In-situ reservoir stresses change during the production period due to the reduction in pore pressure. Consequently, the upper limit of the drilling mud window; i.e., formation fracture pressure, reduces corresponding to the pore pressure depletion. Since drilling operations in critical situations such as deep water and depleted reservoirs require precise prediction of the mud window, it's of vital importance to accurately assess the reservoir stress path; i.e., the change of in-situ stresses with pore pressure. Currently used models for reservoir stress path prediction can be divided into two main categories: space- and time-independent and spatio-temporal models. Space- and time-independent models have been used for several decades. According to industry demand of precise stress path prediction, spatio-temporal models have recently been developed for stress distribution determination within reservoirs. However, the developed stress path models are based on the transient flow regime and can not be utilized in depleted reservoirs wherein the pressure response usually reaches the reservoir boundary.

The aim of this study is to provide an analytical model for predicting reservoir stress changes at different times and locations within reservoirs during the pseudo-steady-state flow regime. Constitutive equations from the theory of poroelasticity are combined with a force-balance equation to find the relationship between reservoir stresses and pore pressure. The application of the proposed model for reservoir stress path prediction is illustrated using a numerical example.

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