| Abstract: | A linear boundary element (BE) model is proposed for the uncoupied simulation of land subsidence due to gas, oil and hot water production over three-dimensional (3-D) arbitrarily shaped reservoirs. The pore pressure decline is assumed to be specified in advance, e.g. via a numerical model of flow. Use is made of the fundamental solution derived in 1885 by Boussinesq for a vertical load acting upon the traction-free surface of a semi-infinite medium. A straightforward application of Betti's (1872) reciprocal theorem allows for the development of a boundary integral whose numerical execution yields directly the downward settlement over the point of interest. The new procedure is applied to assess land sinking caused by an uniform pore pressure decline occurring within fields of elliptical shape and to explore the influence of the assumption of small reservoir thickness which underlies the ‘tension center’ or ‘strain nucleus’ approach previously developed by Geertsma in 1966. The results emphasize the numerical efficiency of the solution and the promising features of the BE method for the evaluation of ground subsidence in 3-D problems. The present model is based on the theory of the linear poroelasticity and is implemented for a mechanically homogeneous and isotropic half-space. It allows for any arbitrary geometry of the reservoir and for a non-uniform distribution of the pore pressure decline. It may easily be extended to other physical settings for which a vertical surface point load solution is available. |
