*Oil & Gas Science and Technology - Rev. IFP*Vol. 48 (1993), No.1, pp. 3-14

## Modèle de compaction élasto-plastique en simulation de bassins

### Elastoplastic Compaction Model for Basin Simulation

Institut Français du Pétrole

Cet article présente un modèle de compaction des sédiments pour simulateurs de bassins sédimentaires. Dans ce modèle, les concepts précédemment utilisés dans le modèle TEMISPACK sont généralisés et décrits en s'inspirant des formalismes propres à la mécanique des roches et à la mécanique des sols. La compaction des sédiments est décrite, à l'échelle des temps géologiques, par un modèle élasto-plastique où les modules d'incompressibilité et d'écrouissage croissent lorsque la déformation augmente et où le seuil de plasticité est variable. La rhéologie est définie par une relation qui lie la porosité (ou le volume) du sédiment à la contrainte effective moyenne en se plaçant dans l'hypothèse de déformation oedométrique. Ce modèle à rhéologie volumiquea été testé sur le logiciel COMP1D qui simule, en 1D, l'histoire géologique d'une colonne sédimentaire. Ce modèle ne doit être considéré que comme un premier pas vers un formalisme plus complet.

Abstract

This article describes a sediment compaction model for sedimentary basin simulators. In this model, the concepts previously used in the TEMISPACK model are generalized and described on the basis of formalisms inherent in rock mechanics and soil mechanics. Sediment compaction is described on the geologic time scale by an elastoplastic model (Fig. 1) in which the moduli of incompressibility and strain hardening increase as deformation increases and in which the plasticity threshold varies. The rheology is defined by an equation connecting the porosity (or volume) of the sediment to the mean effective stress by situating itself within the hypothesis of consolidometric deformation. This model is quite similar to the ones used in soil mechanics. It differs only by the choice of the equations linking the volumic variation of the porous medium to the variation of the mean effective stress likewise, in this part coefficient alpha introduced in the definition of effective stress is close to 1, which is coherent with the hypothesis of considering the grains making up the skeleton as being indeformable. COMP1D is a software that makes a 1D simulation of the geologic history of a sedimentary column. It integrates the physical phenomena described in the first part. The geometric variations caused by sedimentation, erosions and compaction are taken into consideration by introducing various Lagrangian coordinate systems (Fig. 2). The temperature is imposed by a surface temperature and a gradient. The boundary conditions are the ones conventionally used in basin simulators. There are various versions of the software corresponding to different numerical approaches. Our problem was discretized by finite-element methods with linear shape functions, finite-element methods with quadratic shape functions, and finite-volume methods. Numerous tests showed that the pressure solution to convergence is identical for all such methods. However finite-element methods cannot be used to compute a velocity field for the fluid that gives perfect local conservation. This local conservation is absolutely necessary for coupling a transport equation (heat equation, saturation equation for two-phase flows) with the computing of the pressure of the fluid. Only finite-volume methods, which handle nonlinearities (Newton's method) correctly, are locally perfectly conservative. This model improves preceding models, mainly by introducing the concept of elasticity. However, as things now stand and from the theoretical standpoint, it is valid only in the superficial layer of sediments. Its extension to deeper layers is acceptable in basin simulators only because the porosity variation is slight. The introduction of an alpha coefficient in the definition of the effective stress seems necessary. However, the fact of taking this coefficient different from 1 must, for reasons of coherence, lead us to give increased consideration to the mechanical deformations of the grains. The results obtained with this model show that, when consideration is given to variations in the density of the fluid and solid with pore pressure and temperature, this makes for an important change in the porosity values and pressure excess computed. However, these variations are less than the uncertainties concerning the data during a case study. When coefficients alpha and Ko (or v) are taken into consideration, the results obtained are different, but their order of magnitude remains compatible with those given by the model, which does not take these coefficients into consideration (Fig. 3). These concepts will have to be tested for real cases by comparison with more conventional approaches.

*© IFP, 1993*