Reservoir Engineering–General - Multiphase Flow of Water, Oil and Natural Gas Through Vertical Flow Strings

A new method for correlating the data on multiphase flow through vertical pipe is presented. The correlation is based on a "two-phase f factor" concept which was developed and successfully applied to horizontal multiphase flow by Bertuzzi, Tek and Poettmann. Field data previously published on several flowing and gas-lift wells have been used as the basis for the developed correlation. The application of the method to actual two-phase flow problems indicate that this method is capable of predicting the pressure distribution in vertical multiphase flow strings well within the accuracy range usually desired for common engineering and design calculations. A new working chart developed for calculation of two-phase pressure gradients and a graphical step-by-step procedure for the computation of pressure distribution are presented along with an example problem. INTRODUCTION Multiphase flow through vertical pipe is encountered in many engineering installations. In petroleum, chemical process, nuclear engineering and many other industries, problems associated with simultaneous flow of two or more phases through vertical pipe have been of interest for a long time. This interest has increased considerably during recent years due to applications to new processes in petroleum production and refining and to problems of steam generation and heat removal from nuclear reactors. One prominent example of vertical two-phase flow is provided by the gas-lift process where oil, water and gas flow simultaneously. If the pressure profile in a gas-lift well can be predicted within reasonable accuracy, it would be possible to get good estimates of the power required to lift the oil, the optimum depth, the pressure and the rate at which to inject gas. Furthermore, the effect of production rate and tubing sizes on these quantities can be evaluated before any design decision is made on the installation and operation of the flow string. The majority of experimental work available in the literature deals with two-component systems where individual phase flow rates in and out of the pipe remain constant. The general problem of prediction of pressure drops in multiphase flow systems is very complicated. The co-existence of numerous flow patterns of widely different geometry and mechanism, conditions of surface instability and the nature of force fields acting upon the system are among the major difficulties commonly encountered. The classical approach of fluid dynamics which would be based upon the formulation and solution of Navier-Stokes equations has been found by many investigators completely devoid of any hope of success-—not only because of inherent nonlinearities but also because of insurmountable analytical difficulties standirng in the way of setting up the boundary conditions. The presence and effect of interfacial forces on mu1tiphase flow systems further complicate the theoretical approach. For these reasons, many investigators choose to adopt semi-empirical if not purely empirical approaches in order to obtain solutions of engineering utility. A prominent practical solution has been given by Poettmann and Carpenter' in the form of an empirical correlation. In their paper, total flowing densities of fluids and solubility effects of gas in oil have been taken into account for the correlation of field data covering a wide range of operating conditions for oil wells. They treated the gas. oil and water as a single phase of combined propcrties and correlated the multiphase friction factor as a function of the product (pvd), i.e., density X velocity X diameter of the flow string. However, because the product (pvd) is dimensional while the frictior factor is dimensionless, the generality of their result's is somewhat restricted. It seems that the omission 01 viscosity effect may be one of the reasons for the scatter of data as shown in their correlation chart. The concepts of the "two-phase f factor" and the "two-phase Reynolds' number function" were recently developed and successfully applied to correlate horizontal multphase flow by Bertuzzi, Tek and Poettmann.' Recently, two new methods of correlation by Tek and Chan' have been presented on simultaneous flow of liquid and gas through vertical pipe. These two methods of correlation and the working equations in field units necessary for their application are included in this paper. The extension of the conccpt of two-phasc Reynolds' number function successfully developed for horizontal flow into vertical multiphase flow systems, development and evaluation of working charts permitting calculation of two-phase pressure gradients and