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Numericalsimulationofreactiveprocessesinanexperimentwithpartiallysaturatedbentonite.JContamHydrol83(1-2):122-147

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Journal of Contaminant Hydrology 83 (2006) 122–147

www.elsevier.com/locate/jconhyd

Numerical simulation of reactive processes in an

experiment with partially saturated bentonite

Mingliang Xie a,*, Sebastian Bauer a, Olaf Kolditz a,

Thomas Nowak b, Hua Shao b

a Center for Applied Geoscience, Chair of GeoSystemsResearch, University of Tubingen,

Sigwartstr. 10. D-72076 Tubingen, Germanyb Federal Institute for Geosciences and Natural Resources, Stilleweg 2, D-30655, Hannover, Germany

Received 30 August 2004; received in revised form 4 November 2005; accepted 7 November 2005

Abstract

Bentonites are preferred materials for use as engineered barriers for high-level nuclear waste

repositories. Simulation of geochemical processes in bentonite is therefore important for long-term safety

assessment of those repositories. In this work, the porewater chemistry of a bentonite sample subject to

simultaneous heating and hydration, as studied by Cuevas et al. [Cuevas, J., Villar, M., Fernandez, A.,

Gomez, P., Martın, P., 1997. Porewaters extracted from compacted bentonite subjected to simultaneous

heating and hydration. Applied Geochemistry 12, 473–481.], was assessed with a non-isothermal reactive

transport model by coupling the geochemical software PHREEQC2 with the object-oriented FEM

simulator GeoSys/RockFlow. Reactive transport modelling includes heat transport, two-phase flow,

multicomponent transport and geochemical reactions in the liquid phase, i.e. ion exchange, mineral

dissolution/precipitation and equilibrium reactions. Simulations show that the easily soluble minerals in

bentonite determine the porewater chemistry. Temperature affects both two-phase flow and geochemical

reactions. Porosity change due to dissolution/precipitation is low during the experiment. However,

changes of the effective porosity caused by bentonite swelling can be very large. The simulated results

agree well with the experimental data.

D 2005 Elsevier B.V. All rights reserved.

Keywords: Non-isothermal reactive transport; Two-phase flow; Numerical modelling; Geochemical reaction; Bentonite

0169-7722/$ -

doi:10.1016/j.

* Correspon

E-mail add

see front matter D 2005 Elsevier B.V. All rights reserved.

jconhyd.2005.11.003

ding author. Tel.: +49 7071 29 73173.

ress: mingliang.xie@uni-tuebingen.de (M. Xie).

M. Xie et al. / Journal of Contaminant Hydrology 83 (2006) 122–147 123

1. Introduction

Compacted bentonite is selected as buffer material for high-level radioactive waste (HLW)

repositories in many disposal concepts. In this situation, the bentonite is subjected to

simultaneous heating by the nuclear waste canister and hydration from the rock. The processes

within bentonite will be very complex—highly coupled thermal (T), hydraulic (H), mechanical

(M) and chemical (C) processes. Numerical simulation is a powerful tool for understanding and

predicting such complex processes (Gens et al., 1998; Tsang et al., 2003; Xie et al., submitted for

publication).

Simulation of porewater chemistry that may come in contact with the canister and later the

waste matrix is of special importance for the long term safety assessment of a repository. The

chemical composition of porewater and its oxidation potential govern the solubility of

radionuclides and influence the corrosion rate of the canister and waste matrix (Curti, 1993;

Bath, 1993). Furthermore, the material properties of bentonite can be changed or influenced by

heat and porewater chemical composition. Therefore, it is important to specify the chemistry in

the near field (Couture, 1985; Studds et al., 1998; Tessier et al., 1998; Wiebe et al., 1998; Tuller

and Or, 2003; Xie et al., 2004).

Various experimental studies on the chemistry of bentonite porewater have shown that the

composition of these waters is largely controlled by the dissolution or precipitation of reactive trace

solids, which are normally found in minor amounts in bentonite (Grambow et al., 1985; Snellman

and Rantanen, 1985; Wieland et al., 1994; Cuevas et al., 1997). However, such experiments

encompass only bshortQ periods in comparison with the long-term safety requirements of

repositories (over 10 k years) (Chapman and McKinley, 1987). Therefore, numerical modelling

approaches for mass transport and chemical reactions in subsurface systems have been presented

by a number of investigators (Ortoleva et al., 1987; Lichtner, 1985, 1988; Liu and Narasimhan,

1989; Nienhuis et al., 1991; Yeh and Tripathi, 1991; Simunek and Suares, 1994; Steefel and

Lasaga, 1994; Steefel and MacQuarrie, 1996; Parkhurst and Appelo, 1999; Xu and Pruess, 2001).

Three major approaches have been used to couple multi-species transport and geochemical

reactions: 1) The one-step or global implicit approach, which solves the governing equations,

including both reaction and transport terms, simultaneously; 2) The sequential non-iterative

approach (SNIA), which consists of solving the governing equations within a single timestep in

sequence without iteration between them; 3) The sequential iterative approach (SIA), which solves

the transport and the reaction equations separately in a sequential manner with an iterative

procedure. Details of the numerical approaches for modelling reactive transport can be found in

Steefel and MacQuarrie (1996).

The most difficult aspects of non-isothermal reactive transport in highly compacted bentonite

include: 1) treatment of the multiphase multicomponent flow system with extremely high

capillary pressure; 2) involvement of gas as well as liquid phase in the fluid flow, chemical

species transport, and reactions; 3) taking into account the swelling effect of bentonite; 4) the

kinetics of fluid–solid interactions. The model presented by Lasaga (1984) couples water flow,

solute and heat transport, and chemical reactions, and includes also kinetic mineral dissolution

and precipitation processes. The code UNSATCHEM-2D has been developed by Simunek and

Suares (1994). It is a two-dimensional finite element model for simulating the ion equilibrium

and kinetic non-equilibrium geochemistry in unsaturated soils. A multiphase non-isothermal

reactive transport model developed by White (1995) employs a one-step approach that solves all

flow, transport and reaction equations simultaneously. Another multiphase non-isothermal

reactive transport computer code MULTIFLO is presented by Lichtner (1996), and has been

M. Xie et al. / Journal of Contaminant Hydrology 83 (2006) 122–147124

applied for various problems such as pyrite oxidation and hydrothermal systems. The numerical

simulator TOUGHREACT developed by Xu and Pruess (2001) is a multiphase non-isothermal

reactive transport model in unsaturated fractured rocks. Other models can be found in the review

paper by van der Lee and De Windt (2001).

Modelling studies on reactive transport processes in clay and especially in highly compacted

bentonite have been undertaken by many investigators (e.g. Wanner, 1986; Curti, 1993; Wieland

et al., 1994; Snellman, 1994; Ohe and Tsukomoto, 1997; Pusch et al., 1999; Pusch, 2000;

Savage et al., 2002; Bradbury and Baeyens, 2003; De Windt et al., 2004). Bradbury and Baeyens

(2003) calculated porewater compositions in compacted re-saturated bentonite, taking into

consideration factors such as montmorillonite swelling, semi-permeable membrane effects, very

low bfree waterQ volume, and highly effective buffering characteristics. The simulation of the

interaction of bentonite with cement water was presented by Savage et al. (2002), in which the

porosity changes by kinetically controlled dissolution and precipitation of minerals have been

taken into account. Wersin (2003) presented a thermodynamic simulation with two distinct

surface complexation models to identify the geochemical reactions in bentonite at highly varying

solid / liquid ratios. More recently, De Windt et al. (2004) presented a coupled model of cement/

claystone interactions. However, the simulations mentioned above describe the saturated state

without taking the effect of swelling on hydration processes into consideration.

This paper presents the application of the newly developed object-oriented and process-

oriented simulator GeoSys/RockFlow, which couples unsaturated two-phase flow, heat transport

and multi-species reactive transport. The model is thus suited to simulate chemical processes

occurring in compacted bentonite under unsaturated and non-isothermal conditions. The model

is applied to simulate an experiment performed by Cuevas et al. (1997), who studied the

geochemistry in a compacted bentonite sample subject to simultaneous heating and hydration. In

Section 2, specific processes occurring in bentonite are introduced, while Section 3 presents the

governing equations of the numerical simulator. Section 4 presents the experimental design and

the simulation results.

2. Theoretical background

2.1. Swelling

2.1.1. Porosity

With the increase of water content and/or decrease of porewater chemical concentrations,

bentonite swells because of the interlayer porosity change, which can be described by the

chemical swelling model presented by Xie et al. (2004) as summarized in Eqs. (1) and (2):

nIL ¼ Sl� �g

dbdnILmax ð1Þ

nILmax ¼ mS0qd

�ee0RT

2F2I � 103

�12

ð2Þ

in which nIL is the interlayer porosity that represents the space occupied by diffuse double layers

(DDLs), nIL max means the maximum interlayer porosity that represents the swelling potential of

bentonite, Sl is degree of liquid saturation, b represents volume fraction of the expansive

minerals, g is a dimensionless coefficient, R is the universal gas constant [=8.3145(J mol�1

K�1)], T is the absolute temperature [K], F is the Faraday constant [=96485.309(Cdmol�1)],

M. Xie et al. / Journal of Contaminant Hydrology 83 (2006) 122–147 125

e is dielectric constant and e0 the permittivity of free space [=8.854�10�12 (C V�1 m�1)].

The ionic strength I is defined (see e.g. References Stumm and Morgan (1996), Dzombak

and Morel (1990)):

I ¼ 1

2

Xi

ciz2i ð3Þ

where ci is the ith ion concentration of porewater [mol l�1], zi represents the ion valence of

the ith ion.

The number of effective layers m in one particle of an expansive mineral (i.g.

montmorillonite) is a mineral structural parameter, that is defined as the number of layers

contributing to the swelling effect. As the montmorillonite particles are very fine in size, the

average m value is used and calculated by the ratio of total specific surface area Stotal in m2 g� 1

(including the surface between layers, which can separate by swelling) to external specific

surface area S0 in m2 g� 1 (only the surface of particles).

m ¼ Stotal

S0: ð4Þ

The value Stotal is normally determined by the methylene blue and the Keeling hygroscopy

methods. The value S0 is normally measured by BET (Brunauer, Emmet and Teller N2

Adsorption) method (ASTM International, 2001a,b; FEBEX Working groups, 2000).

The nILmax represents the swelling potential of the montmorillonite minerals contained in a

compacted bentonite, it depends on the soil properties of the sample, the mineral properties of

the montmorillonite, and the chemical properties of the porewater. The amount of swelling

depends on the initial water saturation and its variation, the swelling conditions (confined or

unconfined), and the porewater chemistry variation.

According to this model, porosity in bentonite can be distinguished by inter-layer (nIL) and

interparticle porosity (nIP). The latter is of special importance for water flow, and is often called

the effective porosity. During the swelling process, the effective porosity and consequently the

effective permeability of bentonite increase in the case of free swelling and decrease in

confined conditions; this subsequently influences the chemical transport process.

2.1.2. Effective porosity

Effective porosity is the amount of interconnected pore space in a soil or rock through

which fluids can pass, expressed as a percent of bulk volume (US Bureau of Mines, 1997).

Owing to electrostatic attraction, interlayer-water in compacted bentonite is practically

immobile. Therefore, the effective porosity neff of compacted bentonite varies with the

saturation and swelling processes. In the case of confined swelling, the effective porosity

decreases with the saturation process. Theoretically, it can be reduced to zero, which means

the permeability reaches zero. However, this is not the case in practice. A fraction of the

porosity remains, which is defined here as the minimal porosity. It depends on the swelling

pressure and the compressibility of the sample. Therefore, the effective porosity of bentonite in

the case of confined swelling can be derived from the initial porosity n0, interlayer porosity

nIL and minimal porosity nmin:

neff ¼�n0 � nIL ; n0 � nILNnmin

nmin ; elseð5Þ

M. Xie et al. / Journal of Contaminant Hydrology 83 (2006) 122–147126

In the case of free swelling, the volume change should be taken into consideration by

measuring how the total porosity ntot changes with swelling/shrinking. The effective porosity

is:

neff ¼ ntot � nIL ð6Þ

However, if the water content is below the shrinkage limit, free swelling/shrinking is

limited. Macroscopically, volume change nearly vanishes. Microscopically, interlayer porosity

variation changes the interparticle porosity. In this case, Eq. (5) can be used for calculating neff.

2.2. Water in compacted bentonite

Bentonites contain a large quantity of montmorillonite (65–90 wt.%), which determines the

properties of bentonites (Bradbury and Baeyens, 2003). Owing to the special mineral structure,

the relatively high net negative charge on the mineral surface, and the extremely high value in

specific surface, water flows through large pores as well as enters into the interlayer spaces.

Diffuse double layers (DDLs) tend to build up. Bradbury and Baeyens (2003) divided the

water in bentonite into three types—interlayer water, double layer water and free water.

Interlayer water is only one to four monolayers of water molecules thick (b1 nm), and differs

apparently from bfree water Q with respect to the fluid properties (Newman, 1987; Schoen et

al., 1989). Free water exists only in large pores. The rest is the double layer water in the

electric diffuse double layers. DDLs in highly compacted bentonite can overlap. As diffusion

and chemical reactions can also occur in the DDLs, the term bentonite porewater is defined

herein as the double layer water plus free water.

2.3. Two-phase flow

2.3.1. Capillary pressure

The parameters pc(S) (capillary pressure) and krel(S) (relative permeability) are key factors

affecting multiphase flow. In a two phase system with a gas and a liquid phase, capillary

pressure is defined as difference in pressure between the gas and the liquid in capillary spaces.

It is thus a function of the degree of saturation (Helmig, 1997). The pc(S) value can be

measured for a given soil with respect to various fluids.

2.3.2. Relative permeability–saturation

For porous media containing more than one fluid, relative permeability is a key parameter.

It is used to calculate the effective permeability, which is equal to intrinsic permeability

multiplied by relative permeability. Different relationships between relative permeability and

saturation can be found in the literature. These relationships include constant value, linear

function and potential function. The van Genuchten model in conjunction with the approach

of Mualem is adopted in this study (van Genuchten, 1980; Helmig, 1997; Lenhard and

Parker, 1987):

klrel ¼ Sl12

eff 1� 1� Sl1=aeff

� �ah i2ð7Þ

Sleff ¼h � hrhs � hr

ð8Þ

M. Xie et al. / Journal of Contaminant Hydrology 83 (2006) 122–147 127

where a is the van Genuchten parameter, s and r indicate saturated and residual values of the

water content (h), respectively.

kgrel ¼ 1� Sleff

� �12 1� S

l1=aeff

� �h i2að9Þ

2.3.3. Intrinsic permeability for swelling porous media

Intrinsic permeability kintr [m2] is a property of porous material and describes the ease with

which gases or liquids can flow through the medium (Mitchell, 1993). It depends on the pore

structure of the porous media and remains constant if the soil skeleton remains unchanged. As

bentonite swells or shrinks, however, the pore structure varies and kintr varies accordingly.

A large number of studies were aimed at generating methods to independently predict

permeability in sedimentary rocks by bulk porosity (Carman, 1937; Berg, 1970; Bloch, 1991;

Neuzil, 1994). It was found that measured permeabilities of clays and shales vary over the range

of 10�22 to 10�14 m2. Oelkers (1996) suggested a correlation of intrinsic permeability with

effective porosity, which is adopted here for highly compacted bentonite. Based on this, the

intrinsic permeability kintr for highly compacted bentonite is defined as:

kintr ¼ 9:87� 10�12e�10þ8neff ð10Þ

in which neff is the effective porosity as in Eq. (5).

2.4. Geochemical reactions

2.4.1. Ion exchange

Owing to the high permanent negative charge on the surface of montmorillonite, which is

compensated by the preferential sorption of exchangeable cations on the surface layers, the

exchange capacity of montmorillonites are very high. Ion exchange is an important interaction

mechanism between ions in porewater and solid minerals, especially in highly compacted

bentonite where the volume of porewater is small and the fraction of montmorillonite is large

(Bradbury and Baeyens, 2003). Consequently, porewater chemistry can be strongly influenced

by ion exchange.

Ion exchange in soil is normally described using competitive exchange models (Stumm and

Morgan, 1996). Commonly used models are presented by Gaines and Thomas (1953), Gapon

(1933), Vanselow (1932), and Rothmund–Kornfeld (Bond and Phillips, 1990). The Gaines–

Thomas convention is the standard method of PHREEQC, which assumes that the thermody-

namic activity of an exchange species is equal to its equivalent fraction. Optionally, in PHREEQC

the equivalent fraction can be multiplied by a Debye–Huckel activity coefficient (ci) to define theactivity of an exchange species. Both Gaines–Thomas convention and the second option are

adopted for the simulations here. The coefficient (ci) is given by Appelo (1994) as:

logci ¼� Az2e

ffiffiffil

p

1þ Ba0ffiffiffil

p þ bl: ð11Þ

In this equation, ci is the activity coefficient, A and B are constants at a given temperature, lis the ionic strength, ze is the number of equivalents of exchanger in the exchange species, and a0

and b are the Debye–Huckel parameters (Parkhurst and Appelo, 1999). In the simulation, four

ions are taken into consideration for ion exchange, e.g. Na+, K+, Ca2+ and Mg2+. Na+ is taken as

M. Xie et al. / Journal of Contaminant Hydrology 83 (2006) 122–147128

the reference ion, the logK is thus set to 0. Their half reaction equations are listed in Table A.1 in

Appendix. All of the related parameters are given in the PHREEQC database and most of them

are listed in the Appendix in Table A.1.

2.4.2. Dissolution/precipitation

With dissolution and precipitation processes, the porosity n may change. This can be

expressed using:

n ¼ n0 �Xnmj¼1

VjdDMj ð12Þ

where n0 is the original porosity, DMj is change of mass concentration of mineral j, in moles per

unit volume of porous medium, Vj is the molar volume of mineral j, nm is the number of minerals.

2.4.3. Temperature dependence

Owing to nuclei decay in the canister, heat is generated and thus temperature in the buffer

material changes with the time. Therefore, it is important to investigate the temperature

influence on the geochemical reactions. Temperature dependence of reactions is taken into

account in PHREEQC2 in the following two ways, both of which modify the equilibrium

constant K as a function of temperature:

1. the van’t Hoff equation:

lnK2

K1

� �¼ DH0

R

1

T1� 1

T2

� �ð13Þ

in which, K1, K2 are reaction coefficients at temperature T1, T2 in Kelvin, respectively. In

the PHREEQC2 database, reference logK values are given at 25 8C. For example, the logK

values of the chemical reaction of Albite NaAlSi3O8+8H2O=Na++Al(OH)4�+3H4SiO4 at

different temperatures are calculated using Eq. (13) with logK at 25 8C equal to �18.002,

and DH0 equal to 25.896 kcal.

2. an analytical expression for the temperature dependence of logK:

log10K ¼ A1 þ A2T þ A3

Tþ A4log10T þ A5

T2ð14Þ

Up to five coefficients Ai (i =1,2, . . ., 5) for the equation may be specified to calculate the

logK value at a given temperature. In PHREEQC2, the second method is given priority if

parameters for both methods are provided. The logK values of the chemical reaction of

Gypsum CaSO4 :2H2O=Ca2++SO42�+2H2O at different temperatures are calculated using

Eq. (14). logK at 25 8C is �18.002, the coefficients A1, A2, A3, A4 and A5 are 68.2401,

0.0, �3221.51, �25.0627 and 0.0.

3. Governing equations

3.1. Two-phase flow

In the macroscopic model, non-isothermal two-phase flow is considered. In general, there are

two concepts to formulate the balance equations: phase-related and compositional. The

compositional approach is advantageous for multiphase-multicomponental processes with phase

M. Xie et al. / Journal of Contaminant Hydrology 83 (2006) 122–147 129

changes (Gawin et al., 1995; Gens et al., 1998), and is adopted for this study. The porous

medium is conceptualized as a three component system, with the components air, water, and soil.

Each of these components can be present in three phases (gas, liquid and solid phase). In this

study, air and solid are treated as single pseudo components with averaged properties, even if

they consist of several components. In the following equations, the subscript k denotes

component (a—air or w—water), the superscript c denotes the phase (l—liquid, g—gas,

s—solid).

Hydraulic processes resulting from pressure, friction, and gravitation are described by the

extension of Darcy’s law for multiphase flow. The mobility of the fluid phases is

characterized by their relative permeability and capillary pressure via saturation. The mass

balance equation is:

B

BtnSgqg

k þ nSlqlk

� �þjd J

gk þ Jlk

� �¼ Qk ð15Þ

where n is porosity, Sc is phase saturation, qkc is component mass per unit volume of the

fluid phase c. The total flux of component k in phase c consists of advective JAkc

and

diffusive part JDkc.

Jck ¼ J

cAk þ J

cDk ð16Þ

The heat balance equation for porous medium consisting of three phases (solid, gas, liquid) is

described by

B

Bt1� nð Þqsus þ nSgqgug þ nSlqlul

� þjd Jsh þ J

gh þ Jlh

� �¼ Qh ð17Þ

where uc is phase internal energy, qc is phase density, Jhc is the total heat flux in phase c, Qh is

the heat source term, i.e. heat generation rate per unit volume.

Details can be found in Gawin et al. (1995), Helmig (1997) and Kolditz (2002).

3.2. Multicomponent transport

The balance equation for multicomponent mass transport in porous media is given by e.g.

Kolditz (2002):

nSc BCci

Bt¼ � vcjC

ci þj nScD

cijC

cið Þ þ nScQ

ci þ nScCc

i Cc1 . . .C

cm

� �ð18Þ

where Cic is the concentration of the i-th species of an m multi-species system in phase c, vc is

the Darcy velocity of phase c, Dic is the diffusion–dispersion coefficient of component i in

phase c, Qic is the source/sink term and Ci

c(C1c. . .Cm

c) is the source/sink term of species i in

phase c due to temperature dependent equilibrium chemical reactions with all other species

in the same phase.

3.3. Coupling scheme and numerical implementation

The object-oriented program GeoSys/RockFlow was adopted to solve the system of

coupled processes. The coupling processes are schematically described in Fig. 1. Time is

Fig. 1. Schematic representation of the coupling concept used in GeoSys/RockFlow.

M. Xie et al. / Journal of Contaminant Hydrology 83 (2006) 122–147130

discretized using Euler timesteps, spatial discretization is by the Finite Element Method. For

each timestep, two-phase flow and heat transport are calculated. Because these two processes

are strongly coupled via material properties, the program iterates between them (Kolditz and

de Jonge, 2004). Reactive mass transport is separated using an operator splitting technique and

a two-step non-iterative sequential approach. In the first step, conservative transport is

calculated for all chemical components based on the phase velocities calculated for two-phase

flow, while in the second step the geochemical reactions are simulated. In this work, transport

and reactions are calculated only in the liquid phase. For the reaction step, the geochemical

program PHREEQC2 (Parkhurst and Appelo, 1999) is employed (Bauer et al., 2004), which

calculates the geochemical reactions accounting for the temperature dependence of the reaction

coefficients. The GeoSys/RockFlow simulator is designed using object-oriented and process-

oriented methods (Kolditz and Bauer, 2004), which allows the coupling of two-phase flow,

heat transport, mass transport, chemical reactions and deformation in an efficient way (Wang

et al., 2005).

4. Application

4.1. Experiment description

The test presented here is based on an experiment, in which highly compacted bentonite

was simultaneously subjected to heating and hydration (Cuevas et al., 1997) in order to

investigate changes in porewater chemistry resulting from thermal gradients and hydration

M. Xie et al. / Journal of Contaminant Hydrology 83 (2006) 122–147 131

processes. A schematic cross-section of the cylindrical experimental apparatus is shown in

Fig. 2.

The highly compacted bentonite was heated by the plane heater at the top (constant 100 8C ).

At the bottom, deionized water was supplied through two hydration ports joined to a porous

plate. After 15 h of heating, a thermal steady-state was reached. The isotherms are almost

parallel to the heater surface in the range of 100 8C (at the top) to 65 8C (at the bottom). The test

lasted for 2619 h. After that, the sample was divided into 5 sections (parallel to the heater

surface), which were numbered from top to the bottom. By measuring these sections, the

distribution of the final water content was determined. Additionally, the chemical compositions

of solid samples from all sections and porewater from some sections were analyzed. The samples

in sections 1 and 2 were so dry that no porewater could be extracted by exerting a constant

pressure of 60 MPa. Therefore, only solid samples from these two sections were chemically

analyzed (Cuevas et al., 1997).

4.2. Material properties

The material properties of the highly compacted bentonite used for the simulations are

summarized in Table 1.

For simulating multiphase flow, the capillary pressure–saturation and relative permeability–

saturation relationships are key material parameters. Owing to the high capillary pressure in

bentonite as shown in Fig. 3 (Kolditz and de Jonge, 2004), a large suction pressure is initiated,

that strongly favors saturation of the sample from the bottom. The dual relative permeability

model presented by Olivella and Gens (2000) is adopted herein for the modelling. This model is

based on experimental evidence showing different relative permeabilities for gas and liquid in a

two-phase flow system as described in Fig. 3.

Fig. 2. Schematic representation of the thermal hydraulic cell.

Table 1

Material properties of bentonite

Symbol Value Unit

Initial dry density qd 1620* kg/m3

Initial porosity n0 39.6* %

Initial water content w 11.2* %

Intrinsic permeability k intr 5�10�19 m2

Total specific surface S0 37* m2/g

External specific surface S total 516F37z m2/g

Specific heat capacity c 1605.06 J/kg/K

Thermal conductivity k 0.78** W/m/K

*From Cuevas et al. (1997).

**From Olivella and Gens (2000).

zFrom FEBEX Working groups (2000).

M. Xie et al. / Journal of Contaminant Hydrology 83 (2006) 122–147132

4.3. Geochemical properties

The geochemical properties of the bentonite according to the experimental results by Cuevas

et al. (1997) and Villar et al. (1995) are summarized in Table 2. Plagioclase is the group name for

triclinic feldspars of the general formula:

Ca1�xNaxAl2þxO8 ð19Þ

in which x is between 0 and 1. When x =0, the mineral is pure anorthite. When x =1, the mineral

is pure albite. In the simulation, albite is used to represent plagioclase. Minerals comprising less

than 1% by weight are not listed. However, experimental (Muurinen and Lehikoinen, 1999) and

theoretical (Wersin, 2003) results showed that porewater chemistry can be significantly

influenced by the dissolution of gypsum, halite and calcite, which are normally of minor quantity

in bentonite. This is because of their relatively large dissolution rates compared to other minerals

like montmorillonite, quartz, etc. Therefore, a gypsum content of 0.14% is used for the

Fig. 3. Capillary pressure–saturation relationship (left), and dual relative permeability–saturation relationships (right) for

the compacted bentonite (Kolditz and de Jonge, 2004).

Fig. 4. The general model set-up for 1D single-phase simulations.

Table 2

Geochemical properties of bentonite

Mineralogy* (in weight percent) Ion concentration (mmol/L ) in porewater (reference, 25 8C)**

Montmorillonite 92 Ca2+ 14.35

Cristobalite 2 K+ 0.28

Quartz 2 Na+ 105.48

Plagioclase 3 Mg2+ 45.25

Calcite 1 Cl� 185.33

Gypsum 0 (0.14z) SO42� 15.51

HCO3� 2.79

SiO2(aq) 0.20

pH 7.2

Exchangeable cations** (in meq/100 g ) Free silica and soluble salts in the 1 :4 extract (ppm of dry sample)**

Ca2+ 34–46 SiO2(aq) 159–433

Mg2+ 24–35 Cl� 249–433

Na+ 19–26 SO42� 232–391

K+ 2–3

Total 77–101

* From Villar et al. (1995).

** From Cuevas et al. (1997).

z From FEBEX Working groups (2000).

M. Xie et al. / Journal of Contaminant Hydrology 83 (2006) 122–147 133

simulations (FEBEX Working groups, 2000). If gypsum is ignored, the concentration of SO4�2

decreases dramatically, contradicting the experimental data.

5. Results and discussions

5.1. Non-isothermal reactive transport in single-phase flow

Given the symmetrical structure of the experiment, i.e. the sample dimensions and

boundary conditions, and the almost symmetrical distribution of the experimental results, the

model set-up was simplified and one-dimensional simulations were undertaken. The 0.13 m

long column was divided into 50 elements.

The model set-up with boundary conditions for the one-dimensional single-phase

simulations is shown in Fig. 4. In the experiment, water from the bottom was driven by

capillary pressure of the unsaturated bentonite. This process was simplified in this step by

assuming a Darcy velocity of 1.273�10�8 m/s, which is equivalent to one complete pore

volume through the sample within 2619 h. This velocity was derived by using the pressure

gradient as imposed by the boundary conditions and the hydraulic conductivity of the

M. Xie et al. / Journal of Contaminant Hydrology 83 (2006) 122–147134

specimen. During the experiment the water saturation changed up to 0.12 m from the bottom.

Using a Darcy velocity equal to one pore volume over the entire routine ensured that the water

should travel at least to this point (x =0.12 m).

To simulate the reactive transport process observed in the experiment, reasonable

geochemical reactions were set up according to the changing chemical compositions of

porewater observed in the experiment. That is because simulating porewater chemistry by

using the mineral composition listed in Table 2 might give different results because some

minor components that strongly influence the short-term porewater chemistry are not included.

In this study, geochemical reactions were simulated using PHREEQC2. The reactions

accounted for in the simulation were aquatic reactions in porewater, ion exchange and

equilibrium dissolution/precipitation.

Model results are shown in Fig. 5. In the first case (Fig. 5, left side), the reaction system

does not include dolomite and therefore no dolomite appears during the simulation. If

dolomite is included in the reaction system (Fig. 5, right side), calcite dissolves completely

and dolomite precipitates, which disagrees with the experimental observations, where no

dolomite was found. Therefore dolomite was excluded from the reaction system. This result

demonstrates that great care has to be taken to define a consistent reaction system before

starting the reactive transport simulations.

The important reactions and aqueous species related to the minerals in Table 2 are selected

from the PHREEQC2 database (Parkhurst and Appelo, 1999). It is important to note that the

database for the simulation was extracted from the one provided by PHREEQC2; only those

reactions and data that were used in the simulation were selected. This improves the efficiency

of the calculations and avoids unreasonable reactions. This data is listed in Tables A.2 and A.3

in the Appendix.

After these preliminary studies, the simulation was undertaken by using a 1D non-

isothermal saturated model. The ionic concentrations in porewater, the quantity of minerals,

and the exchangeable ion concentration were used as initial conditions (Table 2). Distilled

water entered from one end (x =0.0 m) and flowed through the specimen. The simulation with

heat transport was performed to show the temperature effect on reactive transport. The model

set-up is as shown in Fig. 4, except that an initial temperature of 30 8C and boundary

Fig. 5. Distribution of ions in porewater at 122.7 days by 1D simulation with PHREEQC2-without dolomite (left), with

dolomite (right) in the reaction system.

Fig. 6. Comparison of isothermal with non-isothermal reactive transport (GeoSys/RockFlow)–distribution of ions in

porewater at 110 days.

M. Xie et al. / Journal of Contaminant Hydrology 83 (2006) 122–147 135

conditions of 100 8C at the top and 65 8C at the bottom are used, corresponding to the steady-

state conditions observed in the experiment after about 15 h. With heat transport, the

concentration of most ions in porewater were about 30% higher than without heat transport

(Fig. 6). Only HCO3� concentration decreases slightly because of the heat transport.

The simulation results obtained using the 1D non-isothermal reactive transport in single-

phase flow are compared with the experimental data in Fig. 7. Large differences exist between

them. Simulated ionic concentrations at 110 days are much lower than the measured values (at

110 days). Because water with lower ion concentrations is replacing water with higher ion

concentrations during the simulation, this shows that simulated mass transport is much faster

Fig. 7. Comparison to the experimental (Exp, Cuevas et al., 1997) and simulated (RF) distribution of ions in porewater a

110 days-non-isothermal reactive transport.

t

Fig. 8. Mineral dissolution/precipitation (left), and porosity change (right) for the compacted bentonite.

M. Xie et al. / Journal of Contaminant Hydrology 83 (2006) 122–147136

than in the experiment. This discrepancy is due to the hydraulic simplification of using single-

phase flow instead of two-phase flow.

Due to mineral dissolution and/or precipitation, the porosity of bentonite changes with time.

Especially for almost insoluble minerals like quartz or montmorillonite, this process is very slow.

Effects on such minerals are not observable within the short duration of the experiment. On the

other hand, dissolution/precipitation reactions of more soluble minerals are observable. The

calculated concentrations of two minerals – calcite and albite that are comparatively soluble–are

shown in Fig. 8. In the simulation, Calcite was dissolved at the injection end of the sample and

slight precipitation occurred in the middle of the sample. Dissolution of Albite occurred also at the

injection end of the sample, but no precipitation was observed. The calculated total porosity

change along the sample due to dissolution or precipitation of all minerals considered in the

model is an increase of 0.032. The initial total porosity was 0.396 (Fig. 8 (right)).

5.2. Isothermal and non-isothermal reactive transport with multiphase flow

The model set-up for the simulation of 1D non-isothermal reactive transport with multiphase

flow is shown in Fig. 9. As an intermediate step towards this model, a 1D submodel similar to

that in Fig. 9, but without heat transport, was also calculated. In this case, the temperature at

both ends of the specimen was set to 303 K, the same as the initial temperature.

Fig. 9. Model set-up for 1D non-isothermal reactive transport in multiphase flow.

Fig. 10. Liquid phase saturation distribution and temperature for the 1D isothermal saturation process.

Fig. 11. Liquid phase saturation (left) and temperature distribution (right) for the 1D non-isothermal saturation

process.

M. Xie et al. / Journal of Contaminant Hydrology 83 (2006) 122–147 137

5.2.1. Saturation processes

In the unsaturated bentonite, high capillary pressure exists and causes the water to flow

upwards from the bottom into the specimen. The temperature was set constant 303 K.

Distribution of liquid phase saturation along the specimen increases from the bottom of the

sample and after about 87 days, the saturation process reaches a steady state (Fig. 10).

In the case of non-isothermal saturation, the effect of heat on two-phase flow is

important. It was observed in the experiment that a thermal steady state was reached

within one day. For the remaining 108 days, flow and reactions took place under thermal

steady-state condition. Therefore, the temperature boundary conditions for the model were

simplified and set to 373 K at the top (heater) and 338 K at the bottom. These are not

the exact boundary conditions of the experiment, which has only a heat source on the

M. Xie et al. / Journal of Contaminant Hydrology 83 (2006) 122–147138

top, but they are suitable boundary conditions to model the temperature distribution along

the specimen at steady state. After about 1.16 days, a steady-state temperature was almost

reached in the simulation (Fig. 11). Distribution of liquid phase saturation along the

specimen increased from the bottom to top in the calculation but initially decreased at the

top (near the heater) of the specimen (Fig. 11). After about 87 days, the whole model

was fully saturated. For times larger than 10 days, the modelled saturations obtained

under isothermal and under non-isothermal conditions differ only slightly.

5.2.2. Reactive transport

Concurrently with the saturation process, chemical components were transported along the

specimen in the liquid and gas phases. However, the dominating mode of reactive transport of

ions was in the liquid phase. It was therefore assumed that ion transport occurs only in the

liquid phase. As the liquid saturation was less than 1.0, the amount of mass transported is less

than in saturated specimens if flow velocities are the same.

In the case of reactive transport in isothermal multiphase flow, cations and anions move

along the specimen and can cause temporary local non-equilibrium. However, chemical

reactions between solid phases and solution restores equilibrium. The simulated evolutions of

ionic (Na+ and HCO3�) concentration distributions along the specimen during the transport

process are shown in Fig. 12. It is apparent that the concentration near the bottom decreased

owing to the injection of pure water. The Na+ concentration remained below the start value,

whereas the HCO3� concentration increased above the start value. Note, the start values differ

from the given initial concentrations because of the first chemical reaction calculation at the

start time, which equilibrates the geochemical system.

The simulation results for non-isothermal multiphase flow are different as shown in Fig. 13.

The effect of heat on reactive transport can be clearly seen by comparison of the HCO3�

concentration distributions in Fig. 12 (right) and Fig. 13 (right). The concentration of Na+

increased above the start value as shown in Fig. 13 (left), unlike the result of the isothermal

condition in which Na+ remained below the start value (Fig. 12 (left)). The concentrations of

HCO3� at all times (Fig. 13 (right)) were higher than those in the isothermal condition (Fig. 12

(right)). An overview of the effect of heat on the reactive transport is shown in Fig. 14 by

comparing the concentrations of all cations and anions along the specimen after about 110

Fig. 12. Na+ (left) and HCO3� (right) concentration assuming a constant temperature distribution in the case of isothermal

reactive transport.

Fig. 14. Ion distribution for isothermal and non-isothermal reactive transport after 110 days.

Fig. 13. Na+ (left) and HCO3� (right) concentration in the case of non-isothermal reactive transport in multiphase

flow.

M. Xie et al. / Journal of Contaminant Hydrology 83 (2006) 122–147 139

days in the case of isothermal and non-isothermal reactive transport. Additionally, a non-

reactive tracer was included in the simulation, in order to show the effect of heat on mass

transport alone. This effect observably is small. The ions Na+ and Ca2+, however, are more

strongly affected, making the effect of heat on the chemical reactions readily apparent.

5.2.3. Comparison of simulated with experimental results

The simulation results using the 1D non-isothermal reactive transport model with

multiphase flow are compared with the experimental data in Fig. 15. Some of the modelled

elemental concentrations agree well with the experimental data, especially Mg, Ca, Cl and K.

On the other hand, the modelled elemental concentration for C is too low in comparison to

the measured value. This may be because gases like CO2 in the enclosed system are not

included in the simulation. The concentration of element S was lower in the modelled results

although 0.14% gypsum was included in the simulation (Table 2). In general, the modelled

Fig. 15. Comparison of experimental (EXP—Cuevas et al., 1997) and simulated results at 110 days by non-isothermal

reactive transport in two-phase flow.

M. Xie et al. / Journal of Contaminant Hydrology 83 (2006) 122–147140

concentration values of all elements are lower than the measured data, that is because the

simulated moisture distribution is higher than that measured in the experiment.

5.3. Discussion

The experimental saturation distribution after 2619 h (about 109.1 days) is 100% at the

bottom and 43.1% on the top. However, the modelled result presented in Fig. 11 shows a

fully saturated state after 86.8 days. That shows that the simulated saturation process was

faster than that observed in the experiment. One reason for this difference might be the rapid

evaporation at the heated end (about 100 8C). Another possible cause of the discrepancy is

the swelling effect of bentonite during the moisture transport process (Agus and Schanz,

2004; Xie et al., 2004). A simulation taking swelling into account was executed using the

same model set-up as for the non-isothermal reactive transport with multiphase flow (Fig. 9).

The only difference was that the effective porosity and thus the effective permeability

changed with increasing water saturation. Most parameters used for the simulation are

Fig. 16. Swelling effect on saturation (left) and effective porosity (right).

Fig. 17. HCO3� concentration in the case of non-isothermal reactive transport in multiphase flow, including CO2.

Fig. 18. Na+ concentration in the case of non-isothermal reactive transport in multi-phase flow excluding ion

exchange.

M. Xie et al. / Journal of Contaminant Hydrology 83 (2006) 122–147 141

summarized in Tables 1 and 2. Two additional parameters were used: the effective layer

number m was set at 14, and the ionic strength I was set at 0.28—the value of the initial

porewater calculated by PHREEQC2. The changing water saturation and effective porosity

along the specimen are shown in Fig. 16. The saturation process is clearly slower than the

one shown in Fig. 11.

Once the bentonite is exposed to atmospheric conditions (rain, air), gaseous CO2 will be

present. This gas influences the equilibrium of carbonate and acts as a chemical buffer. In the

experiment the bentonite was installed in an enclosed system. Therefore, the initial amount of

CO2 can be changed by reactions. A simulation including CO2 (partial pressure PCO2assumed

to be 10�3.5 according to Bradbury and Baeyens (2003) in the reaction system is shown in

Fig. 17. In comparison to the simulated data in Fig. 13, this simulation predicts a higher

carbon concentration at the bottom of the sample, and lower concentration at the upper end of

the sample where the temperature is higher.

M. Xie et al. / Journal of Contaminant Hydrology 83 (2006) 122–147142

Owing to the extremely large specific surface area and net negative change on the surface

of montmorillonite, activities at the mineral–water interfaces like ion exchange are essential

for the reactive transport in bentonite materials (Herbert and Moog, 1999; Wersin, 2003). In

the simulation mentioned, only ion exchange between Na+, K+, Ca2+ and Mg2+, which

proved to be the most important forms (Wersin, 2003), were considered. Proton exchange is

not included in the reactions, because the simulated pH value is high (N8.0). A high pH, this

mechanism can be neglected (Appelo, 1994). If ion exchange is not considered, the chemical

reactions system is very different, which can be clearly seen by the comparison of the Na+

concentration distribution including ion exchange in Fig. 13 with that excluding ion exchange

in Fig. 18. In the later case, the initial concentrations and those at different times are much

lower than those with ion exchange.

6. Summary and conclusions

A two-phase and non-isothermal multi-species reactive transport model has been

developed and implemented in the object-oriented and process-oriented simulator GeoSys/

RockFlow. Geochemical reactions are incorporated by coupling of GeoSys/RockFlow to the

geochemistry code PHREEQC2. This allows the simulation of the complex behaviour of

bentonite, which is used as buffer material for underground storage of high level nuclear

waste. The code was applied to simulate an experiment by Cuevas et al. (1997), in which a

sample of highly compacted bentonite was simultaneously heated and hydrated and where

geochemical data at the end of the saturation process were measured.

During the simulations it was found that the definition of a consistent system of chemical

reactions is of major importance. It was observed that during the experiment the highly

soluble minerals like calcite, halite and gypsum strongly determined the porewater chemistry.

However, as these minerals formed only a very small fraction of the bentonite, their fractions

were not determined by Cuevas et al. (1997). As a result, it was necessary to deduce the

reactions from the chemical composition of the bentonite as well as from the experimentally

observed geochemical reactions. This limited the usefulness of this experiment for the

verification of our model.

By starting the numerical simulations with isothermal single-phase flow and increasing the

complexity stepwise to non-isothermal two-phase flow, the effects of the individual processes

on the observed ion distribution at the end of the experiment could be identified. It is found

that both two-phase flow and heat transport have to be included to obtain a good fit between

the simulated and measured values. Temperature affects two-phase flow via the material

parameters and by evaporation occurring at the heater, both enhancing the flow rate.

Geochemical reactions are affected via the reaction coefficients, which typically cause higher

ion concentrations in porewater compared to the case of a constant temperature. Due to the

relatively short duration of the experiment, the porosity change caused by mineral dissolution/

precipitation remained very small. By conducting model runs with and without allowing for

ion exchange it could be shown that ion exchange plays a major role in the studied

geochemical environment, causing significantly higher concentrations of ions in porewater.

Swelling is an important phenomenon in bentonite. With swelling under constrained

conditions, effective porosity and thus effective permeability of the bentonite change. The

swelling potential can also be influenced by variation of the chemical composition of the

bentonite. In the simulations, it was shown that swelling significantly slows down the

saturation process, because swelling reduces the porosity in the bentonite sample. However,

M. Xie et al. / Journal of Contaminant Hydrology 83 (2006) 122–147 143

detailed measurements of the required parameters for swelling would be required to draw

further conclusions. For a better verification of the conceptual and mathematical model, a

well designed experiment would be helpful, where all parameters needed for the simulation

are determined a priori and the measurements are performed in accordance with sensitivities

identified in preliminary modelling studies.

Acknowledgements

The work is supported by the German Federal Institute for Geosciences and Natural

Resources (BGR) and partly by the German Federal Ministry of Education and Research

(BMBF). We thank Dr. Wallner (BGR) for his support of this research work and Robert Walsh

(ZAG) for improving the manuscript.

Appendix A

The following data are extracted from the PHREEQC2 database (Parkhurst and Appelo,

1999). During the simulation, the database includes only the data used for the calculation.

This helps to improve the efficiency of the calculation and more importantly to avoid

unreasonable reactions.

Table A.1

Equations and parameters for ion exchange

Ion Equation LogK DH0 Debye–Huckel parameters

25 8C kcal a0 b

Na+ Na++X�=NaX 0.0 –

K+ K++X�=KX 0.7 �4.3 3.5 0.015

Ca2+ Ca2++2X�=CaX2 0.8 7.2 5.0 0.165

Mg2+ Mg2++2X�=MgX2 0.6 7.4 5.5 0.2

All data are from PHREEQC2 database Parkhurst and Appelo (1999).

Table A.2

Mineral hydrolysis reactions and equilibrium constants

Mineral Hydrolysis reaction LogK DH0

25 8C kcal

Albite NaAlSi3 O8+8H2O=

Na++Al(OH)4�+3H4SiO4

�18.002 25.896

Ca– Ca0.165 Al2.33Si3.67O10(OH)2+12H2O

Montmorillonite =0.165Ca2++2.33Al(OH)�4 �45.027 58.373

+3.67H4SiO4+2H+ �45.027 58.373

Cristobalite SiO2+2H2O=H4SiO4 �3.587 5.5

Calcite CaCO3=CO32� +Ca2+ �8.48 �2.297

Gypsum CaSO4:2 H2O=Ca2++SO42�+2H2O �4.58 �0.109

Quartz SiO2+2H2O=H4SiO4 �3.98 5.990

All data are from PHREEQC2 database Parkhurst and Appelo (1999).

Table A.3

Aqueous species and formation constants used in the modelling

Aqueous species Formation reaction LogK DH0

25 8C kcal

CO32�

HCO3� CO3

2�+H+=HCO3� 10.329 �3.561

Al3+

AlOH2+ Al3+H2O=AlOH2++ H+ �5.0 11.49

Ca2+

CaOH+ Ca2++H2O=CaOH++H+ �12.78 –

H+

OH� H2O=OH�+H+ �14.0 13.362

Cl�

K+

Mg2+

Na+

SO42�

HSO4� SO4

2�+H+=HSO4� 1.988 3.85

SiO2(aq)

H4SiO4 SiO2(aq)+2H2O=H4SiO4 �2.71 3.340

CO2(g) CO2(g)=CO2(aq) �1.468 5.5

All data are from PHREEQC2 database Parkhurst and Appelo (1999).

M. Xie et al. / Journal of Contaminant Hydrology 83 (2006) 122–147144

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