Experimental and numerical upscaling of foam flow in highly permeable porous media

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 behav-ior 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-BulkleyPapanastasiou) 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.