Spatio-Temporal Stress Path Prediction Under Different Deformational Conditions

Abstract

Drilling new infill wells in depleted reservoirs is extremely problematic and costly due to low formation fracture pressure and narrow mud window resulting from in-situ stress changes due to fluid extraction. This is of paramount importance especially for drilling operations in deep-water reservoirs, which requires precise prediction of formation fracture pressure. In turn, this entails accurate prediction of reservoir stress changes with pore pressure depletion, i.e., the stress path. Currently-used models assume a transient flow regime with reservoir depletion. However, flow regime in depleted reservoirs is dominantly pseudo-steady state (PSS). Shahri and Miska (2013) proposed a model under plane-strain assumption. However, subsea subsidence measurements confirm that depletion-induced reservoir deformation mainly occurs in axial direction. We provide analytical solutions for stress path prediction under different deformational conditions namely, plane strain-traction and displacement boundary conditions, generalized-plane-stress, generalized uniaxial strain, and uniaxial-strain. For this purpose, constitutive relations of poroelasticity are combined with equilibrium equations, and pore pressure profile is described by PSS flow regime. In a numerical example, we examine the effects of different deformational conditions on depletion-induced in-situ stress changes. Interestingly, results indicates that stress path in reservoir is significantly affected by reservoir’s boundary conditions. The stress path under plane strain-displacement assumption overestimates the stress path predicted under uniaxial strain state by almost a factor of two. However, the generalized plane stress and traction plane strain conditions underestimates the results of uniaxial strain assumption. The order of stress path values for different boundary conditions can be summarized as: SPps-disp > SPuniaxial > SPps-trac > SPgps.