Direct multiple-point geostatistical simulation of edge properties for modeling thin irregularly-shaped surfaces

Thin irregularly-shaped surfaces such as clay drapes often have a major control on flow and transport in heterogeneous porous media. Clay drapes are often complex curvilinear 3-dimensional surfaces and display a very complex spatial distribution. Variogram-based stochastic approaches are often also not able to describe the spatial distribution of clay drapes since complex, curvilinear, continuous and interconnected structures cannot be characterized using only two-point statistics. 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 using "training images" to characterize the patterns of geological heterogeneity. Multiple-point geostatistics is able to reproduce thin irregularly-shaped surfaces such as clay drapes but is often computationally intensive. To capture the thin surfaces, a small grid cell size should be adopted for the training image. This results in large training images and a large search template size and thus a large CPU and RAM demand (Huysmans and Dassargues, 2009)

Application of multiple-point geostatistics on modelling groundwater flow and transport in a cross-bedded aquifer (Belgium)

Sedimentological processes often result in complex three-dimensional subsurface heterogeneity of hydrogeological parameter values. Variogram-based stochastic approaches are often not able to describe heterogeneity in such complex geological environments. This work shows how multiple-point geostatistics can be applied in a realistic hydrogeological application to determine the impact of complex geological heterogeneity on groundwater flow and transport. The approach is applied to a real aquifer in Belgium that exhibits a complex sedimentary heterogeneity and anisotropy. A training image is constructed based on geological and hydrogeological field data. Multiple-point statistics are borrowed from this training image to simulate hydrofacies occurrence, while intrafacies permeability variability is simulated using conventional variogram-based geostatistical methods. The simulated hydraulic conductivity realizations are used as input to a groundwater flow and transport model to investigate the effect of small-scale sedimentary heterogeneity on contaminant plume migration. Results show that small-scale sedimentary heterogeneity has a significant effect on contaminant transport in the studied aquifer. The uncertainty on the spatial facies distribution and intrafacies hydraulic conductivity distribution results in a significant uncertainty on the calculated concentration distribution. Comparison with standard variogram-based techniques shows that multiple-point geostatistics allow better reproduction of irregularly shaped low-permeability clay drapes that influence solute transport.status: publishe

Estimation of the Effective Permeability of Heterogeneous Porous Media by Using Percolation Concepts

In this paper we present new methods to estimate the effective permeability (k_eff) of heterogeneous porous media with a wide distribution of permeabilities and various underlying structures, using percolation concepts. We first set a threshold permeability (k_th) on the permeability density function (pdf) and use standard algorithms from percolation theory to check whether the high permeable grid blocks (i.e. those with permeability higher than k_th) with occupied fraction of “p” first forms a cluster connecting two opposite sides of the system in the direction of the flow (high permeability flow pathway). Then we estimate the effective permeability of the heterogeneous porous media in different ways: a power law (k_eff=k_th p^m), a weighted power average (k_eff=[p.k_th^m+(1-p).k_g^m ]^(1/m) with k_g the geometric average of the permeability distribution) and a characteristic shape factor multiplied by the permeability threshold value. We found that the characteristic parameters (i.e. the exponent “m”) can be inferred either from the statistics and properties of percolation sub-networks at the threshold point (i.e. high and low permeable regions corresponding to those permeabilities above and below the threshold permeability value) or by comparing the system properties with an uncorrelated random field having the same permeability distribution. These physically based approaches do not need fitting to the experimental data of effective permeability measurements to estimate the model parameter (i.e. exponent m) as is usually necessary in empirical methods. We examine the order of accuracy of these methods on different layers of 10th SPE model and found very good estimates as compared to the values determined from the commercial flow simulators