New Mechanistic Approach to Trapped Foam in Population-Balance Model Enabling Improved Prediction of N2 and CO2 Foams Rheology in Porous Media

Abstract

Abstract As reported in the literature, CO2 foam/emulsion flow in porous media is generally weaker than N2 foam under the same experimental conditions. Additionally, the steady-state CO2-foam quality scan has relatively a more flattened shape in the low-quality foam regime, besides the foam apparent viscosity showing a more gradual transition from the high-quality to low-quality foam regime. These characteristics are not fully captured by the existing foam models and could be indicative of different underlying physics in CO2 foam. Our new model is based on the trapped bubble concept at the pore level. On trapping, the trapped foam lamellae undergo a series of movement and merging events driven by gas diffusion, and they end up at a stationary position near the pore throat. In our approach, the yield stress of trapped foam, which is the total pressure gradient resulting from the effective number of lamellae in the direction of flow, is taken equal to the flowing foam pressure gradient estimated through the bubble population-balance approach. In this new model, the maximum flowing foam texture is updated based on the trapped foam texture established. There is, therefore, a consequential dependance of the flowing foam pressure gradient on the trapped foam texture. Automatic parameter regressions and sensitivity studies have been conducted with both an existing population-balance model and our new model. The results show that both models can fit the N2-foam data, but our new model fits the CO2-foam steady-state data significantly better than the existing population-balance model in both high-and low-quality flow regimes. Our analysis shows that the limiting capillary pressure and the flowing foam texture are crucial for correctly fitting the transition between the high- and low-quality regimes. Matching the gradual transition in the steady-state CO2-foam data helps better estimate the foam generation/coalescence rates. An important novel feature of our model is that it distinguishes the flowing and trapped foam texture, which was not achieved in the literature. With this new feature capturing the physics of trapped foam, our model paves the way for further understanding of the mechanisms of CO2 foam/emulsion flow in porous media for various applications.