10 minutes of reading
Whether for the development of products, processes or services, mathematics is essential to the technological innovation led by IFPEN. In particular, it plays a vital role in the field of numerical simulation, in order to incorporate increasingly complex phenomena and facilitate the design and development of new technological solutions.
Drawn from research projects conducted at IFPEN, the three examples described here illustrate the essential contribution of numerical methods to the description of fluids for problems related to the underground environment. They have been used to overcome three recurrent difficulties posed by the considerable non-linearities of speed, pressure and mixture laws characterizing flows in porous media. Overcoming these obstacles helps improve the performance of simulators used in the field of geosciences.
Beyond the advances made, these examples perfectly reflect the philosophy of fundamental research at IFPEN, with high-quality scientific partnerships involving international PhD students.
A finite volume method for solving the Richards equation in a heterogeneous porous medium
The Richards equation is used to simulate water flows in partially saturated soils. Its resolution is difficult in highly heterogeneous porous media where capillary pressure can strongly vary in space.
A new numerical resolution method for simulating the thermodynamics of multiphase mixtures
Flow simulation in the underground environment involves complex multiphase mixtures in which phases can appear and disappear over time.
Adaptive model for flow simulation in heterogeneous porous media
The calculation of water and gas flows in complex and heterogeneous media is central to technological solutions aimed at tackling current climate and energy challenges.