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A new dual‐porosity model is developed for single‐phase fluid flow in fractured/porous media. Flow is assumed to take place through the fracture network and between the fractures and matrix blocks. The matrix blocks are treated in a lumped parameter manner, with a single average pressure used for each matrix block. Rather than assuming that fracture/matrix flux is proportional to the difference between the fracture pressure and matrix pressure at each point, as is done in the Warren‐Root model, we use a nonlinear equation which more accurately models the flux over all time regimes, including both early and late times. This flux equation is compared with analytical solutions for spherical blocks with prescribed pressure variations on their boundaries. The nonlinear flux equation is also used as a source/sink term in the numerical simulator TOUGH. The modified code allows more accurate simulations than the conventional Warren‐Root method, with a large savings (about 90%) in computational time compared to methods which explicitly discretize the matrix blocks.

Abstract. The unsaturated zone at Yucca Mountain, a potential repository site of highlevel nuclear waste, is a complex hydrologic system in which a variety of important flow and transport processes is involved. To quantify these processes as accurately as possible is a theoretically challenging and practically important issue. In this study, we propose a new formulation for modeling flow and transport in unsaturated fractured rocks. The formulation is mainly based on a hypothesis that only a portion of connected fractures are active in conducting water. Analysis of the relevant data with the new formulation suggests that about 18-27% of the connected fractures in the Topopah Spring welded (TSw) unit (the potential repository unit) of Yucca Mountain are active under ambient conditions. The relatively high percentage of active fractures is consistent with field observations from a variety of sources. Sensitivity analyses are performed to investigate effects of the "activity" of connected fractures on flow and transport behavior in unsaturated rocks.

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This paper presents a new triple-continuum conceptual model for simulating flow and transport processes in fractured rock. Field data collected from the unsaturated zone of Yucca Mountain, a potential repository site of high-level nuclear waste, show that there are significant numbers of small-scale fractures. Although these small fractures may not contribute to the global flow and transport within the fracture networks, they may have a considerable effect on solute transport and liquid flow between the fractures and the matrix. The effect of these small fractures has not been considered in previous modeling investigations within the context of a continuum approach. A new triple-continuum model (consisting of matrix, small-fracture and large-fracture continua) has been developed to investigate the effect of these small fractures. This paper derives the model formulation and discusses the basic triple-continuum behavior of flow and transport processes under different conditions, using both analytical solutions and numerical approaches. The simulation results from the site-scale model of the unsaturated zone of Yucca Mountain indicate that these small fractures may have an important effect on radionuclide transport within the mountain.Key Words: Naturally fractured reservoir, fractured porous media, double-porosity model, dual-permeability model, triple-continuum model, numerical reservoir simulation, and fractured unsaturated rock. 2 IntroductionThe study of flow and transport processes in fractured rock has recently received increased attention because of its importance to underground natural-resource recovery, waste storage, and environmental remediation. Since the 1960s, significant progress has been made towards the understanding and modeling of flow and transport processes in fractured rock (Barenblatt et al., 1960;Warren and Root, 1963;Kazemi, 1969;Pruess and Narasimhan, 1985). Despite these advances, modeling the coupled processes of multiphase fluid flow, heat transfer, and chemical migration in a fractured porous medium remains a conceptual and mathematical challenge. The difficulty stems primarily from (1) the nature of inherent heterogeneity, (2) the uncertainties associated with the characterization of a fracture-matrix system for any field-scale problem, and (3) the difficulties in conceptualizing, understanding, and describing flow and transport processes in such a system.Mathematical modeling using a continuum approach involves developing conceptual models, incorporating the geometrical information of a given fracture-matrix system, and setting up the general mass and energy conservation equations for overlapping fracturematrix domains. The majority of the computational effort is used to solve the governing equations that couple fluid and heat flow with chemical migration either analytically or numerically. The key issue for simulating flow and transport in fractured rock is how fracture-matrix interactions under different conditions involving multiple processes are handled. The commonly us...

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.