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Material-balance studies are based on reservoir production-pressure responses. Mobility ratio characteristics and displacement efficiencies are not included in this zero-dimensional model. For instance, an expanding gas cap physically displaces oil ahead of the invading front. The material-balance method accounts for the changing reservoir volumes as a function of pressure loss, but the effects of the changing relative permeability and viscosity values of the displacing and displaced phases are ignored. The fractional flow concept, presented in this chapter, accounts for these constantly changing relative permeability values.

The calculation procedure results in a graph showing the fraction of the displacing phase flowing in the reservoir as a function of changing saturation. The graph can be used to illustrate how changing reservoir conditions affect the relationship between the displacing and the displaced phases. Solutions are concerned primarily with the efficiency of oil displacement by means of water in a linear system when predicting waterflood performance. Modifications to the 1D fractional flow equation have been proposed that consider the effects of gravity segregation ( Dietz 1953 ; Dake 1978 ). However, the use of reservoir numerical simulation (finite-difference and streamline models) has been widely substituted in those particular cases, and it can account for the multidimensional effects of high heterogeneity in rock and fluid properties, structural complexities, and dipping reservoirs ( Coats et al. 1967 ; Morse and Whiting 1970 ; Datta-Gupta and King 2007 ).

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