WATER RESOURCES RESEARCH, VOL. 20, NO. 3, PAGES 369-378, MARCH 1984 An Advection-Diffusion Concept for Solute Transport in Heterogeneous Unconsolidated GeologicalDeposits R. W. GILLHAM, E. A. SUDICKY,J. A. CHERRY, AND E. O. FRIND Department of Earth Sciences, University of Waterloo In layeredpermeable deposits with flow predominately parallel to the bedding, advection causes rapid solutetransport in the more permeable layers.As the soluteadvances more rapidly in these layers,solute massis continually transferred to the lesspermeable layers as a result of moleculardiffusion due to the concentration gradient betweenthe layers. The interlayer solute transfer causes the concentration to decline along the permeable layersat the expense of increasing the concentration in the less permeable layers, whichproduces strongly dispersed concentration profiles in the direction of flow. The key param- etersaffecting the dispersive capabilityof the layeredsystem are the diffusion coefficients for the less permeable layers, the thicknesses of the layers, and the hydraulic conductivitycontrasts between the layers.Because interlayer solutetransferby transvetse moleculardiffusionis a time-dependent process, the advection-diffusion concept predicts a rate of longitudinalspreading during the development of the dispersion process that is inconsistent with the classical Fickian dispersion model. A second consequence of the solute-storage effect offeredby transverse diffusioninto low-permeability layers is a rate of migration of the frontal portion of a contaminantin the permeable layersthat is less than the groundwa- ter velocity. Although various lines of evidence are presented in support of the advection-diffusion concept, more work is requiredto determine the range of geological materials for which it is applicable and to developmathematicalexpressions that will make it usefulas a predictivetool for application to field cases of contaminant migration. INTRODUCTION In spite of substantial research effortsduring the past two decades, the goal of predicting the migration of dissolved con- taminants in groundwater flow systems composedof per- meableunconsolidated deposits remains elusive. This situation can be attributed primarily to an inadequate knowledge of the effectson dispersion of layers and lenses occurringin these deposits. The problem of simulating dispersion in suchhetero- geneous materials is usuallypursued along one of two basic lines: a conventional approach that utilizes a deterministic form of the advection-dispersion equation and stochastic ap- proachesthat recognize the heterogenitythrough the pre- sumed statisticalproperties of the aquifer. By making use of theseproperties, the uncertainty in masstransportprediction can then be estimated. The advection-dispersion equation considers the solute flux to be the result of the average bulk motion of the fluid in the direction of groundwaterflow (advection) and a Fickian-type mixing betweenthe original and displacing fluid (dispersion). For saturatedflow in isotropic heterogeneous porous media, the governing equation is writtenas c•c c•v•c c• c•c c•t t c•xi c•xi Dij •xj-- 0 (1) where c is the solution concentration (M/L3), vi is the linear groundwater velocity (L/T) andDij is the hydrodynamic dis- persion tensor (L2/T).An early development of the advection- dispersion equation is given by Scheidegger [1954], and its applications are described in detail by Bear [1972] and Fried [1975]. Gillhamand Cherry [1982] discuss several limitations of the model and critically appraise its utility as a predictive tool. The hydrodynamic dispersion tensor is assumed to be the Copyright 1984by the AmericanGeophysical Union. Paper number 3W 1732. 0043-1397/84/003 W- 1732505.00 369 sum of two components, which for isotropic media can be represented as [Bear, 1972] Dij = •rV6i• + (• -- •r)ViV•/V + D*6i• (2) where 0•(L), known as dispersivity, is considered to be a characteristic mixing lengthfor the porousmedium,and D* is the effective molecular diffusion coefficient for a particular solutespecies. The dispersivity tensoris described by its longi- tudinal (%) and tranverse (0•T) principal components in direc- tions parallel to and orthogonalto the flow line, respectively. The product of dispersivityand flow velocity is known as mechanical dispersion, which is a mixing process introduced in the classical development of (1) by averaging irregular ad- vective displacements taking placewithin the pore structure of the medium. Because mechanical dispersion is conventionally treated as a Fickian-type spreadingmechanism, it is repre- sented asa process that is additive to molecular diffusion. In activegroundwater flow in granular media,mechanical disper- sion is usuallyregardedto be much larger than the diffusive term, and thusD* is commonly deleted from (2). The mathematical solutionsto the advection-dispersiøn equation have bSen shown bynumerous investigators to pro- vide accuraterepresentations of solute transport by miscible fluids in homogeneous soil columns. With few exceptions, lab- oratory dispersion experiments reported in the literature pro- vide measurements of% that fall in the range of 10 -4 to 10 z2 m. However, when sølutions to the equation are calibrated with concentration data obtained from large-scalezones of contaminatedgroundwaterin heterogeneous sand or gravel aquifers, values of % in the range of 1 to 100 m are commonly obtained. Anderson [1979] presents a summary of • values determinedfrom field tracer tests and investigations of con- taminant plumes. The large differences in valuesof % obtained from labora- tory tests, field tracer tests, and studies of large-•scale contami- nant plumeshave led numerous investigators to conclude that dispersivity is a parameterdependent on the scaleof the test or on the sizeof the porousdomain through which the solute