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Accueil > Annuaire du LHyGeS

DI CHIARA ROUPERT Raphaël

Lecturer - University of Strasbourg (Maître de Conférences)

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au sein de l’équipe Processus Elémentaire et Modélisation

Adresse : 1 Rue Blessig - 67084 Strasbourg Cedex
(Bureau n° 339)
Contact : dichiara@unistra.fr
Tél : +33(0)3 6885 0429
Fax : +33(0)3 6885 0402

Research activity

Current research
- Dynamics of immiscible fluids (NAPL) in porous media : numerical simulation

Permeability field and streamlines
water injection, quarter-five spot case


- Modeling of organo-chlorine compounds transfer in the vadose zone and the soil-air interface
- Transfer of contaminants in continental hydro-systems

Ph.D. thesis

A method for the simulation of compressible three-phase flows is proposed taking into account gravity and capillary effects. Governing equations are written in a fractional flow formulation in terms of a global pressure equation and two saturation equations. The global pressure satisfying a « Total Differential » (TD) condition was introduced by [Chavent and Jaffré, 1986] to simplify the mathematical formulation of three-phase flows. Approximations using classical multiphase flow approaches have to deal with two capillary pressure gradients appearing in the two saturation equations (four linearized systems). However, due to the TD condition, the global formulation requires only the resolution of two systems (one for each saturation equation). Despite its recognized computational efficiency [Zangxin and Ewing, 1997], TD concept was not widely used. There are two mainly reasons ; one requires the relative permeability and capillary pressure curves to satisfy a TD condition, the volume factors and viscosities have to be evaluated at the global pressure value, and not at the corresponding phase pressure, which could lead to unacceptable errors for large capillary pressures which have been recently highlighted by [Amaziane and Jurak, 2008] for two phase compressible flows.

In absence of experimental three-phase data, we described a first class of TD interpolation introduced in 1985 to construct three-phase data. Regularity, monotonicity and bounded constraints ensure that relative permeabilities are « physical ». Thus, a constrained optimization procedure is used to determine the preliminary secondary variables of the fractional flow from the effective saturation ternary diagram. The obtained three-phase relative permeabilities are compared to those obtained by Stone’s model.

Another TD interpolation class approach recently developped by [Chavent, 2008] is also implemented. Compared to the first formulation, the new formulation is equivalent to the classical formulation with the computational efficiency of the original formulation. The determination of a global capillary function over the ternary diagram is the key to TD-three-phase data. We discuss the construction of this global capillary function using C1 composite finite element, in particular the boundary conditions which need to be satisfied for the three-phase data to honor given two-phase data on the boundary of the ternary diagram [di Chiara Roupert et al.].

Two efficient numerical methods are then used to solve the global pressure equation and the two saturation equations for the water and oil phase. Discontinuous finite elements are used to approximate the convective term of the two saturation equations while the mixed finite element method (with mass lumping) is chosen to solve the global pressure equation and the diffusive part of the saturation equations. Numerical results are given for some analytical test cases and compared with a mean pressure approach.

Last part of the PhD thesis is dedicated to the muliphase transport equation using a mass transfer model for local non-equilibrium dissolution which have been proposed by [Miller et al.]
 ; [Abriola et al.]
 ; [Imhoff et al.]
 ; Quintard M., (2008). A first order mass exchange approximation is used and some mass exchange coefficient correlations are discussed

Selected publications

- di Chiara Roupert R., Chavent G., Schäfer G., "Three-phase compressible flow in porous media : Total Differential Compatible interpolation of relative permeabilities", Journal of Computational Physics 229 (2010), pp. 4762-4780 link

- di Chiara Roupert R., Schäfer G., Ackerer P., Quintard M., Chavent G., "Construction of three-phase data to model multiphase flow in porous media : Comparing an optimization approach to the finite element approach", C.R. Geoscience 342 (2010), pp. 855-863 link

Conferences

- di Chiara Roupert R., Schäfer G., Quintard M., Ackerer P., Chavent, G. and Côme J-M., A global pressure approach for modelling compressible multiphase flow in heterogenous porous media. Presented at the Computational Methods in Water Resources - XVII International Conference. San Francisco, USA, july 6-10, 2008 link

- Chavent, G., di Chiara Roupert R. and Schäfer G., Equivalent Global Pressure Formulation for Compressible Flows : Construction of a Global Capillary Function. Presented at the 3rd International Conference on Approximation Methods and numerical Modeling in Environment and Natural Resources MAMERN 2009. Pau - France, june 8-11, 2009.

- Chavent, G., di Chiara Roupert R. and Schäfer G., Numerical flow simulator for three-phase compressible flow in porous media based on a Total Differential Compatible condition. Presented at the conference Scaling’Up 08, Dubrovnik, october 13-16 2008.

- di Chiara Roupert R., Schäfer G., Quintard M., Chavent, G., Ackerer P. and Côme J-M., Numerical flow simulator for three-phase compressible flow in porous media based on a Total Differential Compatible condition. Presented at the Computational Methods in Water Resources - XVIII International Conference. Barcelona, Spain, june 21-24, 20010.

Teaching activities

- Fluid mechanics, rehology at the IUT Louis Pasteur de Strasbourg (Practical Hydraulics).

Curriculum

since 2009 Post-doc at the Laboratory of Hydrology and Geochemistry of Strasbourg (LHyGeS), UdS /ENGEES, CNRS ; Strasbourg, France)
2006-2009 Ph.D. thesis in fluid mechanics, Development of a multiphase flow multi component simulator at the University of Strasbourg (8/12/2009) link
2003-2006 Civil engineering master degree at the ENGEES

Voir en ligne : Equipe de recherche THeHa


[Chavent and Jaffré, 1986Chavent, G. and Jaffré, J., (1986), Mathematical models and finite elements for reservoir simulation. North Holland

[Zangxin and Ewing, 1997Zangxin, C., and Ewing, R.E., 1997, Comparison of various formulations of three-phase flow in porous media, Journal of Computational Physics 132, pages 362-373

[Amaziane and Jurak, 2008Amaziane B., and Jurak M., 2008, A new formulation of immiscible compressible two-phase flow in porous media, C.R. Mecanique 336

[Chavent, 2008Chavent, G., 2008, A new global pressure formulation for compressible three phase flows, Applicable Analysis, (88), 10 & 11, 1527–1541.

[di Chiara Roupert et al.di Chiara Roupert R., Chavent G., Schäfer G., 2010, Three-phase compressible flow in porous media : Total Differential Compatible interpolation of relative permeabilities", Journal of Computational Physics doi : 10.1016/j.jcp.2010.03.013

[Miller et al.Miller C.T., Christakos G., Imhoff, P.T., McBridge J.F., Pedit J.A. and Trangenstein J.A., 1998, Multiphase Flow and Transport Modeling in Heterogeneous Porous Media : Challenges and Approaches, Advances in Water Ressources 26, 2783-2796

[Abriola et al.Abriola, L.M., Pennel K.D., Weber W.J., Lang, J.R. and Wilkins M.D., 1999, Persistence and Interphase Mass Transfer of Liquid Organic Contaminants in the Unsaturated Zone : Experimental Observations and Mathematical Modeling. Vadose Zone Hydrology : Cutting Across Disciplines. Oxford University Press, pp 210-234.

[Imhoff et al.Imhoff, P.T., Farthing M.W. and Miller C.T., 2003, Modelling NAPL dissolution fingering with upscaled mass transfer rate coefficients, Advances in Water Ressources, 26(10), 1087-1111