Quench Front Progression in a Superheated Porous Medium： Experimental Analysis and Model Development

In case of accident at a nuclear power plant, water sources may not be available for a long period of time and the core heats up due to the residual power. Any attempt to inject water during core degradation can lead to quenching and further fragmentation of core material. The fragmentation of fuel rods and melting of reactor core materials may result in the formation of a ＂debris bed＂. The typical particle size in a debris bed might reach few millimeters （characteristic length-scale： 1-5 mm）. The two-phase flow model for reflood of the degraded core is briefly introduced in this paper. It is implemented into the ICARE-CATHARE code, developed by IRSN （Institut de radioprotection et de surete nucleaire）, to study severe accident scenarios in pressurized water reactors. Currently, the French IRSN sets up two experimental facilities to study debris bed reflooding, PEARL and PRELUDE, and validate safety models. The PRELUDE program studies the complex two phase flow （water/steam）, in a porous medium （diameter 180 mm, height 200 mm）, initially heated to a high temperature （400℃ or 700℃）. On the basis of the experimental results, thermal hydraulic features at the quench front have been analyzed. The two-phase flow model shows a good agreement with PRELUDE experimental results.

Modelling and applications of dissolution of rocks in geoengineering

The subsoil contains many evaporites such as limestone,gypsum,and salt.Such rocks are very sensitive to water.The deposit of evaporites raises questions because of their dissolution with time and the mechanical-geotechnical impact on the neighboring zone.Depending on the configuration of the site and the location of the rocks,the dissolution can lead to surface subsidence and,for instance,the formation of sinkholes and landslides.In this study,we present an approach that describes the dissolution process and its coupling with geotechnical engineering.In the first part we set the physico-mathematical framework,the hypothesis,and the limitations in which the dissolution process is stated.The physical interface between the fluid and the rock(porous)is represented by a diffuse interface of finite thickness.We briefly describe,in the framework of porous media,the steps needed to upscale the microscopic-scale(pore-scale)model to the macroscopic scale(Darcy scale).Although the constructed method has a large range of application,we will restrict it to saline and gypsum rocks.The second part is mainly devoted to the geotechnical consequences of the dissolution of gypsum material.We then analyze the effect of dissolution in the vicinity of a soil dam or slope and the partial dissolution of a gypsum pillar by a thin layer of water.These theoretical examples show the relevance and the potential of the approach in the general framework of geoengineering problems.

On 2D approximations for dissolution problems in Hele-Shaw cells

In this paper, we study the dissolution problems occurring in laterally large 3D systems with very small dimensions along the third coordinate, such as fractures or Hele-Shaw cells. On the basis of the scale separation assumption, we apply upscaling to the 3D pore-scale model using the volume averaging method to develop 2D averaged equations. The influence of the choice of momentum equations on the accuracy of the 2D Hele-Shaw model is discussed, and we show that the results obtained using Darcy-Brinkman equations are better than those obtained using Darcy’s law, because of the consideration of the viscous boundary layer. The validity and accuracy of the resulting 2D model are assessed based on comparisons with full 3D solutions for problems corresponding to the existence of geometrical 3D features to which a simple averaging procedure along a line(i.e., the height of the gap) perpendicular to the 2D plane cannot be applied, such as the dissolution of pillars. The results show that when Péclet and Reynolds numbers exceed certain limits, 3D effects must be considered. Moreover, natural convection effects are important when the Rayleigh number is large.