InterPore2021

ANALYTICAL SOLUTION FOR THE POPULATION-BALANCE MODEL DESCRIBING FOAM

2 Jun 2021, 15:45

15m

Oral Presentation (MS6-A) Physics of multi-phase flow in diverse porous media MS6-A

Speaker

Prof. Grigori Chapiro (Universidade Federal de Juiz de Fora)

Description

Recently a simple but robust model was proposed for describing foam flow in porous media. Numerical solutions to this model were found to be in good agreement with CT scanned nitrogen foam flow experiments in Betheimer sandstone cores, where the foam was stabilized by Alpha Olefin Sulfonate (AOS) surfactant, Simjoo and Zitha 2015. Here, we present analytical solutions for a further simplified version of this population balance foam model. We investigate and classify possible solutions for different injection conditions and varying kinetic foam generation and coalescence parameters, see Lozano et al. 2021. We found that the analytical solutions' behavior changes at the transition between two regions, similar to rarefaction/shock solutions for the Buckley-Leverett equation. Region I presents a traveling wave solution in a good match with two different sets of experimental data. In this region, the analytical solutions also match the original model's numerical simulations. Region II corresponds to solutions as a sequence of waves: one spreading wave and one traveling wave pointing out to flow profiles different from those found in the experiments.

References

[1] M. Simjoo and P. L. J. Zitha. Modeling of foam flow using stochastic bubble population model and experimental validation.Transport in Porous Media,107(3):799–820, 2015.
[2] L. F. Lozano, R. Z. Quispe, and G. Chapiro. Mathematical properties of the foam flow in porous media. Computational Geosciences, 2021.
[3] Valdez, A. R.; Rocha, B. M.; Da Fonseca Façanha, J. M.; De Souza, A. V. O.; Pérez-Gramatges, A.; Chapiro, G.; Santos, R. W. Foam-Assisted Water-Gas Flow Parameters: From Core-Flood Experiment to Uncertainty Quantification and Sensitivity Analysis. Transport in Porous Media, 2021.