The convergence of upstream collocation in the Buckley-Leverett problem

Conference · Wed Sep 01 04:00:00 EDT 1982 · Soc. Pet. Eng. AIME, Pap.; (United States)

OSTI ID:5327165

Allen, M B; Pender, G F

Upstream collocation is a fast and accurate scheme for stimulating multiphase flows in oil reservoirs. In contrast to standard orthogonal collocation, upstream collocation yields numerical solutions to the Buckley-Leverett problem that converge to physically correct solutions. The failure of standard orthogonal collocation is not surprising, since the Buckley-Leverett problem as commonly stated is incompletely posed. The equal-area rule of Buckley and Leverett and the Welge tangent construction both specify additional constraints needed to close the problem properly. An error analysis of upstream collocation shows that this method forces convergence through an artificial dissipative term analogous to the ''vanishing viscosity'' used in shock fitting. This constraint is mathematically equivalent to the more familiar constructions and should prove beneficial in simulating enhanced recovery schemes based on frontal displacement.

• Research Organization: Princeton Univ.
• OSTI ID: 5327165
• Report Number(s): CONF-820927-
• Conference Information: Journal Name: Soc. Pet. Eng. AIME, Pap.; (United States) Journal Volume: SPE 10978
• Country of Publication: United States
• Language: English

Related Subjects

02 PETROLEUM
020300* -- Petroleum-- Drilling & Production
CALCULATION METHODS
ENHANCED RECOVERY
EQUATIONS
FLOW MODELS
FLUID FLOW
FLUID INJECTION
FLUIDS
MATHEMATICAL MODELS
MISCIBLE-PHASE DISPLACEMENT
MULTIPHASE FLOW
NUMERICAL SOLUTION
OIL WELLS
PLANNING
RECOVERY
RESERVOIR FLUIDS
RESERVOIR ROCK
SIMULATION
WELLS