WATER RESOURCES RESEARCH, VOL. 17, NO. 5, PAGES1517-1527, OCTOBER1981 Transportof Ion-Exchanging Solutes in Groundwater: Chromatographic Theory and Field Simulation ALBERT J. VALOCCHI, • ROBERT L. STREET, AND PAUL V. ROBERTS Department of CivilEngineering, Stanford University, Stanford, California 94305 Equations describing the transport of ion-exchanging solutes governed by localchemical equilibrium through a saturated porous medium arewellestablished in theliterature. Concentration profiles resulting from the numerical solution of the general multispecies equations typically exhibitunusual and com- plicated features such asmultiple fronts andplateau zones. Thispaper presents an analytical framework, based upon thetheory of chromatography, which permits a prioricharacterization of certain key concen- tration profile features. The cases studied include bothhomovalent andheterovalent exchange in binary andternary systems. In order to test itsvalidity, the chromatographic analysis is applied to a field project involving direct injection of advanced treated municipal effluent into an aquifer. All of the major fea- tures observed in the available field data are accurately predicted by the chromatographic theory. INTRODUCTION Due to increased interest in wastewater reuse, groundwater recharge of municipal effluents is becoming a common feature of manyregional waterresources plans. It is believed that pas- sagethrough the soil environment will provide further re- moval of certain chemical and microbial contaminants and thusrenderthe recharged water more suitable for reuse pur- poses. Using an advanced wastewater treatment facility and an injection/extraction well fieldlocated in thePalo Alto Bay- lands region, a groupof investigators at Stanford University has been 'involved in an ongoing studyto ascertain whether directinjection of municipaleffluents is a reliableand feasible strategy forproducing potable water [Roberts etal., 1978]. Sig- nificant inorganic chemical changes dueto ion exchange proc- esses have beenobserved in the Palo Alto field studyand in other similar recharge operations [Wesherand Baier, 1970; Grove and Wood, 1979]. In order to morefully understand and predict these chemicalchanges, a mathematicalsimulation model of the transport of ion-exchanging solute s wasdevel- oped and tested. The ion exchange reactions treated in this study are as- sumed to be governed by localchemical equilibrium. The ap- propriate transport equations and numerical solution tech- niques for these types of reactions have been treated extensively in the classic paperof Rubinand James [1973]. Their modelwas based upon steady, one-dimensional flow in a saturated porous medium. They considered the general mul- tispecies system and were thus able to treat problems in- volving such features asheterovalent exchange and changing total concentration of pore fluid ions. The final operational transport model reduced to a complex system of coupled, non- linearpartial differential equations whichwassolved numeri- callyby the Galerkin-finite element method. Schwartz [1975] used the method of characteristics to solve for two-dimen- sional transport through a vertical cross section of an aquifer; however, he studied only two-species exchange underthe as- sumption that the total concentration of pore fluid ions was constant. RubinandJames [1973] presented several hypothet- ical examples illustrating that the concentration profiles result- I NOW at theDepartment of CivilEngineering, University of Illi- nois at Urbana-Champaign, Urbana, Illinois, 61801. Copyright ¸ 1981 by the American Geophysical Union. ing from the general equations oftendisplay unusual features such as multiple fronts and plateau zones. These same phe. nomena have alsobeenobserved by several other investiga- tors, including Grove and Wood [1979] and gan Beek and Pal [1978]. The complex nature of themultispecies transport equations makes it very difficult to predict a priori the general features of theresulting concentration profiles. Thepurpose of this pa- peristo present an analytkal methodology withwhich certain key features of the multisPecies concentration profiles can be characterized. This methodology is based uponthe theory of chromatography, which utilizes simple mass balance argu- ments to deduce analytically the general concentration re- sponse. The most general presentation of thistheory is given by Helfferich and Klein [1970]; however, they focus upon homovalent exchange under the assumption that the total concentration of exchangeable ions in thepore fluid(i.e.,total solution normality) is constant. They also ignore the effects of hydrodynamic dispersion. Recently, this work has been ex- tendedin a preliminary manner by Pope et al. [1978] and Lake andHelfferich [1978] to include monovalent-divalent ex- change and hydrodynamic dispersion. These chromato- graphic theories have been appliedto a certainextentin the fieldof soilscience [e.g., Frissel andPoelstra, 1967]. However, as reviewed by Reiniger and Bolt [1972], all of these appli- cations have been for binary exchange under conditions of constant totalconcentration of exchangeable ions. In thispa- per we extend these theories to the case of multispecies heter- ovalentexchange under conditions of varying total solution normality. In order to performthe chromatographic analysis, we fol- low these previous investigators and assume steady, one-di- mensional flow in a saturated, homogeneous soilcolumn.The theoretical postulates derived from the analysis can be tested by comparison with the actual concentration profiles deter- minedby solving numerically the full setof transport equa- tions. The numerical solution technique used in this study is similarto that employed by Rubinand •ames [1973]. The nu- merical simulation modelis then appliedto predictcation transport in a particular fieldproject involving direct injection of advanced treated municipal effluent into a groundwater aquifer. The purpose of this field simulation is to test the va- lidity of the chromatographic theory for field-scale transport problems. Paper number IW0717. 0043-1397/81/001W-0717501.00 1517