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Dispersed fluids (foam, emulsion, bubbly liquid, etc.) flows through porous media in the form of disconnected droplets or ganglia, which occurs in many subsurface industrial scenarios [1-3]. However, current theoretical models cannot provide a consistent and general description of the dispersed fluids flow in porous media [4,5].
We conducted demonstrative microfluidic experiments on dispersed blobs in a porous medium model. We varied Cad (dispersed fluid capillary number) and Ca (total capillary number), and the micromodel was homogeneous. Surprisingly, we observed significant non-uniform flow as shown in Fig. 1a. Preferential paths carry almost all the dispersed fluid flux, while blobs in other paths flow only occasionally and slowly. We observed similar preferential flow in a simplified doublet system (Fig. 1a). This phenomenon raises the question of whether it is caused by manufacturing errors or arises inherently.
We formulated a generalized model for the pressure drop F in a single channel, expressed as F=f(Ca,Sd) (Sd, dispersed fluid saturation). We then conducted numerical simulations in a doublet system. When residual saturation (Sr) is absent as in classic straight-tube models [6], the droplet flux is equal in both channels. However, when we incorporate Sr to match the physics in porous media [7], a small geometric difference may lead to significant discrepancy in droplet flux at low Ca (Fig. 1b). This asymmetry is suppressed by increasing Ca (Fig. 1b). We theoretically rationalize this observation that highlights the role of residual saturation on breaking the symmetry. Further experiments successfully reproduce this theoretical prediction in a dual-channel system (Fig. 1c). These results demonstrate that manufacturing errors are not the primary cause of preferential flow.
In summary, microfluidic experiments and theory demonstrate that minor geometric differences in dual-channel systems can result in significant differences in dispersed fluids flux. This amplification of geometric asymmetry in flow asymmetry is a result of capillary trapping in the porous structure.
| References | [1] Mehmani Y, Xu K. Capillary equilibration of trapped ganglia in porous media: A pore-network modeling approach[J]. Advances in Water Resources, 2022, 166: 104223. [2] Kovscek A R, Bertin H J. Foam Mobility in Heterogeneous Porous Media [J]. Transport in Porous Media, 2003, 52(1): 17-35. [3] Chen L, He A, Zhao J, et al. Pore-scale modeling of complex transport phenomena in porous media[J]. Progress in Energy and Combustion Science, 2022, 88: 100968. [4] Blunt M J. Multiphase Flow in Permeable Media: A Pore-Scale Perspective [M]. Cambridge: Cambridge University Press, 2017. [5] Shams M, Singh K, Bijeljic B, et al. Direct numerical simulation of pore-scale trapping events during capillary-dominated two-phase flow in porous media[J]. Transport in Porous Media, 2021, 138(2): 443-458. [6] Fuerstman M J, Lai A, Thurlow M E, et al. The pressure drop along rectangular microchannels containing bubbles [J]. Lab on a chip, 2007, 7(11): 1479-89. [7] Armstrong, R. T., A. Georgiadis, H. Ott, D. Klemin, et al. Critical capillary number: Desaturation studied with fast X-ray computed microtomography[J]. Geophysical Research Letters, 2014, 41, 55–60. |
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| Country | China |
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