C. de Fouquet

Conditional Simulation of Random Sets — Application to an Argilaceous Sandstone Reservoir

The validity of dynamic simulations carried out by reservoir engineers depends on the reservoir model used. The continuity of the reservoir layers is poorly known because of the small number of drillholes available and the distance between them. The aim of this study of an outcrop, is to develop a method for simulating the geometry of the reservoir. The sedimentological study provides an image of this outcrop with 4 lithofacies. The interpretation of this image as a realisation of random sets obtained by truncating Gaussian functions leads to a simulation process and a structural analysis method. This process is efficient provided that factorizable covariances of an exponential type, suited to describe sedimentary processes, are used. The 3-D covariance models are fitted to the data from the coredrills carried out behind the cliff. Then simulations of the whole reservoir are made.

Using Geostatistics for Forest Inventory with Air Cover: An Example

The forest of Zurichberg was sampled in order to determine a method to be used for forest inventory. It was carried out in two ways: by an accurate but costly terrestrial survey on regularly spaced plots; by an aerial photographic campaign. The photos give, at low costs, large quantities of less accurate qualitative information.

Geostatistic Indicators of Waterway Quality for Nutrients

This paper aims at constructing geostatistical indicators to quantify water quality for nutrients. It presents a method to estimate the yearly mean and the 90th percentile of concentrations, taking into account temporal correlation, irregularity of sampling and seasonal variations of concentrations. On simulations, segment of influence declustering, kriging weighting and a linear interpolation of empirical quantiles are calculated and compared to the currently used statistical inference, based on the independence of random variables. These methods make it possible to correct the bias of the yearly mean and the quantile, and to improve their precision, giving a better prediction of the estimation variance. The study focuses on nitrates, in the LoireBretagne basin (France).

Estimating indicators of river quality by geostatistics

In order to assess river water quality, nitrate concentrations are measured in different monitoring stations. The information contained in these measurements is summarized in a few synthetic quantitative indicators such as the 90% quantile of yearly concentrations or the annual mean making it possible to compare water quality in different stations, and its yearly evolution. The current French recommendations are based on the French water quality’s evaluation system (SEQ EAU, http://www.rnde.tm.fr/) and the water framework directive in Europe, which aims at achieving good water status for all waters by 2015. These calculations, however, use the classical statistical inference, essentially based on a hypothesis proved to be incorrect for nutrients (Bernard-Michel and de Fouquet 2003): time correlations are not taken into account. Moreover, the seasonal variations of concentrations and the monitoring strategy are ignored. For example, because of the run-off or the leaching of fertilizer, nitrate concentrations of Loire Bretagne basin are often high in winter and low in summer (Payne 1993). Thus, if sampling is increased in winter out of precaution, the annual mean and the quantile can be falsely increased. It is therefore necessary to develop methods that take into account both time correlations and sampling dates, especially in case of preferential sampling. We propose to assign kriging weights or segment of influence weights (Chiles 1999) to measurements for both indicators and to use a linear interpolation of the empirical quantile for the estimation of the 90 percentile. In this paper, methods are presented and compared for nutriments on simulations.

Estimating the Grades of Polluted Industrial Sites: Use of Categorical Information and Comparison with Threshold Values

Sampling of polluted sites often leads to inaccurate estimates, particularly because of the small number of samples, the importance of sampling errors and the high spatial variability at small distance. Auxiliary information like the history of the site or qualitative measurements are of interest to improve the quality of the grade estimates. The relationship between grades and soils information (presence of coal tar, smell, clay...) are examined on a former coking plant, polluted by PAH (Polycyclic Aromatic Hydrocarbons). A sensitivity analysis shows the utility of this auxiliary information known at additional points compared to the univariate kriging of the grades. Delineation of the zones to remediate is frequently carried out by selecting the areas where the estimated grades exceed the chosen remediation grade. If the estimation is subject to large uncertainties, this selection may generate bias. Estimation of the probability that the true grade is greater than the remediation value makes it possible to take into account the uncertainties associated to the estimated grades. Moreover, it is necessary to specify the support to be retained for this selection, which differs generally from the support of the samples. Neglecting this support effect leads to bias in the calculation of the soil volumes to remediate, as the proportion of the values exceeding a given grade varies with the support size (samples, blocks of various sizes). In this paper, conditional expectation and disjunctive kriging are compared for the estimation of the probability to exceed a threshold on blocks. The evaluation of polluted sites is then improved using a consistent methodology.

Distributed Simulation of Daily Stream-Aquifer Exchanged Fluxes in the Seine River Basin at the Regional Scale

The interaction between surface and groundwater is a complex process and depends on many physical factors that are directly related to topography, geology and climate. The description of those interactions in the simulation process is necessary to better assess hydraulic heads in near stream aquifer units and to improve the assessment of stream-aquifer water exchanged fluxes. This motivated researchers to focus on coupled models. Among the coupled models used by the scientific community, the EauDyssee modelling platform, jointly developed by Mines Paristech and UMR 7619 Sisyphe, couples existing specialized models to address water resources and quality in river basins. In the present study, we used 7 models based on the EauDyssee platform to quantify the daily spatially distributed water flow exchanged between aquifer units and surface water systems in the Seine river basin and Basse Normandie’s coastal watersheds (France). The modelled domain covers an area of 69,000 km2 and is composed of a 13,622 km-river network. Models simulations provide a description of the hydrosystem behaviour with regards to different anthropogenic (with and without pumpings) and climatic (dry, humid and pluri-annual) scenarios. Results of the simulation were synthesized in a database which provides a valuable tool to assess river water bodies [Water Framework Directive management units (E.U., Dir 2000)] vulnerability to potential groundwater contamination or groundwater resource depletion.