Modeling and calculation of pressure drop for two-phase flow through porous media

At low void fractions the flow configuration is characterized by the motion of discrete bubbles. Initially, the bubbles tend to adhere to the particle's surface and therefore travel upward along the surface of the particles. After maximum packing at the particle surface has occurred, the bubbles will start to move straight through the pores. At a still higher void fraction α1 the bubbles will merge to form slugs. At void fraction α1 some bubbles will start to merge into slugs. The transition from bubbly to slug flow, however, is a smooth one and there is a range of void fraction in which bubbles and slugs co-exist. The upper bound of this region can be obtained by assuming that transition is complete when the void fraction corresponds to the lightest packing of slugs, i.e. a cubic array. The regime of pure slug flow begins at void fraction α2. As the void fraction increases the slugs are packed more densely together. However, there is an upper value α3 beyond which the slugs themselves will merge to form continuous gas paths. At this void fraction transition to annular flow begins. In obtaining the void fraction corresponding to this transition it is conceptualized that the slugs are replaced by spheres which fill the pores. Even though the packing of slugs may be different from the packing of spheres, it is the center-to-center distance between two adjacent slugs which determines the void fraction at merger. This distance is at a minimum when two slugs are parallel to one another. A maximum is reached when they are perpendicular to each other. On average, this distance may be represented by the diameter of a sphere whose volume is the same as that of a slug. Departure from pure slug flow begins at void fraction α3. The transition to annular flow is also a smooth one with an upper bound α4