Tracking an In-Situ Combustion Front using the Thin Flame Technique

One of the major problems when modelling a field scale in-situ combustion process is that of grid block size effects. Since the grid block thickness is far greater than the flame thickness the length scale in our finite difference model will be too great to observe the sharp gradients occurring over a very short region in the field. The method introduced here overcomes this problem by decoupling the flame from the finite difference model and replacing it with an interface which moves through the region acting as a moving heat source and displacing pump. This representation of the flame in a finite difference model is known as the thin flame technique. In order to apply the thin flame technique we need to determine the velocity and reaction rate of the flame by a separate solution for the decoupled region. A steady state analysis is developed to solve for these parameters. This solves a reduced set of conservation equations over the burning region using a Lagrangian grid and the shooting method to determine the steady state solution: