A hierarchical multiple-point statistics simulation procedure for the 3D reconstruction of alluvial sediments

A correct representation of the heterogeneity of porous formations and of their preferential flow paths is crucial for a reliable modelization of the contaminant transport processes. Several geostatistical tools have been developed to tackle this challenge. Many of these tools are often applied in a multi-scale framework, where the geostatistical simulation is applied fist trying to reproduce the big scale features of the sedimentary formations, and finally to reproduce their small scale features. However, many of the developed multi-scale and hierarchical techniques have a quite complex work-flow and rely on diverse simulation methods. Here a simplified hierarchical simulation procedure is proposed, where only multiple-point statistics (MPS) is used to simulate the target heterogeneities at different scales. The simulation procedure is organized in a tree-like frame, where MPS is applied at each simulation branch using a simplified binary training image and the corresponding available conditioning data. At each simulation branch, the MPS simulation is performed in a sub- domain defined by one of the two facies codes simulated at the parent branch. The proposed procedure is tested in the three-dimensional (3D) reconstruction of two model blocks of alluvial sediments, using the available two-dimensional (2D) outcrop information as training images. It is compared against a non hierarchical MPS simulation procedure in terms of connectivity indicators and breakthrough curves obtained from 3D particle tracking numerical experiments. All the aforementioned tests are performed considering 100 equiprobable realizations for each simulation technique. This allows to make statistically reliable comparisons, and to extract statistical distributions of the transport parameters by fitting analytical curves to the results of the particle tracking experiments. These statistical distributions are used to perform one-dimensional transport experiments on spatial scales ten times bigger than the block scale using the Kolmogorov-Dmitriev approach in a Monte Carlo framework.