(A) study on the single continuum modeling of radionuclide migration in fractured porous media

Abstract

Solute transport in fractured porous media is described by the single continuum model, i.e., equivalent porous medium(EPM) model. For this purpose, one-dimensional solute transport in the fracture and two-dimensional solute transport in the porous rock matrix is considered. The network of fractures embedded in the porous rock matrix is idealized as two orthogonally intersecting families of equally spaced, parallel fractures directed at 45$^\circ$ to the regional groundwater flow direction. Physical processes considered are advection, hydrodynamic dispersion, molecular diffusion, sorption onto the fracture surfaces, sorption in the rock matrix, and radioactive decay. Governing equations are solved by the finite element method, and upstream weighting technique is used in order to prevent the oscillation of solution in case of highly advection dominated transport. The domain is discretized into a network of triangular and quadrilateral elements by intersecting a number of mesh lines between each pair of fracutes. The one-dimensional fracture elements are superimposed onto the boundaries of the porous rock matrix, and equal concentrations are applied as a boundary condition between fractures and porous rock matrix. Validity of the numerical scheme is established by comparison with an analytic solution for the three cases independently, i.e., one- and two-dimensional problems in the porous rock matrix and one-dimensional transport problem in the fracture. An overall numerical scheme is verified by comparison with the analytic solution of one-dimensional solute transport in ordinary porous media. In all cases the numerical scheme is found to be capable of producing reliable results, and more accurate solutions can be obtained by rducing both the mesh size and time step in the case of highly obtained by reducing both the mesh size and time step in the case of highly advection dominated problems. The breakthrough curves are obtained as a function of time according to v...