The use of the generalized formula of L.S. Leibenzon in the hydraulic calculation of pumping oil and petroleum products with small additives of polymers

UDK: 622.692:621.22

DOI: 10.24887/0028-2448-2020-8-110-112

Key words: hydraulic resistance, polymer solutions, empirical dependences, polymer concentration, structure of the calculation formula, generalized formula of L.S. Leibenzon

Authors: M.I. Valiev (The Pipeline Transport Institute LLC, RF, Moscow), A.A. Korshak (The Pipeline Transport Institute LLC, RF, Moscow)

The Darcy - Weisbach formula is traditionally used in the calculation of pipelines through which oil and petroleum products with small additives of polymers are pumped. To calculate the coefficient of hydraulic resistance, it offers a large number of computational dependencies. The article provides a critical analysis of them. The formulas that were obtained as a result of experiments on water are not suitable for solving the problems of pipeline transportation of oil and oil products. All the others are not fully theoretical, because they contain empirical coefficients, which either have to be refined for each pair of "liquid-additive" according to experimental data, or calculated from the approximation dependencies obtained for the conditions of the performed experiments. In principle, most of the described formulas can be used equally. However, some of them are not convenient for solving theoretical problems of pipeline transport of oil and oil products, because they are transcendental. Therefore, according to the authors, the most preferred formula, in which the coefficient of hydraulic resistance when pumping oil and petroleum products with small additives of polymers is presented as a product of a similar coefficient when pumping without polymers in the form of L.S. Leibenzon and correction function, taking into account the concentration of the polymer and the degree of its impact on the resistance of the pipeline. This record of the calculation formula allowed us to show that for the hydraulic calculation of pipelines for pumping oil and petroleum products with small additives of polymers, the generalized formula of L.S. Leibenzon can be used. Moreover, the coefficient β in it is equal to the product of a similar coefficient when pumping oil and oil products without polymer additives by a correction function that takes into account the polymer concentration, the degree of turbulence development and other factors. Since the other has not yet been established, the value of another L.S. Leibenson coefficient m and the methods for calculating the transition Reynolds numbers when using small polymer additives can be considered the same as in the case of pumping without them.
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