Hydrogeology Journal (1999) 7 : 251–263 Q Springer-Verlag Sulfate transport in a Coastal Plain confining unit, New Jersey, USA Amleto A. Pucci, Jr. Received, January 1997 Revised, April 1998, October 1998, January 1999 Accepted, January 1999 Amleto A. Pucci, Jr. Ground-Water Management and Conservation, Inc., PO Box 78 Erwinna, PA 18920, USA Fax: c1-610-294-9475 e-mail: puccia6epix.net Abstract A transient 1-D, two-pathway non-equi- librium deterministic advective dispersion model was used to examine the distribution of chloride (43–100 mg/L) and sulfate (57–894 mg/L) concentra- tions in the 35-m-thick section of the Lower confining unit, Atlantic Coastal Plain, New Jersey, USA. The model was used to constrain hypotheses about how pore-water chemistry changed over time. Explanations of the solute concentrations were explored by inverse and direct methods given a few known constraints, including concentrations of pore-water constituents from 12 core samples, reported simulated flow rates, and estimated hydrogeologic properties. The hypoth- esis that is best supported by the model results is that the distribution of chloride and sulfate concentrations in the confining unit reflect the history of the aquifer system since it was filled with seawater at the last eustatic high, about 84!10 3 yr BP. The model simulates fresh-water flushing of the seawater-permeated silts at a steady upward pore-water flow velocity of 8.8!10 –6 m/d, with a dispersion coefficient of 9.2!10 –7 m 2 /d, a dimensionless partition expression for chloride, b Cl p0.981, and a dimensionless exchange coefficient, v Cl p0.31!10 –2 . Sulfate concentrations were simulated over the flow path using flow and dispersion values calculated for chloride transport plus a retardation term. Parameters for sulfate transport include retardation coefficientp4.51, b SO4 p0.994, and v SO4 p0.31!10 –2 . Sensitivity analysis indicates that the model is most sensitive to flow velocity, and that fresh- water flushing of the confining unit is best simulated by having seawater concentration levels at the inflow boundary of the confining unit exponentially decrease with a concentration half-life rate of 825 yr. Résumé Un modèle déterministe, non à l’équilibre, à deux cheminements fonctionnant en régime transitoire à une dimension en advection-dispersion, a été utilisé pour analyser la distribution des concentrations en chlorures (43–100 mg/L) et en sulfates (57–894 mg/L) dans une section, épaisse de 35 m, de l’unité aquifère inférieure captive (Plaine côtière atlantique, New Jersey, États-Unis). Le modèle a été utilisé pour contraindre les hypothèses concernant la façon dont évolue au cours du temps le chimisme de l’eau des pores. Les différentes explications des concentrations en solutés ont été explorées par des méthodes inverses et directes, à partir d’un petit nombre de contraintes connues, parmi lesquelles les constituants de l’eau des pores de 12 échantillons carottés, les débits simulés et les caractéristiques hydrogéologiques estimées. L’hypothèse répondant le mieux aux résultats du modèle est celle selon laquelle la distribution des concentrations en chlorures et en sulfates dans l’unité captive reflète l’histoire du système aquifère depuis qu’il a été envahi par l’eau de mer lors du dernier stade eustatique haut, il y a environ 84,000 ans. Le modèle simule la chasse de l’eau douce des silts envahis par l’eau de mer à une vitesse constante de l’eau des pores vers le haut de 8,8!10 –6 m/j, avec un coefficient de dispersion de 9,2!10 –7 m 2 /j, un coefficient sans dimen- sion de partition des chlorures b Cl p0,981, et un coeffi- cient d’échange, v Cl p0,31!10 –2 . Les concentrations en sulfates ont été simulées, le long des directions d’écoulement, au moyen de valeurs de flux et de disper- sion calculées pour le transport des chlorures, moyen- nant un facteur de retard. Les paramètres pour le trans- port des sulfates sont, avec un coefficient de retard égal à 4.51, b SO4 p0.994 et v SO4 p0.31!10 P2 . L’analyse de sensibilité indique que le modèle est le plus sensible à la vitesse de l’écoulement, et que la chasse de l’eau douce de l’unité captive est simulée le mieux avec des niveaux de concentration de l’eau de mer à la limite d’entrée de l’unité captive qui décroissent exponentiel- lement selon une «demi-vie» de 825 ans. Resumen Para examinar la distribución de las concen- traciones de cloruro (43–100 mg/L) y sulfato (57–894 mg/L) en una sección de 35 m de espesor de la unidad confinante de la Llanura Costera Atlántica, en New Jersey (EEUU), se utilizó un modelo unidimen-
Sulfate transport in a Coastal Plain confining unit, New Jersey, USA
Amleto A. Pucci, Jr.
Received, January 1997Revised, April 1998, October 1998, January 1999Accepted, January 1999
Amleto A. Pucci, Jr.Ground-Water Management and Conservation, Inc., PO Box 78Erwinna, PA 18920, USAFax: c1-610-294-9475e-mail: puccia6epix.net
Abstract A transient 1-D, two-pathway non-equi-librium deterministic advective dispersion model wasused to examine the distribution of chloride(43–100 mg/L) and sulfate (57–894 mg/L) concentra-tions in the 35-m-thick section of the Lower confiningunit, Atlantic Coastal Plain, New Jersey, USA. Themodel was used to constrain hypotheses about howpore-water chemistry changed over time. Explanationsof the solute concentrations were explored by inverseand direct methods given a few known constraints,including concentrations of pore-water constituentsfrom 12 core samples, reported simulated flow rates,and estimated hydrogeologic properties. The hypoth-esis that is best supported by the model results is thatthe distribution of chloride and sulfate concentrationsin the confining unit reflect the history of the aquifersystem since it was filled with seawater at the lasteustatic high, about 84!103yr BP. The model simulatesfresh-water flushing of the seawater-permeated silts ata steady upward pore-water flow velocity of8.8!10–6 m/d, with a dispersion coefficient of9.2!10–7 m2/d, a dimensionless partition expression forchloride, bClp0.981, and a dimensionless exchangecoefficient, vClp0.31!10–2. Sulfate concentrationswere simulated over the flow path using flow anddispersion values calculated for chloride transport plusa retardation term. Parameters for sulfate transportinclude retardation coefficientp4.51, bSO4p0.994, andvSO4p0.31!10–2. Sensitivity analysis indicates that themodel is most sensitive to flow velocity, and that fresh-water flushing of the confining unit is best simulated byhaving seawater concentration levels at the inflowboundary of the confining unit exponentially decreasewith a concentration half-life rate of 825 yr.
Résumé Un modèle déterministe, non à l’équilibre, àdeux cheminements fonctionnant en régime transitoireà une dimension en advection-dispersion, a été utilisépour analyser la distribution des concentrations enchlorures (43–100 mg/L) et en sulfates (57–894 mg/L)dans une section, épaisse de 35 m, de l’unité aquifèreinférieure captive (Plaine côtière atlantique, NewJersey, États-Unis). Le modèle a été utilisé pourcontraindre les hypothèses concernant la façon dontévolue au cours du temps le chimisme de l’eau despores. Les différentes explications des concentrationsen solutés ont été explorées par des méthodes inverseset directes, à partir d’un petit nombre de contraintesconnues, parmi lesquelles les constituants de l’eau despores de 12 échantillons carottés, les débits simuléset les caractéristiques hydrogéologiques estimées.L’hypothèse répondant le mieux aux résultats dumodèle est celle selon laquelle la distribution desconcentrations en chlorures et en sulfates dans l’unitécaptive reflète l’histoire du système aquifère depuisqu’il a été envahi par l’eau de mer lors du dernier stadeeustatique haut, il y a environ 84,000 ans. Le modèlesimule la chasse de l’eau douce des silts envahis parl’eau de mer à une vitesse constante de l’eau des poresvers le haut de 8,8!10–6 m/j, avec un coefficient dedispersion de 9,2!10–7 m2/j, un coefficient sans dimen-sion de partition des chlorures bClp0,981, et un coeffi-cient d’échange, vClp0,31!10–2. Les concentrations ensulfates ont été simulées, le long des directionsd’écoulement, au moyen de valeurs de flux et de disper-sion calculées pour le transport des chlorures, moyen-nant un facteur de retard. Les paramètres pour le trans-port des sulfates sont, avec un coefficient de retard égalà 4.51, bSO4p0.994 et vSO4p0.31!10P2. L’analyse desensibilité indique que le modèle est le plus sensible àla vitesse de l’écoulement, et que la chasse de l’eaudouce de l’unité captive est simulée le mieux avec desniveaux de concentration de l’eau de mer à la limited’entrée de l’unité captive qui décroissent exponentiel-lement selon une «demi-vie» de 825 ans.
Resumen Para examinar la distribución de las concen-traciones de cloruro (43–100 mg/L) y sulfato(57–894 mg/L) en una sección de 35 m de espesor de launidad confinante de la Llanura Costera Atlántica, enNew Jersey (EEUU), se utilizó un modelo unidimen-
sional, determinista, con flujo transitorio, y en el que seconsideraba advección-dispersión en condiciones deno-equilibrio. El modelo se usó para centrar las hipóte-sis sobre los cambios de la química del agua intersticialcon el tiempo. Se exploraron los valores de concentra-ciones de solutos mediante métodos directos e inversosa partir de unas pocas restricciones que incluían losvalores de concentraciones de solutos en 12 testigos,caudales de flujo y parámetros hidrogeológicos esti-mados. La hipótesis que mejor concuerda con los resul-tados del modelo es la de que las distribuciones decloruro y sulfato reflejan la historia del sistema acuí-fero, desde que se rellenó de agua salada durante elúltimo máximo eustático, hará unos 84,000 anos. Elmodelo simula el lavado mediante agua dulce de loslimos por un flujo vertical ascendente de 8.8!10–6 m/d,un coeficiente de dispersión de 9.2!10–7 m2/d, uncoeficiente de partición adimensional para el cloruro de0.981, y un coeficiente de intercambio adimensional de0.31!10–2. Se simularon las concentraciones de sulfatoa lo largo de una línea de flujo a partir de los valores dedisperión calculados para el cloruro y anadiendo untérmino de retardo. Los parámetros finalmente usadosfueron coeficiente de retardop3D4.51, bSO4p3D0.994 y wSO4p3D0.31pD710-2. Del análi-sis de sensibilidad se desprende que el modelo es muysensible a la velocidad del flujo y que el lavado de loslimos mediante agua dulce se representa mejor consid-erando en el borde de la unidad confinante una concen-tración que disminuye de modo exponencial, con unvalor inicial igual al correspondiente a agua salada yuna vida media de 825 anos.
Key words USA 7 hydrochemistry 7 confining units 7numerical modeling 7 salt-water/fresh-water relations
Introduction
Cross-formational transport of sulfate-rich, mineral-laden fluids from confining units influences regionalaquifer water-quality trends in aquifers beneath theAtlantic Coastal Plain, USA, through numerous chem-ical processes (Chapelle and Knobel 1983; Back 1985;Chapelle and McMahon 1991; Pucci and Owens 1994;Sacks et al. 1995). High sulfate concentrations, as muchas 2200 mg/L (Pucci and Owens 1989), occur in marine-deposited confining-unit sediments in the northernCoastal Plain of New Jersey; however, few descriptionsexist of sulfate concentrations and distributions withinregional confining units. Locations are shown in Figure1.
Sulfate transport from confining units leads tomicrobially-mediated dissimilatory sulfate reduction inthe adjoining aquifers, which produces HCO3 ordissolved organic acids (Chapelle and Lovley 1990;Chapelle and McMahon 1991; Chapelle et al. 1995).Chapelle and McMahon (1991), and Pucci et al. (1992)explain, using geochemical modeling, HCO3 generation
Figure 1 Location of the study area, showing New Jersey CoastalPlain, borehole, and trace of hydrogeologic section
along flowpaths in regional Coastal Plain aquifers byusing sulfate transport from the confining units.Production of alkalinity leads to dissolution ofcarbonate minerals; consequently, release of divalentcalcium and magnesium cations increases, and thesecations exchange for sodium along regional aquiferflow paths, as reported in Coastal Plain aquifers (Chap-elle and Knobel 1983).
Sulfate- and/or iron (III)-reducing bacteria arewidely reported in deep cored sediments (Lovley andPhillips 1987), and in sediments reported in this investi-gation (Szabo et al. 1996). Pyritic concretions, whichprobably represent the sites of sulfate-reduction reac-tions, are reported at or near the aquifer/confining-unitcontacts in the Coastal Plain (Pucci and Owens 1989).This occurrence suggests that sulfate conservativelymigrates in the confining units until reaching reactivesites at the boundary of the confining unit or in theaquifer (Chapelle and McMahon 1991).
During a long eustatic high period, the sedimentspenetrated by a borehole at Atlantic City, New Jersey(NJ) (Figure 1), were probably permeated withseawater. A generalized hydrogeologic section is shownin Figure 2. This condition means that in theseconfining-unit sediments the chloride and sulfateconcentrations were as high as F16,000 mg/L andF2700 mg/L, respectively (Meisler 1989). On the basisof the depositional environment reported for thisregion by Owens and Sohl (1969), it is concluded thatthe elevated sulfate in these sediments is not fromgypsum dissolution. Pucci and Owens (1989) show thatsulfate concentrations in these sediments do not resultfrom simple fresh-water and seawater mixing. Chapelle
Figure 2 Generalized hydrogeologic section of the New JerseyCoastal Plain, showing prepumping flow conditions
and Lovley (1990) explain on the basis of physical pore-throat size that microbiological sulfate-generatingsources within confining units are not likely.
Pucci et al. (1997), sampling at approximately 3.5-mintervals from 168.6–203.0 m in the lower part of theKirkwood Formation at Atlantic City, NJ, extensivelyreport various sediment and pore-water chemistry,mineralogy, and textural heterogeneity for theconfining unit. Pucci (1998) reports statistical andgeochemical analyses that suggest that the sulfate trans-port in these sediments is controlled by (1) aphysical–chemical mechanism of differential migrationof sulfate accompanied by divalent cations, and (2)fresh-water flushing of, and mixing with, residualseawater at paleoflow rates.
Purpose and Scope
Given the known sulfate distribution and a fewconstraints that bear on this problem, the approach isto use a transport analysis to constrain the hypothesisthat the present-day distribution of sulfate concentra-tion within the confining unit is the result of flushing ofseawater by fresh water within the confining unit. Theconstraints are simulated as bounds on flow andsulfate-transport characteristics. Within these bounds,
the modern observed sulfate distribution in theconfining-unit sediments records changes that haveoccurred within in the regional aquifer system. Leakagefrom these confining units may continue to be a sourceof elevated sodium concentrations in aquifer water.
This sulfate transport model is for a 35-m verticalsection of a confining unit. Simulation of sulfate trans-port through an Atlantic Coastal Plain confining unithas not been previously reported. The model simulatesthe flushing of seawater sulfate from confining-unitsediments since the eustatic high of 84!103 yr BP.
Location and Hydrogeologic Setting
Core samples for this analysis were collected in theNew Jersey Coastal Plain at Atlantic City, NJ, June22–27, 1993. Regional hydrogeologic units of the NewJersey Coastal Plain are principally wedge-shapedbodies of interbedded, unconsolidated clay, silt, andsand, except for thin indurated beds (Figure 2). Thehydrogeologic units discussed are all early Miocene inage.
The Rio Grande aquifer and the Lower confiningunit are within the “great diatom bed” of the KirkwoodFormation (Zapecza 1989). The Rio Grande aquifer,which is a minor sand aquifer, is about 12.2 m thick atthe borehole site and overlies the Lower confiningunit.
The Lower confining unit is 35 m thick (depth range,168.6–203.0 m) at the borehole site (Miller et al. 1994)and overlies the Atlantic City 800-ft sand. J. Owens
(US Geological Survey, Geologic Division, ERB, pers.commun., 1993) describes the sediments of the Lowerconfining unit mainly as laminated, marine, micaceoussilt and clay interbedded with some very fine-grainedsand. The unit has thin beds of sandy silt with shells,shell beds, and shelly silt.
Martin (1990) modeled the Lower confining unitand the Atlantic City 800-ft sand as one aquifer layer(unit A8, Figure 2). The calibrated transmissivity of thecombined unit at the borehole site is approximately557 m2/d. Martin (1990) calculates the verticalhydraulic conductivity of the upper confining unit (unitC8, Figure 2) to be 9.0!10–6 m/d.
The Atlantic City 800-ft sand (hereafter “800-ftsand”) is 43.3 m thick at the site (depth range,203–246 m). The aquifer is delineated into “Upper”and “Lower” parts. Most withdrawals in this region arefrom the Lower part of the 800-ft sand (Mullikin1990).
Since paleotimes, recharge to the Lower confiningunit has been by upward leakage from the Upper partof the 800-ft sand. The principal recharge to the aquiferhas been by lateral flow from topographically highoutcrop areas to the northwest in the Coastal Plain ofNew Jersey (Martin 1990; Figure 1). Pope and Gordon(in press) simulated the Coastal Plain of New Jerseyover the last 84!103 yr BP and report that the prede-velopment Darcy flow through the Lower confining unithas been upward, and the velocity has been decreasingover time, from 7.0!10–6 to 1.9!10–6 m/d.
The modern source of water to the Lower confiningunit and the Upper part of the 800-ft sand at the bore-hole is sodium-carbonate type water in the Lower partof the 800-ft sand (Barton et al. 1993). Seawaterpermeated these sediments during the last eustatic high(84!103 yr BP; Meisler et al. 1984).
Data Collection and Measurement Methods
Core samplesFlow through the confining unit is essentially verticalbecause of flow refraction; consequently, core samplesare collinear with the flow path. Core samples werecollected using a core barrel 3 m long with a 4.76-cminside diameter and a continuous mechanical rotary-drilling rig. Figure 3 shows the section that was cored.The 12 samples used in this analysis are from approxi-mately regular intervals in a 35-m section of the Lowerconfining unit. A mechanical pore-squeezer was used toextract mobile, stagnant, and trapped water fromsamples. Details on the data collection; results of majorand minor chemical analyses, mineralogy, and iron andsulfur sediment chemistry; quality control; and qualityassurance done for the collection of these samples arecomprehensively reported by Pucci et al. (1997). Onlysamples that were considered to be undisturbed wereanalyzed.
Figure 3 Stratigraphic column showing lithology, locations ofpore-water samples, core recovery, and hydrogeologic units,lower Miocene Kirkwood Formation, 155–205 m, New JerseyCoastal Plain
Water-quality dataThis paper presents only the results of chemicalanalyses that were used in the evaluation of constraintson how the chemistry of confining-unit pore waterchanged over time using the transport model. Theseconstituents are sulfate, chloride, and sodium; resultsare presented in Table 1. For the 12 confining-unitsamples, the concentration of sulfate ranges from57–894 mg/L, chloride ranges from 43–100 mg/L, andsodium ranges from 42–96 mg/L. Generally, the highestconcentrations of these constituents are in the upperpart of the Lower confining unit. This trend and thefact that flow through the confining unit has beenupward since paleotimes suggest that upward flushingby fresh water is a significant factor in controlling pore-water chemistry in the confining unit. As reported inTable 1, none of the pore-water samples has constituentconcentrations that are as low as those in the RioGrande aquifer and from four nearby wells screened inthe subjacent Upper part of the 800-ft sand (Barton etal. 1993). Gypsum deposits, which might have beensulfate sources, were not observed in the core (J.
Table 1 Pore-water composition for selected constituents fromthe Lower confining unit, 168.5–198 m, at the Atlantic City, NewJersey, borehole, and well-water samples from nearby wellsscreened in the Rio Grande aquifer (~8.0 km distant) and theUpper part of the 800-ft sand (~4.8 km distant)
m, meter; mS/cm, microsiemens per centimeter; mg/L, milligramsper liter; pH in pH units. Sample numbers 7-A1, 7-B1, and 7-B2are from the same core sample. Sample numbers 7-B1 and 7-B2are core samples that were taken within centimeters of eachother. A “–” means a datum was not available
Figure 4 Relation between (1) sodium and sulfate and (2)sodium and chloride concentrations for pore-water samples fromthe borehole, Lower confining unit of the Kirkwood Formation.Lines denote conservative mixing curves
Owens, pers. commun. 1993). An examination of pore-water composition by “simple salt” dissolution wasdone using the SNORM code (Bodine and Jones 1986).The code assumes neither chemical or charge changesnor redox reactions between solutes and/or mineralphases as viable explanations for the observed solutes.Results of these analyses strongly indicate marine-water sources for most samples from the confining unitrather than mineral-dissolution sources.
Plots of concentrations of sodium vs chloride(Na:Cl), and sulfate vs chloride (SO4:Cl) are shown inFigure 4. These results also indicate that pore-waterchemistry is not explainable by simple mixing.Compared to results from combining fresh-water andsalt-water end members, concentrations of sodium areslightly enriched relative to chloride, and sulfateconcentrations are also enriched, especially in the shal-lower samples (Nos. 1–4).
Conceptual Model
Macroscopic Scale
Groundwater within the Lower confining unit wasaffected by variations in eustatic conditions, which inturn have affected flow and water chemistry sincepaleotimes. Although historical sea level was less thanpresent sea level for most of the last 100!103 yr(Zellmer 1979), the difference in head between hydro-geologic units was fairly constant over time, and thusthe vertical flow rates within the confining unitsessentially remained constant (Pope and Gordon, inpress).
This conclusion is based on the assumption that theRio Grande aquifer, the Lower confining unit, and the800-ft sand extend off-shore to where they truncate assubmerged outcrops at the continental margin (Meisleret al. 1984). The result is that pressure differencesbetween these regional aquifers at the truncatedboundary remain constant even though eustatic condi-tions change over time and, therefore, upward paleo-flow in the Lower confining unit is basically steady.
Meisler et al. (1984) assume that eustatic sea levelsin the borehole area are approximated by sea-levelchanges indicated in the Coastal Plain record inVirginia (Zellmer 1979). If so, at about 100!103 yr BPconcentrations of chloride and sulfate in the Lowerconfining unit probably equaled maximum concentra-tions reported from Atlantic Coastal Plain sediments(ClF16,000 mg/L; SO4F2700 mg/L; Meisler et al.1984). These concentrations are somewhat less thanseawater because fresh water moves upward and out ofconfined sediments, even where submerged beneath
the ocean. Since about 84!103 yr BP, the Lowerconfining unit has been flushed by increasingly fresherwater.
Pore-water concentrations in the Lower confiningunit probably have not been significantly affected bygroundwater development. As Nichols (1977)computed for confining units elsewhere in the NewJersey Coastal Plain, it is not likely that significant flowchange has occurred in recent years, because the lowpermeability and massive thickness of the Lowerconfining unit would limit such changes.
Microscopic Scale
Within the available sampling density of the borehole,results indicate many textural, mineralogical, chemical,and pore-volume heterogeneities. Such physical hetero-geneities may also lead to preferential flow pathways,or stream tubes, which would result in variable flowrates. Although the physical models of the microscopicprocesses are different, van Genuchten and Wagenet(1989) report that the concept of preferential flow path-ways in stream tubes is mathematically equivalent to aconcept of flow being partitioned into a flowing“mobile” pathway and a non-flowing “immobile”pathway. Where this hypothesis is discussed in thisreport, the terms mobile and immobile pathway areused to distinguish heterogeneous flow regions forpreferential flow on the smaller scale. Those pathwaysthat carry most flow are “mobile;” pathways that carryminimal or no flow are “immobile.”
Governing Processes
Principal controls on the flushing of seawater constit-uents through the confining unit include (1) constitu-tive flow and transport processes within the confiningunit, and (2) solute-chemistry changes from seawater tofresh water at the flow-input boundary into the Lowerconfining unit between the time of the eustatic high andmodern times.
The conceptual model assumes that all water andsolutes can be flushed from the confining unit and thedispersion mechanism is the same for all constituents.Advective-dispersive transport is mainly in the“mobile” pathway of the sediments, which respondsmost readily to pressure gradients. Water in relativelypermeable stream tubes is free flowing and flows inpreferential “mobile” pathways. The remainder of thesediments comprise the “immobile” pathways, wherewater is less mobile (i.e., low-permeable sediments,dead-end pores, thin films, etc.). The conceptual modelpermits water and solute-concentration exchangesbetween the “mobile” and “immobile” pathway.
Chloride transport is conservative and non-retarded.Sulfate transport in the confining unit is assumedconservative but retarded. Several hypothetical mecha-nisms for retarded sulfate transport are possible; oneplausible mechanism is suggested by the occurrence of
widely distributed shell deposits and calcium-rich sedi-ments. These would create anionic exchange surfaces atthe relatively high pH values that are observed in theconfining unit (Table 1). High pH values would favorthe formation of positive surface charges, which wouldretard negatively charged sulfate ions.
The nature of the inflow boundary conditions isuncertain, because no explicit record exists of move-ment of the fresh-water/salt-water transition zone pastthe inflow boundary during paleotimes. Figure 5 showsgeneralized flow paths and alternative positions of thatinterface. Meisler et al. (1984) report that the modernsimulated fresh-water/salt-water interface in theAtlantic City area is not at an equilibrium position withrespect to the modern sea-level elevation but is movinglandward at about 0.32 km per 10,000 yr for theunpumped system. They further report that the presentfresh-water/salt-water transition zone is no less than35 km seaward from the Atlantic City borehole site andis 16–24 km wide. The transition zone is defined as thedistance between the 5000-mg/L and the 18,000-mg/Lisochlors. Constraints on the duration and rates ofchange in flow and solute concentrations at the inputboundary were evaluated for this study using a sensi-tivity analysis. The model assumes that variations ofchloride and sulfate concentrations at the inflowboundary decrease in similar proportion over the timeof the simulations.
Testing the Conceptual Model
Approach
Feasibility of the conceptual model was examined usinga steady groundwater flow and transient transportmodel through a 1-D core section, 35 m long(203–168 m), of the Lower confining unit. An analyticsolution of the non-equilibrium, two-pathway deter-ministic advective dispersive equation (ADE) using theCXTFIT2 computer code (Toride et al. 1995) was used.This code was also used for modeling the equilibrium,single-pathway, deterministic ADE, and for inversemodeling. This model computes variations along theflowpath for constituent concentrations within mobilestream tubes or pathways, Cmobile; concentrationswithin the immobile stream tubes or pathways, Cimmo-
bile; and mass volume sum for a sediment volume thatcontains both pathways, Ctotal.
Because the conceptual model assumes that pressuredifferences between the inflow and outflow boundaries(or the contacts between the Lower confining unit andthe Upper 800-ft sand and the Rio Grande aquifer)remained constant for the simulation period, the flowwithin the confining unit was forced at external boun-daries. Effects on vertical paleoflow caused by densityare assumed to be secondary for the overall simulationperiod. For those simulations that possibly couldexplain the observed distribution of constituents in theconfining units and that had physically reasonable char-
Figure 5 Schematic hydrogeo-logic section showing twoalternative hypothetical posi-tions of the fresh-water/salt-water interface near the bore-hole site
acteristics, chloride concentrations within the Lowerconfining unit generally decreased below levels inwhich salt-water density effects are considered signifi-cant (ClF4000 mg/L) within the first 20% of the totalsimulation period. Ignoring density effects is most accu-rate for that part of the flow period when chlorideconcentrations are below this level.
The sulfate adsorption model is related to thenumber of exchange sites that are available to themobile liquid phase for linear equilibrium. This relationis contained in a dimensionless partition expression, b:
bpQmc( f )7(rb)7(Kd)
Qc(rb)7(Kd)(1)
where Qm, and Q are the moisture-content terms in themobile pathway and combined mobile and immobilepathway [L3L–3], respectively; f is the fraction ofexchange sites that equilibrates with the mobile liquidphase in the two-pathway model [-], rb is the bulkdensity [ML–3], and Kd is the linear adsorption distribu-tion coefficient [M–1L3].
Solute exchange between the more mobile and lessmobile pathways affects the rate at which solute istransported to exchange sites in the mobile pathwayand is assumed to be a first-order rate process. This
process is described by a dimensionless parameter, v:
vp(a7L)/(Q7v); (2)
where a is a mass transfer coefficient [T–1], L is a char-acteristic length [L], Q is as previously defined, and v isvelocity [LT–1].
An interpretation of the constant, such as the char-acteristic length and mass-transfer coefficient Eq. (2), isnot necessarily derived from a specific physical modeland is not within the scope of this paper.
Boundary Conditions
A constraint on the upward flow condition is a steadyflux. The transport boundary condition at the inflowboundary between the Upper part 800-ft sand andLower confining unit is assumed to be a third type ofboundary condition. The transport boundary conditionat the downgradient boundary between the Lowerconfining unit and the Rio Grande aquifer is assignedas a zero concentration gradient.
Simulation of the Conceptual Model
Flow was initially set equal to reported simulatedpaleoflow velocities (Pope and Gordon, in press).
Parameters that affect the calculation of flow and trans-port had to be simultaneously evaluated; evaluation ofthis requirement is discussed further below. Chlorideconcentrations were used to refine estimates ofvelocity, media properties, and boundary and initialconditions using direct and inverse methods.
The inverse method used in the CXTFIT2 model is anon-linear least-squares method (Toride et al. 1995).Least-squares computations compare the simulatedtotal concentration of constituents at depth along theflow path and the measured concentration. However,these statistics were mainly used as guides in thecomparisons of simulations and observed data and arenot reported. The code was used to do simultaneousinverse calculations for as many as three of five trans-port parameters: v; D, dispersion coefficient [L*L/T];R, retardation factor [-]; f; b; and v. Normal iteration ofthe procedure reduced the number of estimated param-eters to the most sensitive parameters.
Initially, a single pathway ADE was used for thesesimulations, but it was not possible to constrain modelparameters in a way that approximated the reportedchloride concentrations in the Lower confining unit.However, it was possible to approximate chlorideconcentrations using a two-pathway flow model. Flow-parameter estimates and constraints for simulating thechloride values in the Lower confining unit guided theselection of initial values for simulating sulfate trans-port.
Results
Inverse calculations using the distribution of chlorideconcentration determined that optimal upwarddischarge was about 69% of the mean simulateddischarge for the same paleoflow period as reported inthe regional flow model (Pope and Gordon, in press).
Simulated chloride and sulfate concentrationprofiles for the hypothetical model, Ctotal, smoothlyincreased along the upward flow direction in generalagreement with the measured concentration values, asshown in Figures 6a and 6b. Cmobile, or the simulatedconcentrations within the hypothetical “mobile” path-ways, was always less than the measured concentrationvalues. Cimmobile, or the simulated concentrations withinthe hypothetical less mobile or “immobile” pathways,was generally more than measured chloride-concentra-tion values and always more than measured sulfatevalues.
Flow
The computed pore-water flow velocity was chosen as8.8!10–6 m/d, on the basis of the inverse calculationsof chloride transport and sensitivity analysis using themeasured chloride distribution, as described in theconceptual model. The equivalent pore-water traveltime through the Lower confining unit is 10,860 yr,
Figure 6a,b Calibrated total concentration, concentration in themobile pathway, concentration in the immobile pathway, andmeasured values along the flow path; a for chloride; b forsulfate
equal to 7.7 flow volumes through the core interval inthe past 84!103 yr. Porosity indirectly affects the porevelocity in the calculation and was implicitly examinedin the velocity sensitivity analysis. No porosity valueswere available for the Lower confining unit, butaverage porosity of the Upper confining unit deter-mined from cores from a nearby borehole at Pomona,NJ, is 51% (Core Laboratories, Inc., FAA Test WellSpecial Core Analysis report to USGS, Oct. 24, 1985).Using this porosity and the reported upward seepagevelocity for the borehole site (Pope and Gordon, inpress), the pore-water velocity during paleotimesranged from 1.16!10–5 m/d to 1.40!10–5 m/d, about44% higher than the velocity reported for the cali-brated model.
The dispersion coefficient, D, was calculated for chlo-ride and sulfate at 9.2!10–7 m2/d, which is about anorder of magnitude less than the value for diffusivity ofMgSO4 in pure water (2.0!10–6 m2/d). Konikow andRodríguez Arévalo (1993) reached a similar diffusivitycalibration value (7.5!10–7 m2/d). Diffusivities in thisrange indicate that mechanical dispersion is a minimalcomponent of the hydrodynamic dispersion process.
Retardation factor, RThe chloride retardation factor, RCl, was assigned avalue of 1. The calculated sulfate retardation factor,RSO4, is 4.5 (the outlier shown in Figure 6b was notused in this calculation). The computed RSO4 value of4.5 is consistent with the hypothesis that the sulfate ionis a less mobile species within the confining unit. If asingle-pathway transport model had been used just toexamine sulfate transport, the RSO4 would increasefurther to approximate the measured values. Thisdifference is because the two-pathway model delays thetransport of the overall sulfate concentrations by massexchange between the “mobile” and “immobile” path-ways (Figure 6b). This tendency for RSO4 iscompounded if sulfate reaction sinks are included inthe simulation.
b valueThe b value calculated using chloride, bCl, was 0.981.Because Kd for chloride is 0.0, b equals the ratio Qm
and Q. Therefore, using the conceptual model results,Qm is predicted to be about 98% of the total voidvolume. Hypothetical total chloride concentrations,Ctotal, are much closer in magnitude to “mobile”pathway concentrations, Cmobile, than to “immobile”pathway concentrations, Cimmobile, along the flow path(Figure 6a). The conceptual model also indicates thatsome chloride concentrations in the less mobilepathway may have much higher concentrations,although no measured values were of this magnitude.The b value calculated for sulfate transport, bSO4, is0.994. In this case, because Kd10, and RSO411, non-unique values exist for “f” in Eq. (1), or the proportionof exchange sites in equilibrium with the solute in the“mobile” pathway or stream tube.
v valueIndependent calculation of the v value using both chlo-ride and sulfate measurements resulted in a value of0.0031. Therefore, controls on mass transfer rate foreach ion between the “mobile” and “immobile” aresimilar.
Constituent Distribution
The simulation reasonably accounts for constituentvariations. Of the 12 measured values for chloride, 9
are within the simulated Cmobile and Cimmobile range(Figure 5a). Standard deviation, s, between measuredchloride values and simulated Ctotal values is 15.1 mg/L.However, all measured values that had concentrationsless than Cmobile are within 1 s of the predicted Cmobile
for chloride. The residuals for chloride concentrationalong the flow path range from –22.6 to 18.4 mg/L andthey do not appear biased. The s for chloride residualsis 11.6 mg/L; of these residuals, 58% are within 1 s, and100% within 2 s. Some of the variability in these resultsmay be explained by the simplifying assumption thatthe sediments consist of either “mobile” pathways or“immobile” pathways in the 1-D section.
Chloride concentration is 4.8 mg/L in the closestavailable (about 8.0 km away) groundwater sampletaken from a well screened in the Rio Grande aquifer;this value is much less than the 100 mg/L measuredvalue of chloride along the downgradient end (shallowend) of the flowpath in the Lower confining unit(Table 1). If this well-water sample is representative ofthe groundwater Rio Grande aquifer at the boreholesite, then discharge into the Rio Grande aquifer fromthe Lower confining unit is low in proportion to otherfresher sources of water for the aquifer.
The simulated Ctotal for sulfate reasonably repre-sents the measured values. All measured values ofsulfate are within the range for simulated Cmobile andCimmobile in the Lower confining unit (Figure 6b).Standard deviation between measured sulfate valuesand simulated Ctotal values is 275.3 mg/L. The concen-tration residuals for sulfate along the flow path rangefrom –109 to 129.0 mg/L and they do not appear biased.The s of sulfate residuals is 73.0 mg/L; of these resid-uals, 60% are within 1 s, and 100% within 2 s.
Reasonable simulated matches between to the Ctotal
concentration and sulfate measured values wereobtained by using a one-pathway equilibrium ADEanalysis with a much higher R value. However, a one-pathway equilibrium ADE analysis could not simulatethe measured values for chloride unless RCl was greaterthan 1, which is not physically allowed. This resultsupports the use of the conceptual model of “mobile”and “immobile” pathways. Other models of preferen-tial pathways may explain additional variability indata.
Sensitivity
Similar model results could be achieved for the Lowerconfining unit from various non-unique parametercombinations. Some model conditions, such as thetime-dependent concentration boundary conditions,were not documented in any way and were evaluatedon the basis of the conceptual model and sensitivityanalysis. Sensitivity analysis examined flow and trans-port parameters and concentration boundary condi-tions. The sensitivity range was guided by the relativecertainty of parameter estimates based on data availa-bility and limits on the hypothetical model that could
Table 2 Results of calibra-tions and sensitivity analysesfor chloride and sulfate trans-port
Chloride
Parameter (units) Range evaluated Calibrated value
Pore-water velocity (m/d) 3.0!10P7 to 2.7!10P6 8.8!10P6
Dispersion coefficient (m2/d) 0.0 to 5.94!10P5 9.2!10P7
Retardation coefficient (P) 1.0 1.0b (P) [~1.0] 0.980 to 0.998 0.987v (P) [10.0] 0.15!10P2 to 0.88!10P2 0.42!10P2
Sulfate
Pore-water velocity (m/d) 5.5!10P6 to 1.1!10P5 8.8!10P6
Dispersion coefficient (m2/d) 3.2!10P7 to 1.1!10P6 9.2!10P7
Retardation coefficient (P) 1.0 to 5.87 4.51b (P) [~1.0] 0.924 to 0.994 0.994v (P) [10.0] 0.31!10P2 to 0.173!10P1 0.31!10P2
generate physically reasonable results. Results areshown in Table 2.
Sensitivity runs that used a single-pathway model forthe full length of the Lower confining unit generatedchloride concentrations that are about equal to theinflow-boundary concentration, estimated at 12 mg/L.This value is more than 1 s below the minimalmeasured value of 43 mg/L. Simulation of chloridetransport was much improved using a deterministicADE model of two-pathway flow.
The sensitivity for the calculated steady velocity(vF8.8!10–6 m/d) was examined by varying velocitiesfrom one order of magnitude lower to three times thevelocity reported in the regional model for modernflow (Martin 1990; Table 2), and then examining theeffects on simulated sulfate concentrations. In the low-velocity range (vF3.0!10–7 m/d), constituent concen-trations are predicted to be much higher than themeasured values, at about seawater concentrationlevels along the entire flowpath. Small velocityincreases above the calibrated value (vF9.1!10–5 m/d)required proportionately much larger increases insulfate retardation factors or extremely different trans-port parameters (b as low as F0.01 and v F0.1) inorder to match measured sulfate values in the Lowerconfining unit. Values of b (F0.01) and v (F0.1) arelimits for the code and are judged to be physicallyunrealistic. Overall, the model sensitivity to the steady-flow assumption and the magnitude of steady-flowvelocity is considered to be large.
Sensitivity analysis of the assumption that fresh-water flushing through the confining unit began84!103 yr BP was done by running simulations forsulfate transport with initial times at 50!103, 84!103,and 100!103 yr BP. These model simulations hadinput concentrations that decreased from seawatermagnitudes at a half-life time rate of 825 yr. Simula-tions using the three flushing periods each employedthe same final concentration boundary conditions atthe inflow boundary. Results are shown in Figure 7a,b.
For sensitivity runs of 50!103 yr, transport parame-ters were adjusted to obtain a reasonable match to
measured sulfate (Figure 7a). These adjustmentscaused the simulated total solute concentration valueswithin the “immobile” flowpath to be higher for the50!103-yr sensitivity run than for the 84!103-yr and100!103-yr runs. The sulfate concentrations obtainedfor fresh-water flushing beginning 50!103 yr BP wasnot accepted because it would have meant the flushingprocess would have started 30 to 50!103 yr after theinitiation of large declines in the eustatic sea level,which drive the fresh-water flushing processes (Meisleret al. 1984).
Sensitivity simulations using both the 84!103-yr(Figure 6b) and 100!103-yr (Figure 7b) fresh-waterflushing times result in reasonable simulations for Ctotal
of sulfate compared to measured values. The 100!103-yr simulation predicts that a measured value for sulfatecould exceed the maximum predicted in the Cimmobile
pathway.Sensitivity of the rate of solute variation to the
inflow-boundary condition was examined by makingnumerical adjustments that relate to aspects of thefresh-water/salt-water transition zone. These aspectsinclude the seaward flow velocity and the width of thefresh-water/salt-water transition zone. The effect ofthese aspects is represented by the rates that chlorideand sulfate concentrations decreased at the inflowboundary from initial seawater concentrations, as thetransition zone moved in the Lower confining unit atthe borehole site (Figure 5).
Sensitivity runs examined the effects of several ratesof change in which chloride concentrations decreasedat the inflow boundary from the Upper part of the 800-ft sand, from maximum concentrations of 16,000 mg/Lto present-day concentrations of F6 mg/L. Changes inthe inflow boundary condition were simulated as: (1)linearly decreasing over 84!103 yr BP; or (2) exponen-tially decreasing for several fresh-water flushingperiods from 50!103–100!103 yr BP. Results areshown in Table 3.
Ctotal for chloride concentrations could not be simu-lated within two orders of magnitude of measuredvalues using the optimized flow and transport parame-
Figure 7a,b Selected sulfate transport sensitivity runs showingsulfate transport under two inflow boundary conditions; a Begin-ning at 50!103 yr BP; b beginning at 100!103 yr BP
Table 3 Summary of transportboundary conditions, showingtemporal conditions and sensi-tivity analyses. (Inflowboundary condition of thethird type; outflow boundarygradient equals zero)
Type boundary value problem (BVP) Range evaluated Calibrated value
Exponential decrease from16,000 mg/L Cl to 6 mg/L Cl
490–14,000 yra 825 yra
Linear decrease16,000–12 mg/L Cl
16 step decrease inconcentrations over84!103 yr
NA
Temporal conditions at inflow boundary
Duration of boundary condition(only exponential decrease BVP)
50!103–100!103 yr BP 84!103 yr BP
Initial time for concentration decrease atboundary
50!103–134!103 yr BP 84!103 yr BP
a Exponential decrease rates are reported as a half-life rate.
ters when the linearly decreasing boundary conditionwas used at the inflow boundary (Table 3). The modelcould predict the measured chloride values if chlorideconcentrations at the input boundary were described asexponentially decreasing. Several rates were tested, andthe model is judged sensitive to various rates of expon-ential decreases for describing the chloride concentra-tions at the inflow boundary from the Upper 800-ftsand. The final optimum half-life rate of decrease is825 yr at the inflow boundary. A physical interpretationof the shape of the interface within the aquifer is notpossible with the available information.
Conclusions
The conceptual model satisfactorily explains the occur-rence of chloride and sulfate concentrations within theLower confining unit, or the Lower part of the GreatDiatom Bed in the borehole at Atlantic City, NJ. Thehypothesis that the model results support is that thechloride and sulfate concentration distributions in theconfining unit represent information on the history ofthe aquifer system since it was filled with seawater atthe last eustatic high, about 84!103 yr BP. Using flow-and-transport model parameters that were determinedfrom model sensitivity analyses, the model simulatesthe flow and transport pathway within the confiningunit, and the history of the movement of salt waterwithin the upgradient adjoining aquifer.
Simulated chloride values satisfactorily matchmeasured chloride values only by using variable flowpathways. For discussion purposes, these are describedas “mobile” or “immobile” pathways but probablyconsist of a continuum of flow environments. Also, theconceptual model does not require any specific physicalconcept of the origin of the distinct pathways. Themathematical code that simulated the conceptualmodel allows for a physical model of flow pathwaysthrough the confining unit that is based on distinctstream tubes, such as might be created by micro-heter-
ogeneities for hydraulic conductivity; or distributedaggregate media properties, such as dead-end pores ortrapped water; or some combination. Field data for theborehole indicate much heterogeneity of sedimentproperties and pore-water chemistry but data are insuf-ficient to elucidate more about the appropriate flowpathway model. In addition, sulfate migration had to beretarded in the model to explain the observed values.The combined effect of the distinct flow pathways andthe retardation contribute to an overall effect of what isdescribed as preferential flow.
The conceptual model also indicates that a matchbetween the simulated and measured chloride andsulfate concentration values in the confining unit isonly possible if some of the changes during the paleo-flow period within the adjoining Upper 800-ft sandwere included as boundary conditions in the analysis.Specifically, the modern water chemistry in theconfining unit is a result of the history within theadjoining aquifer. Therefore, interpretation of chemicalprocesses within a confining unit should take intoaccount the history of adjoining aquifers.
In future field studies, more data on properties thatcontrol flow and transport in confining units should beobtained in order to further constrain the flow andtransport analyses within them. Sufficient data shouldbe collected to determine the probabilities of encoun-tering selected flow and transport parameters thatwould further elucidate the transport characteristicswithin the confining unit. These parameters especiallyinclude the scale of variation and range in values forhydraulic conductivity; experimental evidence foranionic adsorption, and hence retardation, of sulfate onthe calcareous surfaces of these sediments; pore inter-connectivity; and possibly correlation to the age of thewater from isotope studies.
Acknowledgments. Funding for the research was from NSFGrant No. EAR-9304022. Special thanks are extended to ZoltanSzabo and to Ted Ehlke, both of the US Geological Survey,Water Resources Division, for their contributions to the collec-tion and integrity of these data. Appreciation is also extended toseveral anonymous reviewers of this manuscript.
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