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

Valeria Cristina F. Barbosa, Vanderlei C. Oliveira Jr, Andre D. Arelaro, Filipe Augusto S. Borges


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.


gravitational potential; reservoir compaction; hydrocarbon production, nucleus-of-strain solution; mathematical and numerical modeling

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DOI: http://dx.doi.org/10.22564/brjg.v40i5.2139

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