a b s t r a c tGeertsma's analytical method is often used to compute strain and stress changes around a compacting geological reservoir. The present work extends Geertsma's solution by adding a rigid layer beneath the compacting reservoir. Analytical formulae are presented for all the components of displacement of a point in the subsurface. Our derivation includes the correction of an error found in the paper written by Sharma in 1956.
Time-lapse gravity is a technique sensitive to subsurface change in mass and in mass distribution. We attempted to devise a method to predict gravity effects caused by redistribution of subsurface mass induced by reservoir compaction. First, displacements and strains due to compaction were modeled using a geomechanical model. Then, 4D gravity effects were derived from the displacements and the volumetric strains computed in and around the reservoir. A sensitivity study was carried out for geomechanical parameters, such as Poisson’s ratio, as well as for geometrical parameters, such as reservoir radius and depth. Finally, changes in gravity due to compaction were compared to changes induced by reservoir fluid substitution. Given a rigid basement close below a strongly compacting reservoir, our modeling case showed that the deformation itself could give gravity changes comparable to changes caused by reservoir fluid density changes, which are the changes traditionally targeted by gravity monitoring. For a homogeneous subsurface, the compaction gave negligible gravity changes for our modeling case.
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