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Laboratory of Applied Mathematics

EOR using foam

International collaboration between UFJF (Federal University of Juiz de Fora, Brazil), TU Delft (Delft University of Technology, The Netherlands), and PUC-Rio (Pontifical Catholic University of Rio de Janeiro, Brazil), supported by Shell Brazil.

Phase II: Advancing mathematical and computational modeling to support the implementation of “Foam-assisted WAG” technology in pre-salt reservoirs (2023– )

The project has a strong multidisciplinary focus, integrating mathematical analysis and numerical simulations conducted at UFJF, experimental investigations carried out at PUC-Rio, and physical modeling guided by renowned foam EOR experts from TU Delft.

Main objectives:

  • Investigate field project risks and enhance understanding of foam formation and displacement in porous media, considering foam-assisted water alternating gas (FAWAG) technology in Pre-salt reservoirs.
  • Develop analytical methods and numerical tools to test and validate commercial simulators.
  • Apply numerical and analytical methods to realistic scenarios, including laboratory experiments and Pre-salt reservoir data, with a focus on physical modeling, mathematical analysis, and numerical simulations of gas flow and surfactant solutions in carbonates.

Main deliverables:

  • A simplified theoretical model of foam flow that allows for detailed analytical study and is suitable for foam generation, including solving the Riemann problem and finding solutions with traveling waves.
  • A computational simulator that combines finite volume and finite element methods, validated by analytical results and experimental data, capable of simulating complex multiphase flows including foam.
  • Theoretical analyses including the dynamics of surfactant adsorption and its influence on foam generation in complex scenarios, with validation and adjustment of the models using experimental data from laboratories and real reservoirs.

Phase I: Mathematical and computational modeling of foam injection as an enhanced oil recovery technique applied to Brazil pre-salt reservoirs (2018–2023)

The project has a strongly multidisciplinary appeal bringing together the mathematical analysis and numerical simulations performed in UFJF, experimental investigation realized in PUC-Rio and physical modeling assisted by renowned experts in foam EOR from TU Delft.

Main objectives:

  • Improve the understanding of physics and mathematics describing the foam displacement in porous media as an enhanced oil recovery (EOR) technique applied to Brazil pre-salt reservoirs.
  • Develop analytic and numerical methods that can be used to test and validate commercial simulators.

Main deliverables:

  • Formulation of simple models describing foam displacement, that can be investigated mathematically.
  • Formulation and implementation of precise and robust numerical methods to simulate foam displacement in porous media.
  • The detailed analysis of the solutions obtained mathematically and numerically allowing the validation of commercial simulators.
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