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Analytical Methods for the Prediction of Leachate

Plume Migration by Douglas C. Kent, Wayne A. Pettyjohn and Thomas A Prickett Introduction

A recent (1980) project funded by the U.S. Envir­onmental Protection Agency (EPA) (Pettyjohn, Kent Prickett, LeGrand and Witz, in press) has developed a manual to guide government agencies in evaluating hydrogeologic aspects in permit applications dealing with hazardouswaste treatment,storageand disposalfacilities,asdescribed inSection 3004 ofthe Resource Conservation and Recovery Act. The techniquesdescribed for predicting leachate movement can also be used todevelop monitoring plans, and sowould be useful for consultants and companies having hydro-geologists on their staff.

Major Approach Used The plume evaluation system is quantitative and

centers on an analytical model by Wilson and Miller (1978).This model orequation issuitable for computer manipulation and is directed to determining the extent of plume migration under varying conditions. Because of its logically precise and deterministic framework, the method is suitable for critical waste and contamination situationswherecollection of more accurate information can be economically justified.With less preciseinput data, the method isconceptu­ally useful in approximating hazard potential. The best inputdata may have accuracy no closer thanone order of magnitude in manycases, but the results mayhelp to visualize whether or not a plume might exist and, if so, to what extent the plume might migratewithin a specified time. The understandingof plumemigration acquired through theuseof thesequantita­tive methods should provide another tool for evalu­atinganengineeringdesign and monitoring programfor a proposed or existing hazardous waste site. Following this evaluation, engineering design and monitoring may be modified to provide safety factors sufficient to mitigate any potential plume movement in the ground water.

Data Requirementsand Estimates In order to collect all the facts needed foranalysis,a

list of data requirementswas designed (Table 1).These"

data are essential for solutions to the analyticalmethods for predicting plume migration used in this article.

In anyground water pollutionstudy it isessential to obtain thebackground concentrationof awide vari­ety of chemical constituents, particularly those that might be common both to thelocal ground waterand a leachate.The water inshallow orsurficial aquiferscan undergo substantial fluctuations in chemical qualityand therefore it is not always simple or easy to deter­mine background concentrations, particularly of the more conservative constituents such as chloride or nitrate. In general, samplesshould becollected duringdry periodsand notduringa rainfall period orwithin a week or so following it. Throughout much of North America the major period of ground water recharge occurs in wetter periods of the year (generally in the spring) while minor recharge occursduringorimmed­iately after a rain. These recharge events flush water-soluble compoundsfrom the unsaturated zoneto the water tableand maysubstantiallychange thechemical quality of the ground water (Pettyjohn 1982). Since the quality of shallow ground water may fluctuate within fairlywide limitsduring short intervals, back­ground concentrations should be determined statis­tically by collectingseveral samplesat different times and from different depths.

The severity of ground water pollution depends partly on the characteristics of the waste or leachate, that is, its volume, composition,concentration of the various constituents, time rate of release of the con­taminant, thesize of the source area, and the densityof the leachate, among others. Data describing these parameters are difficult to obtain and are lumpedtogether into the term"mass flow rate."which issub­sequently used in this article.

Once the leachate is formed it begins to migrateslowlydownward throughthe unsaturated zonewhere several physical, chemical and biological forces act upon it Eventually, however, the leachate may reach saturated strata where it will then flow primarily in a horizontal direction as defined by the hydraulic gra­

46 Spring 1985

dient From this point on, the concentration will decrease due to a number of phenomena, includingdilution, filtration, sorption, chemical processes, microbial degradation and dispersion. .

Dispersion of a leachate in an aquifer causes the concentration of the contaminants to decrease with increasing distance from thesource. It is caused by a combination of molecular diffusion, which is impor­tant only at very low velocities, and dispersion (hydro­dynamic mixing). In porous media, different micro­scopic velocitiesand flow pathsareexpected.Leachate moving alonga shorter flow pathor at a highervelocitywould arrive at an end point sooner than that partfollowing a longer path or at a lower velocity, thus resulting in hydrodynamicdispersion.Dispersion can be both longitudinal and transverse:the net resultisa conic form downgradient of a continuous .pollution source.The leachateconcentration isless at the mar­gins of the cone and increases toward the source.

Since dispersion is affected by ground water flow velocity and the configuration of the; aquifer's pore space,coefficients must be determined experimentally or empiricallyfora given aquifer. There isconsiderable confusion regarding the quantification of the disper­sion coefficient. Many published values are fitted values that cannot be transferred from one site to another.

Selection of dispersioncoefficients thatadequately reflect aquifer conditions isa problem that cannot be readily solved.Herein lies one of the major stumblingblocks of chemical transport models (See Bouwer 1978; Anderson 1979; and Freeze and Cherry 1979).

Often confused with the term dispersion (Dx = longitudinal dispersion and Dy = transverse disper­sion) isdispersivity (dx, dy).The former includes veloc­ity; to transform from one to another requires either division or multiplication by velocity.

The rateof advanceof acontaminant plumecan be retarded if there isa reactionbetween itscomponentsand ground water constituents or if'sorption occurs. The plume in which sorption and chemical reactions occur generally will expand more slowly and the con­centration will be lower than those of an equivalent nonreactive leachate.

Hydrodynamicdispersion affectsall solutes equally while sorptionand chemical reactionscan affect vari­ous constituents at different rates. Thus, a leachate source that contains a number of different contami­nants can have each solute moving at a different rate.

Theareal extent of plumesmay rangewithin rather wide extremes dependingon the local geologiccondi­tions, influences on the hydraulic gradient, such as pumping, ground water velocity, and changes in the time rate of release of contaminants.

The many complex factors controlling leachate movement and the overall behavior of contaminant plumes are difficult to assess in that the final effect represents several factorsintegrated collectively. Like­wise.concentrations foreach constituentiria complex waste are difficult to obtain.Therefore, predictions of concentration and plume geometry are best used as estimates, principally to identify whether or not a plume might develop at a proposed site and, if so, where and to what extent it should be monitored.

Plume Evaluation SystemThe methods outlined herein form two different

approaches tothe predictionof leachateplume migra­tion. In Phase I, a simple transport equation is the

basis for three predictive methods,while in Phase II,a number of more sophisticated computer codes are recommended.The latter have appeared in the litera­ture over the past several years and several are well-documented.

Thegraphicaland computer techniquesweredevel­oped to predict or evaluate theseverity of contamina­tion once-a leachate has reached the saturated zone. To make results comparable from one method to another, the literature was searched fora singleequa­tion that the authors considered to be satisfactoiy to model plumfe migration. The equation was obtained from Wilson and Miller (1978) and the techniques in Phase I are based on it:

R- fmexp(x/B) 47rn V DxDy

The Wilson and Miller(1978) analytical model was chosen because it is a simpler model with fewer parameters than the other equations examined. The simpler solution lends itself to developing the nomo­graph and the user-oriented calculatorand TSOcom­puter programs.

The equation and the methods, however, do have significant drawbacks, the most serious being the inability to predict movement through the unsatu­rated zone and to input natural recharge between source and sink into the techniques.Recharge can be introduced by meansof the more advanced models of Phase II.

A generalized flow diagram forleachate plume pre­diction using the methods described therein are shown in Figure 1.

Assumptions and Limitations of AnalyticalSolution Used in Plume Evaluation System

The Wilson and Miller (1978) equation is used to provide a deterministic analytical solution for com­putingtheconcentration distribution in a two-dimen­sional contaminant plume. Definitions of the terms used in the equation are listed in Table 1.

The assumptions on which the analytical solution is based are as follows:

• The ground water flow regime is saturated • Theaquifer is unlimited (infinite)in arealextent • All aquifer properties are homogeneous and

isotropic• Ground water flow iscontinuousand uniformin

direction and velocity• There is no dilution of the plume by recharge

outside the source area • The leachatesource is a point in plan view • Theleachate isevenly distributed over the verti­

cal dimension of the saturated zone. • The leachate source supplies a constant mass

flow rate based on an initial concentration and volume (recharge rate) of leachate reaching the water tableat a point directly below the source.

The first assumption is satisfied where a source concentration is initiated at the top of the saturated zone of at the base of the landfill or lagoon. The assumption of homogeneous and isotropic aquiferproperties is rarely encountered in the field, but the availabilityof data requires theuse of a homogeneousapproximation.The uniform flow velocityin thefourth assumption requires that the water volume from the source is not large enough to significantly affect the

Spring 1985 47

Initial HydrogeologlcField Data

Required for Phase I

PHASE I

Severe Problem or

Site Unsuitable

Additional Data

Collection

Advanced Methods in Data Collection

Method 1 Graphical Solution No Problem Method 2 Calculator Code

I t or

Method 3 Computer (TSO) Model Site Suitable

3

Potentially Complex Problem Additional Data Collection or (Piezometers S Monitoring wells)

Difficult to Determine Site Suitability

PHASE II

Advanced Computer Models

Advanced Methods in Data Collection

Severe Problem No Problem Including Additional or or Piezometers S Monitoring Wells

Site Unsuitable Site Suitable

Figure 1. Generalized flow diagram for leachate plume prediction

natural ground watergradient.Ground waterrechargeand the associated dilution of the plume are not con­sidered. This assumption represents a "worst case." especially in areas of high precipitation and where permeable materials exist near the land surface.

In the theoretical derivation, it isassumed that the leachateenters theground waterdirectly below a point source. However, in practice theequation can be used for locations far enough from a non-point source so that it appears to be a point source. Wilson and Miller (1978) havedeveloped a relationship based on thesize of the source (assuming rectangular dimensions) in order toestablish the minimum distance tothesource. A large non-point source can alsobe handled bvdivid­ing it intosmaller areas.The effect of each sub-area is calculated separatelyand the resulting concentrations are added.

Methods Used in Phase I The analytical solution by Wilson and Miller has

been modified for use as a (1) graphical solution (nomograph). (2) hand calculator program,and (3) an interactive program for microcomputersand the IBM 370 computer.

These three methods can be used to predict the following: (1) the maximum distance of plume migra­tion fora given concentration threshold orlimit:such concentrations might be those that have been estab­lished as standards for safe drinking water by EPA, and (2) the maximum leachate concentration that could be reached at aspecificdistance from the landfill or lagoon. The prediction is not absolute because of the simplifying assumptionsand estimates made for the parameters required in the solution. More impor­tantly, however, the prediction is useful for a better understanding of the hydrogeologic setting and con­taminant behavior at an existing or proposed waste site. In order to use the techniques, an individual

should assessall hydrogeologic factors that are impor­tant in site evaluation. Some parameters may not be well understood evenwithin thescientific community,but reasonable estimates for the "worst case"are use­ful for initialassessment. If data are poorlydefined or unavailable, themethodscan be used to identifyaddi­tional data that are needed and the location where those data should be obtained (Figure 1).

An initialconcentration and volume(recharge rate)of leachate reaching thewater table is estimated fora point directly below the source. Ordinarily the thick­ness of vertical mixing in theground water system is assumed to be the entire saturated thickness of the aquifer: however, thiscan be modified toapproximatethe effects of layering or density stratification.

NomographA graphical solution was developed to provide a

simple computational tool for predicting leachate plume movementand corresponding concentration. It is often necessary to estimate the potential travel dis­tance or length of time required fora plumeto migrate some distance in the saturated zone from a pointdirectly below a contaminant source.The concentra­tion of conservative elements in the plume, such as chloride, can beestimated fromsome selected point in space and timealong a flow path that extends directlydowngradient from the source.

The nomograph is intended as a rapid means for obtaining an approximate solution. It also aids in understanding themodel and usingthe hand calcula­tor or interactive computer methods.The nomographis one-dimensional (restricted to a line) whereas the calculator and TSO computer methods are two-dimensional.

The Wilson and Miller (1978) equation was refor­mulated to introduce scale factors and to provide the basis for the nomograph as follows:

Spring 1985 i 48

C=QS exp ((x/XD V 7 - x/Xq/2) erfc (0) 4 QD \J 7r x/XD

where:

_ x/XD - t/TD<#>

Application allows mapping the center-line con­centration of the plume, with respect to time, in one direction (x distance)directly downgradient from the source. Dilution-dispersive mixing and retardation parametersare included in thesolution. The equationand the nomograph apply to only one chemical com stituent,such aschloride ordissolved solids,at a time.

Three scale factors used in the nomograph are ratios with the primary variablesx(distance), t (time),and QC0 (mass flow rate from source) in the forms of X/DD, t/TD, and QCQ/QD.The y distance isset to zero. The scale factors are

RdDxDv TD = Qd= n m \ /DXD V2

Two of the three ratios are computed directly and the third is found usingthe nomograph.The variables aredefined inTable 1.The factors provide twoconven­iences. First the ratios are dimensionless except for concentration.Secondly, thescalefactorscombine the constant parameters, which makes iteasier to repeatcomputations of concentration (C) for various posi­tions along the x axis (x) or for different times (t).

The nomograph inFigure 2 isdesigned toprovide a simple technique to estimate one of the following:Application 1: Theconcentration (Oata selected dis­

tance (x) and time (t). Application 2: The distance (x) where a selected con­

centration (C) will occuratagiven time (t).

Application 3: The time (t) when the concentration will reach a selected concentration (C) at a pre-determined location.

As time passes, the concentration in a given area approachesa constant pattern known assteady-state.Results forsteady-stateconditionscan bedetermined for the first two applications as follows: Application lb: The maximumconcentration (C) that

would occur at a selected distance after a long,time period.

Application 2b: The maximumdistance(x)at which a selected concentration (C) will occur after a long time period.

HOT8 HOT8I0-*

10re-fwr' HOr»

:: (mg/l) I0-410 J

i (mg/l)

» C

I icr,J

j HO4 L»o

(lb/ft*) 40® J ' O

408 io8 40*

io»

jMo8 No8IO4

IO8. 40*

Mo4 100000

Figure 2. Nomograph forsolutions of time, distance and concentration forany point alongthe principal direction of ground water flow

Spring 1985 49

Table1 Definition of Terms

Primary Variables: Units

C = Concentration of leachate at a specified time and distance (M/L3)

X = Distance from source where concentration of leachate i$ computed. Distance is (L) measured in direction of ground water flow (perpendicylar to gradient)

y = Transverse distance measured from the centerline of ground water flow (assumed to (L) be zero in the nomograph)

t = Sample time from beginning of leachate source flow (T)

Aquifer Parameters:

m = Effective aquifer thickness or zone of mixing C-)

n = Effective porosity of aquifer or zone of mixing (Dimensionless)

V = Velocity of ground water flow within voids: estimated directly or from: y _ KI

where: K = Coefficient of permeability or hydraulic conductivity of aquifer or zone of

mixing:

I = Gradient of ground water flow (Dimensionless)

Transport Parameters:

Dx = Longitudinal dispersion coefficient (mixing rate) with respect to distance in x direc- (L2/T) tion and time: estimated directly or from: Dx = ax V + D*

where:

ax= Longitudinal dispersivity (L)

D* = Molecular diffusion coefficient, which is assumed to be negligible for velocities (L2/T) typical of permeable aquifers. D* may be the dominant process in aquitards where axV would be negligible.

Dy = Transverse dispersion coefficient (mixing rate) with respect to distance in the y (L2/T) direction and time: estimated directly or from:

Dy = ayV + D*

where:

ay = Transverse dispersivity (k)

or estimated as:

Dy = Dx divided by a ratio, which commonly ranges between 5 and10 for mediurn to coarse sand aquifers

Rd = Retardation factor estimated directly or from: (Dimensionless)

Rd=1,_e!>m(orlR v n, Vd

50 Spring 1985

Table1 Definition of Terms

(Continued)

where:

pb= Bulk density of aquifer medium , (M/L3)

nt = Total porosity (Dimensionless)

Kd= Distribution factor for sorption on aquifer medium (from sorption isotherm (L3/M)column studies)

V = Velocity of ground water (L/T)

Vd = Observed velocity of leachate for a given concentration and chemical species (L/T)

- Coefficient for radioactive or biological decay. For no decay, the value of V is one. (Dimensionless) (Assumed to be one in the nomograph.) Calculated from:

7 = + (J^L.) x =TT 4D*'°g<2> : V2 V2t.1/2

where:

A = Decay constant = *1/2 (1/T)

*i/2 " = Halflife: time when half of the original mass remains (T)

Source Rate of Leachate:

QC0 = Mass flow rate estimated directly or obtained from the product of: (M/T) Q = Volume flow rate estimated directly or from: (L3/T)

Q = Aq

where:

A = area of source (L2)

q = recharge rate (L/T)

C0 = Initial concentration (M/L3)

Intermediate Variables (Used for nomograph only):

XD = A characteristic dispersion length or scale factor given by: (L) V _ D„*D~

= A characteristic dispersion time or scale factor given by: (T)

T̂ o: = R<A.I n — y V2

Qd = A characteristic dilution-dispersion flow (L3/T)

Qd = n m y/5K

Theadvantageof application lband 2b Is that it is The estimate of distance (x). time (t) and concen­possible to predict for example, the maximum dis­ tration (C) may requirean adjustment of theconcen­tance of plume migration for a given concentration tration value to correct for significant backgroundthreshold orlimit.Such concentrations might bethose concentrations. In applications1 and lb the estimated that have been established as standards for the safe concentration (C) must be added to the backgrounddrinkingwater by EPA.Alternatively, it isalso possible concentration. In applications2,2band3theconcen­to predict the maximum leachate concentration that tration value used must be the remainder after sub­could bereached at a specified distance from theland­ tracting the natural background concentration. ­fill or lagoon.

51

Hand Calculator Method The TI-59 calculator code isalso based on the Wil­

son and Miller (1978) equation. It was developed for quick and convenient solutions for determining the concentration distribution in a leachate plume in simple two-dimensional problems.With proper inputdata, thecalculator code will allow modelingof disper­sion, ion-exchange or retardation, radioactive decayand dilution from native ground water passing be­neath the landfill from upgradient sources. The cal­culator model includes the capabilities to analyze a small variable strength leachate source, areally dis­tributed landfill sites,and the plan-viewdescription of plume concentrations under non-steady as well as steady-state conditions.

Computer Program A program also based on the Wilson and Miller

(1978) equation, was developed to calculate plume concentrations by means of larger computers. The_ program iswritten in BASIC languageand adapted for use with either a microcomputer or an interactive terminal usingTSO or theIBM 370.The programcan calculate and display the concentration at a singlepoint or as a grid map of concentrations.

Asshown by the flowchart in Figure3, the program operates by requestingacommand codefrom theuser, which designates a particular operation to be per­formed.The codes maybe entered in any order, one at a time. Of course, all desired parameters must be set before requesting the concentration calculation. A detailed explanation of the required parameters is given in Table1.

During program execution all parameters retain their values until changed by the user.When the pro­gram is started, each parameter is initialized. If the initial value is the value desired for the first case to be run, then the parameter need not be entered.This is especially useful for retardationand decay, which are initially set to 1 (no retardation ordecay).

The basic equation for concentration assumes a constant mass flow rate. However, theequation can be applied to a number of time periods, each having a different mass flow rate. The computer programallows thespecification of upto 10 time periods with a starting time and a mass flow rateforeach period.The concentration can be calculated forsample timesdur­ing any time period.

Sensitivity Analysis of Data Used in the Three Methods

The nomograph diagram in Figure 2 provides a visual representation of theplumeconcentration.The solution can be found easily for various locations, timesand concentrations.Thisleads togaininga"feel" for the nature of the plume. As time passes, the con­centration at a given locationreachesa constant value known assteady-state.The steady-state valuefor con­centration can be useful for example asa "worst case" scenario (maximum concentration reached in the infinite time). The upper line on the nomograph represents the timeand distanceat which steady-stateis reached. It is easy to see that before steady-state,small changesin location or time correspond to largechanges inconcentration. In asense, thesteepness of the non-steady-state time lines indicates that the "leading edge" of the plume is relatively narrow and therefore passes a given location in a relatively short

Ood*-*s" / t.9u«»t / / InputThicks***./ J Thicks***

CP4*»"»" Input

2/ k*9u**tVelocity Telocity

. (Oth*t Paraactcr Cod**)

Cod*»".d" ./ »i*pi*y /"7 ?*raa«t*r* /

Cod*"".*" Cosput* Di*pl*yCoBC*Btt*tios i

w.

, (Other Display Cod**)

Figure 3. Program logic flowchart

period of time. Behind the leading edge, the concen­tration remains, constant at the steady-state value represented by thesteady-stateline on thenomograph.

Sensitivity analysis was performed usingthe TSO computer program for the basicaquiferand transport parameters of velocity (V), dispersion coefficient (Dx),dispersion ratio (DX/DJ, retardation factor decaycoefficent (y),aquifer tnickness (m), and porosity (n).Foreach parameter,theconcentration at locationX= 4,200 feet, y = 0 feet, was calculated for a time of 2,333.3 daysand for steady-state (infinite time).

Table 2 lists the results of varying the velocity (V)from 0.015 to 5.0 ft/day. The steady-state concentra­tion is reduced with greater velocitydue to increased dilution. For small values of velocity, the non-steady­state concentration isnegligible because the contam­ination has not arrived at the sample point

Table 3is used to summarize the sensitivity from the most sensitive parameter to the least sensitive. The mathematical expression listed under "effect" gives the rate of changein concentration. Forexample,1/m indicates that increasing the thicknessbya factor of two will decrease the concentration by a factor of two. The expression 1/V indicates that increasing velocity by a factor of four will decrease concentration by a factor of two.

Phase n Hopefully, nearly all new landfill sites can be eval­

uated and permittedor rejected on thebasisofPhase I, and the applicant or permit writer will not have to resort toa complex analysis that requires complicatednumerical modeling techniques to make an accep­

52 Spring 1985

Table 2 Concentration as a Function of Velocity (v)

Velocity (v) To

(ft/day) (ft) (days) (ft3/day) X/Xc

0.015 7,000.000 466,666.700 1307.861 0.600

0.050 2,100.000 42,000.000 — 2.000

0.500 1,050.000 10300.000 — 4.000 0.150 700.000 4,666.700 — 6.000

0.500 210.000 420.000 20.000

1.000 105.000 105.000 40.000

1.250 84.000 67.200 50.000 1.500 70.000 46.700 60.000 1.800 58.300 32.400 72.000 2.000 52.500 26.250 80.000 2.500 42.000 16.800 100.000 3.000 35.000 11.670 120.000 3.500 30.000 8.570 140.000

4.000 26.300 6.560 160.000 5.000 21.000 4.200 200.000

tance/rejection judgment However, there may be occasions when an extended analysis is called for, particularly when an applicant believes there are extenuatingcircumstancesof theirlandfill design and location that go beyond the evaluation techniques of Phase I (Figure 1). Some extenuating circumstances may relate to the effects of pumping wells, changesin land use. ground water rechargeas a dilution mecha­nism, the effects of recharge, constant head, no flow boundaries in the vicinityof thesite, non-homogenei­ties in aquifer and dispersive coefficients, speciallandfill containment designsand effectsof attenuation in the unsaturated zone.

Underspecial circumstances,advanced techniques may be necessary to sort out the effects of unusual conditions. When this becomes the case, one should examinethe possibilityof using the numericalmodels that can account for the complexities that might be of concern. A good collection of numerical ground water models has been assembled by Holcomb Research Institute (1978) and a user may consider usingany numberof models within thatcollection for a particularsiteevaluation.While theHolcombsurveyof models is extensive, several ground water models have been selected as representative of models that may be used in anextended landfill evaluation. Exam­ples of flow models includeTrescott and others (1976),Gupta and others (1975).Townley and Wilson (1980),Prickett and Lonnquist (1971) and Thrailkill (1972).Selected mass transport models include those byKonikow and Bredehoeft (1978),Ahlstrom andothers (1977), Prickettand others(1981). Reddell and Sunada (1971). Duguid and Reeves (1976), and Pickens and

Concentration at point 4,200 fL T/T„ (mg/L) time = Time: Steady-State

2,3333 days QC,/OD 23333 Days (0°)

0.005 460.759 0.000 129.599

0.056 0.000 91.836

0322 0.000 64.989

5.600 0.000 53.063

22.200 0.000 29.064

34.700 0.079 20.551 7t.990" 0.612 18.382

50.000 2.657 16.780

71.990 7.648 15.318

88.890 10.869 14.532

138.890 12.870 12.998 199.997 11.860 11.865

272.218 10.985 10.985

355.500 10.276 10.276

555.500 9.191 9.191

Table 3 Effect of Increasing the Value of a

Parameter on Concentration

Effect Steady- Non-Steady-

Parameter State State

decay coefficient (y) very large very large decrease decrease

aquifer thickness (m) decrease as - decrease as — m

porosity (n) decrease as — decrease as — n n

velocity (V) decrease as-— large increase n/v" at leading edge

dispersion decrease as — moderate coefficient (DJ n/d7 increase at

leading edge

dispersion increase as - increase as • ratio (D/Dy) Sit; n/d;

retardation no change very large factor (Rd) decrease at

leading edge

Spring 1985, 53-

Lennox (1976).

Applications for Phase I HYdrologic Setting

Theground watercontamination case used in this example occurred in South Farmingdale, Nassau County, New York, and was described by Perlmutter and Lieber (1970). Most of the data required for the solution as described herein were obtained directlyfrom their report

Contamination was caused by cadmium and hex­avalent chromium-enriched electroplating wastes that infiltrated from disposal basins into a shallow glacial aquifer.Apparentlydisposal began in1941and continued intermittentlyforseveral years.By theearly1960s a leachate plume originating at the disposalponds extended downgradient about 4,300 feet and wasas much as1,000 feet wideand 70 feet thick.The plume extended to the headwaters of MassapequaCreek,asmall stream that servesasa natural drain for part of the contaminated water (Figure 4).

The surficial or upper glacial deposits, which are" Pleistocene in age,extend fromland surface toa depth of 80 to 140 feet and lie on the Magothy Formation,a unit of alluvial deposits of Late Cretaceous age. The water table in the surficial deposits lies from 0 to about 15 feet below land surface.

Theaquifer is in dynamicequilibrium and receives about 22 inchesor about 1 mgd (million gallons perday) per square mile of recharge from precipitation.The water table gradient averagesabout 1foot in 500 feet and thewater table undergoesan annual fluctua­tion of 2 to 3 feet The direction of ground water flow is southward from thedisposal ponds toward Massa­pequa Creek.Calculations of ground watervelocity for thearea rangefrom 0.5 to 1.5feet perday.Theaveragevelocity for the area is reportedly 1 foot per day.

Chemical analyses of ground water in the South Farmingdale area indicate that the background con­centration of hexavalent chromium is less than 0.01 mg/L. Likewise, the concentration is also less than 0.01 mg/Lin Massapequa Creek upstream of theleach­ate plume. Along that stretch where the plume dis­charges into thestream, thechromium concentration is substantially greater.

During the early 1940s, as much as 200,000 to 300,000 gallons per day of effluent (equivalent to 52 pounds per day of chromium) were discharged into three disposal pits having a combined area of about 15,470square feet.After 1945 the volumeof thewaste stream was reduced substantially and eventually a treatment plant was constructed. On two occasions the chromium concentration in the raweffluent was 28 and 29 mg/L.

The relatively clean nature (free of clay or organic;matter) of the materials forming the surficial aquiferprecluded anysignificant reduction in thechromium load in the plume. That is, ion-exchange during movement was negligible. Maximum chromiumcon­centration in the plume ranged fromabout 40 mg/Lin 1949 to about 10 mg/L in 1962.

The plume is about 200 feet wide at its origin at the disposal ponds. It reaches a maximum length of about 4,300 feet and increases in width to about 1,000 feet.Assuming a velocity of 1.5 feet perday this plume has an average longitudinal dispersion (Dx) of 105 ft2/day, a transverse dispersion (DJ of 21 ftVday. and dispersivities of 70 feet (ax) and 14 feet (ay),respectively.Asummaryof the required data isshown

54 Spring 1985 ­

•ii

niai

4•T H I T

Figure 4. Leachate plume at South Farmingdale, New York

in Table 4. Application of the three methods to this example is given in the followingsections.

Nomograph Solution Application 1 (Figure 5)

To find concentration (C) foradistance (x) of 4.200 feet from the source and time (t) of 2,300 days,calculate

x 4,200 ft. 60 Locate at (A)70 ft.

t 2,300 days1— = 50 Locate curve (E)

TD 46.7 days

QCj.(26,800 ftVday) (31 mfl/L). ̂ mg/L ^^ ([))

QD 1,800 ftVday

Table 4 Summary of Data for Example 1

thickness: m = 110 feet

porosity: n = 0.35

velocity: V =1.5 ft/day

dispersion: Dx = 105 ftVday

Dy = 21 ftVday

retardation: Rd = 1

volume flow rate: Q = 26,800 ftVday

source concentration: C„ =31 mg/L

mass flow rate: QC„ = 26,800 ftVday x 31 mg/L

or QC0 = 52 lb/day

100 1,000 10.000 100.000 X

x D Figure 5. Applications laand lb:using the nomographto estimatethe concentration given valuesof distance and time

or:

QC° = 52 lb/day = .029 lb/ft3 Locate at (Dj QD 1,800 ftVday

Using Figure 5, draw a line vertically from (A) to the intersection with the t/TDcurve (B), then horizontallyfrom (B) to (C) and from (C) through the scale (D) to (E), giving C = 2.6 mg/'L.

Application lb (Figure 5)To find the maximum concentration for a given

distance for large time, use the steady-state line instead of curve(t/TD).Proceedingasabove,aconcen­tration (C) of 20 mg/L is read at F.

Application 2 (Figure 6) To find distance (x) where a concentration (C) of

2.6 mg/Lwill occurata time(t)of2,300 days,calculate:

_JL_ = 2,300 days = 5Q L(jcate at (D)

TD 46.7 days

QC0 = (26300 ftVday) (31 mg/L) =46Q mg/L Locate at (B) QD 1,800 ftVday

Using Figure 6, locate the selected concentration at (A). Draw a line from (A) through (B) to (C). then hori­zontally from (C) to curve (C). and vertically to (E). giving:

•

= 60

Multiply by XD to determine distance (x):

x = (_*—) (x ) = (60) (70 ft) = 4,200 feet XD

Application 2b (Figure 6) To find the maximum distanceat which a selected

concentration will reach a given value for large time, use the steady-state line instead of curve (t/TD) in Figure 6.

Application 3(Figure 7) Tfind time(t) when theconcentration (CI will reach

2.6 mg/L at location (x) of 4,200 feet calculate.

x 4,200 ft _ 60 Locate at (D)70 ft

QC, _ (26300 ftVday) (31 mfiAl = ^mg/L Locate at (B) QD 1,800 ft3 day

Spring 1985 . . . . . . . ) ­

55

E 100 1,000 F 10.000 100,000 X

XD Figure 6. Applications 2a; usingthe nomograph to estimate the distancefor given values of concentration and time

Using Figure 7, locate the selected concentration at (A), drawa line from (A) through (B) to (C), then hori­zontally from (C) toan intersection with a vertical line from (D). giving at (E):

= 50

Multiply by TD to determine time (t):

t = (_L_) (td) = (50) (46.7 days) = 2300 days

Td

If the lines intersect above the steady-state line, the concentration will not reach the given value at that location.

Hand Calculator Method Using the data in Table 4, the calculator method

can be used to determine the same values shown in the previous example: The calculator has a majoradvantage over the nomograph solution in that it can be used to determine the concentrationdistribution throughout a plumeby calculating theconcentration at a sufficient numberofxand y coordinates. Like the nomograph, this method can easily be applied in the field in contrast to the microcomputer-TSO option.

The TI-59 calculator is loaded with the program.

thedataareentered and then the program isexecuted. The concentration will appear on the display and, if available, a printer.An example of theprinteroutput is shown in Figure 8, which reflects a distance from source of4,200feet and a time interval of 10,000days.The other input dataarelisted inTable4.Theconcen­tration is shown in lineC (16.79 mg/L).

Interactive (TSO) Computer Method Using thesame informationlisted inTable 4, two-

dimensional mapscan beproduced by the interactive computer program asshown in Figure9.Adjustmentsin dispersion ratioscan be used tocalibrate the model from an existing landfill of similar waste and hydro-geologic characteristics. Special considerations are required for very small velocities near a largesource. Cases such as these require the use of the computer (Or calculator) version.

SummaryThe methodsdescribed herein can beused toesti­

mate or predict what the concentration in a leachate plume might beat some point in space and time.The value oraccuracy of the prediction,at best can be no better than the estimate of the hydrogeologic and chemical parameters thatare factored into theequa­tions.Because these parameterscan range within wide limits,socan the prediction.Furthermore, the predic­tion mustalsoconform tofundamental hydrogeologicprinciples and common sense. The results of these predictive techniques must not be allowed to take

Spring 1985 56

Figure 7. Application 3: using the nomograph toestimate time-givenvalues of concentration anddistance

precedence oversound field investigation, datacollec­tion and interpretation at potential waste disposalsites. Rather, results should be reflected in a more objective datacollection strategyand in theengineer­ing practices proposed for a potential site.

Programs are available from the following source Mike Roulier, Project Officer Environmental Protection Agency Municipal EnvironmentResearch LaboratoryCincinnati. OH 45268

Similar programs have also been developed for microcomputers (Apple, Kaypro, and IBM-PC) subse­quent to this project, and are available from the authors.

References Ahlstrom, S.W., H.P. Foote. R.C. Arnett C.R. Cole and

RU. Seme. 1977. Multicomponent MassTransportModel:Theoryand NumericalImplementation (dis­crete-parcel-random-walk version). Battelle BNWL­2127 (UC-70.UC-32) preparedfor ERDAandAtlan­tic Richfield Hanford Co.

Anderson, M.P. 1979. Using Models to Simulate the Movement ofContaminants through Ground-Water Flow Systems. CRC Critical Reviews in Environ­mental Control, v.9. Issue 2, pp.97-156.

Bouwer, Herman. 1978. Groundwater Hydrology. McGraw-Hill Inc. New York.480 pp.

Duquid.J.O. and M. Reeves.1976. Material TransportThrough PorousMedia—a Finite Element Galerkin

epa-landfillPLUME MANAGEMENT

4200. 0 .

10000. 69.9 14. 0.35 1.5 0 .

1. i 3. 0042918 01 b 1, 6791569 01 _ c 1. 6791569 01 I

Figure 8. Printer output for hand-held calculator

Spring 1985 57

ISO GRID NAP or CnNCCHIMTKM USIR6

DATE! (»7» AOJWUO DISPIRSION MIIO CASE I WLSON TI1LEI LONO ISLAND SOLUTE I CimOHE

THICKNESS • 1I0.9C0 Tl IQISftRSION MTIO 3 rOROSITT 0.330 - veiocitt I.300 FT/D

IX IUSFERSION- 103.000 ET2/M V (IISPCR9I0N 21.000 FT2/DUWU = RETAADAT ION I.OOO ­OJUWA' I.W3 ­

START TIME » 0.000 DAT MASS RATE (SCO)* 32.000 LS/S I N I I I I

CONCENTRATION • I (HO/LI AT SANPLC TINE 2333.3 DAT

230 300 730 1000 1230 1300 1730 2000 2230 2300 2730 3000 323© 3300 373© 400© 4230 4300 4730 SOOO

I 1 2 2 3 3 3 3 3 3 2 2

• II 13 13 13 14 13 13 12 10 • A 4

34 .31 20 24 24 22 20 IS IS 12 0 4

f II 13 13 13 14 13 13 12 10 0 4 4

2 2 3 3 3 3 3 3 2 2

730

1000

Figure 9. TSO gild mapol concentration using adjusted dispersion ratio

Model Oak Ridge Nat Laboratory.Publ. No.ORML- Pickens,J.F.and W.C. Lennox.1976. NumericalSimu­4928. lation ofWaste Movement in Steady Ground-Water

Freeze, RA andJA Cherry.1980.Groundwater.Pren­ Flow Systems.Water Resources Research, v.12, no. tice Hall Inc. Englewood Cliffs, New Jersey, 604 pp. 2, pp. 171-180.

Gupta, S.K., K.K. Tanii and J.N. Luthin. 1975.AThree- Prickett,TA and C.G.Lonnquist 1971.Selected Digi­Dimensional Finite Element Ground-Water Model. tal Computer Techniques for Ground-Water Contribution No. 152. California Water Research Resource Evaluation. Illinois State Water Survey. Center. Universityof California. Bull. 55,66 pp. •

Holcomb Research Institute. 1978. Utilization of Prickett TA,T. Naymik and C.G. Lonnquist 1981. A Numerical Ground-Water Models for Water Re­ Random-Walk Mass Transport Model for Selected source Management U.S. EnvironmentalProtection Ground-water Quality Evaluations. Illinois State Agency. EPA-600/8-78-012,178 pp. Water SurveyCircular. Urbana, Illinois. In press.

Konikow, L.F. and J.D. Brederhoeft 1978. Computer Reddell, D.L.and D.K.Sunada.1971.NumericalSimu­Model of Two-Dimensional Solute Transport and lation of Dispersion in Ground-Water Aquifers. Dispersion in Ground Water.USGS Techniques of Colorado State University Hydrology Paper 41. Water Resources Investigations. Chapter C2.Book ThrailkillJ.1972.DigitalComputer Modelingof Lime­7. Automated Data Processing and Computations. stone Ground-Water Systems. University of Ken­

Perlmutter, N.M. and M. Lieber. 1970. Dispersal of tucky Research Report Number 50. Plating Wastes and Sewage Contaminants in Townley. L.R.andJ.L.Wilson.1980.Description of and Ground Water and SurfaceWater.South Farming- User's Manual for a Finite Element Aquifer Flow dale-Massapequa Area. Nassau County, New York. Model AQUIFEM-IL.Report No.252 of the Ralph M. U.S. GeologicalSurveyWater Supply Paper 1879-G, Parsons Lab. of MIT. 67 pp. Trescott P.C., G.F. Pinderand SP.Larson.1976.Finite

Pettyjohn.WA, D.C. Kent, TA Prickett. H.E. LeGrand Difference Model for Aquifer Simulation in Two and F.E.Witz. Methods for the Prediction ofLeach- Dimensions with Results of Numerical Experi­ate Plume Migration and Mixing. U.S. Environ­ ments. USGSTechnical Water ResourcesInvestiga­mental Protection Agency. 202 pp. In press. tions Book. Chapter CI.

Pettyjohn,WA1982.Causeand Effectof CyclicChanges Wilson. J.L. and PJ. Miller. 1978. Two-Dimensional inGround WaterQuality.GroundWater Monitoring Plume in Uniform Ground-Water Flow. Journal of Review, v. 2, no. 1, pp. 43-49. Hydraulics Div. Am. Soc. of Civil Eng. Paper No.

13665. HY4, pp. 503-514.

5& Spring 1985

Biographical Sketches Douglas Kent and Wayne Pettyjohn areprofes­sors of geology at Oklahoma State University(Department of Geology, Stillwater, OK 74078).ThomasA. Prickettisa consultant withThomas Prickett and Associates (Consulting Water Resources Eng., 8 Montclair RdL, Urbana, IL 61801).