The use of connectivity clusters in stochastic modelling of highly heterogeneous porous media

Stochastic geostatistical techniques are essential tools for groundwater flow and transport modelling in highly heterogeneous media. Typically, these techniques require massive numbers of realizations to accurately simulate the high variability and account for the uncertainty. These massive numbers of realizations imposed several constraints on the stochastic techniques (e.g. increasing the computational effort, limiting the domain size, grid resolution, time step and convergence issues). Understanding the connectivity of the subsurface layers gives an opportunity to overcome these constraints. This research presents a sampling framework to reduce the number of the required Monte Carlo realizations utilizing the connectivity properties of the hydraulic conductivity distributions in a three-dimensional domain. Different geostatistical distributions were tested in this study including exponential distribution with the Turning Bands (TBM) algorithm and spherical distribution using Sequential Gaussian Simulation (SGSIM). It is found that the total connected fraction of the largest clusters and its tortuosity are highly correlated with the percentage of mass arrival and the first arrival quantiles at different control planes. Applying different sampling techniques together with several indicators suggested that a compact sample representing only 10% of the total number of realizations can be used to produce results that are close to the results of the full set of realizations. Also, the proposed sampling techniques specially utilizing the low conductivity clustering show very promising results in terms of matching the full range of realizations. Finally, the size of selected clusters relative to domain size significantly affects transport characteristics and the connectivity indicators.