Analytical Solution for the Population-Balance Model Describing Foam Displacement

Journal article (2021)

Authors

Rosmery Q. Zavala Universidade Federal de Juiz de Fora

Luis F. Lozano Universidade Federal de Juiz de Fora

P.L.J. Zitha Reservoir Engineering -

Grigori Chapiro Universidade Federal de Juiz de Fora

Research Group

Reservoir Engineering () (TU Delft)

Partial Differential Equations Porous media Foam flow Traveling waves

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http://resolver.tudelft.nl/uuid:0eaf968b-c1e2-438f-bf30-7bfebc6c5883

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Published Date

2021

Language

English

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Faculty

Civil Engineering & Geosciences

Department

Geoscience and Engineering

Research Group

Reservoir Engineering

Abstract

We investigate and classify possible analytical solutions for a simplified version of the foam bubble population model, by varying injection conditions and kinetic foam generation parameter. We prove that the behavior of the analytical solutions changes at the transition between two regions, similar to rarefaction-shock solutions for the Buckley-Leverett equation. In one region (region I), the solutions are in the form of traveling waves, in rather good agreement with CT scanned foam experiments and numerical simulations reported in Simjoo and Zitha (2015). In region II, however, corresponds to solutions as a sequence of waves: one spreading wave and one traveling wave. These corresponding flow profiles are different from those found so far in the experiments.

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