Cuttings transport from wellbore annulus to the surface via drilling fluids is one of the most important problems in gas and oil industries. In the present paper, the effects of viscoelastic property of drilling fluids on flow through wellbore annulus are studied numerically by use of computational fluid dynamics simulation in OpenFOAM software. This problem is simulated as the flow between two coaxial annulus cylinders and the inner cylinder is rotating through its axes. Here, the Giesekus model is used as the nonlinear constitutive equation. This model brings the nonlinear viscosity, normal stress differences, extensional viscosity and elastic property. The numerical solution is obtained using the second order finite volume method by considering PISO algorithm for pressure correction. The effect of elasticity, Reynolds number, Taylor number and mobility factor on the velocity and stress fields, pressure drop, and important coefficient of drilling mud flow is studied in detail. The results predicted that increasing elastic property of drilling mud lead to an initial sharp drop in the axial pressure gradient as well as Darcy-Weisbach friction coefficient. Increasing the Reynolds number at constant Taylor number, resulted an enhancing in the axial pressure drop of the fluid but Darcy-Weisbach friction coefficient mainly reduced.
BourgoyneATMillheimKKChenevertME, et al.Applied drilling engineering. 1st ed.Houston:
Society of Petroleum Engineers, 1986, pp. 122–156.
2.
VolarovichMPGutkinAM.Flow of plastic-viscoplastic material between two parallel flat-walls and in annular space between two coaxial tubes. J Tech Phys1946;
3: 321–328.
3.
FredricksonAGBirdRB.Non-Newtonian flow in annuli. Ind Eng Chem1958;
50: 347–352.
4.
RivlinRS.Solution of some problems in the exact theory of visco-elasticity. Indiana Univ Math J1956;
5: 179–188.
5.
RigbiNGaliliN.Helical flow of some non-Newtonian Liquids. J Tech1971;
9: 447–452.
6.
BatraRLEissaM.Helical flow of a Sutterby model fluid. J Polym-Plast1994;
33: 489–501.
7.
FilipPDavidJ.Quasi similarity of helical flow of power-law fluids in concentric annuli. J Petrol Sci Eng2004;
45: 97–107.
8.
HussnainSMehmoodAAliA.Three-dimensional channel flow of second grade fluid in rotating frame. Appl Math Mech2012;
33: 289–302.
9.
MitsuishiNAoyagiY.Non-Newtonian fluid flow in an eccentric annulus. J Chem Eng Japan1974;
6: 402–408.
10.
GuckesTL.Laminar flow of non-Newtonian fluids in an eccentric annulus. J Eng Ind1975;
97: 498–506.
11.
HaciislamogluMLanglinaisJ.Non-Newtonian fluid flow in eccentric annuli. J Energy Res Technol1990;
112: 163–169.
12.
PhamTVMitsoulisE.Viscoplastic flow in ducts. Can J Chem Eng1998;
76: 120–125.
13.
KaloniPN.On the helical flow of an elasto-viscous fluid. J Pure Appl Phys1965;
3: 1–3.
14.
KulshresthaPK.Helical flow of an idealized elastico-viscous liquid.J Appl Math Phys1962;
13: 553–561.
15.
MoghaddamAKSaadatabadiAR.Rheological modeling of water based drilling fluids containing polymer/bentonite using generalized bracket formalism. J Petrol Sci Eng2020;
189: 107028.
16.
MostafaiyanMKhodabandehlouKSharifF.Analysis of a viscoelastic fluid in an annulus using Giesekus model. J. Non-Newtonian Fluid Mech2004;
118: 49–55.
17.
DapràIScarpiG.Analytical solution for axial flow of a Giesekus fluid in concentric annuli. J Non-Newton Fluid Mech2018;
251: 10–16. [10.1016/j.jnnfm.2017.11.003]
18.
MohseniMMRashidiF.Viscoelastic fluid behavior in annulus using Giesekus model. J Non-Newton Fluid Mech2009;
165: 1150–1553.
19.
KalyonDMMalikM.Axial laminar flow of viscoplastic fluids in a concentric annulus subject to wall slip. Rheol Acta2012;
51: 805–820.
20.
FerrasLLAfonsoAMAlvesMA, et al.
Annular flow of viscoelastic fluids: analytical and numerical solutions. J Non-Newton Fluid2014;
212: 80–91.
21.
NawafHSaeidBSBusahminNumerical investigations of drilling mud flow characteristics in vertical well. Eng Sci Technol2016;
6: 16–22.
22.
MenezesRRMarquesLNCamposLA, et al.Use of statistical design to study the influence of CMC on the rheological properties of bentonite dispersions for water-based drilling fluids. Appl Clay Sci2010;
49: 13–20.
23.
FriedemannCMortensenMNossenJ.Gas–liquid slug flow in a horizontal concentric annulus, a comparison of numerical simulations and experimental data. Int J Heat Fluid Flow2019;
78: 108437.
24.
EpelleEIGerogiorgisDI.Multiparametric CFD analysis of multiphase annular flow for oil and gas drilling applications. Comput Chem Eng2017;
106: 645–666.
25.
EpelleEIGerogiorgisDI.CFD modelling and simulation of drill cuttings transport efficiency in annular bends: effect of particle sphericity. J Petrol Sci Eng2018;
170: 992–1004.
26.
TangMZhangTHeS, et al.
Modeling of laminar flow in an eccentric elliptical annulus for YPL fluid. J Nat Gas Sci Eng2019;
64: 118–132.
27.
ErgeOKarimi VajargahAOzbayogluME, et al.
Frictional pressure loss of drilling fluids in a fully eccentric annulus. J Nat Gas Sci Eng2015;
26: 1119–1129.
28.
VipulanandanCMohammedA.Hyperbolic rheological model with shear stress limit for acrylamide polymer modified bentonite drilling muds. J Petrol Sci Eng2014;
122: 38–47.
29.
MohammadzadehKHashemabadiSHAkbariS.CFD simulation of viscosity modifier effect on cutting transport by oil based drilling fluid in wellbore. J Nat Gas Sci Eng2016;
29: 355–364.
30.
ZareMRoustaeiAFrigaardIA.Buoyancy effects on micro-annulus formation: density stable displacement of Newtonian–Bingham fluids. J Non-Newton Fluid Mech2017;
247: 22–40.
31.
SorgunMOzbayogluME.Predicting frictional pressure loss during horizontal drilling for non-Newtonian fluids. J Energy Sources2011;
33: 631–640.
32.
ZakerianASarafrazSTabzarA, et al.
Numerical modeling and simulation of drilling cutting transport in horizontal wells. J Petrol Explor Prod Technol2018;
8: 455–474.
33.
BrondaniWMCoradinHTFrancoAT, et al. Numerical study of a PTT viscoelastic fluid flow through a concentric annular. In: 19th International Congress of Mechanical Engineering, Brasília, DF, 2007.
34.
OgugbueCCE. Non-Newtonian power-law fluid flow in eccentric annuli: CFD simulation and experimental study. PhD Thesis, University of Oklahoma, USA, 2009, 178 p.
35.
RookiRDoulatiAFMoradzadehA, et al.
CFD simulation of rheological model effect on cuttings transport. J Dis Sci Tech2015;
36: 402–410.
36.
FerrasLLAfonsoAMAlvesMA, et al.
Annular flow of viscoelastic fluids: analytical and numerical solutions. J Non-Newton Fluid Mech2014;
212: 80–91.
37.
GuzekAShufrinIPasternakE, et al.
Influence of drilling mud rheology on the reduction of vertical vibrations in deep rotary drilling. J Petrol Sci Eng2015;
135: 375–383.
38.
GulraizSGrayKE.Investigating the effects of plug viscosity on annular pressure drop and cuttings transport in a concentric annulus. J Nat Gas Sci Eng2020;
76: 103210.
39.
IssaRI.Solution of the implicitly discretized fluid flow equations by operator-splitting. J Comput Phys1986;
62: 40–65.
40.
IssaRIGosmanADWatkinsAP.The computation of compressible and incompressible recirculating flow by a non-iterative implicit scheme. J Comput Phys1986;
62: 66–82.
