Numerical modeling of flow and transport in porous media

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Numerical modeling of flow and transport in porous media


Modeling of flow and transport in porous formations is important for both the management of petroleum reservoirs and environmental remediation. More recently, modeling multiphase flow received an increasing attention in connection with the disposal of radioactive waste and CO2 storage in geological formations.

Numerical modeling of flow and transport processes in porous media provides a formidable challenge and application field for high-performance computing. Relevant continuum-scale models include partial differential equations of elliptic, parabolic and hyperbolic type which are coupled through highly nonlinear coefficient functions. Here we attempt to give an introduction to the mathematics and the numerics behind reservoir simulation.


Number of hours

  • Travaux Dirigés : 12h
  • Cours Magistral : 27h

Form of assessment

First session

Second session

Continuous assessment: 50%

Final examination: 50%

Final examination length: 2 hours

Remedial examination: 100 %

Remedial examination length: 2 hours



During the course, fundamental principles governing subsurface single and multiphase flow and transport in porous media will be presented. This course will focus on the efficient solution of single and two-phase flow with finite volume methods. Numerical simulations will be presented using a homemade C++ code and the parallel multiphase flow simulator DuMuX.

The following themes are developed:

  • Flow and transport in porous media

  • Multiphase flow in porous media

  • Modeling petroleum reservoirs

  • Homogenization, finite and finite volumes methods

  • Description of a reservoir simulator

  • Numerical simulation of multiphase flow in porous media

The course will be followed by a numerical simulation class project for the treatment of typical subsurface engineering situations using a reservoir simulator. The project will be done in C ++ in the environment of DuMuX:

In brief

ECTS credits 4.0

Number of hours 39.0

Level of study Master degree level


Organizational unit

Administrative contact(s)

Secrétariat de Mathématiques

Email : secretariat-mathematiques @


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