Recognizing the Most Accurate Herschel-Bulkley Fluid Pressure Estimation Method for Annulus: An Update to API RP 13D, 7th Edition

Summary The Herschel-Bulkley (HB) model is widely regarded as highly accurate for modeling non-Newtonian fluid flow, applicable across diverse fields such as chemical, mechanical, and petroleum engineering. The American Petroleum Institute and other references recognize the HB model as the most accurate and recommend the industry use it for drilling hydraulics. Pressure estimation models are beneficial for applying the HB model in field settings, as numerical solutions may not be feasible due to the computational demands and time constraints, especially challenging for high-frequency real-time pressure loss estimation (at least 1 Hz). Past literature has presented four estimation methods for the HB fluid, consisting of Zamora and Lord (1974), Merlo et al. (1995), Gjerstad and Time (2015), and the generalized method. However, the recommended practice API RP 13D (2023), “Rheology and Hydraulics of Oilwell Drilling Fluids,” has considered the most traditional Zamora and Lord (1974) as their chosen estimation method for industry use while neglecting to identify the most accurate model. Therefore, to update API RP 13D (2023), this work addresses this shortcoming by investigating the performance of different methods in estimating pressure losses while providing user-friendly, straightforward procedures applicable for field use. To recognize the most accurate estimation method for industry use, different methods’ pressure losses were estimated and compared with the numerical solution as well as experimental data to find the errors. The results showed that the Merlo et al. (1995) method provides the most accurate estimates, with the least average absolute percent error (APE) of maximum 4% underestimating the numerical solution, followed by Zamora and Lord’s error overestimating the numerical solution. The errors may slightly vary depending on the input parameters used, including diameters, mud properties, and circulation rate. The effect of the circulation rate on the accuracy of different methods was also investigated; except for the generalized method, the accuracy of the other methods increases with increasing the circulation rate. This work is a very innovative practical work for finding annular pressure losses accurately without using complex numerical solutions.