section: математическая модельunclassified

Approach to the determination of the heat transfer coefficient between rock and fluid mixture for modeling non-isothermal multiphase flow

Ovchinnikova¹,

Persova²,

Leonovich³

2022

Analysis and data processing systems

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The paper presents an approach to calculation of the coefficient determining the rate of heat transfer between a fluid mixture in oil reservoir and a matrix-rock. This coefficient is necessary for further joint modeling of hydrodynamic and thermal processes that occur in the field reservoir during its development using, for example, thermal methods for enhanced oil recovery. To model the processes of a non-isothermal multiphase flow, an approach based on implicit pressure calculation using the finite element method and explicit calculation of phase saturations is used. The approach to determining the heat transfer coefficient is based on solving the thermal problem in an area corresponding to a channel of a porous medium and a part of the matrix-rock around it. In this case, a fluid mixture with a known temperature value, different from the initial temperature in the channel and matrix-rock, enters the channel at a given rate. A two-dimensional problem is solved in an axisymmetric formulation by the finite element method.Numerical experiments to determine the heat transfer coefficient were carried out on models for various values of the channel size, porosity, initial temperatures of the medium, temperature of the mixture entering the channel, thermal properties of the fluid mixture and rock. As a result of the study, it was found that the channel size and porosity have the most significant effect on the value of the heat transfer coefficient, since these characteristics determine the volume of the matrix-rock, which should “warm up / cool down” when the temperature of the fluid mixture in the channel changes. Also, the coefficient values obtained were quite large, since the heat exchange between the rock and the mixture in the channel occurs in minutes, which practically corresponds to instantaneous heat transfer when it comes to modeling field development processes, where time steps are days and months.

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Section: математическая модельunclassified

Approach to the determination of the heat transfer coefficient between rock and fluid mixture for modeling non-isothermal multiphase flow

Ovchinnikova¹,

Persova²,

Leonovich³

2022

Analysis and data processing systems

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“…Let us find such corrective additives i Q  (where i is the global number of faces) for each finite element, that they, on the one hand, minimize the total system unbalance, and, on the other hand, are close to the calcuated numerical flow. These corrective additives can be found as a result of i Q  minimization following the functional [15]:…”

Section: Finite Element Approximationmentioning

confidence: 99%

Determination of the effect of injection wells on production wells in their work dynamics by using hydrodynamic modeling

Grif¹,

Persova²,

Soloveichik³

2019

Science Bulletin of the NSTU

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“…В данной работе рассматривается специальная технология постобработки потоков, которую мы будем называть методом балансировки [11][12][13][14][15]. Она основывается на выполнении баланса объемов втекающей и вытекающей смеси для всех конечных элементов.…”

Section: Introductionunclassified

Investigation of the efficiency of post-processing methods in solving problems of multi-phase filtration

Grif¹,

Soloveichik²

2022

Analysis and data processing systems

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Methods for post-processing of finite element solutions in the simulation of multiphase flows are considered. To simulate filtration processes, a special method based on the implicit calculation of the pressure field and the explicit calculation of saturations is used. Post-processing of flows is performed using two technologies - the balancing method and the projection method. The method of balancing the numerical flows of the mixture ensures the fulfillment of local conservation laws by finding corrections to the flows of the mixture calculated using the FEM. For the closeness of the modified mixture flows to the original numerical ones, the regularization parameters in the balancing method are calculated using the averaged unbalance. In the projection method, the balanced values of fluxes through the faces of finite elements are corrected by adding constant corrections (constant per element). Computational experiments were carried out on a test problem, a model of a field with a simple structure, and a model of a real oil field in the Republic of Tatarstan. When modeling problems with the appropriate correction of the known mixture flows on the faces of the wells, the solutions obtained using the balancing method and the projection method have little difference. The results of research on problems have shown that both technologies provide conservative solutions for which conservation laws are satisfied. At the same time, the use of the method of balancing the numerical flows of the mixture provides a higher accuracy than the projection method, when the flows in the wells are corrected in the post-processing process (that is, in fact, production/injection is emulated while maintaining a fixed pressure). The projection method can be improved by using the weight functions proposed for the balancing method. However, even in this case, the balancing method allows obtaining more accurate solutions.

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Flow Balancing in FEM Modelling of Multi-Phase Flow in Porous Media

Cited by 6 publications

References 5 publications

Approach to the determination of the heat transfer coefficient between rock and fluid mixture for modeling non-isothermal multiphase flow

Approach to the determination of the heat transfer coefficient between rock and fluid mixture for modeling non-isothermal multiphase flow

Determination of the effect of injection wells on production wells in their work dynamics by using hydrodynamic modeling

Investigation of the efficiency of post-processing methods in solving problems of multi-phase filtration

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