Sedimentological and erosional processes often result in a complex three-dimensional subsurface architecture of sedimentary structures and facies types. Such complex sedimentological heterogeneity may induce a highly heterogeneous spatial distribution of hydrogeological parameter values in porous media at different scales (Klingbeil et al. 1999) and may consequently greatly influence subsurface fluid flow and solute migration (Koltermann and Gorelick 1996). Therefore, groundwater flow and transport models rely on a detailed description of the hydraulic properties of the subsurface. Because of the limited access to the relevant hydraulic properties, deterministic models often fall short in characterizing the subsurface heterogeneity and its inherent uncertainty. In recent decades, numerous stochastic approaches have been developed to overcome this problem.
Most of these methods employ a variogram to characterize the heterogeneity of the hydraulic parameters (Goovaerts 1997; Deutsch and Journel 1998; Caers 2005). Variograms are calculated based on two-point correlations only and therefore have some important limitations. Variograms are not able to describe realistic heterogeneity in complex geological environments. Complex geological patterns including sedimentary structures, multi-facies deposits, structures with large connectivity, curvi-linear structures, etc. cannot be characterized using only two-point statistics (Koltermann and Gorelick 1996; Fogg et al. 1998; Journel and Zhang 2006). Moreover, variograms, as a limited and parsimonious mathematical tool, cannot take full advantage of the possibly rich amount of geological information from outcrops (Caers and Zhang 2004).

Multiple-point geostatistics aims to overcome the limitations of the variogram. The premise of multiple-point geostatistics is to move beyond two-point correlations between variables and to obtain (cross) correlation moments at three or more locations at a time (Guardiano and Srivastava 1993; Strebelle and Journel 2001). Because of the limited direct well information from the subsurface, such statistical information cannot directly be obtained from samples. Instead, “training images” are used to characterize the patterns of geological heterogeneity. A training image is a conceptual explicit representation of the expected spatial distribution of hydraulic properties or facies types. The main idea is to borrow geological patterns from these training images and anchor them to the subsurface data domain. Such data may consist of well observation, geophysical and pumping or tracer tests. Construction of a suitable training image is one of the most critical and difficult steps of multiple-point geostatistics. The training image should be representative of the geological heterogeneity and must be large enough so that the essential features can be characterized by statistics defined on a limited point configuration (Hu and Chugunova 2008). Multiple-point geostatistics have recently been developed in the field of petroleum engineering (Strebelle 2000, 2002; Caers and Zhang 2004; Hu and Chugunova 2008); the method has been applied to several real-case studies (e.g., Strebelle 2002). Applications of the method in the field of hydrogeology are very scarce. Feyen and Caers (2006) applied the method to a synthetic two-dimensional case to conclude that the method is potentially a powerful tool to improve groundwater flow and transport predictions. Ronayne et al. (2008) used multiple-point geostatistics in an inverse modelling approach to identify discrete geologic structures that produce anomalous hydraulic responses.

Objectives

The aim of this study is to investigate to which extent multiple-point geostatistics is a suitable technique to determine the impact of complex geological heterogeneity on groundwater flow and transport in real 3D cases. Obtaining a suitable training image (or multiple training images if uncertain about the underlying geological scenario) is the most critical step of multiple-point geostatistics. Therefore this study focuses on the suitability of different methods to obtain training images for the amount and type of data typically available in hydrogeological studies. Furthermore, this study compares multiplepoint geostatistics with traditional variogram-based methods to determine the advantages of multiple-point geostatistics to predict groundwater flow and transport, e.g., the response to pumping or transport of groundwater pollutants.

Design and methodology

To obtain these goals, the method is applied on synthetic examples and on a real heterogeneous aquifer, i.e., the Brussel Sands. The Brussel Sands are one of the most important and most studied aquifers of Belgium. It is a sandbar deposit with an internal
sedimentary architecture consisting of cross-bedded units. The Brussel Sands are a tidal deposit composed of materials with different grain sizes and hydraulic conductivities. This type of heterogeneity and anisotropy has already resulted in problems with pumping test
interpretation and prediction of pollutant transport. The sedimentological and hydrogeological properties of the Brussel Sands have been intensively studied in our research group (e.g., Houthuys, 1990; Bal, 1998).
This study consists of the following steps:

1. All available geological, sedimentological and hydrogeological information of the Brussel Sands are collected. Extra in situ measurements are carried out to obtain high resolution spatial distributions of the geometry of the different facies and of hydraulic conductivity so that they can be statistically processed. The Bierbeek quarry isthe reference quarry since this outcrop can be assumed as representative for the sandbar facies of the Brussel Sands according to the work of Houthuys (1990).

2. Training images of the Brussel Sands are constructed with different methods. A first method to construct a training image of hydraulic conductivity is the direct method using high resolution measurements of hydraulic conductivity. A second method uses geological and sedimentological information in addition to hydrogeological information. This second method consists of first constructing a training image of the geological structure using outcrop data and conceptual geological sketches and secondly simulating hydraulic conductivity inside each facies. A third method uses, besides hydrogeological and geological information, also high resolution geophysical data, e.g., Ground Penetrating Radar (GPR). These different methods to construct training images are evaluated and the importance of geological, sedimentological and hydrogeological data for obtaining a realistic and representative training image are quantified.

3. Hydraulic conductivity realizations borrowing patterns of geological heterogeneity from the training image are generated using several existing method available from Stanford University. These realizations are conditioned using primary hydraulic conductivity information and secondary information such as grain size measurements and geophysical data.

4. The realizations are used as input in a local hydrogeological model of a pumping well or a pollutant source in the Brussel Sands to determine the effect of complex heterogeneity on groundwater flow and transport. The results of this analysis are compared with the results of more traditional variogram-based stochastic methods.

Results

This study is one of the first studies to apply multiple-point geostatistics on a 3D real case study in the field of hydrogeology. This study clarifies the advantages and disadvantages of this techniques for hydrogeological applications compared to the traditional variogram-based techniques. This study provides guidelines on how the different types of information available in hydrogeological studies can be used to construct training images. The importance of geological, sedimentological and hydrogeological data for obtaining a realistic and representative training image are quantified. The constructed 3D training image of the Brussel Sands is useful for this study, but can also be a model for other sandbar deposits that are important as groundwater and petroleum reservoirs in other parts of the world. This training image can be a part of an international library of training images of different types of geological environments. The impact of the heterogeneity of a sandbar deposit on groundwater flow and transport is quantified. The conditions under which the heterogeneity and anisotropy caused by primary sedimentary structures should be taken into account is determined.

Publications

• Huysmans M. and Dassargues A., 2009, Application of multiple-point geostatistics on modeling groundwater flow and transport in a cross-bedded aquifer, Hydrogeology Journal 17(8), 1901-1911
• Huysmans M., Peeters L., Moermans G. and Dassargues A., 2008, Relating small-scale sedimentary structures and permeability in a cross-bedded aquifer, Journal of Hydrology 361, 41-51
• Huysmans M. and Dassargues A., 2008, Application of multiple-point geostatistics on modeling groundwater flow and transport in a cross-bedded aquifer, Geostatistics for Environmental Applications, Proceedings of the 7th European Conference on Geostatistics for Environmental Applications, Southampton, 8-10 September 2008

References

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• Huysmans M. and Dassargues A., 2009, Application of multiple-point geostatistics on modeling groundwater flow and transport in a cross-bedded aquifer, Hydrogeology Journal 17(8), 1901-1911
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Huysmans M. and Dassargues A., 2009, Application of multiple-point geostatistics on modeling groundwater flow and transport in a cross-bedded aquifer, Hydrogeology Journal 17(8), 1901-1911

Link to article:
http://www.springerlink.com/content/324114506t32573m/fulltext.html

Huysmans M., Peeters L., Moermans G.  and Dassargues A., 2008, Relating small-scale sedimentary structures and permeability in a cross-bedded aquifer, Journal of Hydrology 361, 41-51

Link to article:
linkinghub.elsevier.com/retrieve/pii/S0022169408003569