Pulsating linear in situ combustion: why do we often observe oscillatory behavior?

• Published in: Computational geosciences 2018-08, Vol.22 (4), p.1115-1134
• Main Authors: Bazargan, Mohammad, Kovscek, Anthony R.
• Format: Article
• Language: English
• Subjects: Additives; Air; Air injection; Air-fuel ratio; Catalysts; Combustion; Construction planning; Dimensionless analysis; Earth and Environmental Science; Earth Sciences; Flue gas; Gas composition; Geotechnical Engineering & Applied Earth Sciences; Hydrogeology; Mathematical Modeling and Industrial Mathematics; Metals; Original Paper; Oscillations; Oxygen enrichment; Parameter identification; Parameters; Propagation; Propagation velocity; Soil Science & Conservation; Stability; Stability analysis; Stoichiometry
• ISSN: 1420-0597; 1573-1499
• DOI: 10.1007/s10596-018-9741-9

We have studied simplified, pulsating, one-dimensional, in situ combustion processes. For two cases, with different reaction stoichiometry, oscillations in temperature, flue gas rate, and flue gas composition are demonstrated and the parameter space resulting in oscillatory behavior is identified. To understand the role of different parameters, linear stability of the problem is studied. Because linear stability analysis requires the solution of uniform front propagation, we investigated an asymptotic analytical solution of the problem. We found an original formula for the front propagation velocity. The analytical solution enabled us to define four dimensionless parameters including Zeldovich (Ze) number, Damkohler (Da) number, a specialized air-fuel ratio (B), and a ratio incorporating air and rock heat capacities (Δ 1 ). Using linear stability analysis, we show that the stability of the problem is also governed by these four parameters. Because Δ 1 ≈ 1 for typical laboratory conditions, the set of (Ze, Da, B) is used to construct the stability plane; consequently, several important design considerations are suggested. Both larger air injection rate and air enriched in oxygen increase the front propagation speed but push the system toward oscillatory behavior. Conversely, the introduction of catalysts and metal additives, that decrease the activation energy of reactions, increases the front speed and stability. Similarly, increasing the amount of fuel available for the combustion makes the design more stable and drives the combustion front to propagate more quickly.