A New Stochastic Bubble Population Model for Foam Flow in Porous Media

Foam has been widely used as a mobility control agent for Improved and Enhanced Oil Recovery IOR/EOR, gas blocking, and acid diversion during matrix stimulation. The prediction of foam performance relies on macroscopic modeling. Traditionally, foam modeling approaches include fractional flow theories and population balance models. However, fractional foam models assume implicitly that foam is incompressible and do not account directly for the evolution of bubble population. The population balance models, instead, rely on the idea that foam mobility depends on bubble density and are more comprehensive. Yet, population balance models did not gain full acceptance thus far, because of their perceived complexity, with parameters that are hard to obtain experimentally. This article presents an improved foam model based on a simpler but realistic foam rheology and stochastic bubble generation ideas. Physical ideas in agreement with pictures emerging from recent foam studies using X-ray computed tomography form the basis for the new model.