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- W1998738287 abstract "Summary In this paper we examine the growth of unstable disturbances (viscous fingers) in a water/oil displacement process with a mobile interstitial water saturation. Both linear and weakly nonlinear methods of analysis that include continuously changing mobility and capillary effects are presented. The fingers are assumed to develop as a result of perturbations of a steady displacement. After a brief review of the linear stability results, we implement a weakly nonlinear stability analysis for flow processes near the onset of instability (finite wave-number cutoff). Our numerical results indicate that disturbances near the critical point of the linear theory become stabilized to an equilibrium value, which is a function of the mobility ratio and the capillary number. This behavior suggests supercritical stability, in contrast to the instability predictions of the linear theory. The results of the linear theory are subsequently used to investigate the mechanism of finger growth at the wavelength of the fastest-growing disturbance. Saturation contours and the water flow field are numerically computed as a function of time. The local mechanism for finger growth is shown to be the continuous transfer of water (oil) from oil (water)-rich to water (oil)-rich regions. Although the linear analysis predicts constant increase in the size of the regions, the weakly nonlinear theory shows that fingers eventually stabilize to a configuration of a fixed amplitude. Typical finger growth processes are numerically illustrated." @default.
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- W1998738287 date "1988-11-01" @default.
- W1998738287 modified "2023-09-26" @default.
- W1998738287 title "Investigations on Viscous Fingering by Linear and Weakly Nonlinear Stability Analysis" @default.
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- W1998738287 doi "https://doi.org/10.2118/14367-pa" @default.
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