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Development of numerical methods for reactive transport; Developpement de methodes numeriques pour le transport reactif

Abstract

When a radioactive waste is stored in deep geological disposals, it is expected that the waste package will be damaged under water action (concrete leaching, iron corrosion). Then, to understand these damaging processes, chemical reactions and solutes transport are modelled. Numerical simulations of reactive transport can be done sequentially by the coupling of several codes. This is the case of the software platform ALLIANCES which is developed jointly with CEA, ANDRA and EDF. Stiff reactions like precipitation-dissolution are crucial for the radioactive waste storage applications, but standard sequential iterative approaches like Picard's fail in solving rapidly reactive transport simulations with such stiff reactions. In the first part of this work, we focus on a simplified precipitation and dissolution process: a system made up with one solid species and two aqueous species moving by diffusion is studied mathematically. It is assumed that a precipitation dissolution reaction occurs in between them, and it is modelled by a discontinuous kinetics law of unknown sign. By using monotonicity properties, the convergence of a finite volume scheme on admissible mesh is proved. Existence of a weak solution is obtained as a by-product of the convergence of the scheme. The second part is dedicated to coupling  More>>
Authors:
Publication Date:
Dec 15, 2006
Product Type:
Thesis/Dissertation
Report Number:
CEA-R-6149
Resource Relation:
Other Information: TH: These mathematiques; [115 refs.]
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ALGORITHMS; ANALYTICAL SOLUTION; CHEMICAL REACTION KINETICS; COMPUTERIZED SIMULATION; CONCRETES; CONVERGENCE; DIFFUSION; FINITE ELEMENT METHOD; JACOBIAN FUNCTION; LEACHING; LEAST SQUARE FIT; MESH GENERATION; MINIMIZATION; NONLINEAR PROBLEMS; PRECIPITATION; RADIOACTIVE WASTE DISPOSAL; URANINITES
OSTI ID:
20943026
Research Organizations:
Universite de Provence, 13 - Marseille (France); CEA Saclay, Dept. Modelisation de Systemes et Structures, Service Fluides Numeriques Modelisation et Etudes, Lab. de Modelisation des Transferts en Milieux Solides, 91 - Gif sur Yvette (France)
Country of Origin:
France
Language:
French
Other Identifying Numbers:
TRN: FR0702768096479
Availability:
Available from INIS in electronic form
Submitting Site:
FRN
Size:
239 pages
Announcement Date:
Dec 13, 2007

Citation Formats

Bouillard, N. Development of numerical methods for reactive transport; Developpement de methodes numeriques pour le transport reactif. France: N. p., 2006. Web.
Bouillard, N. Development of numerical methods for reactive transport; Developpement de methodes numeriques pour le transport reactif. France.
Bouillard, N. 2006. "Development of numerical methods for reactive transport; Developpement de methodes numeriques pour le transport reactif." France.
@misc{etde_20943026,
title = {Development of numerical methods for reactive transport; Developpement de methodes numeriques pour le transport reactif}
author = {Bouillard, N}
abstractNote = {When a radioactive waste is stored in deep geological disposals, it is expected that the waste package will be damaged under water action (concrete leaching, iron corrosion). Then, to understand these damaging processes, chemical reactions and solutes transport are modelled. Numerical simulations of reactive transport can be done sequentially by the coupling of several codes. This is the case of the software platform ALLIANCES which is developed jointly with CEA, ANDRA and EDF. Stiff reactions like precipitation-dissolution are crucial for the radioactive waste storage applications, but standard sequential iterative approaches like Picard's fail in solving rapidly reactive transport simulations with such stiff reactions. In the first part of this work, we focus on a simplified precipitation and dissolution process: a system made up with one solid species and two aqueous species moving by diffusion is studied mathematically. It is assumed that a precipitation dissolution reaction occurs in between them, and it is modelled by a discontinuous kinetics law of unknown sign. By using monotonicity properties, the convergence of a finite volume scheme on admissible mesh is proved. Existence of a weak solution is obtained as a by-product of the convergence of the scheme. The second part is dedicated to coupling algorithms which improve Picard's method and can be easily used in an existing coupling code. By extending previous works, we propose a general and adaptable framework to solve nonlinear systems. Indeed by selecting special options, we can either recover well known methods, like nonlinear conjugate gradient methods, or design specific method. This algorithm has two main steps, a preconditioning one and an acceleration one. This algorithm is tested on several examples, some of them being rather academical and others being more realistic. We test it on the 'three species model'' example. Other reactive transport simulations use an external chemical code CHESS. For a realistic case of Uraninite leaching, accelerated Picard methods divide the CPU cost of standard Picard's by three and the number of iteration by five. (author)}
place = {France}
year = {2006}
month = {Dec}
}