Modelling Downhole Separation Efficiency Using a Stream Function Approach
A new technique for solving simultaneously the mass and momentum balance equations for a gas-liquid mixture is proposed in this paper. The technique is based on the vorticity-stream function approach, under a cylindrical coordinate system. Important variables such as slip velocity in the radial and vertical direction, characteristic of the bottomhole, gas and liquid flow rates, pressures, flow pattern, among others, are considered simultaneously in the solution of the problem. The two-phase model proposed in this work allows obtaining the liquid and gas velocities fields as well as the two-phase flow pressure and gas fraction fields. Experimental data is used to close the model. The model was used to simulate downhole separation efficiency and to determine the influence of liquid flowrate, GLR, casing size and liquid viscosity on the natural separation efficiency. The model agrees very well with experimental data obtained by The University of Tulsa.