The steady-state flow of flushing fluid in the annular space of a drill pipe string in the case when the cross section of the channel is an eccentric ring is considered. The drilling mud is considered as a viscoplastic non-Newtonian fluid. The method for calculating the hydraulic parameters of the flushing fluid flow is based on the use of iterative methods of solving nonlinear equations and numerical analysis methods. The method can be used to calculate the hydraulic parameters of the flow in cases of laminar, structural and turbulent modes of fluid motion.
1] J.F. Heyda, "A Green's Function Solution for the Case of Non-Concentric Circular Cylinders", J. Franklin Inst. 267, pp.25-34, 1959.
https://doi.org/10.1016/0016-0032(59)90034-1
https://doi.org/10.1016/0016-0032(59)90034-1
https://doi.org/10.1016/0016-0032(59)90034-1
[2] P.J. Redberger, and M.E. Charles, "Axial Laminar Flow Correction", Cdn. J. Chern. Eng. 41, pp.79-86, 1963.
https://doi.org/10.1002/cjce.5450410213
https://doi.org/10.1002/cjce.5450410213
https://doi.org/10.1002/cjce.5450410213
[3] M. Haciislamoglu, and J. Langlinais, "Non-Newtonian Flow in Eccentric Annuli", Journal of Energy Resources Technology, Vol. 112, pp.163-169, 1990.
https://doi.org/10.1115/1.2905753
https://doi.org/10.1115/1.2905753
https://doi.org/10.1115/1.2905753
[4] J.P. Hartnett, and M. Kostic, "Turbulent Friction Factor Correlation for Power-law Fluids flowing in Ducts of Arbitrary Cross-Section", Int. Comm. Heat Mass Transfer, 17, pp.59-65, 1990.
https://doi.org/10.1016/0735-1933(90)90079-Y
https://doi.org/10.1016/0735-1933(90)90079-Y
https://doi.org/10.1016/0735-1933(90)90079-Y
[5] D.A. Siginer, and S.I. Bakhtiyarov, "Flow of drilling fluids in eccentric annuli", Journal of Non-Newtonian Fluid Mechanics, 78 (2-3), pp.119-132, 1998.
https://doi.org/10.1016/S0377-0257(97)00101-8
https://doi.org/10.1016/S0377-0257(97)00101-8
https://doi.org/10.1016/S0377-0257(97)00101-8
[6] A.Kh. Mirzajanzade and S.A. Shirinzade, Povyshenie effektivnosti n kachestva bureniya glubokih skvazhii [Improving the Efficiency and Quality of Deep Well Drilling]. Moscow, Nedra Publ., 1986. [in Russian].
[7] J.M. Nouri, and H. Umur, and J.H. Whitelaw, "Flow of Newtonian and Non-Newtonian Fluids in Concentric and Eccentric Annuli", J. Fluid Mech, 253, 617-641, ,1993.
https://doi.org/10.1017/S0022112093001922
https://doi.org/10.1017/S0022112093001922
https://doi.org/10.1017/S0022112093001922
[8] M.P. Escudier, et al., "Fully Developed Laminar Flow of Non-Newtonian Liquids Through Annuli: Comparison of Numerical Calculations with Experiments", Experiments in Fluids 33 (1), pp.101-111, 2002.
https://doi.org/10.1007/s00348-002-0429-4
https://doi.org/10.1007/s00348-002-0429-4
https://doi.org/10.1007/s00348-002-0429-4
[9] N. Mitsuishi, and Y. Aoyagi, "Non-Newtonian Fluid Flow in an Eccentric Annulus", Journal of Chemical Eng., Japan, 6, No. 5, pp.402-408, 1973.
https://doi.org/10.1252/jcej.6.402
https://doi.org/10.1252/jcej.6.402
https://doi.org/10.1252/jcej.6.402
[10] A.W. Iyoho, and J.A. Azar, "An accurate slot-flow model for non-Newtonian fluid flow through eccentric annuli", Soc. Pet. Eng. J., pp.565-572 , October 1981.
https://doi.org/10.2118/9447-PA
https://doi.org/10.2118/9447-PA
https://doi.org/10.2118/9447-PA
[11] Y. Luo, and J.M. Peden, "Flow of drilling fluids through eccentric annuli", SPE Prod. Engineering, 5 (1), pp.91-96.
https://doi.org/10.2118/16692-PA
https://doi.org/10.2118/16692-PA
https://doi.org/10.2118/16692-PA
[12] I. Azouz, et al., "Numerical simulation of laminar flow of yield-power-law fluids in conduits of arbitrary cross-section", Trans. ASME J. Fluids Eng., 115, pp.710-716, 1993.
https://doi.org/10.1115/1.2910203
https://doi.org/10.1115/1.2910203
https://doi.org/10.1115/1.2910203
[13] Q.E. Hussein, and M.A.R. Sharif, "Viscoplastic fluid flow in irregular eccentric annuli", J. Energy Res. Tech., 120, pp.201-207, 1997.
https://doi.org/10.1115/1.2795036
https://doi.org/10.1115/1.2795036
https://doi.org/10.1115/1.2795036
[14] T.C. Papanastasiou, "Flow of materials with yield", Journal of rheology, vol. 31., pp.385-404, 1987.
https://doi.org/10.1122/1.549926
https://doi.org/10.1122/1.549926
https://doi.org/10.1122/1.549926
[15] A. Wachs, "Numerical simulation of steady Bingham flow through an eccentric annul arcross-section by distributed Lagrange multiplier/fictitious domain and augmented Lagrangian methods", Journal of Non-Newtonian Fluid Mechanics, 142 (1-3), 183-198, 2006.
https://doi.org/10.1016/j.jnnfm.2006.08.009
https://doi.org/10.1016/j.jnnfm.2006.08.009
https://doi.org/10.1016/j.jnnfm.2006.08.009
[16] E.C. Bingham, Fluidity and plasticity. McGraw-Hill, NY, 1922.
[17] P. Fang, and R. M. Manglik, and M. A. Jog, "Characteristics of laminar viscous shear-thinning fluid flows in eccentric annular channels", Journal of Non-Newtonian Fluid Mechanics, 84(1), pp.1-17, 1999.
https://doi.org/10.1016/S0377-0257(98)00145-1
https://doi.org/10.1016/S0377-0257(98)00145-1
https://doi.org/10.1016/S0377-0257(98)00145-1
[18] J. H. Ferziger, M. Peric, Computational Methods for Fluid Dynamics, 3-rd. ed. Springer Verlad, Berlin, 2002.
https://doi.org/10.1007/978-3-642-56026-2
https://doi.org/10.1007/978-3-642-56026-2
https://doi.org/10.1007/978-3-642-56026-2
[19] R. Glowinski, "Finite element methods for incompressible viscous flow", in P.G. Ciarlet, J.L. Lions (Eds.), Handbook of Numerical Analysis, vol. IX, North-Holland, Amsterdam, pp.3-1176, 2003.
https://doi.org/10.1016/S1570-8659(03)09003-3
https://doi.org/10.1016/S1570-8659(03)09003-3
https://doi.org/10.1016/S1570-8659(03)09003-3
[20] N.Roquet, and P. Saramito, "An adaptive finite element method for Bingham fluid flows around a cylinder", Comput. Meth. Appl. Mech. Eng. 192,pp3317-3341, 2003.
https://doi.org/10.1016/S0045-7825(03)00262-7
https://doi.org/10.1016/S0045-7825(03)00262-7
https://doi.org/10.1016/S0045-7825(03)00262-7
[21] R.R. Huilgol, and Z. You, "Application of the augmented Lagrangian method to steady pipe flows of Bingham, Casson and Herschel-Bulkley fluids", J. Non-Newtonian Fluid Mech., 128 (2-3), pp.126-143, 2005.
https://doi.org/10.1016/j.jnnfm.2005.04.004
https://doi.org/10.1016/j.jnnfm.2005.04.004
https://doi.org/10.1016/j.jnnfm.2005.04.004
[22] T.A. Tong, et al., "Numerical simulation of non-Newtonian fluid flow in partially blocked eccentric annuli", Journal of Petroleum Science and Engineering, vol. 193. № 107368, 2020.
https://doi.org/10.1016/j.petrol.2020.107368
https://doi.org/10.1016/j.petrol.2020.107368
https://doi.org/10.1016/j.petrol.2020.107368
[23] Ansys Fluent 2020 R1.Theory Guide, Ansys Inc., 2021.
[24] E.V. Kharchenko, Dinamicheskie processy burovyh ustanovok [Dynamic processes of drilling rigs]. Lviv, Svit Publ., 1991. [in Russian].
[25] I.A. Charniy, Neustanovivsheesya dvizhenie realnoj zhidkosti v trubah [Unsteady motion of real liquid in pipes]. Moscow, Nedra Publ., 1975. [in Russian].
[26] N.A. Gukasov, Spravochnoe posobie po gidravlike i gidrodinamike v burenii [Reference Manual on Hydraulics and Hydrodynamics in Drilling]. Moscow, Nedra Publ., 1982. [in Russian].
[27] R.I. Shishchenko, B.I. Yesmn, P.I. Kondratenko, Gidravlika promyvochnyh zhidkostej [Hydraulics of flushing fluids]. Moscow, Nedra Publ., 1976. [in Russian].
[28] V.A. Mischevich, and N.A. Sidorov, Spravochnik inzhenera po bureniyu [Reference book of the engineer on drilling]. vol.1. Moscow, Nedra Publ., 1973. [in Russian].