Non-isothermal paraffin oil flow in the pipeline


In this article, Non-isothermal paraffin oil flow in the pipeline with Newtonian fluid transition to viscoplastic state is investigated. Rheological properties of paraffin oil (viscosity, ultimate shear stress) are highly dependent on temperature. During hot pumping of paraffin oil through pipelines, non-isothermal flow occurs due to heat transfer to the environment. This leads to a decrease in flow temperature, an increase in viscosity, ultimate shear stress appearance, wax crystallization and solid particles deposition on the pipeline inner wall. Oil solid particles deposition reduces pipeline flow area, leads to the appearance of a "stagnant zone"with thermal insulation in the near- wall region. Oil structure changes - Newtonian property at high temperatures transits to non-Newtonian state. One-dimensional modeling of non-isothermal paraffin oil flow in the pipeline by traditional averaging of temperature and velocity over the pipe cross section does not allow explaining physics phenomenon. Therefore, in this work, a two-dimensional model of motion and heat transfer of paraffin oil is constructed. Calculated data show Newtonian fluid transition to viscoplastic state due to the heat exchange of paraffin oil with the environment. Obtained results form the basis for modeling anomalous fluid flows with heat and mass transfer and phase transition. Article content will be useful for a wide range of researchers involved in the field of hydrodynamics and heat and mass transfer.


[1] Ahmadpour A., Sadeghy K., Maddah-Sadatieh S.R., "The effect of a variable plastic viscosity on the restart problem of pipelines filled with gelled waxy crude oils", J. Non Newtonian Fluid Mech. 205(2014), 16-27.
[2] Li H., Zhang J., Song C., Sun G., "The influence of the heating temperature on the yield stress and pour point of waxy crude oils", J. Petrol. Sci. Eng. 135(2015), 476-483.
[3] Chala G.T., Sulaiman S.A., Japper-Jaafar A., "Flow start-up and transportation of waxy crude oil in pipelines: a review", Journal of Non-Newtonian Fluid Mechanics 251(2018), 69-87.
[4] Ribeiro F.S., Souza Mendes P.R., Braga S.L., "Obstruction of pipelines due to paraffin deposition during the flow of crude oils", Int. J. Heat Mass Transfer 40(1997), 4319-4328.
[5] Sahu K.C., "Linear instability in a miscible core-annular flow of a Newtonian and a Bingham fluid", J. Non Newtonian Fluid Mech. 264(2019), 159-169.
[6] Aiyejina A., Chakrabarti D.P., Pilgrim A., Sastry M.K.S., "Wax formation in oil pipelines: a critical review", Int. J. Multiphase Flow. 37(2011), 671-694.
[7] Beisembetov I.K., Bekibayev T.T., Zhapbasbayev U.K. et al., Management of energy-saving modes of oil mixtures transportation by the main oil pipelines (Almaty: KBTU, 2016), 215.
[8] Zhumagulov B.T., Smagulov SH.S., Evseeva A.U., Nesterenkova L.A., Truboprovodnyi transport vysokovyazkikh i vysokozastyvayushchikh neftei [Pipeline transportation of highly viscous and highly solidifying oils] (Almaty: Gylym, 2002), 287 [in Russian].
[9] Aldyyarov T.K., Makhmotov E.S., Didukh A.G., Gabsattarova G.A., Boranbaeva L.E., Reologiya neftei i neftesmesei (transportiruemykh AO "KazTransOil ) [Rheology of oils and oil mixtures (transported by "KazTransOil"JSC)] (Almaty: Dala, 2012), 287 [in Russian].
[10] Bekibayev T.T., Zhapbasbayev U.K., Ramazanova G.I., Makhmotov E.S., Sayakhov B.K., "Management of Oil Transportation by Main Pipelines", Communications in Computer and Information Science 8(2019), 44-53.
[11] Bakhtizin R.N., Shutov A.A., Shtukaturov K.YU., Modelirovanie rezhimov raboty truboprovodov s primeneniem kompleksa programm NIPAL 3.0 [Modeling pipeline operation modes using the NIPAL 3.0 software package] (Neftegazovoe delo, 2004),
[12] Shutov A.A., Ob odnom klasse techeniya nen’yutonovskoi zhidkosti [About one class of non-Newtonian fluid flow] (Sb. nauch. trudov, Ufa: IPTER, 1994), 185.
[13] Voller V.R., Swaminathan C.R., Thomas B.G., "Fixed grid techniques for phase change problems: a review", International Journal for Numerical Methods in Engineering 30:4(1990), 875-898.
[14] Hu H., Argyropoulos S.A., "Mathematical modelling of solidification and melting: a review", Modelling and Simulation in Materials Science and Engineering 4:4(1996), 371-396.
[15] Dale Anderson, John C. Tannehill, Richard H. Pletcher, Computational Fluid Mechanics and Heat Transfer (CRC Press, 1990).
How to Cite
ZHAPBASBAEV, U. K.; BOSSINOV, D. Zh.. Non-isothermal paraffin oil flow in the pipeline. Journal of Mathematics, Mechanics and Computer Science, [S.l.], v. 108, n. 4, p. 47-57, dec. 2020. ISSN 2617-4871. Available at: <>. Date accessed: 20 jan. 2021. doi:
Keywords paraffin oil, non-isothermal flow, Newtonian fluid flow transition to viscoplastic state