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Finite element analysis of land subsidence above depleted reservoirs with pore pressure gradient and total stress formulations
Author(s) -
Gambolati Giuseppe,
Ferronato Massimiliano,
Teatini Pietro,
Deidda Roberto,
Lecca Giuditta
Publication year - 2001
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.131
Subject(s) - finite element method , poromechanics , pore water pressure , discontinuity (linguistics) , pressure gradient , mechanics , finite element limit analysis , mixed finite element method , stress (linguistics) , geometry , geology , body force , rotational symmetry , geotechnical engineering , extended finite element method , porosity , mathematics , porous medium , mathematical analysis , structural engineering , engineering , physics , linguistics , philosophy
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. Copyright © 2001 John Wiley & Sons, Ltd.