A Unified Algorithm for the Young–Laplace Method Applied to Porous Media

• Published in: Brazilian journal of physics Vol. 54; no. 3
• Main Authors: Zabot, Alexandre Miers, Camargo, Mario Augusto, Wolf, Fabiano Gilberto, Siebert, Diogo Nardelli, Surmas, Rodrigo, dos Santos, Luis Orlando Emerich, Ferreira, Talita Rosas, Cássaro, Fábio Augusto Meira, Pires, Luiz Fernando
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-06-2024; Springer Nature B.V
• Subjects: Algorithms; Capillary flow; Compressibility; Fluid flow; General and Applied Physics; Imbibition; Incompressible flow; Laplace equation; Physics; Physics and Astronomy; Porous media; Source code; Wettability; Drainage; Two-phase fluid flow; Imbibition; Contact angle; Mathematical morphology; Capillary pressure curve
• ISSN: 0103-9733; 1678-4448
• DOI: 10.1007/s13538-024-01442-w

Young–Laplace equation-based algorithms for simulating capillary-driven flow have been used in porous media research for more than two decades. However, the lack of a uniform mathematical description hinders a wider application of these algorithms, as well as impede their comparison. After conducting a detailed review of the most important publications in the area, we propose a unified algorithm. This resulting framework is capable of handling four distinct physical situations: drainage and imbibition with either compressible or incompressible displacement fluid. Additionally, there is no restriction regarding the geometry or the initial fluid distribution used. The proposed algorithm can simulate variable or mixed wettability, even for imbibition, which has not already been described in the literature. Finally, at the end of the manuscript, we provide an efficient open-source C +  + code for the proposed unified algorithm and also many examples of its use.