Comparison of Two Phase Liquid Holdup and Pressure Drop Correlations Across Flow Regime Boundaries for Horizontal and Inclined Pipes

Abstract

Introduction During the last decade the interest in two-phase flow through horizontal and inclined pipes has increased considerably. Design engineers are primarily concerned with the calculation of pressure drop in two-phase lines and prediction of liquid holdup (in-situ liquid volume fraction), in prediction of liquid holdup (in-situ liquid volume fraction), in order to size flow lines and calculate slug catcher size. These calculations are also important for the design of surface facilities such as pumps, compressors and separators. Due to the complex nature of the different now patterns which exist in two-phase flow, very few theoretical patterns which exist in two-phase flow, very few theoretical mechanistic models have been developed. However, a large number of empirical correlations are available in the literature to calculate pressure drop and liquid holdup. Of this large number, only a few pressure drop correlations compute holdup, friction and acceleration gradients based on the flow patterns within the pipe. Once the correct flow pattern is determined at a specified flow rate, pressure and temperature, the appropriate holdup and pressure and temperature, the appropriate holdup and friction correlations are evaluated for the corresponding flow regime. The method for calculating the acceleration pressure gradient also depends on flow regime in some pressure gradient also depends on flow regime in some cases. LIQUID HOLDUP AND PRESSURE DROP CORRELATIONS Equations describing the pressure drop of a two-phase system are generally developed based on a single flow equation representing homogeneous mixture properties. The general pressure gradient equation is given as: (1) where: And HL is the result of empirical correlation. (2) The definition of the density term used in the friction (pf) and acceleration (P a) gradients varies with different investigators. From the form of Equation (1), it can be easily seen that the total pressure gradient is made up of three individual gradients (1) gravitational, (2) friction and (3) acceleration. Thus Equation (1) can be written as: (3) Many correlations have been developed for predicting liquid holdup and pressure-drop. Different investigators used different assumptions to develop these correlations. Some assumed that the gas and liquid phases travel at the same velocity (no slippage between phases), and evaluated only friction factor empirically. Others developed methods for calculating both liquid holdup and friction factor. The third group of investigators divided the flow conditions into different flow patterns and developed separate correlations for each flow pattern. All the correlations tested in this study belong to the third group. These correlations first predict the flow pattern in the pipeline at the specified physical conditions pattern in the pipeline at the specified physical conditions with the help of a flow pattern map. Some of them use the same map for all pipe inclinations, while the others have different maps for different pipe inclinations. After determining the flow pattern, the corresponding holdup and friction factor correlations are used to calculate pressure drop. Three correlations were evaluated in this study. These are briefly described in the following sections. BEGGS AND BRILL (BB) CORRELATION The Beggs and grill correlation is based on extensive air-water data in 1 and 1.5 in pipes. The correlation uses a base of 58 data points for horizontal flow, along with a large number of points for inclined flow. A flow regime is first determined from a log-log plot of input liquid content and the mixture Froude number. Liquid holdup is then calculated from correlations for the flow regime existing in pipes only.

A Neural Network Model for Prediction of Liquid Holdup in Two-Phase Horizontal Flow

“…Previous studies [3][4][5] have shown that many correlations tend to perform well over certain ranges of liquid holdup and lose accuracy when applied to other ranges. Therefore, the results of this study were analyzed based on range of liquid holdup.…”

“…Consequently, when these correlations are applied to predict liquid holdup for other conditions, the accuracy is often significantly reduced. 3,4 In light of this observation, the current study is based upon five independant experimental data sets encompassing a greater range of flow variables. Table 1 summarizes the overall range of flow conditions in the experimental data totaling 627 liquid holdup measurements.…”

“…One of the problems with this approach is that it is dependent on the accuracy of flow pattern predictions and is subject to discontinuities in predictions made across flow pattern transition boundaries. 3 Comparative studies 4 Neural networks have been shown to exhibit superior performance to conventional approaches in a variety of problems in petroleum engineering. [6][7][8] In particular, problems that are characterized by a complex interaction of variables and are data intensive are good candidates for this approach.…”

A Comprehensive Neural Network Model for Predicting Two-Phase Liquid Holdup Under Various Angles of Pipe Inclinations

“…One of the problems with this approach is that it is dependent on the accuracy of flow pattern predictions and is subject to discontinuities in predictions made across flow pattern transition boundaries. (14) Comparative studies (15) (16) have shown that these models perform inconsistency as flow conditions change. This limitation makes difficult the task of selecting the most appropriate flow correlation.…”