1-D Modelling rock compaction in sedimentary basins using a visco-elastic rheology

Abstract

Recent experimental studies on unlithified sediments suggest that the compaction is in part viscous. At the basin scale and on a geological time scale, processes such as pressure solution can be approached by creep deformation, subjected to a viscous rheology. In the present work, we have studied porosity reduction and fluid pressure development resulting from the visco-elastic compaction of a sedimentary basin during its formation. Model equations include continuity equations, Darcy’s law and a visco-elastic rheology law which relates the strain rate to the effective stress and to the rate of change of this effective stress. Under the assumption that permeability is a power law function of porosity, the equations become essentially non-linear. Model results illustrate how the decrease of porosity starts at the base of the basin and spreads upward with increasing time. In a wide range of input parameter values calculations indicate a zone of almost linear increasing of pore pressure just below the basin surface, a transition zone of rapidly increasing fluid pressure with a large pressure gradient and a zone of lithostatic fluid pressure below. This is consistent with the general features of zoning of fluid pressure distribution in overpressured areas but zones with high pressure also correspond to low porosity at depth. The relative thickness of the zones depends on time, subsidence velocity and the physical parameters of sediments which can be combined in order to define a characteristic compaction length and a characteristic compaction time. In the upper zone, the decrease of porosity results in a boundary layer; within this layer, the porosity decreases from its initial value down to its minimum value. The deeper zone appears when the time of formation of the given depth basin exceeds the characteristic compaction time and the thickness of the basin is in order of compaction length. Zones of fluid overpressure may also develop due to the spatial variations of the physical properties of the sediments.

Introduction

In recent years, basin modelling has been intensively used for fundamental as well as applied research concerning the evolution of sedimentary basins [1], [2], [3]. The rationale of such models is to take into account at the basin scale the various coupled sedimentological, hydrological, mechanical, thermal, diagenetic, etc. processes which interact as a function of time and space. The objective being to propose or to reject some geological scenarios, the results of which should be consistent with the available data.

The mechanical aspects of these coupled phenomena are largely related to the compaction of sedimentary rocks: reduction of porosity during burial. This compaction process is most generally modelled using the principles of soil mechanics which were developed by Terzaghi [4] to describe the 1-D consolidation of superficial soils. With this concept the porosity, or the void ratio, is a given function of effective stress [5], [6], [7]. From a rheological point of view, the underlying mechanical assumption is basically that the rheology of sedimentary rocks is plastic or elasto-plastic (e.g. Muir-Wood [8] for the general case of soil mechanics and Schneider et al. [9] for the application to sedimentary basins). This approach, which is based on experimental [10] and geological evidence [11], appears to be quite valid in laboratory experiments for effective stress up to 50 MPa [12] and for the geological compaction of recent clastic sediments down to 1 or 2 km [13]. A major interest of this approach is the concept of effective stress which implies a coupling between compaction and mechanical deformation on the one hand and of fluid pressure or flow on the other. In some cases, this approach leads to the prediction of fluid overpressure associated with compaction disequilibrium: for example, under conditions of sufficiently low permeability, the sediment loading is expected to result in overpressure [6], [7], [14], [15].

Overpressure is indeed commonly observed in many sedimentary basins [16] and is in many cases related with undercompaction [17]. Many logs of fluid pressure versus depth in a given well or a given field show: (i) an upper part with hydrostatic gradient (i.e. fluid pressure gradient is equal to ρ_fg, ρ_f being the density and g the acceleration of gravity, ρ_fg≅10⁴ Pa m⁻¹≅10⁻¹ bar m⁻¹), (ii) a transition zone where the fluid pressure gradient increases sometimes abruptly and (iii) an overpressured zone where the fluid pressure is larger than its hydrostatic value but its gradient is smaller than in the transition zone and may even be nearly hydrostatic (e.g. [18]).

This general trend of overpressure occurring and increasing with depth can be explained, at least qualitatively, by disequilibrium compaction, i.e. compaction at a rate too rapid for the fluids to be expelled [19]. However, many oil exploration geologists believe that mechanical compaction alone cannot explain specific features of the observed overpressure and argue for the occurrence of pressure compartments bound by very steep pressure gradients [20], [21]. These authors favor the role of chemical phenomena (i.e. compaction and chemical cementation) to explain the occurrence of the pressure seals [22], [23] defined as impervious zones which delineate pressure compartments.

From a mechanical point of view, pressure solution can be approached by a creep deformation (i.e. a time-dependent strain which can be characterized for example by a Newtonian viscosity) as proposed for example by Rutter [24] and others [25]. This approach is also consistent with experimental studies of pressure solution on various salts [26]. Viscous compaction is often assumed to occur in geological processes such as magma extraction [27] or the expulsion of deep fluid in sedimentary basins [28] which result in quite similar physical formulation [29]. However, in operational basin modelling, this approach is quite new and only a few applications seem to have been performed so far and only for specific lithologies: for the compaction of sandstones [30] and of Cretaceous chalk layers [31], [32].

The objective of the present paper is to work at the scale of the sedimentary pile, assuming that all sedimentary rocks have a visco-elastic behavior. Since fine-grained rocks represent the major fraction of most basin infill [33], we implicitly assimilate these rocks with ’clays’ using the soil science granulometric definition although their exact mineralogical nature is not exactly relevant to this study. Nevertheless this statement allows discussion, on the basis of soil physics, of the experimental evidence for a viscous behavior. In the following, we shall first give a rapid overview of the various experimental and natural observations which emphasize a viscous component in the compaction of soils and of sedimentary rocks. Then we develop a 1-D model which takes into account the poro-visco-elastic deformation associated with sedimentation and compaction processes. Finally, we present some numerical results emphasizing the porosity and fluid pressure profiles which can be compared to real data.