Wave sequences for solid fuel adiabatic in-situ combustion in porous media
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 field 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.
| Main Authors: | , , |
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| Format: | Digital revista |
| Language: | English |
| Published: |
Sociedade Brasileira de Matemática Aplicada e Computacional
2006
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| Online Access: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022006000100002 |
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| Summary: | 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 field 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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