Evolution of karst conduit networks in transition from pressurized flow to free-surface flow (original) (raw)
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Generation of complex karstic conduit networks with a hydrochemical model
Water Resources Research
In this paper, we present a hydrochemical model that can be used to generate plausible karstic conduit networks that honor what is known about geology, hydrology, and topography of a karst system. To make the model applicable to a range of natural karst systems, we introduce a flexible and physically realistic flow boundary condition along the land surface. Moreover, whereas comparable existing speleogenesis models use an explicit reactive-transport scheme, we propose an implicit reactive-transport scheme to permit a coarser spatial discretization of the conduit cells. An application to a real karst system illustrates that the model can generate a realistic karstic network that reproduces observed hydrologic behavior in terms of current spring flow rates, regional hydraulic head field as well as average groundwater residence times. Our model provides a useful tool to generate ensembles of possible karstic conduit networks that may be used within a stochastic framework to analyze flow and transport prediction uncertainty associated with a lack of knowledge about network geometry. Stochastic approaches have been used to gain insights into the relation between network geometry and solute transport for hypothetical karst systems [Borghi et al., 2016; Ronayne, 2013]. A stochastic approach requires efficient means of generating ensembles of possible conduit network realizations. Several Key Points: A speleogenesis model is presented that can be used to generate conduit networks at a regional scale Our model accounts for a switch between hydraulic and catchment control and uses an implicit reactivetransport scheme The model is applied to a real system and it is illustrated that the model can generate a realistic conduit network
Advances in Water Resources, 2013
Physics-based distributed models for simulating flow in karst systems are generally based on the discrete-continuum approach in which the flow in the three-dimensional fractured limestone matrix continuum is coupled with the flow in discrete one-dimensional conduits. In this study we present a newly designed discrete-continuum model for simulating flow in karst systems. We use a flexible spatial discretization such that complicated conduit networks can be incorporated. Turbulent conduit flow and turbulent surface flow are described by the diffusion wave equation whereas laminar variably saturated flow in the matrix is described by the Richards equation. Transients between free-surface and pressurized conduit flow are handled by changing the capacity term of the conduit flow equation. This new approach has the advantage that the transients in mixed conduit flow regimes can be handled without the Preissmann slot approach. Conduit-matrix coupling is based on the Peaceman's well-index such that simulated exchange fluxes across the conduit-matrix interface are less sensitive to the spatial discretization. Coupling with the surface flow domain is based on numerical techniques commonly used in surface-subsurface models and storm water drainage models. Robust algorithms are used to simulate the non-linear flow processes in a coupled fashion. The model is verified and illustrated with simulation examples.
Representation of water abstraction from a karst conduit with numerical discrete-continuum models
Hydrology and Earth System Sciences, 2014
Karst aquifers are characterized by highly conductive conduit flow paths embedded in a less conductive fissured and fractured matrix, resulting in strong permeability contrasts with structured heterogeneity and anisotropy. Groundwater storage occurs predominantly in the fissured matrix. Hence, most mathematical karst models assume quasi-steady-state flow in conduits neglecting conduitassociated drainable storage (CADS). The concept of CADS considers storage volumes, where karst water is not part of the active flow system but hydraulically connected to conduits (for example karstic voids and large fractures). The disregard of conduit storage can be inappropriate when direct water abstraction from karst conduits occurs, e.g., largescale pumping. In such cases, CADS may be relevant. Furthermore, the typical fixed-head boundary condition at the karst outlet can be inadequate for water abstraction scenarios because unhampered water inflow is possible. The objective of this work is to analyze the significance of CADS and flow-limited boundary conditions on the hydraulic behavior of karst aquifers in water abstraction scenarios. To this end, the numerical discrete-continuum model MODFLOW-2005 Conduit Flow Process Mode 1 (CFPM1) is enhanced to account for CADS. Additionally, a fixed-head limited-flow (FHLQ) boundary condition is added that limits inflow from constant head boundaries to a user-defined threshold. The effects and the proper functioning of these modifications are demonstrated by simplified model studies. Both enhancements, CADS and FHLQ boundary, are shown to be useful for water abstraction scenarios within karst aquifers. An idealized representation of a large-scale pumping test in a karst conduit is used to demonstrate that the enhanced CFPM1 is able to adequately represent water abstraction processes in both the conduits and the matrix of real karst systems, as illustrated by its application to the Cent Fonts karst system.
Modelling of karst development considering conduit-matrix exchange flow
This paper presents a numerical model study simulating the early karstification of a single conduit embedded in a carbonate matrix system. A hybrid continuum-discrete pipe flow model (CAVE) is used for the modelling. The effects of the coupling of the two flow systems on the type and duration of karstification is studied for different initial diameters of the conduit. Assuming a linear exchange term for the coupling of the conduit and matrix system leads to more rapid development of the conduit in the scenario presented. This effect is most pronounced for small initial diameters, where the rate of karstification is increased by a factor of 15 compared to the case with no exchange flow to the matrix system.
Karst aquifers are important for freshwater supply, but difficult to manage, due to highly variable water levels and spring discharge rates. Conduits are crucial for groundwater flow in karst aquifers, but their location is often unknown, thus limiting the applicability and validity of numerical models. We have applied a conduit model (SWMM) to simulate highly variable flow in a folded alpine karst aquifer system, where the underground drainage pattern is comparatively well-known from previous tracer studies. The conduit model was coupled with a reservoir model representing recharge, storage and transfer of water in the epikarst and unsaturated zone. The global optimization approach (GA) was applied to achieve an efficient model calibration. It was possible to simultaneously simulate the highly variable discharge characteristics of an estavelle, and overflow spring and a permanent spring draining the conduit system. The model allowed for the collection of spatially differentiated information on recharge, rapid flow and slow flow in four individual sub-catchments. The formation of backwater upgradient from conduit restrictions turned out to be a key process in activating overflow springs. The proposed modeling approach appears to be transferrable to other karst systems with predominant conduit drainage, but requires previous knowledge of the configuration of the conduit system.
Modeling of karst aquifer genesis: Influence of exchange flow
Water Resources Research, 2003
This paper presents a numerical model study simulating the early karstification of a single conduit embedded in a fissured system. A hybrid continuum-discrete pipe flow model (CAVE) is used for the modeling. The effects of coupling of the two flow systems on type and duration of early karstification are studied for different boundary conditions. Assuming fixed head boundaries at both ends of the conduit, coupling of the two flow systems via exchange flow between the conduit and the fissured system leads to an enhanced evolution of the conduit. This effect is valid over a wide range of initial conduit diameters, and karstification is accelerated by a factor of about 100 as compared to the case of no exchange flow. Parameter studies reveal the influence of the exchange coefficient and of the hydraulic conductivity of the fissured system on the development time for the conduit. In a second scenario the upstream fixed head boundary is switched to a fixed flow boundary at a specified flow rate during the evolution, limiting the amount of water draining toward the evolving conduit. Depending on the flow rate specified, conduit evolution may be slowed down or greatly impaired if exchange flow is considered.
Simulating the development of solution conduits in hypogene settings
Karst aquifers develop where an enlargement of fractures due to dissolution creates highly permeable conduits. These conduits are embedded in the much less permeable fissured system of the surrounding rock. The hydrogeological characterisation of these heterogeneous, dualistic flow systems requires a deep understanding of the processes involved in karstification. During the last two decades many numerical models have been developed to simulate conduit evolution in karst terrains and to understand and analyze the mechanisms of speleogenesis. In this study, conduit development within a soluble unit of a multi-layer aquifer system is examined by process-based numerical modeling. The dual flow system is adequately represented by a coupled continuum-pipe flow model; the flow model is coupled to a module calculating dissolution rates and the corresponding widening of conduits depending on flow conditions. The simplified model scenarios are largely based on field observations compiled from the gypsum karst terrain of the Western Ukraine. It is demonstrated that the hydraulic conductivity of the rock formation is a crucial factor that controls the frequency distribution of conduit diameters in hypogene speleogenesis. If the permeability of the rock formation is sufficiently high, conduit development is found to be competitive and leads to bimodal aperture distributions. Otherwise flow in low-permeability formations is suppressed and as a consequence, there is a smooth transition from scarcely developed proto-conduits to well-developed conduits rather than a clear and distinct separation. This work further examines the influence of the variability of the initial apertures on dissolutional growth of fissures and the evolving cave patterns. The initial apertures were not spatially correlated and log normally distributed. The influence of the aperture variability was investigated in several scenarios. It is found that in an ensemble average sense the degree of heterogeneity determines the temporal development of the cave patterns, i.e. higher aperture variability generally decelerates the karstification process. The aperture variability, however, appears to be of minor relevance regarding the general structure and geometric properties of the evolving cave patterns.
Acta Geologica Polonica, 2003
The aim of this work is to study the genesis of karst aquifers at the catchment scale. Especially the influence of different boundary conditions and geological setting is investigated in several scenarios. A hybrid continuum-discrete flow model is used for the modelling of conduit development. Effects of heterogeneity in hydraulic conductivity and in fracture spacing are examined in four scenarios. For homogeneous conditions a shallow water-table cave develops. If an area of reduced hydraulic conductivity is introduced, the conduit system evolves around this area and a deep phreatic cave is formed. This is true only, if the contrast in hydraulic conductivity is large enough. If an area of higher fracture density is introduced, this area is more intensely karstified, and a local system of deep karstification develops.
Water Resources Research, 2018
Due to the duality in terms of (1) the groundwater flow field and (2) the discharge conditions, flow patterns of karst aquifer systems are complex. Estimated aquifer parameters may differ by several orders of magnitude from local (borehole) to regional (catchment) scale because of the large contrast in hydraulic parameters between matrix and conduit, their heterogeneity and anisotropy. One approach to deal with the scale effect problem in the estimation of hydraulic parameters of karst aquifers is the application of large‐scale experiments such as long‐term high‐abstraction conduit pumping tests, stimulating measurable groundwater drawdown in both, the karst conduit system as well as the fractured matrix. The numerical discrete conduit‐continuum modeling approach MODFLOW‐2005 Conduit Flow Process Mode 1 (CFPM1) is employed to simulate laminar and nonlaminar conduit flow, induced by large‐scale experiments, in combination with Darcian matrix flow. Effects of large‐scale experiments w...