First wholly-analytical gas volume fraction model for virtual multiphase flow metering petroleum industry applications

In this seminal contribution, the world’s first wholly-analytical gas volume fraction multiphase flow model is formulated and demonstrated in virtual flow meter and production allocation field applications for its differentiated ability to achieve improved reliability of phase flow rate calculations given pressure and temperature measurements at two different locations along multiphase production systems. The presented simple gas volume fraction equation is explicit in form and is validated against both lab data and oilfield flowline data. A crucial requirement for differential pressure flow meters for multiphase production systems, particularly wet gas systems in annular and annular-mist flows, is the calculation of the averaged gas volume fraction. Additional calculations include multidirectional entrainment calculations, which strongly affect the simultaneous entrainment of liquids in the gas phase and the gas in the liquid phases. Historically, prior published gas volume fraction two-phase flow models had closure relations and artificial adjustment (fitting) factors linked to controlled lab-scale conditions involving immiscible fluids that bear no resemblance to the complex petroleum mixtures undergoing phase change in uncontrolled long wellbore and flowline environments. Thus, ambiguous extrapolations were necessary leading to increased uncertainties. Using an asymptotic approximation analysis approach, an analytical gas volume fraction equation is derived that overcomes this empirical-based restriction. In terms of comprehensive validation, the presented analytical gas volume fraction equation is demonstrated first for its ability to reliably reproduce over 2600 two-phase annular and annular-mist flow experimental datasets inclusive of circular and non-circular conduits. Secondly, readily available published experimental data of both constant-diameter as well as variable-diameter sub-critical to critical choke two-phase flows are used for model validation in scenarios involving different flow obstructions. Lastly, an offshore subsea flowline dataset is used to demonstrate the improved reliability of the new equation at field-scale operational conditions.