Stochastic Models for Characterizing Variability of Hydro-Geological Parameters

This review highlights some of the progresses achieved in modelling spatial variability of hydro-geological parameters using the stochastic approach. The reason for this approach is two folds. First, the erratic nature of the hydro-geological parameters observed at field data. Second, the uncertainty due to the lack of information about the subsurface structure that is known only at sparse sampled locations. In this paper the frequently used techniques for unconditional and conditional stochastic models in porous formations have been reviewed. These techniques are the tools to solve stochastic differential equations of flow and transport in porous media either analytically or numerically. In the presented techniques, spatial variability of aquifer parameters is modelled as stationary correlated random fields. These fields are used as input to the classical differential equations to evaluate the effect of spatial variability on flow and transport characteristics. The algorithms used for site characterization and generating heterogeneous descriptions of porous formations are reviewed. These algorithms can be divided broadly into discrete facies models, continuous models and hybrid models. In discrete facies models, the heterogeneity is described as geometrical shapes of geological units, parameter values to which can later be assigned. In continuous models, the heterogeneity is described as random parameters governed by joint probability distributions. In hybrid models both continuous and discrete models are used. The Monte-Carlo approach is a powerful tool to estimate uncertainty. It handles realistic situations where the flow is controlled by complex boundary conditions in comparison with analytical approaches. It handles the non-linearities of the systems