Experimental investigation of inertial flow processes in porous media

Summary

The hydraulic behavior of inertial flows in porous media is experimentally investigated. A vertical metal column was constructed, of dimensions 0.5 m in diameter and 2.30 m in height. Eight different porous media were used in the experiments. Head loss was measured. A total of 454 experimental data were collected. The experimental data indicate that, for a wide spectrum of velocities, both the Forchheimer and Izbash equations offer excellent descriptions of the flow processes. For moderate values of the Reynolds number, a discontinuity in the velocity–hydraulic gradient curve was detected, a behavior also predicted by former numerical studies. The analysis of the hydraulic behavior of bidisperse media indicate the influence of wall effects taking place at the interface between small and large grains. The data are used to validate semi-empirical relations, and give also some insight on the flow processes taking place at the pore-scale for the case of non-Darcian flows.

Introduction

In most studies examining flow processes in groundwater, it is assumed that flow is described by the linear Darcy’s law; standard software and theoretical descriptions are based on this assumption (McDonald and Harbaugh, 1988, Bear, 1979).

As problems involving flow and transport processes in coarse porous media and fractures emerged, an adequate description of these processes became crucial. Therefore, recently, a substantial research effort is focused on “non-conventional” groundwater problems, including coupled flow and transport processes in individual fractures or fracture networks, and inertial flows in groundwater. High-velocity flows in underground geological formations occur in many real-world problems, including the exploitation of hot dry rock formations (Kohl et al., 1997), simulation of pollutant transport in waste rock deposits (Greenly and Joy, 1996), and water extraction issues (Wen et al., 2006, Wen et al., 2008a, Wen et al., 2008b, Mathias et al., 2008), while other applications include design of constructed wetlands (Economopoulou and Tsihrintzis, 2003, Akratos and Tsihrintzis, 2007).

For both coarse porous media and fractures, this type of flow can be adequately described either by the Forchheimer or the Izbash law (Wen et al., 2006, Panfilov and Fourar, 2006). For the one-dimensional case, these equations read, respectively:

$$-\frac{\partial h}{\partial x}=\mathit{aV}+\mathit{bV}|V|$$

$$-\frac{\partial h}{\partial x}=\lambda V^n$$

where x denotes the distance from the origin along the flow path, V is the bulk velocity, h the piezometric head, and a, b, λ and n are coefficients.

The two terms on the right hand side of Eq. (1) represent the viscous and inertial energy loss mechanisms. In Eq. (2) the exponent depends on the flow regime (n = 1 for creeping flow at the pore-scale and n = 2 for fully developed turbulent flow), and λ is a generalized resistance coefficient. While the theoretical background of the Forchheimer equation is well established (Panfilov and Fourar, 2006), the Izbash equation is rather of empirical nature. However, if one assumes that the phenomenological coefficients λ and n are constant, the solution of Eq. (2) offers some technical advantages (Wen et al., 2006).

For low values of the velocity (or equivalently for low values of the Reynolds number), both equations reduce to the Darcy law:

$$V=-K\frac{\partial h}{\partial x}$$

In this study, we focus our interest on the experimental determination of the coefficients of Eqs. (1), (2). Our results are used to discuss the appropriate simulation strategy of inertial flows, while their physical background is also analyzed. The paper is structured as follows: In Chapter 2, recent research efforts on inertial flows in fractures and porous media are presented. In Chapter 3 the experimental setup and procedure are described, while the data are analyzed in Chapter 4. Finally findings are summarized in Chapter 5.