Analysis of Vertical Two-phase Flow Calculations: Crude Oil-gas Flow In Well Tubing
Authors: Gregory G.A. , Fogarasi M. , Aziz K. 
Published: March 2010

Abstract
Pressure drops in oil-well tubing, calculated by five well-known models are compared with actual field data covering a wide range of conditions. A detailed explanation is provided for the observed result that significantly higher accuracy is generally obtained when calculations are based on known bottom-hole conditions rather than known wellhead conditions.
It is demonstrated that greater accuracy may be obtained by using measured bubble-point data than by using calculated values.
The results of this study suggest that either the Aziz, Govier and Fogarasi or the Orkiszewski model should generally be used in preference to other methods for calculating pressure drops in oil-well tubing.

Introduction
A reliable estimate of the pressure drop in well tubing is essential for the solution of a number of important production engineering and reservoir analysis problems. For example, inflow performance calculations require a knowledge of pressure drop in the producing string as a function of flow rate. Many different models and correlations have appeared in the literature for this purpose. In addition, there are a number of correlations available for estimating the fluid properties required for these calculations when experimental data are not available.
In recent years, computer programs containing many of these models and fluid property correlations have been developed and are readily available to the engineer. Unfortunately, however, the choice of the appropriate method for a particular problem is seldom obvious. Thus, some guidelines are required to help resolve the following questions:Which multiphase flow calculation method is the most reliable for a given system?What influence would errors in the estimation of fluid properties have on the pressure-drop calculations?
In this paper, we attempt to answer these two questions for typical oil wells, where gas-oil flow occurs over at least part of the producing string. The resolution of the same two questions for gas-condensate wells requires a somewhat different treatment, and will be considered in a separate paper.

Effect of Calculation Direction
The total pressure drop over a differential length of the tubing may be separated into three components:
(Equation Available In Full Paper)
The first term,, is the contribution to the total pressure change due to the hydrostatic-head effects. It is proportional to the density of the fluid mixture inside the pipe under flowing conditions (in-situ density). The second term, aPr, includes all frictional effects, and it is proportional, among other factors, to the fluid velocity and viscosity. Finally, the third term, ΔPKE, results from velocity changes (acceleration) caused by the expansion of the fluid with decreasing pressure.
In oil wells, the fluid properties are such that the proper engineering design usually requires that the flow pattern be bubble or slug (see reference 1 for a description of various flow patterns). In some situations, the gas/oil ratio (GOR) may be high enough to cause froth flow, but this situation is more common in condensate wells.