Contaminant transport in fractured porous formations is often simulated with dual-porosity models. In such models the heterogeneous formation is separated into two coupled continua, one representing the fractures, one representing the rock matrix. The main objective of the present study is to investigate the effect of spatial variations of matrix block properties (especially such as size and shape) and to determine effective continuum parameters for the matrix continuum. Different averaging approaches are compared with regard to their suitability for continuum representation of the matrix system. A numerical study was performed considering two different sets of simulation runs. One considering the exact matrix properties, and the second using different averaged effective continuum parameters. The breakthrough curves are compared to check the accuracy of the averaging procedures with regard to their application in dual-porosity models.
Fractured porous formations are typified by a high permeable fracture system and a matrix system with very low permeability but high storativity. Due to the different response times in the fractures and in the matrix regional transport takes place in the fractures and is of advective-dispersive character. Transport in the matrix blocks is of diffusive type; it depends on the concentration in the adjacent fractures and is therefore of local nature. Contaminant transport in such systems is often simulated with dual-porosity models. Essential to the principle on homogenization for heterogeneous media is the definition of equivalent model parameters for both media, capable of describing the correct physical behavior of the system. Numerous studies have been performed e.g. by (Long et al. 1982, 1987) in the past to check if a continuum representation of fracture networks is valid. If so equivalent continuum parameters can be derived and the model error associated to this averaging process may be estimated. However, only little work has been done to address this task with regard to the matrix blocks of a given subdomain, which may considerably vary in size, shape or material properties. In most cases of dual-porosity modelling, the matrix continuum parameters are only roughly estimated and error analysis is not performed. Due to the distribution of the fractures the geometric parameters (block size and shape) can be extremely heterogeneous in the matrix system. These heterogeneities are important for the transport behavior of the matrix system. 2 APPROACH For continuum representation of heterogeneous rock formations (e.g. dual-porosity models) averaging procedures for the fracture system as well as for the matrix system are necessary. In many studies the equivalent continuum parameters of fracture systems are derived by determining the heterogeneous behavior of the system using discrete models (discrete representation of the fractures). The accurate description of the matrix volume and cross- section area available for matrix diffusion at a certain distance from the matrix-fracture interface is essential to the correct simulation of matrix diffusion. However, in most of the case studies concerning dual-porosity models the matrix system has been strongly idealized to a set of matrix blocks uniform size and shape and detailed averaging procedures have not been applied.
