Nonuniqueness of steady state fingering solutions in porous media

Journal Article · Thu Oct 01 04:00:00 EDT 1970 · Water Resour. Res.; (United States)

DOI:https://doi.org/10.1029/WR006i005p01411· OSTI ID:5464288

Varnon, J E; Greenkorn, R A

A fluid cannot displace another less mobile fluid in a piston-like manner. Local irregularities produce small protuberances on the front separating the 2 fluids. The more mobile fluid flows into the protuberances causing them to grow. An example is the downward displacement of a low density fluid by a high density one. A less obvious example is the displacement of a viscous liquid by a less viscous fluid. The lengths of the fully developed fingers grow at a uniform rate, but the fingers suffer no other change in shape. Steady-state solutions for single viscous fingers are nonunique, because the position of the interfacial boundary is not specified. Expanding the steady-state problem to include an arbitrary number of fingers does not make the solution unique. The initial value problem, however, does have a unique solution, which suggest that it is futile to look for additional conservation-type equations, in the hope of making the steady-state solutions unique.

• Research Organization: Purdue Univ.
• OSTI ID: 5464288
• Journal Information: Water Resour. Res.; (United States), Journal Name: Water Resour. Res.; (United States) Vol. 6:5; ISSN WRERA
• Country of Publication: United States
• Language: English

Related Subjects

02 PETROLEUM
020300* -- Petroleum-- Drilling & Production
03 NATURAL GAS
030900 -- Natural Gas-- Artificial Stimulation
Plowshare-- (-1989)
ANALYTICAL SOLUTION
DENSITY
ENHANCED RECOVERY
EQUATIONS
FLUID FLOW
FLUID INJECTION
FLUID MECHANICS
FLUIDS
HYPOTHESIS
INTERFACES
MATERIALS
MECHANICS
MOBILITY
NATURAL GAS WELLS
OIL WELLS
PHYSICAL PROPERTIES
POROUS MATERIALS
RECOVERY
RESERVOIR FLUIDS
SHAPE
SIZE
STEADY-STATE CONDITIONS
VISCOSITY
WATERFLOODING
WELLS