Modeling fracture flow with a stochastic discrete fracture network: calibration and validation: 1. The flow model
TL;DR: In this paper, a large-scale investigation of fracture flow was conducted in a granite uranium mine at Fanay-Augeres, France, and four types of data were collected: (1) geometry of the fracture network; (2) local hydraulic properties measured by injection tests in boreholes; (3) global hydraulic behavior from flow rate and piezometric head distribution at a 106 m3 scale; and (4) tracer tests performed at a scale of up to 40 m.
Abstract: A large-scale investigation of fracture flow was recently conducted in a granite uranium mine at Fanay-Augeres, France. Its aim was to develop a methodology for the investigation of possible nuclear waste repository sites in crystalline environments, and thus to determine what measurements to make and what models to use in order to predict the flow and transport properties of the medium, i.e., their average behaviors and spatial variabilities at different scales. Four types of data were collected: (1) geometry of the fracture network; (2) local hydraulic properties measured by injection tests in boreholes; (3) global hydraulic behavior from flow rate and piezometric head distribution at a 106 m3 scale; and (4) tracer tests performed at a scale of up to 40 m. A stochastic fracture network model assuming negligible matrix permeability was developed and calibrated essentially on data 1 and 2 above; this was then used to predict data 3 and 4 in an attempt to validate both the parameters and the structure of the model. In this first part, only the flow problem (data 1) is discussed.
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TL;DR: In this paper, the authors analyze measurements, conceptual pictures, and mathematical models of flow and transport phenomena in fractured rock systems, including water flow, conservative and reactive solutes, and two-phase flow.
1,267 citations
TL;DR: In this paper, the authors present the techniques, advances, problems and likely future developments in numerical modelling for rock mechanics and discuss the value that is obtained from the modelling, especially the enhanced understanding of those mechanisms initiated by engineering perturbations.
976 citations
TL;DR: In this paper, the authors discuss issues associated with the quantification of flow and transport through fractured rocks on scales not exceeding those typically associated with single and multi-well pressure (or flow) and tracer tests.
Abstract: Among the current problems that hydrogeologists face, perhaps there is none as challenging as the characterization of fractured rock (Faybishenko and Benson 2000). This paper discusses issues associated with the quantification of flow and transport through fractured rocks on scales not exceeding those typically associated with single- and multi-well pressure (or flow) and tracer tests. As much of the corresponding literature has focused on fractured crystalline rocks and hard sedimentary rocks such as sandstones, limestones (karst is excluded) and chalk, so by default does this paper. Direct quantification of flow and transport in such rocks is commonly done on the basis of fracture geometric data coupled with pressure (or flow) and tracer tests, which therefore form the main focus. Geological, geophysical and geochemical (including isotope) data are critical for the qualitative conceptualization of flow and transport in fractured rocks, and are being gradually incorporated in quantitative flow and transport models, in ways that this paper unfortunately cannot describe but in passing. The hydrogeology of fractured aquifers and other earth science aspects of fractured rock hydrology merit separate treatments. All evidence suggests that rarely can one model flow and transport in a fractured rock consistently by treating it as a uniform or mildly nonuniform isotropic continuum. Instead, one must generally account for the highly erratic heterogeneity, directional dependence, dual or multicomponent nature and multiscale behavior of fractured rocks. One way is to depict the rock as a network of discrete fractures (with permeable or impermeable matrix blocks) and another as a nonuniform (single, dual or multiple) continuum. A third way is to combine these into a hybrid model of a nonuniform continuum containing a relatively small number of discrete dominant features. In either case the description can be deterministic or stochastic. The paper contains a brief assessment of these trends in light of recent experimental and theoretical findings, ending with a short list of prospects and challenges for the future.
632 citations
Cites background or methods from "Modeling fracture flow with a stoch..."
...…found that a highresolution stochastic continuum model of flow and transport in fractured crystalline rocks at Fanay-Aug res Hydrogeol J (2005) 13:124–147 DOI 10.1007/s10040-004-0397-2 performed as well, and in some important ways better, than the DFN-based models of Cacas et al. (1990a, 1990b)....
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...1, Herbert et al. 1991) of fractures, for the purpose of ascribing random effective parameters to subdomains of the rock mass being analyzed, which would then be treated as a randomly heterogeneous (stochastic) continuum (e.g. Cacas et al. 1990a; Herbert and Splawski 1990)....
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...Another approach has been to simulate flow (e.g. Dershowitz et al. 1991) or transport (e.g. Cacas et al. 1990b) across the entire rock mass using high-resolution DFNs with thousands or tens of thousands of fractures (20,000 in the case of Cvetkovic et al. 2004)....
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TL;DR: The impact of climate change on karst aquifers has been studied in this article, where the authors explore different conceptual models and how they can be translated into numerical models of varying complexity and therefore varying data requirements.
Abstract: Karst regions represent 7–12% of the Earth's continental area, and about one quarter of the global population is completely or partially dependent on drinking water from karst aquifers. Climate simulations project a strong increase in temperature and a decrease of precipitation in many karst regions in the world over the next decades. Despite this potentially bleak future, few studies specifically quantify the impact of climate change on karst water resources. This review provides an introduction to karst, its evolution, and its particular hydrological processes. We explore different conceptual models of karst systems and how they can be translated into numerical models of varying complexity and therefore varying data requirements and depths of process representation. We discuss limitations of current karst models and show that at the present state, we face a challenge in terms of data availability and information content of the available data. We conclude by providing new research directions to develop and evaluate better prediction models to address the most challenging problems of karst water resources management, including opportunities for data collection and for karst model applications at so far unprecedented scales.
556 citations
Cites background from "Modeling fracture flow with a stoch..."
...There have also been attempts to explicitly consider the geometry of the fracture network [Cacas et al., 1990; Dverstorp et al., 1992], but the data required to achieve robust karst water resources predictions are generally not available....
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TL;DR: In this paper, the authors present the techniques, advances, problems and likely future development directions in numerical modeling for rock mechanics and rock engineering, as well as a review of the current state of the art.
510 citations
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TL;DR: In this article, the authors used the theory of flow through fractured rock and homogeneous anisotropic porous media to determine when a fractured rock behaves as a continuum, i.e., there is an insignificant change in the value of the equivalent permeability with a small addition or subtraction to the test volume and an equivalent tensor exists which predicts the correct flux when the direction of a constant gradient is changed.
Abstract: The theory of flow through fractured rock and homogeneous anisotropic porous media is used to determine when a fractured rock behaves as a continuum. A fractured rock can be said to behave like an equivalent porous medium when (1) there is an insignificant change in the value of the equivalent permeability with a small addition or subtraction to the test volume and (2) an equivalent permeability tensor exists which predicts the correct flux when the direction of a constant gradient is changed. Field studies of fracture geometry are reviewed and a realistic, two-dimensional fracture system model is developed. The shape, size, orientation, and location of fractures in an impermeable matrix are random variables in the model. These variables are randomly distributed according to field data currently available in the literature. The fracture system models are subjected to simulated flow tests. The results of the flow tests are plotted as permeability ‘ellipses.’ The size and shape of these permeability ellipses show that fractured rock does not always behave as a homogeneous, anisotropic porous medium with a symmetric permeability tensor. Fracture systems behave more like porous media when (1) fracture density is increased, (2) apertures are constant rather than distributed, (3) orientations are distributed rather than constant, and (4) larger sample sizes are tested. Preliminary results indicate the use of this new tool, when perfected, will greatly enhance our ability to analyze field data on fractured rock systems. The tool can be used to distinguish between fractured systems which can be treated as porous media and fractured systems which must be treated as a collection of discrete fracture flow paths.
909 citations
01 Jan 1985
824 citations
TL;DR: In this paper, the authors studied the fluid flow and solute transport in a tight fractured medium in terms of flow through channels of variable aperture, characterized by an aperture density distribution and a spatial correlation length.
Abstract: On the basis of a review of recent theoretical and experimental studies of flow through fractured rocks, the authors have studied the fluid flow and solute transport in a tight fractured medium in terms of flow through channels of variable aperture. The channels are characterized by an aperture density distribution and a spatial correlation length. Aperture profiles along the channels are statistically generated and compared to laboratory measurements of fracture surfaces. Calculated tracer transport between two points in the fractured media is by way of a number of such channels. Tracer breakthrough curves display features that correspond well with recent data by Moreno et al., which lends support to the validity of our model. Calculated pressure profiles along the channels suggest possible measurements that may be useful in identifying the geometrical characteristics of the channels. Finally, predictions were made for tracer breakthrough curves in the case of single fractures under various degrees of normal stress. These suggest possible laboratory experiments which may be performed to validate this conceptual model.
406 citations
TL;DR: In this article, the authors describe a modeling concept which accounts for macroscopic dispersion not as a large-scale diffusion process but as mixing caused by spatial heterogeneities in hydraulic conductivity.
Abstract: Conventional modeling of mass transport in groundwater systems usually involves use of the dispersion-convection equation with large values of porous medium dispersivity to account for macroscopic dispersion. This work describes a modeling concept which accounts for macroscopic dispersion not as a large-scale diffusion process but as mixing caused by spatial heterogeneities in hydraulic conductivity. The two-dimensional spatially autocorrelated hydraulic conductivity field is generated as a first-order nearest-neighbor stochastic process. Analysis of a variety of hypothetical media shows that over finite domains a population of tracer particles convected through this statistically homogeneous conductivity field does not have the normal distribution and does not yield the constant dispersivity that classic theory would predict. This problem occurs because of insufficient spatial averaging in the macroscopic velocity field by the moving tracer particles. Our analyses suggest that the diffusion model for macroscopic dispersion may be inadequate to describe mass transport in geologic units. Sensitivity analysis with the model has shown that features of transport, such as first arrival of a tracer, are dependent on porous medium structure and that even when the statistical features of porous media are known, considerable uncertainty in the model result can be expected.
304 citations