Linear-stability analysis of immiscible displacement: Part 1-Simple basic flow profiles

Journal Article · Tue Jul 01 04:00:00 EDT 1986 · SPE (Society of Petroleum Engineers) Reserv. Eng.; (United States)

DOI:https://doi.org/10.2118/12692-PA· OSTI ID:5442873

Yortsos, Y C; Huang, A B

The linear stability of immiscible, two-phase-flow displacement processes in porous media is examined. Multiphase-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 early evolution of unstable modes show a certain similarity in the respective cases of negligible and non-negligible capillary effects to the Rayleigh and Orr-Sommerfeld equations governing the stability of unbounded shear flows. The stability of noncapillary displacement is first examined. Growth rates 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 examined next. Stability curves are obtained for step-saturation initial profiles. Both capillary pressure and a smooth initial-mobility profile exert a stabilizing influence on the flow displacement. The results find application in prediction of the onset of instability and description of the early stages of unstable growth in immiscible displacement.

• Research Organization: Univ. of Southern California
• OSTI ID: 5442873
• Journal Information: SPE (Society of Petroleum Engineers) Reserv. Eng.; (United States), Journal Name: SPE (Society of Petroleum Engineers) Reserv. Eng.; (United States) Vol. 1:4; ISSN SREEE
• Country of Publication: United States
• Language: English

Related Subjects

02 PETROLEUM
020300* -- Petroleum-- Drilling & Production
CAPILLARY FLOW
DIAGRAMS
DIFFERENTIAL EQUATIONS
EIGENVALUES
ENERGY SOURCES
ENHANCED RECOVERY
EQUATIONS
EQUATIONS OF MOTION
FLOW MODELS
FLUID FLOW
FLUID INJECTION
FOSSIL FUELS
FUELS
INSTABILITY
MATERIALS
MATHEMATICAL MODELS
OIL WELLS
PARTIAL DIFFERENTIAL EQUATIONS
PERMEABILITY
PETROLEUM
POROSITY
POROUS MATERIALS
PRESSURE DEPENDENCE
RECOVERY
SATURATION
SHEAR
STABILITY
STEADY-STATE CONDITIONS
STIMULATION
SURFACE PROPERTIES
SURFACE TENSION
TWO-PHASE FLOW
WATER SATURATION
WATERFLOODING
WAVELENGTHS
WELL STIMULATION
WELLS