Capillary Tube Models with Interaction Between the Tubes [A Note on 'Immiscible Displacement in the Interacting Capillary Bundle Model Part I. Development of Interacting Capillary Bundle Model', by Dong, M., Dullien, F.A.L., Dai, L. and Li, D., 2005, Transport Porous Media]

摘要

Dong et al. (1998) published an innovative model for flow in tubes. The paper described a model based on two parallel capillary tubes that allowed pressure equilibration between them in the regions where the fluids were the same in both tubes. Dong et al. (2005) published an extension to this model that considered flow in a bundle of capillary tubes. They called this the "interacting capillary bundle" model. Figure 1 illustrates a system consisting of four capillary tubes of different diameters. A wetting fluid invades the system from the left face of the system, displacing a non-wetting fluid which exits from the right face of the system. It will be assumed that the injection rate is constant and the downstream pressure in the non-wetting fluid is at a value of P_(nwd)- The upstream pressure in the wetting fluid will vary and will be denoted by P_(wu). In such a system, the penetration distance of the wetting fluid is inversely proportional to the tube diameter.