IntroductionTheoretical backgroundWorking assumptions and limitationsSpatial variability of apparent parameters in heterogeneous T-fields perfectly represented by an equivalent mediumInterpretation of breakthrough curvesGeneration of the transmissivity fieldExperimental approachExperimental setupExperimentsResults and analysisComputational approachSelection of numerical modelsSimulation featuresModel calibration and validationResults and analysisApparent porosityAnalysis of temporal momentsSummary and conclusionsAcknowledgementsReferencesConvergent-flow tracer tests in heterogeneousmedia: combined experimental–numerical analysisfor determination of equivalent transport parametersDaniel Ferna`ndez-Garciaa,*, Xavier Sa´nchez-Vilab,Tissa H. IllangasekareaaEnvironmental Science and Engineering Division, Colorado School of Mines, 1500 Illinois,Golden, CO 80401, USAbDepartment of Geotechnical Engineering and Geosciences, Technical University of Catalonia,Gran Capita S/N, 08034 Barcelona, SpainReceived 16 February 2001; received in revised form 25 October 2001; accepted 16 November 2001AbstractIn modeling transport within naturally heterogeneous aquifers, it is usually assumed that thetransport equations valid at local scales can also be applied at larger scales. At larger scales, theheterogeneous domain is represented by an equivalent homogeneous medium. Convergent-flowtracer tests constitute one of the most frequently used field tests to estimate effective input parametersof equivalent homogeneous aquifers. Traditionally, statistical approaches applied to groundwaterflow and solute transport have provided tools to estimate these equivalent parameters. Theseapproaches are based on a number of simplifications including the assumption that the pointtransmissivity values follow a multilog-normal random function. Several investigators have foundthat this assumption may not be valid in many field cases. In order to study the applicability of theequivalent homogeneous formulation in a nontraditional stochastic field, a number of experimentaland numerical studies were conducted. The results are used to determine the apparent values ofporosity and dispersivity that would be obtained if convergent-flow tracer tests were conducted in adeterministically generated heterogeneous transmissivity field displaying anisotropy in thecorrelation structure. It is shown that in this particular heterogeneous media, apparent porositystrongly depends on connectivity rather than on transmissivity. This dependence on connectivity0169-7722/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved.PII: S 0169-7722(01)00214-5*Corresponding author. Tel.: +1-303-384-2237; fax: +1-303-273-3629.E-mail addresses: [email protected] (D. Ferna`ndez-Garcia), [email protected](X. Sa´nchez-Vila), [email protected] (T.H. Illangasekare).www.elsevier.com/locate/jconhydJournal of Contaminant Hydrology 57 (2002) 129 – 145questions the theoretical results obtained in continuum equivalent fields to estimate effectiveporosity. D 2002 Elsevier Science B.V. All rights reserved.Keywords: Solute transport; Porous media; Heterogeneity; Spatial variability; Porosity; Dispersion1. IntroductionNumerical models designed to simulate the flow of water and solute migration throu ghaquifers require the discretization of the solution domain into blocks or elements defined bya computational grid. As a result, the computational-scale used in these models usuallybecomes much larger than the representative elemental volume (REV) scale where theclassical governing groundwater flow and solute transport equations are strictly applicable.To overcome this difficulty, it is traditionally considered possi ble to describe the heteroge-neous porous formation defined at the grid-scale by means of an equivalent homogeneousmedium. The properties attributed to this virtual medium are known as equiva lent or blockparameters, and they can be seen as spatial averages of the local properties over thecomputational grid-scale (Dagan, 1986; Desbarats, 1992). Following this approach, it isimplicitly assumed that the use of an e quivalent homogeneous medium yields a goodapproximation to the real problem to be solved. In this sense, the stochastic approach appliedto groundwater flow and solute transport considers the real solution as a small perturbationof the average solution (Dagan, 1989; Gelhar and Axness, 1983) and provides estimates ofthese so-called effective parameters attributed to this artificial field. However, even thoughfield data can only properly explain log-transmissivity as a univariate Gaussian distribution(Freeze, 1975), these traditional stochastic approaches assume the spatial distribution oftransmissivity or hydraulic conductivity to be described by a multilog-normal randomfunction. Recent investigations ha ve studied the magnitude of this extrapolat ion and foundthat real field sites do not display many of the cha racteristics of multi-Gaussian distributions(Go´mez-Herna´ndez and Wen, 19 96; Sa´nchez-Vila et al., 1996).The main objective of this paper is to further investigate the applicability of equivalenthomogeneous fields in a more realistic context as well as to evaluate those transportparameter estimates resulting from the inte rpretation of tracer tests based upon equivalenthomogeneous fields. The analysis is limited to the aquifer parameters typically obtainedfrom convergent radial flow tests, which are porosity and longitudinal dispersivity. Thespatial variability of these two parameters is investigated in a heterogeneous, nonstochas-tically generated domain that displays anisotropy in the correlation structure of the trans-missivity field (T-field). In convergent radial flow tests, water is pumped from a single welluntil steady-state flow is achieved. A tracer is then introduced into a well located at somedistance from the pumping well and the breakthrough tracer concentrations at the pumpingwell are recorded as a function of time. Interpretation of the tracer breakthrough curve (BTC)under the assumption of homog eneity and radial symmetry yields the required aquiferparameters. However, since natural aquifers are heterogeneous, these parameter valuesobtained from ideal isotropic models vary as a function of the injection location. Theseparameters can only be seen as fitting or apparent parameters, and they should be treated asD. Ferna`ndez-Garcia et al. / Journal of Contaminant Hydrology 57 (2002)