Premium
Gravitational and Finite‐Size Effects On Pressure Saturation Curves During Drainage
Author(s) -
Ayaz Monem,
Toussaint Renaud,
Schäfer Gerhard,
Måløy Knut Jørgen
Publication year - 2020
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2019wr026279
Subject(s) - saturation (graph theory) , capillary pressure , porous medium , mechanics , percolation (cognitive psychology) , gravitation , percolation theory , fractal , materials science , porosity , geotechnical engineering , geology , physics , mathematics , classical mechanics , quantum mechanics , conductivity , biology , mathematical analysis , combinatorics , neuroscience
We experimentally and numerically study the influence of gravity and finite‐size effects on the pressure‐saturation relationship in a given porous medium during slow drainage. The effect of gravity is systematically varied by tilting the system relative to the horizontal configuration. The use of a quasi two‐dimensional porous media allows for direct spatial monitoring of the saturation. Exploiting the fractal nature of the invasion structure, we obtain a relationship between the final saturation and the Bond numberS n w F = B o 0 . 097using percolation theory. Moreover, the saturation, pressure, and Bond number are functionally related, allowing for pressure‐saturation curves to collapse onto a single master curve, parameterized by the representative elementary volume size and by the Bond and capillary numbers. This allows to upscale the pressure‐saturation curves measured in a laboratory to large representative elementary volumes used in reservoir simulations. The large‐scale behavior of these curves follows a simple relationship, depending on Bond and capillary numbers, and on the flow direction. The size distribution of trapped defending fluid clusters is also shown to contain information on past fluid flow and can be used as a marker of past flow speed and direction.