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**solution conduits**(Keyword) returned

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The advection-dispersion model (ADM) is a good tool for simulating transport of dye or solutes in a solution conduit. Because the general problem of transport can be decomposed into two problems, a boundary-value problem and an initial-value problem, the complete solution is a superposition of the solutions for these two problems. In this paper, the solution for the general problem is explained. A direct application of the solution for the boundary-value problem is dye-tracing experiments. The purpose is inclusion of the input history of a solute dye into the ADM. The measured breakthrough curve of a dye-tracing experiment is used to invert for the release history of the dye at the input point through the ADM. It is mathematically shown that the breakthrough curve can not be directly used to invert for the boundary condition at a tracer release point. Therefore, a conductance-fitting method is employed to obtain the input history. The inverted history for a simple example is then shown to be a step function with amplitude of 420 mg/L and a duration of 10 minutes. Simulations illustrate that the breakthrough curves at downstream springs provide a means for understanding the migration of dye. A discussion of the implication of the solution for an initial-value problem (e.g., simulating transport of preexisting solutes such as dissolved calcium carbonate in solution conduits) is also included.

Karst aquifers evolve where the dissolution of soluble rocks causes the enlargement of discrete pathways along fractures or bedding planes, thus creating highly conductive solution conduits. To identify general interrelations between hydrogeological conditions and the properties of the evolving conduit systems the aperture-size frequency distributions resulting from generic models of conduit evolution are analysed. For this purpose, a process-based numerical model coupling flow and rock dissolution is employed. Initial protoconduits are represented by tubes with log-normally distributed aperture sizes with a mean of 0.5 mm. Apertures are spatially uncorrelated and widen up to the metre range due to dissolution by chemically aggressive waters. Several examples of conduit development are examined focussing on influences of the initial heterogeneity and the available amount of recharge. If the available recharge is sufficiently high the evolving conduits compete for flow and those with large apertures and high hydraulic gradients attract more and more water. As a consequence, the positive feedback between increasing flow and dissolution causes the breakthrough of a conduit pathway connecting the recharge and discharge sides of the modelling domain. Under these competitive flow conditions dynamically stable bimodal aperture distributions are found to evolve, i.e. a certain percentage of tubes continues to be enlarged while the remaining tubes stay small-sized. The percentage of strongly widened tubes is found to be independent of the breakthrough time and decreases with increasing heterogeneity of the initial apertures and decreasing amount of available water. If the competition for flow is suppressed because the availability of water is strongly limited breakthrough of a conduit pathway is inhibited and the conduit pathways widen very slowly. The resulting aperture distributions are found to be unimodal covering some orders of magnitudes in size. Under these suppressed flow conditions the entire range of apertures continues to be enlarged. Hence, the number of tubes reaching aperture sizes in the order of centimetres or decimetres continues to increase with time and in the long term may exceed the number of large-sized tubes evolving under competitive flow conditions. This suggests that conduit development under suppressed flow conditions may significantly enhance the permeability of the formation e.g. in deep-seated carbonate settings.

Karst aquifers evolve where the dissolution of soluble rocks causes the enlargement of discrete pathways along fractures or bedding planes, thus creating highly conductive solution conduits. To identify general interrelations between hydrogeological conditions and the properties of the evolving conduit systems the aperture-size frequency distributions resulting from generic models of conduit evolution are analysed. For this purpose, a process-based numerical model coupling flow and rock dissolution is employed. Initial protoconduits are represented by tubes with log-normally distributed aperture sizes with a mean ?0 = 0.5 mm for the logarithm of the diameters. Apertures are spatially uncorrelated and widen up to the metre range due to dissolution by chemically aggressive waters. Several examples of conduit development are examined focussing on influences of the initial heterogeneity and the available amount of recharge. If the available recharge is sufficiently high the evolving conduits compete for flow and those with large apertures and high hydraulic gradients attract more and more water. As a consequence, the positive feedback between increasing flow and dissolution causes the breakthrough of a conduit pathway connecting the recharge and discharge sides of the modelling domain. Under these competitive flow conditions dynamically stable bimodal aperture distributions are found to evolve, i.e. a certain percentage of tubes continues to be enlarged while the remaining tubes stay small-sized. The percentage of strongly widened tubes is found to be independent of the breakthrough time and decreases with increasing heterogeneity of the initial apertures and decreasing amount of available water. If the competition for flow is suppressed because the availability of water is strongly limited breakthrough of a conduit pathway is inhibited and the conduit pathways widen very slowly. The resulting aperture distributions are found to be unimodal covering some orders of magnitudes in size. Under these suppressed flow conditions the entire range of apertures continues to be enlarged. Hence, the number of tubes reaching aperture sizes in the order of centimetres or decimetres continues to increase with time and in the long term may exceed the number of large-sized tubes evolving under competitive flow conditions. This suggests that conduit development under suppressed flow conditions may significantly enhance the permeability of the formation, e.g. in deep-seated carbonate settings.

Solute transport in karst aquifers is primarily constrained to solution conduits where transport is rapid, turbulent, and relatively unrestrictive. Breakthrough curves generated from tracer tests are typically positively-skewed and may exhibit multiple peaks. In order to understand the circumstances under which multi-peaked positively skewed breakthrough curves occur, physical experiments utilizing singleand multiple-flow channels were conducted. Experiments also included waterfalls, short-term solute detention in pools, and flow obstructions. Results demonstrated that breakthrough curve skewness nearly always occurs to some degree but is magnified as immobile-flow regions are encountered. Multi-peaked breakthrough curves occurred when flow in the main channel became partially occluded from blockage in the main channel that forced divergence of solute into auxiliary channels and when waterfalls and detention in pools occurred. Currently, multi-peaked breakthrough curves are fitted by a multi-dispersion model in which a series of curves generated by the advection–dispersion equation are fitted to each measured peak by superimposing the measured breakthrough curve to obtain a combined model fit with a consequent set of estimated velocities and dispersions. In this paper, a dual-advection dispersion equation with first-order mass transfer between conduits was derived. The dual-advection dispersion equation was then applied to the multi-peaked breakthrough curves obtained from the physical experiments in order to obtain some insight into the operative solute-transport processes through the acquisition of a consequent set of velocities, dispersions, and related parameters. Successful application of the dual-advection, dispersion equation to a tracer test that exhibited dual peaks for a karst aquifer known to consist of two connected but mostly separate conduits confirmed the appropriateness of using a multi-dispersion type model when conditions warrant.

The solutional growth of karst features involves a simple mass transfer, in which the mass removed from the walls of a void equals the mass removed in solution by flowing water. Mass removed = volume rock density, and mass in solution = discharge solute concentration. Therefore (e.g., in a solution conduit) the rate of volume increase = discharge gain in dissolved load time / rock density. Density is essentially con-stant, so conduit size depends only on the cumulative values of discharge, dissolution rate, and time. All three are essential, and all are equally important.

Discharge in a conduit depends on catchment area and water balance; and the distribu-tion of water among all solution conduits depends on hydraulic variables and conduit geometry. Dissolution rate varies with rock type, undersaturation, and solution kinetics, the last of which can be determined by laboratory and field measurements. Together, they provide a tool for quantifying the local geomorphic history.

These relationships seem simple, but applying them quantitatively is complex. This requires a finely divided 2- or 3-dimensional grid in which each segment varies in dis-charge and dissolution rate within each of many small time increments. Computer modelers use this approach to simulate conduit growh; but the results depend on the specific boundary conditions of the model.

It is more challenging to use this concept intuitively to solve real field problems, where the variables are only partly understood. In this case, one must show that the water source, dissolution rate, and available time are all great enough to account for the ob-served solution features. All three variables are closely linked by a web of interactive processes, all of which can be expressed quantitatively. Whether the goal is to under-stand what is already known, or to predict the unknown, this approach provides a solid basis for interpreting karst systems.

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