Research on a Transient Flow Heat Transfer Model of Gas-Liquid-Solid Three-Phase Flow for Unbalanced Drilling in Deep Shale Wells

Accurate prediction and effective control of bottom hole pressure (BHP) are crucial for underbalanced drilling of deep shale wells. However, convective heat transfer in cuttings, annulus fluid, and surrounding environment significantly impacts the accuracy of traditional BHP calculation models. Therefore, a transient non-isothermal flow model of gas, liquid, and solids within the wellbore was developed. Based on the continuity equation and momentum conservation equation, fluid velocity, phase volume fractions, and pressure were calculated. Meanwhile, the energy conservation equation for different radial layers was solved to obtain the temperature distribution of the entire wellbore–formation system. The temperature, pressure, and fluid properties in the depth and radial directions were coupled and solved using an iterative method. The calculated results of this model exhibited an error of less than 5.0% compared with the field data from underbalanced drilling operations, demonstrating its accuracy and reliability. With the proposed model, a comparative analysis was conducted to assess the differences in pressure and temperature predictions when the presence of cuttings and convective heat transfer effects were considered or neglected. The study also analyzed the impact of factors such as underbalanced pressure difference, rate of penetration (ROP), and geothermal gradient on wellbore pressure and temperature distribution. The transient flow heat transfer model of gas, liquid, and solid phases for underbalanced drilling in deep shale wells provides theoretical support for the efficient application of managed pressure drilling and underbalanced drilling in deep shale oil and gas reservoirs.