Tunnelling and Underground Space Technology 42 (2014) 122–135

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Tunnelling and Underground Space Technology

journal homepage: www.elsevier .com/ locate / tust

A simulator for modeling of porosity and permeability changes in nearfield sedimentary host rocks for nuclear waste under climate changeinfluences

http://dx.doi.org/10.1016/j.tust.2014.02.0100886-7798/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Address: Department of Civil Engineering, University ofOttawa, 161 Colonel by, Ottawa, Ontario K1N 6N5, Canada. Tel.: +1 613 562 5800/6558; fax: +1 613 562 5173.

E-mail address: mfall@uottawa.ca (M. Fall).

Othman Nasir, Mamadou Fall ⇑, Erman EvginCivil Engineering Department, University of Ottawa, Ottawa, Ontario, Canada

a r t i c l e i n f o

Article history:Received 29 January 2013Received in revised form 7 January 2014Accepted 13 February 2014

Keywords:Deep geological repositoryNuclear wastesCoupled processesTHMCSimulator

a b s t r a c t

A new simulation tool is developed to model coupled thermo-hydro-mechanical-geochemical(THM-GeoC) processes that would occur in the near field of deep geological repositories (DGRs) fornuclear wastes, and their impacts on the evolution of the rock porosity and permeability. First, a coupledthermo-hydro-mechanical-chemical (THMC) model, in which, the chemical (C) process is limited tosolute transport, is developed and then implemented into COMSOL Multiphysics finite element code.Then, two types of numerical software are coupled; the first is COMSOL Multiphysics code and the secondis the PHREEQC geochemical code. The coupling of the two types of software is performed by developinga special code that has been written by using MATLAB. COMSOL Multiphysics is used to solve the coupledTHMC processes (the C process is limited to solute transport) and PHREEQC is used to solve the geochem-ical reactions resultant of the transport of chemical species. Simulation results obtained by using theTHM-GeoC simulator are compared with experimental data and data from modeling reactive transport,with good agreement in the results. The developed simulator is applied to investigate the coupled effectof climate changes and water enriched with carbon dioxide gas, which would be generated from low andintermediate nuclear wastes, on the dissolution of the limestone host rock in Ontario (Canada) for nuclearwastes, and porosity and permeability changes within the near field rock. The results show that the max-imum change in porosity is approximately 3.5%, with a gradual decrease to approximately zero. The zoneaffected by the dissolution process is mainly located on the first 10 m within the host rock and does notcause a significant increase in permeability. From safety and environmental assessment perspectives, theimpact of dissolution is not significant. However, parametric studies and experimental investigationsneed to be implemented to support the predicted results.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Deep geological repositories (DGRs) that are used for the longterm containment and isolation of nuclear wastes are consideredas one of the most preferred technologies for the long term man-agement of nuclear waste by preventing the transport of radionu-clide into the biosphere. The main concept of the DGR system isthat there are multiple natural geological and engineered barriersystems against radioactive transport into the biosphere for longlife spans which are hundreds of thousands of years. Sedimentaryrock formations as a natural geological host are currently proposedin several countries (e.g., Canada, France, and Switzerland). In

Canada, a repository for low and intermediate levels radioactivewastes (LILWs) is being proposed by Ontario Power Generation(OPG) in limestone sedimentary rock formations in Ontario (Intera,2011).

LILWs disposed in DGRs contain a wide range of chemicalinventories (Quintessa and Geofirma, 2011). The long term degra-dation, reactions and mixing of LILWs with ground waters withinrepositories will lead to changes in the ground water chemistryand the generation of gases (e.g. carbon dioxide (CO2), methane(CH4), hydrogen (H2), Geofirma and Quintessa, 2011; Fall andNasir, 2011). The geochemical characteristics of ground water playan important role in the process of dissolution or precipitationwithin the pores of carbonate rocks, such as limestone (Engesgaardand Kipp, 1992; Rezaei et al., 2005). The process of precipitationand dissolution has an important role on the long term evolutionof a DGR system with a natural barrier of limestone formation.

Nomenclature

T average temperature of the porous mediumCeq effective volumetric heat capacityKeq effective thermal conductivityCL volumetric heat capacity of the moving fluidu fluid velocity vectorqf fluid densityt timen porositys solidf fluidj permeabilityg dynamic viscosityp pressureD direction of gravitational acceleration (g)eff volumetric deformationKD, KS and Kf bulk moduli of solid matrix, solid grains and water

fluid, respectively

b, bs and bf thermal expansion coefficients for the solid matrix,solid grains and water fluid, respectively

a0 ða�nÞð1�nÞ

r stress tensoreff volumetric deformationC concentration of total dissolved solids (TDS)ui, uj x and y direction displacementsDL hydrodynamic dispersion tensorSc solute source or sinkG shear modulusk Lamé constantci activity coefficientzi ionic charge of the aqueous speciesao

i ion-size parameterSICalcite saturation index of calcite

O. Nasir et al. / Tunnelling and Underground Space Technology 42 (2014) 122–135 123

Porosity and permeability are the key material parameters thatcontrol the (fluid, solute) transport processes in porous media. Theevaluation of such changes is essential for any long term safetyassessments related to DGR systems. The changes in permeabilityand porosity are directly affected by many processes, such asmineral phase dissolution/precipitation, or indirectly, such as thecoupling impact of temperature to the rate of dissolution or precip-itation. Predictions of the long term changes in porosity and per-meability require the implementation of all relevant coupledprocesses, such as temperature, flow of water, fluid–waste orfluid–rock geochemical reactions, and mechanical stress anddeformation. The investigation of such phenomena requires thedevelopment of a mathematical model and numerical tool thatare able to capture and describe all relevant coupled thermo-hy-dro-mechanical-geochemical processes (Zheng and Samper,2008; Taron et al., 2009; Zheng et al., 2010) that occur in the hostrock of DGRs.

In general, numerous contributions have been made in the pastyears to develop single codes that deal with problems related tocoupled processes in porous media or geo-systems. Furthermore,in recent years, there has been a steadily growing interest incoupling two or more codes (Jacques and Šimunek, 2005; Taronet al., 2009; Wissmeier and Barry, 2011; Li and Fall, 2013a) to solveand model coupled processes in geo-systems because of the manyadvantages of this approach (coupled code) over the developmentof a single coupled computer code as described by (Jacques andŠimunek, 2005; Taron et al., 2009; Wissmeier and Barry, 2011).Table 1 shows a list of common single and coupled codes that havebeen frequently used in the modeling of coupled processes orreactive transport in geo-systems. The mentioned works of re-search have significantly contributed to the understanding andthe analysis of coupled processes or reactive transport modelingin geo-systems. However, most of the single or coupled computercodes described in Table 1 or developed during the past years can-not solve and describe all relevant coupled THMC processes thatoccur in the near field of DGRs for nuclear wastes. For example,many single (e.g., Zheng and Wang, 1998; Cheng and Yeh, 1998;Parkhurst and Appelo, 1999; Mayer, 2000; Xu et al., 2006) orcoupled (e.g., Jacques and Šimunek, 2005, Rutqvist and Tsang,2003; Wissmeier and Barry, 2011) codes can only solve some ofthe coupled processes (e.g., HM, THC, THM) or THMC processesin an uncoupled or partially coupled way (e.g., HM, TH, THM,THC). Very few codes consider THMC coupled processes. For

example, TOUGHREACT-FLAC3D (Taron et al., 2009) is one of thecontributions that have investigated THMC coupled processes inporous media. TOUGHREACT-FLAC3D deals with the mechanicalbehaviour by a set of built-in geomechanical modules which areapplicable to a wide range of geotechnical properties. On the otherhand, the geochemical behaviour is solved by using a set of equa-tions and data base files.

The objective of this paper is to develop a new coupled codethat describes and assesses the THMC processes in the near fieldof DGRs and their impacts on the evolution of the rock porosityand permeability. In the current study, (COMSOL Multiphysicscode Comsol, 2009) is used to solve the developed governing THMCpartial differential equations (PDEs), and PHREEQC is used to solvegeochemical reactions. In this developed approach, the geome-chanical component of the code is fully coupled with the thermal,hydraulic and solute transport phenomena or processes. This re-sults in the shortening of the execution times, thus improving com-putational efficiency (compared to linked codes where M is notfully coupled to TH), especially, when the geomechanics are notloosely coupled. The COMSOL–MATLAB interface facilitates usersin accessing and interacting with the governing equations, non-lin-earity of material properties, solutions at different time steps andso many other options. The mentioned options make it possibleto include more physics and processes in conceptual modeling.Moreover, this allows the easy implementation of future advancesin constitutive relationships. In addition to that, the use of a wellestablished geochemical code such as PHREEQC gives additionalconfidence to the developed model.

2. Simulator structure and coupling procedure

In this work, five coupled processes: thermal and mechanicalprocesses, saturated flow, solute transport and chemical reactionsare solved. The numerical modeling follows a two-step solutionconcept. First, a numerical model is developed to simulate the cou-pled THMC processes, in which the C represents the solute trans-port processes without chemical reactions. The second step is thegeochemical reaction that takes place as a result of dynamicchanges in the concentration resultant of solute transport as wellas due to fluid–rock interaction reactions. The THMC model thatis related to the first step is numerically solved by using COMSOLMultiphysics finite element (FE) code (Comsol, 2009) and the

Table 1Examples of codes and software that deal with coupled processes.

Name of the code Reference number Physical and chemical processes included in the code

Flow Heat transfer Mechanical processes Solute transport Chemical reaction

HP1 HYDRUS1D-PHREEQC Jacques and Šimunek (2005) U U U

MIN3P Mayer (2000) U U U

MT3DMS Zheng and Wang (1998) U U

PHREEQC Parkhurst and Appelo (1999) U U U

TOUGH-FLAC Rutqvist and Tsang (2003) U U U

TOUGHREACT Xu et al. (2006) U U U U

3DHYDROGEOCHEM Cheng and Yeh (1998) U U U U

COMSOL – IPHREEQC Wissmeier and Barry (2011) U U

FLAC3D-TOUGHREACT Taron et al. (2009) U U U U U

PROPOSED WORK COMSOL-PHREEQC U U U U U

124 O. Nasir et al. / Tunnelling and Underground Space Technology 42 (2014) 122–135

second step is solved by using a geochemical code (PHREEQC)(Parkhurst and Appelo, 1999). The two step approach which usesa sequential non-iterative approach (SNIA) (Xu et al., 1999;Wissmeier and Barry, 2011) is adopted in this work by using anew simulator code written in MATLAB to couple the developedTHMC model with PHREEQC. The developed simulator includesthree main sub-routines: (1) the generation of geometry, FE mesh,and initial and boundary conditions (BCs); (2) a COMSOL-THMCsolution by using the time iteration loop of Dt until the totalrequired solution time is reached; and (3) PHREEQC solution foreach node during the time step Dt by using an internal iterationloop for all FE nodes. Fig. 1 shows the simulator structure andthe coupling procedure and data flow adopted in this work. Bothporosity and permeability are updated during the internal loopdepending on the amount of mineral dissolution/precipitation.

The new simulator simultaneously controls the running, trans-fer and exchange of data between COMSOL and PHREEQC softwareby using a set of MATLAB ‘‘m’’ files. The main MATLAB file isresponsible for reading the COMSOL solution of each node at eachtime step (e.g. CO2 partial pressure, Ca concentration, calcite moles,etc.). The second MATLAB file is responsible for (a) generating theinput file required to run PHREEQC, (b) running PHREEQC, (c) read-ing the output, and (d) updating the COMSOL solution. Additional

Fig. 1. Simulator structure a

MATLAB files are written for the purpose of model initializationand pre- and post-processing. Special attention is given to unitconversion during the data exchange between the COMSOL andPHREEQC software.

3. Mathematical statements

3.1. Governing equations

In this work, the modeling is done for a coupled THMC problemthat involves more than one kind of coupled physical and chemicalprocess with a set of unknown field variables (dependent variables),including: displacement, pore water pressure, temperature andconcentration of chemical species. This section provides the equa-tions used to model each of the processes involved in this work.

3.1.1. Mechanical deformationThe mechanical behaviour of rock is represented by both the

quasi-static equilibrium equation (Eq. (1)) and the generalizedHooke’s Law stress (r)–strain (e) relationship with linear thermalterms (Eq. (2)).

r � rþ f ¼ 0 ð1Þ

nd coupling procedure.

O. Nasir et al. / Tunnelling and Underground Space Technology 42 (2014) 122–135 125

r ¼ C : ½e� aDT� ð2Þ

where f is body forces (per unit volume), r is the stress tensor, C isthe elasticity tensor, DT is the temperature difference and a is thecoefficient of thermal expansion. The porous medium is assumedto be saturated rock, which comprises two phases (fluid and solid).Two types of stresses can be included, fluid (pressure) and solidskeleton (effective stress as defined by Terzaghi (1923)) as shownin Eq. (3).

r ¼ r0 þ P ð3Þ

where r0 is the effective stress and P is the fluid pore pressure. Bysubstituting Eqs. (2) and (3) into (1), the equilibrium equation canbe written as follows:

G@2ui

@xj@yjþ ðGþ kÞ @

2uj

@xi@yj� ab

@p@xi� bKD

@T@xiþ Fi ¼ 0 ð4Þ

where u is the displacement, G is the shear modulus, k is the Laméconstant, KD is the bulk modulus of the solid matrix, ab is Biot’sporoelastic coefficient 1� KD

KS

� �, KS is the bulk modulus of the solid

grains, and Fi is the force per unit volume and b is the coefficient ofvolumetric thermal expansion.

Eq. (5) (Nasir et al., 2011) shows the coupling effect of porepressure, mechanical deformation and temperature on the poros-ity. In this work, only the contribution of geochemical reaction toporosity is calculated and presented.

dndt¼ ða�nÞdeff

dtþða�nÞ

Ks

dpdt

� �þ �ða�nÞbþð1�nÞðb�bSÞð ÞdT

dt

� �ð5Þ

3.1.2. Water flowThe conservation of fluid and solid mass, as shown in Eqs. (6)

and (7), is used to derive the governing equation for flow in porousmedia.

r � ðqf Uf Þ þ@

@tðqf nÞ þ qf q ¼ 0 ð6Þ

r � ðqsUsÞ þ@

@tðqsð1� nÞÞ þ qq ¼ 0 ð7Þ

where q is the density, U is the fictitious velocity, t is time, n is theporosity, q is the mass source, s is the solid and f is the fluid.

With respect to the fluid flow velocity, it is assumed to be rep-resented by Darcy’s law as shown in Eq. (8):

ðu� usÞ ¼ �jgðrpþ qf grDÞ ð8Þ

where u, us are the mean velocities for the fluid and solid, respec-tively, in which u ¼ U

n ;uS ¼ US1�n

� �, j is the permeability, g is the dy-

namic viscosity, p is the pressure, and D is the direction ofgravitational acceleration (g). It should be emphasized that fullwater saturation is assumed based on high liquid saturations ob-served from experimental investigations at the level of the DGR(Intera, 2011). Moreover, full saturation conditions enable keepinga permanent water supply for the chemical reactions.

By substituting Eq. (8) into the combined Eqs. (6) and (7) (DeMarsily, 1986), the following equation is obtained:

r � qfjgðrpþ qf grDÞ

� ¼ n

@qf

@tþ

qf

1� n@n@t� qn

qsdqS

dtð9Þ

where j is the permeability, g is the dynamic viscosity, p is thepressure, and D is the direction of gravitational acceleration (g).

The conservation of the fluid and solid mass take into consider-ation the compressibility of both the fluid and the solid. The rightside of Eq. (9) shows the influence of variation in fluid and solid

densities to the flow PDE. By setting the right side to zero (assum-ing incompressible fluid, solid and skeleton) Eq. (9) will be simpli-fied to a steady state diffusion equation. However, to include theTHMC coupling effects into the fluid flow, we considered that thevariation in the fluid and solid densities is due to that in the tem-perature, pore water pressure, effective stress and total dissolvedsolids. The final equation of the fluid pressure variable can be writ-ten as (Nasir et al., 2011):

r� qfjgðrpþqf grDÞ

� ¼ ðncÞ@C

@tþqf a

0 deff

dt

þqfa0

Ks� n

KSþ n

Kf

� �dpdt

þqf ðnbS �a0bþ ðb� bSÞ � nbf ÞdTdt

ð10Þ

where a0 ¼ ða�nÞð1�nÞ, a ¼ 1� KD

KS, KD, KS and Kf are the bulk moduli of the

solid matrix, solid grains and water fluid, respectively, b, bs and bf

are the thermal expansion coefficients for the solid matrix, solidgrains and water fluid, respectively; n is the porosity, p is the fluidpore pressure, qf is fluid density, C is concentration of dissolved sol-ids in the pore fluid, T is the average temperature of the porousmedium, eff is volumetric deformation.

The fluid dynamic viscosity [Pa s] is considered to be tempera-ture dependant when the following equation is used (Comsol,2009):

g¼¼1:379�2:122�10�2Tþ1:360�10�4T2�4:645�10�7T3

þ8:904�10�10T4�9:079�10�13T5þ3:845�10�16T6

1:7915�10�3

8>><>>:

9>>=>>;

Whenð273:15 K< T <413:5Þ

WhenðT<273:15 KÞ

( )

3.1.3. Heat transferHeat transfer refers to the movement of energy that originates

from a temperature gradient and/or heat generation or extraction.Heat can be transferred through three mechanisms: conduction,advection and radiation. In this work, heat transfer by convectionand conduction are considered, and heat transfer due to radiationis neglected for two reasons. First, in porous media, radiation is sig-nificant only for high porosity and low density (Daryabeigi, 2010)materials. Second, radiation requires two surfaces (A and B) withsignificantly different temperatures. With DGRs, the issue is thatthe porosity is low and temperature is not significantly high en-ough to include radiation as a form of heat transfer. Taking intoconsideration energy conservation, Eq. (11) is used to model theheat transfer in porous media:

qCp@T@tþ qCLur � T ¼ r � ðKrTÞ þ Q ð11Þ

where q is the average density, (T) represents the average temper-ature of the porous medium, Cp is the average volumetric heatcapacity; K is the average thermal conductivity; CL is the volumetricheat capacity of the moving fluid; u is the fluid velocity vector; andQ is the thermal source or sink component. Chemical reactions canrelease or absorb heat depending on the type of reaction (exother-mic or endothermic, respectively). However, in this study, heat re-lease or absorption that is resultant of a chemical reaction isneglected due to its negligible amount.

3.1.4. Solute transportDiffusion–advection and mechanical dispersion are used to

model the process of multi species solute transport. In general,the developed model allows the user to define the number of sol-utes depending on the user input; however, for the applicationexample, the number is taken to be 8 species:

ns@ci

@tþr � ½�nsDLrci þ uci� ¼ Sci

ð12Þ

126 O. Nasir et al. / Tunnelling and Underground Space Technology 42 (2014) 122–135

where ci is solute i concentration, ns is the porosity; DL is the hydro-dynamic dispersion tensor; u is the vector of the pore fluid veloci-ties; and Sci is the solute source or sink.

3.1.5. Geochemical reactionsPHREEQC is a general geochemical program applicable to many

hydro-geochemical environments developed by Parkhurst andAppelo (1999) and published by the U.S. Geological Survey. Thedeveloped simulator has access and the ability to use all the appli-cations in PHREEQC. However, in this work, three categories ofchemical reactions are considered, including: speciation and satu-ration-index calculations, batch-reaction, and equilibrium reac-tions. The equilibrium reactions included the kinetic dissolution/precipitation of calcite in water resulted from change in concentra-tion of dissolved CO2.

In general, the process of solving geochemical problems withPHREEQC requires a data structure with four main components,including: (1) an input file; (2) a PHREEQC source code; (3) a database file; and (4) an output file. Fig. 2 shows a flow chart with themain components and the data flow among them.

The first component shown in Fig. 2 is the input data generatedby PHREEQC users through the use of a set of keyword data blocks,followed by the input of data related to the keywords (e.g., EQUI-LIBRIUM_PHASES (keyword data block) and calcite (input datafrom user). The second component of PHREEQC is the database file.This component contains the required thermodynamic data foraqueous species, and gas and mineral phases. The third componentis the PHREEQC code which is responsible for running the steps byreading the database file and input data, and performs the calcula-tions requested from the input data. After reading the database fileand input data, PHREEQC uses the thermodynamic activities andmass-action to generate a set of equations with the main un-knowns (aqueous species, activity, activity coefficient, molarityand moles in the solution). Next, PHREEQC solves the equationsby using the Newton–Raphson method.

PHREEQC uses the Davies equation for activity coefficients:

log ci ¼ �Az2i

ffiffiffiffilp1þ ffiffiffiffilp � 0:3l� �

ð13Þ

or the extended Debye–Hückel equation

log ci ¼�Az2

iffiffiffiffilp

1þ Baoiffiffiffiffilp þ bil ð14Þ

where ci is the activity coefficient, zi is the ionic charge of the aque-ous species i, A, B, bi are constants, ao

i is the ion-size parameter, andl is the ionic strength.

The rate of calcite dissolution and precipitation expression pro-posed by Plummer and Busenberg (1987) is adopted in this work.Steps suggested by Parkhurst and Appelo (1999) which areadopted are shown below:

rCalcite ¼ Area� rf � 1� 1023�SICalciteð Þh i

ð15Þ

where

Area ¼ AV� tn

# User Input data, example

3 Calcite

4 CO2 0.03

D

Fig. 2. Data components a

rf ¼ ððK1 � ActHþ Þ þ ðK2 � ActCO2 Þ þ ðK3� ActH2OÞÞ

where SICalcite is the saturation index of calcite, ‘‘A’’ is the calcite sur-face area, V is pore volume, t is (calcite moles/ initial moles of cal-cite), n is the constant, K1, K2, K3 are constants, and ‘‘Act’’ is theactivity coefficient.

Calcite dissolution and precipitation are then converted toporosity changes by using the following equations:

Calcite moles change ¼Moles of calciteat time t � calciteat time t�Dt

Weight of calcite change ¼ Calcite moles change

�molecular weight

Volume of void change ¼ Volume of calcite change ðsolidÞ

¼Weight of calcite change=calcite solid density

Updated porosity ¼ Volume of voids=total volume

where t is time, and Dt is the time step.

3.2. Coupling of mechanical deformation, heat transfer, fluid flow andreactive transport

The processes that are solved in the developed model are cou-pled. The following lists the main types of coupling included inthe model:

– The hydraulic process is coupled with the mechanical processby including a poro-elastic effect in Eqs. (4) and (10). The ther-mal and chemical processes are coupled by introducing theeffect of temperature into the chemical reaction (heat transferis solved by using Eq. (11), and the temperature is set as aninput in PHREEQC as shown in Section 3.1.5). On the other hand,porosity dependent permeability is included by using the Koze-ny–Carman relationship (e.g., Kozeny, 1927, Carman, 1937), andtemperature dependent density and solute concentrationdependent fluid density by using Eq. (10).

– The thermal process is coupled with the hydraulic and chemicalprocesses by including convective heat transfer (Eq. (11)) andsolute concentration dependent density (Eq. (10)).

– The mechanical process is coupled with the hydraulic and ther-mal processes by including poro-elastic and thermal expansion(Eq. (4)).

– The chemical process is coupled with the hydraulic and thermalprocesses by including advection mass transfer (Eq. (12)) andtemperature dependent chemical reactions (PHREEQC inputtemperature). In addition to that, changes in porosity due to dis-solution and precipitation are included in the modeling(Section 3.1.5).

4. Climate changes and future glaciations

A periodical glaciation-deglaciation cycle of 100,000 years wasthe most distinctive feature of the quaternary period which has

PHREEQC

atabase file

Output

nd flow in PHREEQC.

-5

0

5

10

15

20

25

30

-80 -70 -60 -50 -40 -30 -20 -10 0

Time x 1000 (years before present)

Pore

Wat

er P

ress

ure

(MPa

)

Depth 150 mBGS 300 mBGS 500 mBGS 650 mBGS

Fig. 4. History of pore water pressures at different depths with zero surfacepressure BCs (Nasir et al., 2013a,b).

A C D

1234

Out

let f

ace

250 mm

100

mm

Sampling ports

Inle

t fac

e

CaC

l 2N

a 2C

O3

Fig. 5. Diagram of the experimental setup for heterogeneous packing (data fromKatz et al. (2011)).

O. Nasir et al. / Tunnelling and Underground Space Technology 42 (2014) 122–135 127

spanned the past couple of million years, particularly, in the northhemisphere. As a result, the ground surface conditions were sub-jected to transient changes, including: temperate ice loading (asshown in Fig. 3), ice loading is interpolated from The Universityof Toronto Glacial Systems Model (GSM) (‘‘Peltier’s Model’’ modelnn9930 (Peltier, 2008)), permafrost, subglacial permafrost, glacialmelting regimes, etc.

Our previous studies (Fall and Nasir, 2010; Nasir et al., 2011,2013a,b) investigated the hydro-mechanical (HM) and THMC cou-pled processes that have resulted from long term climate changesin the past and glaciation cycles in the sedimentry rocks of south-ern Ontario. The aforementioned works of research predicted thehydraulic, mechanical, thermal and chemical responses of the sed-imentary rock formations of southern Ontario to past glaciations.One of the results obtained from the work on the impact of pastglaciations on vertical flow velocities and pressure at the level ofthe proposed DGR is shown in Figs. 3 and 4. Fig. 3 shows the ver-tical flow velocity resultant of the glaciation effect, and Fig. 4shows the history of pore water pressures at different depths gen-erated from the impact of glaciations (Nasir et al., 2013a,b). FromFig. 3 it can be seen that the value of the flow velocity changes frompositive (upward flow) to negative (downward flow) depending onthe loading and unloading responses due to the poroelastic effect,respectively (Fall and Nasir, 2010; Nasir et al., 2013a,b). Moreover,the previous studies have shown that the permafrost depth resul-tant from glaciations is limited to approximately 45 m (Fall andNasir, 2010; Nasir et al., 2011, 2013a,b).

5. Verification of the simulator

5.1. First example of verification

The first example of verification consists of simulating a labora-tory test performed by Katz et al. (2011) as shown in Fig. 5. In theirtesting, Katz et al. (2011) injected two solutions (sodium carbonate(Na2CO3) and calcium chloride (CaCl2) at concentrations of 5 g/kg-water) from two inlets into a 250 � 100 mm cell packed with glassbeads that were 1 mm in diameter with a measured porosity of0.375. The initial content of the cell was an aqueous solution of so-dium chloride at a concentration of 5 g/kg-water. Ten samplingpoints were selected to obtain samples with time to monitor thereactive transport activities and concentration as shown in Fig. 5.

The experimental work was numerically simulated by using thedeveloped THM-GeoC simulator with the appropriate initial andboundary conditions as shown in Fig. 6. The main BCs were thehydraulic and chemical BCs with a constant convective flux(12 ml/h) and constant pressure with constant concentration (left)as shown in Fig. 6. The mechanical and thermal initial and

Fig. 3. History of flow velocity level at the proposed DGR (Nasir et al., 2013a,b).

boundary conditions are assumed to be fixed and constant, respec-tively, to simulate the lab test conditions.

Fig. 7 shows the calcium carbonate (CaCO3) concentrations thatare the result of a chemical reaction between Na2CO3 and CaCl2 atdifferent times (0–30 h). A higher concentration of CaCO3 precipi-tation is concentrated along the horizontal centerline, at whichthe two flowing reactants are mixed with a lower concentrationto the top and bottoms of the centerline. These results are consis-tent with the white strip of CaCO3 precipitate observed along thecenterline of the flow cell at 30 h, as shown in Fig. 8 (Katz et al.,2011).

In addition to that, the modeling results of the current study arecompared with the data collected by using the sampling ports(Katz et al., 2011) (Fig. 5). Fig. 9 shows a comparison of calcium(Ca) concentration measurements and modeling at points A1 andA2 (point A1 is located 11.4 cm from the left and 1.5 cm belowthe centerline, and point A2 is located 11.4 cm from the left and0.5 cm below the centerline). The comparison shows a reasonableagreement between the modeling and experimental results (upto 15 h), particularly, the Ca values and the timing trend in Ca var-iation. However, the results show that after 15 h, there are discrep-ancies between the predicted values and the experimental data.Similar or larger discrepancies were also observed by the modelingstudies performed by Katz et al. (2011). These discrepancies mightbe due to some errors in the measurements or the calculation ofthe Ca concentration.

Fig. 6. First example of validation – FE model mesh and BCs.

Verti

cal d

ista

nce

(m)

Verti

cal d

ista

nce

(m)

Verti

cal d

ista

nce

(m)

Time = 0 Time = 6 hours

Time = 12 hours Time = 18 hours

Time = 24 hours

Horizontal distance (m)

Time = 30 hours

Horizontal distance (m)

CaC

O3 c

once

ntra

tions

(exp

ress

ed in

mol

es p

er c

ubic

met

er)

Fig. 7. COMSOL-PHREEQC simulation of reactive transport in homogeneous packing. Distribution of CaCO3 concentrations (expressed in moles per cubic meter).

128 O. Nasir et al. / Tunnelling and Underground Space Technology 42 (2014) 122–135

Out

let f

ace

250 mm

100

mm

Inle

t fac

e

CaC

l 2N

a 2C

O3

white strip of calciumcarbonate precipitate

Fig. 8. Calcium carbonate precipitate along the centerline of the flow cell at 30 h(picture from Katz et al. (2011)).

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0.050

0 5 10 15 20 25 30

Time (Hours)

Ca

(mol

/Kg)

Katz et al., 2009 (A1)

Mode (A1)

Katz et al., 2009 (A2)

Model (A2)

Fig. 9. COMSOL-PHREEQC modelling results compared with those by Katz et al.(2011) Ca measurements at points A1 and A2.

Table 2Characteristics of the second validation example.

Characteristic Value Unit

Model length 0.5 mPorosity 0.32 –Density 1800 kg/m3

Initial calcite 2.176 � 10�5 mol/kg of soilPore velocity 9.37 � 10�6 m/spH (initial) 9.91 –

O. Nasir et al. / Tunnelling and Underground Space Technology 42 (2014) 122–135 129

5.2. Second example of verification

The second example of verification is performed by comparingthe results of the current study with the modeling work ofEngesgaard and Kipp (1992). In their work, Engesgaard and Kipp(1992) developed a one dimensional reactive transport model andapplied the model to investigate the process of the dissolution–precipitation of calcite and dolomite as shown in Fig. 10. Table 2shows the primary information for the second example of verifica-tion. The main concept in this example is that the flushing of calciteis simulated by using 0.001 M of a magnesium chloride (MgCl2)solution from one end as shown in Fig. 10. The flushing will causethe dissolution of calcite and precipitation of dolomite.

Fig. 11 shows the FE model mesh and BCs used in the simulationprocess. Fig. 12 shows the calcite dissolution process due to MgCl2

flushing at four different times (1000, 7000, 14,000 and 21,000 s).The distance of flushing at 21,000 s is approximately 0.225 m,which is in agreement with the results presented by Engesgaardand Kipp (1992).

Out

let f

ace

500 mm

water initially in equilibrium with calcite (2.176x10-5 mol/kg soil)

Inle

t fac

e

MgC

l 2

Fig. 10. Diagram of setup for second example of validation as compared withEngesgaard and Kipp (1992).

Fig. 13 shows a comparison of the results from the developedsimulator model and the results obtained by Engesgaard and Kippin 1992 with respect to calcite, magnesium (Mg), Ca, and chloride(Cl) concentrations after 21,000 s of flushing. The results show verygood agreement with the results presented by Engesgaard andKipp (1992) with respect to both spatial and temporal Mg, Ca,and Cl species concentration as well as calcite and dolomite disso-lution-precipitation.

5.3. Third example of verification

The developed COMSOL-THMC model of the proposed simula-tor has been also verified against field data related to the effectsof past glaciation cycles on the THMC regimes in the Ontario (Can-ada) rock formations. The field data were obtained from the geosci-entific site investigations performed by OPG. The verificationresults have shown that there is good agreement between the pre-dicted thermal (temperature), hydraulic (pore water pressure),mechanical (stress) and chemical (TDS profile) parameters andthose measured in the field. The details on the verification studiesperformed are published in Nasir et al. (2011) and Nasir et al.(2013a,b), whereas the main results are summarized below.

– The comparison of the predicted pore water pressures with thespecific pore water pressures (including anomalous under andover-pressure) observed at sites shows that past glaciationshad a contribution to the observed anomalous under andover-pressure.

– Total dissolved solid profile predicted by the THMC modelshows a very good agreement with the site specific observationsas illustrated by Fig. 14.

– Predicted depth of glacial melted water are in good agreementwith the oxygen isotope tracers observed at the specific site.

– Predicted depths of permafrost are consistent with that pre-dicted by other models (e.g., Peltier, 2008) as illustrated byFig. 15.

These verifications provide additional confidence on the use ofthe developed simulator to model coupled THMC processes associ-ated with DGR.

6. Near field application

The developed model was applied onto the DGR proposed byOPG for LILWs at a depth of 680 m within the Ordovician sedimen-tary formation south of Ontario. Several factors and coupled pro-cesses could play important roles in the evolution of theproperties of the host rock formation that could impact the stabil-ity and safety of the DGR system. Examples of these factors andprocesses are: damage that result from excavation processes, gla-cial loadings, and geochemical interactions between the LILWsand the host rock formation. In the case of LILWs, and based onthe inventory studies of the proposed waste Quintessa andGeofirma (2011), many chemical species (including gas, solidsand liquids) are expected to be released which interact with the

500 mm

Initial calcite of 2.176x10-5 mol/kg of soil

Fig. 11. Second validation example – FE model mesh and BCs.

Cal

cite

con

cent

ratio

n m

oles

/kg

of s

oil

Horizontal distance (m)

Vert

ical

dis

tanc

e (m

)

Time = 1000 sec

Time = 7000 sec

Time = 14000 sec

Time = 21000 sec

Fig. 12. COMSOL-PHREEQC simulation of calcite concentrations (expressed in moles per kg of soil). The blue–red interface represents the calcite dissolution front. (Forinterpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

0.0E+00

5.0E-04

1.0E-03

1.5E-03

2.0E-03

2.5E-03

3.0E-03

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Distance (m)

Con

cent

ratio

n, C

a, M

g, a

nd C

l (M

oles

per

Lite

r)

0.00E+00

5.00E-06

1.00E-05

1.50E-05

2.00E-05

2.50E-05

Con

cent

ratio

n of

Cal

cite

(Mol

es p

er K

g of

Soi

l)

Ca-Engesgaard and Kipp, 1992

Ca-Model

Mg-Engesgaard and Kipp

Mg-Model

Cl-Engesgaard and Kipp

Cl-Moodel

Calcite-Engesgaard and Kipp

Calcite-Model

Fig. 13. COMSOL-PHREEQC simulation results as compared with Engesgaard and Kipp (1992).

130 O. Nasir et al. / Tunnelling and Underground Space Technology 42 (2014) 122–135

host limestone during the lifetime of the DGR (e.g., CO2, H, CH4,etc.). However, this work is limited to the effect of dissolved CO2

in ground water on the evolution of porosity and permeability inthe near field (‘‘near field includes the EBS (Engineered BarrierSystem) as well as the host rock within which the repository is

situated, to whatever distance the properties of the host rock havebeen affected by the presence of the repository’’ (OECD, 2003)).Other geochemical processes, such as corrosion and chemicalwater from nuclear wastes, could be coupled and included infuture studies.

GCM Model nn9930

Study Model

Time x 1000 (years before present)

Ice

load

pre

ssur

e (M

Pa)

Perm

afro

st D

epth

(m)

Fig. 14. THMC model simulation results of the history of permafrost depth in the studied area as compared with GCM model nn9930 (Nasir et al., 2013a,b).

-1000

-900

-800

-700

-600

-500

-400

-300

-200

-100

0

0 100 200 300 400 500 600

TDS Concentration (kg/m3)

Dep

th (m

BG

S)

Field data (NWMO2011)

Initial TDS 400M YBP

400 M years Diffusion

Advection-DiffusionPredicted TDS now

Fig. 15. THMC model simulation results of the TDS profile as compared with fieldobservations (comparison between the diffusion and diffusion–advection TDSprofiles with an actual field geochemical distribution) (Nasir et al., 2013a,b).

O. Nasir et al. / Tunnelling and Underground Space Technology 42 (2014) 122–135 131

In this work, the impact of long term THM-GeoC processeswithin the scale of near field due to the dissolved gases generatedfrom LILWs are investigated. From a safety assessment perspective,reactive solute transport is the most relevant process, which de-fines the amount of potential contamination by radionuclide mate-rials. Indeed, reactive transport processes could result in thecoarsening (porosity increase) of the pore structure of the naturalbarrier. This will speed up the migration of the radioactive contam-inants to the biosphere after the failure of the canisters. Conse-quently, the present simulation study will allow us to assesswhether the coupled effect of glaciation cycles and the reactivetransport of the water enriched with carbon dioxide gas could leadto the increase in the porosity (thus in permeability) of limestonehost rock in Ontario (Canada) for nuclear wastes.

6.1. Conceptual modeling

Fig. 16 shows the conceptual modeling approach adopted in thisstudy.

In this work, the following assumptions are adopted:

– The system is assumed to be fully saturated. The main argu-ment that supports this assumption is that the generation ofCO2 requires approximately 35,000 years for commencementafter the closure of the DGR (Geofirma and Quintessa, 2011).This lengthy amount of time is assumed to be enough to satu-rate the DGR system. In addition to that, the maximum CO2

pressure is approximately 7.5% of the hydrostatic pressure atthe repository level, which is assumed to be inadequate to forma significant gas phase. All CO2 gas is assumed to be dissolved inwater, and this assumption will lead to the overestimation ofcalcite dissolution (more conservative approach) as comparedto the case with pure CO2 gas.

– The ratio of the Excavated disturbed Zone (EdZ) is approximatedby 1R (R is the equivalent radius of the excavation reference).

– The impact of future climate changes, represented by future gla-ciations, is extensively investigated in previous works ofresearch (Fall and Nasir, 2010; Nasir et al. 2011, 2013a,b). Theresults obtained from these studies are used to include theimpact of future glaciations by incorporating increase in porewater pressure in the repository room (see Section 4).

– Heat transfer and temperature effects are included in the modelor simulator (THM-GeoC). However, the disposal of LILWs is notexpected to cause significant changes in temperatures (Fall,2010; Quintessa, 2011) and changes in temperature due to longterm climate change are limited to shallow depths at the sur-face (less than 100 m compared to 680 m for the DGR depth(Fall and Nasir, 2010; Nasir et al., 2011). For these two reasons,a constant temperature is assumed at the repository level forthe application example. It should be emphasized that, for thecase of repository for HLWs, the significant change of tempera-ture due to the heat generated by the HLWs has to beconsidered.

The potential chemical reactions at the near field (near field isassumed to be 200 m around the repository rooms) include a setof very complex reactions due to large species inventory withinthe proposed DGR (Intera, 2011). However, in this work, we havefocused on the chemical reactions associated with the interactionof generated CO2 (Geofirma and Quintessa, 2011), water and lime-stone rock. Table 3 shows the chemical reactions that are related tothe potential interaction included in this study.

8.6 m

7 m

200 m

Dissolved CO2

(Calcite) Limestone Rock

Saturated excavation

excavateddisturbedzone (EDZ)

Appox.8.6 m

Finite elements mesh and boundary conditions

Initial conditions

Boundary conditions (BC) 1

BC 2

BC 4

CO2 amount

BC 3

0.0E+00

1.0E+07

2.0E+07

3.0E+07

4.0E+07

5.0E+07

6.0E+07

7.0E+07

8.0E+07

9.0E+07

1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06

Time (year)

CO

2 A

mou

nt (m

ol)

Fig. 16. Conceptual modeling approach (some of the data is adopted from NWMO (2011)).

Table 3Main chemical reaction equations implemented in the current study.

Reaction#

Description Reaction equation

R1 Carbon dioxide dissolution inwater

CO2 ðgÞ () CO2 ðlÞR2 CO2 ðlÞ þ H2O() H2CO3

R3 H2CO3 () Hþ þ HCO�3R4 H2CO3 þ H2O() H3Oþ þHCO�3R5 HCO�3 þH2O() H3Oþ þ HCO2�

3

R6 Dissolution/precipitation ofcalcite with changes in CO2

CaCO3 ðCalciteÞ () Ca2þ þ CO2�3

R7 Hþ þ CO2�3 () HCO�3

Table 4Main material properties used in the simulation.

Property Poisson’sratio

Young’s modulus(GPa)

Permeability(m2)

The(W/

Intact rock 0.2a 39a 2.33e�21b 2EdZ rock 0.2 39 2.33e�20c 2

a Data obtained from Intera (2011).b Data obtained from Geofirma and Quintessa (2011).c Permeability of the EdZ rock approximated to be one order of magnitude more than

Table 5THMC initial conditions used for simulation.

Initial conditions

Mechanical In situ stress measurements of horizontal and vertical stressesa andHydraulic Initial conditions assumed to be hydrostaticChemical Existing total dissolved solids chemistry is taken as initial chemicaThermal Temperature obtained from geothermal gradient at depth of 680 m

a Lo (1978), and Zoback and Zoback (1980).b The measurements of chemical characteristics of pore waters at the level of the DG

conditions.c Regression equation suggested by Vugrinovich (1989).

132 O. Nasir et al. / Tunnelling and Underground Space Technology 42 (2014) 122–135

6.2. Model geometry and material properties

A one dimensional model is used to apply the developed modelto a near field case as shown in Fig. 16. The geometry of the ana-lyzed domain was 7 m in height by 200 m in length. The 200 mlength included a distance of 8.6 m which is the approximatedEdZ that is the result of excavation or stress redistribution; this va-lue is adopted based on the proposed ratio of disturbed zone to theradius of excavation (Bossart et al., 2002). The rest, 191.4 m, isconsidered as intact limestone. The rock is assumed to be fully sat-urated and consists of 100% calcite. The assumption that there is100% calcite is more conservative than assuming there is calcite

rmal conductivity(m K))

Specific heat capacity(J/(kg K))

Porosity Diffusion(m2/s)

700 0.019a 1.2E�10700 0.03b 1.2E�10

the intact rock.

assumed to be dH = 1.5 dv (effective dv = 10.68 MPa)

l conditionsb

is used as initial temperaturec BHT (�C) = 14.5 + 0.0192 � depth (m) = 27.556 �C

R within the limestone obtained by deep boreholes (Intera, 2011) is used as initial

Table 6THMC BCs used for simulation.

BCs BC 1 (top) BC 3 (left side) BC 4 (right side) BC 2 (bottom)

Mechanical Free deformation transient normal stressesa Roller Roller FixedHydraulic Transient pressureb Transient pressureb Transient pressureb Transient pressureb

Chemical Insulation Transient concentrationc Insulation InsulationThermal Constantd Constant Constant Constant

a Transient normal stresses derived from HM analysis at the level of the DGR as shown in Fig. 23 of Nasir et al. (2011) which is resulted from surface glacial load shown inFig. 7 of Nasir et al. (2011).

b Transient pressure derived from HM analysis at the level of the DGR Nasir et al. (2011), as shown in Fig. 4 of the manuscript.c Transient concentration derived from predicted gas generation within the repository rooms due to waste degradation (Geofirma and Quintessa, 2011).d Temperature at the level of the DGR concluded to be constant under all conditions including long term climate changes.

0.0E+001.0E+072.0E+073.0E+074.0E+075.0E+076.0E+077.0E+078.0E+079.0E+07

1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06

Time (year)

CO

2 A

mou

nt (m

ol)

Fig. 17. Amounts of CO2 gas in the vapour phase within the repository (dataadopted from NWMO (2011)).

0.017

0.018

0.019

0.02

0.021

0.022

0.023

0.024

0.025

0.026

0.027

0 10 20 30 40 50 60 70 80

Distance (m)

Poro

sity

35000 a97000 a159000 a220000 a282000 a

Fig. 18. Horizontal porosity profile for five different time periods in the future withrespect to the first scenario.

1E-21

1E-20

0 10 20 30 40 50 60 70 80

Distance (m)

Perm

eabi

lity

(m2 )

35000 a97000 a159000 a220000 a282000 a

Fig. 19. Horizontal permeability profile for five different times in the future withrespect to first scenario.

O. Nasir et al. / Tunnelling and Underground Space Technology 42 (2014) 122–135 133

and other minerals, such as dolomite, for two reasons: (1) calcitedissolves more than dolomite, and (2) the dissolution of dolomitemight lead to calcite precipitation. Table 4 shows the main mate-rial properties used in the simulation.

6.3. Initial and boundary conditions

The near field zone is part of the DGR system which is located680 m below the ground surface. The near field zone is subjectedto several influencing external factors, such as: potential impactof long term climate changes, and the impact of potential LILWs.The initial and boundary conditions related to hydraulic, thermal,mechanical and chemical processes will be directly related to thementioned factors as shown in the following sections.

6.3.1. Initial conditionsFour sets of initial conditions (ICs) that represent the mechani-

cal, hydraulic, chemical, and thermal ICs are considered in thiswork. Table 5 shows the values of the ICs adopted in this study.

6.3.2. Boundary conditionsWith reference to Fig. 16, the BCs (1–4) are set by using the cor-

responding mechanical, hydraulic, chemical, and thermal condi-tions. Table 6 shows the values of the BCs adopted in this study.Fig. 17 shows the estimated CO2 moles generated from the LILWsto be disposed at the proposed DGR (Geofirma and Quintessa,2011). The CO2 transient chemical BCs (mol/m3) at BC 3 is esti-mated by using the data from Fig. 17 and an estimated void volumeof 420,000 m3 for the DGR (Quintessa and Geofirma, 2011).

6.4. Simulation results and discussions

Different sets of results are obtained from this study. However,only selected results relevant to the safety assessment of DGRs willbe presented, including the impact of long term geochemical reac-tions on porosity and permeability within the host rock formation.Two scenarios related to the Excavation disturbed Zone (EdZ) are

investigated. The first scenario is not to include the EdZ effect onthe initial porosity and permeability, and the second scenario isto include the EdZ effect. Fig. 18 shows the horizontal profile ofporosity within the host rock formation for five different time peri-ods in the future (35,000–282,000 years) with respect to the firstscenario. The results show a maximum increase in porosity of0.007 at the excavation face, the porosity changes gradually de-crease and are zero at a distance of 50 m.

Changes in porosity will lead to changes in permeability. Fig. 19shows the estimated profile and changes in permeability that is theresult of porosity changes by using Eq. (15) of Kozeny–Carmanrelationship (Kozeny, 1927; Carman, 1937):

B.C.3 CO2

0.017

0.022

0.027

0.032

0.037

0.042

0 10 20 30 40 50 60 70 80

Distance (m)

Poro

sity

35000 a97000 a159000 a220000 a282000 a

Excavateddisturbedzone (EDZ)

Fig. 20. Horizontal porosity profile for five different time periods in the future with respect to the second scenario.

B.C.3 CO2Excavateddisturbedzone (EDZ)

1E-21

1E-20

1E-19

0 10 20 30 40 50 60 70 80

Distance (m)

Perm

eabi

lity

(m2 )

35000 a

97000 a

159000 a

220000 a

282000 a

Fig. 21. Permeability horizontal profile for five different time periods in the future with respect to the second scenario.

134 O. Nasir et al. / Tunnelling and Underground Space Technology 42 (2014) 122–135

kt ¼ n3

ð1� n2Þ

� t ð1� n2Þn3

� initial

kinitial ð16Þ

where kt is the permeability at time (t), and kinitial is the initial per-meability. It can be noticed that the maximum change in perme-ability is less than one order of magnitude.

Fig. 20 shows the horizontal profile of porosity within the hostrock formation, including the EdZ and the intact zone, for five timeperiods in the future (35,000–282,000 years) with respect to thesecond scenario. The results show a maximum absolute changein a porosity of 0.007 at the EdZ zone as well as a considerable in-crease in porosity within the intact zone for a distance of 20 m.

Fig. 21 shows the estimated profile and change in permeabilitythat is the result of porosity changes for both EdZ and the intact

rock zone. It can be noticed that for both zones, the maximumchange in permeability is still less than one order of magnitude.

From a safety perspective, the changes in both porosity and per-meability do not seem to be significant for the safety of DGRs.

7. Conclusions

In this work, a thermo-hydro-mechanical-geochemical modeland a numerical analysis tool are developed to investigate the longterm THMC processes associated with the disposal of LILWs in aDGR hosted by sedimentary rocks in southern Ontario. The devel-oped tool includes a new simulator that couples two types of soft-ware (COMSOL and PHREEQC). The new simulator is applied to

O. Nasir et al. / Tunnelling and Underground Space Technology 42 (2014) 122–135 135

solve a set of THMC coupled PDEs and geochemical equations for aperiod of 300,000 years in the future in the DGR at the near fieldunder the impact of future glaciations. Simulation results obtainedby using the developed model and simulator are compared withpublished experimental and numerical solutions with good agree-ment. The developed simulator is applied to investigate the evolu-tion of porosity and permeability in a near field scale of a DGR inOntario which takes into account the impact of the geochemicalreactions of LILWs from generated CO2 through limestone calciteas well as the influence of future glaciation and deglaciation cycles.The results show that both permeability and porosity will increaseas a result of calcite dissolution. However, the change in perme-ability is low and limited to less than one order of magnitude.

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