A stochastic multi-channel model for solute transport—analysis of tracer tests in fractured rock

Abstract

Some of the basic assumptions of the advection–dispersion model (AD-model) are revisited. This model assumes a continuous mixing along the flowpath similar to Fickian diffusion. This implies that there is a constant dispersion length irrespective of observation distance. This is contrary to most field observations. The properties of an alternative model based on the assumption that individual water packages can retain their identity over long distances are investigated. The latter model is called the multi-channel model (MCh-model). Inherent in the latter model is that if the waters in the different pathways are collected and mixed, the “dispersion length” is proportional to distance. The conditions for when non-mixing between adjacent streams can be assumed are explored. The MCh- and AD-models are found to have very similar residence time distributions (RTD) for Peclet numbers larger than 3. A generalized relation between flowrate and residence time is developed, including the so-called cubic law and constant aperture assumptions. The two models extrapolate very differently when there is strong matrix interaction. The AD-model could severely underestimate the effluent concentration of a tracer pulse and overestimate the residence time. The conditions are explored for when in-filling particles in the fracture will not be equilibrated but will act as if there was seemingly a much larger flow wetted surface (FWS). It is found that for strongly sorbing tracers, relatively small particles can act in this way for systems and conditions that are typical of many tracer tests. The assumption that the tracer residence time found by cautiously injecting a small stream of traced water represents the residence time in the whole fracture is explored. It is found that the traced stream can potentially sample a much larger fraction of the fracture than the ratio between the traced flowrate and the total pumped flowrate. The MCh-model was used to simulate some recent tracer tests in what is assumed to be a single fracture at the Äspö Hard rock laboratory in Sweden. Non-sorbing tracers, HTO and Uranin were used to determine the mean residence time and its variance. Laboratory data on diffusion and sorption properties were used to “predict” the RTD of the sorbing tracers. At least 30 times larger FWS or 1000 times larger diffusion or sorption coefficients would be needed to explain the observed BTCs. Some possible reasons for such behavior are also explored.