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Geomechanical modelling of a reservoir is important to understand the coupling between pore pressure and stress state in a reservoir. Changes of pore pressure due to injection or depletion implies also a spatio-temporal re-distribution of the stress state. Reservoirs are complex underground storage volumes in which the role of pore pressure stress coupling is not fully understood. To quantify the spatio-temporal evolution of pore pressure stress coupling in complex settings we solve the coupled differential equations of quasi-static poroelasticity with the 3D finite element method. Our modelling results indicate that in the early stage of fluid injection experiments pore pressure stress coupling deviates significantly from a description in the static limit.