Abstract
We use a new volume-of-fluid based finite-volume method to model two-phase flow through simple pore geometries and study the mechanisms controlling two-phase flow at the pore scale. The numerical model is used to study layer flow and snap-off, and investigate the effect of geometry and flow rate on trapping and mobilization of the disconnected ganglia. Furthermore, a new variable, the capillary field, is introduced to characterize the capillary force under dynamic situations, and a force-balance concept is presented to relate flow rates to pore-scale forces—dynamic pressure gradient and the capillary field. This description of the flow has the potential to be used in pore-network models to study the effect of pore-scale structures on the flow at larger scales. As an illustration of the applicability of this concept, we use the relations obtained from the numerical simulations to predict the threshold capillary number for blob mobilization during imbibition and show that this information can be used to reproduce the direct numerical simulation results accurately.
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Notes
Proof: The Laplacian operator (\({\nabla }^2\)) can be considered as the divergence of the gradient \(\nabla \cdot \varvec{\nabla }\), and the divergence (\(\nabla \cdot \)) is a linear operator. Therefore, from Eq. (6), we have: \(\nabla \,\cdot \, {\mathbf f}_\mathrm{c} - \nabla \,\cdot \, \varvec{\nabla } p_\mathrm{c} = 0\ \ \rightarrow \ \ \nabla \,\cdot \, ({\mathbf f}_\mathrm{c} - \varvec{\nabla } p_\mathrm{c})=0 \).
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Raeini, A.Q., Bijeljic, B. & Blunt, M.J. Numerical Modelling of Sub-pore Scale Events in Two-Phase Flow Through Porous Media. Transp Porous Med 101, 191–213 (2014). https://doi.org/10.1007/s11242-013-0239-6
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DOI: https://doi.org/10.1007/s11242-013-0239-6