Effects of Inhomogeneity and Anisotropy on THM Simulations

When modeling the material properties of host rocks for THM simulations for the purpose of barrier integrity investigations in deep geological disposal of radioactive waste, there are numerous modeling aspects to consider. We consider the simple case of stationary Darcy flow in a two-dimensional medium to convey the basic phenomena when constructing a suitable model for host rock permeability with a special focus on the treatment of anisotropy occurring at different spatial scales and the associated uncertainty. If complete information were available, permeability would be a known function of space, and hydrological features such as inhomogeneity (spatial variability) and anisotropy (direction-dependence) can be expressed by spatially varying and tensor-valued permeability coefficients. In reality, uncertainty is present and needs to be considered. One approach is to model the rock medium as piecewise homogeneous in such a way that the permeability values in each homogeneous subregion (e.g. geological layer) are modeled as random variables. The permeability values at any two locations of the same subregion are then completely correlated. Randomness with a more general structure can be modeled by random fields, the realizations of which are functions of space which are not necessarily constant. A common modeling choice is that of a Gaussian random field for log permeability, which is completely determined by its mean and two-point correlation function. Anisotropy can now occur both in the statistical covariance structure, resulting in different correlation lengths along principal axes, and in the hydraulic properties, leading to tensor-valued random fields the realizations of which are anisotropic tensors for which the underlying covariance structure may, in addition, display statistical anisotropy.

In this work we present a number of simulations designed to illustrate the effects of inhomogeneity, randomness as well as statistical and hydraulic anisotropy.