A New approach to pseudofunctions for multiphase flow in stratified porous media

Considering flooding of stratified reservoirs, this paper focus on the case with significant gravity effects. Assuming the fluids are incompressible, we develop a new VerticaI Equilibrium (VE) theory, and introduce pseudo-functions to describe the displacement problem. From the form of the pseudorized equations we conclude that previously proposed analytical methods for assessing flood performance may lead to erroneous results due to incorrect treatment of gravity. We derive travelling wave solutions for the pseudorized problem and compare an example case with numerical simulations. We show that the travelling wave solution can be formulated as a new generalized Dietz solution which accounts for reservoir stratifications and capillary effects. Previously published interface models are obtained in the limit of zero capillary pressure. We derive several results for stationary displacement, and introduce a graphical method for assessing the vertical sweep efficiency under these circumstances.