Prediction of Bottomhole Flowing Pressures in Multiphase Systems Using a Thermodynamic Equation of State
Authors: Barrufet Maria A. , Rasool Ahmed , Aggour Mohamed 
Published: December 2007

Abstract
The simultaneous flow of oil, water and gas in pipes occurs throughout the production systems involved in flowing fluids from the reservoir to the surface.
Accurate prediction of the pressure drop in a multiphase flow system is essential for proper design of well completions, artificial-lift systems, surface flowlines and gathering lines.
The prediction of pressure drop in a multiphase system is further complicated by the interdependence of the controlling variables, i.e., flow regimes, flow rates of the different fluid phases, and fluid properties. The thermodynamic behavior of the flowing hydrocarbon mixture is one of the most dominant factors affecting multiphase flow since the formation of gas and liquid phases and the values of their physical properties are dictated by the pressure and temperature. Because of the complex relation of physical properties, empirical models are still widely used to predict the pressure drop in multiphase systems. Among these models we selected the model by Beggs and Brill1 because it is one of the most widely used and accepted in the petroleum industry.
We have developed a numerical simulator to predict the bottomhole flowing pressure (BHFP) in multiphase systems, where oil/gas or oil/water/gas are flowing together. To improve the accuracy of the prediction we coupled the Beggs and Brill procedure for pressure drop calculations to a thermodynamic equation-of-state (EOS). The Peng-Robinson EOS is used to predict the thermodynamic phase separations along the tube and the fluid phase properties. The length of the flow tube is divided into a number of intervals representing separators, and a linear temperature gradient is assumed between the bottomhole and the surface temperature. The mass of fluid traveling through a specific section in the tubes is flashed at an assumed pressure and at the temperature corresponding to that depth. This pressure is reevaluated from the Beggs and Brill procedure and used to establish phase partitioning and fluid properties. This iterative scheme concludes when the pressure between two successive iterations does not change within a specified tolerance.
We tested data from 56 wells having a wide variation in producing rates, gas/oil ratios, depths, tubing sizes, compositions, andwater cuts. These wells were mainly from the Middle East and from Louisiana. The conventional approach is the Beggs and Brill coupled with fluid property correlations. Our model couples the Beggs and Brill model with the Peng-Robinson EOS. The bottomhole flowing pressures predicted from both procedures were compared with measured values of bottomhole flowing pressures. The average absolute mean predicted error for our model was 9.73% with a standard deviation of 7.55%, as opposed to the conventional approach that gave a 28.44% error with a standard deviation of 21.79%. We believe that the evaluation of phase separation and fluid properties using a thermodynamic EOS will always provide better estimates of the bottom-hole flowing pressures as opposed to generic fluid property correlations. The predictions may be even better for volatile and condensate fluid systems.