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Modélisation mathématique et numérique de la cristallisation fractionnée avec couplage des échanges chimiques et du transport différentiel magma-solide dans les réservoirs magmatiques

Abstract : In this work we study the modelling of the crystallization of a closed magma chamber. The physical and mathematical model couples three elementary phenomena: solidification, sedimentation and chemical reactions between the solid and the magmatic liquid. Adimensionalizing the partial differential equations make two parameters appear: they express the respective ratios of the solidification velocity to the transport velocity, and of the chemical kinetics to the transport velocity. The relative transport velocity between the solid and the liquid, the solidification velocity and the chemical partition law between the solid and the liquid are supposed to be known; this last one may be non-linear and applied for major elements. The model is written for one chemical component. It is splitted into two submodels, the crystallization/sedimentation model and the reactive transport model. The first is expressed by an hyperbolic partial differential equation and is solved by a three-point scheme, the second is solved using non-centered schemes. The computing program is written in Fortran 90, it is then validated by theoretical methods such as the method of characteristic curves, analytical computations or by qualitative considerations. Numerical simulations show that, for some values of the dimensionless parameters and for some shapes of the chemical partition curves, the chemical composition of the magma chamber can be non homogeneous, particularly bimodal, starting from homogeneous initial conditions. The degree of this bimodality notably depends on the shape of the chemical partition law. This model provides an intellectual framework to discuss the phenomena responsible for the variety of composition of magmatic rocks, notably in the same province. It shows in particular that the coupling between three elementary phenomena is enough to account for the bimodality, or more generally the appearance of discontinuities of chemical compositions, without taking into account any additional phenomenon.
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https://tel.archives-ouvertes.fr/tel-00438843
Contributor : Andrée-Aimée Toucas <>
Submitted on : Friday, December 4, 2009 - 6:34:19 PM
Last modification on : Wednesday, June 24, 2020 - 4:18:18 PM
Long-term archiving on: : Thursday, June 17, 2010 - 9:08:15 PM

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  • HAL Id : tel-00438843, version 1

Citation

Morad Lakhssassi. Modélisation mathématique et numérique de la cristallisation fractionnée avec couplage des échanges chimiques et du transport différentiel magma-solide dans les réservoirs magmatiques. Planète et Univers [physics]. Ecole Nationale Supérieure des Mines de Saint-Etienne, 2009. Français. ⟨tel-00438843⟩

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