1 Geochemical Modelling of Hydrogen Gas Migration in Unsaturated Bentonite
1
Buffer 2
3
Majid Sedighi1*, Hywel Rhys Thomas1, Shakil Al Masum1, Philip James Vardon1,2, 4
Duncan Nicholson3, Alex Chen3 5
6
1 Geoenvironmental Research Centre, Cardiff School of Engineering, Cardiff 7
University, Queen’s Buildings, The Parade, Cardiff, CF24 3AA, United 8
Kingdom. *Corresponding author (SedighiM@cf.ac.uk) 9
2 Now at Geo-Engineering Department, Technical University of Delft, Postbus 5, 10
2600 AA, Delft, The Netherlands. 11
3 Arup, 13 Fitzroy Street, London, W1T 4BQ, United Kingdom. 12
13 14
Abstract 15
This paper presents an investigation of the transport and fate of hydrogen gas through 16
compacted bentonite buffer. Various geochemical reactions that may occur in the multiphase 17
and multicomponent system of the unsaturated bentonite buffer are considered. A reactive 18
gas transport model, developed within an established coupled thermal, hydraulic, chemical 19
and mechanical (THCM) framework is presented. The reactive transport module of the model 20
considers the transport of multicomponent chemicals both in liquid and gas phases, 21
together with an advanced geochemical reaction model. The results of a series of 22
numerical simulations of the reactive transport of hydrogen in unsaturated bentonite are 23
presented, in which hydrogen gas has been injected at a realistic rate due to the corrosion of 24
steel canister into a partially saturated bentonite buffer. Gas pressure development and the 25
fate of the hydrogen gas considering the geochemical reactions are studied. The results show 26
the high buffering capacity of unsaturated bentonite, when considering a steel canister, over a 27
period of 10,000 years. The presence of accessory minerals is shown to have an important 28
role in mitigating excess hydrogen ions, thus increasing the dissolution capacity of the system 29
to gas. Development of various forms of aqueous complexations between the inorganic 30
components and hydrogen ions were also found to be important in buffering the excess 31
hydrogen evolved. Based on the results obtained, it is postulated that the presence of various 32
chemical components in the clay buffer may influence the transport and fate of the hydrogen 33
gas. 34
2 The generation and migration of gases within a potential nuclear waste repository has been 36
the subject of considerable attention and interest for a number of years. Research has been 37
commissioned into a number of aspects, covering both the gas generation potential of the 38
materials to be used in the repository and the migration of the generated gases through the 39
surrounding engineered barriers and geosphere (e.g. Pusch et al. 1985; Horseman et al. 1999; 40
Graham et al. 2002). To the authors’ knowledge, this research has largely focused on what 41
might be described as the “physics” of the problem, i.e. the impact of gas generation and 42
migration within performance assessment approaches on the physical condition of a potential 43
high level radioactive waste disposal repository (e.g. Horseman et al. 1999; Vardon et al. 44
2013). 45
The fate of gas and its long term behaviour considering gas-geochemical interactions in the 46
multiphase and multicomponent unsaturated compacted clay buffer system has received less 47
attention. Various chemical reactions may take place between the generated gas and the 48
clay/water system affecting the fate of the gas in the near field. Additionally, these 49
interactions may alter the behaviour of the clay buffer (Yong et al. 2010). A number of 50
studies have investigated the fate of hydrogen considering geochemical reaction in clay 51
system and related to high level radioactive waste disposal (e.g. Xu et al. 2008; Lassin et al. 52
2011; De Windt et al. 2014). Lassin et al. (2011) presented an investigation of the hydrogen 53
solubility in pore water of unsaturated clay (Argillite) in the context of the geological 54
disposal of nuclear waste under different temperatures and capillary pressures. Accordingly, 55
an increase of the hydrogen solubility in the pore water-rock-gas system has been reported 56
with the decrease in relative humidity or capillary water pressure. A number of scenarios of 57
hydrogen production and diffusion have been studied in a disposal cell of high level 58
radioactive waste disposal in argillaceous formation using multiphase multicomponent 59
reactive transport modelling by De Windt et al. (2014). The effects of the saturation state on 60
the fate of gases and geochemical reaction are highlighted in the results. 61
The work presented here attempts therefore to extend current knowledge to accommodate 62
some of the above aspects, so that the impact of gas migration on the geochemical condition 63
of the unsaturated compacted bentonite buffer in a potential nuclear waste repository might 64
be explored. The results of a series of numerical simulations of gas transport in unsaturated 65
bentonite buffer are presented. 66
A reactive gas transport model developed within an established coupled thermal, hydraulic, 67
chemical and mechanical (THCM) framework has been applied to conduct the numerical 68
3 simulations. Recent developments in the gas reactive transport module of the coupled THCM 69
model are presented. 70
The gas reactive transport model has been used under isothermal and constant pore water 71
saturation conditions. Scenarios are then developed considering heterogeneous re-saturation 72
of the buffer which may provide some partially saturated regions for gas flow. In the 73
application presented, the focus has been to examine the importance of the chemical reactions 74
on the buffering the hydrogen gas injected to the system. 75
Interactions of gas with chemical components present in the bentonite-water system through 76
various geochemical reactions are considered in the simulations presented. 77
Compacted MX-80 bentonite has been selected for this study, under three different initial 78
water contents. 79
The results of pressure development and the fate of hydrogen gas are presented. A particular 80
focus of the research is to study of the mechanisms involved in mitigating excess gas 81
generation. The effects of hydrogen reactions on the geochemistry of the bentonite buffer are 82
also discussed. 83
1. Reactive chemical/gas transport model 84
A reactive transport model has been developed based on a coupled thermal, hydraulic, 85
chemical and mechanical (THCM) formulation which includes the transport of multiple 86
chemicals in both liquid and gas phases. The governing equations have been implemented in 87
the numerical coupled THCM model developed at the Geoenvironmental Research Centre, 88
Cardiff University, i.e. COMPASS (e.g. Thomas & He 1998; Thomas et al. 2012). 89
Geochemical reactions that may occur between the components existing in liquid, gas and 90
solid phases have been considered in the model development via coupling a geochemical 91
model, i.e. PHREEQC v2 (Parkhurst & Appelo 1999), with the coupled THCM model 92
(COMPASS) (Sedighi 2011; Thomas et al. 2012) . The COMPASS-PHREEQC platform has 93
been extended by the linkage of the gas transport model with the geochemical model and 94
inclusion of further geochemical features into the coupled platform (Masum 2012). 95
In this paper, an application of the chemical/gas reactive transport model is presented where 96
the recent developments in the chemical and gas reactive transport module (Sedighi 2011; 97
Masum, 2012; Thomas et al. 2012) is presented. These developments in particular include i) 98
the extension of the multicomponent chemical transport model to the gas species (Masum et 99
4
al. 2012; Vardon et al. 2013) and ii) further integration of the geochemical features to the
100
COMPASS-PHREEQC model by including the gas reactions. The governing equations of gas 101
reactive flow are described in this paper as the simulations do not consider the variations in 102
thermal, hydraulic or mechanical processes inside the buffer. Details of the theoretical and 103
numerical formulations of thermal, hydraulic, chemical and mechanical behaviour have been 104
discussed in details elsewhere (e.g. Thomas and He, 1998; Seetharam et al. 2007, Thomas et 105
al. 2012).
106
The reactive transport module of the model (COMPASS-PHREEQC) has been extensively 107
verified and the accuracy of implementation of the theoretical and numerical formulation in 108
the model has been tested against several benchmarks and alternative analytical and 109
numerical models for both the reactive transports of chemicals in liquid phase (Sedighi 2011; 110
Thomas et al. 2012) and chemicals in gas phase (Masum 2012). The reactive transport of 111
multicomponent chemicals in compacted bentonite under coupled thermal, hydraulic and 112
chemical conditions has been also validated against a series of experimental investigations 113
(Sedighi et al. 2012). 114
115
1.1 Formulations of the reactive transport of chemicals 116
The governing equations for transport of chemicals in liquid and gas are based on 117
conservation of mass. Major transport mechanisms including advection, diffusion and 118
dispersion are considered in the formulations. A sink/source term has also been included in 119
the mass conservation equation which represents the geochemical reactions that can occur 120
in/between chemical components in the three-phase (solid-gas-liquid) system of unsaturated 121
soil. 122
The conservation equation is expressed in terms of molar concentration of each chemical 123
component present in the associated phases (i.e. liquid or gas). Under constant temperature 124
and moisture content, the formulations of the chemicals in liquid and gas phases can be 125
simplified as: 126
∙ (1)
where, represents the volumetric content of liquid ( or gas ( . is the 127
chemical concentration of the ith component in liquid or gas phase. represents the
128
sink/source term which represents the total mass gained or lost due to homogeneous and/or 129
5 heterogeneous geochemical reactions occurred in or between the three-phase system, i.e. 130
(solid, water and gas system of the unsaturated soil). stands for time. is the total flux of 131
ith chemical component in the associated phase.
132
As previously described, the total chemical flux considered in the formulation, includes 133
advection, diffusion and dispersion of the components. The details of the transport 134
mechanisms and developments related to multicomponent chemicals in aqueous phase were 135
provided by Thomas et al. (2012). Developments on the transport model include an extended 136
formulation of multicomponent chemicals in liquid phase under combined electrochemical 137
and thermal diffusion potentials. 138
The advective flow of gas components is considered to be driven by the pressure gradient. 139
The mechanism is expressed using Darcy’s law, described as: 140
, (2)
where, , is the advective flux of the ith component in gas phase and is the molar
141
concentration of the gas component. represents the effective permeability to the gas 142
mixture. is the total gas pressure. 143
The total gas pressure is obtained considering ideal gas behaviour, given as: 144
(3)
where, is the universal gas constant, is temperature and represents the number of gas 145
components in the system. 146
Equation (2) and (3) describe the advective flow as a function of the total concentrations of 147
the chemicals in the gas phase. Such approach allows considering the effects of pressure 148
development of each component on the advection of the other components. 149
Diffusive flow of gases is considered via the extended Fick’s law of diffusion for 150
multicomponent gas mixtures (Taylor & Krishna 1993). The diffusion of ith component in gas
151
phase is described in a general form of multicomponent system as: 152
, (4)
where, , is the diffusive flux of the ith component. represents the effective diffusion
153
coefficient of the ith component due to the concentration gradient of the jth component.
6 The governing equation of gas transport, presented in equation (1) can then be presented as: 155
∙ (5)
The component of the geochemical sink/source term in the governing chemical transport 156
equation is calculated using a geochemical model, PHREEQC version 2 (Parkhurst & Appelo 157
1999). The geochemical reactions considered in the coupled model include ion exchange, 158
precipitation and dissolution of minerals, surface complexation, and redox reactions. The 159
transport model (COMPASS) and the geochemical model (PHREEQC) are linked together 160
incorporating a sequential non-iterative approach (Sedighi 2011; Thomas et al. 2012). 161
Detailed information of the COMPASS-PHREEQC development, the coupling scheme and 162
verifications of the model can be found in Sedighi (2011) and Masum (2012). 163
In a general form, the gas transport equation is coupled with all other primary variables of the 164
model which includes: pore water pressure, temperature, chemical concentrations and 165
deformation vector. Such coupling is reflected via the variation of degree of saturation with 166
suction and temperature as well as changes of the porosity related to deformation modelling. 167
Under the conditions of the simulations considered in this work (as described in section 2), no 168
variation of pore water pressure, temperature and porosity is considered and level of coupling 169
with other processes is minimized. The solution to the coupled differential equations is based 170
on finite element for spatial discretisation and finite difference for temporal discretisation 171
(Thomas & He 1998). 172
2.0 Simulation scenarios 173
The problem considered in this study is an unsaturated compacted bentonite exposed to 174
hydrogen gas which is generated due to the corrosion of a steel canister in a high level 175
radioactive disposal repository. The simulation scenarios that are studied are based on a 176
condition that the re-saturation of the clay buffer may occur heterogeneously. In other words, 177
it is assumed that during the hydro-thermal phase, despite the long term exposure of the 178
compacted bentonite re-saturation would not homogenously occur and some areas would 179
remain partially saturated. In fact, the results of a number of mock-up scale experiments and 180
in-situ tests on re-saturation of bentonite have shown that the full saturation has not been 181
observed (e.g. Thomas et al. 2003). Despite the fact that the compacted bentonite buffer may 182
remain for a long time under the effects hydraulic flow from the surrounding rock and an 183
extensive numerical modelling results on re-saturation of bentonite, there is still uncertainty 184
7 about the extent of the saturation with time as clay microstructural effects and rock 185
heterogeneities can considerably affect the hydraulic behaviour and predictions. This implies 186
that there can be some partially saturated regions where gas flow can preferentially occur 187
through them. The hydrogen can then be the subject of various geochemical buffering 188
processes during the migration in the unsaturated clay buffer. 189
The analysed domain is a two dimensional domain of 500×350 mm of bentonite compacted 190
at dry density of 1600 kg/m3. MX-80 bentonite was selected for this study. The porosity 191
associate with the dry density is approximately 0.4. Simulations were carried out for three 192
initial water contents of the soil, i.e. 10%, 15% and 18% (gravimetric percentage) which 193
corresponds to degrees of saturation of 40%, 60% and 70%, respectively. The suction values 194
associated with the initial water contents of the samples are obtained from the water retention 195
data of compacted MX-80 reported in the literature (Åkesson et al. 2005) and by using the 196
well-established van Genuchten’s relationship for soil-water retention curve (van Genuchten 197
1980). The values of suctions associated with each degree of saturation are approximately 198
70MPa, 35MPa and 25MPa corresponding to 40%, 60% and 70% degree of saturation, 199
respectively. It is noted that the total water content has been considered in the chemical 200
reaction calculations. It is acknowledged that in compacted bentonite, water exists in several 201
porosity scales (e.g. Bradbury & Baeyens 2002) and this can affect the distribution of 202
chemicals and the fate of the pore water composition and geochemical reactions due to the 203
available water in each pore space. 204
The physical, chemical and geochemical properties of the MX-80 bentonite required for the 205
analysis have been obtained from data reported by Bradbury & Baeyens (2002). Table 1 206
presents a selective basic mineralogical and geochemical characteristic of the MX-80. 207
Considering the partial re-saturation conditions described and the fact that the corrosion of 208
steel and consequently the release of hydrogen will occur after the thermal phase, the 209
simulations have been carried out under isothermal conditions with no hydraulic variations 210
(constant moisture content). It is acknowledged that both thermal and hydraulic processes can 211
change the initial conditions of the sample and consequently alter the geochemical 212
conditions. However, in the scope of the current study, the main focus has been to investigate 213
the extent of the gas pressure development in an unsaturated buffer and the effects of 214
geochemical reactions on buffering the gas. Simplified conditions have been considered for 215
this study to facilitate the interpretation of the results in relation to the objectives of the 216
investigation. 217
8 The domain was discretised into 80 equally sized quadrilateral elements. A variable time step 218
has been used in this work which allows a variation of time-step depending on the 219
convergence criteria. The simulations have been carried out for a period of 10,000 years. 220
2.1 Initial and boundary conditions 221
The initial pore water composition of the bentonite associated with each water content was 222
obtained via a geochemical analysis of the system using the basic mineralogical and 223
geochemical properties of the MX-80, provided in Table 1. A procedure was followed to 224
analyse and obtain the pore water composition which is similar to that described by Bradbury 225
& Baeyens (2003). Table 2 provides the composition of the pore fluid and Table 3 presents 226
the mineral contents and exchangeable composition of compacted MX-80, calculated from 227
the geochemical analysis. 228
The initial water pressure was obtained from the water retention curve of the compacted MX-229
80 (Börgesson & Hernelind 1999), for each initial water content. 230
Constant flux of gas was considered at one boundary whilst the other boundary was assumed 231
to be impermeable to gas flow (water boundary). Different rates of hydrogen gas 232
development due to the steel corrosion have been reported from theoretical and experimental 233
investigations (e.g. Papillon et al. 2003; Taniguchi et al. 2004; Smart et al. 2006). Based on a 234
comprehensive literature review reported by Masum (2012) and Vardon et al. (2013), the 235
presence of bentonite may enhance the corrosion process, although the protective surface of 236
the consisted may lower the long term corrosion rate. Based on the range of values reported 237
for the hydrogen generation reported by Taniguchi et al. (2004) and Smart et al. (2006) for 238
compacted bentonite, a constant hydrogen flux equal to 2.0×10-11 kg/m2/sec has been selected 239
which corresponds to a range of 1 to 3 μm/year rate of steel corrosion. 240
A schematic diagram of the domain, chemical initial conditions and boundary conditions 241
applied for the case of the scenario with the initial water content of 10% is shown in Fig 1. 242
2.2 Material parameters 243
Material parameters required for the simulations include i) the flow properties and ii) 244
equilibrium constants of chemical reactions considered. 245
The relationship used to describe the gas conductivity was adopted from Ho & Webb (2006) 246
given as: 247
9 (6)
where, is the intrinsic permeability of the clay and is the viscosity of the gas. is the 248
relative gas conductivity: 249
1 1 (7)
where is a constant which is obtained from the water retention curve described by the van 250
Genuchten’s relationship (van Genuchten 1980). This value has been reported to be 0.43 for 251
the MX-80 (Börgesson & Hernelind 1999). , represents the effective saturation, which can 252
be given as: 253
1
⁄ (8)
where, and is the degree of saturation and the residual degree of saturation, 254
respectively. 255
In the absence of the experimental data for the intrinsic gas permeability of compacted MX-256
80 bentonite, an intrinsic permeability value equal to 10-12 m2 has been considered. This value 257
has been obtained from the experimental tests carried on the compacted FEBEX bentonite, 258
indicating a range between 10-12 and 10-16 m2 for specimens with dry densities between 1500 259
and 1700 kg/m3 (Huertas et al. 2000). The dynamic viscosity of the hydrogen gas is assumed 260
to be equal to the air viscosity at standard temperature and pressure. 261
The effective diffusion of hydrogen gas in a single component system has been obtained 262
from: 263
, (9)
where , represents the diffusion of hydrogen in air. is the tortuosity factor for gas 264
transport which was obtained from a relationship proposed by Millington & Quirk (1961): 265
⁄ ⁄ (10)
where, is the porosity of the clay and .is the degree of gas saturation. 266
Similarly, the diffusion coefficients of chemicals in liquid phase were considered via a 267
similar relationship as that described in equation (9): 268
10 where, , represents the self diffusion coefficients of ions in water. is the tortuosity factor 269
of chemical flows obtained from the relationship proposed by Millington & Quirk (1961): 270
⁄
(12)
2.3 Geochemical reactions 271
Various geochemical reactions that may occur due to the exposure of the system to hydrogen 272
gas have been considered. All the reactions included are calculated under equilibrium with 273
gas pressure, considering a “closed” thermodynamic system. 274
Four main categories of geochemical reactions were considered in the simulations: 275
1) Redox reactions including hydrogen phase exchange between gas and liquid phases (i.e. 276
hydrogen gas dissolution in water). 277
2) Precipitation/dissolution of minerals. 278
3) Aqueous complexations between different components in liquid phase. 279
4) Exchange of ions between the components in liquid phase and exchangeable ions of the 280
clay. 281
Table (4) presents the reactions considered and the equilibrium constants associated with 282
each reaction. The equilibrium constants of the reactions described in categories 1 to 3 have 283
been obtained from the values provided in PHREEQC ver 2.15 (Parkhurst & Appelo 1999). 284
The equilibrium constants of ion exchange reactions described under the category 4 were 285
obtained from the values presented by Bradbury & Baeyens (2003) for MX-80 bentonite. 286
It is noted that under the scenarios considered the water pressure is highly negative and the 287
water in under metastable condition (Lassin et al. 2005). The implies that the application of 288
Henry’s low and the equilibrium constant of the hydrogen dissolution may involve a degree 289
of approximation under the high negative pore water as it has been described in the literature 290
(e.g. Lassin et al. 2005). Under high negative water pressure, application of other 291
relationships such as the equation state proposed by Spycher & Reed (1988) has been 292
suggested and tested for hydrogen solubility in hydrogen solubility in pore water of partially 293
saturated argillites (Lassin et al. 2011). It is acknowledged that the application of the Henry’s 294
low used in this study under the high negative pore water conditions of the simulations may 295
underestimate the extent of the hydrogen dissolution in water. 296
11 An assumption has been considered that all the chemical reactions are assumed to be under 297
equilibrium conditions. However, it is acknowledged that further analysis is required to 298
assess the effects of the kinetically controlled reactions on the fate of hydrogen. In particular, 299
the effects of kinetics on sulphate reduction reaction which play an important role in 300
buffering the excess hydrogen ions (as it is shown in the results) requires further analysis. 301
This is due to the fact that long half-life has been reported for the sulphate reductions under 302
the conditions related to the radioactive waste disposal (Truche et al. 2009). Future work will 303
be required to provide a more comprehensive understanding of the system under mixed 304
equilibrium and kinetically controlled reactions. 305
3.0 Simulation results and discussion 306
The variations of the major gas and chemical variables/components observed from the 307
simulations at three different initial water contents, i.e. 10, 15 and 18 %, are presented. It is 308
noted that no water flow into/from the boundaries have been considered in the simulations. 309
Therefore, the initial moisture content considered remains the same which allows 310
investigating the geochemical effects at three partially saturated samples with the initial water 311
contents described above. 312
Selective results presented and discussed here include the variations of i) concentration of 313
hydrogen gas, ii) pH and pe (pe is defined as the activity of the free electron in water, i.e. 314
pe log e ) and iii) major minerals. 315
The results are only presented for the boundary condition adjacent to the gas injection face of 316
the soil domain. At this location (representing the canister-bentonite buffer interface), the 317
buffers may experience longer physical and chemical interactions due to the hydrogen influx 318
than the other locations of domain. At this location, a higher gas pressure development is 319
more likely as the soil-water system is exposed to a constant hydrogen flux whilst in 320
downstream of the sample, buffering of the gas due to chemical reactions at locations closer 321
to the gas injection boundary may hinder the pressure development. This location is however 322
can be considered as a representative of the domain under the long term simulations. 323
Considering the size of the domain (35 cm) and closed boundary conditions at the 324
downstream of the sample, a uniform distribution of chemicals and gas has been observed in 325
the entire domain in the results of 10,000 years or higher (Masum 2012). Since the focus of 326
the paper has been to study the gas pressure development in long term analysis, the results of 327
12 the location selected for the results can be considered as the representative of the whole 328
domain in 10,000 years analysis. 329
3.1 Hydrogen gas evolution 330
The result of prediction of hydrogen concentrations at the gas injection face is presented in 331
Fig. 2 for three initial water contents. The maximum gas concentration developed at the 332
boundary is related to the highest water content. A “S” shape type of behaviour is observed 333
for all three scenarios which indicates a gradual accumulation of gas at the boundary, 334
followed by a relatively sharp increase in the concentration. The concentration then follows 335
another period of gradual increase. The available pore space for gas decreases in the 336
simulation scenarios with higher initial water contents, therefore, an increase of the gas 337
concentration is observed with increasing the initial water content. 338
At the end of simulation period, the maximum gas concentration at 10% water content has 339
reached an equivalent pressure of 2.45 bar. This value is significantly lower compared to a 340
similar prediction in which only dissolution of gas into pure water has been considered, i.e. 341
maximum gas pressure 9.0 bar (Masum et al. 2012). This observation suggests that 342
significant involvement of geochemical processes can mitigate the excess gas generated in 343
the system. In terms of the spatial distribution of hydrogen, the results of analysis show a 344
uniform gas concentration/pressure across the domain at 10,000 years. 345
Based on the prediction results obtained, the saturation index of hydrogen after 10,000 years 346
simulation shows a negative value of -6.43. The saturation index (SI) represent the logarithm 347
of ratio of the ion activity product ( to the solubility product constant ( , i.e. 348
. This suggests that the solution is under-saturated and able to accommodate 349
more hydrogen. The results of similar simulation for up to 100,000 years indicated that after 350
60,000 years, the gas pressure starts to build up rapidly in the system to a maximal value of 351
4.95 MPa. A detailed explanation of the possible chemical reactions to buffer the gas in the 352
system is presented later in the discussion. 353
3.2 pH and pe 354
The pH and redox potential (pe) variations of the buffer at the gas injection face are presented 355
in Fig. 3 and 4, respectively. Several processes are involved to control the pH behaviour of 356
the buffer including the hydrogen dissolution in water and mineral precipitation/dissolution. 357
Relatively small variations of the pH are observed. The values obtained at the end of 358
13 simulations remain closely to the initial pH value of the system (around 8.0) for all three 359
initial water contents. 360
The redox behaviour shows a three -stage evolution pattern with time. The evolution involves 361
a gradual decrease, with a rapid drop in a short period of time, which is followed by relative 362
steady-state for long term. In general, the intrusion of hydrogen to the system reduces the 363
redox potential of the system by increasing the activity of free electron in water, i.e. pe. The 364
first phase of gradual decrease is more highlighted in the case of the scenario with 10% initial 365
water content. 366
Higher reduction in pe is observed for samples with higher water content in Fig. 4. The pe 367
decreases from the initial value of -4.75 to -5.35, -5.57 and -5.64 for 10%, 15% and 18%, 368
respectively. The variations of the redox potential can affect the dissolution and precipitation 369
behaviour of the minerals (Appelo & Postma 2005). 370
Similar time scale can be observed for the sharp rise of the gas concentration (or pressure) 371
from Fig. 2 and the sharp decrease of pe. These observations will be discussed along other 372
geochemical variations in section 3.4. 373
3.3 Minerals (Gypsum and Calcite) 374
The evolution of gypsum and calcite at the gas entrance boundary is presented in Fig. 4 and 375
5, respectively. The initial concentration of gypsum varies from 0.0113 to 0.003 mol/kg of 376
the soil with increasing the water content from 10% to 18%. As shown in Fig. 4, in scenario 377
with 10% initial water content, the total amount of available gypsum in the system is 378
dissolved almost linearly in the pore-water after a period of approximately 6000 years. The 379
dissolution of gypsum has occurred faster in scenarios with higher water content. Dissolution 380
of gypsum increases the amount of calcium (Ca2+) and sulphate (SO42-) ions in the pore-381
water. 382
The amount of calcite shows an increase with time. During the prediction period, calcite 383
mineral has accumulated in the system from an initial value of approximately 0.0705 to 384
0.0822 (mol/kg of soil). 385
It is noticeable from Fig. 6 that the precipitation of calcite continues for a relatively long 386
duration for the scenario with 10% initial water content. The calcite precipitation has also 387
linearly continued for approximately 4700 years until it reaches a steady state in the case of 388
18% water content simulation. The increasing precipitation of calcite is related to the 389
progressive dissolution of gypsum, as shown in Fig. 5. This process involves the reaction of 390
14 bicarbonate ions with calcium ions added by dissolution of gypsum. In the case of scenario 391
with 18% initial water content, after approximately 4700 years, the saturation index of calcite 392
reaches zero. This suggests that the pore-water has become saturated with precipitated calcite. 393
It is noted that the change in calcite content also affects the concentration of calcium, 394
bicarbonate ions and exchangeable ions. 395
3.4 Discussion of the results 396
Based on the prediction results presented in previous section, a large amount of injected 397
hydrogen gas was found to be buffered in clay-water system. The mitigation of hydrogen gas 398
in the system involved several geochemical reactions as shown in Table 4. These reactions 399
directly or indirectly increase the capacity of the system to adsorb gas and buffer it in the 400
system. 401
Dissolution of hydrogen gas into water is the main phase change process, given as: 402
H ↔ 2H 2e 403
The dissolution of hydrogen into pure water has limited capacity to buffer the excess 404
hydrogen in the system. In the absence of other chemical components or minerals in water, 405
only a small quantity of gas can be dissolved in water according to Henry’s law. However, by 406
considering the whole geochemical system, the pore water demand for hydrogen ion can be 407
increased considerably due the larger number of reactions which involve hydrogen ions. 408
The constant influx of hydrogen increases the amount of (H ) ion and decreases the redox 409
potential of the porewater. At lower pe, the solution has a higher tendency to donate protons 410
or H to the system. As an example, the demand for SO42‐ and H increases when HS is
411
produced through the redox reaction: 412
SO42‐ 9H 8e‐↔HS‐ 4H 2O
It is noted that the sulphates reduction presented in the above reaction is reported to occur 413
only under bacterial activity and considering the long half-life of the reaction reported should 414
be analysed as a kinetically controlled reaction (Truche et al. 2009). In this study all 415
reactions, including the sulphate reaction has been considered under equilibrium. It is 416
acknowledged that further analysis considering kinetics of the reaction will provide further 417
insight into the natural conditions. 418
This process increases the dissolution of gypsum in the water to provide SO42‐ ions. 419
15 The gypsum dissolution in fact provides excess amount of SO42- and Ca2 ions in the system, 420
required to generate a number of other hydrogen impregnated compounds such as species 421
CaHSO , H S, HCO , CaHCO . The evolution of these species in the solution accelerates the 422
consumption of both hydrogen ions (H ) and (e ), shifting the equilibrium position of the 423
hydrogen dissolution (H ↔ 2H 2e ) from left to right causing more hydrogen to be 424
dissolved in the solution from gas phase. 425
After the completion of the dissolution of all gypsum, the demand for hydrogen in liquid 426
phase reduces and a rapid rise of hydrogen concentration in gas phase can be observed (Fig. 427
1). Other aqueous complexation process has continued to mitigate the excess amount of 428
hydrogen in the system but less effectively than when gypsum was available in the system. 429
During the gypsum dissolution period the increasing amount of H+ ions in the liquid from gas 430
phase causes the pH of the solution to drop (Fig. 3). The pH started to rise gradually 431
following the calcite precipitation process until both calcite precipitation and pH evolution 432
reaches to a steady state. Over the duration of the simulation, the pH of the system has not 433
changed considerably and only varied from an initial value of 8.0 to a final value of 8.12. It is 434
noted that surface complexation reactions can also control the pH buffering. These include 435
the reactions of hydrogen ions with weak sites (SOH) in MX-80 (Bradbury & Baeyens 2002). 436
The latter process was not included in the simulations presented. 437
438
4.0 Conclusions 439
The transport and fate of hydrogen gas in an unsaturated bentonite has been studied through a 440
series of numerical simulations. Various chemical reactions that may occur due to the 441
presence of excess hydrogen gas have been considered. 442
The results show the high buffering capacity of bentonite buffer to accommodate the amount 443
of gas generated considering a realistic corrosion rate of a steel canister over a period of 444
10,000 years. The presence of accessory minerals was found to have an important role in 445
mitigating the excess hydrogen ions, thus increasing the dissolution capacity of the system to 446
gas. Development of various forms of aqueous complexations between the inorganic 447
components and hydrogen ions has also been found to be important in buffering the excess 448
hydrogen evolved. 449
16 Based on the results obtained, it is postulated that the presence of various chemical 450
components in the clay buffer may influence the transport and fate of the hydrogen gas. It is 451
suggested that this investigation of gas flow/geochemical interactions has provided some new 452 insights. 453 454 Acknowledgement 455
Financial support from Arup, in the form of a PhD Fellowship to the third author, is 456 gratefully acknowledged. 457 458 References 459
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List of Tables 551
552
Table 1: Mineralogical/geochemical composition of MX-80 (adopted form Bradbury and 553
Baeyens, 2002). 554
Table 2: Pore water composition of compacted MX-80. 555
Table 3: Quantities of minerals and exchangeable ions in compacted MX-80. 556
Table 4: Geochemical reactions considered in the simulations and the equilibrium constants 557
(log ) of the reactions. 558
559
List of Figures 560
561
Fig. 1: The schematic diagram of the initial and boundary conditions for the simulation 562
scenario with 10% initial water content. 563
Fig. 2: Hydrogen evolution at the injection face for 10,000 years. 564
Fig. 3: Evolution of pH in the buffer at various water contents. 565
Fig. 4: Redox behaviour during the simulation period of 10,000 years. 566
Fig. 5: Evolution of gypsum in the buffer due to hydrogen influx. 567
Fig. 6: Evolution of calcite in the buffer due to hydrogen influx over a period of 10,000 year. 568
569 570 571
Fig.1.
572 573 574 575 576 Fig.2. Fig.3. 21
577 578 579 580 581 Fig.4. Fig.5. 22
582 583 584 585 Fig.6. 23
