Freiburger Schriften zur Hydrologie

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Band/volume 2: MALOSZEWSKI P. (1994):

Mathematical Modelling of Tracer Experiments in Fissured Aquifers

Models of solute transport in fissured rocks applicable for the interpretation of tracer experiments are discussed in detail. All the models derive from the Parallel Fissure Dispersion Model (PFDM), which couples the transport equation in fissures with the diffusion equation in matrix. In short-term tracer experiments its approximation, i.e. the Single Fissure Dispersion Model (SFDM), or the Single Fissure Piston Flow Model (SFPFM), are shown to be applicable.
For long-term tracer experiments and for the interpretation of environmental tracer data, the common Dispersion Model (DM) with parameters governed by matrix diffusion is shown to be adequate. Other models applicable to the dating of old waters are obtaihed from steady and transient states solutions to the basic model, i.e. the PFDM. The influence of parameters on the tracer curves yielded by particular models is investigated theoretically and demonstrated graphically by making use of direct solutions.
Case studies show how the inverse problem can be solved, i.e. how some parameters of an investigated system can be found by calibration (fitting) of the model to the experimental data. It is shown, that a good fit is a necessary but not sufficient condition for the applicability of a model. Validation, or a partial validation at least, should be obtained wherever possible.
Conditions for the applicability of the approximate models have beerl derived and their usefulness demonstrated. In all field case studies interpreted so far by the author, the matrix diffusion was shown to playadominant or important role.
The mean transit time of water obtained from the 14C or tritium ages, interpreted without taking into ac count the retardation factor resulting from the matrix diffusion, is shown to lead to greatly overestimated volumes of mobile water in fissured systems. Artificial tracer experiments, designed for finding the retardation factor caused by matrix diffusion and possible reactions, are shown to be potentially useful for the interpretation of environmental tracer data. On ce the retardation factor is known, it can be used to interpret the mobile water content and/or other hydrogeological parameters from the environmental tracer ages. However, the concept of the retardation factor, which is weIl defined for conservative tracers, is not generally applicable for relating the environmental radiotracer ages with hydrogeological parameters. Its applicability has to be examinated for each case study.

It has also been demonstrated, that the parameters of the common dispersion model (DM) cannot be obtained from short-term tracer experiments, even if a good fit of that model is obtained. However, the SFDM applied to short-term experiments can be used to determine the physical parameters of the system, which can in turn serve for obtaining the parameters of the DM, applicable at large scales, and then for the prediction of pollutant movement.

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