G. de Marsily

Calculating equivalent permeability : a review

Abstract The purpose of this article is to review the various methods used to calculate the equivalent permeability of a heterogeneous porous medium. It shows how equivalence is defined by using a criterion of flow or of the energy dissipated by viscous forces and explains the two different concepts of effective permeability and block permeability. The intention of this review is to enable the reader to use the various published techniques and to indicate in what circumstances they can be most suitably applied.

Modelling storage behaviour in a fractured rock mass

Abstract A transient model was used to represent single borehole injection tests in fractured rock masses, on the basis of a three-dimensional stochastic description of the fracture network and of the mechanical behaviour of the fractures. The rock matrix remains impervious and storage occurs in the fractures, with a nonlinear compliance effect depending on both fluid pressure and normal closure stress acting on the joints. The aim of the study is to show how the shortest, weakly connected joints can be removed and replaced in the system by an equivalent parameter. These efforts can save computer time or enlarge the modelled rock volume. Moreover, this approach may be helpful in addressing the troublesome up-scaling problem in discontinuous media.

A model for simulating the influence of a spatial distribution of large circular macropores on surface runoff

This paper reports the development and test, at the scale of 1 m 2 , of an event-based model that aims at simulating the influence of a spatial distribution of large circular macropores on surface runoff. The main originality of this model is that it focuses on the way macropores are supplied with water at the soil surface, by coupling an original model for water interception by individual macropores to a high-resolution spatialized overland flow model. A three-step evaluation of the model was carried out, involving (1) an experimental test of the model for water interception by macropores; (2) a sensitivity analysis of the model to time and space discretization; and (3) a comparison between numerical and field results in the case of runoff on a crusted soil surface with a population of large macropores made by termites in the Sahel. The model was found to accurately simulate the effect of a spatial distribution of large macropores on runoff, and it showed that small heterogeneities, like macropores or areas where a crust has been destroyed, which cover a very limited proportion of the soil surface, can have a high impact on runoff.

The thermogravitational effect in porous media: A modelling approach

The thermogravitational effect may induce large concentration contrasts, particularly in porous media. This phenomenon arises from a coupling of the Soret effect and convection currents in a temperature field. The present study of this phenomenon is motivated by the safety assessment of nuclear waste repositories, which are sources of thermal energy. Here, we present a modelling approach of laboratory experiments carried out at the University of Toulouse. The results of this model, though more adequate than the analytical solution to account for the influence of permeability, remain far from the experimental ones. In conclusion, it appears that the research must now focus on both a comprehensive phenomenology of the transport processes and experiments with new dimensional constraints.

Production Data Integration Using a Gradual Deformation Approach: Application to an Oil Field (Offshore Brazil)

History matching of geostatistical reservoir models requires efficient tools for coherently modifying model realizations. In recent years, the gradual deformation approach has been developed and successfully applied to several simple (synthetic or pseudo-real) cases. This paper presents the application of the gradual deformation method for history matching to a real oil field located offshore Brazil. The oil reservoir consists of turbiditic sandstones interbedded by shales and marls. The data set includes 47 wells with lithofacies description and 15 years production history. A fine scale geostatistical lithofacies model was built using the non-stationary truncated Gaussian approach. The model is conditioned to the lithofacies data at wells and takes into account the non-stationary distribution of the lithofacies. The sensitivity of the dynamic behavior with respect to the model realizations was studied. Preliminary results of using gradual deformation method for improving history matching are presented.

Simplified Renormalization: A New Quick Upscaling Technique

A new technique for the quick upscaling of absolute permeabilities is presented. It is shown that this method and the tensorial renormalization are more reliable than the standard renormalization, the Kruel-Romeu formula and the algebraic means, for the two high anisotropy ratios, for the two different block sizes and for the two geostatistical models we have tested. The comparison of the execution time for the different techniques leads us to recommend the use of the new method in the case where the non-diagonal terms of the permeability tensors are not necessary. If the non-diagonal terms are necessary we recommend the use of the tensorial renormalization.

Results from a Comparison of Geostatistical Inverse Techniques for Groundwater Flow

The Waste isolation Pilot Plant (WIPP) is a U.S. Department of Energy (DOE) facility located in southeastern New Mexico which is currently being evaluated to assess its suitability for isolating transuranic wastes generated by defense programs in the U.S. The proposed repository is located within the bedded salt of the Salado Formation at a depth of about 660 meters. The Culebra Dolomite, located within the Rustler Formation at a depth of about 250 meters, has been characterized as the most transmissive, laterally continuous hydrogeologic unit above the repository, and is considered a potentially important transport pathway for offsite radionuclide migration within the subsurface. This could occur if, for example, in the future, a well drilled for exploration purposes created an artificial connection between the waste and the Culebra aquifer. Such a scenario is part of a Probabilistic Performance Assessment (PA) that the U.S. Environmental Protection Agency (EPA) requires the DOE to perform to demonstate the compliance of the repository system with regulations governing disposal of radioactive wastes. Because the EPA regulation is probabilistic, Pas must accurately reflect the variability and uncertainty within all factors that contribute to the simulation of repository performance for isolating the wastes.