Modelling the effects of water chemistry and flowrate on clay erosion
Introduction
Presently, mined geological disposal concepts are the preferred options for the long-term management and safe isolation of a high-level radioactive waste (HLW). Conceptual designs for the disposal in fractured rocks are based on constructing engineered barrier systems (EBS). A key component of EBS is the clay buffer which can be subject to erosion as the result of clay interaction with groundwater at the interface between the clay and host rock during the long-term performance of the barrier. Long term erosion can create potential pathways for radionuclides leaving the waste form to migrate into the surrounding rock with potentially significant environmental and public health impacts. Understanding the hydro-chemical effects on clay erosion and encoding them in a robust predictive model is therefore critical for the faithful assessment of EBS performance over the long-term repository function (tens of thousands of years).
Fitness-for-service assessment of the clay buffer requires a comprehensive understanding of bentonite extrusion, erosion and radionuclide release. These result from the clay interaction with groundwater, whose physical and chemical conditions may vary over time. Experimental studies of bentonite erosion have demonstrated that the erosion processes are affected strongly by both solution chemistry and fluid velocity (Schatz et al., 2013; Sane et al., 2013; Reid et al., 2015; Navarro et al., 2016; Smith et al., 2017; Missana et al., 2018; Alonso et al., 2018; Zhang et al., 2019; Bian et al., 2019; Bouby et al., 2020; Xiang et al., 2020). The experiments conducted by Baik et al. (2007) show that the flowrate of groundwater induced a significant impact on the total eluted volume of bentonite particles in the case studies. The experimental pinhole tests conducted by Sane et al. (2013) and Navarro et al. (2016) showed that the erodibility coefficients of MX-80 bentonite at high salinity (e.g. 70 g/L) were two orders magnitude larger than those at low salinity (e.g. 10 g/L). No erosion was observed for sodium montmorillonite for solution compositions from 0.5 g/L to 10 g/L NaCl (Schatz et al., 2013). The erosion rates reported for low velocity (0.0001 L/min) were more than an order of magnitude lower than those for high velocity (0.00284 L/min) (Schatz et al., 2013; Reid et al., 2015).
These experimental observations, which highlight the importance of both physically and chemically induced erosion, show the need for predictive modelling to estimate the long-term impacts of water chemistry and water/clay interactions on erosion. The process clay buffer erosion by groundwater includes three main physical processes: (i) the initial hydration of solid clay from solid to gel and eventually discontinuously transformed into diluted sol particles; (ii) the diluted clay particles (sol) detached at the interface of clay/fluid; (iii) detached particles taken away be seeping water (Sedighi et al., 2021; Yan et al., 2021). This mechanistic understanding, however, is not fully reflected in the existing predictive models for buffer erosion (e.g., Pusch, 1999; Neretnieks et al., 2009, Neretnieks et al., 2017; Moreno et al., 2011; Navarro et al., 2017; Asensio et al., 2018). They remain largely empirical, based on experimental data for specific hydro-chemical conditions, which limits the confidence with which they could be applied to systems subjected to variable geological conditions. The limited progress in erosion modelling is in sharp contrast with the important progress made in coupling mechanical behaviour with hydro-chemical effects on clays for analyses of deformation and consolidation. The key elements missed in the existing models for erosion are the mathematical description of particle's detachment at the clay/water interface and its strong coupling with hydro-chemical processes. A model with particles detachment was firstly presented by Sedighi et al. (2021) and successfully applied to bentonite erosion.
The aim of this work is to underpin future fitness-for-purpose assessments of clay buffer by providing new insights into the effects of groundwater interaction with clay on erosion. For this, we present new developments of our mechanistic modelling approach (Sedighi et al., 2021), based on peridynamics (PD). PD is a non-local approach, particularly suitable for resolving discontinuities emerging and phase evolution (Silling, 2000; Silling and Bobaru, 2005), e.g. transport phenomena in discontinuous or highly heterogeneous systems, and stress induced corrosion (Bobaru and Duangpanya, 2012; Chen and Bobaru, 2015; Jafarzadeh et al., 2019a, Jafarzadeh et al., 2019b). Furthermore, PD has been used successfully in different areas, such as hydraulic fracturing (Ouchi et al., 2015), thermally-induced cracking (Oterkus et al., 2014; Wang et al., 2018, Wang et al., 2019), dynamic fracture (Rabczuk and Ren, 2017; Ren et al., 2017; Wang et al., 2016, Wang et al., 2017), and chemical transport in unsaturated fracture systems (Yan et al., 2020). The present model aims to incorporate the fundamental physical and chemical interactions controlling the erosion, with PD formulations of expansion, detachment of diluted particles and detached particles transport processes. It has been demonstrated that PD has the capacity to resolve the moving interface without any additional interface constraints, which is significant for simulating the moving-boundary of continuously expansion of diluted clay particles (Sedighi et al., 2021). This leads to an improved understanding of the combined impacts of the chemistry and flowrate.
The paper is arranged as follows. Section 2 presents the continuum formulation of processes and the development of Peridynamics (PD) frameworks for clay buffer erosion, including PD formulations of swelling, detachment and particle transport. Section 3 present results used for model validation and analysis of additional conditions of interest. Conclusions from the work are given in Section 4.
Section snippets
Clay-water interaction and erosion
The continuum and peridynamics formulations of the erosion in clays have been presented in the earlier work by the authorship team (i.e. Sedighi et al., 2021). This section provides a brief summary of the erosion model by Sedighi et al. (2021), which intends to support the new and further developments presented here. Sedighi et al. (2021) presented the main mechanisms and theoretical aspects involved in clay erosion and demonstrated how the erosion model can capture the key processes through a
Validations and applications
The validation of the PD model has been performed by comparisons of model predictions with experimental data for two cases reported in the literature. The data reproduced from the literature is obtained by using the function of Digitizer in Origin Pro 2016. Section 3.1 deals with bentonite expansion in a stagnant water/solution system, including bentonite extrusion and free swelling in strong sodium chloride solution and calcium chloride solution. Section 3.2 deals with bentonite erosion in a
Conclusions
A non-local model of clay erosion was presented by developing and integrating bond-based peridynamic formulations for clay swelling, particle detachment, and detached particle transport. The model was implemented within a computational framework (Pyramid; Yan et al., 2020). The model was validated by comparing its predictions to a series of experimental test, firstly under conditions prohibiting particle detachments (bentonite expansion and extrusion) and then under conditions facilitating
Author statement
Huaxiang Yan: Main developer of idea, concept, theory, implementation, validations and analysis, writing up the original draft, editing and revision.
Majid Sedighi: Major contribution to the development of idea, concept and theory, analysis of results, co-writing up the original draft, editing and revision. Supervision of the research.
Andrey P. Jivkov: Major contribution to the development of idea, concept and theory, analysis of results, co-writing up the original draft, editing and revision.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
Yan acknowledges the financial support through a joint PhD Scholarship by the China Scholarship Council (CSC No.201808350074) and the Department of Mechanical, Aerospace and Civil Engineering at the University of Manchester. Sedighi acknowledges gratefully the financial support provided by the Royal Society, UK, via IEC\NSFC\181466. Jivkov acknowledges the financial support from the Engineering and Physical Sciences Research Council (EPSRC), UK, via Grant EP/N026136/1.
References (51)
- et al.
Sol–gel transitions of sodium montmorillonite dispersions
Appl. Clay Sci.
(2000) - et al.
Erosion behaviour of raw bentonites under compacted and confined conditions: Relevance of smectite content and clay/water interactions
Appl. Geochem.
(2018) - et al.
Salinity effects on the erosion behaviour of MX-80 bentonite: a modelling approach
Appl. Clay Sci.
(2018) - et al.
Erosion of bentonite particles at the interface of a compacted bentonite and a fractured granite
Eng. Geol.
(2007) - et al.
Swelling behavior of compacted bentonite with the presence of rock fracture
Eng. Geol.
(2019) - et al.
The peridynamic formulation for transient heat conduction
Int. J. Heat Mass Transf.
(2010) - et al.
A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities
J. Comput. Phys.
(2012) - et al.
Erosion dynamics of compacted raw or homoionic MX80 bentonite in a low ionic strength synthetic water under quasi-stagnant flow conditions
Appl. Clay Sci.
(2020) - et al.
Study of individual Na-montmorillonite particles size, morphology, and apparent charge
J. Colloid Interface Sci.
(2005) - et al.
Peridynamic modeling of pitting corrosion damage
Journal of the Mechanics and Physics of Solids
(2015)
MRI profiles over very wide concentration ranges: application to swelling of a bentonite clay
J. Magn. Reson.
Pitting, lacy covers, and pit merger in stainless steel: 3D peridynamic models
Corros. Sci.
A peridynamic mechano-chemical damage model for stress-assisted corrosion
Electrochim. Acta
Relating clay yield stress to colloidal parameters
J. Colloid Interface Sci.
Permeability and expansibility of sodium bentonite in dilute solutions
Colloids Surf. A Physicochem. Eng. Asp.
Colloidal properties of different smectite clays: significance for the bentonite barrier erosion and radionuclide transport in radioactive waste repositories
Appl. Geochem.
Erosion of sodium bentonite by flow and colloid diffusion
Physics and Chemistry of the Earth, Parts A/B/C
Swelling and mechanical erosion of MX-80 bentonite: Pinhole test simulation
Eng. Geol.
Modelling of compacted bentonite swelling accounting for salinity effects
Eng. Geol.
Hydraulic flow through saturated clays[M]//Clays and Clay Minerals
Pergamon
Fully coupled peridynamic thermomechanics
J. Mech. and Phys. of Solids
A peridynamics formulation for quasi-static fracture and contact in rock
Eng. Geol.
Dual-horizon peridynamics: A stable solution to varying horizons
Comput. Methods Appl. Mech. Eng.
Reformulation of elasticity theory for discontinuities and long-range forces
Journal of the Mechanics and Physics of Solids
Peridynamic modeling of membranes and fibers
Int. J. Non-Linear Mech.
Cited by (11)
Peridynamic analysis of thermal behaviour of PCM composites for heat storage
2024, Computer Methods in Applied Mechanics and EngineeringModelling artificial ground freezing subjected to high velocity seepage
2024, International Journal of Heat and Mass TransferNon-local modelling of freezing and thawing of unsaturated soils
2024, Advances in Water ResourcesPrediction model of particle loss based on seepage tests of sediment in water-level-fluctuation zone of reservoir
2023, Engineering Failure AnalysisCo-transport of less soluble accessory minerals during expansion of compacted bentonite and its impacts on erosion
2022, Engineering GeologyCitation Excerpt :The sample was then exposed to Grimsel groundwater, which mainly contains 0.04 g/L NaCl and 0.016 g/L CaCl2 (corresponding to 0.68 mM Na+ and 0.14 mM Ca2+). It is reported that the sodium bentonite, when contacted with calcium solution, is expected to equilibrate rapidly with the solution due to the ion exchange reaction Ca2+/Na+ (Karnland et al., 2011; Yan et al., 2021). Consequently, the ion concentration is assumed to be 0.96 mM Na+ in the solution.
Numerical estimate of critical failure surface of slope by ordinary state-based peridynamic plastic model
2022, Engineering Failure AnalysisCitation Excerpt :Among them are criteria for elastic-brittle materials [39–46], plastic materials [45,47] and viscoelastic materials [48]. With the flourishing of the peridynamics, it has been successfully applied in many fields, such as naval engineering [18,49], aerospace engineering [50], and civil engineering [51,52]. PD theory has been widely used in the field of geotechnical engineering [53].