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Speleology in Kazakhstan

Shakalov on 04 Jul, 2018
Hello everyone!   I pleased to invite you to the official site of Central Asian Karstic-Speleological commission ("Kaspeko")   There, we regularly publish reports about our expeditions, articles and reports on speleotopics, lecture course for instructors, photos etc. ...

Speleology in Kazakhstan

Shakalov on 04 Jul, 2018
Hello everyone!   I pleased to invite you to the official site of Central Asian Karstic-Speleological commission ("Kaspeko")   There, we regularly publish reports about our expeditions, articles and reports on speleotopics, lecture course for instructors, photos etc. ...

Speleology in Kazakhstan

Shakalov on 11 Jul, 2012
Hello everyone!   I pleased to invite you to the official site of Central Asian Karstic-Speleological commission ("Kaspeko")   There, we regularly publish reports about our expeditions, articles and reports on speleotopics, lecture course for instructors, photos etc. ...

New publications on hypogene speleogenesis

Klimchouk on 26 Mar, 2012
Dear Colleagues, This is to draw your attention to several recent publications added to KarstBase, relevant to hypogenic karst/speleogenesis: Corrosion of limestone tablets in sulfidic ground-water: measurements and speleogenetic implications Galdenzi,

The deepest terrestrial animal

Klimchouk on 23 Feb, 2012
A recent publication of Spanish researchers describes the biology of Krubera Cave, including the deepest terrestrial animal ever found: Jordana, Rafael; Baquero, Enrique; Reboleira, Sofía and Sendra, Alberto. ...

Caves - landscapes without light

akop on 05 Feb, 2012
Exhibition dedicated to caves is taking place in the Vienna Natural History Museum   The exhibition at the Natural History Museum presents the surprising variety of caves and cave formations such as stalactites and various crystals. ...

Did you know?

That thief zone is the zone through which drilling fluid is lost into a formation through the borehole wall [16].?

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Your search for turbulent flow (Keyword) returned 48 results for the whole karstbase:
Showing 1 to 15 of 48
A New Equation Solver for Modeling Turbulent Flow in Coupled Matrix‐Conduit Flow Models, ,

Karst aquifers represent dual flow systems consisting of a highly conductive conduit system embedded in a less permeable rock matrix. Hybrid models iteratively coupling both flow systems generally consume much time, especially because of the nonlinearity of turbulent conduit flow. To reduce calculation times compared to those of existing approaches, a new iterative equation solver for the conduit system is developed based on an approximated Newton–Raphson expression and a Gauß–Seidel or successive over-relaxation scheme with a single iteration step at the innermost level. It is implemented and tested in the research code CAVE but should be easily adaptable to similar models such as the Conduit Flow Process for MODFLOW-2005. It substantially reduces the computational effort as demonstrated by steady-state benchmark scenarios as well as by transient karst genesis simulations. Water balance errors are found to be acceptable in most of the test cases. However, the performance and accuracy may deteriorate under unfavorable conditions such as sudden, strong changes of the flow field at some stages of the karst genesis simulations.

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Mixing corrosion in CaCO3/1bCO2/1bH2O systems and its role in the karstification of limestone areas, 1981, Dreybrodt W,
Mixtures of two saturated H2O/1bCO2/1bCaCO3 solutions of different chemical composition gain renewed capability of dissolving calcite. This is an important mechanism in the solution processes of limestone during karstification. Using recent data on the kinetics of calcite dissolution, dissolution rates in mixture corrosion are calculated. In the region of the chemical composition of natural karst waters the solution rate is approximated by:R=-[alpha]([Ca2] - [Ca2]s where [Ca2], [Ca2]s are the concentrations of the Ca2 ion in the solution and at saturation, respectively. [alpha] ranges from 10-4 to 3[middle dot]10-4 cm s-1.This result is applied to the solution of limestone in karst water mixtures flowing in cylindrical conduits. The saturation length, i.e. the length xs which the solution has to travel to drop to 37% of its renewed dissolving capability, is calculated in the region of turbulent flow. This region starts at conduit radii R of several millimeters. At the onset of turbulent flow the saturation length is 260 m, increasing with R1.665. The increase of conduit radii is calculated from the dissolution rates of calcite solution to be on the order of 10-3 cm yr.-1.The results are discussed for a comprehensive model of karstification and cave development, which for the first time gives a realistic theoretical time region for cave development, in agreement to experience

Les vagues d'rosion, 1987, Lismonde B. , Lagmani A.
CURRENT MARKINGS OR SCALLOPS - The scallops pattern on the wall of limestone cave result from the interaction of a soluble surface and a turbulent flow. The main results of Curl, particularly, the dependence of the velocity flow on the scallops length are presented.

EARLY DEVELOPMENT OF KARST SYSTEMS .1. PREFERENTIAL FLOW PATH ENLARGEMENT UNDER LAMINAR-FLOW, 1994, Groves C. G. , Howard A. D. ,
Modeling of flow and solutional processes within networks of interconnected conduits in limestone aquifers indicates that enlargement occurs very selectively during the early stages of karst aquifer development under laminar flow. If initial flow paths are uniform in size, almost all enlargement occurs along a single set of connected conduits that lie along a direct path between recharge and discharge locations and are aligned along the hydraulic gradient. With a sufficiently large variation in initial aperture widths, enlargement occurs along the flow path offering the least resistance to flow, but since flow rates in laminar flow are proportional to the fourth power of diameter but only linearly proportional to hydraulic gradient, the preferentially enlarged set of fractures may follow an indirect path. Results disfavor earlier suggestions that nonselective cave patterns result from artesian flows (at least under laminar flow conditions) and that all passages should be competitive until the onset of turbulent flow

DAMPENING OF TRANSVERSE DISPERSION IN THE HALOCLINE IN KARST LIMESTONE IN THE NORTHEASTERN YUCATAN PENINSULA, 1995, Stoessell R. K. ,
A range of hydrodynamic dispersion coefficients was estimated for fracture-fluid and combined fracture and pore-fluid now within the halocline of the limestone aquifer forming the surface of the northern Yucatan Peninsula. The coefficients are fit parameters in a model reproducing observed halocline profiles in a sinkhole and in a borehole near the northeastern coast. Fitted coefficients range from 10(-7) to 10(-4) cm(2)/sec, of which molecular diffusion, without transverse (vertical) dispersion, can account for 10(-7) to 10(-5) cm(2)/sec. The mechanical stability of the vertical density gradient in the halocline dampens transverse dispersion in pore fluids and in fracture fluids that are transitional between laminar and turbulent flow. The dampening is proportional to the ratio of the energy needed for the fluid to rise and displace a less dense fluid to the vertical component of the kinetic energy of the fluid. The ratio of these two energies is at a maximum during the initial stage of development of a halocline and decreases as the halocline widens

EARLY DEVELOPMENT OF KARST SYSTEMS .2. TURBULENT-FLOW, 1995, Howard A. D. , Groves C. G. ,
A simulation model developed to explore patterns of fracture enlargement within incipient limestone karst aquifers has been extended to turbulent flow. In contrast to the highly selective passage enlargement that occurs early in cave network development under laminar flow, the transition to turbulent flow results in more general passage enlargement, leading to maze networks when initial fractures are large and hydraulic gradients are high. These results support previously published hypotheses for the development of maze patterns, including formation within structural settings that have created initially large fractures or within flow systems periodically inundated by flooding. Maze development is also favored under turbulent flow when passages are entirely water filled, and where the groundwater flow system is long-lived. By contrast, branched patterns are most common when passages become free-surface subterranean streams, because depression of the piezometric surface along main passages, downcutting along main passages, and possible infilling with sediment of side passages limit the sharing of discharge among interconnected fractures or bedding planes that promote maze development

Discussion on 'The Chalk as a karstic aquifer: evidence from a tracer test at Stanford Dingley, Berkshire, UK': Quarterly Journal of Engineering Geology, 28, S31-S38, 1996, Banks D, Davies C, Davies W,
M. Price writes: Banks et al. (1995) address the nature of the permeability of parts of the Chalk aquifer, provide useful data from a tracer test, and draw attention to the potential dangers of disposing of agricultural and road run-off to swallow holes. The paper includes a calculation of fissure conductivity and aperture from the results of the tracer test. In this it has to be emphasized that the calculations relate to Darcian flow in an equivalent smooth, plane, parallel-plate opening, not the more likely turbulent flow in a natural fissure. The true average aperture of the fissure is therefore likely to be significantly greater than that calculated (Price 1987, 1996). The situation described at Stanford Dingely is one where drainage originating from impermeable Tertiary strata flows onto the Chalk and sinks into the aquifer. The majority of active Chalk sinks appear to be of this type; the drainage sinking into them originates as run-off from other strata. Rain falling anywhere on the outcrop of the Chalk is normally able to infiltrate, so water flowing across the Chalk outcrop is almost invariably allogenic drainage or water that has infiltrated the Chalk and emerged as baseflow. Drainage to sinks is therefore a minor component of recharge to the Chalk. The tracer test undertaken into at Stanford Dingley involved introducing tracer into a known point of entry in the aquifer, and observing its arrival at a known point of emergence. Such tests almost inevitably measure the speed of groundwater movement along a ... This 250-word extract was created in the absence of an abstract

Structure et comportement hydraulique des aquifers karstiques, DSc thesis, 1996, Jeannin, P. Y.

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.


Risk assessment methodology for karst aquifers .2. Solute-transport modeling, 1997, Field Ms,
Ground-water flow and solute-transport simulation modeling are major components of most exposure and risk assessments of contaminated aquifers. Model simulations provide information on the spatial and temporal distributions of contaminants in subsurface media but are difficult to apply to karst aquifers in which conduit flow is important. Ground-water flow and solute transport in karst conduits typically display rapid-flow velocities, turbulent-flow regimes, concentrated pollutant-mass discharge, and exhibit open-channel or closed-conduit how Conventional groundwater models, dependent on the applicability of Darcy's law, are inappropriate when applied to karst aquifers because of the (1) nonapplicability of Darcian-flow parameters, (2) typically nonlaminar flow regime, and (3) inability to locate the karst conduits through which most flow and contaminant transport occurs. Surface-water flow and solute-transport models conditioned on a set of parameters determined empirically from quantitative ground-water tracing studies may be effectively used to render fate-and-transport values of contaminants in karst conduits. Hydraulic-flow and geometric parameters developed in a companion paper were used in the surface-water model, TOXI5, to simulate hypothetical slug and continuous-source releases of ethylbenzene in a karst conduit. TOXI5 simulation results showed considerable improvement for predicted ethylbenzene-transport rates and concentrations over qualitative tracing and analytical ground-water model results. Ethylbenzene concentrations predicted by TOXI5 simulations were evaluated in exposure and risk assessment models

Precipitation kinetics of calcite in the system CaCO3-H2O-CO2: The conversion to CO2 by the slow process H?->CO2? as a rate limiting step, 1997, Dreybrodt W, Eisenlohr L, Madry B, Ringer S,
Precipitation rates of CaCO3 from supersaturated solutions in the H2O - CO2 - CaCO3 system are controlled by three rate-determining processes: the kinetics of precipitation at the mineral surface, mass transport of the reaction species involved to and from the mineral surface, and the slow kinetics of the overall reaction HCO3- H --> CO2 H2O. A theoretical model by Buhmann and Dreybrodt (1985a,b) taking these processes into account predicts that, due to the slow kinetics of this reaction, precipitation rates to the surface of CaCO3 minerals depend critically on the ratio V/A of the volume V of the solution to the surface area A of the mineral in contact with it, for both laminar and turbulent flow. We have performed measurements of precipitation rates in a porous medium of sized particles of marble, limestone, and synthetic calcite, with V/A ratios ranging from 3.10(-4) to 1.2-10(-2) cm at 10 degrees C. Calcite was precipitated from supersaturated solutions with [Ca2] approximate to 4 mmol/L and an initial P-CO2 of 5.10(-3) or 1.10(-3) atm, respectively, using experimental conditions which prevented exchange of CO2 with the atmosphere, i.e., closed system. The results are in qualitative agreement with the theoretical predictions. Agreement with the observed data, however, is obtained by modifying the rate law of Plummer et al. (1978) to take into account surface-controlled inhibition effects. Experiments with supersaturated solutions containing carbonic anhydrase, an enzyme which enhances the conversion of HCO3- into CO2, yield rates increased by a factor of up to 15. This provides for the first time unambiguous experimental evidence that this reaction is rate limiting. We have also measured precipitation rates in batch experiments, stirring sized mineral particles in a solution with V/A ranging from 0.03 to 0.75 cm. These experiments also give clear evidence on the importance of the conversion of HCO3- into CO2 as rate limiting step. Taken together our experiments provide evidence that the theoretical model of Buhmann and Dreybrodt (1985a,b) can be used to predict reliable rates from the composition of CaHCO3- solutions with low ionic strength in many geologically relevant situations. Copyright (C) 1997 Elsevier Science Ltd

Dissolution kinetics of calcium carbonate minerals in H2O-CO2 solutions in turbulent flow: The role of the diffusion boundary layer and the slow reaction H2O? reversible arrow H?, 1997, Liu Z. H. , Dreybrodt W. ,

Role of Speleology in Karst Hydrology and Hydrogeology., 1997, Bonacci O.
Technology of speleological investigations enables special measurements of features of underground conduits, caves, pits, jamas, shafts and the other solutional sculpturings such as scallops and cave rocky relief. Speleologic investigations can reveal the positions, dimensions and interactions of underground and surface karst features and water flow in the karst and on its surface. Speleologists are capable of investigating the hydraulic conditions under which laminar or turbulent flows occur in conduits and small and narrow karst fractures. From such investigations crucial parameters for hydraulic, hydrologic and hydrogeologic modelling such as dissolution-bedform and hydraulically-transported sediment, can be obtained. For these reasons, the role of speleology in karst hydrology and hydrogeology should (and undoubtedly will) in future be given much more importance. This paper briefly explains the main theoretical aspects and gives some practical examples and experiences from Dinaric and others karst regions.

Modeling of storm responses in conduit flow aquifers with reservoirs, 1998, Halihan Todd, Wicks Carol M. ,
In aquifers containing large voids, such as karst aquifers with caves or basaltic aquifers with lava tubes, hydrographs at wells or springs are used to analyze the structure and response of the hydrogeological system. Numerical modeling of hydrograph response is commonly based on either inverse techniques or postulated flow geometries. However, the range of mechanisms for generating hydrograph responses have not been fully investigated.Physical modeling of these complex non-Darcian systems permits better understanding of the storm responses that conduit systems may generate. Using a numerical model of conduit flow systems which incorporates turbulent flow, some of the mechanisms that can alter storm pulses were investigated by treating them as combinations of pipes that connect reservoirs.The results indicate that the response of a conduit-flow aquifer can range from what has been called 'diffuse' or 'steady' to 'conduit' or 'flashy', without employing a diffusive component. A full range of behavior can be the result of changes from phreatic to epiphreatic conditions in a conduit, changes in conduit geometry, or multiple springs draining the same system. The results provide a quantitative tool to assess spring and well hydrographs, and illustrate mechanisms that can generate observed responses, which have previously been qualitatively interpreted

Influence of aperture variability on dissolutional growth of fissures in karst formations, 1998, Hanna R. B. , Rajaram H. ,
The influence of aperture variability on dissolutional growth of fissures is investigated on the basis of two-dimensional numerical simulations. The logarithm of the fissure aperture before dissolution begins is modeled as a Gaussian stationary isotropic random field. The initial phase of dissolutional growth is studied up to the time when turbulent flow first occurs at a point within the fissure (the breakthrough time). The breakthrough time in variable aperture fissures is smaller than that in uniform fissures and decreases as the coefficient of variation of the aperture field (sigma/mu) increases. In comparing uniform and variable aperture fissures in limestone, the breakthrough time with sigma/mu = 0.1 is about a factor of 2 smaller than that in a uniform fissure. The breakthrough time is reduced by about an order of magnitude with sigma/mu = 2.0. The mechanism leading to reduced breakthrough times is the focusing of flow into preferential flow channels which are enlarged at a faster rate than the surrounding regions of slower flow. Dissolution channels are narrower and more tortuous as sigma/mu. increases. Investigations of the influence of reaction rate reveal that the influence of aperture variability is more pronounced in rapidly dissolving rock. In uniform fissures in rapidly dissolving minerals, breakthrough times are very long since water becomes saturated with respect to the mineral within a short distance of the entrance to the flow path. However, in variable aperture fissures, breakthrough occurs rapidly because of selective growth along preferential flow channels, which progressively capture larger fractions of the total flow. These results partly explain why conduits develop rapidly in gypsum, although previous one-dimensional studies suggest that conduit growth will not occur

Structure et comportement hydraulique des aquifers karstiques, DSc. Thesis, faculte des Sciences de l'Universite de Neuchatel., 1998, Jeannin Py.
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.

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