A Mixture Model for Foamy Oil Flow in Porous Media

The processes of nucleation, bubble growth and finally the creation of connected gas during the pressure draw-down in an oil reservoir are discussed. From these mechanisms, possible descriptions of foamy oil production appear. One of these mechanisms is the creation of bubbles, small compared to pore sizes, which move with the oil phase and which push the oil out of the reservoir. If this mechanism occurs, a very simple model can describe the production of foamy oil. This model is obtained by establishing an equilibrium relation between gas fraction and pressure, which then is modified into a constitutive equation relating gas fraction and pressure in a dynamic context where supersaturation is present. Together with a mixture mass conservation equation and Darcy’s law, a two equation description of foamy oil production is obtained, depending on only two dimensionless numbers. It is thought that this is the most simple possible way to describe some particular cases of anomalous behavior of foamy oil. [Mention results]. The implications of the model for the production of foamy oil reservoirs are eventually discussed.