Two-Phase Flow Through Vertical, Inclined, or Curved Pipe
Authors: Gould Thomas L. , Tek M. Rasin , Katz Donald L. 
Published: December 2007

A model for predicting pressure distribution in two-phase flow through vertical, inclined, or curved pipes combines the best available correlations for predicting pressure gradients for each flow regime. It has been evaluated statistically against literature data and directly against field data from directionally drilled offshore wells. On the whole, the model performs commendably.

Introduction
Problems related to two-phase flow are frequently Problems related to two-phase flow are frequently encountered in the design and operation of oil and gas production or storage fields. In addition, two-phase flow technology is of great interest to chemical engineers in dealing with such areas as boilers, condensers, heat exchangers, reactors, and process piping. Many of the concepts and correlations developed piping. Many of the concepts and correlations developed originally for petroleum operations are being extended to other fluids and new applications. The energy shortage, currently so much the focus of public attention, has recently stimulated interest in new areas, many of which closely relate to the current understanding of two-phase flow. Simultaneous long-distance pipelining of crude oil and natural gas, harnessing of pipelining of crude oil and natural gas, harnessing of geothermal energy in the form of steam and hot water, production from offshore locations, pipelining of production from offshore locations, pipelining of LNG, and mining and dredging from the bottom of the oceans are among the new areas where recently developed technology in two-phase flow is being evaluated in the light of economic feasibility. The basic engineering problem in calculating the pressure distributions in conduits subject to pressure distributions in conduits subject to two-phase flow may be spelled out as follows: Knowing the geometry of conduit, physical properties of the two-phase flow system, and conditions prevailing at one end, predict pressure profiles along the pipe. Contributions to solving various aspects of two-phase flow problems have been numerous in the literature. This paper will be limited to an investigation of those pressure-drop models that are currently available for vertical and inclined flow. We shall consider both the quantitative and the qualitative aspects of the models and discuss their extension to inclined and curvilinear flow. Through the years, a number of investigators in vertical two-phase flow chose to correlate both slippage and friction losses by a unique and single energy-loss factor. The results of their efforts fell short of their desired goal because their correlations did not include the effects of all pertinent variables, and, more importantly, they did pertinent variables, and, more importantly, they did not reflect the effect of various flow regimes. Another school of thought is represented by other investigators who chose to define, measure, and predict slip or holdup as an intermediate parameter predict slip or holdup as an intermediate parameter leading to the calculation of pressure drop. This approach, along with considerations of energy balance, led to an interpretation of pressure gradient as a sum of three individual gradients: density, acceleration, and friction. One of the principal reasons for the failure of most vertical two-phase flow correlations was the coexistence of several flow regimes along the same pipe for a given set of operating conditions.
JPT
P. 915