Abstract
ABSTRACT A versatile implicit four-point centered method for two-phase flow is presented. The formulation is based on the conservation laws of continuity and momentum. The system of quasi-linear first partial differential equations are show to be hyperbolic and are solved numerically. The equations of state for the pipe wall, oil and gas are included in order to accurately predict temporal and spatial variation in sound speed. The modified Peng-Robinson equation of state provides accurate means of predicting volumetric properties of the liquid phase and variable wave related velocity. Numerical examples are presented for many transient flow problems. Flow sequence in a buildup test with a variable upstream reservoir pressure is considered. The effect of change in diameter (casing/tubing junction) is considered. Transients generated by choking—instantaneous valve shut-in vs. a slow shut-in are investigated. Other boundary conditions are constant pressure downstream and flow from a constant pressure reservoir. How above the bubble-point, as a special case shows excellent agreement with analytical solution.
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