A study of two-phase drift-flux modeling in wells and corresponding slip relations

Abstract

It was desired to investigate the two-phase drift-fl ux model's behavior in both steady-state and transient settings and shed some light on required slip relations. A numerical MATLAB model of the one-dimensional two-phase drift-fl ux model developed by Dr. Steinar Evje has been used to simulate gas-liquid fl ow in a vertical pipe. Diff erent slip parameters have been tested, compliant with the general formulation from Zuber and Findlay [22]. Optimized slip parameters from Shi et al. [15] have been implemented in the numerical model, and simulation runs for both steady- state and transient conditions are included. Ten steady-state simulations have been carried out, matching the experimental holdup data very well with a root-mean square error of only 0.039. The optimized slip parameters have then been directly applied in a transient setting, in which a 17.8 dm3 slug is put at the bottom of a 10.9 m, 15.24 cm diameter pipe and allowed to migrate towards the closed outlet, similar to what would happen in a kicking well. It is observed that the optimized slip is not able to reproduce the typical Taylor bubble fl ow expected to occur in such a setting, as the gas distribution of the slug was seen to spread over the length of the pipe. As the gas is seen to accumulate at top, unphysical behavior is observed, and it is believed that the slip model from Shi et al. causes the drift- flux model failing to remain hyperbolical. This has given way for a desire to implement di fferent slip parameters able to reproduce more typical Taylor-bubble behavior. Basic slip parameters for slug fl ow and parameters for Taylor bubbles from Hibiki and Ishii [6] have been implemented. Although the complexity of the Taylor bubble slip far outweighs that of the simple slug flow slip, the results where found to be in good agreement with each other with regards to gas distribution in the pipe. The slug flow slip was able to let the gas slug maintain a maximum average gas volume fraction of a g;max = 0.79, while the Taylor bubble slip gave a respectable average gas fraction of g;max = 0.82. Also, the Taylor-bubble-slip proved to increase the overall rise velocity of the slug, allowing it to traverse the pipe at a somewhat higher velocity than when using slug fl ow slip.