Application of Hofer’s formula in thermal hydraulic calculations of oil transportation systems

Hydrodynamic calculations are a mandatory procedure when designing new and upgrading and operating existing oil transportation systems, which are performed using computer methods. The implementation of new calculation technologies creates conditions for the use of more accurate mathematical models to describe the hydrodynamic processes that accompany the movement of liquid hydrocarbons in a pipeline. For this purpose, based on theoretical studies and mathematical modelling, the article proposed an improved method of thermal-hydraulic calculation of a pipeline for pumping oil and oil products, which takes into account the non-isothermal regime caused by the difference between the product temperature at the beginning of the pipeline and the ground temperature and the release of frictional heat of the flow. The method is based on the application of the universal Hofer’s formula for determining the hydraulic drag coefficient in three friction zones of the turbulent regime, involves finding the variable regime coefficients in the Leibenson mathematical model in each section of the pipeline, and applies an integral method for calculating thermal and hydraulic energy losses during the transportation of oil and oil products. The method is suitable for creating computational algorithms and computer programs for design and operational calculations of oil and oil products transportation by pipelines without preheating the products and in the case of using special technologies that involve their preheating. The method was tested by performing multivariate calculations and analysing the results. The analytical dependences of the Leibenzon’s model mode coefficients on the Reynolds number and relative surface roughness of the pipe were obtained, which can be used in the thermal-hydraulic calculations of pipelines of all standard diameters at different values of surface roughness