An Analytical Solution for Depletion-induced Principal Stress Rotations In 3D and its Implications for Fault Stability

Abstract:

Depletion-induced faulting in hydrocarbon reservoirs has mostly been attributed to poroelastic effects: in-situ stresses are coupled with a pore pressure change according to a stress path. As a result, for a fault of certain orientation, the shear stress and normal stress resolved on the fault increase in a manner such that the stress state exceeds the shear failure envelop. An underlying assumption associated with this mechanism is that homogeneous pore pressure depletion occurs on both sides of the fault.

This study addresses an additional mechanism for depletion-induced faulting in cases where the pore pressure reduction is bounded by a hydraulically impermeable fault. We assume that the overburden and shear stresses are decoupled from pore pressure, while the two horizontal principal stresses are coupled with pore pressure by their respective stress paths (we show that the poroelastic coupling effect is anisotropic). Unbalanced pore pressure changes on the two sides of the fault, in conjunction with the poroelastic response, cause redistribution of the stress state. Given a fault that is arbitrarily oriented with respect to the original stress field, we derive a generalized 3D analytical solution for the new state of stress after depletion. We then quantify the magnitude change and the rotation of the three principal stresses. Finally, we compare the corresponding Coulomb Failure Functions and Mohr circles before and after depletion. For demonstration purposes, we determine the stress path tensor using poroelastic plane strain solutions in conjunction with frictional equilibrium for three different stress regimes. Our hypothetical case studies show that, for bounded reservoirs, depletion-induced principal stress rotation and magnitude changes have a significant impact on fault stability, and are a complex function of fault orientation, the original in-situ stress state and pore pressure, the degree of depletion, and the degree of poroelastic coupling.