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Computer Research and Modeling, 2018, Volume 10, Issue 5, Pages 709–728 (Mi crm680)  

This article is cited in 2 scientific papers (total in 2 papers)


Application of the streamline method for nonlinear filtration problems acceleration

Ya. V. Nevmerzhitskiy

Moscow Institute of Physics and Technology, Computer Science and Computational Mathematics Department, 9 Institutskiy per., Dolgoprudny, Moscow Region, 141700, Russia

Abstract: The paper contains numerical simulation of nonisothermal nonlinear flow in a porous medium. Two- dimensional unsteady problem of heavy oil, water and steam flow is considered. Oil phase consists of two pseudocomponents: light and heavy fractions, which like the water component, can vaporize. Oil exhibits viscoplastic rheology, its filtration does not obey Darcy's classical linear law. Simulation considers not only the dependence of fluids density and viscosity on temperature, but also improvement of oil rheological properties with temperature increasing.
To solve this problem numerically we use streamline method with splitting by physical processes, which consists in separating the convective heat transfer directed along filtration from thermal conductivity and gravitation. The article proposes a new approach to streamline methods application, which allows correctly simulate nonlinear flow problems with temperature-dependent rheology. The core of this algorithm is to consider the integration process as a set of quasi-equilibrium states that are results of solving system on a global grid. Between these states system solved on a streamline grid. Usage of the streamline method allows not only to accelerate calculations, but also to obtain a physically reliable solution, since integration takes place on a grid that coincides with the fluid flow direction.
In addition to the streamline method, the paper presents an algorithm for nonsmooth coefficients accounting, which arise during simulation of viscoplastic oil flow. Applying this algorithm allows keeping sufficiently large time steps and does not change the physical structure of the solution.
Obtained results are compared with known analytical solutions, as well as with the results of commercial package simulation. The analysis of convergence tests on the number of streamlines, as well as on different streamlines grids, justifies the applicability of the proposed algorithm. In addition, the reduction of calculation time in comparison with traditional methods demonstrates practical significance of the approach.

Keywords: splitting by physical processes, streamlines method, compositional reservoir simulation, nonlinear flow.


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UDC: 519.6
Received: 30.08.2018
Revised: 23.09.2018

Citation: Ya. V. Nevmerzhitskiy, “Application of the streamline method for nonlinear filtration problems acceleration”, Computer Research and Modeling, 10:5 (2018), 709–728

Citation in format AMSBIB
\by Ya.~V.~Nevmerzhitskiy
\paper Application of the streamline method for nonlinear filtration problems acceleration
\jour Computer Research and Modeling
\yr 2018
\vol 10
\issue 5
\pages 709--728

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    This publication is cited in the following articles:
    1. E. A. Mikishanina, “Issledovanie koeffitsienta filtratsii uprugo-poristoi sredy pri ploskoi deformatsii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:3 (2019), 396–407  mathnet  crossref
    2. Ya. V. Nevmerzhitskii, A. V. Konyukhov, “Metod linii toka dlya rascheta kompozitsionnoi neizotermicheskoi filtratsii vyazkoplastichnykh neftei”, Matem. modelirovanie, 32:4 (2020), 75–93  mathnet  crossref
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