This project develops advanced scientific computing tools for the mathematical modeling of physical phenomena in porous media, applying multi-fidelity methods to complex and computationally expensive inverse problems.
The project addresses the computational challenges associated with simulating fluid flow in highly heterogeneous porous media, using the SPE10 benchmark dataset. The main objective is to overcome the high computational cost of high-resolution models (Full-Order Models) through three main phases:
- Permeability upscaling: Implementation of a numerical upscaling procedure based on Darcy's law to generate permeability tensors on coarse grids. The process was optimized through parallelzsation with the
jobliblibrary, halving execution times. - Optimal injection well placement: Development of a coarse-to-fine hierarchical strategy to identify the optimal location of an injection well that minimises flow imbalance in the system.
- Identification of pollutant sources: Solving an inverse problem to locate the source of a pollutant by monitoring concentration profiles over time. To speed up this phase, a surrogate transport model was created.
As a potential future development, the integration of an Autoencoder was explored to correct errors introduced by coarse grid solvers, improving the accuracy of reconstructed concentration profiles.
The source code developed for this project is hosted in a private repository and cannot be made public due to privacy reasons. The report included here documents the entire workflow and results of the project.
The scientific report included in this repository is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0). You are free to share and redistribute the material in any medium or format, provided that appropriate credit is given.
For questions, clarifications, or further information about the project, feel free to contact me at mattia.gastoldi@mail.polimi.it. Upon request, further details can be provided.