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# The versatility of the generalized formulas of L.S. Leibenson

UDK: 621.691.4
DOI: 10.24887/0028-2448-2019-5-105-108
Key words: hydraulic calculation, liquefied gases, gas distribution, main gas pipelines, anti-turbulent additives, oil, petroleum products, the unity of the laws of hydraulics, Darcy – Weisbach formula, generalized formula Of L.S. Leibenzon
Authors: A.A. Korshak (The Pipeline Transport Institute LLC, RF, Moscow)

Historically, hydraulic calculations of pipelines for pumping homogeneous liquid and gaseous media are carried out according to different formulas: in the first case, as a rule, - the pressure losses are calculated by the Darcy – Weisbach formula for friction, and in the second case, the difference between the squares of the initial and final pressures in the gas pipeline (the exception is the case of gas flow in low – pressure pipelines, where the Darcy – Weisbach formula is also used). Developing independently from each other, methods for calculating the hydraulic resistance of pipelines for these media have diverged to such an extent that, contrary to the unity of the laws of hydraulics, even the friction zone of the turbulent regime of gas workers began to be called "modes" ("mixed", "quadratic"). The origin of the data "technologisms” is due to the practical absence of the laminar regime in the practice of gas pipeline transportation, but, in fact, gives the impression that the hydraulics in the flow of gases in gas distribution systems and gas pipelines other than oil and oil product pipelines. Another problem with hydraulic calculations is that up to the present time calculation of the head losses in the pumping of oil and oil products with small additions of macromolecular substances (drag-reducing additive) and liquefied gases is performed according to the formula Darcy – Weisbach, and for pumping oil and oil products with no drag-reducing additive (in the solution of theoretical problems) – L.S. Leibenzon generalized formula.

The author has carried out studies to ensure a unified methodological approach in the calculation of the hydraulic resistance of pipelines in the case of pumping homogeneous liquid and gaseous media. It is proved that the generalized formula of L.S. Leibenzon can be used in hydraulic calculations of pumping a wide variety of media: oil, petroleum products, gas, LPG. This result can be explained by the unity of hydraulic laws for droplet liquids and gases. For the first time the values of the coefficients of L.S. Leibenzon in cases of gas pumping through the main gas pipelines, oil and oil products with drag-reducing additive, liquefied hydrocarbon gases are established.

References

1. Leybenzon L.S., Vil'ker D.S., Shumilov P.P., Yablonskiy V.S., Gidravlika: rukovodstvo dlya neftyanykh VUZov, tekhnikumov i rabotnikov neftyanoy promyshlennosti (Hydraulics: a guide for oil universities, technical schools and oil industry workers), Moscow – Leningrad: Publ. of ONTI NKTP SSSR, 1932, 310 p.

2. Yablonskiy V.S., Novoselov V.F., Galeev V.B., Zakirov G.Z., Proektirovanie, ekspluatatsiya i remont magistral'nykh nefteproduktoprovodov (Design, operation and repair of oil product pipelines), Moscow: Nedra Publ., 1965, 410 p.

3. Leybenzon L.S., On the application of the formula of the Lang formula type in the pipeline business (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 1926, no. 6, pp. 789–793.

4. Leybenzon L.S., The theoretical formula for determining the pressure loss during fluid flow in a circular pipe (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 1927, no. 3, pp. 386–394.

5. Zaytsev L.A., Yasinskiy G.S., Regulirovanie rezhimov magistral'nykh nefteprovodov (Regulation of the regimes of trunk pipelines), Moscow: Nedra Publ., 1980, 187 p.

6. Aliev R.A., Belousov V.D., Nemudrov A.G. et al., Truboprovodnyy transport nefti i gazaВ  (Pipeline transportation of oil and gas), Moscow: Nedra Publ., 1988, 386 p.

7. Korshak A.A., Zabaznov A.I., Novoselov V.V. et al., Truboprovodnyy transport nestabil'nogo gazovogo kondensata (Pipeline transport of unstable gas condensate), Moscow: Publ. of VNIIOENG, 1994, 224 p.

8. Seredyuk M.D., Yakimiv Y.V., Lisafin V.P., Truboprovidnyy transport nafti i naftoproduktiv (Pipeline transport of oil and oil products) Ivano-Frankivs'k, 2001. – 517 s.

9. Korshak A.A., Shmanov N.N., Mamonov F.A. et al., Magistral'nye truboprovody (Main pipelines), Ufa: DizaynPoligrafServis Publ., 2008, 448 p.

10. Korshak A.A., Nechval' A.M., Proektirovanie i ekspluatatsiya gazonefteprovodov (Design and operation of gas and oil pipelines), Rostov-na-Donu: Feniks Publ., 2016, 540 p.

11. Korshak A.A., Korshak An.A., Pshenin V.V., O granitsakh zon treniya turbulentnogo rezhima v gazoraspredelitel'nykh i magistral'nykh gazoprovodakh (In Russ.), Problemy sbora, podgotovki i transporta nefti i nefteproduktov =

12. Peterfalvi F., Drag reducing agent application on MOL high pressure liquid hydrocarbon pipelinesВ  (In Russ.), Nauka i tehnologii truboprovodnogo transporta nefti i nefteproduktov = , 2015, no. 4, pp. 29–41.

13. Gol'yanov A.I., Gol'yanov A.A., Mikhaylov D.A. et al., Trunk oil pipeline work specifics with anti-turbulent additive application (In Russ.), Nauka i tekhnologii truboprovodnogo transporta nefti i nefteproduktov, 2013, no. 2, pp. 36–43.

14. Abdurashitov S.A., Tupichenkov A.A., Truboprovody dlya szhizhennykh gazov (Pipelines for liquefied gases), Moscow: Nedra Publ., 1965, 215 p.

15. Morozova N.V., Korshak A.A., Pipeline hydraulic calculations and border Reynolds numbersВ  (In Russ.), Neftegazovoe delo, 2007, no. 5, pp. 120–125.

16. Chernikin A.V., Leybenzon formula helps pipeline hydraulic calculation (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 1996, no. 4, pp. 65–66.

17. Chernikin A.V., Talipov R.F., About Colebrook equation using at pipelines hydraulic calculation by generalized formula (In Russ.), Truboprovodnyy transport (teoriya i praktika), 2010, no. 4, pp. 14–16.В  В В

Historically, hydraulic calculations of pipelines for pumping homogeneous liquid and gaseous media are carried out according to different formulas: in the first case, as a rule, - the pressure losses are calculated by the Darcy – Weisbach formula for friction, and in the second case, the difference between the squares of the initial and final pressures in the gas pipeline (the exception is the case of gas flow in low – pressure pipelines, where the Darcy – Weisbach formula is also used). Developing independently from each other, methods for calculating the hydraulic resistance of pipelines for these media have diverged to such an extent that, contrary to the unity of the laws of hydraulics, even the friction zone of the turbulent regime of gas workers began to be called "modes" ("mixed", "quadratic"). The origin of the data "technologisms” is due to the practical absence of the laminar regime in the practice of gas pipeline transportation, but, in fact, gives the impression that the hydraulics in the flow of gases in gas distribution systems and gas pipelines other than oil and oil product pipelines. Another problem with hydraulic calculations is that up to the present time calculation of the head losses in the pumping of oil and oil products with small additions of macromolecular substances (drag-reducing additive) and liquefied gases is performed according to the formula Darcy – Weisbach, and for pumping oil and oil products with no drag-reducing additive (in the solution of theoretical problems) – L.S. Leibenzon generalized formula.

The author has carried out studies to ensure a unified methodological approach in the calculation of the hydraulic resistance of pipelines in the case of pumping homogeneous liquid and gaseous media. It is proved that the generalized formula of L.S. Leibenzon can be used in hydraulic calculations of pumping a wide variety of media: oil, petroleum products, gas, LPG. This result can be explained by the unity of hydraulic laws for droplet liquids and gases. For the first time the values of the coefficients of L.S. Leibenzon in cases of gas pumping through the main gas pipelines, oil and oil products with drag-reducing additive, liquefied hydrocarbon gases are established.

References

1. Leybenzon L.S., Vil'ker D.S., Shumilov P.P., Yablonskiy V.S., Gidravlika: rukovodstvo dlya neftyanykh VUZov, tekhnikumov i rabotnikov neftyanoy promyshlennosti (Hydraulics: a guide for oil universities, technical schools and oil industry workers), Moscow – Leningrad: Publ. of ONTI NKTP SSSR, 1932, 310 p.

2. Yablonskiy V.S., Novoselov V.F., Galeev V.B., Zakirov G.Z., Proektirovanie, ekspluatatsiya i remont magistral'nykh nefteproduktoprovodov (Design, operation and repair of oil product pipelines), Moscow: Nedra Publ., 1965, 410 p.

3. Leybenzon L.S., On the application of the formula of the Lang formula type in the pipeline business (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 1926, no. 6, pp. 789–793.

4. Leybenzon L.S., The theoretical formula for determining the pressure loss during fluid flow in a circular pipe (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 1927, no. 3, pp. 386–394.

5. Zaytsev L.A., Yasinskiy G.S., Regulirovanie rezhimov magistral'nykh nefteprovodov (Regulation of the regimes of trunk pipelines), Moscow: Nedra Publ., 1980, 187 p.

6. Aliev R.A., Belousov V.D., Nemudrov A.G. et al., Truboprovodnyy transport nefti i gazaВ  (Pipeline transportation of oil and gas), Moscow: Nedra Publ., 1988, 386 p.

7. Korshak A.A., Zabaznov A.I., Novoselov V.V. et al., Truboprovodnyy transport nestabil'nogo gazovogo kondensata (Pipeline transport of unstable gas condensate), Moscow: Publ. of VNIIOENG, 1994, 224 p.

8. Seredyuk M.D., Yakimiv Y.V., Lisafin V.P., Truboprovidnyy transport nafti i naftoproduktiv (Pipeline transport of oil and oil products) Ivano-Frankivs'k, 2001. – 517 s.

9. Korshak A.A., Shmanov N.N., Mamonov F.A. et al., Magistral'nye truboprovody (Main pipelines), Ufa: DizaynPoligrafServis Publ., 2008, 448 p.

10. Korshak A.A., Nechval' A.M., Proektirovanie i ekspluatatsiya gazonefteprovodov (Design and operation of gas and oil pipelines), Rostov-na-Donu: Feniks Publ., 2016, 540 p.

11. Korshak A.A., Korshak An.A., Pshenin V.V., O granitsakh zon treniya turbulentnogo rezhima v gazoraspredelitel'nykh i magistral'nykh gazoprovodakh (In Russ.), Problemy sbora, podgotovki i transporta nefti i nefteproduktov =

12. Peterfalvi F., Drag reducing agent application on MOL high pressure liquid hydrocarbon pipelinesВ  (In Russ.), Nauka i tehnologii truboprovodnogo transporta nefti i nefteproduktov = , 2015, no. 4, pp. 29–41.

13. Gol'yanov A.I., Gol'yanov A.A., Mikhaylov D.A. et al., Trunk oil pipeline work specifics with anti-turbulent additive application (In Russ.), Nauka i tekhnologii truboprovodnogo transporta nefti i nefteproduktov, 2013, no. 2, pp. 36–43.

14. Abdurashitov S.A., Tupichenkov A.A., Truboprovody dlya szhizhennykh gazov (Pipelines for liquefied gases), Moscow: Nedra Publ., 1965, 215 p.

15. Morozova N.V., Korshak A.A., Pipeline hydraulic calculations and border Reynolds numbersВ  (In Russ.), Neftegazovoe delo, 2007, no. 5, pp. 120–125.

16. Chernikin A.V., Leybenzon formula helps pipeline hydraulic calculation (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 1996, no. 4, pp. 65–66.

17. Chernikin A.V., Talipov R.F., About Colebrook equation using at pipelines hydraulic calculation by generalized formula (In Russ.), Truboprovodnyy transport (teoriya i praktika), 2010, no. 4, pp. 14–16.В  В В

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