## 1. Introduction

[2] Modeling contaminant movement is a fundamental prerequisite to support geoenvironmental risk evaluation as well as the management and remediation of water resources. Presently, most of operational modeling tools have been constructed around the resolution of the so-called advection-dispersion equation (ADE) assuming that dispersion behaves as a diffusion-like (Fickian) process [*Adams and Gelhar*, 1992]. In this case, the mean and the variance of the contaminant (or tracer) spatial distribution scale with time (*t*) and , respectively, and the variance of the temporal distribution (i.e., of the breakthrough curve measured at a given observation spot) is finite. However, an increasing number of examples, both from situ [*Adams and Gelhar*, 1992; *Meigs and Beauheim*, 2001; *Becker and Shapiro*, 2003] and laboratory [*Silliman and Simpson*, 1987; *Berkowitz et al.*, 2000; *Levy and Berkowitz*, 2003] tracer tests, display strongly asymmetric BTCs with long tails (i.e., for times after the advective peak has passed) that appears to decrease more or less as a power law of time *C*(*t*)∼*t*^{−α}, and indicates an apparently infinite variance of the BTCs. Then, it becomes more and more certain that Fickian models fails to capture the real nature of the dispersion in natural systems submitted to common hydrological stresses; even in those thought as macroscopically homogeneous [*Levy and Berkowitz*, 2003]. In most cases, BTC analysis gives fitted values of the exponent *α* ranging from 1.5 and 2.5. However, it is generally difficult to measure accurately the BTC power law slope. Indeed, in the vicinity of the main concentration peak, measured concentration may be corrupted by the transition from the Fickian concentration decrease to the rate-limited decrease. Then, as concentration decreases toward very low values, measurement inaccuracy may spoil the estimate of the slope. Finally, it is difficult to evaluate if the observed BTC tail represents effectively the asymptotic behavior of the tracer recovery or a transitional behavior. To tackle the asymptotic non-Fickian dispersion behavior, high-resolution sensors and long-lasting recording of the tracer recovery are required.

[3] Non-Fickian dispersion properties, their origin and their relation to the geological heterogeneity are still debated. Authors have explored different approaches for better capturing the processes that control non-Fickian dispersion. Non-Fickian dispersion may be the result of long-range spatial correlation of geological structures and permeability. Multichannel model, in which all the velocities are infinitely correlated is the end-member case of this class model [*Becker and Shapiro*, 2003; *Gylling et al.*, 1999]. The overall mass transport is the sum of elementary transport in channels of distinctly different properties (leading to different flow rate and residence time), each of the channels being independent from each others. With this model, it is possible to reproduce power law-tailed BTC, by choosing the appropriate distribution of channel properties. Yet, recent results obtained by *Becker and Shapiro* [2003] when analyzing both well-to-well and single-well injection withdrawal tracing experiments show that the scaling of the residence time distribution is strongly controlled by the boundary condition (either prescribed flow rate or prescribed pressure) at the injection point and by flow geometry. The existence of long-range spatial correlation is also the basic assumption in models that describe dispersion as the result of alpha-normal (Levy flight) velocity distribution [*Benson et al.*, 2001], although quantitative relation between alpha-normal velocity distribution and the effective velocity correlation is not straightforward [*Le Borgne et al.*, 2007].

[4] Alternatively, non-Fickian dispersion may be represented by long-range temporal correlations of the solute motion that may be due to mass transfers in small-scale geological structures. For instance, the mobile-immobile mass transfer (MIM) model assumes mass exchanges between the moving fluid and a less permeable domain in which fluid is considered as immobile [*Haggerty and Gorelick*, 1995; *Carrera et al.*, 1998; *Haggerty et al.*, 2000]. The discrimination between the effects of spatial correlations controlled by large-scale structures and temporal correlations controlled by small-scale structures, both leading to non-Fickian transport, is a difficult task because it is most probable that both may be present simultaneously in some heterogeneous reservoirs. Nevertheless, it is possible to minimize velocity spatial correlation by performing single-well injection withdrawal (SWIW) tracing experiments and selecting reservoir targets displaying large-scale homogeneity.

[5] SWIW tracing tests, also called push-pull or echo tracer tests, consist in injecting a given mass of tracer in the medium and reversing flow after a certain time in order to measure the tracer breakthrough curve at the injection point [*Gelhar and Collins*, 1971, *Tsang*, 1995, *Haggerty et al.*, 2001, *Khrapitchev and Callaghan*, 2003]. This technique presents several advantages. First, the reversal of flow warrants an optimal tracer mass recovery. Second, SWIW tracer test allows measuring the irreversible dispersion (or mixing) whereas reversible dispersion; that is, the spreading due to long-range correlated path, taking place during the tracer push phase is canceled during the withdrawal phase [*Becker and Shapiro*, 2003, *Khrapitchev and Callaghan*, 2003]. The quantification of the reversible and irreversible dispersion refers to a given scale of observation which, in our case, is the maximal distance moved by the tracer during the SWIW tracer test. More precisely, velocity correlation, over distance smaller than the exploration size will result in irreversible dispersion (diffusion and mixing) whereas adjective spreading due to velocity correlation larger than the exploration size will be canceled (Figure 1). Thus, the measured dispersion using SWIW tests is only caused by tracer molecules that do not follow the same path on the injection and the withdrawal phases. Third, using SWIW tests, tracer may be pushed at different distances from the injection point, thus visiting different volumes of the system using a single well. This latter aspect, which was barely investigated in previous studies, allows exploring the dispersion processes for increasing volumes of reservoir, and testing, and subsequently validating, the predictive nature of the models.

[6] A set of SWIW tracer tests is presented in this paper. Our objective was to obtain high-quality measurements to explore the asymptotic behavior of this type of mass transfers and to investigate the scale effect on dispersion. For this first set of experiments, the intention was to focus on the study of the diffusion processes in immobile zones (i.e., matrix diffusion). Consequently, we intentionally targeted an aquifer displaying large-scale homogeneity (i.e., no fractures or large range correlated permeability zones), but small-scale heterogeneity. A second requirement was to minimize regional flow that may invalidate the radial symmetry assumption. For that seawater intrusion zones are ideal, because of the relative motionlessness due to the strong hydrostatic constraints imposed by the water layering configuration.

[7] The purpose of this paper is to describe the tracing experiments, compare them to previously published data and discuss the results in the frame of non-Fickian dispersion. First, the test site and the rock properties are presented in section 2. The experimental setup, together with the description of the new equipment and methodology developed for this purpose are presented in section 3. In section 4, the set of SWIW tracer tests is presented and results are discussed and tentatively modeled by the classical MIM mass transfer model. Finally, summary and conclusions are given in section 5. In a companion paper [*Le Borgne and Gouze*, 2008], an improved MIM mass transfer model is explored using a continuous time random walk model explaining the observations at large scales.