[Internship postion] Numerical study of species transport across porous media during immiscible drainage

Institute GeM is a Joint Research Unit supervised by Nantes Université, Centrale Nantes and the CNRS. Founded in 2004, the objective was to bring together within the same laboratory all the skills in the Nantes Saint-Nazaire area in the fields of civil engineering, materials and processes, modelling and simulation in structural mechanics.

The mission of our research institute is to propose innovative manufacturing processes and simulation tools adapted to the dimensioning and life cycle management of products, structures and works, taking into account the influence of severe stresses and environmental actions.

The research carried out at GeM is balanced between advanced and applied research. The unit is characterised by its significant and differentiating testing resources, with several technological platforms: civil engineering (test slab, durability characterisation, environment), manufacturing (bio-printing and additive manufacturing, composite processes), materials (X-ray diffraction, composite durability), structures (membrane structures, static and dynamic tests)

The projects are conducted in close collaboration with industry, project owners and companies specialising in mechanical and civil engineering. It is also the subject of scientific collaboration with other French and foreign research centres, in particular as part of European programmes or networks.

Context & problem statement

What happens when a third species is advected and diffuses within a bi-phasic immiscible porous media flow that is a priori conditionally stable ? The process of immiscible displacement of a wetting fluid by injection of a non-wetting fluid is a process known as drainage and is known to manifest as instabilities of distinct regimes (viscous and capillary fingering). The role of a third species in such a scenario is played, for instance a) during CO2 sequestration, by H+ ions in an acidified CO2-brine which is subject to buoyancy pressure against a sealing caprock a priori saturated by brine, b) during rain water infiltration alternated by extreme drying events, by contaminant species in polluted soils. The project aims to model and analyze the conditional loss of stability of an advancing drainage front while accounting for presence of such third species, its transport via diffusion within bulk of the fluids, as well as across their interface. The tools will be continuum-scale Cahn-Hilliard fluid modeling, associated generalized Darcy-like flow model, Traveling wave (TW) analysis and Linear stability analysis (LSA).

Scientific approach & internship objectives

The project is structured into 4 phases as follows:

1. Literature review to identify, in the context of CO2 sequestration and ground water flow, the order of magnitude of the transport coefficients (permeability of fluids, diffusivity of species) & dissolution rate of CO2 in the case of sequestration.
2. Formulating a minimal model and identifying the dimensionless numbers that govern the phenomena.
3. Resolution of the coupled system involving advection-diffusion, Darcy flow and dissolution model using FD method to identify the regimes, (for instance for varying injection rates), of manifestation of TWs as diffused shocks
4. Performing LSA on TW solutions to identify conditional stability and its consequence on species transport.

During the internship, the student will apply skills acquired in Numerical methods & analysis, be able to collaborate with a dynamic research group & have the opportunity to learn from leading researchers.

Internship advisors

• Siddhartha Harsha OMMI (Maître de Conférences), Institut de Génie Civil et Mécanique (GeM), Ecole Centrale de Nantes
• Giulio SCIARRA (Professeur des Universités), Institut de Génie Civil et Mécanique (GeM), Ecole Centrale de Nantes

Additional information

• The internship will be conducted in its entirety at the Institut de Génie Civil et Mécanique (GeM), Ecole Centrale de Nantes, 1, rue de la Noë, 44321 Nantes cedex 03, FRANCE.
• The internship will start on 23 February 2026 and lasts 6 months (possible extension to a PhD thesis).
• The gratification will be 4.35 €/hour (≈ 600 €/month) according to the French law.
• The internship is funded by the Projet TRANSEC (TRANsport de contaminants dans les géomatériaux influencé par des conditions de SEChage extrêmes) financed by the region PdL.

Required competences:

• We are looking for an enrolled master student in Civil Engineering or Mechanical Engineering or Physics (Computational, Applied, Mathematical) being interested in applied research activities and numerical methods for PDEs and numerical analysis. 
• Familiarity with numerical methods for coupled problems.
• Strong programming skills using Python and Matlab.
• Fluent in written/spoken English.