Modeling of Multi Phase Flow in Porous Media: Operator Splitting, Front Tracking, Interfacial Area and Network Models

In this work several new numerical methods and a new mathematical model related to multi phase flow in oil reservoirs have been developed, implemented and tested. The numerical difficulties in multi phase flow stem from the highly nonlinear nature of the equations. The solution can develop sharp fronts that travel through the reservoir. We have used front tracking to capture these fronts in our numerical methods. In addition corrected operator splitting for systems has been used and developed because of the advection dominated nature of the equations. The new mathematical model was developed to improve short comings of existing models and to include interfacial area as a new independent variable