A stochastic multi-channel model for solute transportanalysis of tracer tests in fractured rockIvars Neretnieks*Department of Chemical Engineering and Technology, Royal Institute of Technology, 10044 Stockholm, SwedenReceived 26 July 2000; received in revised form 7 September 2001; accepted 24 September 2001AbstractSome of the basic assumptions of the advectiondispersion 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 Aspo Hard rock laboratory in Sweden. Non-sorbing tracers, HTO and Uranin were0169-7722/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S0169-7722(01)00195-4*Fax: +46-8-105228. E-mail address: niquelket.kth.se center (I. Neretnieks).www.elsevier.com/locate/jconhydJournal of Contaminant Hydrology 55 (2002) 175211used 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. D 2002 Elsevier Science B.V. All rights reserved.Keywords: Groundwater; Solute transport; Fractures; Modelling1. Introduction and backgroundIt has been increasingly recognized that dispersion is not always Fickian. Compilations of dispersion data show that over a very large range of observation distances, the dispersion length increases with distance (Lallemand-Barres and Peaudecerf, 1978; Matheron and de Marsily, 1980; Neretnieks, 1981, 1983, 1993; Gelhar et al., 1992; Gelhar, 1993). It is, however, common practice to use the advectiondispersion (AD) equation, with a constant dispersion length, to analyze, simulate and predict tracer transport in the ground. For a given distance, the advectiondispersion, the channeling, the channel network and probably several other models can be made to adequately describe a tracer breakthrough curve. In the AD-model, a constant dispersion length is then typically used. This has some strange consequences. Assume that we choose a dispersion length a when simulating the tracer breakthrough curve at distance L along the flowpath. The commonly used analytical solutions have been obtained based on the assumption that a is constant all along the path. With the same solution, one could predict the tracer breakthrough curve also at, say a distance L/10 along the flow path. This, however, is in violation of the observations that at distance L/10 the dispersion length is a/10. We would thus obtain a different breakthrough curve, were we to use a/10 to make pre- dictions for the distance L/10. It may thus be concluded that the common analytical solution(s) based on a constant a cannot give a correct representation of the transport along all the flowpath. Let us then consider an alternative approach. Assume that a increases with distance from the point where the tracer is injected and downstream. This is readily incorporated in numerical schemes to solve the ad