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

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.

Well-posedness and variational numerical scheme for an adaptive model in highly heterogeneous porous media

“…In Section 3.1, two examples are proposed with two or more highly conductive channels and a background heterogeneity, as inspired by [32]. The examples in Sections 3.2 and 3.3 are based on the SPE10 benchmark study [8], where we consider, respectively, a single layer and multiple layers.…”

“…3.1 Highly permeable channels. This test case is based on the examples reported in [32] for a Darcy-Forchheimer system, and adapted here for our purposes. We consider in particular two configurations depending on the number of highly conductive channels that are present in the problem.…”

“…Unless stated otherwise, we fix the error tolerance δ = 0.1[−], yielding the critical Forchheimer number Fo δ ≃ 0.11[−] (cf. Section 2.6); moreover, as chosen in [32], we let m = 1, corresponding to the classical Darcy-Forchheimer model, with coefficient c F = 0.55[−] (cf. Section 2.5).…”

“…The paper is organized as follows: in Section 2, we summarize the various nonlinear laws considered by our model, we derive an expression for the flux threshold depending on the prescribed tolerance and we recall the adaptive and regularized models of [13,14]; in Section 3, we show the validity of the approach by experimenting on four different test cases in two and three space dimensions, the first two cases being inspired by an application in landfill management [32] and the remaining two cases being taken from the SPE10 benchmark reservoir scenario [8]. The codes used to obtain our results are written in Python and can be found at [12], while the underlying discretization and equation resolution are performed using the open source Python simulation tool PorePy [1,17].…”

Simulation of Piston Effects on Platform Screen Doors Considering Air Leakage

“…In this study, simple homogeneity is assumed for the porous medium, and Equation ( 2) can be simplified as [34]:…”