Maximal energy accumulation in a superadiabatic filtration combustion wave

Aldushin, A. P.; Rumanov, Igor; Matkowsky, B. J.

doi:10.1016/s0010-2180(98)00163-1

“…Remark 7.6. We conclude that this model does not support case (b) of Aldushin et al [4] that they call the reaction trailing structure.…”

Section: Hot Downstream Combustioncontrasting

confidence: 90%

“…In this section we also discuss the Rankine-Hugoniot jump conditions for the combustion wave. In Section 5 we prove that for the physical parameters considered in this paper, there are no resonances between waves, as opposed to the case analyzed by Aldushin et al in [4]. As a consequence of the absence of resonances, we obtain two distinct temperature relationships for the combustion front, which we call the hot upstream and the hot downstream combustion cases.…”

Section: Aj De Souza Iy Akkutlu and D Marchesin 29supporting

confidence: 49%

“…A large number of studies on the structure of the combustion front have been reported since 1950s, see [1,2,3,4,5,6,8,20,21,23,26], for instance. These studies did not take into account other waves that occur in the combustion problem.…”

Section: Introductionmentioning

confidence: 99%

“…We develop simplifi ed theoretical models for forward (co-flow) combustion under varying boundary conditions and obtain the wave sequences in the Riemann solution. The formulation of the problem is the same as in [4], while the nomenclature follows [1].…”

Section: Introductionmentioning

confidence: 99%

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Wave sequences for solid fuel adiabatic in-situ combustion in porous media

Souza¹,

Akkutlu²,

Marchesin³

2006

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Abstract.We study the Riemann problem with forward combustion due to injection of air into a porous medium containing solid fuel. We neglect air compressibility and heat loss to the rock formation. Given initial reservoir and injection conditions, we prove that there is a unique time asymptotic wave sequence for combustion with complete oxygen consumption. The sequence consists of a region of unburned air at injection temperature, a warming discontinuity, a hot region with unburned air, a combustion wave and a region with burned air and unburned fuel at the initial reservoir temperature. The waves have very different speeds, and therefore they cannot be detected in laboratory experiments that focus on the combustion wave. However, they should occur in fi eld scale.By introducing a cut-off in Arrhenius' law, the reaction rate vanishes at reservoir temperature, and two types of wave sequences are possible. One was already described. The other occurs for incomplete oxygen consumption. In this case, the wave sequence contains another wave, i.e., there is another region ahead of the combustion wave containing incompletely burned air at reservoir temperature, and a gas composition discontinuity that moves fast. However, instead of a unique solution for each Riemann data, there is a one parameter family of wave speeds and strengths.This multiplicity of solutions may to be due to the cut-off.

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“…It is called superadiabatic combustion, which is desirable in other practical applications. The structure of such a combustion wave was analyzed in [4]. …”

Section: Remark 52mentioning

confidence: 99%

Wave sequences for solid fuel adiabatic in-situ combustion in porous media

Souza¹,

Akkutlu²,

Marchesin³

2006

Comput. Appl. Math.

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Abstract.We study the Riemann problem with forward combustion due to injection of air into a porous medium containing solid fuel. We neglect air compressibility and heat loss to the rock formation. Given initial reservoir and injection conditions, we prove that there is a unique time asymptotic wave sequence for combustion with complete oxygen consumption. The sequence consists of a region of unburned air at injection temperature, a warming discontinuity, a hot region with unburned air, a combustion wave and a region with burned air and unburned fuel at the initial reservoir temperature. The waves have very different speeds, and therefore they cannot be detected in laboratory experiments that focus on the combustion wave. However, they should occur in fi eld scale.By introducing a cut-off in Arrhenius' law, the reaction rate vanishes at reservoir temperature, and two types of wave sequences are possible. One was already described. The other occurs for incomplete oxygen consumption. In this case, the wave sequence contains another wave, i.e., there is another region ahead of the combustion wave containing incompletely burned air at reservoir temperature, and a gas composition discontinuity that moves fast. However, instead of a unique solution for each Riemann data, there is a one parameter family of wave speeds and strengths.This multiplicity of solutions may to be due to the cut-off.

show abstract