Fracture network simulators have been extensively used in the past for containing a better understanding of flow and transport processes in fractured rock. However, most of these models do not account for fluid or solute exchange between the fractures and the porous matrix, although diffusion into the matrix pores can have a major impact on the spreading of contaminants. In the present paper a new finite element code TRIPOLY is introduced which combines a powerful Lagrangian-Eulerian approach for solving flow and transport in networks of discrete fractures with an efficient method to account for the diffusive interaction between the fractures and the adjacent matrix blocks. The code is capable of handling large-scale fracture-matrix systems comprising individual fractures and matrix blocks of arbitrary size, shape, and dimension.
In fractured reservoirs the transport of contaminants mainly occurs in a small volume of high-permeability interconnected fractures. However, most of the capacity for storing a pollutant is provided by the pore system of the rock matrix. Due to the much slower transport in the matrix, strong concentration gradients may occur from the fractures into the porous blocks. This can lead to significant solute transfer between fractures and matrix and may strongly influence the concentration field in a fractured porous formation. Generally, the numerical simulation of flow and transport processes in fractured porous rock can be performed with either discrete models or continuum models. Discrete models describe the spatial structure of the rock-matrix system in great detail and thus allow for a more accurate simulation than continuum models. However, the discretization and computational effort is very large, and often discrete models are limited to the fracture network only, not taking into account the rock matrix. Such discrete models, which may be called fracture network models, have often been used in the past, e.g. for studying dispersion phenomena or deriving equivalent continuum parameters. However, the numerical solution of advection-dispersion in fractures can become a crucial task, since natural fracture networks are very heterogeneous with regard to flow velocities, and numerical problems such as artificial dispersion or oscillations may occur. In recent years Lagrangian-Eulerian schemes have been used more and more to avoid such numerical problems in the solution of the advection-dispersion equation, especially for advection-dominated problems (e.g. Neuman 1984). The idea is to decompose the advection-dispersion equation in two parts, one controlled by pure advection and the other by dispersion. The advected concentration profiles are calculated by Lagrangian approaches such as particle tracking methods, whereas the dispersed concentration profiles are solved by conventional numerical techniques (FDM, FEM) on Eulerian grids. Karasaki (1986) introduced a Lagrangian-Eulerian finite element code TRINET for transport in two- or three- dimensional fracture networks (Segan and Karasaki, 1993). Several attempts have been made in the past to include fracture-matrix interaction in discrete fracture models. A straightforward technique would be to fully discretize both the fractures (as planar elements in 3D-space) and the matrix blocks (as volume elements in 3D-space), and simultaneously solve for solute transport in the entire domain.
