A Dynamical Network Model for Percolation Problems in Performance Assessment of Radioactive Waste Management
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A DYNAMICAL NETWORK MODEL FOR PERCOLATION PROBLEMS IN PERFORMANCE ASSESSMENT OF RADIOACTIVE WASTE MANAGEMENT HIROYASU TAKASE*, M. INAGAKI*, M. D. IMPEY** AND P. GRINDROD** *JGC Corporation, 1-14-1 Bessho, Minami-ku, Yokohama, 232 Japan **Intera Information Technologies, Chiltern House, 45 Station Road, Henley-on-Thames, RG9 I AT, UK ABSTRACT A semi-analytical model for percolation problems, called the Dynamical Network Model, is developed. Because of its semi-analytic nature, the model is more efficient than the existing numerical techniques especially for three dimensional problems and, thus, can be used to a wide range of percolation-like problems in performance assessment of radioactive waste disposal. INTRODUCTION For media which consist of two or more different materials, drastic changes of the bulk property at a critical mixing ratio have been widely observed. In performance assessment of radioactive waste disposal, quantitative treatment of these changes could be important. This is particularly true if the phenomena related to changes from closed systems to open systems or from impermeable media to permeable media are considered. For example, hydrogen gas produced by metal corrosion in a repository may accumulate inside barriers, such as a clay buffer, until it desaturates the pores in the buffer and, eventually, physically damages the clay barrier and/or generates fractures[1 ][2][3]. At the early stages of gas accumulation, when the gas pressure is lower than the capillary pressure of the largest pores, all the pores are impermeable to gas. As the gas pressure increases, it exceeds the capillary pressure of a small fraction of the pores and these pores become potentially permeable[4]. However, since the number of potentially permeable pores is still limited, these pores are not connected to one another. Thus the buffer, as a whole, remains impermeable to gas. If the gas pressure increases further, the ratio of potentially permeable pores reaches a threshold value and (at least) one chain of permeable pores is formed throughout the region. This makes the media permeable to gas. This type of change in the property of a material is best addressed by percolation theory[5]. Percolation theory is also applicable to a number of similar issues related to the performance assessment, e.g., stress corrosion cracking of the canister[6], fracturing of chemically degraded concrete materials[7] etc., since these phenomena can be viewed as the permeation of gas, water or solutes through a mixture of permeable and impermeable constituents. Application of percolation theory to these problems may be done using numerical simulations which require the generation of an array of stochastic realizations of the medium[8]. This is a time consuming process, particularly if one wishes to analyze three dimensional problems. The purpose of this study is to provide an alternative, more efficient approach to the problems described above. To do this, we have developed a semi-analytical model called the Dynamical Network Model, which is ba
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