Constitutive relations for unsaturated flow in a fracture network

Abstract

RESEARCH OBJECTIVES A commonly used approach for modeling water flow in unsaturated fractured rocks is the continuum approach, in which the constitutive relation models originally developed for porous media have often been borrowed to represent constitutive relations for the fracture continuum. While these models have been successfully used for soils and other porous media, their usefulness and limitations have not been investigated for the fracture continuum. The objective of this study is to present an evaluation of the commonly used van Genuchten and Brooks-Corey models and to develop improved constitutive relation models based on the evaluation results. APPROACH Because it is generally difficult to directly measure constitutive relations for a fracture network in the field, we have determined these relations from numerical simulations of steady-state unsaturated flow in two-dimensional fracture networks (Figure 1). In these simulations, a fracture network is considered as an effective porous medium. The rock matrix is treated as being impermeable for purpose of focusing on the fracture continuum. The fracture networks consist of vertical and horizontal fractures with different hydraulic properties. ACCOMPLISHMENTS It was found that the van Genuchten model could reasonably well match the simulated water retention curves except for high saturations, but both the van Genuchten and Brooks-Corey models generally underestimate relative permeability values except at low saturations. We propose a new relative permeability-saturation relation for the fracture continuum by modifying the Brooks-Corey relation. The combination of this new relation and the van Genuchten capillary pressure-saturation relation can represent the simulated curves and may provide an improved set of constitutive relations for the fracture continuum. However, this study is mainly based on the numerical experiment results and further investigation based on relevant field observations are needed. SIGNIFICANCE OF FINDINGS The constitutive relations are a key element of the unsaturated flow model based on the continuum approach. The accuracy of modeling results is largely determined by the accuracy of these constitutive relations that characterize flow processes at a subgrid-scale. The use of the constitutive relations developed for porous media for describing unsaturated flow in subgrid-scale fracture networks may not be valid, because the geometry of a fracture network is considerably different than the pore geometry in a porous medium. Moreover, unsaturated flow behavior in a fracture network, which is mainly determined by the gravity, is not necessarily the same as that in porous medium.

Experimental Study on the Measurement of S-p Relations of LNAPL in a Porous Medium

“…However some simpliˆed researches have been made. In a fracture network, it was found that, both the VG and BC models generally underestimate relative permeability values, while the BC model gives better results than the VG model (Liu and Bodvarsson, 2001). In porous media, the predictions based on the BC model also agreed better with experimental observations than the predictions based the VG model (Schroth et al, 1998).…”

The Parabolic Variational Inequalities for Variably Saturated Water Flow in Heterogeneous Fracture Networks

“…One approach to establish the related constitutive relationships for either single fractures [23] or fracture networks [4,24] is to simply borrow or modify empirical functions from porous media. A commonly used functional relationship is the one proposed by van Genuchten [25], based on the earlier work by Mualem [26], where the pressure headsaturation and relative permeability-saturation relationships are expressed by…”

“…Note that all or most connected fractures are expected to participate in variably saturated flow in the fracture network and that the fracture dead ends and fractures that are isolated from the major part of the network may not be hydraulically connected and thus can be disregarded in studies of unsaturated flow processes in fracture networks. Similar fracture networks have also been implemented by other researchers to study flow and transport properties of fractures [24,42] To investigate how the extent and density of fractures affect the variably saturated flow infiltration processes in the rock square, two types of fracture systems are mimicked and their related statistical parameters are given in Table 1. Obviously, the horizontal and vertical fractures have the same statistical parameters in each case, except the aperture size.…”

Assessing the timing and magnitude of precipitation-induced seepage into tunnels bored through fractured rock

“…Seepage into underground tunnels, cavities, and drifts gained increasing attention during the past few decades as a result of its potential impacts on the construction process (Chen & Tolon, 2012;Huang et al, 2011;Fernandez & Moon, 2010a;Li et al, 2009;Cesano et al 2000;Kitterod et al, 2000), water resources and environment (Vincenzi et al, 2009;Gleeson et al, 2009;Gargini et al, 2008;Scanlon, et al, 2006;Kim et al, 2005;Seyfried, et al, 2005;Rademacher et al, 2003;Scanlon et al, 2002;Shimojima et al, 1993), and the quality of nuclear waste repositories Bagtzoglou & Cesano, 2007;Trautz & Wang, 2002;Liu & Bodvarsson, 2001;Philip & Knight, 1989). Various processes have been identified that govern the spatial and temporal variability of net infiltration, recharge, and seepage into soil and rock excavations and cavities.…”

“…Due to the complexities in behavior, including film flow in fractures, it is very difficult to accurately model using this technique (Pruess et al, 1999). The most accurate techniques for modeling fracture networks are with Discrete Fracture Network (DFN) models, Stochastic Continuum (SC) models, and a combination of the two (Liu & Bodvarsson, 2001;Ohman & Niemi, 2003;Huang et al, 2011); all of which are becoming common approaches.…”