Control of displacement front in a model of immiscible two-phase flow in porous media

Akhmetzyanov, A. V.; Kushner, Alexei G.; Lychagin, Valentin

doi:10.1134/s1064562416040074

Cited by 6 publications

(3 citation statements)

References 5 publications

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“…Namely, we find a class of multivalued solutions to the Euler system (see also [16]), and singularities of their projection to the plane of independent variables are exactly what drives the appearance of the shockwave [17]. Similar ideas are used in a series of works [18][19][20], where multivalued solutions to filtration equations are obtained along with analysis of shocks. To find such solutions, we use the idea of adding a differential constraint to the original PDE in such a way that the resulting overdetermined system of PDEs is compatible [21].…”

Section: Introductionmentioning

confidence: 97%

Singularities in Euler Flows: Multivalued Solutions, Shockwaves, and Phase Transitions

Lychagin

Roop

2020

Symmetry

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In this paper, we analyze various types of critical phenomena in one-dimensional gas flows described by Euler equations. We give a geometrical interpretation of thermodynamics with a special emphasis on phase transitions. We use ideas from the geometrical theory of partial differential equations (PDEs), in particular symmetries and differential constraints, to find solutions to the Euler system. Solutions obtained are multivalued and have singularities of projection to the plane of independent variables. We analyze the propagation of the shockwave front along with phase transitions.

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Section: Introductionmentioning

confidence: 97%

Singularities in Euler Flows: Multivalued Solutions, Shockwaves, and Phase Transitions

Lychagin

Roop

2020

Symmetry

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“…Then, singularities of projections of multivalued solutions to the space of independent variables is exactly what corresponds to a formation of shock waves [24]. This concept has been used to describe shock waves in non-stationary filtration problems [25,26,27].…”

Section: Introductionmentioning

confidence: 99%

Singularities in one-dimensional Euler flows

Roop

2021

Preprint

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In this paper, a system of one-dimensional gas dynamics equations is considered. This system is a particular case of Jacobi type systems and has a natural representation in terms of 2-forms on 0-jet space. We use this observation to find a new class of multivalued solutions for an arbitrary thermodynamic state model and discuss singularities of their projections to the space of independent variables for the case of an ideal gas. Caustics and discontinuity lines are found.

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“…At present, the existence of the W-D-M effect has been verified by both field tests and laboratory experiments (Huang et al., 2016a, 2016b). However, according to the basic theory of immiscible two-phase fluid in porous media, free methane in a position with high pore pressure migrates to the position with low pore pressure (Akhmetzyanov et al., 2016; Schlüter et al., 2016). When high pressure water is injected into a coal rock mass, an increase in the pore pressure will turn free methane into adsorption methane, resulting in consumption of the free methane (Lu et al., 2020).…”

Section: Introductionmentioning

confidence: 99%

Experimental investigation of the functional mechanism of methane displacement by water in the coal

Huang

Chen

et al. 2020

Adsorption Science & Technology

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During hydraulic fracturing in a high-methane coal seam, there is a water-displacing-methane effect. A pseudo triaxle experimental system, which is opposite to the name of true triaxial system, for the water-displacing-methane effect was created. First, cylindrical coal samples in a methane adsorption equilibrium state, spontaneously desorbed. And then water was injected into the coal samples. The following was shown: (1) The displacement methane volume gradually rises with an increase of injected water, while the displacement methane rate tends to rise at first before declining later. Simultaneously, the water-displacing-methane process is characterised by a time effect. The methane displacement lags behind water injection. (2) Competitive adsorption and displacement desorption between the water and methane will promote adsorption methane into free methane, while the pore pressure increase caused by water injection will turn free methane into adsorption methane. The net free methane of the combination action provides a methane source for the water-displacing-methane effect. (3) A pore pressure gradient, which provides a power source for the water-displacing-methane effect, is formed and reduces gradually at the front of the water seepage along the seepage direction. The increase in water pressure can rapidly improve the pore pressure gradient and boost the displacement methane volume as well as improve displacement methane efficiency. (4) A starting porosity pressure gradient and limit pore pressure exist in the process of water-displacing-methane. When the pore pressure gradient is less than the starting pore pressure gradient, there is free methane in the coal rock, but it cannot be displaced. When the pore pressure is between the starting pore pressure and the limit pore pressure, the free methane can be displaced. When the pore pressure is greater than the limit pore pressure, the methane is almost completely adsorption methane, and water cannot be used to displace the free methane.

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Control of displacement front in a model of immiscible two-phase flow in porous media

Cited by 6 publications

References 5 publications

Singularities in Euler Flows: Multivalued Solutions, Shockwaves, and Phase Transitions

Singularities in Euler Flows: Multivalued Solutions, Shockwaves, and Phase Transitions

Singularities in one-dimensional Euler flows

Experimental investigation of the functional mechanism of methane displacement by water in the coal

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