Prediction Method for Critical Gas Velocity of Sulfur-Carrying in Gas–Liquid Two-Phase Flow in High-Sulfur Gas Wells

During the production of high-sulfur-content gas–water wells, elemental sulfur saturated in natural gas gradually precipitates as solid particles with decreasing wellbore temperature and pressure. When these sulfur particles cannot be continuously carried upward in the gas–liquid–solid three-phase flow formed with natural gas and formation water, they tend to deposit in the wellbore, potentially blocking the production string and even severely restricting the gas well’s deliverability. Current research on predictive models for the critical gas flow velocity required to carry sulfur particles remain inadequate. Therefore, accurately predicting this critical velocity and adjusting production to prevent deposition are crucial for managing high-sulfur gas wells. The primary innovation of this study lies in the development of a predictive model for the critical gas flow velocity required for sulfur particle entrainment. Grounded in the “gas–liquid coalescence–liquid film entrainment” coupling mechanism revealed by preliminary experiments, this model is established through a mechanical analysis of sulfur particles within liquid films in vertical and inclined pipes. Recognizing liquid film thickness and velocity as pivotal parameters for model solving, auxiliary models for predicting these two parameters in inclined pipe annular flow were developed based on experimental results and the momentum balance principle. The proposed model comprehensively incorporates factors such as well inclination angle, pipe diameter, liquid flow rate, and sulfur particle size, rendering it applicable to diverse well configurations including vertical, horizontal, and deviated wells. Evaluation against 48 sets of experimental data yielded a Mean Absolute Percentage Error (MAPE) of 2.28%, demonstrating high predictive accuracy. Furthermore, an engineering calculation program for the critical gas flow velocity was developed. A case study involving a well in the Puguang Gas Field was conducted to predict and diagnose sulfur deposition conditions, thereby verifying the model’s practical utility. This research provides a scientific basis for the safe and efficient development of high-sulfur gas fields.