RESUMEN
The main purpose of this work is to present a new analytical solution to study the transient matrix diffusion problem in fractured rocks. The solution is based on a Dual Continuum Model (DCM) and accounts for a zero-order source term in the matrix. The new solution can therefore be applied to describe transport of naturally occurring elements in rock minerals, such as those generated by radioactive decay, i.e., Helium. Also presented in this paper, is a conceptual model to estimate the DCM parameters from properties of an equivalent continuous porous medium (ECPM), thus allowing to incorporate transport calculations within a secondary continuum, i.e., matrix, in ECPM models. For practical applications, the new analytical solution is implemented in a Fortran module that can be readily coupled to a multi-component transport solver, i.e., DarcyTools. This allows DarcyTools to apply the DCM as a subgrid model and thus carry out simultaneous matrix diffusion and transport calculations in a bedrock, with or without including the source term. Since due to the apparent difference in transport time scales in fracture and matrix, simulation results can be sensitive to the grid size and time step taken by the solver, a comparison study is carried out to evaluate the accuracy of the numerical results in a two-dimensional fracture-matrix system. Implementation of the DCM is also verified by comparing the DarcyTools predicted results with exact solutions. For this purpose, a new semi-analytical solution is also derived in the Laplace domain to calculate a solute breakthrough curve in the fracture. Excellent agreement in results is found for the two solutes considered, namely, a non-reactive tracer and Helium generated as alpha particles by radioactive decay in the matrix. Furthermore, the DCM is incorporated in a large-scale three-dimensional transport model to describe concentration distribution of the given solutes in a fractured bedrock. The results suggest that the DCM implementation can effectively capture the impact of mass exchange between fractures and rock matrix in the bedrock.
Asunto(s)
Helio , Movimientos del Agua , Simulación por Computador , Modelos Teóricos , DifusiónRESUMEN
The rock matrix of granites is expected to be an important buffer against the dispersion of contaminants, e.g. radionuclides, and against the ingress of oxygenated glacial meltwater. The influence of matrix heterogeneity on O2 diffusive transport is assessed here by means of numerical experiments based on a micro-Discrete Fracture Network (micro-DFN) representation of the diffusion-available pore space along with random realisations of idealized biotite grains, to simulate the heterogeneous nature of granitic rocks. A homogeneous-based analytical solution is also presented and used to assess possible deviations of the numerical experiments from the assumption of homogeneity. The analytical solution is also used to test upscaled values of mineral surface area. The numerical experiments show that the matrix behaves as a composite system, with the coexistence of fast and slow diffusive pathways. This behavior is more evident at low Damköhler numbers. Our interpretation of the numerical experiments points out the importance to properly characterise the heterogeneity of the rock matrix.