The Effect of the Slip Velocity on the Differential Pressure in Multiphase Venturi Flow Meters

Venturi tubes and orifice plates are devices largely used in the petroleum industry for measuring multiphase flows. In the project and calibration of these flow meters, the homogeneous model is commonly used. This model calculates the velocity and pressure drop of the mixture using correlations for single phase flow with a modified viscosity and density to account for the presence of the other phase, but no consideration is made about the relative velocity between the phases. However, the pressure difference, the measuring variable in these flow meters, is known to be affected by the relative velocity between phases, which becomes more and more important when the flow mixture accelerates. This paper addresses this issue and aims to demonstrate the importance of the slip velocity in the calculation of the flow velocity in a venturi meter. For this purpose, pressure-difference values obtained using the two-fluid model based on an Eulerian-Eulerian approach for the multiphase flow are compared with the results of the homogeneous model and with experimental data. Both theoretical calculations are performed using the CFX4.4 package, code which solves multidimensional multiphase flows. Considerations about the two-fluid model are presented, focusing, in particular, on the effects of the stress tensor in the dispersed phase. Considerations regarding the two-dimensional nature of the flow are also made. Test cases are presented in order to determine the dependency of the differential pressure with void fraction and slip velocity.