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

Including stratigraphic hierarchy information in geostatistical simulation: a demonstration study on analogs of alluvial sediments

When building a geostatistical model of the hydrofacies distribution in a volume block it is important to include all the relevant available information. Localised information about the observed hydrofacies (hard data) are routinely included in the simulation procedures. Non stationarities in the hydrofacies distribution can be handled by considering auxiliary (soft) data extracted, for example, from the results of geophysical surveys. This piece of information can be included as auxiliary data both in variogram based methods (i.e. co-Kriging) and in multiple-point statistics (MPS) methods. The latter methods allow to formalise some soft knowledge about the considered model of heterogeneity using a training image. However, including information related to the stratigraphic hierarchy in the training image is rarely straightforward. In this work, a methodology to include the information about the stratigraphic hierarchy in the simulation process is formalised and implemented in a MPS framework. The methodology is applied and tested by reconstructing two model blocks of alluvial sediments with an approximate volume of few cubic meters. The external faces of the blocks, exposed in a quarry, were thoroughly mapped and their stratigraphic hierarchy was interpreted in a previous study. The bi-dimensional (2D) maps extracted from the faces, which are used as training images and as hard data, present a vertical trend and complex stratigraphic architectures. The training images and the conditioning data are classified according to the proposed stratigraphic hierarchy, and the hydrofacies codes are grouped to allow a sequence of interleaved binary MPS simulation. Every step of the simulation sequence corresponds to a group of hydrofacies defined in the stratigraphic hierarchy. The blocks simulated with the proposed methodology are compared with blocks simulated with a standard MPS approach. The comparisons are performed on many realisations using connectivity indicators and transport simulations. The latter are performed with the Kolmogorov-Dmitriev method, which allows to investigate the transport behaviour at a spatial scale one order of magnitude bigger than the scale of the model blocks, using the transport properties statistics extracted from the results of particle tracking simulations on the model blocks. To allow a direct comparison with the observed facies maps, which are available in 2D only, all the aforementioned comparison are first performed in 2D and subsequently on the three-dimensional blocks

A stochastic multi-scale approach to study contaminant transport in heterogeneous alluvial sediments

Equiprobable spatial distributions of hydrofacies can be modelled by stochastic simulations, conditioned on field data. Such 3D arrays can be used as input data in numerical models of groundwater flow and contaminant transport, which can be used to assess how the fine scale heterogeneity affects contaminant transport at large scale. The most common stochastic simulation method is Sequential Indicator Simulation (SISIM). Despite being widely used, SISIM suffers some weaknesses, e.g., in integrating geological information and in reproducing structures with curved shapes. This work deals with a modification of SISIM with a hierarchical approach (HSISIM), which consists in the repeated application of SISIM to perform binary simulations at different hierarchical levels. The advantages of this approach are (1) the possibility of designing a hierarchy based on geological information and (2) the shorter simulation time than for the standard approach, because the time required by SISIM dramatically increases with the number of hydrofacies that are simultaneously simulated. We illustrate the advantages of the proposed hierarchical method over the standard SISIM using the hydrofacies mapped on the sides of three blocks of glacio-fluvial sediments that were dug in a open air quarry in the Ticino valley (Northern Italy). Each block has a volume of few cubic meters and most of their lateral sides have been analyzed and mapped from the sedimentological point of view with a resolution of 5 cm. From the three field data sets, different ensembles were obtained both with SISIM and with two different HSISIM applications: the first one based on the relative abundance of the hydrofacies; the second one based on geological arguments. Then, the results of the geostatistical simulations were used to perform numerical transport experiments that yielded the statistical distribution of average pore water velocity and effective longitudinal dispersion coefficients at a scale length of the order of 1 m. Finally, these probability distributions were used to predict the fate of toxic and radioactive contaminants over a length scale of 100 m with a 1D stochastic model of solute transport model based on the Kolmogorov-Dmitriev theory in a Montecarlo framework. The results confirm that a proper estimate of contaminant transport requires a precise reconstruction of the heterogeneity field at the fine scale

A multidisciplinary research on aquifer analogues to assess the effect of hydrofacies heterogeneities at fine scale on solute transport al large scale

A multidisciplinary approach (sedimentology, hydrology, geophysics, applied mathematics and informatics) is necessary to study "field virtual aquifers" or "aquifer analogues", i.e., geological bodies which are well exposed, can be analyzed with field surveys, and can be assumed to be similar to the buried aquifers from the geometrical and lithological point of view. They are used to build "numerical virtual aquifers", i.e., 3D arrays of categorical or continuous variables, which describe the spatial distribution of physical properties, share the same statistical properties as the field data and can be the basis to perform synthetic experiments with numerical flow and transport models. Therefore, virtual aquifers are a tool to understand the effects that fine scale hydrofacies heterogeneity has on solute transport at large scale. This is done through the following steps. a. Collection of geological, geophysical and hydrological field data. b. Hydrostratigraphic description of the aquifer analogues. c. Laboratory analysis on samples to determine grain-size-distribution and hydraulic conductivity of different facies. d. Geostatistical simulation of the hydrofacies distribution. e. Set up of virtual aquifers. f. Flow modelling and determination of the equivalent conductivity tensor. g. Numerical experiments of 3D convective transport of a non-reactive solute for an average 1D flow and determination of the lagrangian dispersion tensor and of the effective eulerian dispersion coefficients. h. Numerical experiments of 1D large-scale convective transport with stochastic transport models based on the Kolmogorov-Dmitriev theory in a Montecarlo framework. This approach has been tested on aquifer analogues representative of the hydrostratigraphic features of the alluvial Po plain (Northern Italy)