Mathematical modelling of in-situ combustion for enhanced oil recovery.
In-situ combustion is an oil recovery technique in which air, or oxygen enriched
air is injected into a reservoir in order to displace the oil. Under suitable conditions
the oxygen will burn with part of the oil, raising the temperature of the
reservoir and reducing the viscosity of the oil, hence allowing it to flow more
A serious problem with mathematical modelling of in-situ combustion is that
of flame extinction due to grid block size effects. When modelling a field scale
process using finite difference techniques the grid block size will be far larger
than the flame length. Since parameters such as temperature and saturations
are averaged over a grid block they will be misrepresented in the Arrhenius
reaction rate equation, and the flame may die out.
The approach taken to overcome the problem is to decouple the flame from a
conventional finite difference simulator and solve separately for the reaction rate
and flame velocity. This is achieved using a steady state analysis that applies
a reduced set of the conservation equations in a moving frame over the flame
region, and solves the resulting eigenvalue problem using a shooting method.
The reaction rate and flame velocity determined by the steady state analysis
are then used to apply the 'thin flame' technique to the conventional simulator.
This treats the flame as a moving heat source and displacing pump, travelling
through the domain with the velocity obtained by the steady state analysis.
The steady - state analysis is compared with experimental results glvmg good
agreement for the flame parameters. The thin flame method produces excellent
agreement with the conventional simulator on laboratory scale simulations, and
on field scale simulations it greatly reduces the problems associated with grid
block size effects.