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 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 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.

中文翻译：

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引力和有限尺寸对排水过程中压力饱和度曲线的影响

我们通过实验和数值研究在缓慢排水过程中重力和有限尺寸效应对给定多孔介质中压力饱和度关系的影响。通过使系统相对于水平配置倾斜，系统地改变了重力的影响。准二维多孔介质的使用允许对饱和度进行直接的空间监控。利用入侵结构的分形性质，我们获得了最终饱和度与键数之间的关系使用渗流理论。此外，饱和度，压力和键数在功能上是相关的，允许压力-饱和曲线折叠成一条主曲线，并由代表性的基本体积大小以及键和毛细管数来参数化。这样可以将在实验室中测得的压力饱和度曲线按比例放大到储层模拟中使用的大代表性基本体积。这些曲线的大规模行为遵循简单的关系，具体取决于键和毛细管数以及流向。捕获的防御流体簇的大小分布也显示为包含有关过去流体流动的信息，并且可以用作过去流体流动速度和方向的标记。