A comparative study of the modelling of cement

Applied Geochemistry xxx (2011) xxx–xxx

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Applied Geochemistry journal homepage: www.elsevier.com/locate/apgeochem

A comparative study of the modelling of cement hydration and cement–rock laboratory experiments David Savage a,⇑, Josep M. Soler b, Kohei Yamaguchi c, Colin Walker c, Akira Honda c, Manabu Inagaki c, Claire Watson a, James Wilson a, Steven Benbow a, Irina Gaus d, Joerg Rueedi d a

Quintessa Ltd., The Hub, 14 Station Road, Henley-on-Thames, RG9 1AY, UK Institute of Environmental Assessment and Water Research (IDAEA-CSIC), Jordi Girona 18-26, 08034 Barcelona, Spain Japan Atomic Energy Agency (JAEA), Tokai-mura, Naka-gun, Ibaraki-ken 319-1194, Japan d Nagra, Hardstrasse 73, Wettingen CH-5430, Switzerland b c

a r t i c l e

i n f o

Article history: Received 23 December 2010 Accepted 6 April 2011 Available online xxxx Editorial handling by R. Fuge

a b s t r a c t The use of cement and concrete as fracture grouting or as tunnel seals in a geological disposal facility for radioactive wastes creates potential issues concerning chemical reactivity. From a long-term safety perspective, it is desirable to be able model these interactions and changes quantitatively. The ‘Long-term Cement Studies’ (LCS) project was formulated with an emphasis on in situ field experiments with more realistic boundary conditions and longer time scales compared with former experiments. As part of the project programme, a modelling inter-comparison has been conducted, involving the modelling of two experiments describing cement hydration on one hand and cement–rock reaction on the other, with teams representing the NDA (UK), Posiva (Finland), and JAEA (Japan). This modelling exercise showed that the dominant reaction pathways in the two experiments are fairly well understood and are consistent between the different modelling teams, although significant differences existed amongst the precise parameterisation (e.g. reactive surface areas, dependences of rate upon pH, types of secondary minerals), and in some instances, processes (e.g. partition of alkali elements between solids and liquid during cement hydration; kinetic models of cement hydration). It was not conclusive if certain processes such as surface complexation (preferred by some modellers, but not by others) played a role in the cement–rock experiment or not. These processes appear to be more relevant at early times in the experiment and the evolution at longer timescales was not affected. The observed permeability profile with time could not be matched. The fact that no secondary minerals could be observed and that the precipitated mass calculated during the simulations is minor might suggest that the permeability reduction does not have a chemical origin, although a small amount of precipitates at pore throats could have a large impact on permeability. The modelling exercises showed that there is an interest in keeping the numerical models as simple as possible and trying to obtain a reasonable fit with a minimum of processes, minerals and parameters. However, up-scaling processes and model parameterisation to the timescales appropriate to repository safety assessment are of considerable concern. Future modelling exercises of this type should focus on a suitable natural or industrial analogue that might aid assessing mineral–fluid reactions at these longer timescales. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction The use of cement and concrete as fracture grouting or as tunnel seals in a geological disposal facility for radioactive wastes creates potential issues concerning chemical reactivity. The elevated pH (pH > 11) of pore fluids in such materials can lead to the instability ⇑ Corresponding author. Present address: Savage Earth Associates Limited, 32 St. Alban’s Avenue, Queen’s Park, Bournemouth BH8 9EE, UK. Tel./fax: +44 1202 514304. E-mail address: [email protected] (D. Savage).

of minerals in the host formation, due to OH accelerated hydrolysis reactions, increased solubility of primary minerals and precipitation of secondary solids. Accompanying this increased reactivity may be changes in physical properties, such as porosity and/or permeability. From a long-term safety perspective, it is desirable to be able to model these interactions and changes quantitatively. Such modelling has been carried out by a number of authors over the last 20 a. Early studies of cement–rock modelling used closed system reaction-path models (no transport) to evaluate potential mineral parageneses and porosity changes (e.g. Fritz et al., 1988; Savage and Rochelle, 1993). A temporal mineral

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Please cite this article in press as: Savage, D., et al. A comparative study of the modelling of cement hydration and cement–rock laboratory experiments. Appl. Geochem. (2011), doi:10.1016/j.apgeochem.2011.04.004

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D. Savage et al. / Applied Geochemistry xxx (2011) xxx–xxx

alteration sequence of calcium silicate hydrate (C–S–H), followed by zeolites and feldspar was predicted. Porosity increases for Na– K–Ca–OH fluids and decreases for Ca(OH)2 fluids were predicted, respectively. The effects of transport were first included in attempts to predict the interaction of cement with clay at shallow sites for the disposal of radioactive waste in the UK. (Haworth et al., 1988). A (conservative) migration distance for alkaline alteration of 5 m after 1 ka was calculated (assuming a pore water velocity of 1010 m s1). The ‘quasi-stationary steady-state’ approach to water–rock interaction modelling was applied to cement pore fluid migration by Lichtner and Eikenberg (1994), using the MPATH code to investigate the migration of cement pore fluids through a ‘marl’ at a potential repository site in Switzerland. The rate of plume migration was predicted to be 1–2 orders of magnitude less than that of the groundwater (the latter travelling at an assumed rate of 1 m/a). Steefel and Lichtner (1994, 1998) investigated reactions in an alkali-filled fracture in a marl host rock. Simulation of diffusion of fluid into the rock matrix suggested that the matrix porosity could be filled by calcite precipitation within 10–500 a. A slight increase in porosity adjacent to the fracture was also calculated. Since 2000, attention has been aimed more at understanding the interaction of cement pore fluids with clay, with a whole plethora of publications addressing clay used in engineered barriers (e.g. Savage et al., 2002; Gaucher et al., 2004; Metcalfe and Walker, 2004; Michau, 2005; Fernández et al., 2007; Ueda et al., 2007; Watson et al., 2009; Yamaguchi et al., 2007), or in clay host rocks (Adler, 2001; De Windt et al., 2008; Soler, 2003). These investigations concluded that mineral alteration is likely to proceed through a reaction sequence involving C–S–H, zeolites and clays, leading to a closure of porosity over timescales from hundreds to thousands of years. The physical scale of alteration has been calculated to be in the order of a few cm to a few m, depending on the exact composition of the cement pore fluid and timescales. Studies carried out in the last 10 a related to the understanding of the interactions of cement pore fluids with fractured hard rocks have been those associated with the ‘Hyperalkaline Plume in Fractured Rock’ (HPF) Experiment at the Grimsel Underground Laboratory in Switzerland (Soler and Mäder, 2007; Soler et al., 2006), and those associated with the development of the Onkalo facility in Finland (Montori et al., 2008). The HPF studies highlighted that dissolution of primary minerals was kinetically-controlled, but there were difficulties in establishing reactive surface areas for minerals a priori, both in simulations of the field and laboratory experiments. Montori et al. (2008) noted that the rock generally did not have sufficient reactivity to significantly reduce the pH of the circulating solutions within the calculation domain. However, there was some reduction of pH for: the slowest flow conditions; the lowest pH cases; when Mg-containing secondary minerals were included in the calculations; and when reactive surface areas of the primary minerals were large (due, for instance, to the presence of fault gouge). Many of these studies have highlighted difficulties in scaling reactive surface areas, not only as applied to mineral dissolution (Hoch et al., 2004; Soler et al., 2006; Soler and Mäder, 2007), but also to mineral growth (Watson et al., 2009). The incorporation of geometric or BET surface areas in simulations to model mineral dissolution has led to the overestimation of reaction rates by up to two orders of magnitude (Hoch et al., 2004; Soler et al., 2006; Soler and Mäder, 2007). The issues associated with the up-scaling of laboratory-derived kinetic data to model at the natural system scale has previously been encountered during the evaluation of weathering in groundwater catchments in granitic rocks (e.g. White and Brantley, 1995, 2003). In these studies, it is wellestablished that mineral dissolution rates calculated from mass

fluxes in groundwater are 2–3 orders of magnitude less than those measured in the laboratory. Consequently, it may be appropriate to consider these natural systems data (with relevant corrections for pH dependence and solution saturation state) for up-scaling the modelling of cement–rock interactions in natural fractured rock systems. The LCS Experiment is one of a number of in situ tests being conducted at the Grimsel Underground Laboratory in Switzerland, hosted by the Swiss radioactive waste management organisation, Nagra. The ‘Long-term Cement Studies’ (LCS) project was formulated with an emphasis on in situ field experiments with more realistic boundary conditions and longer time scales compared with preceding experiments. The overall aim of the LCS project is to increase the understanding of high-pH cement interaction effects in the repository near field and the geosphere in order to make confident, robust, and safety-relevant statements concerning the future system behaviour, irrespective of repository host rock, engineered barrier system (EBS), and waste type. As part of the project programme, a modelling inter-comparison has been conducted, involving modelling teams representing the NDA (UK), Posiva (Finland), and JAEA (Japan). This model inter-comparison is described in more detail below. 2. Model test cases To start up the modelling activities in the LCS project it was agreed upon to model two different examples of water–rock– cement interactions. The purpose of this modelling was not to perform a classical benchmark exercise whereby all modellers use exactly the same processes and parameters to model a certain case. Here, it is assumed that the computer codes are working adequately and that simulating exactly the same problem would not lead to significantly different outcomes. The comparison described here aims at the conceptual interpretation of the problem, the assumptions that are made, and the processes that are thought to be needed to obtain a good fit. The comparison thus tells us how unique the models are in matching the observations, and in how far the experiments are capable of discriminating processes involved. There are not many well-documented cement interaction experiments that serve the above-described purpose. Two examples were selected: firstly, a cement hydration experiment (Lothenbach and Winnefeld, 2006), because it illustrates the complex chemical behaviour of the cement hydration process (both solid and liquid phase) and the need to include adapted kinetic rate laws; and secondly, the HPF core experiment (Soler and Mäder, 2007), because it is a well-defined experiment with high-quality and high-resolution experimental data. 2.1. Cement hydration experiment The cement hydration experiment is a batch experiment focusing on the hydration behaviour of OPC. The experiment, as well as the modelling, is described in Lothenbach and Winnefeld (2006). The experiment was carried out using an ordinary Portland cement (OPC), CEM I 42.5N, at 20 °C for a duration of 10,000 h. The composition of the cement and the calculated amount of the clinker phases in the unhydrated cement are compiled in Tables 1 and 2 of Lothenbach and Winnefeld (2006). Distilled water was used as an initial fluid. At certain intervals, both the pore solution as well as the solids were sampled. The extent of cement hydration was estimated using XRD analysis and the evolution of the composition of the pore solution was monitored through chemical analysis. The modelling exercise was based on: the measured composition of the OPC (cf. Tables 1 and 2 in Lothenbach and Winnefeld, 2006); defined dissolution rates of the clinker phases; a thermodynamic


3


model, ideally based on the Nagra/PSI Chemical Thermodynamic Database (Hummel et al., 2002), complemented with additional data for solids that are expected to form under cementitious conditions (thermodynamic constants used are summarised in the Appendix of Lothenbach and Winnefeld, 2006). 2.2. HPF core experiment Within the framework of the HPF project (‘Hyperalkaline Plume in Fractured Rock’) at the Grimsel Test Site (Switzerland), a small-scale core infiltration experiment was performed at the University of Bern (Soler and Mäder, 2007). In this experiment, a high-pH (K–Na–Ca–OH) solution (ionic strength 0.2 mol/kg, pH: 13.36, T = 15 °C) was continuously injected under a constant pressure gradient into a cylindrical core of granite containing a fracture (see Fig. 1) and collected for analysis at the outlet. The fracture was approximately planar, 5–10 mm wide, and filled with fault gouge. The injection lasted 9 months. Before injecting the high-pH solution, a tracer (NaCl) test was performed to estimate the porosity, dispersivity, and hydraulic conductivity of the fracture. The parameters measured included the pH and concentrations of Al, Si and Ca at the outlet of the granite core. The pH did not seem to undergo a significant retardation or buffering with respect to the injected hydroxyl concentration. A decrease in fluid flow with time was observed, which indicated a decrease in hydraulic conductivity and implied an increasing water residence time within the sample. After the experiment, the observed amount of mineral alteration in the core was only minor and difficult to detect. The amounts were so small, that it was not possible to fully characterise the secondary phases that precipitated except for a qualitative identification of C–S–H phase. The experiment is described in detail by Mäder et al. (2002, 2006). Previous modelling attempts of the experiment are described in Pfingsten et al. (2006), Soler et al. (2006) and Soler and Mäder (2007). For the purpose of this modelling comparison, the Soler and Mäder (2007) approach was used as the basis, with the following processes being included: one-dimensional reactive transport (taking into account constant hydraulic head boundary conditions); advective – dispersive transport in a porous medium (fault gouge), assuming a constant fracture width; aqueous speciation; and mineral hydrolysis reactions described by kinetic rate laws. 3. Modelling teams and software tools The partner groups participating in this project were: JAEA of Japan (Kohei Yamaguchi, Manabu Inagaki, Colin Walker and Akira Honda); Posiva of Finland (Josep Soler at IDAEA-CSIC) and the UK Nuclear Decommissioning Authority (David Savage, Claire Watson, James Wilson and Steven Benbow at Quintessa Limited). JAEA used PHREEQC (Parkhurst and Appelo, 1999) and PHREEQC-TRANS (JAEA, 2005) for model computations. PHREEQC is a geochemical computer program that is capable of batch-reaction and reaction-transport calculations allowing the inclusion of kinetically controlled reactions, solid solutions, and equilibrium between solid and liquid phases (see http://wwwbrr.cr.usgs.gov/ projects/GWC_coupled/phreeqc/). Reactive transport modelling for Posiva was performed using CrunchFlow (Steefel, 2008), which is a software package for simulating multi-component multi-dimensional reactive transport in porous media. Details of the code can be found in the user’s manual (downloadable from www.csteefel.com). The Quintessa team utilised its proprietary computer code, QPAC (Quintessa, 2010; Savage et al., 2010a,b) to carry out the modelling presented in this study. QPAC is a flexible generalpurpose multi-physics code which has a geochemical reactive

Fig. 1. Schematic of the HPF core experiment. From Soler and Mäder (2007).

transport module. With respect to reactive chemical transport modelling, QPAC has the following features (amongst others): the capacity to model complex coupled systems in which the evolution of mineral assemblages (including changes in volumes and porosity) may affect fluid transport properties; the capability to model transport and reaction in more than one dimension; the flexibility to adapt the model to consider different spatial scales (e.g. from laboratory to field); the ability to model both equilibrium thermodynamic and kinetic reactions; the facility to include solid solution models, e.g. for C–S–H gel; and the capability to model time-dependent surface areas of secondary minerals, including processes of nucleation, precursor cannibalisation, and Ostwald ripening effects.

3.1. Cement hydration experiment 3.1.1. JAEA All simulations were run at 25 °C, corresponding to the temperature for which thermodynamic data were available, despite Lothenbach and Winnefeld (2006) conducting their experiments at 20 °C. PHREEQC by default uses 1 L of water in a simulation. Equating this to 1 kg of pure water thus requires 2 kg of OPC clinker to give an initial water/solid (w/s) ratio = 0.5, as used by Lothenbach and Winnefeld (2006). The analysis and quantification of the oxide components in OPC clinker provides the data necessary to calculate a normative mineral assemblage which is here described in Table 1. Lothenbach and Winnefeld (2006) used three rate equations to describe the hydration and dissolution of each of the four main OPC clinker phases (C3S, C2S, C3A and C4AF), thereby providing a continuous supply of dissolved Ca, Si, Al and Fe, and K, Na, Mg, and S due to the traces of K2O, Na2O, MgO, and SO3 they contained. The hydration rate corresponding to nucleation and growth, Rt,1, is given by:

Rt;1 ¼

K1 A Ea ð1 at Þð lnð1 at ÞÞ1N1 exp Aref N1 R ðT ref TÞ

ð1Þ

The hydration rate corresponding to diffusion, Rt,2, is given by:

Rt;2 ¼

K 2 ð1 at Þ2=3 1 ð1 aÞ1=3

exp

Ea R ðT ref TÞ

ð2Þ

The hydration rate corresponding to the formation of a hydration shell, Rt,3, is given by:


4


Rt;3 ¼ K 3 ð1 at ÞN3 exp

Ea R ðT ref TÞ

ð3Þ

where K1, N1, K2, K3, and N3 are empirical constants (–), at is the fraction of clinker phase hydrated (–) (also referred to as the degree of hydration), A is the total surface area of the OPC clinker (m2 kg1), Aref is the reference surface area (385 m2 kg1), Ea is the activation energy (J mol1), R is the universal gas constant (8.314 J mol1 K1), Tref is the reference temperature (293.15 K), and T is the temperature of interest (298.15 K). A representative surface area of 400 m2 kg1 was chosen for all simulations undertaken as part of this study. The fraction of clinker phase hydrated is given by at = at 1 + DtRt,x1, where t is time (days) and can be initiated by an arbitrarily chosen low value of 1 1015. For any given time, the lowest value of Rt,x, is the rate controlling step. A critical degree of the hydration term H is added to Eqs. ()(1)–(3) in the case of at > Hw/s to account for differences in water/solid (w/s) ratio, given by:

f ðw=sÞ ¼ Rt;x ð1 þ 3:333ðH w=s atot ÞÞ4

ð4Þ

where atot is the overall degree of hydration of the four main OPC clinker phases taken as a whole. The approach to modelling different solids in the modelling carried out by JAEA is summarised in Table 2 and the most recent values of the parameters used in these rate equations by Lothenbach et al. (2008a) are given in Table 3. A w/s = 0.5 was chosen

Table 1 Procedure used by JAEA to calculate a normative composition of OPC clinker. Oxide component

Phase assigned to

Oxide component(s) adjusted

SrO CaO(free) MgO CO2 Fe2O3 Al2O3 Na2O K2O SO3 CaO SiO2

– Lime (CaO) Periclase (MgO) Calcite (CaCO3) Ferrite (C4AF) Aluminate (C3A) Na2SO4, Na2O K2SO4, K2O Anhydrite (CaSO4) C3S, C2S

– – – CaO CaO, Al2O3 CaO SO3 SO3 CaO CaO, SiO2

Table 2 Dissolution/hydration behaviour of the OPC clinker components as defined by Lothenbach and Winnefeld (2006) and as used in PHREEQC.

a Presumably, the kinetic hydration/dissolution was proportional to the OPC clinker phases they were in, assuming they were homogeneously distributed.

for all simulations in the current study as used by Lothenbach and Winnefeld (2006). 3.1.2. Posiva (IDAEA-CSIC) The initial composition and porosity of the Portland cement used in the model were determined from the normative composition and water/cement ratio (w/s = 0.5) reported by Lothenbach and Winnefeld (2006) and phase densities. Table 4 shows the secondary solids that were considered in the model (solids observed during the experiment). Initial surface areas for all solids were set to an arbitrary value equal to 10,000 m2/m3. This large surface area, together with the large rate constants, led to fast precipitation/dissolution for the secondary solids (conditions very close to local equilibrium). Table 5 shows the rate parameters used for the clinker solids (alite, belite, aluminate, ferrite). Simple irreversible rates (Rm = Am km) were used for these solids, instead of the more complicated rate functions reported in Lothenbach and Winnefeld (2006). In order to reproduce the decrease in rate with time, three different values of km were used for each solid. The values of km were adjusted to fit the observed results. For all the other solids, rate laws were written according to a simple transition-state theory equation (no pH effect) with large reaction rate constants (km = 103 –104 mol/m2/s) to simulate local equilibrium with respect to those solids. Although pure water was used in the experiment, in the model, readily soluble K2SO4 and Na2SO4 were included in the solution (very fast dissolution), and in order to put Ca atoms on the cation exchange complex, Ca in solution was set to 0.1 mol/kg H2O. However, due to supersaturation with respect to anhydrite (or gypsum), Ca precipitated quickly at the beginning of the simulations to approach the concentration measured in the experiment. The observed experimental increase in Na and K concentrations with time is mainly controlled by the consumption of water by the hydration of the clinker phases. However, Na increases to a larger degree than K. Therefore, there must be another process affecting those concentrations. Lothenbach and Winnefeld (2006) argued that Na and K were incorporated into the precipitating C–S–H gel and they modelled it using an empirical distribution coefficient for both Na and K. Here, only the uptake of K has been simulated

Table 3 Parameters in the hydration rate equations as used by Lothenbach et al. (2008a). Parameter

C3S

C2S

C3A

C4AF

K1 (empirical constant) N1 (empirical constant) K2 (empirical constant) K3 (empirical constant) N3 (empirical constant) H (empirical constant) Ea (activation energy) (J mol1) at (fraction of individual phase hydrated) atot (overall fraction of OPC hydrated) A (initial total surface area) (m2 kg1) Aref (reference surface area) (m2 kg1) R (universal gas constant) (J mol1 K1) Tref (reference temperature) (K) T (temperature) (K)

1.5 0.7 0.05 1.1 3.3 1.8 41,570

0.5 1 0.02 0.7 5 1.35 20,785

1 0.85 0.04 1 3.2 1.6 34,087

0.37 0.7 0.015 0.4 3.7 1.45 54,040

w/s (water/solid ratio)

0 < 1 given by at1 + DtRt1 0 OCaþ þ 2Hþ () > OHþ ð0:001 sites=m2 Þ 2 Ca > O þ Hþ () > OH ð0:005 sites=m2 Þ þ 2 > OHþ 2 () > OH þ H ð0:005 sites=m Þ

6.2 5.5

6.2

In order to best fit the data, a primary mineral surface area of 0.7 105 m2 m3 was used. This was scaled by the volume fraction of each individual mineral to give a specific surface area. This is roughly two orders of magnitude smaller than the measured BET surface area (5 106 to 8 107 m2 m3).

Table 9 Potential secondary phases included in the Posiva/IDAEA-CSIC model. Reactions are written as the dissolution of 1 mol of mineral and in 2 + terms of Al3+, SiO2(aq), Na+, K+, Ca2+, Mg2+, HCO 3 , SO4 , H , Cl , F and H2O. Mineral

Composition

log K

Calcite Portlandite Brucite C–S–H-1667 C–S–H-14 C–S–H-12 C–S–H-10 C–S–H-08 C–S–H-06 C–S–H-04 C–S–H-02 C–S–H-00 Analcime Laumontite Mesolite Natrolite Scolecite Stilbite Gismondine Mordenite Wairakite Prehnite Foshagite Gyrolite Hillebrandite Okenite Tobermorite-14A

CaCO3 Ca(OH)2 Mg(OH)2 C–S–H ss, Ca/Si = 1.67, 1.00SiO21.67Ca(OH)21.00H2O C–S–H ss, Ca/Si = 1.4, 1.00SiO21.40Ca(OH)20.95H2O C–S–H ss, Ca/Si = 1.2, 1.00SiO21.20Ca(OH)20.91H2O C–S–H ss, Ca/Si = 1.0, 1.00SiO21.00Ca(OH)20.86H2O C–S–H ss, Ca/Si = 0.8, 2.27SiO21.82Ca(OH)21.82H2O C–S–H ss, Ca/Si = 0.6, 1.72SiO21.03Ca(OH)21.03H2O C–S–H ss, Ca/Si = 0.4, 1.39SiO20.56Ca(OH)20.56H2O C–S–H ss, Ca/Si = 0.2, 1.16SiO20.23Ca(OH)20.23H2O C–S–H ss, Ca/Si = 0.0, SiO2 Na-zeolite, Na0.96Al0.96Si2.04O6H2O Ca-zeolite, CaAl2Si4O124H2O Na-Ca-zeolite, Na0.68Ca0.66Al1.99Si3.01O102.65H2O Na-zeolite, Na2Al2Si3O102H2O Ca-zeolite, CaAl2Si3O103H2O Na-Ca-zeolite, Na0.14K0.01Ca1.02Al2.18Si6.827.33H2O Ca-zeolite, Ca2Al4Si4O169H2O Na-Ca-zeolite, Ca0.29Na0.36Al0.94Si5.06O123.47H2O Ca-zeolite, CaAl2Si4O12.2H2O Ca2Al2Si3O10(OH)2 C–S–H phase, Ca/Si = 1.33, Ca4Si3O9(OH)20.5H2O C–S–H phase, Ca/Si = 0.66, Ca2Si3O7(OH)21.5H2O C–S–H phase, Ca/Si = 2.0, Ca2SiO3(OH)20.17H2O C–S–H phase, Ca/Si = 0.5, CaSi2O4(OH)2H2O C–S–H phase, Ca/Si = 0.83, Ca5Si6O16(OH)29.5H2O

2.0050 23.3400 16.9760 30.1640 23.9420 19.4580 15.0800 25.4330 13.7100 6.6928 2.0311 1.2416 6.5548 14.6980 14.6450 19.5900 17.0550 1.4087 41.7170 5.4107 19.4280 34.7560 68.0480 23.3530 38.0350 10.4640 65.1370


8


In the scoping calculations, the permeability, k (m2), of the fracture was determined using a Kozeny–Carmen formulation (e.g. Bear, 1988):

k/

e3

ð8Þ

ð1 eÞ2

where e is the porosity. The rapid pore-blocking by tobermorite led to a dramatic reduction in porosity and hence permeability, which in turn, led to a rapid decrease in flow rate through the fracture. As might be expected, the rate of this decrease in flow could be controlled by the rate at which tobermorite was allowed to precipitate (by altering the reactive surface area), and it was possible to obtain a flow evolution similar to the one observed in the experiments. However, there was no evidence of pore blocking in the experiments and only small amounts of secondary minerals were observed. Thus the model for permeability given above was deemed inappropriate for this situation. Following the approach used in previous modelling with the 3FLO code (Soler et al., 2006), the hydraulic conductivity, K (m a1), was fitted to the measured flow curve, abandoning any relationship with the fault gouge porosity. The expression used was:

K ¼ K min þ K ini K min expðV CSHCk Þ

ð9Þ

Here Kini is the initial hydraulic conductivity at the start of the simulation (2.8E–9 m s1); Kmin is the minimum hydraulic conductivity during the simulation (2.7E–12 m s1); VC–S–H is the volume of precipitating C–S–H gels (m3 of mineral per total m3) and ck (–) is a fitting parameter (2200). The values of Kini, Kmin and ck were simply chosen to fit the data. Clearly, this scheme would not be appropriate for use in predictive modelling. Fluid flow and reaction was assumed to take place in the fault gouge only. The initial mineralogical composition and porosity of the rock (fault gouge filling the fracture) used in the model is given in Table 8. The compositions of the high-pH solution injected into the granite core and that of the water in the pores of the fault gouge were as described by Soler and Mäder (2007) and as shown in Table 10. All minerals were assumed to dissolve/grow at a rate governed by the following equation:

rate ¼ Ak0 ðaHþ Þn ðX 1Þ

ð10Þ

IAP , K eq

where X ¼ k0 is the rate constant, A is the reactive surface area, IAP is the ion activity product, Keq is the equilibrium constant, and n is the dependence of rate upon H+. Kinetic data for primary minerals are listed in Table 7. Primary minerals are taken to have a total constant surface area of 0.7 e5 m2 m3. This was then distributed amongst the minerals in proportion to their volume fraction. The exception was albite, the surface area of which was multiplied by Table 12 Kinetic data (25 °C) for secondary minerals in the NDA/Quintessa modelling of the HPF core experiment, n is the dependency of k0 upon [H+]. Mineral

Log k0

Calcite Tobermorite-14A Laumontite Gibbsite Kaolinite Katoite Analcime Phillipsite Chalcedony Brucite Sepiolite Montmor-Na Montmor-K Montmor-Ca Montmor-Mg

5.2 10.0 12.3 16.7 17.05 10.0 13.9 13.9 14.5 8.2 8.2 13.6 13.6 13.6 13.6

n

Source 0.9

– – 0.8 0.472 – 0.4 0.4 0.5 – – 0.15 0.15 0.15 0.15

a factor of 0.001 to slow down its dissolution. Secondary minerals were assumed to be comprised of spherical grains with a radius of 0.01 lm with a corresponding geometric reactive surface area. Despite the experimental evidence of a lack of secondary minerals, a range of them was considered in the modelling with QPAC (Table 12). Minerals were selected from those considered most likely to form at elevated pH in the system Na2O–K2O–CaO– MgO–Al2O3–SiO2–H2O, considering both thermodynamic and kinetic data (e.g., Arthur et al., 2005; Savage et al., 2007). Since the data in Table 12 are all derived from laboratory studies, it is likely that use of these data will also overestimate field rates. White and Brantley (1995) have shown that reactive surface area in field studies is generally two orders of magnitude less than that indicated by BET or geometric area. Consequently for the modelling with QPAC, reactive surface area for secondary minerals was assumed to be two orders of magnitude less than geometric surface area (5 104 m2 per m3 rock). Preliminary modelling included both ion-exchange and surface complexation reactions, the inclusion of which did not improve fits to experimental data. Therefore, these reactions were excluded from the final model configuration.

Busenberg and Plummer (1986) Estimated Savage et al. (1993) Nagy (1995) Palandri and Kharaka (2004) Estimated Savage et al. (2001) Analcime used as an analogue Plettinck et al. (1994) Nagy (1995) Brucite used as an analogue Sato et al. (2004) Montmor-Na used as an analogue Montmor-Na used as an analogue Montmor-Na used as an analogue

4. Results 4.1. Cement hydration experiment 4.1.1. JAEA The wt.% of the remaining minerals all closely match those modelled by Lothenbach and Winnefeld (2006) (Fig. 2), although anhydrite is dissolved completely after 9 h as opposed to 12 h (Lothenbach and Winnefeld, 2006). Brucite precipitates from the complete instantaneous dissolution of periclase and so is present in the mineral assemblage for the first 43 h. Differences in both the longevity and occurrence of anhydrite and brucite are attributed to the exclusion of the more gradual release of the SO3 and MgO components, respectively, from the four main OPC clinker phases. Syngenite does not precipitate, but is close to equilibrium with a maximum saturation index (log IAP/Ksp) = 0.35 after 8.5 h. The solution composition as measured by Lothenbach and Winnefeld (2006) and predicted by the PHREEQC OPC hydration model (including CO2 3 ), is shown in Fig. 3. With the exception of Fe, there is a reasonable overall agreement between the measured and predicted solution compositions in terms of the general trends being reproduced at the appropriate times and concentrations. The assignment of the initial model K and Na concentrations in solution to provide a reasonable fit to the long term measured K and Na concentrations is the most questionable assumption in this modelling exercise. Consequently, the predicted initial concentrations of K and OH are too low before matching the experimentally measured data after 0.01 a (4 days). The initial assignment of Na concentration = 26 mM, as measured by Lothenbach and Winnefeld (2006) after 0.02 h (cf. Table 3 in Lothenbach and Winnefeld, 2006) provides an excellent match to the measured Na concentrations throughout the simulation by the simple consumption of water. This is largely coincidental, but means for this particular OPC composition that the net change in Na provided by the dissolution of the Na2O component in the 4 main OPC clinker phases (as modelled by Lothenbach and Winnefeld, 2006) is broadly equal to the uptake of Na by the C–S–H gel. The short term buffering of S in solution by anhydrite provides a reasonable fit to the experimental data. 4.1.2. Posiva (IDAEA-CSIC) Overall, the results of this modelling exercise compare well with those reported by Lothenbach and Winnefeld (2006), despite



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content is smaller than that calculated by Lothenbach and Winnefeld (2006). No hydrotalcite is formed in these simulations due to the absence of Mg from the composition of the clinker phases in the model. The evolution of total concentration and pH during the experiment is shown in Fig. 5. In the early stages, S and Ca concentrations are controlled by equilibrium with respect to CaSO4. Sulphur and Ca concentrations decrease when anhydrite (or gypsum) is completely dissolved (Fig. 4). A better fit for Ca is obtained when CaSO4 is initially present as anhydrite rather than gypsum. Concentrations of Si and Al and pH increase at that same point in time, due to a common-ion effect induced by the decrease in Ca concentration (C–S–H and monocarbonate are precipitating at local equilibrium). Sodium concentration increases only due to the consumption of water by the hydration of the clinker phases. Potassium also increases due to the consumption of water, but it is also affected by uptake by C–S–H (modelled as Ca – K exchange). Without this additional process, the calculated K concentrations would overestimate the observed values. The calculated Fe concentration in solution is very small, which is consistent with the experimental observations (concentrations below detection limit), except for the measured values in the very early stages (up to 10 h).

Fig. 2. Evolution of water and g 100 g1 (wt.%) of minerals in the solid phase in the results of the JAEA modelling of the cement hydration experiment. C3S, C2S, C3A, and C4AF are not shown.

the simpler rate laws for clinker phase hydration and the different treatment of alkali uptake by C–S–H. The calculated evolution of solid phases during the experiment is shown in Fig. 4. Of the clinker phases, alite shows the fastest hydration. Anhydrite (or gypsum) is completely consumed after about 20 h. Regarding the hydration products, C–S–H, portlandite, and ettringite contents and evolution are very similar to those reported by Lothenbach and Winnefeld (2006). For C–S–H, the calculations show that only the high-Ca/Si end-member precipitates. For ettringite, only the Al end-member precipitates. Monocarbonate (Al end-member) also precipitates in the simulations, but its

4.1.3. NDA (Quintessa) The evolution of the major C–S–H solid phases over time is shown in Fig. 6, with the results of the Lothenbach and Winnefeld model and experimental results. It may be seen that the QPAC model output agrees closely with the measured hydration rates and the amounts of portlandite and C–S–H. The evolution of the major species in solution is shown in Fig. 7. The modelled data are seen to fit well with those measured, with only K showing an inconsistent trend for large times. In the model, the concentration of K plateaus after around 20 h and then decreases very gradually as the simulation proceeds, whereas the measured data suggest that the concentration should continue to increase. Overall, the QPAC model provides a reasonable fit with reported experimental data and the model published by Lothenbach and Winnefeld (2006), with the exception of dissolved S and Al concentrations (data not shown). However, the predicted quantities of the clinker and hydrated phases are in very good agreement with the experimental data. At very early times (