The need to understand various mechanisms governing fluid-fluid displacements associated with enhanced oil recovery provides the motivation for this study. These displacements are characterized by fluctuations in flow due to interfacial phenomena such as Haine's jumps, droplet break-up and coalescence etc., which at present are only qualitatively understood. This study is an attempt to quantitatively describe these phenomena for a specific idealized pore geometry using approximate quasi steady-state calculations. The progress of a non-wetting oil droplet down a periodically convergent-divergent pore, the basic unit of which is a trancated bicone, Shows a fluctuating, piecewise continuous track that resembles Haine's jumps.

In addition to Haine's jumps, variations in the motion of droplets may also occur due to their break-up and coalescence. Different parts of a droplet may be required to adjust to different curvatures and sometimes it may fail to maintain a constant mean curvature throughout its interface. Consequently, while flowing through constrictions, a droplet may break-up. Some pieces of the broken droplets might travel in the middle of the pore and sometimes may coalesce with each other in some different portion of the pore. The droplets become immobilized whenever the pressure gradients available across them are insufficient to overcome the threshold pressure offered by their interfaces.

Possible implications of these phenomena in entrapments of residual oil, hysteresis in capillary pressure and relative permeability curves and, fluctuations in the flow of multiphase flow of fluids through porous media are discussed.


Production of oil and gas by primary depletion below the bubble point, or by secondary or tertiary recovery techniques usually involves the simultaneous flow of two or more phases through reservoir rocks. The motivation for causing this multiphase flow is to displace the more valuable oil by less valuable gas, water or other displacing phases. In order to improve the displacement efficiency, it is important to fully understand various displacement mechanisms associated with multiphase flow through porous media.

Multiphase flow through porous media is much more complex than is commonly appreciated. The situation is compounded due to the existence of multitude of parameters and variables needed to fully define the fluid-rock system. This paper deals with a simplified, idealized system and attempts to give a quantitative discussion of displacement under dynamic conditions in an irregular capillary. In the process it also points out some of the implications and complexities associated with quantitative description of multiphase flow through porous media.

Simple Problem

It has long been suggested that the various phenomena associated with multiphase fluid flow through porous media (e.g. entrapment of residual fluids, hysteresis and jerky motions) are related to pore structure or the shapes of individual pores1,2. Once the multiphase flow phenomena in individual pores are sufficiently understood, one may study the composite flow behavior of a porous medium, viewed as a network of inter-connected capillaries3.

Here we consider a special case of flow of two fluids through a periodically convergent-divergent pore, the basic unit of which is a trancated bicone (Figure 1).

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