• Journal of the Korean Mathematical Society
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• v.38 no.4
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• pp.723-761
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• 2001

The objects of this paper are to formulated a model for the transport of a chain of radioactive waste products in a fractured porous medium, to devise an effective and efficient numerical method for approximating the solution of the model, and to demonstrated the convergence of the numerical method. The formulation begins from a model in an unfractured (single porosity) medium, passes through a double porosity model in a fractured medium, and ends with a modified single porosity model that takes the relevant time scales of the flow and the nuclear decay.

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.4 no.1
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• pp.9-15
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• 2006

For the accurate safety assessment of potential radioactive waste disposal site which is located in the crystalline rock it is important to simulate the mass transportation through engineered and natural barrier system precisely, characterized by porous and fractured media respectively. In this work the methods to construct discrete fracture network for the analysis of flow and mass transport through fractured-porous medium are described. The probability density function is adopted in generating fracture properties for the realistic representation of real fractured rock. In order to investigate the intersection between a porous and a fractured medium described by a 2 dimensional rectangular and a cuboid grid respectively, an additional imaginary fracture is adopted at the face of a porous medium intersected by a fracture. In order to construct large scale flow paths an effective method to find interconnected fractures and algorithms of swift detecting connectivities between fractures or porous medium and fractures are proposed. These methods are expected to contribute to the development of numerical program for the simulation of radioactive nuclide transport through fractured-porous medium from radioactive waste disposal site.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2005.10a
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• pp.195-196
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• 2005

• Nuclear Engineering and Technology
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• v.56 no.5
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• pp.1747-1753
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• 2024

The accurate determination of formation density and the physical properties of rocks is the most critical logging tasks which can be obtained using gamma-ray transport and detection tools. Though the simulation works published so far have considerably improved the knowledge of the parameters that govern the responses of the detectors in these tools, recent studies have found considerable differences between the results of using a conventional model of a homogeneous mixture of formation and fluid and an inhomogeneous fractured medium. It has increased concerns about the importance of the complexity of the model used for the medium in simulation works. In the present study, we have suggested two various models for the flow of the fluid in porous media and fractured rock to be used for logging purposes. For a typical gamma-gamma logging tool containing a ¹³⁷Cs source and two NaI detectors, simulated by using the MCNPX code, a simplified porous (SP) model in which the formation is filled with elongated rectangular cubes loaded with either mineral material or oil was investigated. In this model, the oil directly reaches the top of the medium and the connection between the pores is not guaranteed. In the other model, the medium is a large 3-D matrix of 1 cm³ randomly filled cubes. The designed algorithm to fill the matrix sites is so that this realistic random (RR) model provides the continuum growth of oil flow in various disordered directions and, therefore, fulfills the concerns about modeling the rock textures consist of extremely complex pore structures. For an arbitrary set of oil concentrations and various formation materials, the response of the detectors in the logging tool has been considered as a criterion to assess the effect of modeling for the distribution of pores in the formation on simulation studies. The results show that defining a RR model for describing heterogeneities of a porous medium does not effectively improve the prediction of the responses of logging tools. Taking into account the computational cost of the particle transport in the complex geometries in the Monte Carlo method, the SP model can be satisfactory for gamma-gamma logging purposes.

• Tunnel and Underground Space
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• v.13 no.1
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• pp.20-32
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• 2003

To understand the behavior of migration of contaminants in a fractured porous medium is a key to assure the overall safety of a potential radwaste repository. The feasible retention mechanism of contaminant transport in a tinctured medium are sorption of contaminants on solid surface and matrix diffusion of contaminants from a fracture into an adjacent porous medium. The acceleration mechanisms are the migration of contaminants in the form of pseudo-colloids and the limit of a volume f3r matrix diffusion. In this paper, the effects of these two acceleration mechanisms are studied mathematically, then semi-analytically computed by the application of the Talbot theorem and verified. Results indicate that the acceleration processes cannot be neglected in the modeling of contaminant transport in a fractured porous medium.

• Nuclear Engineering and Technology
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• v.54 no.9
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• pp.3390-3397
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• 2022

Among the different techniques available, nuclear methods, including gamma-gamma logging tools, are of special importance. Though the real environment which surrounds the drilled borehole is a complex fractured medium which the fluid can flow through the porosities, simulation studies generally use the traditional model of a homogeneous mixture of formation and the liquid. Considering a previously published study, which shows that modeling of fluid flow in fractured reservoirs and simulating the formation as an inhomogeneous fractured medium leads to different results compared with those of homogeneous mixture, here we study the effect of the presence of drilling fluid (mudcake) on the response of the detectors in both the models. To study this effect, a typical gamma-gamma logging tool was modeled by using the MCNPX Monte Carlo code. The results show that the responses of the detectors in the mixture model in the presence of various thicknesses of mudcake are sensitive to the density of the formation material. However, this effect is not notable in the inhomogeneous fractured medium. These results emphasize the importance of the model employed for simulation of the medium in gamma-gamma well-logging.

• Proceedings of the Korean Radioactive Waste Society Conference
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• 2005.06a
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• pp.231-238
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• 2005

On the basis of flow resistance theory the conceptual model and related mathematical descriptions is proposed for resistance modeling of groundwater flow in CPM(continuum Porous medium), DFN(discrete fracture network) and fractured-porous medium. The proposed model is developed on the basis of finite volume method assuming steady-state, constant density groundwater flow. The basic approach of the method is to evaluate inter-block flow resistance values for a staggered grid arrangement, i.e. fluxes are stored at cell walls and scalars at cell centers. The balance of forces, i.e. the Darcy law, is utilized for each control volume centered around the point where the velocity component is stored. The transmissivity (or permeability) at the interface is assumed to be the harmonic average of neighboring blocks. Flow resistance theory was utilized to relate the fluxes between the grid blocks with residual pressures. The flow within porous medium is described by three dimensional equations and that within an individual fracture is described by a two dimensional equivalent of the flow equations for a porous medium. Newly proposed models would contribute to develop flow simulation techniques with various matrix characteristics.

• Nuclear Engineering and Technology
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• v.25 no.4
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• pp.529-538
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• 1993

A stochastic way using continuous time Markov process is presented to model the one-dimensional nuclide transport in fractured rock matrix as an extended study for previous work ［1］. A nuclide migration model by the continuous time Markov process for single planar fractured rock matrix, which is considered as a transient system where a process by which the nuclide is diffused into the rock matrix from the fracture may be no more time homogeneous, is compared with a conventional deterministic analytical solution. The primary desired quantities from a stochastic model are the expected values and variance of the state variables as a function of time. The time-dependent probability distributions of nuclides are presented for each discretized compartment of the medium given intensities of transition. Since this model is discrete in medium space, parameters which affect nuclide transport could be easily incorporated for such heterogeneous media as the fractured rock matrix and the layered porous media. Even though the model developed in this study was shown to be sensitive to the number of discretized compartment showing numerical dispersion as the number of compartments are decreased, with small compensating of dispersion coefficient, the model agrees well to analytical solution.

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.2 no.4
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• pp.253-262
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• 2004

Construction of tunnels in a deep crystalline host rock for a potential High-Level Radioactive Waste(HLW) repository inevitably generates an excavation disturbed zone (EDZ). There have been a series of debates on whether a permeability in an EDZ increases or not and what would be the maximum depth of an EDZ. Recent studies show mixed opinions on permeability. However, there has been an international consensus on the thickness of an EDZ; 30 cm for TBM and 1 meter for controlled blast. One of the impacts of an EDZ is on determining the distance between adjacent deposition holes. The void gap by the excavation hinders relaxation of temperature profiles so that the current Korean reference designing distance between holes should be stretched out more to keep the maximum temperature in a buffer region below 100 degrees Celsius. The other impact of an EDZ is on the long-term post closure radiological safety. To estimate the impact, the reference scenario, the well scenario, is chosen. Released nuclides diffuse through a bentonite buffer region experiencing strong sorption and reach a fracture surrounded by a porous medium. Inside a fractured porous region, radionuclides migrate by advection and dispersion with matrix diffusion into a porous medium. Finally, they reach a well assumed to be a source of potable water for local residents. The annual individual dose is assessed on this well scenario to find out the significance of an EDZ. A profound sensitivity study was performed, but all results show that the impact is negligible. Even though the role of an EDZ turns out to be limited on overall safety assessment, still it is worthwhile to study the chemical role of an EDZ, such as a potential source for natural colloids, potential sealing of an open fracture by fine clay particles generated by the process of an EDZ, and alteration of a sorption mechanism by an EDZ in the future.

• The Journal of Engineering Geology
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• v.9 no.3
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• pp.187-206
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• 1999

A computer program to numerically predict the permeability tensor of fractured rocks is developed using information on discontinuities which Borehole Televiewer and Borehole Image Processing System (BIPS) provide. It uses orientation and thickness of a large number of discontinuities as input data, and calculates relative values of the 9 elements consisting of the permeability tensor by the formulation based on the EPM model, which regards a fractured rock as a homogeneous, anisotropic porous medium. In order to assess feasibility of the program on field sites, the numerically calculated tensor was obtained using BIPS logs and compared to the results of pumping test conducted in the boreholes of the study area. The degree of horizontal anisotropy and the direction of maximum horizontal permeability are 2.8 and $N77^{\circ}CE$, respectively, determined from the pumping test data, while 3.0 and $N63^{\circ}CE$ from the numerical analysis by the developed program. Disagreement between two analyses, especially for the principal direction of anisotropy, seems to be caused by problems in analyzing the pumping test data, in applicability of the EPM model and the cubic law, and in simplified relationship between the crack size and aperture. Aside from these problems, consideration of hydraulic parameters characterizing roughness of cracks and infilling materials seems to be required to improve feasibility of the proposed program. Three-dimensional assessment of its feasibility on field sites can be accomplished by conducting a series of cross-hole packer tests consisting of an injecting well and a monitoring well at close distance.