Abstract Foam in porous media has been studied as a tool for various applications. Recently, the technology has become relevant for contaminated-aquifer remediation, where porous media are highly permeable. Therefore, the behavior of foam flow in high permeability porous media still raises numerous questions. In particular, upscaling of the foam flow from pore to Darcy scale is still under debate. Since the behavior of bulk foam has been studied principally in the food and cosmetics industries, and foam flow in porous media has mainly been investigated in the oil industry, the link between bulk-foam behavior and foam flow in porous media is still missing. The upscaling of foam flow from the pore scale to the laboratory scale could give valuable insight for understanding foam flow in aquifers. We studied the behavior of pre-generated foam with different foam qualities through the rheological characterization of bulk foam using a rheometer and also when flowing in a porous medium composed of 1 mm glass beads. Foam was formed by co-injecting surfactant solution and nitrogen gas through a porous column filled by fine sand. The homogenization method is used to study macroscopic foam flow properties in porous media by solving the non-linear boundary value problem. The rheology of bulk foam is then used as an input in the upscaling procedure for foam flow in different periodic model 2D and 3D unit cells. From our experiments, we found that the bulk foam is a yield-stress fluid and that the yield-stress values increase with foam quality. Moreover, the rheology of bulk foam corresponds well to the yield stress (Herschel-Bulkley-Papanastasiou) model. We found that foam behaves as a continuous yield-stress fluid in highly permeable porous media. It was also shown that the apparent foam viscosity in porous media increases with the foam quality at the same total flow rate. The results obtained from the rheometer successfully match the outcomes of apparent foam viscosity obtained by flow in porous media by a shifting parameter for the same foam quality. The apparent foam viscosity found in 1 mm glass-bead packing was much higher than bulk foam viscosity. Experimental results were compared to numerical results on simple unit cells. Although we observed considerable differences between the experimental and numerical results of upscaling, the general trend was identical. The differences can be explained by the complexity of the foam flow in porous media, especially foam compressibility. We found that foam flow at low capillary numbers is influenced by the trapping effect and at high pressure gradients by the compressibility. Compressibility was estimated for foam flow in 1 mm glass-bead packing. When foam compressibility is insignificant, the upscaling model can predict foam-flow behavior well at the Darcy scale.

中文翻译：

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高渗透多孔介质中泡沫流动的实验和数值放大

摘要 多孔介质中的泡沫已被研究作为各种应用的工具。最近，该技术已与受污染的含水层修复相关，其中多孔介质具有高渗透性。因此，泡沫在高渗透多孔介质中的流动行为仍然提出了许多问题。特别是，泡沫流从孔隙到达西规模的升级仍在争论中。由于散装泡沫的行为主要在食品和化妆品行业进行研究，而多孔介质中的泡沫流动主要在石油工业中进行研究，因此仍然缺少散装泡沫行为与多孔介质中泡沫流动之间的联系。泡沫流从孔隙尺度到实验室尺度的放大可以为理解含水层中的泡沫流提供有价值的见解。我们通过使用流变仪对散装泡沫进行流变表征以及在由 1 毫米玻璃珠组成的多孔介质中流动时，研究了具有不同泡沫质量的预生成泡沫的行为。泡沫是通过将表面活性剂溶液和氮气通过填充有细砂的多孔柱共同注入而形成的。均质化方法通过求解非线性边值问题，研究多孔介质中宏观泡沫的流动特性。然后将大量泡沫的流变学用作不同周期模型 2D 和 3D 晶胞中泡沫流动放大程序的输入。从我们的实验中，我们发现大块泡沫是一种屈服应力流体，并且屈服应力值随着泡沫质量而增加。而且，散装泡沫的流变性与屈服应力 (Herschel-Bulkley-Papanastasiou) 模型非常吻合。我们发现泡沫在高渗透性多孔介质中表现为连续的屈服应力流体。研究还表明，在相同的总流速下，多孔介质中的表观泡沫粘度随着泡沫质量的增加而增加。从流变仪获得的结果成功地匹配了在多孔介质中通过移动参数获得的表观泡沫粘度的结果，以获得相同的泡沫质量。在 1 毫米玻璃珠填料中发现的表观泡沫粘度远高于散装泡沫粘度。将实验结果与简单晶胞的数值结果进行比较。尽管我们观察到放大的实验结果和数值结果之间存在相当大的差异，但总体趋势是相同的。这些差异可以用多孔介质中泡沫流动的复杂性来解释，尤其是泡沫的可压缩性。我们发现低毛细管数下的泡沫流动受捕集效应的影响，而在高压梯度下则受可压缩性的影响。对 1 毫米玻璃珠填料中的泡沫流动估计了可压缩性。当泡沫可压缩性不显着时，放大模型可以很好地预测达西尺度下的泡沫流动行为。