Hydrocarbons Migration in Basin Modelling: is the Combined Use of Finite Element and Control Volume Possible?

The problem we consider in this paper concerns the treatment of hydrocarbons migration in basin simulators. Generaly, migration is computed using the classical numerical schemes developped for reservoir simulators. The classical approach has been used in order to perform a reference solution. In this paper, we present a new approach where a pressure equation is established and solved with a finite element method; the saturation equation is solved with a control volume method. We show that mixing these two numerical approaches can only be possible if the numerical scheme is localy conservative for the total flux (total flux = water flux + hydrocarbons flux). In order to respect this constraint, we suggest to distribute the fluid mass balance error on the total flux approximations. Results on several 1D examples are very close to those obtained on the reference solution. Future works are necessary to validate this approach, for 2D and 3D cases, and for compressible fluids.