Stress-strain analysis in productive gas/oil reservoirs

A numerical study of the stress-strain distribution in a thin disc-shaped r eservoir embedded in a pore-elastic half-space and subject to a unit pore p ressure decline is presented. The results are then compared with those of a geometrically equivalent porous cylindrical body which is either free to o r prevented from expanding laterally (oedometric analogy). The analysis is based on the linear theory of pore-elasticity solved with the aid of the fi nite element method. The strength source is provided by the pressure gradie nt generated in a small region surrounding the gas/oil held where pore pres sure dissipates. The influence of the burial depth c is also investigated. The results show that the reservoir rock undergoes a vertical compaction de lta which is independent of c and very close to the compaction of the equiv alent confined cylinder. The confinement factor is also similar. The horizo ntal 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 ad dition, at the outer reservoir margin shear stresses develop which are tota lly missing in both the free and the constrained cylinders. It is shown tha t the vertical displacements of reservoir top and bottom, as well as the ra dial ones, are sensitive to c, especially in shallow formations. Finally, t he largest shear stress is found to be related to the magnitude of the pres sure gradient, i.e. to the radial size of the neighbouring volume where por e pressure vanishes. Copyright (C) 1999 John Wiley & Sons, Ltd.