In situ recovery of heavy oil generally involves the use of steam or hot water to displace the oil. The recovery is controlled by the extent to which the displacing fluid can mobilize the oil and saturate the pores of the reservoir. Modelling of any such recovery process requires a knowledge of the permeabilities of the oil-water-rock system.

Relative permeabilities are often measured in cores using displacement experiments. These permeabilities are measured as a function of saturation and are sometimes correlated as power law functions of the initial water saturation, Swc, and residual oil saturation, Sor. The "end" of the displacement process is assumed to be after four to five pore volumes of fluid injection with the exact value somewhat arbitrarily chosen by each particular researcher, often on the basis of capillary number considerations.

In this paper, the method of characteristics solution of the one-dimensional flow equations is used to investigate the effects of various parameters, such as mobility ratio, on the number of pore volumes of injected fluid that are required to reach the residual oil saturation. For some heavy oils, it is shown that of the order of one hundred or more pore volumes of injected water may be required before reaching the residual oil saturation. The apparent steady saturation profile observed by some researchers may have resulted in premature termination of some experiments. Also, the apparent " end-effect" observed by many researchers can be attributed in part to the extreme variations in the permeability-saturation profile.

The main advantage of this analysis is an iterative approach which enables a researcher to design suitable experiments for relative permeability determinations. Also, with an assumed mathematical form of the permeability versus saturation relationship, the total curve can be generated from a limited number of displacement experiments.

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