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ABSTRACT
The relative effects of the bulk viscosity, viscous stresses, wetting, capillary number and volume fraction of an oil upon its displacement from bundle of cylindrical straight capillary tubes are quantitatively determined. The results are limited by assumptions that: (1) all fluids are Newtonian. (2) The normal viscous stress is assumed uniform along the fluid-fluid phase interface where the interface is a spherical segment. (3) The bulk viscous forces dominate surface viscous forces at the interface.
The conditions for validity of two latter assumptions are discussed and the condition for significant influence of the bulk viscous stress is found. The data available for a system, relevant to tertiary oil recovery, indicate that the stress is important for displacement process.
A new equation is established for description of both single liquid outflow and the liquid-liquid outflow from the bundle of capillaries. The equation can be reduced, under certain (limited) conditions, to the Darcy's law. We revealed qualitatively different types of influence of the capillary number and wetting upon an oil, water or emulsion displacement. In the case of emulsions, the rate of displacement depends upon the droplet size, volume fraction of an oil, and upon the dynamic wetting conditions related to contact angle hysteresis.
Optimal conditions for oil displacement have been found with respect to average droplet size, volume fraction of dispersed phase and interfacial tension. We have shown that the minimal interfacial tension is not always an optimum condition for oil displacement from a porous structure.
Our theoretical predictions agree with available experimental results on tertiary oil recovery.