ON THE NUMERICAL-SOLUTION OF NONLINEAR RESERVOIR FLOW MODELS WITH GRAVITY

Based on a two-phase fluid model for immiscible displacement in a poro us medium, we develop and analyse numerical solution techniques for ce rtain non-linear phenomena. Two different solution strategies for the treatment of gravity effects, which are non-trivial to model by existi ng solution techniques and may be of great influence in many practical flow situations, are presented. The solution procedures are based on an operator-splitting technique, combining the modified method of char acteristics with finite element techniques and adaptive grid refinemen t.