Research Article CFD Method for Predicting Annular ...

Research ArticleCFD Method for Predicting Annular Pressure Losses andCuttings Concentration in Eccentric Horizontal Wells

Titus N Ofei1 Sonny Irawan1 and William Pao2

1 Petroleum Engineering Department Universiti Teknologi PETRONAS Bandar Seri Iskandar 31750 Tronoh Malaysia2Mechanical Engineering Department Universiti Teknologi PETRONAS Bandar Seri Iskandar 31750 Tronoh Malaysia

Correspondence should be addressed to Titus N Ofei titusofeihotmailcom

Received 28 December 2013 Accepted 10 March 2014 Published 10 April 2014

Academic Editor Markus Kraft

Copyright copy 2014 Titus N Ofei et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In oil and gas drilling operations predictions of pressure losses and cuttings concentration in the annulus are very complex dueto the combination of interacting drilling parameters Past studies have proposed many empirical correlations to estimate pressurelosses and cuttings concentrationHowever these developed correlations are limited to their experimental data range and setup andhence they cannot be applicable to all cases CFDmethods have the advantages of handling complex multiphase flow problems aswell as an unlimited number of physical and operational conditions The present study employs the inhomogeneous (Eulerian-Eulerian) model to simulate a two-phase solid-fluid flow and predict pressure losses and cuttings concentration in eccentrichorizontal annuli as a function of varying drilling parameters fluid velocity diameter ratio (ratio of inner pipe diameter to outerpipe diameter) inner pipe rotation speed and fluid type Experimental data for pressure losses and cuttings concentration fromprevious literature compared very well with simulation data confirming the validity of the current model The study shows howreliable CFD methods can replicate the actual yet complex oil and gas drilling operations

1 Introduction

Predictions of pressure losses and cuttings concentrationin annular wells are strongly affected by varying drillingparameters such as fluid velocity fluid properties (densityviscosity) cuttings size and density hole-pipe eccentricitydrill pipe rotation and annular diameter ratios There arefew attempts made by some investigators to estimate pressurelosses and cuttings concentration in annular geometrieswith and without drill pipe rotation by employing eitherexperimental or numerical approaches

Among the first authors to conduct extensive exper-imental study on cuttings transport at varying angles ofinclinations is Tomren et al [1] The authors studied theeffects of fluid velocity fluid rheological properties pipe-holeeccentricity drill pipe rotation and flow regimes on cuttingsconcentration at steady state condition They concludedthat fluid velocity hole inclination and mud rheologicalproperties were the major factors affecting mud carryingcapacity Becker and Azar [2] also investigated experimen-tally the effects of mud weight and annular diameter ratio

on the performance of hole cleaning in inclined wellboresThe authors observed that variations in the drill pipe haveminimum effect on particle concentration for the samefluid velocity According to Adari et al [3] the practicaluse of drilling factors in controlling cuttings transport ismuch dependent on their controllability in the field It isbelieved that cuttings transported in the annulus are notalways affected by a single parameter but a combinationof parameters to ensure efficient hole cleaning [4] Otherstudies have also confirmed that increase in fluid velocityresults in a decrease in cuttings accumulation in the wellbore[5ndash7] Ozbayoglu and Sorgun [8] also conducted cuttingstransport experiment and developed empirical correlationsfor estimating pressure losses with the presence of cuttingsand drill pipe rotation in horizontal and inclined wellboresThey observed that the influence of drill pipe rotationon pressure loss is more significant if fluid is more non-Newtonian The annular test section has diameter ratio of062 Similar cuttings transport experiment study was carriedout by Sorgun et al [9] in horizontal and inclined annulargeometry of diameter ratio of 062 The authors observed

Hindawi Publishing CorporationJournal of Petroleum EngineeringVolume 2014 Article ID 486423 16 pageshttpdxdoiorg1011552014486423

2 Journal of Petroleum Engineering

that the existence of cuttings in the system caused anincrease in pressure loss due to a decrease in flow area insidethe annular gap Further observation was that drill piperotation decreases the pressure loss significantly if the drillpipe is making orbital motion in eccentric annulus Anotherexperimental study was conducted [10] to analyse the effectsof some ldquovery difficult to identifyrdquo data on the estimation oftotal pressure loss and cuttings concentration in horizontaland inclined annulus Results from this study indicate thatdrill pipe rotation does not have significant influence onpressure loss for constant rate of penetration (ROP) and fluidvelocity The annular test section has diameter ratio of 064

One of the pioneering works by Markatos et al [11] mod-elled single phase Newtonian flow in nonuniform narrowannular gaps using finite difference technique The velocityflow fields as well as static pressure were predicted in a two-dimensional flow

Han et al [12] is among the first to conduct experimentaland CFD studies on solid-fluid mixture flow in vertical andhighly deviated slim hole annulus They concluded thatannular pressure losses increase with mixture fluid velocityannular angle of inclination and drill pipe rotation speedThe annular test section has diameter ratio of 070 Mokhtariet al [13] employed CFD method to model the effects ofeccentricity and flow behaviour index on annular pressureloss and velocity profile for varying diameter ratios from 030to 090 The authors however did not include cuttings in theannular mainstream Recently Ofei et al [14] also employedCFD technique to analyse the influence of diameter ratiofluid velocity fluid type fluid rheology and drill pipe rotationspeed on pressure loss in eccentric horizontal wellbore withthe presence of cuttings

The present study also utilises a CFD technique toexamine the effects of fluid velocity annular diameter ratio(ranging from 064 to 090) drill pipe rotation and fluid typeon the prediction of pressure loss and cuttings concentrationfor solid-fluid flow in eccentric horizontal wellbore Contoursof cuttings volume fraction 3D cuttings velocity streamlinesand radial cuttings velocity profiles are also presented to givefurther insight on cuttings transport The new findings fromthis study would provide better understanding and guidein the selection of optimum drilling parameters in narrowannuli drilling such as casing drilling and slim holes

2 Materials and Methods

Multiphase component of CFD software ANSYS-CFX 140is adopted in this study In ANSYS-CFX a multiphaseflow containing dispersed particles may be modelled usingeither Lagrangian Particle Tracking model or Eulerian-Eulerian model The inhomogeneous (Eulerian-Eulerian)model sometimes called the two-fluid model regards bothcontinuous and dispersed phases as continuous media Inthis study the Eulerian-Eulerian model is preferred to theLagrangian Particle Tracking model due to its ability tohandle high solid volume fractions Furthermore it accountsfor solid particle-particle interaction and includes turbulenceautomatically [15] A drawback of this model is however that

they need complex closure relationsThe following continuityand momentum equations representing the two-phase flowmodel are described for the sake of brevity

21 Continuity Equations The fluid phase continuity equa-tion assuming isothermal flow condition can be expressed as[16 17]

120597

120597119905(h119897) + nabla (h119897119880119897) = 0 (1)

Similarly for a solid phase

120597

120597119905(h119904) + nabla (h119904119880119904) = 0 (2)

where the solid and fluid phase volume fraction sum up asfollows

k119904 + k119897 = 1 (3)

At steady state condition 120597120597119905 = 0

22 Momentum Equations The forces acting on each phaseand interphase momentum transfer term that models theinteraction between each phase are given below [16 17]

For fluid phase

120588119897k119897 [120597119880119897

120597119905+ 119880119897 sdot nabla119880119897] = minusk119897nabla119901 + k119897nabla sdot 120591119897 + k119897120588119897119892 minus119872

(4)

Similarly for solid phase

120588119904h119904 [120597119880119904

120597119905+ 119880119904 sdot nabla119880119904]

= minush119904nabla119901 +h119904nabla sdot 120591119897 + nabla sdot 120591119904 minus nabla119875119904 +h119904120588119904119892 +119872

(5)


23 Other Closure Models

231 Interphase Drag Force Model For spherical particlesthe drag force per unit volume is given as

119872119889 =3119862119863

4119889119904

k1199041205881198971003816100381610038161003816119880119904 minus 119880119897

1003816100381610038161003816 (119880119904 minus 119880119897) (6)

For densely distributed solid particles where the solid volumefractionk119904 lt 02 theWen and Yu [18] drag coefficient modelmay be utilised This model is modified and implemented inANSYS-CFX to ensure the correct limiting behaviour in theinertial regime as

119862119863 = kminus165

119897max[ 24

1198731015840Re119901(1 + 015119873

1015840 0687

Re119901 ) 044] (7)

where1198731015840Re119901 = k119897119873Re119901 and119873Re119901 = 120588119897|119880119897 minus 119880119904|119889119904120583119897

Journal of Petroleum Engineering 3

For large solid volume fraction k119904 gt 02 the Gidaspowdrag model may be used with the interphase drag force perunit volume defined as [19]

119872119863 =150(1 minus k119897)

2120583119897

k1198971198892119904

+7

4

(1 minus k119897) 1205881198971003816100381610038161003816119880119897 minus 119880119904

1003816100381610038161003816

119889119904

(8)

In this study both Wen and Yu and Gidaspow drag modelswere employed depending on the computed solid volumefraction An approximate method for computing the solidvolume fraction is presented in (18)

232 Lift Force Model For spherical solid particles ANSYS-CFX employs the Saffman and Mei lift force model as

119872119871 =3

2120587

radic]119897

119889119904radic1003816100381610038161003816nabla times 119880119897

1003816100381610038161003816

1198621015840

119871h119904120588119897 (119880119904 minus 119880119897) times (nabla times 119880119897 + 2Ω)

(9)

Saffman [20 21] correlated the lift force for low Reynoldsnumber past a spherical solid particle where 1198621015840

119871= 646 and

0 le 119873Re119901 le 119873Re120596 le 1 For higher range of solid particleReynolds number Saffmanrsquos correlation was generalised byMei and Klausner [22] as follows

1198621015840

119871=

646 sdot 119891 (119873Re119901 119873Re120596) for 119873Re119901 lt 40

646 sdot 00524 sdot (120573119873Re119901)12

for 40 lt 119873Re119901 lt 100

(10)

where 120573 = 05(119873Re120596119873Re119901)

119891(119873Re119901 119873Re120596) = (1 minus 0331412057305) sdot 119890minus01119873Re119901 + 03314120573

05

(11)

and119873Re120596 = 1205881198971205961198971198892

119904120583119897 120596119897 = |nabla times 119880119897|

233 Turbulence 119896-120576 Model in Multiphase Flow The 119896-120576turbulence model offers a good compromise in terms ofaccuracy and robustness for general purpose simulations Itis a semiempirical model based on transport equation for theestimation of turbulent length scale and velocity scale fromthe turbulent kinetic energy (119896) and dissipation rate (120576) [23]In multiphase flow the transport equations for 119896 and 120576 arephase dependent and assume a similar form to the single-phase transport equations respectively as

120597

120597119905(119862120572120588120572119896120572) + nabla sdot (119862120572 (120588120572119880120572119896120572 minus (120583 +

120583119905120572

120590119896

)nabla119896120572))

= 119862120572 (119875120572 minus 120588120572120576120572) + 119879(119896)

120572120573

(12)

120597

120597119905(119862120572120588120572120576120572) + nabla sdot (119862120572120588120572119880120572120576120572 minus (120583 +

120583119905120572

120590120576

)nabla120576120572)

= 119862120572

120576120572

119896120572

(1198621205761119875120572 minus 1198621205762120588120572120576120572) + 119879(120576)

120572120573

(13)

Inlet Outlet

Fixed outer cylinder

Inner cylinder

m g

L

Tconst

Pref

120596

Figure 1 Physical model for solid-fluid flow

Diffusion ofmomentum in phase120572 is governed by an effectiveviscosity as

120583eff = 120583 + 120583119905120572 (14)

The 119896-120576model assumes that the turbulence viscosity is linkedto the turbulence kinetic energy and dissipation by thefollowing relation

120583119905120572 = 119862120583120588120572

1198962

120572

120576120572

(15)

The governing sets of partial differential equations werediscretized using finite volume technique The discretizedequations together with initial and boundary conditions aresolved iteratively for each control volume of pressure dropand cuttings concentration using ANSYS CFX 140 solver

24 Physical Model and Carrier Fluid Two-phase solid-fluidflow in eccentric horizontal annulus with stationary outerpipe and rotating inner pipe is presented The inner piperepresents the actual drill pipe while the outer pipe representsthe hole Four annular 3D geometries are modelled withdiameter ratios 120581 = 064 070 080 and 090 using ANSYSWorkbench

In order to eliminate end effects and ensure fully devel-oped flow the length of the annular pipe must be longerthan the hydrodynamic entrance length For a single phaseNewtonian fluid flowing in a pipe the hydrodynamic lengthis presented by Shook and Roco [24] as

119871ℎ = 0062119873Re (119863) (16)

However for a two-phase flow in annular gap with a non-Newtonian fluid such expression as in (16) does not yet existin literature As a rule of thumb the authors have adopted (16)by replacing the pipe diameter 119863 with a hydraulic diameter119863ℎ = 1198632 minus1198631 It should be noted that a much longer annularlength would only result in a computationally expensive CFDsimulation Figure 1 shows the physical model for solid-fluidflow The fluid is considered incompressible steady stateand isothermal The rheology of the fluid is described bybothNewtonian (water) and Power-LawmodelThe apparentviscosity for Power-Law model is given as

120583119886 = 119870 120574119899minus1 (17)


120581 = 064 120581 = 070

120581 = 080 120581 = 090

Figure 2 3D section of meshed annular geometry

where 119870 is consistency index 120574 is shear rate and 119899 is flowbehaviour index For 119899 = 1 (17) reduces toNewtonianmodel119899 lt 1 fluid is shear thinning and 119899 gt 1 fluid is shearthickening In this study 03 lt 119899 le 1

25 Boundary Conditions and Meshing Amixture mass flowrate boundary condition was specified at the inlet whilezero gauge pressure specified at the outlet No-slip boundaryconditions were imposed on both inner and outer pipe wallsfor both fluid and particles The 3D annular geometries weremeshed into unstructured tetrahedral grids of approximately066ndash215 times 106 elements Inflation layers were created nearthe walls covering about 20 of the inner and outer radiifor resolving the mesh in the near-wall region as well asaccurately capturing the flow effects in that region Figure 2shows the 3D section of the meshed annular geometries

26 Grid Independence Study To optimise the mesh sizesuntil results were insignificantly dependent on mesh sizegrid independence study was conducted for all diameterratios The carrier fluid used is water flowing at a velocity of2743ms and the inner pipe rotation speed is 80 rpm Thecuttings feed concentrationwhich gives an idea of the amountof particles in motion that are introduced to the annularspace This is computed as a function of area of bit fluidvelocity and rate of penetration (ROP) as [6]

119862cf =(ROP) 119860bit119877119879119876

(18)

where 119877119879 is defined as the ratio of the particle transportvelocity to the average annular fluid velocity For the purposeof this study 119877119879 is taken as 05 based on experimentalfindings [9] Figures 3(a) to 3(d) show the variation of

pressure losses as a function of element sizes In Figures3(a) and 3(b) element size of 0003m and below wouldresult in insignificant changes in pressure losses howevermore computational time is required for elements sizes below0003m In Figures 3(c) and 3(d) element size of 0003m andabove also shows no significant changes in pressure losses Anoptimum element size of 0003m is chosen for all diameterratios resulting in approximately 066ndash215 times 106 number ofelements with increasing diameter ratio from 064 to 090The CPU time recorded in this study ranges between 72 times103 s to 54 times 104 s The simulations were run on a computerwith the following specificationsWindows 7 64-bit operatingsystem with 4GB RAM and Pentium Dual-Core processorat 23 GHz

27 Simulation Model Validation The simulation modelsetups were validated against experiment data available fromprevious studies Pressure loss and cuttings concentrationdata for cuttings-water flow in a horizontal wellbore wereadopted from Osgouei [25] Also pressure loss data usingnon-Newtonian fluid of 04 CMC solution for cuttingstransport experiment were adopted from Han et al [12]Table 1 summarises the rheological properties and operatingparameters for the experimental studies

From Figure 4(a) the calculated pressure loss slightlyoverpredicted the experimental data by a mean percentageerror of 084 Similarly the calculated cuttings concentra-tion data slightly overpredicted the experimental data by amean percentage error of 12 as shown in Figure 4(b) Thetotal cuttings concentration 119862cT is defined as

119862cT =Net volume occupied by particles

Total volume of annlulustimes 100 (19)

Moreover Figure 4(c) shows the calculated pressure lossdeviating slightly from the experimental data by a mean per-centage error of 25 The analyses show a good agreementbetween calculated and experimental data confirming thevalidity of the current model setup

28 Simulation Study Table 2 summarises the simulationsetup including fluid rheological properties and drillingparameters The present study adopts the Eulerian-Eulerianmodel to simulate a two-phase solid-fluid flow in eccentrichorizontal annuli ANSYS-CFX solver which is based on afinite volume method [26] is used to solve the continuityand momentum equations with the appropriate initial andboundary conditions The solution is assumed to be con-verged when the root mean square (RMS) of the normalisedresidual error reached 10minus4 for all simulations Both Newto-nian (water) and non-Newtonian (Power-Law model) fluidsare used as carrier fluids Variations in annular pressure lossesand cuttings concentration as a function of fluid velocitydiameter ratio inner pipe rotation speed and fluid type areanalysed and results are presented In addition contours ofcuttings volume fraction and cuttings velocities streamlinesof cuttings velocities as well as profiles of cuttings velocitiesare also presented


120581 = 064

3720

3680

3640

3600

Pres

sure

loss

(Pa

m)

No of elements =No of elements =No of elements =No of elements =

00050004000300020001

Element size (m)246E + 06

176E + 06

066E + 06

034E + 06

(a)

120581 = 070

No of elements =

No of elements =No of elements =No of elements =

6200

6160

6120

6080

Pres

sure

loss

(Pa

m)

00050004000300020001

Element size (m)

047E + 06

259E + 06

163E + 06

072E + 06

(b)

120581 = 080


18550

18500

18450

18400

Pres

sure

loss

(Pa

m)

00050004000300020001

Element size (m)

205E + 06

168E + 06

113E + 06

103E + 06

(c)

120581 = 090


129600

129300

129000

128700

128400

Pres

sure

loss

(Pa

m)

00050004000300020001

Element size (m)

260E + 06

217E + 06

215E + 06

210E + 06

(d)

Figure 3 Grid independence study (a) 120581 = 064 (b) 120581 = 070 (c) 120581 = 080 (d) 120581 = 090 at 80 rpm

Table 1 Summary of experimental data from previous studies

Experimentaldata source

Fluid density(kgm3) 119899 (mdash) 119870 (Pa s119899) Pipe rotation

(rpm) 120581 (11986311198632) 119890 (mdash)Fluidvelocity(ms)

Avgcuttingssize (m)

Cuttingsdensity(kgm3)

ROP(ms)

Osgouei [25] 9985 10 0001 80 064 0623 1524ndash27432 000201 27614 000508

Han et al [12] 9985 075 0048 0 070 0 0327ndash0654 0001 2550 000526

3 Results and Discussion

31 Effect of Fluid Velocity Previous studies [1 4] haverevealed that fluid velocity is a dominant factor duringcuttings transport This phenomenon is also observed in thisstudy Figure 5 presents the variations in pressure loss andcuttings concentration as a function of increasing annularfluid velocity at constant diameter ratio and 80 rpm Usingboth water andmud as carrier fluids increasing fluid velocitysignificantly increases pressure losses while a decrease incuttings concentration occurs for each constant diameterratio This effect is however more pronounced for 120581 = 090

Figures 5(a)ndash5(d) depict these observations For instancewhen using mud as carrier fluid in Figure 5(c) and for 120581 =090 annular pressure loss was dramatically increased by 97when the flowing fluid velocity increased from 1524ms to2749ms Similarly as shown in Figure 5(d) the cuttingsconcentration decreased by 37 in the annulus as fluidvelocity increased from 1524ms to 2749ms for 120581 =

090 Another observation is that in Figure 5(b) where thecarrier fluid is water there is almost no variation in cuttingsconcentration as fluid velocity increases for 120581 = 090 Thisindicates that in extreme narrow annuli lower fluid velocitiesare capable of transporting enough cuttings from the annulus


29241914

Fluid velocity (ms)

4000

3400

2800

2200

1600

1000

Pres

sure

loss

(Pa

m)

Osgouei [2010]CFX-model

(a)

29241914

Fluid velocity (ms)

190

150

110

70

30


Cutti

ngs c

once

ntra

tion

()

(b)

0706050403

Fluid velocity (ms)

Pres

sure

loss

(Pa

m)

CFX-modelHan et al [2010]

2100

1800

1500

1200

900

(c)

Figure 4 Experimental and simulation data comparison (a) pressure loss data for cuttings-water flow (b) cuttings concentration data forcuttings-water flow (c) pressure loss data for cuttingsmdash04 CMC flow

Table 2 Simulation data for cuttings fluid flow

Rheological and drilling parameter Case 1 Case 2Water Mud

Fluid density (kgm3) 9985 10063Cuttings density (kgm3) 27614Avg cuttings size (m) 000201Flow behaviour index 119899 1 051Viscosity consistency 119870 (Pa s119899) 0001 0289Fluid velocity (ms) 1524ndash27432Inner pipe rotation speed (rpm) 0 80 120Diameter ratio (120581 =11986311198632) 064 070 080 090Eccentricity (119890) 0623ROP (ms) 000508

as higher fluid velocities will not improve on the amount ofcuttings transport but will also increase the annular pres-sure dramatically which may adversely affect the formationpressure A slight variation in cuttings concentration couldhowever be observed in Figure 5(d) as fluid velocity increases

from 1524ms to 2749ms for 120581 = 090when the carrier fluidis mud

32 Effect of Diameter Ratio Figure 6 presents the influenceof diameter ratio on pressure loss and cuttings concentrationat constant fluid velocity and 80 rpm Analyses are shown forbothwater andmud as carrier fluids For all cases as diameterratio increases from 120581 = 064 to 090 an increase in pressureloss also occurs whereas a decrease in cuttings concentrationis observed for each constant fluid velocity This influenceis however more pronounced for 120581 = 090 As the annulargap becomes narrower there are more interactions betweencuttings-fluid and pipe walls which results in an increasein friction and hence pressure losses It is worth notingthat while the pressure loss difference between 120581 = 064

and 120581 = 090 could result in extreme increase by over3600 a decrease of about 86 could be realised for cuttingsconcentration as water flows with a velocity of 1524ms (seeFigures 6(a) and 6(b)) Moreover in Figure 6(b) where thecarrier fluid is water there is almost no disparity in cuttingsconcentration when 120581 = 090 for each constant fluid velocityAlthough better cuttings transport could be observed in very


Pres

sure

loss

(Pa

m)

14 19 24 29Fluid velocity (ms)

80 rpm

120581 = 064 water120581 = 070 water

120581 = 080 water120581 = 090 water

00E + 0

20E + 4

40E + 4

60E + 4

80E + 4

10E + 5

12E + 5

14E + 5

(a)

10

50

90

130

170

14 19 24 29

Cutti

ngs c

once

ntra

tion

()

Fluid velocity (ms)

80 rpm

120581 = 064 water120581 = 070 water

120581 = 080 water120581 = 090 water

(b)

Pres

sure

loss

(Pa

m)


80 rpm

120581 = 064 mud120581 = 070 mud

120581 = 080 mud120581 = 090 mud

00E + 0

20E + 4

40E + 4

60E + 4

80E + 4

10E + 5

12E + 5

14E + 5

(c)

Cutti

ngs c

once

ntra

tion

()


14

34

54

74

94

80 rpm

120581 = 064 mud120581 = 070 mud

120581 = 080 mud120581 = 090 mud

(d)

Figure 5 Effect of fluid velocity at constant diameter ratio on (a) pressure loss with water as carrier fluid (b) cuttings concentration withwater as carrier fluid (c) pressure loss with mud as carrier fluid (d) cuttings concentration with mud as carrier fluid

narrow annuli optimumdrilling parametersmust be selectedto prevent excessive damage to the formation

33 Effect of Drill Pipe Rotation The effect of increasing drillpipe rotation on pressure loss and cuttings concentration isshown in Figure 7 when using both water and mud as carrierfluids In Figures 7(a) and 7(c) an increase in drill piperotation speed from 80 rpm to 120 rpm did not result in anysignificant increment in pressure losses with both water andmud as carrier fluids The effect on cuttings concentration isquite predominant especially in annular gaps with diameterratio below 120581 = 070 For water as carrier fluid as shownin Figure 7(b) the influence of increasing drill pipe rotationspeed from 80 rpm to 120 rpm had a negative impact wherethe cuttings concentration increased when the diameter ratiois below 120581 = 070 To explain this behaviour the lowviscous water would generate high turbulence as a functionof both axial and rotational flows which in addition to

gravity could cause rapid settling of cuttings in the annulusAbove 120581 = 070 the influence is virtually the same oncuttings concentration for each constant fluid velocity Onthe contrary when the carrier fluid is mud as shown inFigure 7(d) increasing drill pipe rotation speed from 80 rpmto 120 rpm shows a decrease in cuttings concentration for adiameter ratio range of 064 le 120581 lt 080 Above 120581 = 080the influence is relatively negative on cuttings concentrationIn all cases the rotation effect is dominant at lower fluidvelocities

34 Effect of Fluid Type The effect of Newtonian (water)and non-Newtonian Power-Law fluid (mud) on pressure lossand cuttings concentration are analysed in Figures 8(a) and8(b) respectively at 120 rpm With mud as carrier fluid highpressure losses were recorded compared to water especially atlow fluid velocity and 120581 = 090 (see Figure 8(a)) Similarly themud transportedmuch cuttings compared to water especially


(a) (b)

(c) (d)

Figure 6 Effect of diameter ratio at constant fluid velocity on (a) pressure loss with water as carrier fluid (b) cuttings concentration withwater as carrier fluid (c) pressure loss with mud as carrier fluid (d) cuttings concentration with mud as carrier fluid

at a constant diameter ratio of 120581 = 064 and low fluidvelocities (see Figure 8(b)) For example 192 and 60concentration of cuttings remained in the annulus afterflowing with water and mud respectively for 120581 = 064 andfluid velocity of 1524ms The performance of both fluids oncuttings concentration is quite similar at high diameter ratios

35 Cuttings Volume Fraction Velocity and Profiles withWater as Carrier Fluid Figures 9ndash11 show the contours ofcuttings volume fraction 3D streamlines of cuttings veloc-ities and radial measurements of cuttings velocity profilesrespectively flowing with water at 1524ms As shownin Figure 9 the cuttings concentration accumulates in thenarrowest gap of the eccentric annuli forming a bed due togravity and the low viscosity of the carrier fluid Howeverthe rotation of the drill pipe from 0 rpm to 120 rpm reducesthe cuttings bed by sweeping it into the widest gap where thefluid velocity is high to transport them to the surface This

observation is evident for all diameter ratios and shows thesignificance of drill pipe rotation in minimising differentialpipe sticking cuttings bed erosion as well as excessivepressure losses Figure 10 also depicts 3D streamlines ofcuttings velocity From the colour legend the velocity ofcuttings is high at some distance from the annular inlet anddecreases to a minimum velocity towards the exit of theannular geometries The decrease in cuttings velocity is anindication of cuttings settling to form a bed due to the lowviscous nature of the carrier fluid and gravity Drill piperotation induces a rotational flow on the cuttings bed intothe annular mainstream and carries them to the surfaceThisrotation effect reduces the annular bed area for all diameterratios The radial measurements of cuttings velocity profilesat 1524ms and 120 rpm are also presented in Figure 11 Theradial distance is normalised In the widest gap of the annulararea as shown in Figure 11(a) cuttings velocity increases withincreasing diameter ratio where the peak velocities calculatedare 1896ms 1970ms 2043ms and 1999ms for 120581 =


(a) (b)

(c) (d)

Figure 7 Effect of drill pipe rotation speed on (a) pressure loss with water as carrier fluid (b) cuttings concentration with water as carrierfluid (c) pressure loss with mud as carrier fluid (d) cuttings concentration with mud as carrier fluid

Pres

sure

loss

(Pa

m)

060 070 080 090

1524ms water ms water1524ms mud

2749

2749ms mud

120 rpm

00E + 0

20E + 4

40E + 4

60E + 4

80E + 4

10E + 5

12E + 5

14E + 5

120581 = D1D2

(a)

10

50

90

130

170

210

Cutti

ngs c

once

ntra

tion

()

060 070 080 090

120 rpm


2749

2749ms mud

120581 = D1D2

(b)

Figure 8 Effect of fluid type on (a) pressure loss and (b) cuttings concentration


1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

0993

0893

0794

0695

0596

0496

0397

0298

0199

0099

0000

0993

0894

0795

0695

0596

0497

0397

0298

0199

0099

0000

0994

0895

0796

0696

0597

0497

0398

0298

0199

0099

0000

0994

0895

0795

0696

0597

0497

0398

0298

0199

0099

0000

0995

0896

0796

0697

0597

0498

0398

0299

0199

0100

0000

0999

0899

0799

0699

0599

0499

0400

0300

0200

0100

0000

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

0998

0898

0798

0699

0599

0499

0399

0299

0200

0100

0000

Figure 9 Contours of cuttings volume fraction for varying diameter ratios and inner pipe rotation with water as carrier fluid at 1524ms


1643

1310

0977

0644

0310

1659

1322

0984

0647

0309

1687

1325

0963

0601

0239

1659

1304

0950

0595

0241

2060

1562

1065

0568

0071

2046

1555

1065

0574

0083

1542

1247

0953

0658

0364

1654

1313

0972

0631

0290

1678

1320

0963

0605

0247

2024

1538

1051

0565

0079

1539

1239

0938

0637

0336

1541

1248

0955

0662

0369

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

Figure 10 3D streamlines of cuttings velocity for varying diameter ratios and inner pipe rotation with water as carrier fluid at 1524ms

00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R

Cuttings velocity (ms)

Widest gap water

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00

02

04

06

08

10

00 01 02 03 04 05

Nor

mal

ised

radi

al d

istan

ce R


Narrowest gap waterInner pipe

Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)

Figure 11 Cuttings velocity profiles with water as carrier fluid for varying diameter ratios at 1524ms and 120 rpm (a) gap above inner pipeand (b) gap below inner pipe


064 070 080 and 090 respectively On the contrary inFigure 11(b) the cuttings velocity in the narrowest annulargap show irregular profiles as diameter ratio increases Theeffect of drill pipe rotation is seen to have greater impact onthe cuttings velocity especially near the vicinity of the drillpipe where there is high shear For example at 120581 = 090 thepeak cuttings velocity recordedwas 0481ms and it occurredat the vicinity of the drill pipe

36 Cuttings Volume Fraction Velocity and Profiles with Mudas Carrier Fluid With mud as carrier fluid and flowing at1524ms and a drill pipe rotating at 120 rpm Figure 12 showsa very small cuttings volume fraction within the annular gapDue to the high viscous nature of the mud many cuttingsare able to be suspended in the mud and then transportedto the surface This reduces the cuttings tendency to slipto the bottom of the wellbore to form a bed The cuttingsvelocity presented in 3D streamlines (see Figure 13) showshow the cuttings travel in almost the entire annular spacefor all diameter ratios This indicates better carrying capacityof the mud in transporting the cuttings to the surface Theradialmeasurements of the cuttings velocity profiles as shownin Figure 14 further illustrate the mudrsquos carrying capacityin both the widest and narrowest annular gaps The peakcuttings velocity also increases with increasing diameter ratioand is recorded in the widest gap as 1698ms 1758ms1838ms and 1840ms for 120581 = 064 070 080 and 090respectively as shown in Figure 14(a) In the narrowest gapas shown in Figure 14(b) the cuttings velocity profiles showirregular behaviours and are also very similar in magnitudefor all diameter ratiosThe peak cuttings velocities calculatedare 1000ms 1304ms 1025ms and 1071ms for 120581 =

064 070 080 and 090 respectively (see Figure 14(b))

4 Conclusions

The present study employs a CFD method to analyse theeffects of fluid velocity annular diameter ratio (ranging from064 to 090) drill pipe rotation and fluid type on theprediction of pressure losses and cuttings concentration forsolid-fluid flow in eccentric horizontal annular geometriesThe following can be inferred from this study

(1) Using water as carrier fluid simulation data forpressure loss and cuttings concentration are in goodagreement with experimental data with mean per-centage errors of 084 and 12 respectively Simi-larly with mud as carrier fluid only 25 mean errorexists between simulation and experimental pressuredata confirming the validity of the current modelsetup

(2) Increasing annular fluid velocity significantlyincreases pressure losses while a decrease in cuttingsconcentration occurs for each constant diameterratio This effect is however more pronounced for120581 = 090 when using both water and mud as carrierfluids Annular pressure loss is dramatically increasedby 97 while cuttings concentration is decreased by

37 when the flowing mud velocity increased from1524ms to 2749ms for 120581 = 090

(3) When other drilling parameters are kept constantincreasing diameter ratio increases pressure losswhereas a decrease in cuttings concentration isobserved for each constant fluid velocity This influ-ence is however pronounced for 120581 = 090 Over3600 increase in pressure loss could be realisedwhile a decrease of about 86 in cuttings concen-tration is observed between diameter ratios of 120581 =064 and 120581 = 090 for water flowing at a velocity of1524ms

(4) Increasing drill pipe rotation speed from 80 rpm to120 rpm did not result in any significant increment inpressure losses with bothwater andmudThe rotationeffect on cuttings concentration is quite predominantespecially in annular gaps with diameter ratio below120581 = 070 and at low fluid velocities Contours ofcuttings volume fraction show how rotation effectsweeps cuttings bed into the annular mainstream andtransports them to the surface

(5) Although mud recorded higher pressure losses com-pared to water it has better carrying capacity asopposed towater especially at smaller diameter ratiosThe performance of both fluids on cuttings concen-tration is quite similar at high diameter ratios

Nomenclature

119860bit Area of bit (m2)119862119863 Drag coefficient (mdash)119862cf Cuttings feed concentration (mdash)119862cT Total cuttings concentration (mdash)119862120572 Volume fraction of phase 1205721198621205761 (119896-120576) turbulence model constant (144)1198621205762 (119896-120576) turbulence model constant (192)119862120583 (119896-120576) turbulence model constant (009)119889119904 Solid particle mean diameter (m)1198631 Outer diameter of inner pipe (m)1198632 Inner diameter of outer pipe (m)119863ℎ Hydraulic diameter1198632 minus 1198631 (m)119890 Eccentricity (2120575(1198632 minus 1198631))119892 Gravity vector (ms2)h119897 Fluid phase volume fraction (mdash)h119904 Solid phase volume fraction (mdash)119870 Consistency index (Pasdotsn)119896120572 Turbulence kinetic energy (m2s2)119871 Annular geometry length (m)119871ℎ Hydrodynamic length (m) Mass flow rate (kgs)119872 Interphase momentum transfer119872119889 Drag force per unit volume (Nm3)119872119871 Lift force per unit volume (Nm3)119899 Flow behaviour index (mdash)119873Re Fluid Reynolds number (mdash)119873Re119901 Solid particles Reynolds number (mdash)119873Re120596 Vorticity Reynolds number (mdash)


120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

0290

0261

0232

0203

0174

0145

0116

0087

0058

0029

0000

0315

0284

0252

0221

0189

0158

0126

0095

0063

0032

0000

0323

0291

0259

0226

0194

0162

0129

0097

0065

0032

0000

0324

0292

0259

0227

0194

0162

0130

0097

0065

0032

0000

0312

0281

0250

0219

0187

0156

0125

0094

0062

0031

0000

0336

0302

0269

0235

0201

0168

0134

0101

0067

0034

0000

0507

0456

0406

0355

0304

0253

0203

0152

0101

0051

0000

0548

0493

0438

0383

0329

0274

0219

0164

0110

0055

0000

0563

0507

0451

0394

0338

0282

0225

0169

0113

0056

0000

0619

0557

0495

0433

0371

0309

0247

0186

0124

0062

0000

0615

0553

0492

0430

0369

0307

0246

0184

0123

0061

0000

0700

0630

0560

0490

0420

0350

0280

0210

0140

0070

0000

Figure 12 Contours of cuttings volume fraction for varying diameter ratios and inner pipe rotation with mud as carrier fluid at 1524ms


1699

1437

1174

0912

0649

1697

1409

1121

0833

0546

1698

1416

1133

0851

0568

1755

1395

1037

0577

0318

1759

1415

1070

0726

0382

1760

1428

1097

0765

0434

1848

1453

1058

0563

0268

1838

1436

1035

0633

0231

1823

1413

1003

0593

0183

1777

1602

1426

1250

1074

1777

1585

1394

1202

1011

1774

1581

1389

1197

1005

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

Figure 13 3D streamlines of cuttings velocity for varying diameter ratios and inner pipe rotation with mud as carrier fluid at 1524ms

00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R


Widest gap mud

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00 02 04 06 08 10 1200

02

04

06

08

10

Nor

mal

ised

radi

al d

istan

ce R


Narrowest gap mudInner pipe

Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)

Figure 14 Cuttings velocity profiles with mud as carrier fluid for varying diameter ratio at 1524ms and 120 rpm (a) gap above inner pipeand (b) gap below inner pipe


119875120572 Phase pressure (Pa)119875119904 Solid particle pressure (Pa)119876 Volumetric flow rate (m3s)119903 Radial distance (m)119877 Normalised radial distance ((1198772 minus 119903)(1198772 minus 1198771))1198771 Outer radius of inner pipe (m)1198772 Inner radius of outer pipe (m)ROP Rate of penetration (ms)119877119879 Transport ratio (mdash)119879(120576)

120572120573 Interphase transfer for 120576

119879(119896)


119880120572 Phase velocity vector (ms)119880119897 Fluid phase velocity vector (ms)119880119904 Solid phase velocity vector (ms)

Symbols

120575 Offset distance (m)120576120572 Turbulence dissipation rate (m2s3)120588120572 Phase density (kgm3)120588119897 Fluid phase density (kgm3)120588119904 Solid phase density (kgm3)120591 Viscous stress tensor (Pa)120581 Diameter ratio (11986311198632)120590120576 (119896-120576) turbulence model constant (13)120590119896 (119896-120576) turbulence model constant (10)120583 Dynamic viscosity (Pasdots)120583119886 Apparent viscosity (Pasdots)120583eff Effective viscosity (Pasdots)120583119905120572 Phase turbulent viscosity (Pasdots)120592 Specific volume (m3kg)120596 Angular velocity (1min)120574 Shear rate (1s)Ω Rotation vector (1min)

Unit Conversion Factors

ft times 03048 119864 + 00 = minch times 254 119864 minus 03 = mGal (US) times 3785 119864 + 00 = litergalmin (gpm) times 6309 119864 minus 05 = m3spsi times 68948 119864 minus 03 = MPappg times 1198 119864 + 02 = kgm3

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] P H Tomren A W Iyoho and J J Azar ldquoExperimentalstudy of cuttings transport in directional wellsrdquo SPE DrillingEngineering vol 1 no 1 pp 43ndash56 1986

[2] T E Becker and J J Azar Mud-Weight and Hole-GeometryEffects on Cuttings Transport While Drilling Directionally Soci-ety of Petroleum Engineers SPE-14711-MS 1985

[3] R B Adari S Miska E Kuru P Bern and A Saasen ldquoSelectingdrilling fluid properties and flow rates for effective hole cleaningin high-angle and horizontal wellsrdquo in Proceedings of the SPEAnnual Technical Conference and Exhibition paper SPE-63050-MS pp 273ndash281 Dallas Tex USA October 2000

[4] T R Sifferman and T E Becker ldquoHole cleaning in full-scaleinclined wellboresrdquo SPE Drilling Engineering vol 7 no 2 pp115ndash120 1992

[5] R Ahmed M Sagheer N Takach et al ldquoExperimental studieson the effect ofmechanical cleaning devices on annular cuttingsconcentration and applications for optimizing ERD systemsrdquoin Proceedings of the SPE Annual Technical Conference andExhibition paper SPE-134269-MS pp 2016ndash2028 FlorenceItaly September 2010

[6] M E Ozbayoglu A SaasenM Sorgun and K Svanes ldquoCriticalfluid velocities for removing cuttings bed inside horizontal anddeviated wellsrdquo Petroleum Science and Technology vol 28 no 6pp 594ndash602 2010

[7] J O Ogunrinde and A Dosunmu ldquoHydraulic optimizationfor efficient hole cleaning in deviated and horizontal wellsrdquo inProceedings of the SPE Nigerian Annual Technical Conferenceand Exhibition paper SPE 162970 Abuja Nigeria August 2012

[8] M E Ozbayoglu and M Sorgun ldquoFrictional pressure lossestimation of water-based drilling fluids at horizontal andinclined drilling with pipe rotation and presence of cuttingsrdquoin Proceedings of the SPE Oil and Gas India Conference andExhibition paper SPE-127300-MS Mumbai India January2010

[9] M Sorgun I Aydin and M E Ozbayoglu ldquoFriction factorsfor hydraulic calculations considering presence of cuttings andpipe rotation in horizontalhighly-inclined wellboresrdquo Journalof Petroleum Science and Engineering vol 78 no 2 pp 407ndash4142011

[10] O M Evren E Reza O O A Murat and Y Ertan ldquoEsti-mation of ldquovery-difficult-to-identifyrdquo data for hole cleaningcuttings transport and pressure drop estimation in directionaland horizontal drillingrdquo in Proceedings of the IADCSPE AsiaPacific Drilling Technology Conference and Exhibition paperSPE-136304-MS pp 668ndash685 Ho Chi Minh City VietnamNovember 2010

[11] N C G Markatos R Sala and D R Spalding ldquoFlow in anannulus of non-uniform gaprdquo Transactions of the Institution ofChemical Engineers vol 56 no 1 pp 28ndash35 1978

[12] S-M Han Y-K Hwang N-S Woo and Y-J Kim ldquoSolid-liquid hydrodynamics in a slim hole drilling annulusrdquo Journal ofPetroleum Science and Engineering vol 70 no 3-4 pp 308ndash3192010

[13] M Mokhtari M Ermila A N Tutuncu and M KarimildquoComputational modelling of drilling fluids dynamics in casingdrillingrdquo in Proceedings of the SPE Eastern Regional Meetingpaper SPE-161301-MS Lexington Ky USA October 2012

[14] T N Ofei S Irawan andW Pao ldquoModelling ofpressure drop ineccentric narrowhorizontal annuli with the presence of cuttingsand rotating drillpiperdquo International Journal of Oil Gas andCoal Technology In press

[15] G M Faeth ldquoMixing transport and combustion in spraysrdquoProgress in Energy and Combustion Science vol 13 no 4 pp293ndash345 1987


[16] M Eesa and M Barigou ldquoHorizontal laminar flow of coarsenearly-neutrally buoyant particles in non-Newtonian convey-ing fluids CFD and PEPT experiments comparedrdquo Interna-tional Journal of Multiphase Flow vol 34 no 11 pp 997ndash10072008

[17] B G M van Wachem and A E Almstedt ldquoMethods for mul-tiphase computational fluid dynamicsrdquo Chemical EngineeringJournal vol 96 no 1ndash3 pp 81ndash98 2003

[18] C Y Wen and Y H Yu ldquoMechanics of fluidizationrdquo ChemicalEngineering Progress Symposium Series vol 62 pp 100ndash1111966

[19] D Gidaspow Multiphase Flow and Fluidization AcademicPress 1994

[20] P G Saffman ldquoThe lift on a small sphere in a slow shear flowrdquoJournal of Fluid Mechanics vol 22 no 2 pp 385ndash400 1965

[21] P G Saffman ldquoThe lift on a small sphere in a slow shear flowmdashcorrigendumrdquo Journal of Fluid Mechanics vol 31 no 3 p 6241968

[22] R Mei and J F Klausner ldquoShear lift force on spherical bubblesrdquoInternational Journal of Heat and Fluid Flow vol 15 no 1 pp62ndash65 1994

[23] B E Launder and D B Spalding ldquoThe numerical computationof turbulent flowsrdquoComputerMethods inAppliedMechanics andEngineering vol 3 no 2 pp 269ndash289 1974

[24] C A Shook and M C Roco Slurry Flow Principles andPractice Butterworth-Heimemann London UK 1991

[25] R E Osgouei Determination of cuttings transport propertiesof gasified drilling fluids [PhD thesis] Middle East TechnicalUniversity Ankara Turkey 2010

[26] S V Patankar Numerical Heat Transfer and Fluid Flow Hemi-sphere Publishing Corp 1980

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that the existence of cuttings in the system caused anincrease in pressure loss due to a decrease in flow area insidethe annular gap Further observation was that drill piperotation decreases the pressure loss significantly if the drillpipe is making orbital motion in eccentric annulus Anotherexperimental study was conducted [10] to analyse the effectsof some ldquovery difficult to identifyrdquo data on the estimation oftotal pressure loss and cuttings concentration in horizontaland inclined annulus Results from this study indicate thatdrill pipe rotation does not have significant influence onpressure loss for constant rate of penetration (ROP) and fluidvelocity The annular test section has diameter ratio of 064

One of the pioneering works by Markatos et al [11] mod-elled single phase Newtonian flow in nonuniform narrowannular gaps using finite difference technique The velocityflow fields as well as static pressure were predicted in a two-dimensional flow

Han et al [12] is among the first to conduct experimentaland CFD studies on solid-fluid mixture flow in vertical andhighly deviated slim hole annulus They concluded thatannular pressure losses increase with mixture fluid velocityannular angle of inclination and drill pipe rotation speedThe annular test section has diameter ratio of 070 Mokhtariet al [13] employed CFD method to model the effects ofeccentricity and flow behaviour index on annular pressureloss and velocity profile for varying diameter ratios from 030to 090 The authors however did not include cuttings in theannular mainstream Recently Ofei et al [14] also employedCFD technique to analyse the influence of diameter ratiofluid velocity fluid type fluid rheology and drill pipe rotationspeed on pressure loss in eccentric horizontal wellbore withthe presence of cuttings

The present study also utilises a CFD technique toexamine the effects of fluid velocity annular diameter ratio(ranging from 064 to 090) drill pipe rotation and fluid typeon the prediction of pressure loss and cuttings concentrationfor solid-fluid flow in eccentric horizontal wellbore Contoursof cuttings volume fraction 3D cuttings velocity streamlinesand radial cuttings velocity profiles are also presented to givefurther insight on cuttings transport The new findings fromthis study would provide better understanding and guidein the selection of optimum drilling parameters in narrowannuli drilling such as casing drilling and slim holes

2 Materials and Methods

Multiphase component of CFD software ANSYS-CFX 140is adopted in this study In ANSYS-CFX a multiphaseflow containing dispersed particles may be modelled usingeither Lagrangian Particle Tracking model or Eulerian-Eulerian model The inhomogeneous (Eulerian-Eulerian)model sometimes called the two-fluid model regards bothcontinuous and dispersed phases as continuous media Inthis study the Eulerian-Eulerian model is preferred to theLagrangian Particle Tracking model due to its ability tohandle high solid volume fractions Furthermore it accountsfor solid particle-particle interaction and includes turbulenceautomatically [15] A drawback of this model is however that

they need complex closure relationsThe following continuityand momentum equations representing the two-phase flowmodel are described for the sake of brevity

21 Continuity Equations The fluid phase continuity equa-tion assuming isothermal flow condition can be expressed as[16 17]

120597

120597119905(h119897) + nabla (h119897119880119897) = 0 (1)

Similarly for a solid phase

120597

120597119905(h119904) + nabla (h119904119880119904) = 0 (2)

where the solid and fluid phase volume fraction sum up asfollows

k119904 + k119897 = 1 (3)


22 Momentum Equations The forces acting on each phaseand interphase momentum transfer term that models theinteraction between each phase are given below [16 17]

For fluid phase

120588119897k119897 [120597119880119897

120597119905+ 119880119897 sdot nabla119880119897] = minusk119897nabla119901 + k119897nabla sdot 120591119897 + k119897120588119897119892 minus119872

(4)

Similarly for solid phase

120588119904h119904 [120597119880119904

120597119905+ 119880119904 sdot nabla119880119904]

= minush119904nabla119901 +h119904nabla sdot 120591119897 + nabla sdot 120591119904 minus nabla119875119904 +h119904120588119904119892 +119872

(5)


23 Other Closure Models

231 Interphase Drag Force Model For spherical particlesthe drag force per unit volume is given as

119872119889 =3119862119863

4119889119904

k1199041205881198971003816100381610038161003816119880119904 minus 119880119897

1003816100381610038161003816 (119880119904 minus 119880119897) (6)

For densely distributed solid particles where the solid volumefractionk119904 lt 02 theWen and Yu [18] drag coefficient modelmay be utilised This model is modified and implemented inANSYS-CFX to ensure the correct limiting behaviour in theinertial regime as

119862119863 = kminus165

119897max[ 24

1198731015840Re119901(1 + 015119873

1015840 0687

Re119901 ) 044] (7)

where1198731015840Re119901 = k119897119873Re119901 and119873Re119901 = 120588119897|119880119897 minus 119880119904|119889119904120583119897



119872119863 =150(1 minus k119897)

2120583119897

k1198971198892119904

+7

4

(1 minus k119897) 1205881198971003816100381610038161003816119880119897 minus 119880119904

1003816100381610038161003816

119889119904

(8)



119872119871 =3

2120587

radic]119897


1003816100381610038161003816

1198621015840


(9)


119871= 646 and


1198621015840

119871=


646 sdot 00524 sdot (120573119873Re119901)12

for 40 lt 119873Re119901 lt 100

(10)

where 120573 = 05(119873Re120596119873Re119901)


05

(11)

and119873Re120596 = 1205881198971205961198971198892

119904120583119897 120596119897 = |nabla times 119880119897|


120597

120597119905(119862120572120588120572119896120572) + nabla sdot (119862120572 (120588120572119880120572119896120572 minus (120583 +

120583119905120572

120590119896

)nabla119896120572))

= 119862120572 (119875120572 minus 120588120572120576120572) + 119879(119896)

120572120573

(12)

120597

120597119905(119862120572120588120572120576120572) + nabla sdot (119862120572120588120572119880120572120576120572 minus (120583 +

120583119905120572

120590120576

)nabla120576120572)

= 119862120572

120576120572

119896120572

(1198621205761119875120572 minus 1198621205762120588120572120576120572) + 119879(120576)

120572120573

(13)

Inlet Outlet


Inner cylinder

m g

L

Tconst

Pref

120596



120583eff = 120583 + 120583119905120572 (14)


120583119905120572 = 119862120583120588120572

1198962

120572

120576120572

(15)




119871ℎ = 0062119873Re (119863) (16)


120583119886 = 119870 120574119899minus1 (17)


120581 = 064 120581 = 070

120581 = 080 120581 = 090





119862cf =(ROP) 119860bit119877119879119876

(18)










120581 = 064

3720

3680

3640

3600

Pres

sure

loss

(Pa

m)


00050004000300020001


176E + 06

066E + 06

034E + 06

(a)

120581 = 070

No of elements =


6200

6160

6120

6080

Pres

sure

loss

(Pa

m)

00050004000300020001

Element size (m)

047E + 06

259E + 06

163E + 06

072E + 06

(b)

120581 = 080


18550

18500

18450

18400

Pres

sure

loss

(Pa

m)

00050004000300020001

Element size (m)

205E + 06

168E + 06

113E + 06

103E + 06

(c)

120581 = 090


129600

129300

129000

128700

128400

Pres

sure

loss

(Pa

m)

00050004000300020001

Element size (m)

260E + 06

217E + 06

215E + 06

210E + 06

(d)






Avgcuttingssize (m)


ROP(ms)

Osgouei [25] 9985 10 0001 80 064 0623 1524ndash27432 000201 27614 000508

Han et al [12] 9985 075 0048 0 070 0 0327ndash0654 0001 2550 000526






29241914

Fluid velocity (ms)

4000

3400

2800

2200

1600

1000

Pres

sure

loss

(Pa

m)


(a)

29241914

Fluid velocity (ms)

190

150

110

70

30


Cutti

ngs c

once

ntra

tion

()

(b)

0706050403

Fluid velocity (ms)

Pres

sure

loss

(Pa

m)


2100

1800

1500

1200

900

(c)










Pres

sure

loss

(Pa

m)


80 rpm

120581 = 064 water120581 = 070 water

120581 = 080 water120581 = 090 water

00E + 0

20E + 4

40E + 4

60E + 4

80E + 4

10E + 5

12E + 5

14E + 5

(a)

10

50

90

130

170

14 19 24 29

Cutti

ngs c

once

ntra

tion

()

Fluid velocity (ms)

80 rpm

120581 = 064 water120581 = 070 water

120581 = 080 water120581 = 090 water

(b)

Pres

sure

loss

(Pa

m)


80 rpm

120581 = 064 mud120581 = 070 mud

120581 = 080 mud120581 = 090 mud

00E + 0

20E + 4

40E + 4

60E + 4

80E + 4

10E + 5

12E + 5

14E + 5

(c)

Cutti

ngs c

once

ntra

tion

()


14

34

54

74

94

80 rpm

120581 = 064 mud120581 = 070 mud

120581 = 080 mud120581 = 090 mud

(d)







(a) (b)

(c) (d)






(a) (b)

(c) (d)


Pres

sure

loss

(Pa

m)

060 070 080 090


2749

2749ms mud

120 rpm

00E + 0

20E + 4

40E + 4

60E + 4

80E + 4

10E + 5

12E + 5

14E + 5

120581 = D1D2

(a)

10

50

90

130

170

210

Cutti

ngs c

once

ntra

tion

()

060 070 080 090

120 rpm


2749

2749ms mud

120581 = D1D2

(b)



1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

0993

0893

0794

0695

0596

0496

0397

0298

0199

0099

0000

0993

0894

0795

0695

0596

0497

0397

0298

0199

0099

0000

0994

0895

0796

0696

0597

0497

0398

0298

0199

0099

0000

0994

0895

0795

0696

0597

0497

0398

0298

0199

0099

0000

0995

0896

0796

0697

0597

0498

0398

0299

0199

0100

0000

0999

0899

0799

0699

0599

0499

0400

0300

0200

0100

0000

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

0998

0898

0798

0699

0599

0499

0399

0299

0200

0100

0000



1643

1310

0977

0644

0310

1659

1322

0984

0647

0309

1687

1325

0963

0601

0239

1659

1304

0950

0595

0241

2060

1562

1065

0568

0071

2046

1555

1065

0574

0083

1542

1247

0953

0658

0364

1654

1313

0972

0631

0290

1678

1320

0963

0605

0247

2024

1538

1051

0565

0079

1539

1239

0938

0637

0336

1541

1248

0955

0662

0369

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)


00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R


Widest gap water

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00

02

04

06

08

10

00 01 02 03 04 05

Nor

mal

ised

radi

al d

istan

ce R



Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)






4 Conclusions








Nomenclature



120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

0290

0261

0232

0203

0174

0145

0116

0087

0058

0029

0000

0315

0284

0252

0221

0189

0158

0126

0095

0063

0032

0000

0323

0291

0259

0226

0194

0162

0129

0097

0065

0032

0000

0324

0292

0259

0227

0194

0162

0130

0097

0065

0032

0000

0312

0281

0250

0219

0187

0156

0125

0094

0062

0031

0000

0336

0302

0269

0235

0201

0168

0134

0101

0067

0034

0000

0507

0456

0406

0355

0304

0253

0203

0152

0101

0051

0000

0548

0493

0438

0383

0329

0274

0219

0164

0110

0055

0000

0563

0507

0451

0394

0338

0282

0225

0169

0113

0056

0000

0619

0557

0495

0433

0371

0309

0247

0186

0124

0062

0000

0615

0553

0492

0430

0369

0307

0246

0184

0123

0061

0000

0700

0630

0560

0490

0420

0350

0280

0210

0140

0070

0000



1699

1437

1174

0912

0649

1697

1409

1121

0833

0546

1698

1416

1133

0851

0568

1755

1395

1037

0577

0318

1759

1415

1070

0726

0382

1760

1428

1097

0765

0434

1848

1453

1058

0563

0268

1838

1436

1035

0633

0231

1823

1413

1003

0593

0183

1777

1602

1426

1250

1074

1777

1585

1394

1202

1011

1774

1581

1389

1197

1005

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)


00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R


Widest gap mud

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00 02 04 06 08 10 1200

02

04

06

08

10

Nor

mal

ised

radi

al d

istan

ce R



Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)





119879(119896)



Symbols






References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119872119863 =150(1 minus k119897)

2120583119897

k1198971198892119904

+7

4

(1 minus k119897) 1205881198971003816100381610038161003816119880119897 minus 119880119904

1003816100381610038161003816

119889119904

(8)



119872119871 =3

2120587

radic]119897


1003816100381610038161003816

1198621015840


(9)


119871= 646 and


1198621015840

119871=


646 sdot 00524 sdot (120573119873Re119901)12

for 40 lt 119873Re119901 lt 100

(10)

where 120573 = 05(119873Re120596119873Re119901)


05

(11)

and119873Re120596 = 1205881198971205961198971198892

119904120583119897 120596119897 = |nabla times 119880119897|


120597

120597119905(119862120572120588120572119896120572) + nabla sdot (119862120572 (120588120572119880120572119896120572 minus (120583 +

120583119905120572

120590119896

)nabla119896120572))

= 119862120572 (119875120572 minus 120588120572120576120572) + 119879(119896)

120572120573

(12)

120597

120597119905(119862120572120588120572120576120572) + nabla sdot (119862120572120588120572119880120572120576120572 minus (120583 +

120583119905120572

120590120576

)nabla120576120572)

= 119862120572

120576120572

119896120572

(1198621205761119875120572 minus 1198621205762120588120572120576120572) + 119879(120576)

120572120573

(13)

Inlet Outlet


Inner cylinder

m g

L

Tconst

Pref

120596



120583eff = 120583 + 120583119905120572 (14)


120583119905120572 = 119862120583120588120572

1198962

120572

120576120572

(15)




119871ℎ = 0062119873Re (119863) (16)


120583119886 = 119870 120574119899minus1 (17)


120581 = 064 120581 = 070

120581 = 080 120581 = 090





119862cf =(ROP) 119860bit119877119879119876

(18)










120581 = 064

3720

3680

3640

3600

Pres

sure

loss

(Pa

m)


00050004000300020001


176E + 06

066E + 06

034E + 06

(a)

120581 = 070

No of elements =


6200

6160

6120

6080

Pres

sure

loss

(Pa

m)

00050004000300020001

Element size (m)

047E + 06

259E + 06

163E + 06

072E + 06

(b)

120581 = 080


18550

18500

18450

18400

Pres

sure

loss

(Pa

m)

00050004000300020001

Element size (m)

205E + 06

168E + 06

113E + 06

103E + 06

(c)

120581 = 090


129600

129300

129000

128700

128400

Pres

sure

loss

(Pa

m)

00050004000300020001

Element size (m)

260E + 06

217E + 06

215E + 06

210E + 06

(d)






Avgcuttingssize (m)


ROP(ms)

Osgouei [25] 9985 10 0001 80 064 0623 1524ndash27432 000201 27614 000508

Han et al [12] 9985 075 0048 0 070 0 0327ndash0654 0001 2550 000526






29241914

Fluid velocity (ms)

4000

3400

2800

2200

1600

1000

Pres

sure

loss

(Pa

m)


(a)

29241914

Fluid velocity (ms)

190

150

110

70

30


Cutti

ngs c

once

ntra

tion

()

(b)

0706050403

Fluid velocity (ms)

Pres

sure

loss

(Pa

m)


2100

1800

1500

1200

900

(c)










Pres

sure

loss

(Pa

m)


80 rpm

120581 = 064 water120581 = 070 water

120581 = 080 water120581 = 090 water

00E + 0

20E + 4

40E + 4

60E + 4

80E + 4

10E + 5

12E + 5

14E + 5

(a)

10

50

90

130

170

14 19 24 29

Cutti

ngs c

once

ntra

tion

()

Fluid velocity (ms)

80 rpm

120581 = 064 water120581 = 070 water

120581 = 080 water120581 = 090 water

(b)

Pres

sure

loss

(Pa

m)


80 rpm

120581 = 064 mud120581 = 070 mud

120581 = 080 mud120581 = 090 mud

00E + 0

20E + 4

40E + 4

60E + 4

80E + 4

10E + 5

12E + 5

14E + 5

(c)

Cutti

ngs c

once

ntra

tion

()


14

34

54

74

94

80 rpm

120581 = 064 mud120581 = 070 mud

120581 = 080 mud120581 = 090 mud

(d)







(a) (b)

(c) (d)






(a) (b)

(c) (d)


Pres

sure

loss

(Pa

m)

060 070 080 090


2749

2749ms mud

120 rpm

00E + 0

20E + 4

40E + 4

60E + 4

80E + 4

10E + 5

12E + 5

14E + 5

120581 = D1D2

(a)

10

50

90

130

170

210

Cutti

ngs c

once

ntra

tion

()

060 070 080 090

120 rpm


2749

2749ms mud

120581 = D1D2

(b)



1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

0993

0893

0794

0695

0596

0496

0397

0298

0199

0099

0000

0993

0894

0795

0695

0596

0497

0397

0298

0199

0099

0000

0994

0895

0796

0696

0597

0497

0398

0298

0199

0099

0000

0994

0895

0795

0696

0597

0497

0398

0298

0199

0099

0000

0995

0896

0796

0697

0597

0498

0398

0299

0199

0100

0000

0999

0899

0799

0699

0599

0499

0400

0300

0200

0100

0000

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

0998

0898

0798

0699

0599

0499

0399

0299

0200

0100

0000



1643

1310

0977

0644

0310

1659

1322

0984

0647

0309

1687

1325

0963

0601

0239

1659

1304

0950

0595

0241

2060

1562

1065

0568

0071

2046

1555

1065

0574

0083

1542

1247

0953

0658

0364

1654

1313

0972

0631

0290

1678

1320

0963

0605

0247

2024

1538

1051

0565

0079

1539

1239

0938

0637

0336

1541

1248

0955

0662

0369

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)


00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R


Widest gap water

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00

02

04

06

08

10

00 01 02 03 04 05

Nor

mal

ised

radi

al d

istan

ce R



Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)






4 Conclusions








Nomenclature



120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

0290

0261

0232

0203

0174

0145

0116

0087

0058

0029

0000

0315

0284

0252

0221

0189

0158

0126

0095

0063

0032

0000

0323

0291

0259

0226

0194

0162

0129

0097

0065

0032

0000

0324

0292

0259

0227

0194

0162

0130

0097

0065

0032

0000

0312

0281

0250

0219

0187

0156

0125

0094

0062

0031

0000

0336

0302

0269

0235

0201

0168

0134

0101

0067

0034

0000

0507

0456

0406

0355

0304

0253

0203

0152

0101

0051

0000

0548

0493

0438

0383

0329

0274

0219

0164

0110

0055

0000

0563

0507

0451

0394

0338

0282

0225

0169

0113

0056

0000

0619

0557

0495

0433

0371

0309

0247

0186

0124

0062

0000

0615

0553

0492

0430

0369

0307

0246

0184

0123

0061

0000

0700

0630

0560

0490

0420

0350

0280

0210

0140

0070

0000



1699

1437

1174

0912

0649

1697

1409

1121

0833

0546

1698

1416

1133

0851

0568

1755

1395

1037

0577

0318

1759

1415

1070

0726

0382

1760

1428

1097

0765

0434

1848

1453

1058

0563

0268

1838

1436

1035

0633

0231

1823

1413

1003

0593

0183

1777

1602

1426

1250

1074

1777

1585

1394

1202

1011

1774

1581

1389

1197

1005

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)


00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R


Widest gap mud

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00 02 04 06 08 10 1200

02

04

06

08

10

Nor

mal

ised

radi

al d

istan

ce R



Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)





119879(119896)



Symbols






References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










120581 = 064 120581 = 070

120581 = 080 120581 = 090





119862cf =(ROP) 119860bit119877119879119876

(18)










120581 = 064

3720

3680

3640

3600

Pres

sure

loss

(Pa

m)


00050004000300020001


176E + 06

066E + 06

034E + 06

(a)

120581 = 070

No of elements =


6200

6160

6120

6080

Pres

sure

loss

(Pa

m)

00050004000300020001

Element size (m)

047E + 06

259E + 06

163E + 06

072E + 06

(b)

120581 = 080


18550

18500

18450

18400

Pres

sure

loss

(Pa

m)

00050004000300020001

Element size (m)

205E + 06

168E + 06

113E + 06

103E + 06

(c)

120581 = 090


129600

129300

129000

128700

128400

Pres

sure

loss

(Pa

m)

00050004000300020001

Element size (m)

260E + 06

217E + 06

215E + 06

210E + 06

(d)






Avgcuttingssize (m)


ROP(ms)

Osgouei [25] 9985 10 0001 80 064 0623 1524ndash27432 000201 27614 000508

Han et al [12] 9985 075 0048 0 070 0 0327ndash0654 0001 2550 000526






29241914

Fluid velocity (ms)

4000

3400

2800

2200

1600

1000

Pres

sure

loss

(Pa

m)


(a)

29241914

Fluid velocity (ms)

190

150

110

70

30


Cutti

ngs c

once

ntra

tion

()

(b)

0706050403

Fluid velocity (ms)

Pres

sure

loss

(Pa

m)


2100

1800

1500

1200

900

(c)










Pres

sure

loss

(Pa

m)


80 rpm

120581 = 064 water120581 = 070 water

120581 = 080 water120581 = 090 water

00E + 0

20E + 4

40E + 4

60E + 4

80E + 4

10E + 5

12E + 5

14E + 5

(a)

10

50

90

130

170

14 19 24 29

Cutti

ngs c

once

ntra

tion

()

Fluid velocity (ms)

80 rpm

120581 = 064 water120581 = 070 water

120581 = 080 water120581 = 090 water

(b)

Pres

sure

loss

(Pa

m)


80 rpm

120581 = 064 mud120581 = 070 mud

120581 = 080 mud120581 = 090 mud

00E + 0

20E + 4

40E + 4

60E + 4

80E + 4

10E + 5

12E + 5

14E + 5

(c)

Cutti

ngs c

once

ntra

tion

()


14

34

54

74

94

80 rpm

120581 = 064 mud120581 = 070 mud

120581 = 080 mud120581 = 090 mud

(d)







(a) (b)

(c) (d)






(a) (b)

(c) (d)


Pres

sure

loss

(Pa

m)

060 070 080 090


2749

2749ms mud

120 rpm

00E + 0

20E + 4

40E + 4

60E + 4

80E + 4

10E + 5

12E + 5

14E + 5

120581 = D1D2

(a)

10

50

90

130

170

210

Cutti

ngs c

once

ntra

tion

()

060 070 080 090

120 rpm


2749

2749ms mud

120581 = D1D2

(b)



1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

0993

0893

0794

0695

0596

0496

0397

0298

0199

0099

0000

0993

0894

0795

0695

0596

0497

0397

0298

0199

0099

0000

0994

0895

0796

0696

0597

0497

0398

0298

0199

0099

0000

0994

0895

0795

0696

0597

0497

0398

0298

0199

0099

0000

0995

0896

0796

0697

0597

0498

0398

0299

0199

0100

0000

0999

0899

0799

0699

0599

0499

0400

0300

0200

0100

0000

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

0998

0898

0798

0699

0599

0499

0399

0299

0200

0100

0000



1643

1310

0977

0644

0310

1659

1322

0984

0647

0309

1687

1325

0963

0601

0239

1659

1304

0950

0595

0241

2060

1562

1065

0568

0071

2046

1555

1065

0574

0083

1542

1247

0953

0658

0364

1654

1313

0972

0631

0290

1678

1320

0963

0605

0247

2024

1538

1051

0565

0079

1539

1239

0938

0637

0336

1541

1248

0955

0662

0369

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)


00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R


Widest gap water

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00

02

04

06

08

10

00 01 02 03 04 05

Nor

mal

ised

radi

al d

istan

ce R



Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)






4 Conclusions








Nomenclature



120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

0290

0261

0232

0203

0174

0145

0116

0087

0058

0029

0000

0315

0284

0252

0221

0189

0158

0126

0095

0063

0032

0000

0323

0291

0259

0226

0194

0162

0129

0097

0065

0032

0000

0324

0292

0259

0227

0194

0162

0130

0097

0065

0032

0000

0312

0281

0250

0219

0187

0156

0125

0094

0062

0031

0000

0336

0302

0269

0235

0201

0168

0134

0101

0067

0034

0000

0507

0456

0406

0355

0304

0253

0203

0152

0101

0051

0000

0548

0493

0438

0383

0329

0274

0219

0164

0110

0055

0000

0563

0507

0451

0394

0338

0282

0225

0169

0113

0056

0000

0619

0557

0495

0433

0371

0309

0247

0186

0124

0062

0000

0615

0553

0492

0430

0369

0307

0246

0184

0123

0061

0000

0700

0630

0560

0490

0420

0350

0280

0210

0140

0070

0000



1699

1437

1174

0912

0649

1697

1409

1121

0833

0546

1698

1416

1133

0851

0568

1755

1395

1037

0577

0318

1759

1415

1070

0726

0382

1760

1428

1097

0765

0434

1848

1453

1058

0563

0268

1838

1436

1035

0633

0231

1823

1413

1003

0593

0183

1777

1602

1426

1250

1074

1777

1585

1394

1202

1011

1774

1581

1389

1197

1005

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)


00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R


Widest gap mud

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00 02 04 06 08 10 1200

02

04

06

08

10

Nor

mal

ised

radi

al d

istan

ce R



Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)





119879(119896)



Symbols






References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










120581 = 064

3720

3680

3640

3600

Pres

sure

loss

(Pa

m)


00050004000300020001


176E + 06

066E + 06

034E + 06

(a)

120581 = 070

No of elements =


6200

6160

6120

6080

Pres

sure

loss

(Pa

m)

00050004000300020001

Element size (m)

047E + 06

259E + 06

163E + 06

072E + 06

(b)

120581 = 080


18550

18500

18450

18400

Pres

sure

loss

(Pa

m)

00050004000300020001

Element size (m)

205E + 06

168E + 06

113E + 06

103E + 06

(c)

120581 = 090


129600

129300

129000

128700

128400

Pres

sure

loss

(Pa

m)

00050004000300020001

Element size (m)

260E + 06

217E + 06

215E + 06

210E + 06

(d)






Avgcuttingssize (m)


ROP(ms)

Osgouei [25] 9985 10 0001 80 064 0623 1524ndash27432 000201 27614 000508

Han et al [12] 9985 075 0048 0 070 0 0327ndash0654 0001 2550 000526






29241914

Fluid velocity (ms)

4000

3400

2800

2200

1600

1000

Pres

sure

loss

(Pa

m)


(a)

29241914

Fluid velocity (ms)

190

150

110

70

30


Cutti

ngs c

once

ntra

tion

()

(b)

0706050403

Fluid velocity (ms)

Pres

sure

loss

(Pa

m)


2100

1800

1500

1200

900

(c)










Pres

sure

loss

(Pa

m)


80 rpm

120581 = 064 water120581 = 070 water

120581 = 080 water120581 = 090 water

00E + 0

20E + 4

40E + 4

60E + 4

80E + 4

10E + 5

12E + 5

14E + 5

(a)

10

50

90

130

170

14 19 24 29

Cutti

ngs c

once

ntra

tion

()

Fluid velocity (ms)

80 rpm

120581 = 064 water120581 = 070 water

120581 = 080 water120581 = 090 water

(b)

Pres

sure

loss

(Pa

m)


80 rpm

120581 = 064 mud120581 = 070 mud

120581 = 080 mud120581 = 090 mud

00E + 0

20E + 4

40E + 4

60E + 4

80E + 4

10E + 5

12E + 5

14E + 5

(c)

Cutti

ngs c

once

ntra

tion

()


14

34

54

74

94

80 rpm

120581 = 064 mud120581 = 070 mud

120581 = 080 mud120581 = 090 mud

(d)







(a) (b)

(c) (d)






(a) (b)

(c) (d)


Pres

sure

loss

(Pa

m)

060 070 080 090


2749

2749ms mud

120 rpm

00E + 0

20E + 4

40E + 4

60E + 4

80E + 4

10E + 5

12E + 5

14E + 5

120581 = D1D2

(a)

10

50

90

130

170

210

Cutti

ngs c

once

ntra

tion

()

060 070 080 090

120 rpm


2749

2749ms mud

120581 = D1D2

(b)



1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

0993

0893

0794

0695

0596

0496

0397

0298

0199

0099

0000

0993

0894

0795

0695

0596

0497

0397

0298

0199

0099

0000

0994

0895

0796

0696

0597

0497

0398

0298

0199

0099

0000

0994

0895

0795

0696

0597

0497

0398

0298

0199

0099

0000

0995

0896

0796

0697

0597

0498

0398

0299

0199

0100

0000

0999

0899

0799

0699

0599

0499

0400

0300

0200

0100

0000

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

0998

0898

0798

0699

0599

0499

0399

0299

0200

0100

0000



1643

1310

0977

0644

0310

1659

1322

0984

0647

0309

1687

1325

0963

0601

0239

1659

1304

0950

0595

0241

2060

1562

1065

0568

0071

2046

1555

1065

0574

0083

1542

1247

0953

0658

0364

1654

1313

0972

0631

0290

1678

1320

0963

0605

0247

2024

1538

1051

0565

0079

1539

1239

0938

0637

0336

1541

1248

0955

0662

0369

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)


00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R


Widest gap water

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00

02

04

06

08

10

00 01 02 03 04 05

Nor

mal

ised

radi

al d

istan

ce R



Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)






4 Conclusions








Nomenclature



120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

0290

0261

0232

0203

0174

0145

0116

0087

0058

0029

0000

0315

0284

0252

0221

0189

0158

0126

0095

0063

0032

0000

0323

0291

0259

0226

0194

0162

0129

0097

0065

0032

0000

0324

0292

0259

0227

0194

0162

0130

0097

0065

0032

0000

0312

0281

0250

0219

0187

0156

0125

0094

0062

0031

0000

0336

0302

0269

0235

0201

0168

0134

0101

0067

0034

0000

0507

0456

0406

0355

0304

0253

0203

0152

0101

0051

0000

0548

0493

0438

0383

0329

0274

0219

0164

0110

0055

0000

0563

0507

0451

0394

0338

0282

0225

0169

0113

0056

0000

0619

0557

0495

0433

0371

0309

0247

0186

0124

0062

0000

0615

0553

0492

0430

0369

0307

0246

0184

0123

0061

0000

0700

0630

0560

0490

0420

0350

0280

0210

0140

0070

0000



1699

1437

1174

0912

0649

1697

1409

1121

0833

0546

1698

1416

1133

0851

0568

1755

1395

1037

0577

0318

1759

1415

1070

0726

0382

1760

1428

1097

0765

0434

1848

1453

1058

0563

0268

1838

1436

1035

0633

0231

1823

1413

1003

0593

0183

1777

1602

1426

1250

1074

1777

1585

1394

1202

1011

1774

1581

1389

1197

1005

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)


00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R


Widest gap mud

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00 02 04 06 08 10 1200

02

04

06

08

10

Nor

mal

ised

radi

al d

istan

ce R



Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)





119879(119896)



Symbols






References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










29241914

Fluid velocity (ms)

4000

3400

2800

2200

1600

1000

Pres

sure

loss

(Pa

m)


(a)

29241914

Fluid velocity (ms)

190

150

110

70

30


Cutti

ngs c

once

ntra

tion

()

(b)

0706050403

Fluid velocity (ms)

Pres

sure

loss

(Pa

m)


2100

1800

1500

1200

900

(c)










Pres

sure

loss

(Pa

m)


80 rpm

120581 = 064 water120581 = 070 water

120581 = 080 water120581 = 090 water

00E + 0

20E + 4

40E + 4

60E + 4

80E + 4

10E + 5

12E + 5

14E + 5

(a)

10

50

90

130

170

14 19 24 29

Cutti

ngs c

once

ntra

tion

()

Fluid velocity (ms)

80 rpm

120581 = 064 water120581 = 070 water

120581 = 080 water120581 = 090 water

(b)

Pres

sure

loss

(Pa

m)


80 rpm

120581 = 064 mud120581 = 070 mud

120581 = 080 mud120581 = 090 mud

00E + 0

20E + 4

40E + 4

60E + 4

80E + 4

10E + 5

12E + 5

14E + 5

(c)

Cutti

ngs c

once

ntra

tion

()


14

34

54

74

94

80 rpm

120581 = 064 mud120581 = 070 mud

120581 = 080 mud120581 = 090 mud

(d)







(a) (b)

(c) (d)






(a) (b)

(c) (d)


Pres

sure

loss

(Pa

m)

060 070 080 090


2749

2749ms mud

120 rpm

00E + 0

20E + 4

40E + 4

60E + 4

80E + 4

10E + 5

12E + 5

14E + 5

120581 = D1D2

(a)

10

50

90

130

170

210

Cutti

ngs c

once

ntra

tion

()

060 070 080 090

120 rpm


2749

2749ms mud

120581 = D1D2

(b)



1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

0993

0893

0794

0695

0596

0496

0397

0298

0199

0099

0000

0993

0894

0795

0695

0596

0497

0397

0298

0199

0099

0000

0994

0895

0796

0696

0597

0497

0398

0298

0199

0099

0000

0994

0895

0795

0696

0597

0497

0398

0298

0199

0099

0000

0995

0896

0796

0697

0597

0498

0398

0299

0199

0100

0000

0999

0899

0799

0699

0599

0499

0400

0300

0200

0100

0000

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

0998

0898

0798

0699

0599

0499

0399

0299

0200

0100

0000



1643

1310

0977

0644

0310

1659

1322

0984

0647

0309

1687

1325

0963

0601

0239

1659

1304

0950

0595

0241

2060

1562

1065

0568

0071

2046

1555

1065

0574

0083

1542

1247

0953

0658

0364

1654

1313

0972

0631

0290

1678

1320

0963

0605

0247

2024

1538

1051

0565

0079

1539

1239

0938

0637

0336

1541

1248

0955

0662

0369

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)


00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R


Widest gap water

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00

02

04

06

08

10

00 01 02 03 04 05

Nor

mal

ised

radi

al d

istan

ce R



Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)






4 Conclusions








Nomenclature



120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

0290

0261

0232

0203

0174

0145

0116

0087

0058

0029

0000

0315

0284

0252

0221

0189

0158

0126

0095

0063

0032

0000

0323

0291

0259

0226

0194

0162

0129

0097

0065

0032

0000

0324

0292

0259

0227

0194

0162

0130

0097

0065

0032

0000

0312

0281

0250

0219

0187

0156

0125

0094

0062

0031

0000

0336

0302

0269

0235

0201

0168

0134

0101

0067

0034

0000

0507

0456

0406

0355

0304

0253

0203

0152

0101

0051

0000

0548

0493

0438

0383

0329

0274

0219

0164

0110

0055

0000

0563

0507

0451

0394

0338

0282

0225

0169

0113

0056

0000

0619

0557

0495

0433

0371

0309

0247

0186

0124

0062

0000

0615

0553

0492

0430

0369

0307

0246

0184

0123

0061

0000

0700

0630

0560

0490

0420

0350

0280

0210

0140

0070

0000



1699

1437

1174

0912

0649

1697

1409

1121

0833

0546

1698

1416

1133

0851

0568

1755

1395

1037

0577

0318

1759

1415

1070

0726

0382

1760

1428

1097

0765

0434

1848

1453

1058

0563

0268

1838

1436

1035

0633

0231

1823

1413

1003

0593

0183

1777

1602

1426

1250

1074

1777

1585

1394

1202

1011

1774

1581

1389

1197

1005

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)


00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R


Widest gap mud

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00 02 04 06 08 10 1200

02

04

06

08

10

Nor

mal

ised

radi

al d

istan

ce R



Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)





119879(119896)



Symbols






References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Pres

sure

loss

(Pa

m)


80 rpm

120581 = 064 water120581 = 070 water

120581 = 080 water120581 = 090 water

00E + 0

20E + 4

40E + 4

60E + 4

80E + 4

10E + 5

12E + 5

14E + 5

(a)

10

50

90

130

170

14 19 24 29

Cutti

ngs c

once

ntra

tion

()

Fluid velocity (ms)

80 rpm

120581 = 064 water120581 = 070 water

120581 = 080 water120581 = 090 water

(b)

Pres

sure

loss

(Pa

m)


80 rpm

120581 = 064 mud120581 = 070 mud

120581 = 080 mud120581 = 090 mud

00E + 0

20E + 4

40E + 4

60E + 4

80E + 4

10E + 5

12E + 5

14E + 5

(c)

Cutti

ngs c

once

ntra

tion

()


14

34

54

74

94

80 rpm

120581 = 064 mud120581 = 070 mud

120581 = 080 mud120581 = 090 mud

(d)







(a) (b)

(c) (d)






(a) (b)

(c) (d)


Pres

sure

loss

(Pa

m)

060 070 080 090


2749

2749ms mud

120 rpm

00E + 0

20E + 4

40E + 4

60E + 4

80E + 4

10E + 5

12E + 5

14E + 5

120581 = D1D2

(a)

10

50

90

130

170

210

Cutti

ngs c

once

ntra

tion

()

060 070 080 090

120 rpm


2749

2749ms mud

120581 = D1D2

(b)



1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

0993

0893

0794

0695

0596

0496

0397

0298

0199

0099

0000

0993

0894

0795

0695

0596

0497

0397

0298

0199

0099

0000

0994

0895

0796

0696

0597

0497

0398

0298

0199

0099

0000

0994

0895

0795

0696

0597

0497

0398

0298

0199

0099

0000

0995

0896

0796

0697

0597

0498

0398

0299

0199

0100

0000

0999

0899

0799

0699

0599

0499

0400

0300

0200

0100

0000

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

0998

0898

0798

0699

0599

0499

0399

0299

0200

0100

0000



1643

1310

0977

0644

0310

1659

1322

0984

0647

0309

1687

1325

0963

0601

0239

1659

1304

0950

0595

0241

2060

1562

1065

0568

0071

2046

1555

1065

0574

0083

1542

1247

0953

0658

0364

1654

1313

0972

0631

0290

1678

1320

0963

0605

0247

2024

1538

1051

0565

0079

1539

1239

0938

0637

0336

1541

1248

0955

0662

0369

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)


00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R


Widest gap water

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00

02

04

06

08

10

00 01 02 03 04 05

Nor

mal

ised

radi

al d

istan

ce R



Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)






4 Conclusions








Nomenclature



120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

0290

0261

0232

0203

0174

0145

0116

0087

0058

0029

0000

0315

0284

0252

0221

0189

0158

0126

0095

0063

0032

0000

0323

0291

0259

0226

0194

0162

0129

0097

0065

0032

0000

0324

0292

0259

0227

0194

0162

0130

0097

0065

0032

0000

0312

0281

0250

0219

0187

0156

0125

0094

0062

0031

0000

0336

0302

0269

0235

0201

0168

0134

0101

0067

0034

0000

0507

0456

0406

0355

0304

0253

0203

0152

0101

0051

0000

0548

0493

0438

0383

0329

0274

0219

0164

0110

0055

0000

0563

0507

0451

0394

0338

0282

0225

0169

0113

0056

0000

0619

0557

0495

0433

0371

0309

0247

0186

0124

0062

0000

0615

0553

0492

0430

0369

0307

0246

0184

0123

0061

0000

0700

0630

0560

0490

0420

0350

0280

0210

0140

0070

0000



1699

1437

1174

0912

0649

1697

1409

1121

0833

0546

1698

1416

1133

0851

0568

1755

1395

1037

0577

0318

1759

1415

1070

0726

0382

1760

1428

1097

0765

0434

1848

1453

1058

0563

0268

1838

1436

1035

0633

0231

1823

1413

1003

0593

0183

1777

1602

1426

1250

1074

1777

1585

1394

1202

1011

1774

1581

1389

1197

1005

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)


00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R


Widest gap mud

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00 02 04 06 08 10 1200

02

04

06

08

10

Nor

mal

ised

radi

al d

istan

ce R



Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)





119879(119896)



Symbols






References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)

(c) (d)






(a) (b)

(c) (d)


Pres

sure

loss

(Pa

m)

060 070 080 090


2749

2749ms mud

120 rpm

00E + 0

20E + 4

40E + 4

60E + 4

80E + 4

10E + 5

12E + 5

14E + 5

120581 = D1D2

(a)

10

50

90

130

170

210

Cutti

ngs c

once

ntra

tion

()

060 070 080 090

120 rpm


2749

2749ms mud

120581 = D1D2

(b)



1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

0993

0893

0794

0695

0596

0496

0397

0298

0199

0099

0000

0993

0894

0795

0695

0596

0497

0397

0298

0199

0099

0000

0994

0895

0796

0696

0597

0497

0398

0298

0199

0099

0000

0994

0895

0795

0696

0597

0497

0398

0298

0199

0099

0000

0995

0896

0796

0697

0597

0498

0398

0299

0199

0100

0000

0999

0899

0799

0699

0599

0499

0400

0300

0200

0100

0000

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

0998

0898

0798

0699

0599

0499

0399

0299

0200

0100

0000



1643

1310

0977

0644

0310

1659

1322

0984

0647

0309

1687

1325

0963

0601

0239

1659

1304

0950

0595

0241

2060

1562

1065

0568

0071

2046

1555

1065

0574

0083

1542

1247

0953

0658

0364

1654

1313

0972

0631

0290

1678

1320

0963

0605

0247

2024

1538

1051

0565

0079

1539

1239

0938

0637

0336

1541

1248

0955

0662

0369

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)


00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R


Widest gap water

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00

02

04

06

08

10

00 01 02 03 04 05

Nor

mal

ised

radi

al d

istan

ce R



Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)






4 Conclusions








Nomenclature



120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

0290

0261

0232

0203

0174

0145

0116

0087

0058

0029

0000

0315

0284

0252

0221

0189

0158

0126

0095

0063

0032

0000

0323

0291

0259

0226

0194

0162

0129

0097

0065

0032

0000

0324

0292

0259

0227

0194

0162

0130

0097

0065

0032

0000

0312

0281

0250

0219

0187

0156

0125

0094

0062

0031

0000

0336

0302

0269

0235

0201

0168

0134

0101

0067

0034

0000

0507

0456

0406

0355

0304

0253

0203

0152

0101

0051

0000

0548

0493

0438

0383

0329

0274

0219

0164

0110

0055

0000

0563

0507

0451

0394

0338

0282

0225

0169

0113

0056

0000

0619

0557

0495

0433

0371

0309

0247

0186

0124

0062

0000

0615

0553

0492

0430

0369

0307

0246

0184

0123

0061

0000

0700

0630

0560

0490

0420

0350

0280

0210

0140

0070

0000



1699

1437

1174

0912

0649

1697

1409

1121

0833

0546

1698

1416

1133

0851

0568

1755

1395

1037

0577

0318

1759

1415

1070

0726

0382

1760

1428

1097

0765

0434

1848

1453

1058

0563

0268

1838

1436

1035

0633

0231

1823

1413

1003

0593

0183

1777

1602

1426

1250

1074

1777

1585

1394

1202

1011

1774

1581

1389

1197

1005

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)


00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R


Widest gap mud

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00 02 04 06 08 10 1200

02

04

06

08

10

Nor

mal

ised

radi

al d

istan

ce R



Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)





119879(119896)



Symbols






References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)

(c) (d)


Pres

sure

loss

(Pa

m)

060 070 080 090


2749

2749ms mud

120 rpm

00E + 0

20E + 4

40E + 4

60E + 4

80E + 4

10E + 5

12E + 5

14E + 5

120581 = D1D2

(a)

10

50

90

130

170

210

Cutti

ngs c

once

ntra

tion

()

060 070 080 090

120 rpm


2749

2749ms mud

120581 = D1D2

(b)



1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

0993

0893

0794

0695

0596

0496

0397

0298

0199

0099

0000

0993

0894

0795

0695

0596

0497

0397

0298

0199

0099

0000

0994

0895

0796

0696

0597

0497

0398

0298

0199

0099

0000

0994

0895

0795

0696

0597

0497

0398

0298

0199

0099

0000

0995

0896

0796

0697

0597

0498

0398

0299

0199

0100

0000

0999

0899

0799

0699

0599

0499

0400

0300

0200

0100

0000

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

0998

0898

0798

0699

0599

0499

0399

0299

0200

0100

0000



1643

1310

0977

0644

0310

1659

1322

0984

0647

0309

1687

1325

0963

0601

0239

1659

1304

0950

0595

0241

2060

1562

1065

0568

0071

2046

1555

1065

0574

0083

1542

1247

0953

0658

0364

1654

1313

0972

0631

0290

1678

1320

0963

0605

0247

2024

1538

1051

0565

0079

1539

1239

0938

0637

0336

1541

1248

0955

0662

0369

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)


00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R


Widest gap water

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00

02

04

06

08

10

00 01 02 03 04 05

Nor

mal

ised

radi

al d

istan

ce R



Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)






4 Conclusions








Nomenclature



120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

0290

0261

0232

0203

0174

0145

0116

0087

0058

0029

0000

0315

0284

0252

0221

0189

0158

0126

0095

0063

0032

0000

0323

0291

0259

0226

0194

0162

0129

0097

0065

0032

0000

0324

0292

0259

0227

0194

0162

0130

0097

0065

0032

0000

0312

0281

0250

0219

0187

0156

0125

0094

0062

0031

0000

0336

0302

0269

0235

0201

0168

0134

0101

0067

0034

0000

0507

0456

0406

0355

0304

0253

0203

0152

0101

0051

0000

0548

0493

0438

0383

0329

0274

0219

0164

0110

0055

0000

0563

0507

0451

0394

0338

0282

0225

0169

0113

0056

0000

0619

0557

0495

0433

0371

0309

0247

0186

0124

0062

0000

0615

0553

0492

0430

0369

0307

0246

0184

0123

0061

0000

0700

0630

0560

0490

0420

0350

0280

0210

0140

0070

0000



1699

1437

1174

0912

0649

1697

1409

1121

0833

0546

1698

1416

1133

0851

0568

1755

1395

1037

0577

0318

1759

1415

1070

0726

0382

1760

1428

1097

0765

0434

1848

1453

1058

0563

0268

1838

1436

1035

0633

0231

1823

1413

1003

0593

0183

1777

1602

1426

1250

1074

1777

1585

1394

1202

1011

1774

1581

1389

1197

1005

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)


00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R


Widest gap mud

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00 02 04 06 08 10 1200

02

04

06

08

10

Nor

mal

ised

radi

al d

istan

ce R



Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)





119879(119896)



Symbols






References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

1000

0900

0800

0700

0600

0500

0400

0300

0200

0100

0000

0993

0893

0794

0695

0596

0496

0397

0298

0199

0099

0000

0993

0894

0795

0695

0596

0497

0397

0298

0199

0099

0000

0994

0895

0796

0696

0597

0497

0398

0298

0199

0099

0000

0994

0895

0795

0696

0597

0497

0398

0298

0199

0099

0000

0995

0896

0796

0697

0597

0498

0398

0299

0199

0100

0000

0999

0899

0799

0699

0599

0499

0400

0300

0200

0100

0000

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

0998

0898

0798

0699

0599

0499

0399

0299

0200

0100

0000



1643

1310

0977

0644

0310

1659

1322

0984

0647

0309

1687

1325

0963

0601

0239

1659

1304

0950

0595

0241

2060

1562

1065

0568

0071

2046

1555

1065

0574

0083

1542

1247

0953

0658

0364

1654

1313

0972

0631

0290

1678

1320

0963

0605

0247

2024

1538

1051

0565

0079

1539

1239

0938

0637

0336

1541

1248

0955

0662

0369

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)


00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R


Widest gap water

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00

02

04

06

08

10

00 01 02 03 04 05

Nor

mal

ised

radi

al d

istan

ce R



Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)






4 Conclusions








Nomenclature



120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

0290

0261

0232

0203

0174

0145

0116

0087

0058

0029

0000

0315

0284

0252

0221

0189

0158

0126

0095

0063

0032

0000

0323

0291

0259

0226

0194

0162

0129

0097

0065

0032

0000

0324

0292

0259

0227

0194

0162

0130

0097

0065

0032

0000

0312

0281

0250

0219

0187

0156

0125

0094

0062

0031

0000

0336

0302

0269

0235

0201

0168

0134

0101

0067

0034

0000

0507

0456

0406

0355

0304

0253

0203

0152

0101

0051

0000

0548

0493

0438

0383

0329

0274

0219

0164

0110

0055

0000

0563

0507

0451

0394

0338

0282

0225

0169

0113

0056

0000

0619

0557

0495

0433

0371

0309

0247

0186

0124

0062

0000

0615

0553

0492

0430

0369

0307

0246

0184

0123

0061

0000

0700

0630

0560

0490

0420

0350

0280

0210

0140

0070

0000



1699

1437

1174

0912

0649

1697

1409

1121

0833

0546

1698

1416

1133

0851

0568

1755

1395

1037

0577

0318

1759

1415

1070

0726

0382

1760

1428

1097

0765

0434

1848

1453

1058

0563

0268

1838

1436

1035

0633

0231

1823

1413

1003

0593

0183

1777

1602

1426

1250

1074

1777

1585

1394

1202

1011

1774

1581

1389

1197

1005

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)


00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R


Widest gap mud

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00 02 04 06 08 10 1200

02

04

06

08

10

Nor

mal

ised

radi

al d

istan

ce R



Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)





119879(119896)



Symbols






References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1643

1310

0977

0644

0310

1659

1322

0984

0647

0309

1687

1325

0963

0601

0239

1659

1304

0950

0595

0241

2060

1562

1065

0568

0071

2046

1555

1065

0574

0083

1542

1247

0953

0658

0364

1654

1313

0972

0631

0290

1678

1320

0963

0605

0247

2024

1538

1051

0565

0079

1539

1239

0938

0637

0336

1541

1248

0955

0662

0369

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)


00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R


Widest gap water

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00

02

04

06

08

10

00 01 02 03 04 05

Nor

mal

ised

radi

al d

istan

ce R



Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)






4 Conclusions








Nomenclature



120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

0290

0261

0232

0203

0174

0145

0116

0087

0058

0029

0000

0315

0284

0252

0221

0189

0158

0126

0095

0063

0032

0000

0323

0291

0259

0226

0194

0162

0129

0097

0065

0032

0000

0324

0292

0259

0227

0194

0162

0130

0097

0065

0032

0000

0312

0281

0250

0219

0187

0156

0125

0094

0062

0031

0000

0336

0302

0269

0235

0201

0168

0134

0101

0067

0034

0000

0507

0456

0406

0355

0304

0253

0203

0152

0101

0051

0000

0548

0493

0438

0383

0329

0274

0219

0164

0110

0055

0000

0563

0507

0451

0394

0338

0282

0225

0169

0113

0056

0000

0619

0557

0495

0433

0371

0309

0247

0186

0124

0062

0000

0615

0553

0492

0430

0369

0307

0246

0184

0123

0061

0000

0700

0630

0560

0490

0420

0350

0280

0210

0140

0070

0000



1699

1437

1174

0912

0649

1697

1409

1121

0833

0546

1698

1416

1133

0851

0568

1755

1395

1037

0577

0318

1759

1415

1070

0726

0382

1760

1428

1097

0765

0434

1848

1453

1058

0563

0268

1838

1436

1035

0633

0231

1823

1413

1003

0593

0183

1777

1602

1426

1250

1074

1777

1585

1394

1202

1011

1774

1581

1389

1197

1005

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)


00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R


Widest gap mud

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00 02 04 06 08 10 1200

02

04

06

08

10

Nor

mal

ised

radi

al d

istan

ce R



Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)





119879(119896)



Symbols






References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













4 Conclusions








Nomenclature



120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

0290

0261

0232

0203

0174

0145

0116

0087

0058

0029

0000

0315

0284

0252

0221

0189

0158

0126

0095

0063

0032

0000

0323

0291

0259

0226

0194

0162

0129

0097

0065

0032

0000

0324

0292

0259

0227

0194

0162

0130

0097

0065

0032

0000

0312

0281

0250

0219

0187

0156

0125

0094

0062

0031

0000

0336

0302

0269

0235

0201

0168

0134

0101

0067

0034

0000

0507

0456

0406

0355

0304

0253

0203

0152

0101

0051

0000

0548

0493

0438

0383

0329

0274

0219

0164

0110

0055

0000

0563

0507

0451

0394

0338

0282

0225

0169

0113

0056

0000

0619

0557

0495

0433

0371

0309

0247

0186

0124

0062

0000

0615

0553

0492

0430

0369

0307

0246

0184

0123

0061

0000

0700

0630

0560

0490

0420

0350

0280

0210

0140

0070

0000



1699

1437

1174

0912

0649

1697

1409

1121

0833

0546

1698

1416

1133

0851

0568

1755

1395

1037

0577

0318

1759

1415

1070

0726

0382

1760

1428

1097

0765

0434

1848

1453

1058

0563

0268

1838

1436

1035

0633

0231

1823

1413

1003

0593

0183

1777

1602

1426

1250

1074

1777

1585

1394

1202

1011

1774

1581

1389

1197

1005

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)


00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R


Widest gap mud

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00 02 04 06 08 10 1200

02

04

06

08

10

Nor

mal

ised

radi

al d

istan

ce R



Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)





119879(119896)



Symbols






References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

0290

0261

0232

0203

0174

0145

0116

0087

0058

0029

0000

0315

0284

0252

0221

0189

0158

0126

0095

0063

0032

0000

0323

0291

0259

0226

0194

0162

0129

0097

0065

0032

0000

0324

0292

0259

0227

0194

0162

0130

0097

0065

0032

0000

0312

0281

0250

0219

0187

0156

0125

0094

0062

0031

0000

0336

0302

0269

0235

0201

0168

0134

0101

0067

0034

0000

0507

0456

0406

0355

0304

0253

0203

0152

0101

0051

0000

0548

0493

0438

0383

0329

0274

0219

0164

0110

0055

0000

0563

0507

0451

0394

0338

0282

0225

0169

0113

0056

0000

0619

0557

0495

0433

0371

0309

0247

0186

0124

0062

0000

0615

0553

0492

0430

0369

0307

0246

0184

0123

0061

0000

0700

0630

0560

0490

0420

0350

0280

0210

0140

0070

0000



1699

1437

1174

0912

0649

1697

1409

1121

0833

0546

1698

1416

1133

0851

0568

1755

1395

1037

0577

0318

1759

1415

1070

0726

0382

1760

1428

1097

0765

0434

1848

1453

1058

0563

0268

1838

1436

1035

0633

0231

1823

1413

1003

0593

0183

1777

1602

1426

1250

1074

1777

1585

1394

1202

1011

1774

1581

1389

1197

1005

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)


00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R


Widest gap mud

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00 02 04 06 08 10 1200

02

04

06

08

10

Nor

mal

ised

radi

al d

istan

ce R



Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)





119879(119896)



Symbols






References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1699

1437

1174

0912

0649

1697

1409

1121

0833

0546

1698

1416

1133

0851

0568

1755

1395

1037

0577

0318

1759

1415

1070

0726

0382

1760

1428

1097

0765

0434

1848

1453

1058

0563

0268

1838

1436

1035

0633

0231

1823

1413

1003

0593

0183

1777

1602

1426

1250

1074

1777

1585

1394

1202

1011

1774

1581

1389

1197

1005

120581 = 064

120 rpm120581 = 064120581 = 064

80 rpm

120581 = 070120581 = 070120581 = 070

0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120 rpm80 rpm0 rpm

120581 = 080120581 = 080120581 = 080

120581 = 090120581 = 090120581 = 090

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

Y

XZ

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)

(ms

)(m

s)


00

02

04

06

08

10

00 04 08 12 16 20

Nor

mal

ised

radi

al d

istan

ce R


Widest gap mud

Outer pipe

Inner pipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(a)

00 02 04 06 08 10 1200

02

04

06

08

10

Nor

mal

ised

radi

al d

istan

ce R



Outerpipe

120581 = 064

120581 = 070

120581 = 080

120581 = 090

(b)





119879(119896)



Symbols






References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119879(119896)



Symbols






References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article CFD Method for Predicting Annular ...

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