The work was performed to evaluate the influence of the stress variations, thus simulating a production history, on the volumetric behaviour of some unconsolidated sands. The compaction tests were performed on preserved cores from three clastic reservoirs, chosen to cover a wide spectrum of porosity and depths. Two different stress paths were selected for the experimental program: an isotropic stress path, obtained by increasing both the radial and the vertical effective stresses such that their ratio, keff, is equal to 1, while for the second one, different values of keff (keff=0.7 and keff= 0.5) were selected. Finally, some tests have been performed by varying the pore pressure and keeping the stress ratio constant, thus closely simulating a depletion process. The main results indicate that generally the compressibility reduces as the stress path goes from isotropic stress conditions to anisotropic ones and that despite what is usually reported for this kind of porous materials, the Biot coefficient neither cannot be considered constant nor equal to 1. The results shows, indeed, that 0.8-0.9 are more realistic values and that for large depletions values down to 0.4-0.6 can be observed.
1. INTRODUCTION
It is known that one of the main mechanical parameters involved in reservoir geomechanics is the compressibility of porous media. It is also well known that the rock compressibility is a function of both the in-situ stresses and the reservoir fluid pressure and that it can not be considered constant through the entire life of the reservoir. However the simplifications sometimes introduced when analysing the reservoir behaviour, both for production prognosis or compaction estimation, like neglecting or simplifying too much the rock compressibility, may lead to erroneous conclusions and this fact may have large operative impact in the case of the presence of weak rocks like chalk, unconsolidated sand or weak sandstone.
The consequences of the reservoir deformations during its production history are well known: far from being an exhaustive list, one may quote subsidence [1], casing integrity [2,3], permeability reduction [4,5,6] and the related reservoir geomechanical modelling [7-10]. Moreover, compaction induced changes of the state of stress may influence several other activities like infill well planning, hydraulic fracture design, cap rock integrity, fault sealing, etc. [11-17].
Some previous works were already devoted to the characterization of the volumetric behaviour of weak or more consolidated sandstones and to the effects of stress variations upon permeability and compressibility [18-20]. The purpose of this work was to evaluate at the laboratory scale the influence of the stress variations, thus simulating a production history, on the volumetric deformational behaviour of some unconsolidated sands.
2. COMPRESSIBILITY
Despite its simple definition, the rock compressibility is a variable which is not really easy to evaluate. Before dealing with the experimental part, a brief overview of the compressibility definition as derived from poroelasticity will be given.
In the incremental form, the basic equations of poroelasticity for a porous medium may be written:
(available in full paper)
where sij is the total stress (negative in compression), eij is the strain and pp is the pore fluid pressure; moreover ¿?and G are the Lamè's coefficients, ¿ e= ¿V/V is the volumetric deformation, M the Biot modulus, athe Biot coefficient, ¿the fluid density and ¿m the fluid mass variation.
