Dual permeability variably saturated flow and contaminant transport modeling of a nuclear waste repository with capillary barrier protection Michal Kuráz ˇ a,⇑ , Petr Mayer b , Vojte ˇch Havlíc ˇek a , Pavel Pech a , Jirka Pavlásek a a Czech University of Life Sciences Prague, Faculty of Environmental Sciences, Department of Water Resources and Environmental Modeling, Czech Republic b Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mathematics, Czech Republic article info Keywords: Richards equation Convection dispersion reaction equation Distinct unsaturated hydraulic properties Problem conditionality Matrix balancing abstract This paper presents a new release of the DRUtES computer program, a finite element numerical solver in one and two dimensions of flow and contaminant transport in a dual porosity variably saturated porous medium. The main part of this paper evaluates the capillary barrier based structure on the Richard – Litome ˇr ˇice nuclear waste facility in the Czech Republic. The barrier structure is evaluated for various cases under normal regime flow conditions and under emergency conditions caused by intense infiltration. The capillary barrier is based on the unsaturated hydraulic properties of gravel. A failure of the barrier function due to saturation is successfully sim- ulated, and is presented here. Ó 2011 Elsevier Inc. All rights reserved. 1. Introduction The problem of predicting fluid movement in an unsaturated/saturated zone is important in many fields, ranging from agriculture, via hydrology to technical applications of dangerous waste disposal in deep rock formations. The mathematical model of unsaturated flow was originally published by Richards [1]. Together with the convection–dis- persion–reaction equation a full contaminant transport model is formed. The Richards equation problem has undergone various investigations and numerical treatments. Its finite element solu- tion was originally published by Neuman in 1970 for several engineering applications, e.g. dam seepage modeling, see [2,3]. The existence and the uniqueness of its solution was discovered 10 years later, by Alt and Luckhaus [4]. A fundamental work analyzing a mass conservation numerical method for the Richards equation was published in 1990 by Celia et al. [5]. A new technique for adaptive time discretization was recently published by Kuráz ˇ et al. [6]. A new version of the DRUtES [7] computer code, a finite element numerical solver of contaminant transport in a dual porosity variably saturated porous medium, was recently released by Kuráz ˇ. This code was already presented in [6]. Com- pared to the previous release, the current version supports the two dimensional problem of variably saturated flow and sol- uble contaminant transport. The code is written in F-language – a subset of Fortran programming language, including the recent Fortran 2008 standard – coarrays (parallel computing support). The aim of this paper is to present the application of DRUtES to a real technical problem – an evaluation of an engineering barrier on the Richard – Litome ˇr ˇice nuclear waste repository. The barrier is evaluated for two distinct cases – under a normal flow regime (pseudo-steady-state flow conditions) – for a simulation time of 200 years, and under intense infiltration into an 0096-3003/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2011.08.109 ⇑ Corresponding author. E-mail address: michal.kuraz@fsv.cvut.cz (M. Kuráz ˇ). Applied Mathematics and Computation 219 (2013) 7127–7138 Contents lists available at SciVerse ScienceDirect Applied Mathematics and Computation journal homepage: www.elsevier.com/locate/amc