A�software�to�interpret�tracer�testsin�porous�medium

TRAC�Project

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GUTIERREZ�Alexis1,�KLINKA�Thomas1,THIERY�Dominique1

Water Division

Tracer�6�Conference Oslo�6�8�June 2011International�Conference�on�Tracers�and�Tracing�Methods

1BRGM - Water Division3 avenue C. Guillemin BP 3600945060 Orléans Cedex 2 France

Plan�of�the�presentation

> Uses�of�tracer�tests�in�hydrogeology• Applications• Tracers

> Motivations�to�develop TRAC

> Example of�application• Interpretation

> TRAC�features

> Conclusion

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Uses�of�tracer�tests�in�hydrogeology

> Qualitative�:�existence�of�hydraulic connection between twopoints?

> First�known scientific tracer�test�in�hydrogeology in�1887(Immendingen,�Danube�<�>�Ach spring)

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Injection�of�fluorescent�tracers in�skinholes

Uses�of�tracer�tests�in�hydrogeology

> Quantitative�:�characterize the�transport�properties of�the�aquifer,�i.e.�:�kinematic porosity (�c),�dispersivity (�),�filtration�velocity (u)

> Possibility to�take into account of�others process :• Adsorption�:����������������������������(linear equilibrium adsorption)

• Degradation :

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L T VC C C C Cu D D Dt x x x y y z z

� �� � � � � � � �� � � �� � � � �� � � � � � � �� � �

L LD u�� T TD u�� V VD u��D

c c

V Kiu� �

� �

� � � �0 expM t M t�� � ; 1 2ln 2t�

�

1 dKR ��

�

Applications> The�interpretation�of�the�restitution�curve�is�very�instructive�on�the�potential�

transfer�of�contaminants�and�in�the�description�of�hydrodispersive�parameters> To�improve�management�and�protection�of�groundwater�resources

> Groundwater :• Delineation of�the�catchment;• Study�of�the�respective�contributions�of�different�waters

> Areas�of�groundwater protection�:• Study�of�transit�time�/�protection�zone• 50�days�transit�time

> Determine the�transport�parameters ofthe�aquifer�for�discretized�modeling

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Tracers

> To�track�the�movement�of�water�molecules,�one�must�choose�a�tracer�that�is�(ideally):• chemically�stable�and�inert�to�mineral�constituent�rocks�of�the�aquifer,�so�that�

the�tracer�is�not�disturbed�sorption�reactions;• still�detectable�in�very�high�dilution,�its�movement�can�be�tracked�over�long�

distances;• nontoxic�to�humans�and�the�environment;

> The�type�of�tracer�used�depends�on:• objectives�tracing• constraints�of�the�tracing�(water�chemistry,�etc.).• means�(technical�and�financial)�available�(sampling,�analysis,�...)

> The�artificial�tracers�commonly�used�are�water�soluble�tracers

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Tracer�comparison

> Source�:�Utilisation�des�traceurs�artificiels�en�hydrogéologie�– SSH,�2002

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Motivations�to�develop a�tool

> Lack of�simple�tool

> CATTI�software�(Sauty,�Kinzelbach,�1991)

> A�tool that helps the�interpretation and�design�of�tracer�tests

> Based�on�the�use�of�analytical�solutions�(no�spatial�discretization)�:• Homogeneous�aquifer;• Infinite�in�terms�of�extension;• Dimensions�of�flow�(1D,�2D,�3D,�radial);• Monolayer;• Uniform�flow�(not�for�radial).

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Analytical solutions

> TRAC�offers�a�panel�of�12�analytical�solutions• Compared with numerical�models, analytical�models are generally

useful at�a�first�stage of a project�when�information regarding�the complexity of�the�environment is�not�known

• Advantage of numerical�models is�their�ability to take into account this�complexity, including heterogeneity of�the geology or the�boundary�conditions

• Analytical�solutions�assume that the geometry�of�simulated�domain is relatively simple. Despite their�limitations,�analytical�modelscan be very useful for simplified analysis and are therefore widely�usedin�practice.

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A�set�of�analytical solutions

> Analytical�solutions�of�advective�dispersive�solute�transport�equation�(ADE)�are�useful�in�predicting�the�fate�of�solutes�in�groundwater

> Actual available methods :• 1D,�2D,�radial�converging/diverging flow;• Instantaneous (Dirac),�continuous,�step�injection;• Delay�factor�(in�development);• Degradation constant�(exponential form);• Variable�direction�of�the�groundwater flow.

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Applications

> Hypothesis of�uniform flow�is valid :• In�laboratory,�for�soil�column experiments (Q�constant,�u�constant)• On�the�field,�for�tracer�tests�under natural conditions�in�an�homogenous and�

isotrope�aquifer

> Forced flow�:�radial�convergent

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Observation pointInjection point

Observation pointInjection point

TRAC�– Session�sample

> Two modes�:�« simulate and�design »�/�« interpret tracer�test »

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Tracer�test�configuration

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Parameterization

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International System of Units are used in TRAC, you can still add units from other systems : feet, inch, gallon …

Theorical breakthrough

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Optimal�mass�to�inject

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Sampling frequency

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Interpretation mode

> Fill the�description�of�tracer�test�and�the�technical informations> Import�your field/lab data�:�concentration,�time,�flow> Select�an�adequate solution> Adjust the�parameters by�trial�and�errors

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Soil column tracer�test

> Filled with differents materials (glass�ball,�small gravel)> Fixed flow> Injection�of�fluoresceine in�the�middle�with a�needle> Measure of�concentration�with fluorimeter

> Tracer�tests�with :• Variable�height of�column• Variable�diameter of�column• Differents flows• Differents concentrations�of�tracer

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Q

Injection (M0)

sampling& analyse

x

d

Context informations

> Description�of�the�tracer�test> Technical informations> Opening an�existing project

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Import�data

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Selection of�an�adequate solution

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Parameterization

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Optimization process

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Estimation�of�transport�parameters

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Estimation�of�transport�parameters

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small gravel

medium gravel

0.00

0.20

0.40

0.60

0.80

1.00

0.00 0.50 1.00 1.50 2.00 2.50

Dia

mèt

re m

oyen

du

mat

éria

u (c

m)

Dispersivité (cm)

Relation dispersivité/diamètre moyen

Ø=f(�)

Linéaire (Ø=f(�))

mix of small and medium gravel glass ball

Field�scale

> Pollution�of�drinkable water�supplyby�two industrials sites�(chloronitobenzen)

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Features – Radial�converging/diverging flow

> Tracer�experiments�on�groundwater�radial�flow�provide�an�economical�method�of�determining�transport�parameters

> The�interpretation�of�the�breakthrough�curves�gives�rise�to�some�difficulties�since�there�is�no�exact�analytical�solution�that�can�easily�be�used�for�transport�in�radial�flow

> Development�of�an�accurate�semi�analytical�solution�(D.�Thiéry,�to�be�published)• Maximize�the�recovery�of�tracer;• Accelerate�the�experimental�procedure�(higher�velocity);

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Features – Step�injection

> The�hypothesis�of an instantaneous�injection is valid when�the�injection�period is negligible�compared�with�that of�the average�transit�time.

> Use�of�superposition�principle�for�continuous�injection

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For t < Ti : � � � �tCtC c�

For t � Ti : � � � � � �c c iC t C t C t T� � �

time

Cinj

C0

Ti0

-C0

Features – Step�injection> Example to�take into account of�injection�length

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time

Cinj

C1

C2

C3

C4

t1 t2 t3 t40

For t < t1 : C(t) = Cc(C1,t)For t1 � t < t2 : C(t) = Cc(C1,t) � Cc(C1,t-t1) + Cc(C2,t-t1)

For t2 � t < t3 : C(t) = Cc(C1,t) � Cc(C1,t-t1) + Cc(C2,t-t1) � Cc(C2,t-t2) + Cc(C3,t-t2)

And so on …

Features – Add your own analytical solution

> Tracer�testing methods continue�to�evolve> New�interpretation methods are�being developped

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20 ( )( , ) exp exp( )

44 LL

M x utC x t tD tA D t

�� �

� ��� � �� �

� �

Crank, 1956 – Bear 1972, modified

Injection of mass in an infinite medium

Translation of formula in TRAC : M_0/(A*omega*2*sqrt(Pi*D_L*t))*exp(-pow(x-u*t,2)/(4*D_L*t))*exp(-lambda*t)

Features – Basic�calculations

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� �

� �

� �

� �0

0

n échantillonsmoy

n échantillons

t c t dt t c t tT

c t tc t dt

�

�

� �� ��� �� �

� ���� �

����

Mass recovered (at constant rate) :

� � � �0

Rn échantillons

m Q c t dt c t t�

� �� � ��� ���

For an ideal tracer : Vmoy = u

Conclusion

> Now :• Simple�tool• Versatile• Free�(first�beta�version�released in�January 2011)• Available in�french,�spanish and�english

> Future�:• Expecting the�community of�users to�suggest analytical solutions�/�needs

– Push�pull�solution– Dual�porosity solution– First�order chemical reactions

> To�be published :• Validation�report• User�manual /�tutorial• Semi�analytical solution�radial�converging flow

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Acknowledgements

> Our�partners :

> J.�Bodin�(HydrASA,�university of�Poitiers)�for�illustrations

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Thank you

Qualitative�tracer�test�in�La�Touvre,�France,�30�09�2008

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