Probabilistic modeling of slug frequency in gas/liquid pipe flow using the Poisson probability theory

Abstract

Abstract Slug frequency is a critical characteristic of two-phase slug flow in pipes that impacts production system operation, design and flow assurance aspects. For example, slug frequency is not only a required input for mechanistic models to predict pressure gradient and liquid holdup, but also is related to pipeline erosion/corrosion rates, pipeline structural integrity and stability and downstream separation and process facilities sizing. 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. Comprehensive studies by Zabaras (2000) and 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. Therefore, this study, as oppose to previous studies, aims to develop a probabilistic model to predict slug frequency and quantify the associated probability. The proposed model can predict the P10, P50, and P90 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 that can be used for efficient pipeline and downstream facility design and optimum operation. In addition, these probability values are important in predicting the possible maximum and minimum corrosion/erosion rates to efficiently design corrosion inhibitor program, which has a significant impact on project economic. For transient slug tracking model such as OLGA, application of the proposed slug frequency probabilistic model can be to calculate the Delay Constant Parameter, the time interval between two initiated slugs, which requires a probabilistic distribution to quantify its uncertainty and impact on the slug tracking predictions. Poisson probability theory is proposed in this study to model slug frequency predictions in horizontal pipeline. A Poisson probability model is used because of its suitability to predict the probability associated with events occurring during a specific time interval, such as slug frequency in a pipeline. In addition, a new slug frequency empirical correlation is proposed to predict the mean slug frequency in a horizontal pipeline, which is used in the Poisson probability modeling. Validation study of the slug frequency empirical correlation show a very good results, especially for the tuned model. In addition, the slug frequency Poisson probabilistic modeling predicted the probability associated with a specific value or range of slug frequency, slug frequency confidence interval for a given probability value, and the expected range of slug frequency values under normal operation.