Monte Carlo simulation of radionuclide migration in fractured rock for the performance assessment of radioactive waste repositories

Cadini, Francesco; Sanctis, J. De; Bertoli, I.; Zio, Enrico

doi:10.1016/j.ress.2012.10.002

Cited by 5 publications

(8 citation statements)

References 26 publications

(40 reference statements)

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“…Within the framework of the KDPT approach, this model improvement is easily achieved by the introduction of a new particle type, i.e., a soluton in pore water between edges, which (i) can undergo the additional transition of a transformation into a soluton in the interlayer with rate λ pi and (ii) migrates in a different, stochastic pore network. This approach stems from a doubleporosity representation of the diffusion domain and is similar to that adopted in Cadini et al 15 Moreover, the method is consistent with the comprehensive analysis of literature data presented in Bourg et al 23 Several simulations (each with M = 2000 tracer particles) are then performed in correspondence of different values of the rate λ pi , which assumes values of the form 10 x , with x varying in the interval [4; 10] at regularly spaced intervals of width Δx = 0.1. Figure 2 shows the resulting sample scale diffusion coefficients D x and D y as a function of the rate λ pi .…”

Section: Resultsmentioning

confidence: 99%

“…In this section, we briefly recall the continuous-time PT algorithm based on the KD model of contaminant transport in a porous medium (KDPT). − The presentation is tailored to the case of diffusive transport of solutes in clays.…”

Section: Kolmogorov–dmitriev Particle-tracking Modelmentioning

confidence: 99%

“…The KDPT benefits from the well-known advantages of Lagrangian methods over Eulerian methods, i.e, (i) avoiding the computational burden arising from the need to handle huge and sparse matrices, especially when dealing with strongly heterogeneous porous media 18 and (ii) automatically preserving the total solute mass. In addition, by the introduction of new particle types, the discrete-state nature of the KDPT method allows a straightforward and simultaneous inclusion of many physical and chemical processes, as shown for example in Marseguerra and Zio 14 and Cadini et al 15 For this, no additional modeling efforts are required, but additional model parameters are introduced. Finally, the KDPT is continuous in time; thus, adaptive time stepping, which is required by spacebased methods, is avoided and a larger computational efficiency in the presence of heterogeneous media is potentially achieved.…”

Section: Kolmogorov−dmitriev Particle-tracking Modelmentioning

confidence: 99%

“…In analogy to the approach proposed in Ferrara et al 20 and Cadini et al, 15 a term-by-term relation can be set up with the classical mass transport equations of one-dimensional diffusive solute transport to identify the transition rates of the KD model. The one-dimensional diffusion-reaction equation for the solute concentration reads 4,21…”

Section: Kolmogorov−dmitriev Particle-tracking Modelmentioning

confidence: 99%

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Simulation of Reactive Diffusion in Clays By a Continuous-Time Markovian Particle-Tracking Scheme

Cadini

Zio

2013

J. Phys. Chem. C

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Clay minerals and clay rocks are considered as efficient components of engineered and natural barriers in many high-level radioactive waste disposal programs worldwide because of their low permeabilities and high sorption capabilities. In this paper we present an approach for modeling solute diffusive transport in saturated clay minerals at the structure map scale based on an extension of the Kolmogorov−Dmitriev theory of stochastic branching processes. The proposed modeling framework allows a simple description of (i) the dual-porosity behavior typical of some compacted clay structures, where diffusion occurs both in the interlayers and in the pore space between clay particles, and (ii) the chemical interactions between the dissolved ions and the solid matrix surfaces (both at nonequilibrium and equilibrium conditions). Furthermore, the Markovian nature of the modeling approach lends itself to a continuous-time particle-tracking scheme of resolution of the model equations, which, in general, easily allows us to deal with the complex geometrical structures of the porous media. Finally, in order to account for the uncertainty in the geometrical properties of the clay samples within the proposed modeling framework, the structure map is represented as a stochastic network of interconnected, one-dimensional interlayers with different lengths and orientations. The combined methods are demonstrated on a two-dimensional literature case study of diffusion through a compacted clay sample, and the resulting average diffusion coefficients are in general agreement with those obtained by a different simulation-based technique found in the literature. Then, the methods are applied to model the diffusion of the weakly sorbing cation Na + , providing results in accordance with physical intuition.

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Section: Resultsmentioning

confidence: 99%

Section: Kolmogorov–dmitriev Particle-tracking Modelmentioning

confidence: 99%

Section: Kolmogorov−dmitriev Particle-tracking Modelmentioning

confidence: 99%

Section: Kolmogorov−dmitriev Particle-tracking Modelmentioning

confidence: 99%

See 2 more Smart Citations

Simulation of Reactive Diffusion in Clays By a Continuous-Time Markovian Particle-Tracking Scheme

Cadini

Zio

2013

J. Phys. Chem. C

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“…Monte Carlo simulation (MCS) is one of the common approaches used in a variety of probabilistic analyses [5][6][7][8][9][10][11]. But unlike total-probability and FOSM 2 algorithms, Monte Carlo Simulation allows us to obtain a variable's probability function in addition to its mean value and standard deviation.…”

Section: Introductionmentioning

confidence: 99%

Evidence in support of seismic hazard following Poisson distribution

Wang

Chang

2015

Physica A: Statistical Mechanics and its Applications

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Modeling the release and transport of 90Sr radionuclides from a superficial nuclear storage facility

Cadini

Tosoni

Zio

2015

Stoch Environ Res Risk Assess

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This work illustrates an integrated model for (i) predicting the evolution of radionuclide concentrations due to releases from a spent fuel storage pool and (ii) providing a preliminary assessment of the radiological risk for the local population. The model integrates (i) a particle tracking algorithm for radionuclide transport based on the Kolmogorov-Dmitriev theory of branching stochastic processes and (ii) a semi-empirical model for representing the effects of seasonal variations in the water table level on the radionuclide concentrations. A real case study is considered concerning the release of 90 Sr from the spent fuel storage pool at the EUREX site in Italy. The integrated model is calibrated by a genetic algorithm optimization based on observation data of water table levels and 90 Sr concentrations available from the local monitoring network. The proposed model offers a satisfactory trade-off between a detailed physical and geometrical description of the transport processes and computational efficiency.

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Monte Carlo simulation of radionuclide migration in fractured rock for the performance assessment of radioactive waste repositories

Cited by 5 publications

References 26 publications

Simulation of Reactive Diffusion in Clays By a Continuous-Time Markovian Particle-Tracking Scheme

Simulation of Reactive Diffusion in Clays By a Continuous-Time Markovian Particle-Tracking Scheme

Evidence in support of seismic hazard following Poisson distribution

Modeling the release and transport of 90Sr radionuclides from a superficial nuclear storage facility

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