Practical Aspects of Predicting Errors in Two-Phase Pressure-Loss Calculations
Authors: Browne E.J.P. 
Published: December 2007

Recently, attention has been focused on the accuracy of schemes for predicting flow behavior in multiphase systems. Prediction of pressure loss in two-phase flow is prone to error. A Monte Carlo simulation technique is used to evaluate the effect of these errors on the rate available from a well connected to a flow network.

Introduction
The prediction of pressure loss in two-phase flow is prone to error. Measures of accuracy and precision are determined when published techniques are used for predicting pressure losses in two-phase flow and these predictions are compared with measured values.
The effect of these and other errors on the rate available from a well connected to a flow network, or on the pressure loss across the network, is evaluated by a Monte Carlo simulation technique. From the results of these simulations a "calibration" is made between a calculated rate or pressure loss, free from errors, and the expected value and its uncertainty.

Background
Recently, much attention has been focused on the accuracy of schemes for predicting flow behavior in multiphase systems. Methods founded on empirical observations and on theoretical bases have been proposed; in most cases, authors have compared their prediction technique with field or laboratory data to determine the efficacy of the prediction system. An example of such an approach is that taken by Baxendell,1 who, having deduced a correlation for the prediction of pressure losses in vertical flow based on certain data, showed the distribution of errors that resulted from its application in a predictive manner.
In the process of establishing his composite flow-behavior prediction scheme, Orkiszewski2 took data used by several authors in establishing alternative schemes, along with some original data, to compare the errors that resulted from his and other correlations. Other works containing comparisons are too numerous to mention individually. All this work was systematized by Lawson and Brill,3 Vohra et al.,4 and Hernandez and Brill.6 These authors formed two data bases - one for horizontal flow measurements and another for vertical flow data. With these data sets and many of the currently used predictive techniques, they determined for each technique a measure of its accuracy and precision. In vertical flow, for example, a measure of the predicted pressure loss compared with that measured was used as an expression for the accuracy of the flow prediction method and an error, defined asE=(measured ?p-predicted ?p)/(measured ?p).
This error quantity was assumed to follow, within the limit, a normal distribution. Therefore, the measure of precision used was the standard deviation. In the case of horizontal flow, the analysis was made of the accuracy of the predicted and measured holdup and friction factor.
Despite the large amount of literature on the errors that arise in the use of various two-phase flow-prediction schemes, no work has investigated the effect of these errors on the accuracy and precision of predicting the total pressure loss or expected rate from a well of a given productivity index. It is the effect of these errors that this paper describes.