Determination of the optimal diameter of the heat pipeline by solving the optimization problem

Abstract

At the design stage of engineering networks, an important issue remains the choice of diameters of the pipeline system with minimal capital investments for transporting the working medium from the source to consumers. The purpose of the study is to determine the diameter of the pipeline, which achieves maximum savings in money for the transportation of heat carrier for specified conditions. Based on the classical laws of hydraulics and heat transfer, a computational equation has been obtained using software calculations, which allows determining the diameter of a heat pipeline with an optimal ratio of monetary costs for electrical and thermal energy. The final formula takes into account such important operational parameters as heat carrier flow, pipeline roughness and local hydraulic resistances, tariffs for thermal and electrical energy, etc. Using the example of the main pipeline section of the district heating system located in the city of Vologda (Russian Federation), a software solution of the equation proposed in the article is obtained. It was found that with a mass flow rate of 32.9 t/h, the optimal diameter of the steel electric-welded pipeline is 76×3 mm. Taking into account the current tariffs for thermal and electric energy, the monetary costs of transporting the heat carrier for the heating period of the year amounted to 4912 rubles per 1 cubic meter of pipeline. For comparison, with a pipeline diameter of 57×3 mm, the unit cash costs turned out to be 7887 rubles, and with 89×3.5 mm – 5524 rubles. For the case considered in the article, the dependence between the optimal diameter of the pipeline and the mass flow rate of the heat carrier is obtained.