Uncertainty quantification of the factor of safety in a steam-assisted gravity drainage process through polynomial chaos expansion

Abstract

The factor of safety (FoS) is a measure of the operational safety of a reservoir and is defined as the ratio of the yield strength to the applied effective stress. In the steam assisted gravity drainage (SAGD) process, maintaining the caprock FoS within the prescribed limits during the operation is crucial in adhering to safe operational standards. Deformations associated with the development of the steam chamber in the reservoir affect the FoS of the caprock significantly. With a limited number of well-logs, precise quantification of heterogeneity in petrophysical and geomechanical parameters is a challenge in coupled reservoir-geomechanics modelling; this, along with nonlinearity in the process dynamics, gives rise to non-Gaussian uncertainties in the pore pressure/temperature, which poses severe challenges in reservoir control and optimization. The large scale nature of the reservoir imposes computational complexity in uncertainty quantification through first-principles modelling; hence, a data-driven methodology using the results from first-principles simulations is valuable. In this work, a data-driven polynomial chaos expansion (PCE)-based proxy model is developed from sequentially coupled reservoir-geomechanics simulation. Proper orthogonal decomposition (POD) combined with the PCE yields a proxy model which can provide a quick and accurate estimation of caprock FoS along with quantifying its uncertainty.