Derivation and study of a new mathematical model of oil movement. Accounting for the limited fractality of a porous medium (2020)

Project Type: Work Project, Math Modeling, Academic Research
Programming Language: Python 3, Maple 18
Project Full Description (in English): Article.pdf
Company: Research Lab GAMMETT

I. Motivation and Problem

To take into account the heterogeneity of a porous medium, the ideas of fractals are used. The paper compares two approaches to taking into account the fractality of the medium in one hydrodynamic model.

III. Key Results

• Implemented the algorithm for constructing a mass function from the article https://arxiv.org/abs/0906.0676 (Calculus on Fractal Curves in R^n);
• A new model of Buckley-Leverett in fractal media has been developed and the mathematical consistency of the model has been shown;
• A comparative analysis was carried out with a computationally simpler generalization method, a case is shown when this can be done.

III. Content

Project Full Description (in English): Article.pdf

The project code contains 11 scripts.