The paper proposes two numerical models ot the mechanical behaviour of chalk. First, an elastoplastic constitutive law reproduces the different plastic mechanisms of the chalk and the influence of pore fluids by introducing the concept of suction. Secondly, a model able to reproduce time dependence behaviour. Eventually, the paper gives a simulation of an academic reservoir during depletion and waterflooding phase.

Der Artikel stellt zwei numerische Modelle des mechanischen Verhaltens der Kreide vor. Das erste ist ein elasto-plastisches Modell, das verschiedene plastische Mechanismen der Kreide und den Einfluss von Porenfluessigkeit, unter dem Begriff der Suktion, reproduziert. Das zweite Modell beruecksichtigt darueberhinaus das zeitabhangige Verhalten. Schliesslich zeigt die Veröffentlichung eine Simulation einer theoretischen Lagerstatte wahrend der Entleerung und der Wasserinjektion. L'article propose deux modèles numeriques du comportement mecanique de la craie. Le premier est une loi elasto-plastique qui reproduit les differents mecanismes plastiques de la craie et l'influence du fluide interstitiel par l'introduction de la notion de succion. Le second est un modèle prenant en compte les effets differes. Enfin, l'article presente une simulation d'un reservoir academique durant les phases de depletion et d'injection d'eau.

Introduction

Compaction of chalky reservoirs during oil extraction, implying seabed subsidence, and other important problems are related to the mechanical properties of chalk. The most remarcable behaviour of chalk is its water-sensitivity: water injection in the reservoir induce additional subsidence. Though many studies have been already performed on chalks, the basis mechanism of the water sensitivity was not defined. The ongoing EC Research Program Pasachalk aims to give a better understanding of the chalk behaviour. The origin of the research comes from the comparison between experimental results obtained on Lixhe chalk and on Jossigny silt which showed that the influence of water on pure high porosity chalk is similar to that on partially saturated soils (Delage et al. 1996). Hence the idea appeared to apply the knowledge, the approach, and the tools of the partially saturated soil mechanics to the understanding, description, and modelling of chalk behaviour during changes in saturation fluids, such as when waterflooding.

This paper presents the developed constitutive model, which is a cap type plasticity model coupled with the Barcelona one (Alonso et al. 1990) for taking the suction effect into account.

The model parameters are calibrated based on the experimental results. The validation of the model is performed on a waterflooding experiment.

A second model on viscous is also presented; this is an elasto-visco-plastic model following Perzyna's approach. First numerical results are shown and some comparisons with experiment are given.

Unsaturated flow formulation is necessary here as far as suction has to be known. The flow model used is based on works in relation with the problem of nuclear waste disposal (Collin et al. 2002a). For each fluid (Water and oil), balance equations and state equations are written. In partial saturation conditions, the permeability and the storage law have to be modified: a generalised Darcy's law defines the fluid motion (Bear 1972).

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