Finite element analysis of land subsidence above depleted reservoirs
with pore pressure gradient and total stress formulations
G. Gambolati, M. Ferronato, P. Teatini
Dept. Mathematical Methods and Models for Scientific
Applications, University of Padova, Padova, Italy
R. Deidda, G. Lecca
CRS4 - Centro di Ricerca, Sviluppo e Studi Superiori in Sardegna,
Cagliari, Italy
ABSTRACT
The solution of the poroelastic equations for predicting land subsidence
above productive gas/oil fields may be addressed by the principle of
virtual works using either the effective intergranular stress, with the
pore pressure gradient regarded as a distributed body force, or the total
stress incorporating the pore pressure. In the finite element (FE) method
both approaches prove equivalent at the global assembled level. However, at
the element level apparently the equivalence does not hold, and the strength source
related to the pore pressure seems to generate different local forces on the element
nodes. The two formulations are briefly reviewed and discussed for triangular
and tetrahedral finite elements. They are shown to yield different results
at the global level as well in a three-dimensional axisymmetric porous medium
if the FE integration is performed using the average element-wise radius.
A modification to both formulations is suggested which allows to correctly
solve the problem of a finite reservoir with an infinite pressure gradient,
i.e. with a pore pressure discontinuity on its boundary.
