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, S, 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 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. 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 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.
In situ recovery of heavy oils generally involves the use of thermal recovery methods. Steam or hot water, either alone or with various additives is injected to heat the oil, thus lowering its viscosity and allowing subsequent production.
In order to assess the effectiveness of such production processes, mathematical reservoir models are generally used. These models contain equations for the conservation of mass, momentum and energy of the flowing components along with the necessary constitutive equations. Given the initial and the boundary conditions of the reservoir, injection and production system, the production performance can be estimated. production performance can be estimated. The most important parameters used in the reservoir model in describing the complex multi-phase flows in the reservoir rock are probably the relative permeabilities of the oil-water system. probably the relative permeabilities of the oil-water system. Relative permeabilities can be determined by the steady state (Penn-State) methods and the unsteady state method which uses the Buckley-Leverett displacement theory. Relative permeability is usually expressed as a function of the saturation of the flowing phases. However, in the complex thermal recovery flow situations, this simple relationship is altered by various factors such as the viscosities and interfacial tensions of the displacing and the displaced fluids. A review of the various Investigations of these parameters Is given by Torabzadeh and Handy who also report some results on the effect of temperature and interfacial tensions on oil-water relative permeabilities.