Empirical and Optimization-Based Solutions for Thermal Behavior of Newtonian Fluids in Rough Pipes

The increasing demand for alternative energy has driven the integration of geothermal operations into the oil and gas industry, presenting engineering challenges due to high formation temperatures in geothermal wells. Effective thermal management is crucial, as temperature fluctuations can affect drilling fluid properties and downhole equipment performance. This study tackles these challenges by using a flow loop with 2 7/8″ tubing to study thermal behavior under transient conditions. Additionally, the study develops an empirical equation to investigate how the friction coefficient varies with temperature by considering the changes of temperature over time. To achieve the best fit between the empirical equation and experimental data, three methodologies—the interior-point algorithm, minimax algorithm, and particle swarm optimization algorithm—were employed. The analysis demonstrated that all predicted values fell within a 90% confidence interval, confirming the model’s reliability and practical applicability in drilling operations. The absolute average percentage error for the applied methods was approximately 4%. The key findings of this study provide practical insights for geothermal and oil drilling operations by enabling improved management of time-dependent thermal effects in wellbore systems. The proposed model allows for reliable estimation of friction factor evolution using easily measurable dimensionless parameters such as Reynolds and Prandtl numbers, along with duration. This predictive capability supports more accurate evaluation of pressure losses and heat transfer behavior in dynamic flow environments. Overall, this study contributes to enhancing the simulation of thermal–fluid behavior, supporting industrial applications and advancing scientific understanding of transient thermal–fluid interactions.