Multiphase flows capillary number

Relative permeability and capillary pressure functions, collectively called multiphase flow functions, are required to describe the flow of two or more fluid phases through permeable media. These functions primarily depend on fluid saturation, although they also depend on the direction of saturation change, and in the case of relative permeabilities, the capillary number (or ratio of capillary forces to viscous forces). Dynamic experiments are used to determine these properties [32]. 

The major forces controlling multiphase flow pafferns are capillary forces, viscous forces, and buoyancy forces. These forces are often compared using three key dimensionless numbers the ratio of the displaced to the invading fluid viscosities. 

In the foregoing discussion, the assumption is that each phase is transported in its own percolating network by a pressure-driven flow mechanism. This is the generally accepted view of multiphase flow in subsurface applications, and is certainly true at low values of the capillary number Ca = vfi/a). However, blob mobilization is a dominant form of transport in many unit operations in chemical engineering, where the capillary number and Reynolds number are higher. In these cases, specialized correlations for multiphase flow should be used. 

This section discusses how to select the parameters to calculate capillary number. Initially, capillary number was proposed to correlate the residual saturation of the fluid (oil) displaced by another fluid (water) in the two-phase system. In surfactant-related flooding, there is multiphase flow (water, oil, and microemulsion), especially at the displacing front. If we use up/a to define the relationship between capillary number and residual oil saturation, which phase u and p and which o should be used then To the best of the author s knowledge, this issue has not been discussed in the literature. The following is what we propose. 

Capillary number (Ca) is a parameter that expresses the competition between viscous and interfacial forces, and is generally used to describe multiphase flow behavior in micro- and nanocharmels. Ca is defined as the ratio between the viscous and interfacial force ... 

Ranking the importance of different forces helps in categorizing the increasing number of experimental studies with the ultimate goal to predid multiphase flow behavior in microchannel networks and formulate guidelines for their design. Multiphase microflows are charaderized by the ratio of viscous to surface forces, the capillary number (Co) and by the ratio of fluid viscosities ... 

For completeness, we mention the most common other dimensionless numbers which are frequently encountered in the literature on multiphase flow. These are the Archimedes number, Capillary number, and Ohnesorge number, defined as... 

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