资源环境科技发展态势分析平台

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 number S_nw^F = Bo^0.097 using 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 follow a simple relationship, depending on Bond and Capillary number, 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.