Finite element analysis of land subsidence above depleted reservoirs with pore pressure gradient and total stress formulations

The solution of the poroelastic equations for predicting land subsidence ab ove productive gas/oil fields may be addressed by the principle of virtual works using either the effective intergranular stress, with the pore pressu re gradient regarded as a distributed body force, or the total stress incor porating the pore pressure. In the finite element (FE) method both approach es prove equivalent at the global assembled level. However, at the element level apparently the equivalence does not hold, and the strength source rel ated to the pore pressure seems to generate different local forces on the e lement nodes. The two formulations are briefly reviewed and discussed for t riangular and tetrahedral finite elements. They are shown to yield differen t results at the global level as well in a three-dimensional axisymmetric p orous medium if the FE integration is performed using the average element-w ise radius. A modification to both formulations is suggested which allows t o correctly solve the problem of a finite reservoir with an infinite pressu re gradient, i.e. with a pore pressure discontinuity on its boundary. Copyr ight (C) 2001 John Wiley & Sons, Ltd.