Singularity of a Combustion Wave Profile: A Clue to the MultiComponent Theory for Liquid-Gas Filtration

Kokubun, M. A. Endo; Mailybaev, Alexei A.

doi:10.1137/16m1099558

Cited by 2 publications

(7 citation statements)

References 27 publications

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“…It turns out that the conditions at the singular point determine the macroscopic properties of the combustion wave, i.e., wave speed and combustion temperature, which ultimately determine the recovery efficiency. Recently, it was shown that such singularity is relevant for the problem of reactive immiscible displacement [15,16]. Here, we identify the emergence of a similar structure for reactive miscible displacement.…”

Section: Introductionmentioning

confidence: 67%

“…According to (3.38), this point is a singular point inside the wave and which is given by where the left-hand side of Eq. (3.41) is evaluated at the singular point, i.e., the resonance point [15,16]. If a travelling wave solution exists and passes through the singular point, it means that the upstream and downstream states must lie at opposite sides of the surface (3.37) projected into c 1 .…”

Section: Internal Profile Of the Combustion Wavementioning

confidence: 99%

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Reactive miscible displacement of light oil in porous media

Kokubun,

Gargar,

Marchesin

et al. 2020

Preprint

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We develop a theory for the problem of high pressure air injection into deep reservoirs containing light oil. Under these conditions, the injected fluid (oxygen + inert components) is completely miscible with the oil in the reservoir. Moreover, exothermic reactions between dissolved oxygen and oil are possible. We use Koval's model to account for the miscibility of the components, such that the fractional-flow functions resemble the ones from Buckley-Leverett flow. This allows to decompose the solution of this problem into a series of waves. We then proceed to obtain full analytical solutions in each wave. Of particular interest is the case where the combustion wave presents a singularity in its internal wave profile. Evaluation of the variables of the problem at the singular point determines the macroscopic parameters of the wave, i.e., combustion temperature, wave speed and downstream oil fraction. The waves structure was observed previously for reactive immiscible displacement and we describe it here for the first time for reactive miscible displacement of oil. We validate the developed theory using numerical simulations.

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Section: Introductionmentioning

confidence: 67%

Section: Internal Profile Of the Combustion Wavementioning

confidence: 99%

Reactive miscible displacement of light oil in porous media

Kokubun,

Gargar,

Marchesin

et al. 2020

Preprint

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“…I also thank him for various helpful discussions and for his enduring encouragement and guidance while I was a post-doc at IMPA. I also thank Prof. Alexei Mailybaev for pointing out reference [10] to me. I thank an anonymous referee for mentioning the relation of the current paper to the relaxation systems in [2,9,15].…”

Section: Acknowledgementsmentioning

confidence: 99%

“…However, this approach has three major drawbacks. First, there exists balance laws in Petroleum Engineering for which G fails to be invertible on points or hypersurfaces in state space [10,Chapter 5.1]. Secondly, in practice, inverting the accumulation function G explicitly is often an obstacle too hard to overcome, regardless whether G −1 exists theoretically.…”

Section: Introductionmentioning

confidence: 99%

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Constrained systems of conservation laws: a geometric theory

Reintjes¹

2017

Methods and Applications of Analysis

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We address the Riemann and Cauchy problems for systems of n conservation laws in m unknowns which are subject to m − n constraints (m ≥ n). Such constrained systems generalize systems of conservation laws in standard form to include various examples of conservation laws in Physics and Engineering beyond gas dynamics, e.g., multi-phase flow in porous media. We prove local well-posedness of the Riemann problem and global existence of the Cauchy problem for initial data with sufficiently small total variation, in one spatial dimension.The key to our existence theory is to generalize the m × n systems of constrained conservation laws to n×n systems of conservation laws with states taking values in an n-dimensional manifold and to extend Lax's theory for local existence as well as Glimm's random choice method to our geometric framework. Our resulting existence theory allows for the accumulation function to be non-invertible across hypersurfaces.M.R. is currently supported by FCT/Portugal through (GPSEinstein) PTDC/MAT-ANA/1275/2014 and UID/MAT/04459/2013. The mayor part of this work was done while M.R. was Post-Doctorate at IMPA in Rio de Janeiro, funded through CAPES-Brazil.

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Singularity of a Combustion Wave Profile: A Clue to the MultiComponent Theory for Liquid-Gas Filtration

Cited by 2 publications

References 27 publications

Reactive miscible displacement of light oil in porous media

Reactive miscible displacement of light oil in porous media

Constrained systems of conservation laws: a geometric theory

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