Non‐iterative Green's function approach for 2D unbounded heterogeneous fluid‐saturated media

Abstract

AbstractThe 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.