A boundary element solution to land subsidence above 3‐D gas/oil reservoirs

Abstract

SUMMARYA linear boundary element (BE) model is proposed for the uncoupled 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.

Modeling of the three‐dimensional subsidence diffusion–convection problem above a trapdoor

“…This observation is similar with the one made in where the SEH was verified everywhere for b c = 2.0, and for b c = 4.0 was verified only close to the center of the ellipse ( x , y ) = (0,0).…”

“…proposed that the subsidence trough of a geostructure over an approximated elliptical reservoir (with major axis B 2 and minor axis B 1 ) exhibits an intermediate behavior between the two corresponding axisymmetric ones (e.g. disk‐shaped reservoirs with a diameter of the circumscribed circle equal to B 2 and an inscribed circle with diameter equal to B 1 as is shown in Figure (a)), following the geometrical bounds, and (ii) in , Gambolati et al . proposed the use of an equivalent area axisymmetric problem with radius .…”

“…Gambolati et al . proposed that the use of an area equivalent axisymmetric problem (i.e. the axisymmetric problem with radius ) provides similar results with the simulation of the elliptical domain.…”

“…Nonetheless, approximation of surface subsidence produced from elliptic reservoirs is considered in the context of poroelasticity theory in and . Ferronato et al .…”

3D Coupled Displacement Discontinuity and Finite Element Analysis of Reservoir Behavior during Production in Semi-infinite Domain

“…For example, Gambolati et al (1987) proposed a linear boundary element (BE) model for the uncoupled simulation of land subsidence due to gas, oil and hot water production over three dimensional reservoirs. Their model allows for any arbitrary geometry of the reservoir and for non-uniform distribution of the pore pressure decline.…”