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Papers by Marc Sin
Computational & Applied Mathematics, 2006
We study the Riemann problem with forward combustion due to injection of air into a porous medium... more 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 cutoff in Anhenius' 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 bumed 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 i nd strengths.
Computational & Applied Mathematics, 2006
We study the Riemann problem with forward combustion due to injection of air into a porous medium... more 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 cutoff in Anhenius' 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 bumed 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 i nd strengths.