A New Approach to the Sedimentation and Compaction of Basin Based on Continuum Mechanics Concepts

Jean-François Barthelemy¹, Jean-Luc Rudkiewicz¹, and Luc Dormieux^2
1IFP 1&4 Av. De Bois-Préau 92852 Rueil-Malmaison Cedex, France
²LMSGC, ENPC, 6-8 Av. Blaise Pascal, 77455 Marne-La-Vallée Cedex 2, France

The current context has led the oil industry to focus its interest on more and more complex zones and, in particular, on zones showing strong overpressures. The latter are due to fluid trapping during the compaction history and can be severely increased by tectonic effects. However, most numerical tools used today in the oil industry may not be well adapted to model such situations. Indeed, whereas significant efforts have been made in the past twenty years to accurately simulate the hydrocarbon genesis and migrations including multiphase flows, the mechanical modelling has remained much too simple. The pioneering work of Athy (1930) led to a characterization of the mechanical compaction as a relationship between porosity and depth depending on the sediment nature. Starting from this work, the current simulators are based on empirical scalar constitutive laws relating the porosity to the effective stress under the additional assumptions of uniaxial compaction and lithostatic vertical stress (see Schneider et al., 1996) which can be very questionable for tectonically complex zones. Moreover, such laws fail to take into account the 3D tensorial effects of the stress on the porosity as well as on the skeleton deformation and can not provide estimate of the horizontal stresses even in the case of a simple basin with uniaxial compaction. Hence, it has become crucial to introduce more sophisticated constitutive laws able to account for complex 3D kinematics and built using parameters having a physical meaning instead of freely adjustable ones.

This work has three objectives. The first one consists in the elaboration of a 3D tensorial constitutive law by means of micromechanical tools so that the properties of the rock seen as a porous medium at the macroscopic scale depend on the microstructure and the properties of the constituents at the lower scale. In a second step, this law will be implemented in a finite element code handling the sedimentation, i.e. the matter supply, possibly the erosion and the hydro-mechanical compaction of the sediments. Finally, the code will be used on a real case showing clearly the gain provided by the use of continuum mechanics concepts.

One of the main difficulties arising from the problem of sediment compaction after the deposit is that the porous medium undergoes large strains. The best evidence remains the porosity decrease (from 50% or more to possibly less than 10%) but they can also induce major changes in the microstructure possibly implying anisotropy. In the framework of finite strains mainly due to irreversible phenomena, a poroelastoplastic law has already been obtained (see Bernaud et al., 2002) and used for the problem of basin sedimentation (see Bernaud et al., 2006). The elastic and plastic properties of this law are obtained thanks to a micromechanical reasoning making them depend on the solid phase properties and on the porosity under the assumption of isotropy. Therefore, their evolution during the process and the consequences on the material behavior can be taken into account. Nevertheless, the pressure solution phenomenon, which is responsible for large strains at great depth, still remains to be considered as it is in the uniaxial law (see Schneider et al., 1996). To this end, a model based on a microstructure made of grains surrounded by a viscous interface is proposed. This model leads to a viscous law at the macroscopic scale which depends on the porosity and the interface properties related to the pressure solution phenomenon. To complete the description of the material properties in the framework of a coupled hydro-mechanical model, it is worth mentioning that the permeability can also be related to the current porosity, using for instance the Kozeny-Carman expression.

A finite element code built thanks to the library Getfem++ is then presented. This code allows modelling the matter supply or erosion as punctual events and the evolution of the basin in the meantime using the finite strain poroelastoviscoplastic law previously determined. Between two events, the time is subdivided in sub-increments in order to progressively activate the density of the added layers. Available in 1D, 2D or 3D, this code also gives the possibility to apply any boundary conditions as for instance prescribed displacements on the lateral sides of the domain in 2D or 3D as a tectonic loading. As outputs, the stress tensor and pressure fields, among others, can be followed during the whole simulation.

This code is finally applied on a foreland basin in a compressive zone undergoing tectonic effects. The influence of the latter on the porosity and pressure evolutions with possible overpressure development is put in evidence.

AAPG Search and Discovery Article #90091©2009 AAPG Hedberg Research Conference, May 3-7, 2009 - Napa, California, U.S.A.