Homogénéisation numérique / Numerical Upsacaling

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Homogénéisation numérique / Numerical Upsacaling


Understanding and controlling the effects of different scales in porous media requires more and more systematic use of numerical simulation and upscaling methods.

The aim of this course is to present flow modeling methods in porous media, which take into account physical phenomena that take place on a lower (microscopic) scale.

The following topics will be developed:

1. Multiscale modeling of multiphase flow in porous media.

2. Introduction to homogenization (upscaling) of partial differential equations by the technique of two-scales asymptotic expansions.

3. Derivation of effective equations governing single and multiphase flows in porous media.

4. Numerical computation of effective parameters: absolute permeability, porosity, relative permeabilities, capillary pressure, dispersion, etc.

5. Description and use of a platform for the numerical computation of effective flow properties.

6. Applications to the numerical modeling of multiphase flows in heterogeneous porous media resulting from problems of petroleum engineering.

7. Realization of a class project using a reservoir simulator (Reveal, Eclipse, etc.) to simulate multiphase flows in heterogeneous porous media: Application to secondary oil recovery.


Key word : Upscaling, Homogenization, Reservoir Simulation


This course will present different techniques of mathematical and numerical modeling of multiphase flow in porous media and their applications to petroleum engineering.

Introduction to mathematical and numerical methods of homogenization (upscaling) of flow and transport properties in petroleum reservoirs.

The course will be followed by a multiscale numerical simulation class project for the treatment of typical oil engineering situations using a reservoir simulator

Volume horaire

  • CM : 19.5
  • TD : 19.5
  • TP : 12


Project + Examination

En bref

Crédits ECTS 4

Nombre d'heures 51

Niveau d'étude BAC +5




Amaziane Brahim

Tél : +33 559407547

Email : brahim.amaziane @ univ-pau.fr