A New Modification to the Hagedorn-Brown Correlation for Prediction of Two-Phase Pressure Gradient in Horizontal Wells

Abstract This investigation is dedicated to refining the Hagedorn and Brown correlation—an established empirical methodology for predicting multiphase flow pressure drops in wellbores. Although widely employed in vertical configurations, the correlation is notably poor at predicting flow regimes and is known to underpredict pressure gradients, with particularly limited efficacy in accurately estimating pressure losses in deviated wells under diverse flow patterns. Consequently, the usage of the Hagedorn and Brown correlation, as well as other no-slip correlations such as Fancher and Brown, is largely limited to benchmarking and establishing upper and lower bounds when matching test data for correlation selection during well modeling. Over the years, various modifications have been made to address this limitation, particularly for cases where the calculated liquid holdup falls below the no-slip holdup. Notably, Hagedorn suggested a correction for bubble flow using the Griffith and Wallis criteria, while subsequent modifications have replaced the original liquid holdup with more accurate measurements, adjusted for mist or transition flows, and introduced alternative pressure-gradient equations. This research builds on previous modifications by integrating the Beggs and Brill slip holdup formula into the Hagedorn and Brown correlation. The modeling process was implemented using Python, leveraging its computational efficiency for large datasets and complex numerical modeling and analysis of pressure losses across various well inclinations, particularly horizontal wells. Python was chosen for its computational efficiency in handling large datasets and performing complex numerical modeling. The modified model was applied to both the kerosene-air and water-air datasets, and performance was evaluated by calculating the R² values for different flow regimes (segregated, intermittent, and distributed), using Python-based algorithms to perform the necessary calculations and comparisons. The dataset used for this study, published by Minami in 1987, includes essential measurements of liquid slip velocity, gas slip velocity, average pressure, and temperature from experiments involving kerosene and air, as well as water and air. This setup effectively models the liquid and gas phases within the tubing. The proposed modification was rigorously tested against different flow patterns—namely segregated, intermittent, and distributed. The kerosene-air dataset achieved an impressive R² of 100% for segregated flow, compared to just 7.7% with the original correlation. For intermittent flow, our modified model had an R² of 72.7%, as compared to 67.3% for the original. In distributed flow, the new correlation delivered an R² of 91.8%, far exceeding the original's 5.17%. Overall, the new model produced an R² of 94.3% across all regimes, contrasting with the original's 64.7%. Similarly, the water-air dataset showed remarkable improvements. The modified method achieved an R² of 100% for segregated flow, with intermittent and distributed flows resulting in R² values of 92.6% and 97.7%, respectively, compared to 4.2%, 85.3%, and 1.89% with the original correlation. Across all flow patterns, the new model's overall R² reached 98.8%, a substantial increase from the original's 52.5%. The integration of the Beggs and Brill slip holdup formula into the Hagedorn and Brown correlation enhances pressure loss predictions, particularly for horizontal wells and various flow conditions. This modification improves the model's accuracy, optimizing reservoir modeling, well design, and reducing uncertainties in multiphase flow analysis, offering a more reliable tool for better decision-making in the oil and gas industry.