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# Search in KarstBase

**three-dimensional**(Keyword) returned

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This thesis aims to provide a better knowledge of karst flow systems, from a functional point of view (behaviour with time), as well as from a structural one (behaviour in space). The first part of the thesis deals with the hydrodynamic behaviour of karst systems, and the second part with the geometry of karstic networks, which is a strong conditioning factor for the hydrodynamic behaviour.

Many models have been developed in the past for describing the hydrodynamic behaviour of karst hydrogeological systems. They usually aim to provide a tool to extrapolate, in time and/or space, some characteristics of the flow fields, which can only be measured at a few points. Such models often provide a new understanding of the systems, beyond what can be observed directly in the field. Only special field measurements can verify such hypotheses based on numerical models. This is an significant part of this work. For this purpose, two experimental sites have been equipped and measured: Bure site or Milandrine, Ajoie, Switzerland, and Holloch site, Muotathal, Schwyz, Switzerland. These sites gave us this opportunity of simultaneously observe hydrodynamic parameters within the conduit network and, in drillholes, the "low permeability volumes" (LPV) surrounding the conduits.

These observations clearly show the existence of a flow circulation across the low permeability volumes. This flow may represent about 50% of the infiltrated water in the Bure test-field. The epikarst appears to play an important role into the allotment of the infiltrated waters: Part of the infiltrated water is stored at the bottom of the epikarst and slowly flows through the low permeability volumes (LPV) contributing to base flow. When infiltration is significant enough the other part of the water exceeds the storage capacity and flows quickly into the conduit network (quick flow).

For the phreatic zone, observations and models show that the following scheme is adequate to describe the flow behaviour: a network of high permeability conduits, of tow volume, leading to the spring, is surrounded by a large volume of low permeability fissured rock (LPV), which is hydraulically connected to the conduits. Due to the strong difference in hydraulic conductivity between conduits and LPV, hydraulic heads and their variations in time and space are strongly heterogeneous. This makes the use of piezometric maps in karst very questionable.

Flow in LPV can be considered as similar to flow in fractured rocks (laminar flow within joints and joints intersections). At a catchment scale, they can be effectively considered as an equivalent porous media with a hydraulic conductivity of about 10-6 to 10-7 m/s.

Flow in conduits is turbulent and loss of head has to be calculated with appropriate formulas, if wanting any quantitative results. Our observations permitted us to determine the turbulent hydraulic conductivity of some simple karst conduits (k', turbulent flow), which ranges from 0.2 to 11 m/s. Examples also show that the structure of the conduit network plays a significant role on the spatial distribution of hydraulic heads. Particularity hydraulic transmissivity of the aquifer varies with respect to hydrological conditions, because of the presence of overflow conduits located within the epiphreatic zone. This makes the relation between head and discharge not quadratic as would be expected from a (too) simple model (with only one single conduit). The model applied to the downstream part of Holloch is a good illustration of this phenomena.

The flow velocity strongly varies along the length of karst conduits, as shown by tracer experiments. Also, changes in the conduit cross-section produce changes in the (tow velocity profile. Such heterogeneous flow-field plays a significant role in the shape of the breakthrough curves of tracer experiments. It is empirically demonstrated that conduit enlargements induce retardation of the breakthrough curve. If there are several enlargements one after the other, an increase of the apparent dispersivity will result, although no diffusion with the rock matrix or immobile water is present. This produces a scale effect (increase of the apparent dispersivity with observation scale). Such observations can easily be simulated by deterministic and/or black box models.

The structure of karst conduit networks, especially within the phreatic zone, plays an important role not only on the spatial distribution of the hydraulic heads in the conduits themselves, but in the LPV as well. Study of the network geometry is therefore useful for assessing the shape of the flow systems. We further suggest that any hydrogeological study aiming to assess the major characteristics of a flow system should start with a preliminary estimation of the conduit network geometry. Theories and examples presented show that the geometry of karst conduits mainly depends on boundary conditions and the permeability field at the initial stage of the karst genesis. The most significant boundary conditions are: the geometry of the impervious boundaries, infiltration and exfiltration conditions (spring). The initial permeability field is mainly determined by discontinuities (fractures and bedding planes). Today's knowledge allows us to approximate the geometry of a karst network by studying these parameters (impervious boundaries, infiltration, exfiltration, discontinuity field). Analogs and recently developed numerical models help to qualitatively evaluate the sensitivity of the geometry to these parameters. Within the near future, new numerical tools will be developed and will help more closely to address this difficult problem. This development will only be possible if speleological networks can be sufficiently explored and used to calibrate models. Images provided by speleologists to date are and will for a long time be the only data which can adequately portray the conduit networks in karst systems. This is helpful to hydrogeologists. The reason that we present the example of the Lake Thun karst system is that it illustrates the geometry of such conduits networks. Unfortunately, these networks are three-dimensional and their visualisation on paper (2 dimensions) is very restrictive, when compared to more effective 3-D views we can create with computers. As an alternative to deterministic models of speleogenesis, fractal and/or random walk models could be employed.

Studies of carbonate aquifers usually either concentrate on sampling the channel flow (egsink-to-spring tracer testing, spring monitoring) or on sampling the non-channel flow (egborehole measurements)A comprehensive approach is advocated here, involving the integration of both sources of information, as well as measurements of the porosity and permeability of the unfractured rockRepresentative sampling can be achieved by treating carbonates as triple-porosity aquifers, with one-, two-, and three-dimensional porosity elementsThe division of carbonate aquifers into "karstic" or "non-karstic" types is unwarranted

Nuclear magnetic resonance imaging is applied to measure flow patterns in natural, water-saturated, rough-walled rock fractures. From three-dimensional water density and velocity vector images the fracture morphology and flow patterns are determined. The parabolic nature and asymmetry of the velocity profiles, and thus the accuracy of local cubic law flow rate predictions, vary greatly. This depends on the degree of wall roughness. Particularly complex flow patterns are found in one sample which contains a sharp fracture wall discontinuity. A power law for the flow rate versus aperture for the low-flow region was found without considering the hydraulic gradients.

The application of nuclear magnetic resonance imaging (NMRI) to the direct three-dimensional measurement of flow in rough-walled water-saturated rock fractures is presented for the first time. The study demonstrates the abilities of NMRI to noninvasively measure rock-water interfaces and water flow velocities in these fractures and investigates the effects of wall morphology on flow patterns inside a typical rock fracture. Two- and three-dimensional flow-encoded spin-echo pulse sequences were applied. The stability and reproducibility of the water flow patterns were confirmed by analyzing two-dimensional velocity images. A variety of geometrical and hydraulic features were determined from three-dimensional velocity images, including the rock-water interfaces, the fracture aperture distribution, and the critical aperture path; velocity profiles and volumetric flow rates; flow and stagnant regions; and the critical velocity path. In particular, the effects of a sharp step discontinuity of the fracture walls and the applicability of the cubic law were examined. As a result of the complex three-dimensional geometry, velocity profiles are generally parabolic but often highly asymmetric, with respect to the fracture walls. These asymmetric velocity profiles are clustered together, with significant correlations; they are not just local random phenomena. However, theoretical considerations indicate that the effects of the measured asymmetry on volumetric flow rates and hydraulic conductivities are insignificant, in that the overall flow inside rough fractures still obeys the cubic law. The features discussed in this study emphasize the strong heterogeneity and the highly three-dimensional nature of the flow patterns in natural rock fractures and consequently the need for three-dimensional flow analysis.

We present a three-dimensional (3-D) model of fractures that within the same framework, allows a systematic study of the interplay and relative importance of the two key factors determining the character of flow in the system. The two factors of complexity are () the geometry of fracture plane structure and interconnections and (2) the aperture variability within these planes. Previous models have concentrated on each separately. We introduce anisotropic percolation to model a wide range of fracture structures and networks. The conclusion is that either of these elements, fracture geometry and aperture variability, can give rise to channeled flow and that the interplay between them is especially important for this type of flow. Significant outcomes of our study are (1) a functional relationship that quantifies the dependence of the effective hydraulic conductivity on aperture variability and on the network structure and fracture element density, (2) a relation between aperture variability and the Peclet number, and (3) a basis for a new explanation for the field-length dependence of permeability observed in fractured and heterogeneous porous formations.

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