A finite element formulation of the two-phase flow equations for oil reservoirs

Journal Article · Fri Feb 01 04:00:00 EST 1985 · Soc. Pet. Eng. AIME, Pap.; (United States)

DOI:https://doi.org/10.2118/13516-MS· OSTI ID:5470848

Gulbrandsen, S; Wille, S O

In the present paper, the differential equations governing two phase, immiscible flow in porous media is solved by the finite element method. The saturation of the wetting phase (water) and the non wetting phase (oil) have been used as independent variables. In this finite element formulation the saturation and pressure equations are solved simultaneously and the formulation is entirely implicit. The time derivatives are approximated by backward Euler differences. The Newton Raphson method is applied to solve the non linear equations. The differential equations are solved in the original form without simplifications. The simulations are performed in a two dimensional model, but the algorithms will have equal advantages in three dimensional simulations. The results of the simulations are presented as saturation and pressure isocurves, and velocity vector field.

• Research Organization: Univ. of Oslo
• OSTI ID: 5470848
• Journal Information: Soc. Pet. Eng. AIME, Pap.; (United States), Journal Name: Soc. Pet. Eng. AIME, Pap.; (United States) Vol. SPE13516; ISSN SEAPA
• Country of Publication: United States
• Language: English

Related Subjects

02 PETROLEUM
020300* -- Petroleum-- Drilling & Production
COMPUTERIZED SIMULATION
DIFFERENTIAL EQUATIONS
ENGINEERING
ENHANCED RECOVERY
EQUATIONS
FINITE ELEMENT METHOD
FLOW MODELS
FLUID FLOW
FLUID INJECTION
FLUID MECHANICS
HYDRODYNAMICS
MATHEMATICAL MODELS
MECHANICS
MISCIBLE-PHASE DISPLACEMENT
NUMERICAL SOLUTION
OIL WELLS
RECOVERY
RESERVOIR ENGINEERING
RESERVOIR ROCK
SIMULATION
TWO-PHASE FLOW
WELLS