Uncertainties consideration in elastically heterogeneous fluid-saturated media using first-order second moment stochastic method and Green's function approach

Abstract

The present work proposes a stochastic statistical method, called Green-FOSM, to consider the uncertainties associated with the mechanical properties of rocks that form geological profile. This method intended to help improve the decision-making process associated with production of oil and gas, the extraction of water, and the storage of CO2 or natural gas. The novelty of the method lies in the use of the Green's function approach, which, together with the FOSM method (first-order second moment method), is used to propagate uncertainties associated with the material to the displacement field of the geological formation. Furthermore, using the concepts of stochastic grid and autocorrelation function, the proposed method allows the consideration of the spatial variability of the random variables that represent these mechanical properties. This method is applied to a 2D model subject to two processes of pore pressure changes (depletion only and depletion combined with injection) with different levels of correlation and variability. The statistical results obtained by the proposed method agree well with the results obtained using Monte Carlo simulation. In problems with more than 1500 random variables, the relationship between the CPU times demonstrates that the proposed method is up to 30 times faster than the Monte Carlo simulation.