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The Green's function approach (GFA) developed in previous work uses the classical Green's function for point load (Kelvin's fundamental solution, Melan's fundamental solution, and others) and the reciprocity theorem to capture changes in the displacement, strain, and stress fields of a geological formation subjected to the processes of extraction or injection of fluids. The great advantage of this method compared to the classical finite element method (FEM) is that it does not require the imposition of boundary conditions and the problem analysis can be performed considering only the reservoir or other regions of interest. In the original version of the GFA, the displacement field is calculated using an iterative numerical scheme, which decreases the computational performance of the method and may present convergence problems. Such limitations have made it difficult to use the GFA in real problems. The present work proposes a non‐iterative numerical scheme capable of expanding the applicability of GFA and, simultaneously, improving its computational performance. The results presented in this work demonstrate that using this numerical scheme, the GFA consumes up to 17.5 times less CPU time compared to iterative scheme and this relationship can be even greater if the heterogeneity of the material increases. Using a geological profile constructed from seismic images of the Brazilian pre‐salt (Tupi field located in the Santos basin), it is shown that the non‐iterative GFA allows the analysis of complex geological formations. [ABSTRACT FROM AUTHOR]

ABSTRACT The present work proposes a new version of the Green‐FOSM (first‐order second moment) method, which eliminates the iterative calculation process of the original version and, simultaneously, solves the convergence problems related to the mechanical properties of rocks that form the geological formation. In this calculation scheme, the iterative process is eliminated by using a matrix that correlates the nodal displacement vector with the strain vector. Considering the same computational resources, this non‐iterative version of the Green‐FOSM method is up to 200 times faster than the original iterative process. In addition, it allows analyzing problems with more than 10,000 random variables, value that in the original method is less than 3000. To demonstrate its validity, the proposed method is applied to two hypothetical models subjected to different fluid extraction processes. For all the different levels of correlation and spatial variability, the statistical results obtained by the proposed method agree well with the results obtained via Monte Carlo Simulation (MCS). The relationship between CPU times demonstrates that the proposed method is at least 50 times faster than MCS. In the end, the non‐iterative Green‐FOSM method is used to obtain the displacement, strain, and stress fields of a geological section constructed from a seismic image of Brazilian pre‐salt oil region. The results found show that, depending on the levels of spatial variability, the analyzed fields can assume values up to 30.6% higher or lower than the values obtained deterministically. [ABSTRACT FROM AUTHOR]