Geometric singular perturbation analysis of oxidation heat pulses for two-phase flow in porous media |
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Authors: | S Schecter D Marchesin |
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Institution: | (1) Mathematics Department, North Carolina State University, 27695 Raleigh, NC, USA;(2) Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, RJ, Brazil |
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Abstract: | When air or oxygen is injected into a petroleum reservoir, and oxidation or combustion is induced, a combustion front forms if heat loss to the surrounding rock formation is negligible. Here, we employ a simple model for combustion, which takes into account oil viscosity reduction, but neglects gas density dependence on temperature and uses a simplified oxidation reaction. We show that for small heat loss, this combustion front is actually the lead part of a pulse, while the trailing part of the pulse is a slow cooling process. If the heat loss is too large, we show that such a pulse does not exist. The proofs use geometric singular perturbation theory and center manifold reduction.Dedicated to Constantine Dafermos on his 60th birthdayThis work was supported in part by: CNPq under Grant 300204/83-3; CNPq/NSF under Grant 91.0011/99-0; MCT under Grant PCI 650009/97-5; FINEP under Grant 77.97.0315.00; FAPERJ under Grants E-26/150.936/99 and E-26/151.893/2000; NSF under Grant DMS-9973105. |
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Keywords: | combustion porous medium multiphase flow conservation laws |
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