Groundwater now in fractured rock is treated as now in fracture network. Based on cubic law of now in a single fracture and graph theory, flow model in fracture network is established. On the basis of now model in fracture network, analytical solutions to radionuclides migration in fractured rock are given to the following three problems:
one-dimensional transport with advection and dispersion in a single fracture,
advection and dispersion in a set of parallel fractures with diffusion in microfissured matrix (early time solution), and
problem 2 with radioactive decay. An example study is also presented.
The radionuclides transport in various kinds of rocks has become an area of large interest in the last two decades because of various national and international efforts in studying the final disposal of radioactive wastes from nuclear power plants. Generally, crystalline rock has been selected as the most suitable bedrock in which to build a repository. In crystalline rock the water moves in fissures which may be fairly far apart at larger depths. The radionuclides, carried by the water, will interact in various ways with the rock. They may be strongly retarded by sorption on the surfaces of the fissures and, in a given time, may also penetrate into the intercrystalline microfissures of the matrix of the rock. The problem of prediction of nuclides migration usually is divided into two parts. The first consists of determining the water movement, and the second is the transport of radionuclides by the water.
2.1 Some definitions Definition1: groundwater flow in fractured rock is treated as flow in fracture network.
3.1 The coupled partial differential equations of radianuclides migration Consider a system of parallel, horizontal fractures separated by unfractured rock as shown in Fig.2. As proposed by Rasmuson and Neretnieks (1981). 3.2 The analytical solutions to radionuctides migration The analytical solutions are given to the following three problems:
one-dimensional transport with advection and dispersion in a single fracture,
advection and dispersion in a set of parallel fractures with diffusion in microfissured matrix (early time solution), and
problem 2 with radioactive decay. 3.2.2 Advection-dispersion in parallel fractures with diffusion in rock matrix:early time solution (nonpenetrating case) Consider the geometry in Fig.2 A set of parallel horizontal fractures with definite apertures are spaced a few meters apart. Within the fracture, fluid moves at a constant velocity. As mentioned formerly, it is assumed that flow in the fracture obeys cubic law. The analytical solution to advection- dispersion in parallel fractures with diffusion in rock matrix was obtained by assuming that the rock slabs are replaced by spheres having the same surface to volume ratio as the slabs. As discussed in reference (Rasmuson et al., 1982), this approximation is very good at early times.
Consider a fracture network as illustrated in Fig.3.
