Contaminant Plume Migration in an Aquifer: Finite Element Modeling for the Analysis of Remediation Strategies: A Case Study

N3T FOR QUOTATION WITHOUT PERMISSION

OF THE AUTHOR

CONTAMINANT PLUME

MIGRATION IN AN AQUIFW:

FINITE ELEXEN' MODELING FOR

THE

ANALYSIS OF REMEDIATION SI'RATEGES: A CASE SIVDY

H.-J. Diersch S. Kaden

April 1384 CP-84-11

Collaborative Papers report work which has not been performed solely a t t h e International Institute for Applied Systems Analysis and which has received only limited review. Views or opinions ex-pressed herein do not necessarily represent those of t h e Institute, its National Member Organizations, or other organizations supporting the work

INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS 2361 Laxenburg, Austria

Hans-Jorg Diersch is from t h e Institute for Mechanics of t h e -4cademy of Sci- ences of t h e German Democratic Republic, Berlin.

Stefan Kaden is with t h e Regional Water Policies project of t h e Institutions and Environmental Policies Program a t the International Institute for Applied Sys- t e m s Analysis, Laxenburg, Austria.

Intense regional development in m a n y parts of t h e world c r e a t e s an increasing p r e s s u r e on t h e environment both by consuming n a t u r a l resources a n d by discharging wastes t h a t a r e hazardous t o t h e population and t o n a t u r a l ecosystems. A substantial p a r t of these interactions between regional socio- economic a n d environmental systems takes place through regional groundwa- t e r systems. Apart from being t h e resource t h a t is highly vital for socio- economic development and for t h e evolution of ecosystems, t h e regional groundwater system is often a basic medium through which local h u m a n interventions penetrate t o and a r e "felt" in o t h e r p a r t s of t h e region, a n d also frequently beyond its boundaries.

To s t u d y t h e role of n a t u r a l groundwater systems in regional development a n d also regional policies capable of preventing f u r t h e r degradation of ground- water a r e one of t h e goals of t h e "Regional Water Policies" project a t IIASA. One of t h e challenges in this r e s e a r c h is to cope with t h e i n h e r e n t complexity of

"hidden" groundwater processes. Depending on t h e goals of a particular stage of t h e analysis models of varying sophistication should be used. This paper exemplifies t h e use of a r a t h e r elaborated model for t h e analysis of a rela- tively "local" scale of the m e a n s t o prevent t h e spreading of contaminants in a groundwater aquifer. After discussing t h e model and its verification using field data, t h e a u t h o r s make a comparative long-term analysis of 3 types of remediation strategies for a case region in t h e GDR.

S. Orlovski Project Leader

Regional Water Policies

Groundwater resources a r e becoming more and more endangered of being depleted by over-exploitation and of being polluted a s a consequence of environmentally insensitive economic activities and population growth in m a n y regions and countries of t h e world.

Causes and consequences of quantitative and qualitative changes in groundwater s t a t e s c a n be separated by decades and centuries. Once contam- inated o r depleted, groundwater resources may be permanently impaired.

This fact becomes especially obvious i n t h e case of groundwater pollution by hazardous wastes. Necessary remediation strategies may be extremely time a n d money consuming. Therefore, t h e optimal design of s u c h remediation strategies is of g r e a t importance.

The paper describes t h e r e s u l t s of a case study dealing with historical and predictive modeling of t h e migration of a real contaminant plume in an allu- vial aquifer threatening t h e nearby operating extraction wells for municipal water supply. As a modeling case s t u d y i t primarily aims a t modeling a n d exa- mining c u r r e n t and intended remediation strategies. The consequences and benefits of a hydraulic barrier in continuous or i n t e r m i t t e n t operation and t h e i r combination with pumpage from interception wells a r e investigated and discussed.

For these purposes a horizontal plane transport model based on a finite e l e m e n t approach has been developed a n d applied. The model has been t e s t e d a n d calibrated through a history matching procedure comparing model com- putations with observed field data, where hydrodynamic dispersivities a r e identified a s principal parameters. The obtained prognostic r e s u l t s allow several practical conclusions on t h e design of remediation strategies.

The used finite e l e m e n t model simulator FEFLOW h a s proved t o be a con- venient and powerful tool in modeling t h e complex flow and t r a n s p o r t processes of t h e contaminant plume. It demonstrates t h e abilities in prospec- tive simulations for decision purposes.

CONTENTS

1. Introduction

2. Numerical Simulation of Local Groundwater Contamination 2.1. Background

2.2. Basic Equations and Parameters 2.3. Finite Element Simulator FEF'LOW

3. The Case Study

3.1. Description of the contamination Problem 3.2. Transport Model

3.2.1. Hydrogeologic and Hydrochemical Description 3.2.1.1. Groundwater Flow

3.2.1.2. Contaminant Migration 3.2.2. Mathematical Formulation

3.2.2.1. Discretization of the Study Area 3.2.2.2. Boundary and Initial Conditions 3.3. Simulation Results

3.3.1. Contamination Epignosis and Model Verification 3.3.2. Prognosis for Contaminant Intercepting

and Aquifer Remediation

3.3.2.1. Hydraulic Barrier by Recharge

3.3.2.2. I n t e r m i t t e n t Operation of Hydraulic Barrier 3.3.2.3. Interception Pumping of Contaminant Plume 3.4. Conclusions

4. Research Needs

5. Appendices

Appendix A: Finite Element Approximation

Appendix B: S u m m a r y of Physical Parameters Used Appendix C: Nomenclature

References

CONTAMINANT PLUMB MIGRATION

IN

AN AQ FlNRJZ ELEMENT MODELING

FDR THE

REZEDIATION EXRATEGIES:

A CASE

SI'UL)Y

H.-J.

Diersch a n d S. Kaden

1. Introduction

Groundwater r e s o u r c e s a r e an increasingly i m p o r t a n t component of t h e regional development in many regions. General awareness about t h e impor- t a n c e of t h e precious groundwater r e s o u r c e s h a s g r e a t l y extended in r e c e n t times. In many c o u n t r i e s of t h e world, groundwater is valued for i t s high qual- ity, its avaibility close to t h e u s e r a n d i t s reliability, satisfying an i m p o r t a n t part of t h e drinking water supply.

Nowadays groundwater resources a r e becoming m o r e a n d m o r e endangered of being depleted by over-exploitation and of being polluted as a consequence of environmentally insensitive economic activities a n d popula- tion growth in m a n y regions a n d c o u n t r i e s of t h e world. The most i m p o r t a n t impacts on groundwater a r e c a u s e d by agriculture (e.g. n.itrate pollution), industry (hazardous and toxic waste disposal, landfills, e t c . ) , mining opera- tions (especially open-cast mines), and drinking a n d irrigation water with- drawals.

Causes a n d consequences of quantitative a n d qualitative changes in groundwater regimes can be s e p a r a t e d by decades or c e n t u r i e s . Once contarn- i n a t e d or depleted, groundwater resources may be p e r m a n e n t l y impaired.

This is one of t h e m o s t c h a r a c t e r i s t i c "creeping" problems, which calls

foremost for preventive actions and appropriate policies to avoid situations which a r e extremely difficult to cure and rectify. Groundwater degradation is progressing at such a speed t h a t g r o u n d w a t e r d e p l e t i o n a n d p o l l u t i o n is con- sidered in many qountries to be the m o s t i m p o r t a n t w a t e r - r e l a t e d p r o b l e m of t h e 80s.

The present paper deals with one special problem of groundwater degrada- tion

-

t h e contamination due t o hazardous wastes. Groundwater contamina-' tion, particularly from hazardous wastes, has been recognized as a very seri- ous national problem in many countries (Wood e t al. 1984). Our advanced technological society implies the increasing danger of chemical contamina- tion throughout the environment, especially t h e soil and the groundwater resources. The number of potential solid and liquid contaminants of commer- cial and industrial wastes is tremendous and the number of serious groundwa- t e r contaminations from hazardous wastes is manifold (for instance, see Jack- son e t al. 1980, Wood e t al. 1984). Such contaminations necessitate rernedia- tion measures above all in cases of aquifers being used for water supply. Dif- ferent techniques for subsurface improvement of groundwater quality a r e available as for instance the pumpage of contaminated water, t h e building up of hydraulic barriers by the help of artificial recharge or subsurface water treatment technologies. All these tech*iques m a y be extremely time and money consuming and they have to be investigated frequently within t h e framework of regional water or more general environmental policies.

A l l these problems mentioned above explain a continuing and growing need for the analysis and design of regional policies capable of providing t h e rational use and protection of groundwater and surface water resources as well as t h e remediation of degraded resources.

The IIASA project "Regional Water Policies" aims a t the elaboration of a conceptual framework, methodology, and computer-based methods, which can assist t h e analysis of such policies. Thereby, t h e groundwater resources have t o be considered a part of t h e complex socio-economic and environmental sys- tems. Consequently, modeling principles for groundwater subsystems should be developed, which focus on their links with economic. social and other processes pertinent t o regional human activity. Due to the complexity of these links and t h e varying scale in space a n d time as well as t h e different modeling goals, hierarchical systems of models a r e required.

The range of models includes highly sophisticated multidimensional models with distributed p a r a m e t e r s but also simplified models with lumped

'

parameters. For modeling groundwater flow, appropriate models for almost

I

all purposes a r e available. Difficulties arise in t h e case of modeling ground-

w d e r quality. Generally, a sophisticated modeling framework is used t o simu- late those complicated processes. The paper describes t h e use of such a r a t h e r elaborated model. Generalized methods for t h e development of simpli- fied models based on t h e sophisticated models a r e not yet available.

The design of remediation strategies for contaminated aquifers is a typi- cal problem which necessitates the use of sophisticated numerical models. In

1

t h e following, t h e results of a methodological case study dealing with modeling t h e migration of an actual contaminant plume in an alluvial aquifer a r e described. The study was mainly directed towards examining c u r r e n t and intended remediation strategies. For t h e numerical modeling t h e finite ele- m e n t m e t h o d has been used. By way of introduction, some theoretical development for numerical simulation of local groundwater contamination is given.

The paper characterises possibilities a n d bounds of sophisticated model- ing for policy design. In conclusion, research needs from the point of view of t h e analysis and design of regional water policies a r e o u t l i n e d

2. Numerical Simulation of h c a l Groundwater Contamination

2.1. Background

In t h e following we assume t h a t a contaminant plume consisting of relevant chemical components (contaminants) e n t e r s an aquifer or is located within it. The causes of t h e formation of t h e plume may be neglected. Depen- dent on t h e physical-chemical properties of t h e contaminants two fundamen- tal different approaches a r e common:

-

^{t h e} s i n g l e phase flow, considering a binary chemical system consisting of two miscible species (with similar density a n d viscosity): t h e solution characterised by t h e contaminant and t h e solvent water, which is assumed t o be an ideal (or colloid) solution;

-

t h e mdtifluid or multiphase flow of nonsoluble fluids with different den- sity a n d viscosity.

The first approach (mixing or dilution) is applicable t o a g r e a t class of inor- ganic and organic compounds, depepdent on t h e solubility a n d the concentra- tion of the contaminants. In this range, for i n s t a n c e n i t r a t e , pesticides and phenols (see Zilliox e t al. 1974) can b'e incorporated. We will concentrate on this approach below. The second approach is typical for petroleum and organic solvant contamination.

The movement of contaminants within porous m e d i a is called migration or mass C r a n s p o ~ t processes.

The displacements and changes of chemical species in groundwater a r e governed a n d influenced by t h e following physical a n d chemical pr!ocesses:

(1) convection [chemicals a r e moving (translating) with t h e flowing ground- water]

(2) hydrodynamic dispersion [spreading by physicochemical effects ( molecu- lar diffusion) a n d mechanical effects in t h e macroscopic scale of aquifer (hydromechanical dispersion)]

(3) medium-surface interaction of species [reaction between t h e dissolved species a n d t h e solid aquifer material (sorption)]

(4) mass change processes [chemical and/or biological processes within t h e mixture].

The description of t h e s e processes in a complex hydrogeological system with its geoscale spatial a n d temporal dimension is usually based on deterministic m o d e l s describing t h e m a s s (including species concentration)and momentum conservation. (See, for instance, Bear 1972). Recently, stochastic modeling approaches a r e getting m o r e consideration (Dagan 1983), forced by difficulties describing t h e scale dependent dispersion (see below). In developing t h e deterministic models, statistical averaging p r o c e d u r e s a r e used t o transform the pore-scale microscopic processes to t h e large scale (see, Hassanizadeh a n d Gray 1979). This leads to a system of macroscopic conservation equations valid for a given volume t h e so-called REV (representative elementary volume). Statistical influences a r e involved in p a r a m e t e r relations, primarily for t h e mechanical dispersion, incorporating t h e m e a s u r e of heterogeneity (microscopic, macroscopic) of t h e medium or a r e a (column, field or regional scale), as described below. As an essential consequence t h e transport

processes have t o be t r e a t e d in their real scales. For regional-scale transport, these processes a r e long-term, measured in t h e order of months or years.

This emphasizes both, t h e r e s t r i c t e d applicability of experiments a n d observa- tions, and t h e necessary application of mathematical modeling.

The m a t h e m a t i c a l solution of t h e deterministic conservation equations for complicated problems can only be done numerically. Analytical solutions a r e known only for some special cases, often for one-dimensional transport (v.

Genuchten e t al. 1982, Voigt a n d Hafner 1983). Also, for numerical solutions t h e g e n e r a l three-dimensional migration processes a r e simplified t o two- dimensional processes, due t o the lack of data, t h e required accuracy a n d t h e computing effort. The movement of local groundwater contaminations (con- t a m i n a n t plumes) within aquifers usually is supposed to be a horizontal plane movement. The three-dimensional, sometimes nonlinear partial differential equations of t h e migration process c a n be transformed into two-dimensional vertically averaged equations (see, Gray 1982) based on t h e Dupuit assump- tions.

Bredehoeft a n d Pinder (1973) developed horizontal aquifer transport equations which were utilized in modelling t h e groundwater contamination a t Brunswick, Georgia, USA. To solve numerically t h e horizontal aquifer model f i n i t e d i f f e r e n c e m e t h o d s a n d t h e method of characteristics were used. ~e s a m e concept was applied by Konikow (1977) for an extensive contarninati0.n study of t h e Rocky Mountain Arsenal, n e a r Denver, Colorado. USA However, these n u m e r i c a l methods h a s been found to be unsuitable for s o m e hydro- dynamic situations commonly encountered in t h e field The finite element mnthod (e.g., Pinder a n d Gray 1977) h a s proved to be a more general (vis-a-vis ad hoc) simulation technique well suited t o hydrogeological field problems in modeling realistic groundwater contamination, because of its f l e ~ i b i l i t y a n d such i n h e r e n t numerical properties a s

(1) a c c u r a t e approximation of velocity field (conservativity)

(2) a c c u r a t e approximation regarding t h e species concentration t o avoid relevant influences by numerical dispersion (unrealistic sloping and spreading of concentration waves or fronts)

(3) stable solution especially for significant convection.

The finite element method was used by Pinder (1973) to model practically t h e movement of a plume of contaminated groundwater on Long Island, New York.

F u r t h e r works concerning the modeling of contamination-problems i n ground-

4

water can be found (e.g., Segol and Pinder 1976, Pickeris a n d Grisak 1981b,

4

Pinder and Gray 1977, Pickens and Lennox 1976, Mohsen e t al. 1978. Diersch 1979, 1981a, Diersch and Nillert 1984a, Gray and Hoffman 1981, s e e also their references) demonstrating the advantageous performance. Galerkin-finite e l e m e n t formulations using time-weighted approximations (Crank-Nicolson a n d implicit schemes) have become prominent i n t h e field. Upwind schemes for numerical stability have been used only in special cases because they can induce a g r e a t measure of false numerical dispersion. Locally exact upwind s c h e m e s developed for one-dimensional transport equations using finite differ- e n c e s and finite elements (Enquist a n d Kreiss 1979, Stoyan 1979) can also cause problems if extended t o higher dimensional processes. Moreover, a n investigation and discussion can be found e.g., in Diersch (1983b).

In mathematical simulation of species transport in groundwater an important problem is t h e approach and validation of representative parame- t e r s of aquifer dispersion in t e r m s of dispersivities (Bertsch 1978, Fried 1975) t h a t a r e macro-dispersivities. In general, field m e a s u r e m e n t s a r e necessary due t o t h e inability t o describe t h e real groundwater system using t h e coeffi- cients derived from laboratory experiments. Frequently well t r a c e r experi- m e n t s (e-g., Beims 1983, Hibsch a n d Kreft 1979) in t h e aquifer investigated a r e carried on. However, the application t o large-scale contamination processes is not generally or only conditionally possible (see also Section 2.2). To over- come t h e s e difficulties i t is usual in modeling practice t o fit t h e numerical model t o observed space-time concentration field distributions via historical epignosis (history match) simulations, e.g., Konikow (1977), Pinder (1973), Gray and Hoffman (1981), Das Gupta and Yapa (1982). This strategy is also used in the present study. Difficulties regarding this procedure can r e s u l t from t h e multiparameter influence including t h e numerical accuracy of models a n d t h e time consumption of model fitting. Beims (1983) h a s a t t e m p t e d t o empirically relate dispersivities t o corresponding a r e a scales, ranging from laboratory experiments t o regional results as shown in Figure 1.

However, i t should be clear t h a t even more so for regional contamination problems, these values can only be rough values due to field a n d model influ- e n c e s on macro-dispersivities.

Robren, 1974 Robsen, /197

Konikow, 1976 Wilson, 1978

Konikow, 1974 Fried. 1975

*

^{Pindr, 1973}

Wilson, 1971

lo1 -I

Fried, 1975

Mercada. 1966

lo0-: Beims. 1979 Rousselot, 1977 Oako. 1976

"Fiirrtenwalda". 1982 lo-'+

Nitsche. 1982

10-2 _10-1 , , , ,

/.,

_{1 o0} ^{, , , ,}

.

^,

.,.,

_{1 o1} ^,

. . . ^. . ...,

_{1 o3}

. . . . . ^....,

_{l o J} ^,

. . . ^{. . ...,}

_{1 '0}

^{. . . . .}

^{T . . ' 1} _{I o5}

.

Area scale length [ml

Figure 1. Dependence of longitudinal dispersivity on t h e a r e a scale length, from Beims (1983)

To improve t h e representativeness and t o generalize t h e dispersivity dependence within aquifers i t has recently been attempted t o describe t h e heterogeneity of aquifers by large-scale spatial distribution in hydraulic con- ductivity with geostatistical methods (Smith and Schwartz 1980). Here, t h e dispersivity becomes dependent on migration path (travel distance from t h e contaminant source) and t h e mean and variance of velocities (Tang e t al.

1982). Pickens and Grisak (1981b) have shown t h a t t h e distance-dependent diapersivities, however, are not important for long-term predictions.

Summarizing t h e discussion above, for the modeling of regional transport of .a local c o n t a m i n a n t plume, the following premises should be taken into account:

(1) Flow a n d t r a n s p o r t processes a r e (at least) two-dimensional (horizontal).

(2) There is a large-scale spatial a n d temporal movement of t h e contaminant plume. ^'

(3) The p a r a m e t e r estimation (dispersivities) has t o be done via history m a t c h simulations.

(4) The finite e l e m e n t method should be used as t h e most general a n d accu- r a t e technique.

2.2. Basic Eguations and Parameters

The flow a n d species .transport processes i n three-dimensional aquifer systems a r e described by t h e balance equations (summation convention is for i, j

=

1,2,3 ), (Bear 1979, Diersch e t al. 1983c) as follows:

with

for conservation of groundwater mass,

for m o m e n t u m conservation of groundwater (generalized Dacy's law), a n d

for conservation of species mass ( t r a n s p o r t equation) with s

where (see also Appendix C):

specific storage coefficient ( L - I ) ;

hydraulic head ( L ) ; kinematic porosity ( L o );

components of average pore velocity ( L T - I ) ; groundwater density ( ~ L L J ) ;

reference groundwater density (ML-');

gravitational acceleration (LT-2);

skeleton compressibility ( 1 ) ;

compressibility of ,groundwater (1);

tensor of hydraulic conductivity ( L T - I ) ;

components of gravitational unit vector in t h e direction x , ( l ) ; solute concentration of chemical component (ML-');

solute concentration sorbed ( M L ~ ) ; Dij

=

tensor of hydrodynamic dispersion ( L 2 T - I ) ;

Dd

=

medium diffusion coefficient ( L ~ T - ~ ) ;

Br 8r =

coefficients of longitudinal a n d transverse dispersivity, respectively ( L ) ;

V =

( v ~ v ~ ) ~ ' ~ , absolute pore velocity ( L T ~ ) ; dij

- -

^{for i}

=

j Kronecker tensor

0 for

i

# j

b = I

^l

reaction t e r m ( ~ ~ ~ ' 7 - l ) ; A,

=

concentration decay r a t e ( T - I ) .

Considering regional flow fields where their horizontal extent dominates over t h e aquifer thickness the three-dimensional equations c a n be reduced to horizontal two-dimensional ones because vertical variations a r e generally not important compared with t h e i r horizontal dynamics, a n d c a n therefore be neglected. For deriving t h e representative horizontal flow a n d transport model t h e three-dimensional equations (1) to (3) a r e i n t e g r a t e d in t h e vertical z3-direction associated with an averaging process of t h e dependent variables C, h, and vi as well as t h e remaining parameters in t h e form of

with

M

= aquifer thickness ( L ) ,

a n d analogous for ;,Gi etc. using t h e Dupuit approximation. Accordingly, this leads for i , j

=

1.2 t o (see Bredehoeft and Pinder 1973, Scholz 1982, Diersch et al. 1 9 8 3 ~ )

a E -ah^ a

-

aE

MR- +

P C a t

+

+Eifi

- ^nD..

-)

=

a t azi

a ~ ,

with t h e aquifer storage coefficients

S = n o + q M

and

as the retardation factor assuming a linear isotherm equilibrium absorption;

further the specific Darcy flux

and t h e well function

with

QB

=

discharge of single wells a t (z 11 , Z ~ ) ( L ~ T - ' ) (withdrawal (sink)

=

positive sign)

b

=

number of wells 8 0

=

Dirac delta €unction;

with t h e transmissivity

and t h e tensor of aquifer macrodispersion

- -

9i9j

Dij =

( D ~ M

+

pTV)$

+ (pL -pT)-

v

where f u r t h e r

n o

=

drainable or fillable porosity ( L O ) ;

W

=

groundwater accretion ( L T - I ) ; K:

=

sorption coefficient (1):

C' =

well-sink/source concentration (ML9);

C" =

accretion-related input concentration ( M L ~ ) ;

(pi

absolute specific flux ( L ~ T - I ) .

The formulation is applied t o an unconfined aquifer with gssumption that t h e phreatic (free) surface is equal to the hydraulic head. ~ o i s i d e r i n ~ unconfined aquifer for all practical purposes one holds no

>> S'M.

The equations for con- ^' fined aquifer can be derived from above when using S = SL

=

SSM.

The practical modelling of contaminant migration in an aquifer is there- fore attributed to t h e prelimivary computation of hydraulic head

6

and t h e resulting Darcy fluxes ?ji by sdlving t h e flow equations (5) and (6) incorporat- ing the parameters

coefficient of storativity S

sink-source relations ^{B y}

w

transmissivity ^! Tij

and the subsequent prediction of the contaminant concentration in aquifer by solving the transport equation (7) associated with t h e parameters

aquifer thickness

M

porosity n

sorption coefficient n:

sink-source relations A,,Ao, C', C"

longitudinal and transverse

dispersivity

BLSBT.

Extended beyond the usual hydraulic parameter data necessity, for migration studies parameters describing sorption and possible chemical/biological reac- tions as well a s pararne ters of dispersivity quantifying the hydrodynamic dispersion (spreading, dilution) become of importance. These parameters depend on the chemical components considered and the material through which flow takes place as well a s possibly on the chemical/biological environ- m e n t in t h e aquifer. For conservative mobile components (e.g., salts, hydro- carbons and similar products) these actions do not play a role or a r e negligi- bly small. The dispersivity parameters give the quantitative measure of longi- tudinal and transverse spreading of species in groundwater caused by hydro- dynamic actions resulting from, on t h e one hand, the microscopic hetero- geneity of pore space and, on the other hand, the macroscopic heterogeneity (conductivity distribution) of aquifer. Normally, their effects exceed signifi- cantly t h e isotropic mixing intensities produced by molecular diffusion.

ThereFore, u n d e r practical conditions it can be assumed Dd

=

0.

The heterogeneity influence on dispersion is expressed by the scale of study a r e a occurring (Pickens and Grisak 1981a, Klotz 1982a). So

BL

is in t h e range of

0.01-3 c m for laboratory scale (column experiments) 0.1 -2 m for field scale (well injection tests)

2 -150 rn for regional scale (model history match) (maximum values known 900 m!, Das Gupta and Yapa 1982).

2.3. Finite Element Simulator F'EFLOW

For modeling of two-dimensional processes in porous media, the Academy of Sciences of the German Democratic Republic developed a finite element program system FEFLOW (Diersch 1980a). It has already been successfully applied to contaminant transport resulting from hazardous intrusion due to bankfiltration from a s t r e a m (Diersch and Nillert 1983a), to saltwater intru- sion (upconing) below pumping wells (Diersch e t al. 1984a, Diersch and Nillert 1984b), and t o density-coupled intrusion processes (Diersch 1981b, 1 9 8 1 ~ ) . In the following this program and i t s mathematical foundation is outlined.

In context of the finite element method the entire flow domain

R

with its boundary

r

is subdivided into a finite number of subdomains

R e ,

called finite elements, e a c h bounded by

le.

The unknown dependent variables a r e

fi,&(i =

1,2) a n d

e.

^In the interest of simplicity t h e i r averaging symbols, introduced by equations (4) and ( l o ) , will be subsequently omitted and a r e approximated by the trial functions

with a

=

1,Z; 1

=

1,2, ^a

. .

^,m,

where Nl a r e basis Functions and rn corresponds to t h e number of discrete mesh-nodal points. For t h e present study biquadratic interpolation

expressions modelled by isoparametric curved eight-noded quadrilateral ele- m e n t s a r e used advocating a higher accuracy and flexibility.

The solution of t h e two-dimensional differential equations (5). (6) a n d (7) is based on a substitution model accomplished when the Darcy equation (6) is introduced into t h e continuity equation (5). Reducing t o the solution of t h e primary unknowns h a n d C the computations a r e significantly simplified, as often practised, e.g., by Konikow (1977) a n d Pinder a n d Gray (1977). The necessary determination of velocities pi (secondary unknowns) is h e r e based on a derivative evaluation of the discrete h-fields applying the equations (6) a n d (14). Consequently, however, t h e conformity regarding qi is no longer g u a r a n t e e d which can lead t o numerical e r r o r s under certain c i r c u m s t a n c e s in zones with high velocity gradients. Accordingly, for some applications (Diersch 196lb,c) formulations in all primitive variables were preferred involv- ing, however, a corresponding higher computational effort. Both ways c a n be applied via the user-oriented FEF'LOW code developed (Diersch 1980a). The ele- m e n t type a s used h e r e with higher interpolation order s e e m s to be an appropriate compromise between effort a n d velocity accuracy necessary for two-dimensional transport processes. In this case t h e velocities vary bil- inearly over the element. As f u r t h e r outlined in Appendix A it follows super- convergent velocity dependences when using a suitable derivative concept.

The finite element model equations resulting from a Galerkin-version of m e t h o d of weighted residuals (e.g., Pinder a n d Gray 1977) applied t o equations ( 5 ) , (6) and (7) a n d after using Green's theorem a r e given by

a n d

where N represents the basic function N1 (xi) and

as well a s

correspond t o t h e Darcy volumetric flux component and t h e concentration flux in n o r m a l direction positive outward t o boundary

I?

t o be assigned, respec- tively; ni a r e t h e directional cosines.

The following initial (I.C.) a n d boundary

(B.C.)

conditions hold:

hrydradic head h I.C. h(zi,O)

=

ho(zi,O)

B.C. h ( q . t )

=

h F on

rl

^x t [ ~ , m )

(first kind or Dirichlet boundary condition) qh

=

q,f on

rZ

x t [O,m)

(second kind or Neumann boundary condition) qh

=

~ ~ ( h !

-

h ) on

r3

x t [ ~ , m )

(third kind or Cauchy boundary condition) Concentration C

I.C. c(z,,o)

=

c,(z,

,o)

B.C. ~ ( z , , t )

= cf

^on

r,

x

t [ o , m )

(first kind or Dirichlet boundary condition) q,

=

q,R on

r5

x t

[o,=)

(second kind or Neumann boundary condition) q,

= ~ ( C , R - ^{C] on}

^{x t [o,-)}

(third kind or Cauchy boundary condition),

where r l u r Z u r 3

=

r4ur5ur6 = F, the values identified by

d

designate prescribed boundary ones for t h e hydraulic head and concentration, Al a n d

A2

indicate aquifer-surface water interactions and concentration transfer coefficients, respectively.

After introducing equations (14) into (15) and (16) one

ina all^

obtains sys- t e m s of algebraic equations, as described in Appendix A (equations ( A l l ) and (A12)). These equations c a n be written symbolically in m a t r i x form as follows:

when using a time-weighted difference scheme, where H a n d C a r e vectors containing t h e nodal unknowns For hydraulic head a n d concentration, a n d

At

r e p r e s e n t s the time step. The necessary "velocityu-field V is computed via a numerical derivation of t h e H-solution according to equation (6) a n d (A7), respectively. The s t r u c t u r e of t h e s e matrices a n d vectors as well as t h e pro- perties of s c h e m e s a r e f u r t h e r described in Appendix A.

Because chemical transport is m u c h slower t h a n m o m e n t u m t r a n s p o r t , for long-term quality simulations short-term perturbations in groundwater flow may be neglected a n d t h e groundwater flow be considered steady s t a t e as indicated below. In such cases, equation (18) reduces t o (Appendix A)

In Appendix A, appropriate singular well e l e m e n t s proposed by Char- beneau a n d S t r e e t (1979a,b) a r e introduced. being a combination of t h e local analytical well equation with numerical field solution allowing groundwater- flow fields n e a r well-(point) singularities to model advantageously. They will be used especially i n subsequent simulating the interception pumping of t h e c o n t a m i n a n t plume (see Section 3.3.2.3).

To solve t h e symmetric and unsymmetric equation systems t h e FORTRAN-coded finite element program FEF'LOW (Diersch 1980a) utilizes effec- tive profile (envelope) and f r o n t elimination techniques. The present sirnula- tions were r u n or1 a BESM-6 computer.

3. The Case Study

3.1. Description of the Contamination Problem

In t h e vicinity of a drinking water supply station in t h e GDR, a groundwa- t e r contamination problem exists. Due to the destruction of an industrial plant in World War 11 a g r e a t quantity of organic contaminants were released and migrated t o t h e underlying alluvial aquifer leading t o a significant con- tamination of the groundwater resource in this area.

As

illustrated in Figure 2a, a contaminant plume has been observed within t h e groundwater basin of t h e drinking water supply station.

The pumping wells of the drinking water supply station obtain fresh groundwa-

!

t e r from the n o r t h e r n tableland and infiltrated water from adjacent lakes in t h e east and the south. The study area is bounded to the west by a subsurface watershed. Due to this hydrogeologic setting and the increasing of pumping contaminated groundwater moved on an ever increasing scale toward t h e pumping well gallery A , posing a severe t h r e a t to water supply. The qualita- tive development of the pumping capacity is shown in Figure 3.

Recognizing t h e potential danger to public water supply, several field investigations and sampling of t h e contaminated a r e a were carried out. In order to meet the demand, new pumping wells of t h e gallery A had to be con- s t r u c t e d in the western part while the eastern wells exposed to the contarn- inant plume were becoming increasingly affected by t h e contamination and had to be partially taken out of action. In this period, a t t h e beginning of t h e seventies, an extensive increase of contaminant concentration in t h e exposed wells ( t h e well section (h'WS) as indicated in Figures 2a and 4) was observed.

By this time t h e contaminant plume h a d expanded t o about 1000 m in length and a width of between 130 m and 300 m a s shown in Figures Za and 5.

There was only a relatively short distance of the plume from the SWS (see Fig- u r e 5). First assessments concerning a protection of t h e water supply wells

- - - - -

Hydroisohyprr ^M.m groundwater movement CMtaminlnt p l u m

Figure 2. Location of the contaminant plume

a) Migration of the plume toward the supply wells (period from 1945 to 1977)

b) Intercepting the supply wells by an infiltration basin (period from 1977)

- +

a- -

am

:

a= -

YI

-

-

Q ^m_L ^.

^-

^{Gallery A QA}

C . , , ,

-

^{Gallery B QB}

.-

-

0

^{- -.}

^,

^.

^, Groundwater recharge Q,

m L

- -

-

.-

"-

C

-

.- -0 C

-

m

- . - . - . - . - . - . - . - -

m

C

-

.- n E ₃

- _-

a

.

Prognostic period

l i

1 1 1 1 ~ 1 1 1 1 ( 1 ~ 1 1 ( 1 1 1111 1 1 ( 1 1 1 1 1 1 1 1 1 1 ~ 1*ill ~ 1 1 1 1 I

1950 1960 1970 1980 1990 2000

t [ t r l

F-igure 3. Development of day-averaged pumping rate (including basin infiltra- tion) for the galleries of t h e drinking water supply station.

were devised. These assessments were connected with planning a second pumping well gallery B (see Figure 2b), required by an augmented water s u p ply. To control t h e contamination, an infiltration basin has been proposed which should be capable of both intercepting t h e flow of contaminated ground- water towards t h e extraction wells and compensating t h e fresh groundwater losses due t o the reduced groundwater resources. Its dual functions regarding a hydraulic barrier and an artificial groundwater recharge a r e shown in F'igure 2b. The groundwater flow field is relatively complicated, having regions with different flow travelling both toward and away from t h e adjacent lakes, and areas with virtually no groundwater movement (in t h e eastern part of study area). Previously, t h e investigations concerning t h e location and design of the infiltration basin only resorted t o mathematical modeling of t h e regional flows.

In 1978 the hydraulic barrier was installed. At the same time gallery B was put into operation. Since 1975 t h e pumping r a t e of the gallery :A has decreased successively as indicated in Figure 3. At present its level &quals

i

gallery B's capacity. In the future we expect t h a t this level for pumping (Fig- ure 3) will be maintained.

Hydraulic modeling studies concerning t h e movement of the contaminant plume alone are adequate for making administrative, judicial, and public deci- sions on the control and assurance of groundwater quality and management of t h e supply station. Although the performance of t h e hydraulic barrier can be evaluated using hydraulic models, for a detailed prediction of the contaminant plume both, the advective and hydrodynamic dispersive behaviour of t h e con- taminant plume have to be considered.

In determining the performance and benefits of the hydraulic barrier, t h e following aspects a r e of special interest

(i) t h e spatial and temporal distribution of t h e contaminant plume, (ii) t h e duration of contaminant removal,

(iii) t h e rate t h a t t h e contaminant (effluent) is entering the adjacent surface waters,

(iv) t h e endangering of uncontrolled flow of contaminated groundwater removing t o the gallery or short-circuit travelling around t h e hydraulic b ~ r r i e r .

The present paper as a modeling case study deals with these problems on how t h e system operates. A further objective of this study is to investigate other remedial schemes and strategies of intercepting the contaminant plume.

Potential strategies include:

(v) t h e intermittent operation of t h e hydraulic barrier, and (vi) t h e pumping of t h e contaminated groundwater.

The model studies can be subdivided into phases:

(1) fitting the observed contamination (history matching)

(2) t h e prediction for contaminant interception and aquifer remediation.

The first phase serves a s a calibration of the transport model developed in Section 3.2. For this use, historical data in the study area a r e available. The model is tested and calibrated through a history matching procedure compar- ing model computations with t h e observed contaminant breakthrough in t h e SWS up t o its abandonment (see Figure 10). This period covers t h e years from 1

1968 through 1977. The principal parameter which had to be identified in t h e calibration process is the hydrodynamic dispersion.

The prediction phase begins in 1978, the date of starting t h e hydraulic barrier, and aims a t the simulation and evaluation of interception and remedi- ation activities. The simulation results a r e presented and hscussed in Section 3.3. In Section 3.4 some conclusions are given.

3.2. The R a n s p o r t Model

3.2.1. Hydrogeologic And Hydrochemical Description

3.2.1.1. Groundwater Flow

The study area is located in the sand formation of a primeval stream val- ley. Sand sequences at.tain relatively large thicknesses ranging between 30 and 60 rn. The sand beds a r e underlain by silt, silty sand and clay. In t h e western part lenses of boulder marl and silt are interbedded locally. The hydrogeologic exploration leads t o primary data regarding the aquifer proper- ties and t h e hydraulic regime. Concernihg a model-adequate assortment of data bases t h e present study relies on the hydrogeologic parameters estimated in previous research of t h e Institute for Water Management.

According to a hydrogeological schematization regardmg t h e aquifer thick- ness M a n d the isotropic transmissivity T the study a r e a can be primarily sub- divided into four subregions exhibited in Figure 4. The aquifer thicknesses and transmissivities specified subregionally a r e summarized in Appendix B.

For t h e porosity n a uniform value of 30% is assumed because no direct measurements were available. Assumptions regarding the storativity S(=S*) of about 0.20 and the groundwater recharge W of about 10.5 rnm/month a r e based on previous research. In t h e case of interception pumping of t h e con- taminant plume, i t is intended t o use single wells each with capacity 1000 m3/ day.

/

Subregion 1 T= 1.25 lo-' m M==35m 1 I

/

P\ f / / Subregion 2 1

'.

\ / / T=1.93.10- / \

.

M=42m 1 \ /

3.2.1.2. Contaminant Migration

At t h e end of the 1960's observation wells were drilled t o quantifyithe sub- surface contamination in the area. The t e s t wells characterizing the contarn- inant plume are indicated in Figure 5, only 12 test wells are available. To quantify the effective contaminant concentration within the plume five well samples a r e available as shown in Figure 5.

The contaminant measurements designate over t h e depth of t h e aquifer a concentration distribution varying in some cases quite drastically. The rea- sons for this are essentially unclear. According to horizontal mbdeling of the groundwater contamination problem, a depth-weighted vertical averaging of contaminant concentration is performed. The resulting concentration means for the wells a r e given in J3gure 5. From t h e available measurements t h e r e is an areal extent of the contaminant plume at 1968 as displayed in Figure 5.

The measurements carried out in the subsequent years have referred to both selected t e s t wells a n d producing wells. However, the observations a r e not systematic and the results have proved essentially to be unsuitable for characterization of the plume velocity. On the other hand, certain continuous field data have been available directly for t h e supply station wells. Here, t h e measured contaminant concentrations in the

SWS

of the gallery A exposed to the contaminant plume are of particular interest. ^I

The measured contaminant breakthroughs into the wells of SWS in t h e 1970's up to their abandonrnents a r e shown later in Figure 10 (p. 36) concern- ing maximum and year-averaged mean concentrations normalized. Obviously,

to

calibrate the mathematical model the breakthrough characteristic of

SWS

appears to be best suitable due to its complete and unambiguous description and to be essentially t h e only possibility cornpared with t h e remaining con- taminant data available. In t h e sense of a conservative fitting, the model fit- ting should be based on measured maximum contaminant values.

To model the contaminant migration t h e dispersivities

PL

and

PT

have to be estimated. According to t h e regional extent of t h e contaminant plume, for the present investigations ranging from several hundred meters up to one thousand meters, t h e longitudinal dispersivity

PL

is expected t o be i.n t h e range between 3 and 12 m (see Figure 1). However finally, t h e representative value can be primarily obtained by a n appropriate historical model adaption

- 24 -

4 = Depth-weighted mean contaminant concentration normalized by Cmf

5. Observed areal extent of the contaminant plume in 1968 regarding test wells.

as will be discussed in Section 3.3.1. The transverse dispersivity

pT

is related directly t o longitudinal dispersivity

PL.

Its magnitude is commonly much smaller than

pL

ranging between 2

< P L / p T <

20 (see Klotz 1982b). According to values reported previously for similar investigations (e.g. Sauty 1980, Segol and Pinder 1976, Klotz 1982b. Bruch Jr. 1970), t h e present study utilizes a con- stant ratio of longitudinal and transvers dispersivity as follows

In modeling t h e contaminant migration in t h e case study it was inherently assumed t h a t the pollutant discharging the pore space is widely conservative; consequently sorption and possible interaction processes may be neglected, i.e.

Furthermore, it is assumed C'

=

C"

=

0. Due to the predominance of mechani- cal dispersion effects t h e molecular diffusion is also negligible, i.e.,

Dd =

0.

The migration and hydrogeologic data used in the mathematical model are summarized in Appendix B.

3.2.2. Mathematical Formulation

3.2.2.1. Discretization of Study Area

The study a r e a

fl

is appropriately discretized using biquadratic iso- parametric element types. The finite element meshes employed for the fitting and predictive modeling are displayed in Figures 6 a n d 7. The meshes consist of 99 elements (339 node) and 100 elements (341 nodes), respectively. Inner and outer boundary contours can easily be accommodated and accurately modeled. Reasonable mesh refinements are used in areas with higher flow and/or concentration gradients to improve solution accuracy. These areas a r e particularly located in t h e plume front region (the characteristic extent of t h e contaminant lense for 1968 is designated in Figure 6) and near t h e well galleries and barrier facility.

galleries and barrier facility.

Wgure 8. Finite element idealization of study area applied to epignontic modeling (99 elements, 339 nodes).

Figure 7. Finite element idealization of study area applied to prognostic modeling (110 elements, 341 nodes).

The well galleries A and B are idealized by line sinks. For t h e wells for interception pumping of contaminated groundwater singular well elements with circular contour a r e utilized. The arrangement a n d configuration of well e l e m e n t s t o be used in the simulation a r e shown in Figure 7. Their element radius R, a m o u n t s t o 25 m.

3.2.2.2. Boundary and Initial Conditions

For i n n e r a n d o u t e r boundaries of t h e study a r e a (see Figure 4), following boundary conditions a r e formulated which a r e s u m m a r i z e d in Table 1 for t h e fitting period.

Table 1. Boundary conditions for t

>

⁰ applied t o epignostic simulation.

Boundary section of

r

i

lu a h

2

6

Y, o

2

ci

a c

5

m

0 L 4 P)

0 7

f?

0

=

₁₆

^e

w

Hydraulic head h

a b bc c d de e f fg gh

hi ijk ka

lmnopq

1 s t kind h f [ m ]

-

-

-

- -

- - -

33.0

-

-

Contaminant concentration C 1st kind

ce

[ m g / i l

0.

0.

0.

0.

0.

- -

0.

0.

0.

- 2nd kind

qh R [ m 2 / d l

- -

- -

- - -

-

0.

Q A ( ~ )

=

¹

2nd kind

Qc R

[?:I

- -

-

0 . 0 .

- - -

0.

3rd kind

h z ~ [ m ]

32.3 32.3 32.2 32.3 31.9 32.3 32.3 32.4

- -

A, [ m / d l

5.08 5.39 6.55 8.18 10.63 0.04 3.85 12.4

-

The kinds of boundary conditions correspond to the notation introduced in Section 2.3. The suitable boundary conditions for t h e prediction simulation a r e given in Table 2.

Table 2. Boundary conditions for t

>

0 applied t o prognostic simulation.

The formulation of third-kind boundary conditions for hydraulic head h along t h e bank line a 4 allows for bottom sealing effects of t h e surface waters to be include.

For t h e north boundary, a constant water table h e a d of 33m is prescribed in accordance with m o r e global flow predictions. The section ka along t h e watershed is t h e only impermeable boundary with qh

=

0. The flow boundary conditions of second kind for the gallery A and B (Tables 1 a n d 2) result from t r a n s i e n t pumping r a t e s

QA

, QB according to Figure 3. Associated with their circumference lengths L 1 , L 2 , L 3 , t h e line sinks will be prescribed as

L 1

=

1640m

LZ =

1200m L g

=

2050m

Here,

L2

identifies t h e r e d u c e d L 1 length of gallery A by t h e omissipn of SWS after 1977. The QA- a n d Qg-time relations are calculated numerically by a stepwise c o n s t a n t function approach with a one-year interval. For t h e hydraulic boundary conditions along the infiltration basin (barrier) it is m o r e realistic a n d preferred h e r e t o abandon the direct estimation of t h e infiltra- tion r a t e

QI,

a n d u s e a constant hydraulic head distribution of 33.5 m as estimated according t o field measurements.

Considering t h e values of contaminant concentration it is possible a n d necessary to u s e homogeneous boundary conditions of first and second kind as indicated in Tables 1 and 2 for t h e corresponding boundary sections. In t h e fitting period the groundwater along t h e bank line a-i c a n be considered to be essentially uncontaminated, i.e., C = 0, in comparison with t h e plume concen- tration with t h e exception of t h e region f -h near t h e c o n t a m i n a n t plume.

According to t h e initial conditions to be described below, relatively high con- t a m i n a n t concentrations r e a c h t h e surface waters. Therefore, as long as t h e r e is a groundwater inflow across t h a t boundary section a n unlimited e n t r a n c e of contaminants occurs. This is always appropriate in t h e c a s e of operating without a hydraulic barrier (fitting phase a n d i n t e r m i t t e n t opera- tion of t h e barrier), in c o n t r a s t t o t h e case with an operating barrier. This c a n be a t t a i n e d via t h e n a t u r a l boundary condition q,

=

0 by implying t h a t t h e concentration input is purely convective h e r e and t h e bouridary c o n t a m i n a n t concentration r e m a i n s a t t h e t h e initial condition. Such a conservative prob- lem description is supported by t h e observed contaminant distribution in 1968 (compare Figure 5). On t h e o t h e r hand, a (too) optimistic variant would imply C

=

^0. As a compromise a boundary conditions prescription of t h i r d kind would be necessary. However, for this t h e transfer coefficients

n;!

a r e

unknown.

f For the boundary section ijka, in any case, the specification of uncon- taminated groundwater ( C

=

⁰⁾ is reasonable. Along groundwater pumping sections (outflushing contaminants} it is appropriate t o use natural boundary conditions q,

=

0. Herewith, contaminant intrusions into t h e wells can suffi- ciently be described.

Operating with t h e hydraulic barrier, the groundwater in t h e region of the contaminant plume moves essentially in a direction towards the surface waters. The prescription of t h e 2nd-kind boundary conditions, (g,

=

0) accord- ing to Table 2, is appropriate then along the bank section e 4. Deviations can result if there is a reversal of t h e flow direction near t h e lake, which can only occur when there is a hypothetical four-fold increase in pumpage. This will be discussed further in Section 3.3.2.1., Under such conditions involving flow shearing one holds C

=

0 on t h a t boundary through which groundwater flows in. For t h e infiltration basin C

=

0 is used because detailed quality data of the infiltration water are not available.

In t h e case of interception pumping of t h e contaminant plume with one or two wells (each Qg

=

lOOOrnq the natural boundary condition for contam- inant concentration q,

=

0 is also applied to t h e singular well region. For as long as groundwater infiltrates (only for two wells as yet t o be proved below), t h e maintaining of t h e condition q,

=

0 along the bank region f g does not allow t h e remediation to be complete without contaminant effluent entering t h e surface waters (a conservative variant). Then, t h e specification of C

=

⁰

along ej'ghi is more suitable for an "optimistic" study. Both variants will be discussed in Section 3.3.2.3.

For t h e transient modeling study, corresponding initial conditions for h and C a r e necessary. Separate sensitivity tests have proved, however, t h a t the transient effect on t h e head h by t h e t e r m S a h / a t is only important over short duration transients compared with t h e relatively long times encoun- tered in transient concentration travels. Therefore, i t is appropriate and suf- ficient t o r u n t h e model with (varying) steady-flow conditions. Due t o t h e time development of pumping capacity (Figure 3) different time-stepping steady- s t a t e solutions are obtained.

The initial contaminant concentration field C in t h e study area is given for the observed contaminant distribution in 1968 as further indicated in Fig- ure 5. Due t o relatively sparse measured data t h e r e is the problem to quantify t h e contaminant concentration field and to estimate the extent of t h e plume.

4

A formal transformation of concentration contour plots (Figure 5) interpolated from measured data t o t h e finite element mesh is shown in Figure 6. For all nodal points lying within t h e interior of the contaminant plume, concentra- tion values based on a simple interpolation between the measured data according to Figure 5 a r e assigned. On the o t h e r hand, outside this region all nodes have initially C(zi,O)

=

0. Finally, one yields t h e contaminant concen- tration field shown in Figure 9a for 1968 a t t h e beginning of fitting period.

3.3. Simulation Results

3.3.1. Contamination Epignosis and Model Verification

The modeling of contaminant intrusion into gallery A especially t h e SWS, during t h e seventies serves as the model verfication period and estimation of hydrodynamic dispersion parameters. According t o t h e given boundary condi- tions, t h e finite element method computed velocity fields as, for instance, illustrated in F'igure 8 for t h e year 1968.

Here t h e average pore velocities expressed by 6;

=

iji/

M

n are displayed. The computations of t h e contaminant concentration fields based on a series of dif- ferent dispersivities. The best reproduction of t h e observed contaminant intrusion into the SWS was achieved with a longitudinal dispersivity of

PL =

4 n and a transverse dispersivity of

pT =

0.4 m . Higher dispersivities led t o a faster and more intensive contaminant breakthrough t h a n observed. The evolutionary migration of t h e contaminant plume from 1968 to 1977 is illus- t r a t e d in Figure 9 by t h e computed concentration patterns, where contam- inant iso-concentration lines a r e normalized by a reference concentration

A comparison of t h e theoretical spreading with t h e observations is attained via t h e contaminant concentration pumped from t h e SWS (mixing concentration), It represents t h e integrated average of local (point)

Figure 8. Computed velocity field for 1968 (Gi

= gi/

M n )

contaminant concentrations encompassing the

SWS

(F'igure 4) as follows

~ t h

U =

Ll

- ^L2.

The theoretical contaminant mixing water contents evaluated via equa- tion (21) are compared in Figure 10 with the measured peak values and yearly averaged values of contaminant concentration in t h e SWS. Here, the corn- puted curve is in reasonable agreement with the measured peak data: how- ever, it is clearly above t h e observed yearly averaged values. As has been shown by tests, a readjustment to match with the year-mean breakthrough behaviour cannot be obtained without essential quantitative changes regard- ing the representative contaminant distribution a t 1988 and by decreasing the