Stress-strain analysis in productive gas/oil reservoirs
G. Gambolati, P. Teatini, L. Tomasi
Dept. Mathematical Methods and Models for Scientific
Applications, University of Padova, Padova, Italy
ABSTRACT
A numerical study of the stress-strain distribution in a thin
disc-shaped reservoir embedded in a poro-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 poro-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 field 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 D 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 field and is of the same
order of magnitude as D.
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.
