Investigations on viscous fingering by linear and weakly nonlinear stability analysis
- Univ. of Southern California, CA (US)
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.
- OSTI ID:
- 6806519
- Journal Information:
- SPE (Society of Petroleum Engineers) Reserv. Eng.; (United States), Journal Name: SPE (Society of Petroleum Engineers) Reserv. Eng.; (United States) Vol. 3:4; ISSN SREEE
- Country of Publication:
- United States
- Language:
- English
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BLOOD VESSELS
BODY
CAPILLARIES
CARDIOVASCULAR SYSTEM
COMPUTER CALCULATIONS
DISPLACEMENT FLUIDS
DISTURBANCES
FLUIDS
GEOLOGIC DEPOSITS
GROUND WATER
HYDROGEN COMPOUNDS
INTERSTITIAL WATER
MINERAL RESOURCES
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
OIL FIELDS
OIL SPILLS
ORGANS
OXYGEN COMPOUNDS
PETROLEUM DEPOSITS
PHASE STABILITY
RESOURCES
ROCK-FLUID INTERACTIONS
SATURATION
STABILITY
SUPERCRITICAL STATE
WATER
WATER SATURATION