Probabilistic Modeling of Slug Frequency In Gas/liquid Pipe Flow Using Poisson Probability Theory

Slug frequency is a critical characteristic of two-phase slug flow for predicting pressure gradient, erosion/corrosion rates, pipeline structural integrity and designing downstream separation and process facilities. Conversely, slug frequency is the least accurately predicted parameter in two-phase flow, due to the high uncertainty of slug frequency predictive empirical correlations and models. A comprehensive study by Zabaras (2000) and a recent study by Al-Safran (2009) showed that the error in existing slug frequency correlations' predictions averages around 75% for horizontal flow and 115% for horizontal and inclined flows. For this reason, probability modeling is necessary to quantify the uncertainty and calculate the probability associated with slug frequency predictions. Such modeling can predict the P10, P50, and P90 accuracy of slug frequency predictions for a given flow condition. These probability values can be propagated in a mechanistic model to predict the expected, low- and high-end values of pressure gradient and liquid holdup for proper pipeline design and optimum operation. In addition, these values are important in properly designing corrosion inhibitor injection rates and their economical evaluation. Another important application of slug frequency probabilistic modeling is the calculation of the time interval between two initiated slugs and its probability. This time interval, normally called Delay Constant Parameter, is a tuning parameter in slug tracking models, such as OLGA, which require a probabilistic distribution to quantify its uncertainty. In addition, a slug frequency empirical correlation is proposed to predict the mean slug frequency in a horizontal pipeline, which is used in Poisson probability modeling. Preliminary results of the probabilistic modeling show an ability to predict: the probability associated with a specific value or range of slug frequency, slug frequency interval for a given probability value, and the expected range of slug frequency under normal operation.