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Mathematical properties of the foam flow in porous media

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Abstract

Foam is used in enhanced oil recovery to improve the sweep efficiency by controlling the gas mobility. A common way to describe the foam displacement is by using population balance models, which consider the foam texture as part of the gas phase. Numerical simulation of such equations presents serious difficulties connected to the high non-linearity in the fractional flow. The linear kinetic model is studied mathematically for large initial reservoir water saturation and all possibilities of injection saturation. It was observed that the model contains some structural instabilities, i.e., a small variation in some parameters leads to qualitatively different solutions. One of these solutions presented localized decay in relative gas mobility, indicating that this behavior is due to the equations’ mathematical properties.

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Acknowledgements

The authors are grateful to Prof. Dan Marchesin and Prof. Pacelli Zitha for their suggestions and advice during this work elaboration. The authors thank A. Chapiro for pointing some typos and improving the language of this text. The authors thank the reviewer for valuable suggestions improving this text.

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Authors and Affiliations

  1. Laboratório de Matemática Aplicada (LAMAP), Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil

    Luis F. Lozano, Rosmery Quispe Zavala & Grigori Chapiro

  2. Programa em Modelagem Computacional, Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil

    Rosmery Quispe Zavala

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  1. Luis F. Lozano
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  2. Rosmery Quispe Zavala
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  3. Grigori Chapiro
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Correspondence to Grigori Chapiro.

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This research was carried out in association with the ongoing R&D project registered as ANP 20715-9, “Modelagem matemá-tica e computacional de injeção de espuma usada em recuperação avançada de petróleo” (Universidade Federal de Juiz de Fora (UFJF) / Shell Brasil / ANP) – Mathematical and computational modeling of foam injection as an enhanced oil recovery technique applied to Brazil pre-salt reservoirs, sponsored by Shell Brasil under the ANP R&D levy as “Compromisso de Investimentos com Pesquisa e Desenvolvimento”. This project is carried out in partnership with Petrobras. G.C. was supported in part by CNPq grant 303245/2019-0.

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Lozano, L.F., Zavala, R.Q. & Chapiro, G. Mathematical properties of the foam flow in porous media. Comput Geosci 25, 515–527 (2021). https://doi.org/10.1007/s10596-020-10020-3

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