Fracture mechanics approach to the problem of subsidence induced by resource extraction

•A subsidence model is proposed based on approximating a deforming reservoir by a dislocation loop.•For long shallow reservoirs the model matches the observed surface deformation.•Simple approximate expressions are developed for surface deformation.•Green’s function type expressions are derived for computations of the free surface deformation. A new area of application of Fracture Mechanics methods is proposed: the determination of surface deformation induced by internal volume change (e.g. due to underground hydrocarbon extraction). The finite layer-like zone of volume alteration is modelled as a crack, that is as a continuous distribution of dislocation loops. This approach allows the determination of surface deformation and can serve as the basis for monitoring of the volume alteration from surface measurements. In a limiting case of nearly uniform deformation of the reservoir boundaries the model consists of a single dislocation loop (an inserted cylindrical body of a constant height) in half-space and results in simple approximate expressions for the normal and tangential displacement components of the free surface. For the example of subsidence in the Groningen gas field the proposed method produces more realistic results describing reality better than the traditional models based on representing the reservoir as a collection of independent dilation centres. Also, analytical expressions are proposed for the nuclei – the basic Green’s function type expressions that allow representation of a planar horizontal reservoir layer of an arbitrary shape as a distribution of infinitesimal dislocation loops. For the case of a cylindrical reservoir, the nuclei integration recovers the exact distribution of the surface displacements.