Novel Lattice Models for Porous Media
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Novel Lattice Models for Porous Media Andrey P. Jivkov1,2 and Joseph E. Olele2 RCRD, University of Manchester, Williamson Building, Manchester, M13 9PL, UK. 2 MACE, University of Manchester, George Begg Building, Manchester, M13 9PL, UK.
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ABSTRACT Network models of porous media are beneficial for predicting evolution of macroscopic permeability. This work proposes novel models based on truncated octahedral support. Systems with different pore coordination spectra for a given average coordination number can be constructed to match experimental data. This feature, and the allowed pore coordination of 14, make the proposed models more realistic and flexible than existing models with cubic support. Experimental data for two sandstones with substantially different properties are used to demonstrate the models' ability to predict permeability. A strategy for calculating its evolution with internal damage is also described and results are presented. Developments of this strategy are suggested for deriving mechanism-based constitutive laws for engineering applications. INTRODUCTION Several barriers in a nuclear waste repository, such as waste immobilisers, backfills and host rocks are porous. While their hydraulic permeability maybe very low at the construction stage, it may evolve over the repository lifetime due to mechanisms that could change the pore space geometry and connectivity. Examples for such mechanisms are cracking, electrochemical and/or bacterial corrosion, and possibly irradiation. Predicting permeability evolution with such changes is critical to the assessment of radionuclide transport. This can be achieved by appropriate pore space models amenable to mechanism-driven changes. Pore-network models (PNM) offer an advantageous pore space description [1]. PNMs contain a set of pores, e.g. spheres of different radii, connected by throats, e.g. cylinders with different radii. Pores reside at sites of a regular lattice and throats link some neighbouring pores. Early PNMs were based on a cubic lattice with a maximum pore coordination of six [2]. Later experimental studies showed that pores with larger pore coordination numbers (PCN) can be substantial fractions of all coordinated pores [3]. These lead to proposals of PNMs with larger maximum PCN, e.g. 26 in [4], still based on cubic support. Although such PNMs are topologically admissible, they are physically unrealistic because large numbers of throats intersect at points that are not pores. Further, for a given average PCN the existing models reproduce only one PCN spectrum, i.e. fractions of pores coordinated by different numbers of throats. This spectrum may not correspond to experimentally determined spectra, such as in [3]. This work has four objectives. Firstly, to present PNMs based on a novel lattice support with truncated octahedral cells and provide physical justification for its selection. Secondly, to demonstrate the abilities of the models to produce various PCN spectra and to predict experimentally measured permeability. Thirdly, to illustrate ho
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