A Study on Darcy versus Forchheimer Models for Flow through Heterogeneous Landfills including Macropores

Roman Winter,Holger Class,Archontoula Valsamidou,Bernd Flemisch

doi:10.3390/w14040546

Abstract

Flow through heterogeneous landfills that include macropores may occur under Reynolds numbers higher than those where Darcy’s law is valid. Extensions, such as a Forchheimer approach, may be required to include inertial effects. Our aim is developing predictive models for such landfills that are built from the low-level radioactive waste and debris of dismantled nuclear power plants. It consists of different materials, which after crushing result in a spatially heterogeneous distribution of porous-media properties in the landfills. Rain events or leakage, for example, may wash out radionuclides and transport them with the water flow. We investigate here the water flow and consider an inclusion of macropores. To deal with possibly high velocities, we choose the Forchheimer model and, taking different Forchheimer coefficients into account, compare it to the Darcy model. The focal points of the study are (i) the influence of the macropores on the flow field and (ii) the impact of the choice of the Forchheimer coefficient both on the solution and the computational effort. The results show that dependent on their size, macropores can dominate the flow field. Furthermore, Forchheimer coefficients introducing more inertial effects are associated with considerably higher runtimes.

Highlights

When developing predictive models for flow through heterogeneous landfills, flow velocities beyond the validity of Darcy’s law [1,2] may be encountered
Motivated by flow events in heterogeneous landfills from debris of dismantled nuclear power plants, we investigated the differences between Darcy’s law and the Forchheimer extension in the presence of macropores
Based on numerical scenarios, which all featured Reynolds numbers beyond the validity of Darcy’s law and, an expected influence of inertia effects, we found that different approaches to calculating Forchheimer were showing different behavior in representing inertia effects

Summary

Introduction

When developing predictive models for flow through heterogeneous landfills, flow velocities beyond the validity of Darcy’s law [1,2] may be encountered. To incorporate inertial effects at higher Reynolds-number regimes, there are approaches related to Forchheimer’s extension of Darcy’s law discussed in the literature [3,4,5,6]. We focus on flow events in heterogeneous landfills from debris of dismantled nuclear power plants after their clearance. Such debris consists mainly of demolished material such as concrete, plaster, bricks, metal, valves, piping, etc. According to [7], clearance is defined as “the removal of radioactive materials or radioactive objects within authorized practices from any further regulatory control by the regulating body”

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Conclusion