3D Displacement and Stress Fields of Compacting Reservoir: Alternative Solutions

Abstract

ABSTRACT. We have presented alternative solutions for the displacement and stress fields outside and inside of a 3D right rectangular prism under constant pressure. These solutions are obtained by integrating the well-known nucleus-of-strain solution over the volume of the prism. They are based on the similarity between the gravitational potential yielded by a volume source under a density variation and the thermoelastic displacement potential yielded by a volume source in a half-space under a pressure variation. This similarity enables the use of closed expressions of the gravitational potential and its derivatives. We use our solution for approximating the displacement and stress fields due to a reservoir with arbitrary shape and under arbitrary pressure changes. We discretized the reservoir as a grid of 3D right rectangular prisms juxtaposed in the horizontal and vertical directions. Each prism has homogeneous pressure; however, pressure variations among different prisms are allowed. This parametrization of the reservoir yields a piecewise constant distribution of pressure in the subsurface. We validate the resultant displacement and stress fields due to the reservoir by numerical simulations including a reservoir with arbitrary geometry and under arbitrary pressure distribution, based on a production oil field in offshore Brazil.