Stress strain analysis in productive gas/oil reservoirs

A numerical study of the stress-strain distribution in a thin disc-shaped reservoir embedded in a pore-elastic half-space and subject to a unit pore pressure decline is presented. The results are then compared with those of a geometrically equivalent porous cylindrical body which is either free to or prevented from expanding laterally (oedometric analogy). The analysis is based on the linear theory of pore-elasticity solved with the aid of the finite element method. The strength source is provided by the pressure gradient generated in a small region surrounding the gas/oil held where pore pressure dissipates. The influence of the burial depth c is also investigated. The results show that the reservoir rock undergoes a vertical compaction delta which is independent of c and very close to the compaction of the equivalent confined cylinder. The confinement factor is also similar. The horizontal displacement is, however, much larger. Its maximum value occurs at the boundary of the held and is of the same order of magnitude as delta. In addition, at the outer reservoir margin shear stresses develop which are totally missing in both the free and the constrained cylinders. It is shown that the vertical displacements of reservoir top and bottom, as well as the radial ones, are sensitive to c, especially in shallow formations. Finally, the largest shear stress is found to be related to the magnitude of the pressure gradient, i.e. to the radial size of the neighbouring volume where pore pressure vanishes.