Modèle de compaction élastoplastique et viscoplastique pour simulateur de bassins sédimentaires Elastoplastic and Viscoplastic Compaction Model for the Simulation of Sedimentary Basins

Abstract

Cette étude complète un travail antérieur (Schneider, 1993) qui a permis d'interpréter et de formaliser le modèle de compaction classiquement utilisé dans des simulateurs comme Temispack (Doligez et al, 1986; Ungerer et al. , 1990). Le nouveau modèle présenté ici se distingue du précédent par l'introduction d'une composante viscoplastique dans l'équation qui décrit la compaction. L'ajout de cette composante permet de prendre en compte de façon macroscopique les phénomènes visqueux de la compaction comme la pression-dissolution. En utilisant des valeurs de coefficients de viscosité extrapolées à partir d'expériences de laboratoire, une étude de sensibilité montre que la déformation visqueuse est significative pour des bassins vieux de plus de 1 Ma. Certains tests montrent que le coefficient de viscosité peut être calibré simplement à partir de données de puits et d'expériences simples de laboratoire. À partir de données extraites de la littérature, il a été possible de calibrer un coefficient de viscosité de 2,5 GPa. Ma (= 8 x 10 puissance (22) Pa. s) pour la craie. This article contains formulas (***) which can not be displayed on this screen. This study completes a previous work (Schneider, 1993) in which the compaction model that is conventionally used in models such as Temispack (Doligez et al. , 1986, Ungerer et al. , 1990), has been interpretated and formalized. The new model described here differs from the previous one by the introduction of a viscoplastic component in the formulation of the stress-strain relationships. The addition of this component, allows to take into account, at a macroscopical scale, viscous phenomena of compaction such as pressure solution. The volumetric rheology is then defined by the following system of equations:(***)where phi is porosity; sigma is the effective stress defined as the difference between the overburden weight and the pore pressure; phi index (m) is the maximum effective stress reached by the sediment during its burial. The elastoplastic parameters (Ee, Ea, Eb, phi index (a), phi index (b), phi index (r)) of function Beta can be easily calibrated from experimental data or from well logs data (Hamilton, 1959; Schneider et al, 1993). The viscoplastic parameters (µ index b, phi to the power of (min)) of function alpha can be calibrated from well logs data as shown in this study. They can also be extrapolated, for a given lithology, from experimental data (Gratier and Guiguet, 1986). A sensitivity analysis has been carried out with different values of extrapolated viscous coefficients. The viscous deformation is important (50% of the total strain) for basins older than 1 Ma when the viscous coefficient is lower than a critical value of 10 MPa. Ma This critical value is equal to 100 MPa. M for basin older than 10 Ma and is equal to 1000 MPa. Ma for basin older than 100 Ma. With field data from Scholle (1977), it is possible to estimate the elastoplastic and viscoplastic parameters which define a chalk rheology. Assuming that chalk which had no suffer diagenesis, has been compacted along an elastoplastic path, it is possible to calibrate easily the elastoplasic parameters. Such a calibration can be also performed with laboratory measurements as suggested by Hamilton (1959). When chalk has suffered diagenesis, we assume that the present-day porosity versus effective-stress relationships, extracted from well logs, result both from elastoplastic deformation and viscoplastic deformation. With this assumption, chalk viscosity is evaluated around 2. 5 GPa. Ma. According to the sensitivity analysis, chalk pressure solution (viscoplastic deformation) is noteworthy (10% of the total strain) for basin older than 20 Ma. In conclusion, this model allow to take into account, in a realistic way, pressure solution phenomena which participate to sediments compaction. The major hypotheses are : (1) the transport of species in solution can be neglected in regard to the size of the considered cells; (2) the viscous coefficient is constant for a given lithology; (3) mechanical compaction and chemical compaction depend on the same effective stress. In spite of these restrictive hypotheses, the model gives solutions which are physically acceptable.