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), Vol. 3:4
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
DISPLACEMENT FLUIDS
SUPERCRITICAL STATE
OIL FIELDS
ROCK-FLUID INTERACTIONS
NONLINEAR PROBLEMS
CAPILLARIES
COMPUTER CALCULATIONS
DISTURBANCES
INTERSTITIAL WATER
NUMERICAL SOLUTION
OIL SPILLS
PHASE STABILITY
WATER SATURATION
BLOOD VESSELS
BODY
CARDIOVASCULAR SYSTEM
FLUIDS
GEOLOGIC DEPOSITS
GROUND WATER
HYDROGEN COMPOUNDS
MINERAL RESOURCES
ORGANS
OXYGEN COMPOUNDS
PETROLEUM DEPOSITS
RESOURCES
SATURATION
STABILITY
WATER
020200* - Petroleum- Reserves
Geology
& Exploration
020300 - Petroleum- Drilling & Production