[Internship postion] Numerical study of species transport across porous media during immiscible drainage
il y a 2 jours
Description 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: 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. Formulating a minimal model and identifying the dimensionless numbers that govern the phenomena. 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 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, Nantes cedex 03, FRANCE. The internship will start on 23 February and lasts 6 months (possible extension to a PhD thesis). The gratification will be 4.35 €/hour (≈ €/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. Profile 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. Starting date -02-23
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