wells Water

Aquifers

CLAUDIO GALLO 1;2

AND GIANMARCOMANZINI

3;

1

CRS4,ZonaIndustrialeMa hiareddu,Uta,Cagliari{Italy

2

Dept.ofCivilEngineeringandGeos ien es,TUDelft,Delft,{ TheNetherlands

3

IAN-CNR,via Ferrata1,27100Pavia, {Italy

SUMMARY

Theadoptionofasuitablepumping-inje tingwellnetworkandthehumanenhan ementofthea tivity

ofsoilba teria,whosemetabolism ontributestodegradeandtransformmanypollutantsinnon-toxi

substan es,maybe ru ialinthepro essofremediationof ontaminatedsoils.Organi ontaminant

transport in a subsurfa e aquifer and its biologi al degradation kineti s is numeri ally addressed

by usinga four ontaminant spe ies model. A numeri al approa his proposed,that is based ona

ell- enter nite volume method for the system of adve tion-dispersion equations of ontaminants

with amixed-hybridniteelementmethodfor thesolutionof asingle-phaseDar y'sequation.The

ee tivenessofthemethodanditsa ura yinretainingthemainphysi alpropertiesofthe ontinuous

mathemati almodelisillustrated bysimulatingthetimeevolutionof ontaminant on entrationsin

asetofrealisti s enarios. Copyright 2000JohnWiley&Sons,Ltd.

key words: bioremediation, ontaminanttransport,mixedniteelements,nitevolumes

1. INTRODUCTION

Soil ontamination has re ently be ome a problem of major so ial on ern, be ausea wide

rangeofpollutantagentsofdierent hemi alnatureandtoxi itymaybepresentinsubsurfa e

aquifers.Pollutionsour esareeithera identalevents,likespillsandleaks,or ommonhuman

a tivities, like disposal of urban sewage, industrial wastes, and the use of pesti ides and

fertilizersinagri ulture,seeReferen es[24,25,22,20,9,8℄.The ontaminantsinasubsurfa e

aquiferaresubje tto omplexphysi aland hemi alpro esses,su hasdispersion,adve tion

bygroundwater ow, hemi alrea tionsandbiologi aldegradationduetosoilmi roorganisms.

Thegroundwater owisdes ribedbyasinglephaseDar y'sequation,whilethesubsurfa e

transport of dierent hemi al spe ies aremodeledby aset of oupled adve tion-dispersion-

rea tionequations[3℄.



The biologi al degradation depends on the mi roorganism population whose metabolism

is ae ted by the availability in soilsof substrates like organi arbon, ele tron a eptors {

oxygenandnitrogen{andnutrients[17, 19℄.

Theorgani arbonneededtosustainba teriallifeisnaturallypresentinsoil,whilenutrients

{su hasphosphates,nitrates,ammonia{maybeprovidedalsobyhumaninput,forinstan e

fertilizers. The ba terial population is normally stable be ause it dynami ally tends to an

equilibriumstateinwhi hitsgrowthrateisbalan edbyitsde ayrate.Whenthe on entration

ofnutrientsaugmentsduetoanexternalsupply, theba terialpopulationin reasesofseveral

orders of magnitude and tends to anew equilibrium state. The remarkable fa t is that the

ba terialmetaboli pro essesmayee tivelyredu ehazardousorgani pollutantstoharmless

byprodu ts,su hasCO

2 andH

2

O[1℄.Inthis ontext,aremediation strategy anbedevised

whi h relies on the enhan ement of the biodegradation a tivity, see Referen e [23℄ for a

literaturereviewonthistopi .Thebiodegradationkineti s modelsproposedinliteratureare

usually lassiedinthreedistin t lasses,respe tivelytermedfree-ba teria,mi ro olony-based

andbiolm models[16,11℄.

Thesimplestmodelsbelongtotherst lass[18℄.Theybasi allyassumethatba teriaexist

as individual parti les within the aqueous phaseor adsorbed by soil grains.No assumption

is made on the mi ros opi onguration and distribution of ba teria in soil pores, and on

the waythe organismsaregrouped togetheronthe solidporesurfa e.These latterfa ts are

onsideredirrelevantforthema ros opi des riptionofba terialpopulationgrowthandde ay.

In the se ond lass of models, ba teria do not exist as individual parti les but in small

dis rete olonies, or mi ro olonies, atta hed to the soilgrain surfa es.Growthand de ay of

the biomass ontained in mi ro olonies are formulated either by taking that the ba terial

olonydimension angrowby onsumptionoforgani substrateandele trona eptorsorby

assuming the olonydimension onstantand varying their on entration, i.e., thenumberof

oloniesperunit volume[21℄.

The main feature of the models in the third lass is that the solid parti les onstituting

theaquifermaterialare overedbyabiolm withinwhi h onsumptionofthesubstratesand

ele tron-a eptorstakespla e [26, 16,11℄. Thekeypro essesarethemassex hangebetween

bulk owandthebiolmandtheinternaldegradationoforgani substrates.

Amoredetaileddis ussionofthesimilaritiesanddieren esbetweenthesemodelsisbeyond

thes opeofthepresentwork.Werefertheinterestedreadertothedis ussioninReferen e[2℄{

seealsothebibliographytherein{whereitisshownthatunderasetofsimplifyingassumptions

the three approa hes redu e to an essentially equivalent des ription of the biodegradation

pro ess.This,however,istrueonlyforverysimple ases.

Our approa h relies on the four-spe ies model do umented in Referen es [21, 27℄ in the

ontextof the moregeneralmi ro olony-based on ept. The main feature of this model lies

in its apability of des ribing how the metabolism of subsurfa e mi robes an be enhan ed

by on urrent metabolization of oxygen, nitrogen and nutrients. From the omputational

viewpoint, it is a ompromise between the simpler free-ba teria model whi h tends to

overestimate the degradation extent, and the more a urate but also more omplex and

expensivebio-lmmodel.

Thenumeri alapproximationofthe ompletemathemati almodelisaresear hissue,and

manydierentaspe tsmakethenumeri alsimulationofabioremediationpro ess hallenging.

Wemention in thefollowinglist thetopi swefeelthe mostsigni antandthat we onsider

 Treatment ofhighly heterogeneoussoil:the valueof thepermeability andierforfour

ordersofmagnitudeormorein twoadja entmesh ells.

 Adve tion-dominated transport: the model spe ies on entrations in the groundwater

bulk- ow an feature strong gradient regions when sharp on entrations fronts move

throughoutthe omputationaldomain.

 Non-linear ouplingee ts,evenifthesoilisasaturatedone.Thekineti softheba terial

population depends on the ontaminants whi h diuse within the mi ro olonies from

the groundwater bulk ow. It also exerts its in uen e on the bulk- ow ontaminant

on entrationsviaasetofrea tivesour etermsinthetransportequations.

These issueshavealreadybeeninvestigatedbytheauthorsin thesepreviousworks.

In[4℄wepresentedsomepreliminaryresultsonthedis retizationofthe owandtransport

equationsbyusingmixedniteelements andnite volumes.

The ouplingof the ontaminanttransport equationswithaba terialpopulationequation

and its numeri al dis retization was investigated in [12℄.In this work the model spe ies are

passivelyadve ted by a onstant velo ity and pressure elds. In order to solve the Dar y's

equation we adopted a high-order a urate mixed nite element s heme (BDM

1

). Despite

is a ura y, this approa h is not appropriate to simulate non-linear phenomena requiring a

frequentupdateofthevelo ityandpressureelds be auseofthehigh omputational ost.

Abetterapproa hfromthisviewpointisbasedonthemixed-hybrid s hemeproposedin[13℄.

Inthisworkwevalidatedthemethodonthestandardquarter-of-ve-spotsproblem,fo using

theattentiononthetreatmentofthesoilheterogeneity.

Finally,theworkpresentedinthispaper opeswiththebioremediationofaeld-sizeaquifer

thathasbeen ontaminatedbyana identalleakout.Dierentbioremediationte hniquesand

humaninterventionstrategiesarenumeri allyinvestigatedtopredi tthe lean-uptimeforan

almost ompleteremovalofpollutants.

A ordingwith ourpreviousexperien eweproposethefollowingnumeri alapproa h.The

steady groundwaterbulk owis approximatedby using thelowest-ordermixed-hybridnite

element method. This approa h yields an approximation to the steady velo ity eld that is

more a urate than the one provided by straightforward dierentiation of the onforming

nite element approximation of the pressure eld. In parti ular, we emphasize that the

mixed-hybrid nite element method ensure lo al { i.e. ell-wise { mass onservation, while

the onformingnite elementapproximationla kslo almass onservation. The ontaminant

transportequationsareapproximatedinspa ebyanunstru turedtriangle-basednitevolume

method and advan ed in time by a semi-impli it two-stage Runge-Kutta s heme. A TVD

stability onditionisimposedbyamultidimensionallimitingpro edure.Theresultings heme

is formally se ond-order a urate, onservative, and apable of apturing strong solution

gradientfrontsmovingatthe orre tphysi alpropagationspeeds.

Thespe iesintera tionsaretakenintoa ountinthefull-spe iesmodelbysolvingiteratively

theirnon-linearintera tion oupling.

Theoutlineofthepaperfollows.InSe tion2,wereviewthemathemati almodeldes ribing

single-phasebulk ow, ontaminanttransportandba terialkineti s.Thedis retizationmethod

issummarizedinSe tion3.Weaddressherethenitevolumedis retizationofthe ontaminant

transport equations aswell asthe mixed-hybridnite element approximationofthe Dar y's

phase pressure and velo ity elds. In Se tion 4 we present the results of a set of numeri al

dierentnetworksofextra tion/inje tionwells,whoserunningmodehasbeensele tedonthe

basisoftheplumelo ationandthesoilremediationstatus.The on lusionsfollowinSe tion5.

2. THEMATHEMATICALMODEL

se :mathemati al_model

2.1. TransportEquations

Transport phenomenaare mathemati allydes ribedbyasystemof N

DS

oupled adve tion-

dispersion-rea tion equations, where N

DS

is the numberof dissolved spe ies. In divergen e

form they an bewrittenas follows

R

i

C

i

t

+div(uC

i D

i (u)rC

i )=B

i

; i=1;:::;N

DS

: (1) eq:transport

The variables C

i

in equations (1) representthe bulk ow on entrationof ea h transported

spe ies;thetermsR

i

aretheretardationfa tors,whi htakeintoa ount hemi aladsorption

pro esses, the terms D

i

(u) are the velo ity-dependent dispersion tensors. The r.h.s. sour e

terms B

i

des ribe the oupling between the spe ies on entrations transported in the bulk

owand theones within mi ro olonies.Also equations(1) aresupplementedbyappropriate

boundary onditions,su h as inlet, outlet and no- ow, and initial solution statesto spe ify

theappli ationproblems.

2.2. The Dar y's Equation

Groundwater bulk ow in an heterogeneoussaturated soil is mathemati ally formulatedby

theDar y'sequation[10℄

8

<

:

u = Krp; in

divu = f; in :

(2) eq:dar y

The pressure eld is indi ated by p and the groundwater velo ity eld by u, K(x) is the

transmissivitytensor, and f(x)asour e/sinkterm. Equations(2) are ompleted by aset of

suitableboundary onditionsofNeumann/Diri hlet-type,modelizinginlet/outletandno- ow

boundary ongurations.

2.3. The Bioremediation Model

Mi ro olony-basedmodelsassumethatba teriaresideanda twithinmi ro olonies,des ribed

as a set of pat hes atta hed to soil grains [21℄. From the bulk phase, hemi al spe ies

an rea h mi ro olonies via diusive mass ex hange. Depending on the mass-transfer

oeÆ ient, on entrations within mi ro oloniesgovernthedegradationratekineti s and an

besigni antlydierentfromthosein thebulkphase.

Inthis lassofmodels,thetermB

i

ofequation(1)isexpressedintermsofadiusivemass

ex hangefrom thebulktothemi ro olonyphase,

B

i

=N



i A

(C

i

i )

; i=1;:::;N

DS

; (3) eq:B_term

where

i

isthemass-ex hange oeÆ ientbetweenbulk owandmi ro olonies,A

isthe onta t

area of one mi ro olony for the mass diusion pro ess, Æ is the thi kness of the boundary

layerbetweenbulk owandmi ro olonies,

i

isthe on entrationof the omponentiin the

mi ro oloniesandN

isthenumberofmi ro oloniesperunit volume.

Theassumptionthat thebiodegradationpro essworksessentiallyat asteady-stateregime

yieldsthefollowingform forther.h.s.termsB

i in(3):



i A

(C

i

i )

Æ

=

0;i m

N

EA

X

k =1 Y

i;k 2

4 N

i

D S

Y

j=1

j

K

j;k +

j 3

5

I k 1

b +Q

i I

i 1

b

; i=1;:::;N

DS

; (4) eq:mi ro ol

where 

0;i

are the maximumrate oeÆ ients, m

is themass of ami ro olony, Y

i;k

are the

yield oeÆ ientswhi h a ount forthe stoi hiometryand eÆ ien y of degradation,K

j;k are

the half saturation onstants,andI k 1

b

are theinhibition fun tions [21℄. Inequation (4)the

symbol N

EA

denotes the number of ele tron a eptors and N i

DS

the number of dissolved

spe iesinvolvedinthedegradationofthei-thspe ies.ThetermQ

i

isnonzeroonlywhenthe

omponentiisanele trona eptor{forinstan e oxygenornitrate.Inthis ase,ittakesthe

form

Q

i

=

i

i

K

i +

i

; i=1;:::;N

EA

; (5)

where 

i

is theele trona eptor oeÆ ientfor themaintainan eenergyof ba teria,andK

i

istheele trona eptorsaturation onstant.

This degradation equation states that the total amount of a ompound entering a

mi ro olony in a given interval of time is equal to the amount of spe ies that is degraded

in the same interval. The rate of degradation and onsequently the on entration within

mi ro olonies,isroughlyproportionaltothe on entrationoutsidethe olonies.ThetermsQ

i

introdu e intothe model the onsumption ofoxygendue to ba terialde omposition [21, 27℄

asarstorderde ayterm.

Ba terial kineti s is modeled by the following time-dependent dierential equation that

des ribesthemi ro olonypopulationdynami s,

1

N

(N

)

t

= ND H

X

i=1 2

4



0;i NEA

X

k =1 Y

i;k 0

 N

i

D S

Y

j=1

j

K

j;k +

j 1

A 3

5

k

d

; (6) equ:ba t_growth

where k

d

is thepopulationde ay onstant,N

DH

isthe numberof dissolved hydro arbons {

organi substrates{andistheporosityofthemedium [21,27℄.

3. THENUMERICALMODEL

se :numeri al_model

3.1. The FiniteVolumeDis retizationof theTransport Equations

The numeri aldis retization in the framework of thenite volume s heme is dened onthe

samemeshT

h

()usedforthemixed-hybrids hemeofthepreviuousse tion.Theindexhisthe

maximumdiameter oftheN

T

trianglesformingthemesh, i.e.h=max

T2T

h ()

h

T

, whereh

T

isthelenghtofthelongestedgeofthetriangleT.Asusual,these triangulationsareassumed

Equations(1)arereformulatedina ell-wiseintegralformbyintegratingonea htriangular

ell T and then applying the Gauss divergen e theorem to transform the spatial divergen e

term into abalan e ofedge integral uxes. Letus introdu efor everyT 2T

h

() theve tor

U

T

,whoseelementsarethe ell-averaged on entrationsofthetransportedspe ies,

U

T j

i

= 1

jTj Z

T C

i

dT: (7)

Thesemi-dis retenitevolumeapproximationis

jTjR dU

T

dt +

X

e2(T) G

e (u

e

; e

U

T

; e

U

Te

;n

e )+

X

e2(T) H

e (u

e

; e

U

T

; e

U

Te

;n

e )

+ X

e2

0

(T) F

(b )

e

= X

q

!

T;q S

T (

e

U

T (x

T;q

)); foreveryT2T

h ();

(8) eq:FV

where the diagonalmatrixR=diag(R

1

;:::;R

N

D S

) olle tstheretardation fa tors, andfor

every ellT,

- jTjisthemeasureofitsarea,andT itsboundary;

- (T)is thesubset of itsinternal edges; these latters arethe edgesthat T shares with

an adja ent mesh ell indi ated by T

e

, so that for every e 2 (T) there exists a ell

T

e 2T

h

()su hthate=T\T

e

;

-  0

(T) is the subset of the edges of T lo ated at the boundary of the omputational

domain;thatis, foreverye2 0

(T)wehavee=T\.

The ellinterfa e uxintegralisevaluatedbyusingsuitableadve tiveanddispersivenumeri al

uxesa rosstheedgee,that are

G

e (u

e

; e

U

T

; e

U

Te

;n

e )j

i

 Z

e

n
uUj

i

dl; (9) equ:numeri al_fluxes

H

e (u

e

; e

U

T

; e

U

Te

;n

e ) 

Z

e n
Dj

i

(u)rU j

i

dl; (10)

andthenumeri al uxfun tion F (b )

e

atboundaryedges.

The numeri al ux ve torfun tions G

e andH

e

introdu ed in (9)depend on u

e

, whi h is

thevalueofthevelo ityelduatthemidpointoftheedgeesharedbythetrianglesT andT

e ,

and onn

e

, whi h isthenormalto eorientedoutwardfrom T andinwardintoT

e

.Theyalso

dependon e

U

T and

e

U

T

e

,whi harethepie ewisepolynomialrepresentationsofthesolutionin

T andT

e

.Thisfun tionaldependen eimpliestheusageofpointwisevaluesoftheapproximate

solution at quadraturenodes on e.These values arere onstru ted from the ellaveragesby

an interpolation pro edure at ea h time step and a multidimensional slope limiter must be

onsideredtotakeunder ontrolthenumeri alos illations,seetheappendixofReferen e[12℄.

Theintegraladve tivetermG

e

isdis retizedbyastandardupwind uxsplittingapproa h,

whiletheintegraldispersiontermH

e

,whi hinvolvesse ondderivativesinspa e,bya entral

dierentiationalgorithm.Furtherdetailsaboutthederivationandthea ura yofthismethod

Thenumeri al uxfun tion F (b )

e

at theboundaryedgee=T\dependsonthetra e

e

U

T j

e

of there onstru ted solution e

U

T

within theunique boundary triangleT, andin some

suitableformonasetofexternal dataU (b )

e .

Theintegralsour etermS

T (

e

U

T (x

T;q

))isapproximatedbyasurfa equadraturerulewith

nodesfx

T;q

gwithin thetriangleT andweightsf!

T;q g.

Thetime-mar hings hemeisobtainedbyapproximatingthetimederivativeofU

T

{whi h

appearsintherstterminthesemi-dis reteformulation(8){byrst-ordernitedieren es

dU

T (t)

dt 







t=t n

 U

n+1

T U

n

T

t

; (11)

where U n+1

T

and U n

T

are the ell-averaged solutions in T at times t n+1

and t n

, and
t =

t n+1

t n

. This yields a full dis rete semi-impli it s heme where resultingsymmetri linear

algebrai problem is solvedby astandardKrylovsolver,su hasa pre onditioned onjugate

gradient method. Higher (se ond) order a ura y in time is attainable by a semi-impli it

Runge-Kuttamethod, builtbytwodistin tstagesof thesameform[12℄.

3.2. The Mixed-HybridDis retization ofthe Dar y's Equation

The oupledsystemofequations(2)intheunknownspanduisdis retizedbyamixed-hybrid

nite elementapproa h. Fora detailed exposition of mixed and mixed-hybridnite element

methods we refer the readerto Referen es [5, 6℄, while for the des riptionof thenumeri al

formulationadoptedin thisworkwerefertoReferen e[12℄.

In the mixed-hybrid nite element method adopted in the present work we approximate

thevelo ityeldbyusingthelowest-orderRT

0

dis ontinuouselements,whi his omposedby

two-dimensionalfun tionswhoserestri tiontoanymeshtriangleT isoftheform

uj

T



T



x

y



+





T

T



; (12)

where thereal s alar oeÆ ients

T ,

T and

T

depend onthetriangleT.Thepressureeld

is approximatedby the triangle-basedpie ewise onstant fun tions while the pressure tra e

overea h ell-interfa ebytheedge-basedpie ewise onstantones.

With respe t to Referen e [12℄, thepresentwork diers substantially in the hoi e of the

dis rete fun tional spa eused fortheapproximationofthe velo ityeld u. Weuseherethe

lowest-orderRT

0

dis ontinuouselementsinsteadoftheBDM

1

onesofReferen e[12℄,wherea

fulllineardependen eontheposition is onsidered.Noti ealsothatthe ontinuity ondition

ofthenormal omponentofthevelo ity uxisrelaxed,andaweaker onditionisimposedby

asetofsuitableLagrangemultiplierswhi happroximatesthepressuretra es.

Weexperien edin fa t that RT

0

elementsoersasatisfa torya ura ylevelataredu ed

omputational ostwithrespe ttoBDM

1

elements,seeReferen e[13℄.Theselatteronesare

formallymorea uratebutalsosigni antlymoredemandingfroma omputationalviewpoint

be ausetheyinvolvetwi ethenumberofunknownstobestoredand al ulated.

Thisissueisparti ularlyimportantbe auseinthisworkthepressureandthevelo ityelds

are iterativelyupdatedat ea h time step,see Referen e [11℄, while in thework des ribed in

Referen e [12℄ they were al ulatedonly on e at the beginning of ea h simulation and then

3.3. Rea tionSour eTermsandMi robial Population Equation

Therea tiontermsdes ribedinequations(6)are omputedbysolvingasetofnodewisenon-

linear systems via aNewton iterative method with fra tional multistep integration s heme,

see Referen e[12℄.

4. NUMERICALEXPERIMENTS

se :experiment

In this se tion we illustrate the performan e of the proposed mathemati al and numeri al

model in predi ting the ee tiveness of a human remediation intervention to redu e the

ontaminant on entrationof a pollutedaquifer. Theaquifer is hara terized by a onstant

porosity  = 0:3 and a heterogeneous isotropi transmissivity, whose prin ipal values are

assumed to be onstant on ea h triangle of the omputational mesh, and dier triangle by

triangleintherangebetween10 5

and1m 2

/day,ina ordwithanequiprobabilitysto hasti

distribution.

The rst test ase that wepresentin this paper onsists in the initial soil ontamination

phaseand islabeledby T1.Thesoil ontaminationisdue tothe leakageofCy lo-Aromati -

Hydro arbons, CAH, whi h forms a plume transported by the groundwater ow eld and

spreadinthesaturatedaquifer.

Thenextthreetest ases,labeledbyT2,T3andT4,des ribesthreepossibleinterventions

fortheremediationphase.Basi ally,we onsideranetworkofpumpingwellsthatextra tthe

polluted water and onveyit to a treatment plant, where the ontaminant is removed. The

puriedwatermaybeenri hedinoxygenandnutrientstostimulatesoilba terialgrowthand

isthen re-inje tedin theaquiferviaanetworkofinje tion wells.Figure1sket hesthewater

treatmentpro edure.

All ofthewells anbesele tivelyusedeitherin inje tionorin extra tionmodeandareall

supposed to be onne tedvia pipelines to the watertreatment plant. Point \A" is also the

lo ationoftheleakingtankwhen ontaminationo urs.Theproperpositionand onguration

ofthewellshasbeen hosenbyinvestigatingtheir apabilityofinter eptingthe ontaminated

plumetransportedbythegroundwater owinasetofpreliminarysimulations.

These simulations are based on the four spe ies model proposed by Molz et al. [21℄ and

Widdowson et al. [27℄, and des ribed in [12℄. For the sake of ompleteness, we report the

modelinthenalappendix,givingalsothevaluesoftheparametersusedin thesimulations.

The ontaminantCAHistheorgani substrateSofthemodel,whiletheotherspe iesinvolved

arethedissolvedoxygeninthesoil,O,some ompounds hemi allybasedonnitrates,N,and

some ammonia-based ompounds whi h onstitute a generi nutrient supply A. The initial

on entrationsofthesespe iesfollowarandomdistribution,withvaluesintherangesreported

in TableI.

Figure 2depi tstheben hmark aseand theposition of thewellsonthe aquifer|labels

\A" through \M" | in the remediation phase. A onstant gradient of
p=
x = 0:04 is

superimposedonthesubsurfa ebulk oweldintheaquifer,whi histhusorientedalongthe

TableI.Mi ro olony on entrationranges(ing=m 3

)atthebeginningofthesimulation(t=0).

tab:initial_values

S

(t=0)

O

(t=0)

N

=

A (t=0)

(g/m 3

) (g/m 3

) (g/m

3

)

[0:1;1℄ [0:1;1℄ 1000

TableII.Simulationrunparameters

tab:simulation_parameters

RunLabel

Parameter

T1 T2 T3 T4

t(days) 0.5 0.2 0.05 0.05

T

max

(days) 410 2800 500 700

wells Water

Treatment

Water Enricher O 2

Recycled water Contaminated

water

Nutrients waste

Contaminant

From pumping wells

To injection

Figure 1.Te hni al s hemeofthe remediationplant installedasideofthe wellnetworkfor polluted

watertreatmentand leanwaterenri hment.

fig:plant

ondition,withanhydrauli pressureheadgivenasafun tion ofx.Forea h simulationrun,

wereportin TableII thetimestep
tandthenal timeT

max

atwhi hthesimulationends

up.

During the initial pollution phase (T1), the plume of CAH spreads with an irregular,

or \ngered", front be ause of the sto hasti soil heterogeneity whi h establishes several

preferentialpaths. Figure 3 illustrates the situation at the intermediate time t = 410 days,

River

B

C

D

E G

H I F L

M A

Groundwater flow

Figure2.Planarsket hofthewelllo ations.

fig:wells

of the onning river.A steadystate solutionisrea hed at t=600days,shownin gure 3,

when the ontaminantplume doesnot spreadfurther and thetransport of the ontaminant

alongsomepreferentialpathsisthusestablished.

Three dierent possible interventionstrategies havebeen investigated. Remediation starts

after t = 410 days sin e the pollution started, that is before the ontaminant rea hes the

river onningwiththeaquifer.Wesupposethat the ontaminantsour eisremovedandthe

lean-up of the soilis performedby using anetwork of extra tion/inje tionwells. Forall of

thesimulationswewillshowthespatialdistributionoftheorgani substrate,CAH,andofthe

dissolvedoxygen,DO{thespe iesOin ourfourspe iesmodel.

InthesimulationT2we onsidertheso- alledpump-and-treatmethod.ThewellsGthrough

M of the pipeline network are a tive and extra t the ontaminated water, whi h is then

onveyedtowatertreatmentplants.

The owboundary onditionsare thesameasforthe soil ontamination phase,ex ept at

the lo ation orrespondingto the pumping wells: here,ade rease of 0.5 m in pressurehead

withrespe ttothenaturalgradient onditionisimposedinorder tomodifythe owpattern

for ontaminant re overy. As in the soil ontamination phase, just one hemi al spe ies is

onsidered inthesimulation,bynegle tingtheee tsoftheotherspe ies.

The resultof the simulation is shown in gure 5at the intermediate time t =1490 days,

that is about4yearsafter theremovalof the ontaminantsour e. Heterogeneitystill ae ts

The omputersimulationisterminated att=2500days{about7years.Itisworthnoti ing

that theremovaloftheorgani ontaminantplumehasnotyet beenfully ompleted.

The bioremediation interventions onsidered in this paper{ simulationsT3 and T4{are

essentiallybasedon thestimulation ofthe growthof thesubsurfa e ba terialpopulationby

in reasing the on entrationofoxygenand nutrientsdissolvedin soil. Weassumethat these

hemi al substan es be dire tly supplied via inje tion of \enri hed water" into the aquifer.

Part of the wells are, thus, used for extra ting the ontaminated water to be onveyed to

treatmentplants.Partoralloftheremainingwellsareusedforre-inje tingwaterwith hemi al

additivesinto thesoil. Theee tiveness of thisstrategy stronglydependson theextra tion-

inje tionoperationalmode hosenin thewell ongurationpattern, whi hisdierentforthe

twosimulationsT3andT4.

Inthe ongurationofthesimulationT3thewellsA throughD work ininje tion mode {

anoverpressureof0:5misimposed.Nutrientsandnitratesaredeliveredinex ess,sin etheir

solubility in water is mu h largerthan the one of oxygen. This latter hemi al is kept at a

onstant on entrationof20mg/l.Theremainingwellsworkinextra tionmode,atthesame

pressure onditionofthe\pump-and-treat"method.

The result of this simulation is shown at the intermediate time t = 178 days after the

removalofthe ontaminantstarted.Nosigni antimprovementsin ontaminantsremovalare

a hievedfromthis ongurationof pumpingandinje tingwellsaftert=360days.A \dead-

zone"developsin thetriangularregiondened bythewells\F-G-H",allworkinginpumping

onditions.Itisevidentby omparinggures8and6thedieren einthe ontaminantremoval

betweenthe urrentsimulationandthepre edingone,parti ularlywheredissolvedoxygenhas

beendelivered.

Inthe ongurationofthesimulationT4wellsGthroughMstillworkin extra tionmode,

wellsEandFinje tnutrientsandoxygen,whilewellsAthroughDaredismissed.gure9shows

the ontaminant and dissolved oxygen distributions at the intermediate time t = 600 days.

Weremarkthatthemajorpartoftheresidual ontaminantmassintheaquiferisremoved.A

ompleteremovalofthe ontaminantisa hievedatthenaltimet=875days,asillustrated

byFigure9.

Finally, gure 11 reports the residual ontaminant mass in the aquifer as a de reasing

fun tion oftimeandsummarizestheperforman eofthedierentremediationapproa hesT2,

T3andT4.Thisgureemphasizeshowthebioremediationstrategy anbemoreee tivethan

thesimplepump-and-treatmethod.AlthoughbothinterventionstrategiesT2andT4a hieves

analmost ompleteremovalofthe ontaminant,theremediationtime isverydierentinthe

two ases.Nevertheless,bioremediation analsobesensitivetothewell ongurationnetwork

hosenfortheintervention,asshownbytheperforman e urveT3.

4.1. ModelPerforman es

Inthisse tionwereportsomeinformationaboutthe ostsintermofCPUtimeofthe omputer

simulations.

All the simulations des ribed in the previous se tion were run on a omputational mesh

omposed of about 5000 triangles using an IBM RISC 6000/390 ma hine. The simulations

involvingthefullfour-spe iesmodelareveryexpensiveandtakeabout12hours,whilesingle-

Table 2:CPU Costs(minutes)

RunLabel

Parameter

T1 T2 T3 T4

CPU 80 90 720 720

The CPU ost is quite high in the former ase be ause all of the non-linear intera tions

among the dierent spe ies must be taken into a ount. A 44 non-linear systems must

be solved for ea h ell at ea h time step, by using a Newton iterative s heme, whi h takes

approximately40% of the total CPU osts. Moreover,the nite volume method requires a

limitedpie ewise-linearre onstru tionofea hunknowneld toensure2 nd

-order a ura yin

spa e.Thelimitingpro edureisneededtoensuremonotoni ityofre onstru tedgradientsand

to preservenon-linear stability,see Referen e [12℄ fordetails.The omputational ost ofthe

re onstru tion pro edure is also signi ant, being about35% of the total CPU osts of the

simulation.Thisin rementisevidentwhenthefullspe iesmodelis onsideredinsteadofthe

single-spe iesone.

CPU ostsare alsoin uen edbythewaythesimulationisrun.Forinstan e,in theinitial

pollutantphaseT1,the ontaminantistransportedbyasteadygroundwater oweld,whi h

is omputedonlyon e at thebeginningof therun.Instead,thesimulationT2stills involves

a single-spe ies model, but makes usage of a transient groundwater velo ity eld, whi h is

updatedevery50transport steps,thusresultinginamoreexpensive omputation.

5. CONCLUSIONS

In this work we illustrated a numeri al model to investigate the bioremediation pro ess

in heterogeneous saturated aquifers and its appli ations in devising dierent intervention

strategiesonaeld-sizes enarios.Themethodisparti ularlysuitableindete tingdead-zones

due to theheterogeneityof themedium anddependentonthe welllo ationand operational

mode.

Ourapproa hisbasedonthedis retizationofamultispe iestransportmodel oupledwitha

ba terialdegradationkineti sofMonodtype.Themi ro olonydes riptionofba teriala tivity

is onsidered.Thebulk owvelo ityisapproximatedbyamixed-hybridniteelementmethod

whilethespe iestransportequationsaredis retizedbyusingasemi-impli it ell- enternite

volumes heme.

The performan e of the method are assessed by studying the ontamination pro ess and

severalremediationstrategiesonarealisti subsurfa es enario.

A omparison of the numeri al experiments reported in this work learly illustrates the

advantageofa ombinedbiologi al-hydrauli interventionwithrespe ttothesimplehydrauli

oneinthe aseofasto hasti allyheterogeneoussoil.Theremediationtimeintheformer ase

is shown to be about half the oneof the latter ase. This fa t implies that the operational

ostsmaybesubstantiallyredu ed.

When theaquifer is stronglyheterogeneous, preferential owzones mayappear and large

quantities of ontaminant may remain isolated if the simplest pump-and-treat remediation

presentwhen remediation is enhan ed byba terial a tivity. In su h a ase, an optimal well

ongurationhasadramati impa tontheee tivenessofthehumanintervention.Forthese

reasons,itis evidentthat abetterunderstandingofhowandwheretrappingzonesappearis

riti alin devisinganee tiveremediationstrategy.

Inorder tostudy thenear-sour e ontamination zone,that isthethezone surroundingan

organi ontaminantspill,amultiphasemodelisneeded,be auseanorgani phaseappears.It

is informativeto saythatsomepreliminarywork[14, 11℄hasbeenperformedbytheauthors

todevelopasuitablenumeri alapproa htomultiphasesimulationsaswellas onsideringthe

problem of pore- loggingin biolm models. However,these topi swill betheissue of future

work.

ACKNOWLEDGEMENT

The work of Claudio Gallo has been nan ially supported by Sardinian Regional Authorities.

The authors would like to thank Dr. Fabio Bettio for his help in visualization and

Dr. Enri o Bertolazzi (University of Trento, Italy) for his areful reading of the preliminary

version of the paper and his useful suggestions. The unstru tured Delaunay grids were

generated by the mesh generator Triangle, a ode implemented by Shew hu k, see the

URL:http://almond.srv. s. mu.edu /afs / s/ proje t/q uake/ publ i /w ww/tr iang le.ht ml.

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Figure3.Contaminationphase(T1):pollutant on entrationatt=410days

s enario1a

Figure4.Contaminationphase(T1):pollutant on entrationatt=600days|steadystate s enario1b

Figure5.Pump-and-treatremediation(T2): on entrationatt=1450 days PAT1a

Figure6.Pump-and-treatremediation(T2): on entrationatt=2500 days PAT1b

Figure7.Bioremediationby1 st

well onguration(T3): on entrationatt=178days bio1a

Figure8.Bioremediationby1 st

well onguration(T3): on entrationatt=360days bio1b

Figure9.Bioremediationby2 nd

well onguration(T4): on entrationatt=600days(200daysafter

theswit h)

bio2a

Figure 10. Bioremediationby2 nd

well onguration (T4): on entration at t=875days (475days

aftertheswit h)

bio2b

Figure11. Contaminantresidualmassremovalvsremediationtime. ompeff

APPENDIX

Thekineti degradationratesof on entrationswithinmi ro oloniesin(3)forthefourspe iesmodel

usedinallofthesimulationsare

SA (C

S

S )

Æ

= m YS;O0;O



S

K

S;O +

S



O

K

O +

O



A

K

A;O +

A



+ m

Y

S;N



0;N



S

K

S;N +

S



N

K

N +

N



A

K

A;N +

A



I 1

b

(13) S_ olony



O A

(CO O)

Æ

= m

Y

O



0;O



S

KS;O+ S



O

KO+ O



A

KA;O+ A



+ Okd;O



O

K

O 0+ O



; (14) O_ olony

NA (C

N

N )

Æ

= m YN0;N



S

K

S;N +

S



N

K

N +

N



A

K

A;N +

A



I 1

b

;

+ 

N k

d;N



N

K

N 0+

N



I 1

b

; (15) N_ olony

AA

(CA A)

Æ

= m YA;O0;O



S

KS;O+ S



O

KO+ O



A

KA;O+ A



;

+ m YA;N0;N



S

KS;N+ S



N

KN+ N



A

KA;N + A



I 1

b

; (16) A_ olony

andthemi robialgrowth/de ayequationis

1

N

N

t

=



0;O



S

KS;O+ S



O

KO+ O



A

KA;O+ A



kd;O



+



0;N



S

K

S;N +

S



N

K

N +

N



A

K

A;N +

A



k

d;N



I 1

b

(17) eq:ba t_growth

where

- 

S

=1:0310 5

[m 2

/day℄,

O

=2:1910 5

[m 2

/day℄,

N

=1:5010 5

[m 2

/day℄,

A

=1:8610 5

[m 2

/day℄ are the mass ex hange oeÆ ients for the bulk ow and the mi ro olony spe ies

on entrations;

- A =3:76810 10

[m 2

℄,isthe onta tareaofthemi ro olonyforthemassdiusionpro ess;

- Æ=5:010 4

[m℄isthethi knessoftheboundarylayerbetweenbulk owandmi ro olonies;

- m =2:8610 11

isthemi ro olonymass;

- 0;O=4:34[1/day℄and0;N =2:9[1/day℄arethespe i aerobi andanaerobi growthrates;

- YS;O=0:278andYS;N =0:5aretheheterotrophi yield oeÆ ients;

- YO =0:278 [{℄ and YN =0:5 [{℄ are the oeÆ ients for theoxygenand nitrogensynthesisof

heterotrophi biomass;

- 0=0:0402[{℄ andN =0:1[{℄ aretheoxygenandnitrogenuse- oeÆ ientsformaintenan e

energyofba teria;

- YA;O =0:122 andYA;N =0:122 are the ammonia-nitrogen oeÆ ients for produ ingbiomass

underaerobi andanaerobi onditions;

- K

S;O

=40 [g/m 3

℄,K

O

= 0:77 [g/m 3

℄, and K

A;O

= 1[g/m 3

℄are the substrate, oxygen, and

ammonia-nitrogensaturation onstantsunderaerobi onditions;

- K

S;N

=40 [g/m 3

℄,K

N

=2:6 [g/m 3

℄,andK

A;N

=1[g/m 3

℄are the substrate,nitrogen, and

ammonia-nitrogensaturation onstantsunderanaerobi onditions;

- K

O

0 =0:77 [g/m 3

℄andK

N

0=2:6[g/m 3

℄aretheoxygenandnitrogensaturation onstants;

- I 0

b

=1and I 1

b

=K

b;N

=(K

b;N +

O

) are theinhibition fun tionsof the oxygen-basedand the

nitrogen-basedrespiration,andK =0:0001[g/m 3

℄istheinhibition oeÆ ient;

- k

d;O

= 0:02 [1/day℄ and k

d;N

= 0:02 [1/day℄ are the ba terial death-per-unit-time de ay

onstantsforaerobi andanaerobi metabolism.