Linear Stability Analysis of Immiscible Displacement Including Continuously Changing Mobility and Capillary Effects: Part II-General Basic Flow Profiles
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The linear stability of immiscible, two-phase flow displacement processes in porous media is examined. Multi-phase flow characteristics are included in the stability description through relative permeability and capillary pressure functions. A linear stability analysis of the steady-state saturation and pressure distributions is carried out in terms of normal modes. The resulting linearized eigenvalue problems describing the evolution of unstable modes resemble, in the respective cases of negligible and non-negligible capillary effects, the Rayleigh and Orr-Sommerfeld equations governing the stability of unbounded shear flows. First, the stability of non-capillary, two-phase, immiscible displacement is examined. Rates of growth of the unstable modes as a function of the wavelength of instability are explicitly obtained for specific classes of initial total mobility profiles. The Saffman-Taylor instability and layer instability follow directly as limiting cases of the initial mobility profiles. The effect of capillarity on flow stability is next examined. Stability curves that include capillary effects are obtained for several simple initial saturation profiles. The effects of capillary pressure, viscosity ratio and relative permeability characteristics on the stability curves are discussed. It is shown that both capillary pressure and a smooth initial mobility profile exert stabilizing influences on flow displacement. The linear stability analysis predictionsmore » are compared to the results of Chuoke et al. obtained by use of an ''effective interfacial tension.'' The results find applications in mobility control and viscous fingering problems.« less