minimum transport velocity

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Copyright 2003, Society of Petroleum Engineers Inc.

This paper was prepared for presentation at the SPE/ICoTA Coiled Tubing Conference held inHouston, Texas, U.S.A., 8–9 April 2003.

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AbstractCoiled Tubing Drilling, grown significantly in recent years, isnormally associated with high angle to horizontal andextended reach wells. It is, however, in these applications thathole problems become more troublesome because ofinefficient cuttings removal. Among the many parameters

affecting efficient cuttings transport in Coiled Tubing Drillingare pump rates, well dimensions, fluid properties, solids sizes,solids loading and hole inclination. Several attempts have beenmade to determine the optimum operating range of these parameters but complete and satisfactory models have yet to be developed.

The purpose of this paper is to provide a critical review of thestate of the art on efficient cuttings transport during CoiledTubing Drilling, present the critical parameters involved,establish their range according to what is observed in practiceand propose a different approach for predicting the minimum

suspension velocity. Finally the laboratory system that hasalready been set up is presented. Its primary purpose is toallow the gathering of good quality data, missing from theliterature, which could enhance our understanding of the flowof solid – liquid mixtures in annuli.

IntroductionThe advantages of Coiled Tubing Drilling (CTD) arenumerous and have been indicated and proved in practice by alarge number of investigators. A significant drawback is thedifficulty for efficient cuttings transport primarily because the pipe is not rotated.

Cuttings transport during drilling (either conventionally orwith Coiled Tubing) has a major impact on the economics of

the drilling process. Inefficient hole cleaning from the cuttingscan lead to numerous problems such as stuck pipe, reduced

weight on bit leading to reduced rate of penetration (ROP),transient hole blockage leading to lost circulation conditions,extra pipe wear, extra cost due to additives in the drilling fluidand wasted time by wiper tripping.

These many problems have prompted significant research into

cuttings transport during the past 50 years. Excellent reviewson the subject have been given in the past1-3. Pilehvari et al.1-2 state that fluid velocities should be maximized to achieveturbulent flow and mud rheology should be optimized to

enhance turbulence in inclined / horizontal sections of thewellbore. Turbulent flow of non-Newtonian fluids needs muchmore work and should be extended to include pipe rotationand dynamics for conventional drilling. Future work shouldfocus on getting more experimental data, validation of fluidmodels, cuttings transport mechanistic models verified by

comprehensive experimental data. Azar & Sanchez3 conclude

that a combination of appropriate theoretical analyses(complete free body diagrams, accurate rheological models,

accurate annular flow models), experimental studies (extensivetesting concentrating on individual variables or phenomena),statistical modeling (rheological models, unstable cuttings

transport conditions), and high – tech research facilities(accurate measurement of pertinent variables, analysis ofvideo to develop flow pattern maps) will be necessary forfurther progress.

While many cuttings transport problems were addressed quite

successfully for conventional drilling in vertical, inclined andhorizontal wells in the past, the increase in activity of CTD hascalled for renewed interest into cuttings transport problems inhorizontal and highly inclined annular geometries with no

rotation of the inner pipe.

In recent years there have been several theoretical, semi-theoretical and experimental investigations for assessing theimportant parameters for efficient cuttings transport in highlyinclined and horizontal geometries during CTD4-10 orconventional drilling but not taking into account the rotation ofthe inner pipe11-15.

Despite these efforts, there is still lack of good quality published data against which models can be compared with.Many models use data for validation not applicable to thesituation at hand (e.g. using data with inner pipe rotation4,12) or

even no data at all13

, or compare their results with results of

SPE 81746

Flow Patterns and Minimum Suspension Velocity for Efficient Cuttings Transport inHorizontal and Deviated Wells in Coiled-Tubing DrillingV. C. Kelessidis, SPE, G. E. Mpandelis, Technical University of Crete, Greece



2 V. C. Kelessidis, G. E. Mpandelis SPE 81746

other models11. Some authors present the data together withtheir own theoretical analysis6-8 but they give very limitedinformation on experimental parameters (e.g. rheology of

fluids, cuttings concentrations, etc.).

The approach taken by many investigators on modelingcuttings transport for highly inclined and horizontal annuli

(with no inner pipe rotation) is that of two or three layermodel. The basic model proposed for annuli4,6,9,11-15 is adopted

from the one proposed for solids transport in pipes16

, laterextended by the same authors17-19.

The steady state models are based on mass balance equationsfor solids and liquid plus momentum balance equations for thetwo or three layers resulting in a system of coupled algebraic

equations. Closure relationships that describe the interactionof the two phases are needed in order to solve these equations

and these are taken from published correlations.

Flow Patterns

During the flow of solid - liquid mixtures in horizontalconduits, the liquid and solid phases may distribute in a

number of geometrical configurations depending on flowrates, conduit shape and size, fluid and solid properties andinclination. Natural groupings, or flow patterns, exist withinwhich the basic characteristics of the two-phase mixtureremain the same.

The main parameters determining the distribution of solids inthe liquid, i.e. the flow patterns, are the liquid velocity, thesolids loading and the properties of liquid and solids (rheologyand density of liquid, density, diameter & sphericity of solids).

Experimental observations of solid – liquid flow in horizontal pipes and annuli, even at low solids concentrations, suggestthe following flow patterns (depicted in Figure 1), in thedirection of decreasing flow rate (or velocity)

4,7,12,16,19-21.

At high liquid velocities the solids may be uniformlydistributed in the liquid and normally the correct assumption is

made that there is no slip between the two phases11,12,14,16

, i.e.the velocity of the solids is equal to the velocity of the liquid.

This flow pattern is normally observed for fairly fine solids,less than 1mm in diameter, not normally occurring duringdrilling applications. This flow pattern is called the fully

suspended symmetric flow pattern (Fig. 1a).

As the liquid flow rate is reduced there is a tendency for the

solids to flow near the bottom of the pipe (or outer pipe of theannulus), but still suspended, thus creating an asymmetricsolids concentration. This is called the asymmetric flow

pattern with the solids still moving with the liquid (Fig. 1b).

A further reduction in the liquid flow rate results in the

deposition of solid particles on the bottom of the pipe. Thesolids start forming a bed, which is moving in the direction ofthe flow, while there may be some non uniformly distributedsolids in the liquid layer above. This is the moving bed flow

pattern and the velocity below which this is happening has

been given different names like, limit deposit velocity,suspension velocity, critical velocity (Fig. 1c).

Further reduction in liquid velocity results in more and moresolids deposited resulting in three layers (Fig. 1d). A bed of

solids that is not moving, forming a stationary bed, a moving bed of solids on top of the stationary bed and a heterogeneous

liquid – solid mixture above. There is a strong interaction between the heterogeneous solid – liquid mixture and the

moving bed, with solids deposited on the bed and re-entrainedin the heterogeneous solid – liquid mixture. There is a point of

equilibrium where, with the increase in height of the solids bed, the available area for flow of the heterogeneous mixtureis decreased resulting in higher mixture velocities and hencean increase in the erosion of the bed by the mixture.

At even lower liquid velocities the solids pile up in the pipe

(or annulus) and full blockage may occur. Experimentalevidence and theoretical analysis indicate that this may occurat relatively high solids concentration, not encountered during

normal drilling operations. It may occur, however, if cuttingstransport is inefficient resulting in high solids concentration,especially in sections where large cross sectional areas exist

(e.g. in annulus washouts).

It should be stressed that the solids concentration in the liquidis fairly low during normal drilling operations, and for CTDrarely exceeds 2 – 4% by volume (Appendix A).

Two Layer ModelingThe two layer model (moving bed & clear liquid in laminarflow) proposed by Gavignet and Sobey22 made a basicadvance but data did not conform to model predictions. The

model was extended4,13,21,23 to account for suspended solids inthe liquid layer and covered the flow patterns described above.This resulted in a system of four algebraic equations and oneintegral equation for turbulent diffusion of solids.

Following these approaches, for steady state conditions and forhorizontal concentric annulus, the two layer model is as

follows (Figure 2):

There is a layer of liquid on the top side of the annuluscontaining suspended solids and a layer of solids on the bottom of the outer pipe which may be moving, albeit at a verylow velocity.

Mass balance for the solids gives,

M M M B B B s s s C AU C AU C AU =+ (1)

And mass balance for the liquid gives,

)1()1()1( M M M B B B s s s C AU C AU C AU −=−+− (2)

The momentum equations for each of the two layers are

s s s i i

dp A S S

dz τ τ = − − (3)



SPE 81746 Flow Patterns and Minimum Suspension Velocity for Efficient Cuttings Transport in Horizontal and Deviated Wells in Coiled Tubing Drilling 3

B B B B i i

dp F S S

dz τ τ = − − + (4)

For the mean concentration of the solids in the liquid layer,

sC , the turbulent diffusion equation is solved (Appendix B)

yielding

( )iioo s

B s Int d Int d

AC C **2

22 −= (5)

where,

∫

−−=

2/2)(cos

2

sinexp

π

θ

γ γ γ

o

o p

od ood

ho

D

d u

o Int (5a)

∫

−−=

2/2)(cos

)/(2

sinexp

π

θ

γ γ γ

i

id iod

h

id od

i

D

d u

i Int o p (5b)

There are 5 equations and 5 unknowns, namely, h, U s , C s , U B ,dp/dz. For the solution we need closure relations for the shear

stresses, the friction force, particle settling velocity u p anddispersion coefficient, D (Appendix B). The shear stresses areestimated by:

2

2

1 s s s s U f ρ τ = (6)

( )2

2

1 B s sii U U f −= ρ τ (7)

2

2

1 B B B B U f ρ τ = (8)

Walton4 expresses the friction factors in a standard way, but

no indication is given whether the ones he uses are for Newtonian or non-Newtonian fluids (presumed Newtonian).Doron et al.16 use the following relationships valid for Newtonian fluids, for turbulent flow,

2.0Re,

046.0

s

s N

f = (9)

and for laminar flow

Re,

16 B

B

f

N

= (10)

with

Re, s s hs

s

s

U D N

ρ

µ = (11)

Re, B B hB

B

B

U D N

ρ

µ = (12)

)1( s s p s C C −+= ρ ρ ρ (13)

)1( B B p B C C −+= ρ ρ ρ (14)

µ µ µ == s B (15)

i s

shs

S S

A D

+=

4 (16)

B

B

hB S

A D

4= (17)

Martins and Santana13 also use the Fanning friction factor andfrom experimental work 24 they use, for turbulent flow,

7.0Re,645.000454.0 −+= gn s N f (18)

with

( ) n

nhs

n s

gn

n

n K

DU N

+=

−

132

8 2

Re,

ρ (19)

For the interfacial friction factor, i f , most researchers use the

expression proposed by Televantos et al.25 ,

+−=

i s

hs p

i f N

Dd

f 2

51.2

7.3

/ln86.0

2

1

Re,

(20)

which assumes an interfacial roughness equal to a particlediameter, d p. Accounting for particle collisions with the bedand for entrainement and deposition of particles, which tend to

increase i f , Televantos et al.25

use the factor (2* i f ) instead

of ( i f ) in the above expression (20), which is the Colebrook

formula for Newtonian fluids flowing in rough pipes. And asstated

26 according to the study of Televantos, the magnitude of

i f is not of critical importance in the model.

However, Martins et al.27 found that the value of i f can have a

dramatic impact on the results of the model. By measuring the

bed thickness, they correlated the interfacial friction factor

with various parameters. They got the dependence of i f on

N Re,gn, given by equation (19), the fluid behavior index, n, the

particle diameter, d p, and the hydraulic diameter of thesuspension, Dhs. Their results, however, do not show anysignificant correlation with neither of these parameters, as a

simple inspection of their proposed figures easily reveal. Nevertheless, they proceed and propose a relation such as

( ) ( ) 34539.2360211.207116.1Re, /966368.0

−−= hs p gni Dd n N f (21)

which is also used in their next paper 14

.

B F in equation (4) is the friction force opposing the motion of

the bed of solids. At the point of slip of the bed, B F is equal in

magnitude to the maximum sliding friction force between the

particles and the wall, max F ,




( )

+−===

φ

τ ρ ρ η η

tanmax

ii B B p N B

S A gC F F F (22)

where the first term in the r.h.s. represents the submergedweight of the bed and the second term represents the Bagnoldstresses28-29. Bagnold showed that when a fluid flows over adeposit of solid bed, there exists a normal stress at the

interface of solids - wall associated with the shear stressexerted by the fluid on the solids. However, caution should beexercised, since Bagnold’s experiments were conducted atrelatively high solid concentrations (> 15%

20,26).

Martins and Santana13 used the basic formulation describedabove. They do not reference how they estimate the solids

dispersion coefficient, D , needed in the diffusion equation(5). They presumably use the one proposed elsewhere16,

described in Appendix B. For pu , they refer to a procedure for

non–Newtonian fluids30, but do not give the equations.

Published equations give pu for non–Newtonian31-35

and for

Newtonian liquids16,26,36. Their model predicts that increasingthe flow rate and the density of the liquid are the mosteffective ways to enhance cuttings transport. Rheological

parameters have only a moderate effect, but no comparisonwith experimental data is given. However, in a subsequent

paper 14

they found that the type of rheological model usedinfluenced significantly the predictions. No suggestions,however, is given on the appropriate rheological model,supported by experimental data.

Walton4 also used the above formulation. For pu he used

correlations for Newtonian fluids, as Doron et al.16, while for

D he proposes a slightly different approach, also described inAppendix B. He compares his simulation results, using water,with data taken with inner pipe rotation at 50 RPM

37, hence, as

he states, no quantitative agreement is expected. Thesimulation predicts the trend of the data, however, at high flowrates data show no bed for concentric annulus which isdifferent from his predictions. He produces a flow regime map

and a map that shows how the minimum flow rate forcomplete suspension varies with fluid viscosity and particleconcentration. Fluids of moderate viscosities are moreefficient than low viscosity fluids such as water or highviscosity gels, with optimum viscosity around 20 – 30 cp at170 s-1. Furthermore he predicts that cleanouts in horizontal

and highly deviated wells require pump rates an order ofmagnitude higher than vertical wells.

Kamp and Rivero11

, who made an excellent review of layermodels, use also a two layer model with eccentric annuli. Theyuse mass flux of cuttings per unit interface that are deposited,

dep s,φ , or resuspended, susp s,φ , mass balance equations for

solid, liquid and mixture and momentum equations for theheterogeneous layer and the bed. They use also the diffusion

equation for the concentration in the suspension layer, but

instead of using BC in the solution, they use the average

concentration, sC . The deposition of particles, dep s,φ , is taken

as proportional to C s and U s. The resuspension flux, susp s,φ is

taken as a function of interfacial shear stress, iτ . The settling

velocity, pu , is derived for Newtonian fluids through standard

procedures16,26,36, while some reference is given on the effect

of non-Newtonian fluids. There is no equation given for thesolid dispersion coefficient, D , except referencing appropriatemodeling38, also followed by Doron et al.16 as well as otherwork 39, where, though, no specific equation is given for the prediction of D .

Their results, using as a base case a rather large annulus for

CTD, ind 5.170 = and ind i 0.9= and a flow rate

gpmQ 50= resulting in very low velocity in the annulus

( s ft /092.0 !) and hr ft ROP /50= (hence volumetric

concentration ~ 17%) showed that starting from welldistributed solids at the entrance there is almost immediately bed formation in the annulus. The height of the bed thenremains constant along the flow channel. Similar results arealso derived for the other pertinent parameters. The bed height

decreases as the flow rate is increased but the rate of decreaseis much smaller at higher flow rates, contrary to what isexpected. Results are not very sensitive to mud viscosity, incontrast to experimental and field evidence which show thatturbulence promotes cuttings transport. They compare theirresults with predictions of correlation based models40-42.

Predictions show similar trends but they are far from beingquantitatively close. It is recognized that the modeloverpredicts cuttings transport at a given liquid flow rate.They state the need for good closure terms with respect to particle resuspension and particle settling velocities.

Li and Walker 6 presented results of their experimental studyusing various empirical correlations, devised from their owndata as well as from other investigators. They assume thatcuttings erosion follows logarithmic expression with time.They developed a computer model based on dimensionalanalysis and using these correlations they study the sensitivity

of predictions on various important parameters (includingunderbalanced conditions). Most important variable is theliquid velocity, but in general, no quantitative data is given.They extended their study7 to cover the effects of particlediameter, fluid rheology and eccentricity. They conclude thatfine particles are easier to clean and spherical particles with d p~ 0.03in. pose the greatest difficulty. Fluid rheology plays a

significant role with low viscosity fluids in turbulent flowgiving optimum results for hole cleaning, similar to otherresults

4. Furthermore, the critical velocity for full suspension

is higher for fully eccentric annulus compared to theconcentric annulus. However, the differences observed amongthe operational parameters were not substantial and in addition

they tested only three particle sizes ( ininin 275.0,03.0,006.0 ).

A similar two layer model has also been used forunderbalanced drilling under transient conditions31. Here thetwo phase (gas – liquid) mixture in the suspension layer isconsidered as pseudo–homogeneous with fixed properties.

The authors also consider deposition fluxes, derived from




hindered settling of solids and erosion (or resuspension) fluxesas a function of interfacial shear velocity, similar to otherapproaches11. They allowed slip between the particles and the

fluid both in the suspension layer and the bed and accountedfor the non-Newtonian behavior of the liquid. They use a

correlation for solids settling velocity for non-Newtonianfluids but use hindered settling expression proposed for

Newtonian fluids, as elsewhere16.

Their results (run for water and mud only, without a gas phase), showed that for the fully suspended asymmetric flow

pattern, cuttings velocity matches that of liquid, i.e. there is noslip between the two phases. However, when a bed is formed,then the solids in the suspension move at velocities muchlower (about 50%) of the liquid velocity. Their predictions

compare favorably with their experimental results, except inthe cases of very dilute solid concentrations (less than 0.05%

by volume) because a smooth interface (assumed in the model)did not really existed. Effective transport is achieved whencuttings velocity is greater than zero and they establish a range

of parameters from which they can determine the minimuminlet cuttings concentration for this to be achieved.

Three Layer ModelingThe ‘inadequacies’ in the predictions from the two layermodels when compared to limited data and the extension ofthe two layer to the three layer model for flow of solid – liquidmixtures in pipes17 led to the extension of the two layer modelin annulus to the three layer model9,12.

The development follows that of the two layer modelapproach, with the inclusion of a stationary bed below themoving bed. For a horizontal concentric annulus, the three

layer models, depicted in Figure 3:

The mass balance equations are

M M M mBmBmB s s s C U AC U AC U A =+ (23)

for solids, and

)1()1()1( M M M mBmBmB s s s C U AC U AC U A −=−+−

(24)

for liquid.

For the momentum equations we have, for the suspended

layer,

s s s smB smB

dpS S

dz τ τ = − − (25)

while, for the moving bed layer,

mB mBsB mB mBsB mBsB

mB mB smB smB

dp A F F S

dz

S S

τ

τ τ

= − − −

− +

(26)

and for the stationary bed,

sB mBsB mBsB mBsB sB

dp F S F

dz

τ + + ≤ (27)

where the various stresses and friction forces are shown in Fig.3.

The equation for the stationary bed (27) serves as a conditionto be satisfied whenever a stationary bed is predicted but it is

not part of the solution17

.

The concentration in the suspension layer is derived from thediffusion equation, as for the two layer model, with the

interface now being ( mB ), rather than ( sB ).

The solution to the above equations requires closurerelationships for the shear stresses and the friction forces,which are taken through the use of Reynolds number and

friction factor relationships, as for the two layer modeling.

Nguyen and Rathman12

use the above formulation but avoidusing the diffusion equation. Instead, they predict the

thickness of the moving bed, mBh , based on analysis of

Bagnold forces, as derived by Wilson and Tse

43

φ ρ ρ

τ

tan)( mB p

simB

gU h

−= (28)

where the moving bed velocity, mBU , is predicted from

turbulent boundary layer theory as

v

smBmB

K U

ρ τ /

3

4= (29)

The authors predict full erosion of bed at annular velocity of

s ft U M /8.3≈ for flow of water in a 5 by 1.9 in. annulus,

with particle diameter of 0.25 in., ROP = 50 ft / hrcorresponding to 0.42% solids volumetric concentration at thisvelocity. This compares favorably with other experimentalresults

44-45 who measured minimum transport velocity of

3.3 ft/s for similar conditions. Various runs of the simulatorshowed that liquid density and annulus eccentricity hadsignificant effect. The use of the assumed value of CB = 0.62

(instead of the standard used of 0.52) had minor effect, while alow viscosity bentonite mud showed better cuttings transportcompared to that of water.

Cho et al.9 follow the above three layer formulation but use thediffusion equation (equation 5) and an experimental

expression for the settling velocities of solids through non- Newtonian fluids46

( )2 0.45 / exp(5 )

19.45exp(5 )( )( / ) 0

p p p p

p p

u u d

d

µ ρ φ

φ ρ ρ

+

− ∆ = (30)

with φ p taken as 0.8 for drill cuttings. Hindered settling is alsoconsidered, taken from the correlation developed by Thomas

47

)9.5exp( s ph C uu −= (31)

For the particle dispersion they use the approach of Walton4.

Their base case is a low viscosity bentonite mud, with




7.0=n and 2100/605.0 ft slb K n f = , in a 5 by 1.9 in.

annulus, ρ p = 21.7 ppg, ρ = 9.16 ppg and d p = 0.09 in.

Their results show that for liquid annulus velocities in therange of 1 – 5 ft/s, typical velocities encountered in CTDapplications, a bed of cuttings is formed. At about 2 to 3 ft/s

suspension starts to occur, similar to previous results12

, and thecritical velocity for full suspension is around 4 to 5 ft/s. Themost significant parameter is the annulus liquid velocity. Itshould be of the order of 3.6 to 4.6 ft/s, compared toconventional drilling of 2 to 3 ft/s because both the minimum pressure drop and a minimum height of stationary bed isobtained at these flow rates. There is a slight effect of

rheological parameters. When the moving bed vanishes, themodel does not reduce to a two layer model (as it should do asa limiting case). Instead, a new model covering the two layersis solved. No comparison is made to the predictions versus thatof two layer model to justify the added complexity of the threelayer model.

Discussion on the Layer ModelsCareful analysis of the published results shows that a two orthree layer pattern will form almost immediately, even whenstarting from a homogeneous distribution of solids at theentrance of the annulus. The bottom solids concentration, or

equivalently the height of the bed, are constant at two to threeannulus hydraulic diameters from the entrance11,15!

From the proposed tentative solutions from the variousinvestigators it is evident that the framework for the problemsolution is similar, with main differences whether a two or a

three layer model is used and the closure relationships which

include, among others:• Solid distribution in the heterogeneous liquid - solid layer

• Interfacial friction factor between the heterogeneousliquid layer and the moving bed of solids

• Whether Bagnold stresses are taken into account

• Terminal velocity of solids in Newtonian or non- Newtonian fluids, taking into account the effect of

hindered settling and the effect of walls (normally nottaken into account)

• Fluid friction factors for fluid and walls of annulus,

normally taken for Newtonian fluids and usingcorrelations developed for pipe flow.

Full suspension, derived from full erosion of beds, occurs atannulus velocities of 4 to 5 ft/s

9,12, which are at the upper limit

of the flow rates encountered in CTD. It appears though that

the critical flow rate for bed erosion is seldom sufficient tomaintain the particles in suspension5

. These authors finally

conclude that

• hole cleaning in bed transport is inefficient

• a suspension condition that relies only on bed erosion willunder predict the flow rate necessary for efficientsuspension, and hence cuttings removal.

If the flow in the annulus is laminar, the cuttings will

inevitably form a bed, given sufficient length

5

. Since in CTD

there is no pipe rotation, the role of turbulence must beexamined for maintaining particles in suspension5,9,12. Thequestion then posed is whether the flow rate necessary to

suspend the particles in turbulent flow is practical in view ofthe limitations on maximum flow rate and pressure drop

imposed for CTD. Leising and Walton5 predicted that fluids of

low to moderate viscosity (5 – 15 cp at nominal shear rate of

170s-1) were optimal for hole cleaning. A full model, however,for predicting these critical velocities in terms of the flow

parameters for full suspension of particles is not given.

Minimum Suspension Velocity for Horizontal FlowMost of the work done and reported in the literature for theminimum suspension velocity of solids in conduits is for the pipe geometry, since this is the geometry used for solids

transport using liquids (mainly water)20,29

. In addition, much ofthe reported work is for high solids loading, up to 40 – 50%,

with different particle sizes, from fines to coarse particles (up

to in275.0 ). The differences of the studied situations with the

ones we encounter during drilling applications, especially for

drilling with coil tubing are:

• the geometry is annulus (most often eccentric)

• the inlet concentration of solids is fairly low, rarelyexceeding 4% by volume

• the fluid used could be non-Newtonian, shear thinning,

many times modeled as power law fluid

• there is a limitation on the maximum flow rate to beachieved with the upper limit defined by the capacity of

downhole motor and maximum surface pressuresustained

5.

Based on work on solids transport in pipes20,26, the critical

velocity for solids suspension can be derived fromconsideration of forces acting on the particles and the

requirement that the forces balance so that particles remain insuspension. Very relevant is the work of Davies

48 where for

full suspension of solids, but not necessarily for the fullysyspended symmetric flow pattern, the balance of forces is between:

• the downward sedimentation force, Fds, and,

• the upward eddy fluctuation force, Fue = eddy pressure *area

These forces are estimated as:

β

ρ π

)1(6

3 s pds C g d F −∆= (32)

( ) 4/'22 pue d u F π ρ = (33)

Hindered settling has been taken into account through the term β )1( sC − .

When these forces balance, we get

( ) ρ ρ β

/182.0' ∆−= g d C u p s (34)




The fluctuating velocity (u’) for liquid only is related toenergy dissipation from dimensional considerations andturbulence theory and the fact that we are concerned with

eddies of the size of the particle diameter, hence,

( ) p M d P u =3' (35)

where PM is the power dissipated per unit mass of fluid, givenfor a pipe by,

d

U f P M s

M

32= (36)

derived from dimensional considerations. Using Blasius

relationship, for Newtonian fluids,

25.0Re,

079.0

s

s N

f = (37)

we get finally

( ) ( ) ( ) ( ) ( )42.03/192.012/13/1

/16.0' −

= d d U u p M ρ µ (38)

the equation being dimensional and valid for pipe flow andonly Newtonian liquid flowing. Davies

48 claims that the

presence of solids dampens 'u and he takes this into account

by letting,

s p

C

uu

α +=

1

'' (39)

were α is a constant. This is in agreement with some investiga-tors

26,49-50 but contradictory to others. For example, Julian and

Dukler 51

, as mentioned in20

studied vertical gas solid flow in pipes (with results equally applicable to horizontal flows of

solid – liquid mixtures). They state that for dilute gas – solidsystems ‘the solids make their influence felt by modifying

local turbulence in the gas phase, increasing turbulencefluctuations, mixing length, eddy viscosity and hence frictional

pressure drop, p∆ ’. This is also evident from measured curves

of pressure drop which is higher in the presence of solids than

for pure gas or liquid flowing16-17

.

Equations (35) and (39), after some algebra, give,

( ) ( ) ( ) ( )

( ) ( )

0.181.09 0.55

0.54

0.09 0.46

1.08 1 1

2/

M s s pU C C d

g d

β α

ρ µ ρ ρ

−

= + −

∆

(40)

with the equation being dimensional. Utilizing the observedmaximum versus concentration, Davies estimates the value of

64.3=α . This final equation is then similar to Durand’s

correlation52

, apart from the concentration dependence. Thevalue of (β) is set from the equations for hindered settling,taken as β = 4 for 1 < N Re,p < 10 falling to ~ 3 when N Re, p approaches 100. Davies final predictions were close to published experimental data but about 1.35 times higher.

If we replace, d, with, d h , and keep everything else the same,

for some typical values, d p = 0.079 in., p ρ = 12.5 ppg, ρ =

8.33 ppg, d h = 2.0 in., C s = 2%, µ = 15 cp, β = 3, we estimate

U M = 5.1 ft/s!

The above mentioned approach has not been used neither forthe flow in an annulus nor for non–Newtonian fluids, exceptin53. The main challenges are then1. to relate (u’ ) to main flow velocity (U M ) for an annulus

and for non-Newtonian fluids. It can be done through theuse of annulus hydraulic diameter and a generalizedReynold number

2. to examine the dampening or not of the non-Newtonianliquid velocity fluctuations by the presence of solids andquantify it

3. to examine the effect of hindered settling for solids4. to compare predictions with good quality data5. to verify whether values of U M so predicted conform to

the maximum flow rate and pressure drop imposed forCTD.

Experimental SystemIn order to shed more light into efficient cuttings transport forCTD and aiming at providing good quality data, weestablished an experimental system for studying the solidscarrying capacity of liquids in horizontal and inclined annulus,

with no inner pipe rotation.

Before embarking into the setting up of the experimentalsystem, a dimensional analysis was done to determine thesignificant parameters affecting the process. If we visualize the process for the two layer model (Newtonian liquid – solid

suspension and a stationary bed), the height of the bed, h , will

depend on the following parameters:

g uU d d d p p M io p ,,,,,,,, ρ ρ µ

Dimensional analysis suggests equation (41) below,

Hence, the main parameters are, geometrical parameters, d 0 , d i ,

d p , d h , physical properties, , , p ρ ρ µ , velocity ratio (u p / U M ),

the Reynolds number N Re. The last term in the r.h.s., can beconsidered the Galileo number based on hydraulic diameter,

3 2

2

hGa

d g N

ρ

µ = (42)

with

ih d d d −= 0 (43)

Hence, for full simulation of field conditions, we should have

between our system and field conditions not only geometric

similarity, i.e. similar values for )/( 00 id d d − , pd d /0 ,

id d −0 , but also dynamic similarity, i.e. similar values for

velocity ratio (~ volumetric concentration), the Reynolds

( ))41(

)(

2

230

0

0

00

0 f

i

e p

k

M

p

d i M

b

i

a

pi

g d d

U

u

d d U

d d

d

d

d

d d

h

−

−

−

−

∝

−

µ

ρ

ρ

ρ ρ

µ

ρ




number and properties (Galileo number).

Literature review of SPE papers describing case studies with

CTD, since its first application in 1991 to date4,54-66

gave usthe data of the relevant parameters and are shown in Table 1.

Typical flow rates range between 2 – 5 bpm, which for typical

annulus sizes results in the velocity of the fluid in the annulusin the range of 1 to 5 ft/s. It is unfortunate that some

information is missing, as it was not stated explicitly. In particular, the viscosity of the fluids used, while density was

mentioned and ranged from that of water to a maximum of 9.5 ppg. Based on the above values, we have constructed a flowloop, shown in Figure 4.

The annulus, made of plexiglass, is 16.4 ft long, with outerdiameter d0 = 2¾ in. and inner diameter di = 1.57 in. and

currently is concentric. It is supported by a metal structure thatcan be tilted from horizontal to vertical. A plastic tank holds132 gal of liquid and is equipped with a 2hp variable speed

agitator. The flow is achieved with a 10 hp slurry pumpdelivering 185 gpm at 64 psig. The flow rate, the density andtemperature are monitored with a Coriolis mass flow meter

(Rheonik, RHM 30). A Validyne pressure transducer monitorsfrictional pressure drop in the annulus measuring station at twoaxial spacings (15.75 in. and 35.43 in.). Viscosity of liquids ismeasured with a continuously variable shear rate coaxialcylinder viscometer (Grace, type M3500a) with shear ratescontinuously varying from 0.01 to 600 RPM. Spherical glass

beads of different diameters (0.04 in., 0.08 in., 0.16 in.) will beused to simulate drilled cuttings.

A comparison of the pertinent variables between the

experimental system and field operations is given in Table 2.In Figure 5 we show photos of layer patterns taken from the

preliminary test runs.

ConclusionsA critical review has been presented on the effects of thevarious parameters on efficient cuttings transport in horizontalconcentric and eccentric annuli. The modeling andexperimental results show that:

• the most significant parameter is the annulus mixturevelocity (flow rate and cross sectional area)

• flow should be turbulent in the annulus

• maximum flow rates should conform to maximum ratesimposed by downhole motor and maximum pressure

allowable for Coiled Tubing

• liquid density is an important parameter

• eccentricity plays a significant role with a dramaticdecrease in cuttings transport efficiency for fullyeccentric annulus

• modeling shows that rheology has a small effect incontradiction to experimental and field results.

From the published results and models to date, the main issues

are the following:

• the need for collecting good quality cuttings transport

data, for concentric and eccentric annulus, with conditions

similar (dynamic similarity) to the ones observed in thefield

• the establishment, theoretically, of the observed link (inthe field and experiments) between fluid rheology andefficient cuttings transport

• the establishment of the best rheological models for theliquids, two versus three parameter models, since the

added complexity of three parameter models is stillquestionable

• resolving the contradiction for using low viscosity fluidsversus moderate viscosity fluids, where simulation resultsshow better suspension characteristics for the latter but theformer promote turbulence

• to better understand the solids distribution in thesuspension layer. The dispersion coefficient of solids isvery critical and better predictions are needed, especiallyfor non-Newtonian fluids

• should the approach be the determination of minimumsuspension velocity or the modeling of layers for efficient

cuttings transport ?• for the modeling of minimum suspension velocity, theneeds are:

o to find relationships to link the turbulent fluctuatingvelocity component to the main flow parameters forannulus and non-Newtonian fluids

o to get better relationships for hindered settling ofsolids in non-Newtonian fluids

o to examine the effect of the presence of solids on theturbulent fluctuating velocity for non-Newtonianliquids

o to compare predictions with good quality data

• for the layer modeling, the needs are for

o justification of the use of three layers (more complex)vs the two layer model with good quality data

o better prediction of the solids dispersion coefficient, D, hence determination of Peclet number

o validation of the ‘diffusion’ equation for the annulus

o better relationships for the interfacial friction factor, between heterogeneous layer and moving bed

o better relationships for the wall friction factors for the

heterogeneous layer and for the moving bed, valid fornon-Newtonian fluids.

Appendix A – Volumetric Concentration of SolidsDuring CTD

The solids concentration in the liquid is fairly low duringnormal drilling operations, and for CTD rarely exceeds 2 – 4% by volume. It can easily be estimated from the following

)1(*)*4/(*)(

)1(*)*4/(*)(2

2

φ π

φ π

−+

−=

holem

hole

d ROP Q

d ROP C (A-1)

It should be noted that in the many studies referenced herein,the bed porosity is rarely taken into account.

For the various field parameters shown in Table 1, taking two

values of holed (5 in. and 3 ¾ in.), we can easily compute the

volumetric concentration of solids, C , for various flow rates




and we find that the volumetric concentration of cuttings canvary from about 0.1% to a maximum of 3.5% for the observed parameters in practice.

Appendix B: Concentration of Solids in theHeterogeneous MixtureMany researchers use the ‘solid – diffusion’ equation for

predicting the concentration of solids in the heterogeneousmixture for two or three layer modeling. This equation is

derived on the assumption that turbulent eddies counterbalancethe settling of solids due to gravity.

With reference to Figure B-1 and using 1-D modeling, with‘y’ the vertical coordinate, a balance between rate of settlingand upward transport by turbulent forces results in4,11,16

02

2

=+dy

C d D

dy

dC u p (B-1)

The equation is solved using two boundary conditions,

Boundary Condition 1, no flux of solids at the top wall,

[ ] 0=

−+−

−−

==

oo

d yd y p

dy

dC DC u (B-2)

Boundary Condition 2,

at BC C h y == , (B-3)

with C B normally taking the value of 0.52, assuming cubic packing of the solids.

Assuming that D and pu do not vary in the vertical direction,

the solution is,

−+=

D

yu B A yC

pexp)( (B-4)

and using (B-2) we get, A = 0.

Using (B-3) and defining the Peclet number , Peo, as,

D

d u Pe

o po = (B-5)

the above give,

−−=

ooo

B d

h

d

y Pe

C

yC exp

)( (B-6)

valid for the values of h y > .

Equation (B-6) describes the distribution of the particles in thesuspension layer.

The mean concentration of the solids in the suspension is

derived as follows4:

Let y x, the horizontal and vertical coordinates. Let also

oγ the angle above horizontal of any point on the perimeter of

the outer pipe and iγ on the perimeter of the inner pipe (Fig.

B-1 and Fig. 2). Then,

2/sin ooo d y γ = (B-7)

2/cos ooo d x γ = (B-8)

2/cos oooo d d dy γ γ = (B-9)

2/sin iii d y γ = (B-10)

2/cos iii d x γ = (B-11)

2/cos iiii d d dy γ γ = (B-12)

The suspension area, s A is given by

−

=

−=

∫ ∫

∫ ∫

−− −−

−− −−

2/

)(

2/

)(

2222

)( )(

)(cos)(cos2

1

2

π

θ

π

θ

γ γ γ γ

O i

o

o

i

o

iiiooo

R

h R

R

h Riioo s

d d d d

dy xdy x A

(B-13)

The mean concentration is

∫∫=

s A s

s dA yC A

C )(1

and finally,

( )iioo s

B s Int d Int d

A

C C **

2

22 −= (B-14)

where,

∫

−−=

2/2)(cos

2

sinexp

π

θ

γ γ γ

o

od ood

hoo Peo Int (B-14a)

∫

−−=

2/2)(cos

)/(2

sinexp

π

θ

γ γ γ

i

ii

oio

ioi d

d

h

d d Pe Int (B-14b)

Equations (B-14, B-14a and B-14b) are equations (5, 5a, 5b)given in the main article.

For these solutions it has been implicitly assumed that both the

settling velocity, pu , and the solids dispersion coefficient, D ,

are independent of the vertical distance, hence pu is the

terminal, not the hindered terminal velocity of solids. Doron etal.16 and Walton4, although they assumed this, they later use

the hindered settling velocity which is obviously not correct,as already pointed out11.




Estimation of Pe Number

It has been shown above that the concentration of solids in the

heterogeneous layer depends on Peclet number, Pe , defined

by equation (B-5). For 1<< Pe , the process is diffusion

(dispersion) controlled and we expect a more uniform

distribution of solids in the heterogeneous layer. For 1>> Pe ,

the process is gravity controlled and we expect to see thesolids accumulating near the bottom of the annulus. Therefore,for full suspension of particles, the process should be diffusion

controlled, or Pe should be minimum.

To get the minimum value of Pe that could be encountered

during CTD, pu and od should be minimum, while D should

be maximum. We take .0394.0min, ind p ≈ From the proposed

correlations for the terminal velocity the minimum uP is of theorder of 0.0262ft/s, while for d 0 the minimum is ~ 2 ¾ in.(Table 1).

For the dispersion coefficient D, there are two approachessuggested so far in the literature, covering the case of

Newtonian liquids:

APPROACH of Doron et al.16

:The authors suggest that

))((052.0 * RU D = (B-15)

where U * is the friction velocity given by

2/* s M f U U = (B-16)

and R is the hydraulic radius, which for a full pipe (no bed) isequal half the pipe diameter.

Extending this to the annulus, we can write,

)2/)((052.0 * h DU D = (B-17)

using the annulus hydraulic diameter.

The annulus velocity, U M , varies from 1.3 to 4.9 ft/s (Table 1).

For Newtonian fluids it has been suggested5 that optimum µ ~

10 – 20 cp.

For turbulent flow,25.0

Re

079.0

s

s N

f = .

For D to be maximum, U M should be maximum and f s

maximum or N Re,s minimum. N Re,s is minimum at the onset ofturbulent flow (~ 2100) and hence, f max = 0.0116.

Hence,

s ft

D f U D h

/10*9.2

)2/)(2/(052.023

maxmaxmaxmax−

≈=

APPROACH of Walton4 :

The author suggests that

3/1Re,0 ***014.0 s p p N ud D D = (B-18)

where D0 is given as

0.5

0 1.24 0.050.12

C D if C

= <

(B-19)

05.012.0

25.0

0 >

= C if

C D (B-20)

Equation (B-19) is the case for CTD, and for C = C max = 0.05 ,(D0 )max ~ 0.8.

For this situation, for D to be maximum, D0 should bemaximum (0.8), (d p )max ~ 0.236in., (u p )max ~ 0.65 ft/s and

maxRe, s N ~ 10000 (from values from Table 1), hence

s ft D /10*3 23max

−≈ , which is the same order of

magnitude as the approach of Doron et al16

.

Thus, the minimum value of Pe expected for annulus fortypical applications of CTD is of the order of

3~/10*3

)12/75.2)(/0026.0(~23 s ft

ft s ft Pe−

It is worthwhile to examine the concentration distribution for

various values of Pe. Using equation (B-6) we calculated thevalues of C(y)/C B for various values of Pe. The results areshown in Figure B-2 for h/d o = 0.1.

The solids may be distributed close to the pipe bottom at theminimum estimated value of Pe (~ 3 ). The effect is more

pronounced for Pe ~ 5. For Pe ~ 1, there is a good distributionof solids throughout the channel.

The above analysis holds for Newtonian fluids. It shows thatthe value of Pe is very critical for determining the solidsdistribution in the suspension and the main parameter for

estimating Pe is the solids dispersion coefficient. Furthermore,it has been shown that no consensus has been reached on the proper correlation for the solids dispersion coefficient, evenfor Newtonian fluids. And no such correlation has beenestablished for solids dispersion coefficient for non-Newtonianfluids, which is the case encountered in CTD.

Nomenclature A B = cross sectional area occupied by the bed, L2, in.2

A M = total cross sectional area, area of annulus, L2, in.

2

A s = cross sectional area occupied by the suspensionlayer, L2, in.2

C = solid volumetric concentration

C B = mean concentration of solids in bedC M = mean feed concentration

C s = mean concentration of solids in the suspensionlayer

d = pipe diameter, L, in.d h = hydraulic diameter of annulus, L, in.

d hole = open hole diameter, L, in.d ι = diameter of inner pipe of annulus, L, in.d 0 = diameter of outer pipe of annulus, L, in.d p = spherical particle diameter, L, in.

dp = pressure drop due to friction, M/Lt2, psi




D = dispersion coefficient of solids, L2/t, ft2/s DhB = hydraulic diameter of the bed, L, in. Dhs = hydraulic diameter of the suspension, L, in.

f = friction factor f B = friction factor for bed – wall

f i = friction factor for bed – suspension interface f s = friction factor for the suspension – wall

F B = friction force between the bed and the wall, ML/t2,lbf

F mB = friction force between the moving bed and the wall,ML/t2, lbf

F max = maximum sliding force, ML/t2, lbf

F N = normal force on bottom wall, ML/t2, lbf

F ds = downward sedimentation force, ML/t2, lbf

F ue = upward eddy fluctuatiung force, ML/t2, lbf

g = acceleration of gravity, L/t2, ft/s

2

h = bed height, L, in.

K = Consistency index, M/Ltn, lbfs

n/100ft

2

K v = von Karman constantn = power law index

N Ga = Galileo number =3 2

2

hd g ρ

µ

N Re = Reynolds number

N Re,s = Reynolds number of suspension, = s

hs s s DU

µ

ρ

N Re,B = Reynolds number of bed, = B

hB B B DU

µ

ρ

N Re,gn = Generalized Reynolds number =n

nhs

n s s

n

n K

DU

+

−

)13(2

8 2 ρ

N Re,p = particle Reynolds number =µ

ρ p pd u

ROP = Rate of penetration, L/t, ft/hr

Ri = radius of inner pipe, L, in. Ro = radius of outer pipe, L, in.

S = wetted perimeter, L, in.S B = wetted perimeter of bed, L, in.S i = wetted perimeter of interface, L, in.S s = wetted perimeter of suspension, L, in.

Qm = mud flow rate, L/t3, gpm

u’ = fluctuating component of transverse velocity, L/t,ft/s

' pu = fluctuating component of transverse velocity in the

presence of particles, L/t, ft/suh = hindered settling velocity of solids, L/t, ft/su p = settling velocity of solids, L/t, ft/s

U B = mean velocity of the bed, L/t, ft/sU M = mixture velocity, L/t, ft/s

U mB = moving bed velocity, L/t, ft/s

U s= mean velocity of suspension, L/t, ft/s y = vertical coordinate, L, in.

z = horizontal coordinate, L, in.

Greek Letters

ρ ∆ = difference between solid and liquid density, M/L3,

lbm/gal

η = dry friction coefficient between particles and walls

ο θ = as in Figure 2

iθ = as in Figure 2

µ = liquid viscosity, M/Lt, cp

ρ = fluid density, M/L3, lbm/gal

ρ Β = density of bed, M/L3, lbm/gal

p ρ = solid particle density, M/L3, lbm/gal

s ρ = density of suspension, M/L3, lbm/gal

τ Β = wall stress between bed and walls, M/Lt2, psi

iτ = stress at the interface between suspension and bed,

M/Lt2, psi

sτ = wall stress between suspension and walls, M/Lt2,

psi siτ = intergranular shear stress, M/Lt

2, psi

φ = formation porosity (here taken as 20%)

pφ = sphericity of particles

sφ = coefficient of internal friction between particles

Subscripts

B = bedhB = hydraulic, bedhs = hydraulic, suspension

i = inside, interface

M = mixturemB = moving bedmBsB = moving bed – stationary bed

o = outside p = particle s = suspension

sB = stationary bed smB = suspension – moving bed

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TABLE 1: Field Data for CTD Parameters

SOURCE dhole di dh Q U ROP ρ

(in) (in) (in) (bpm) (ft/s) (ft/hr) (ppg)

SPE 23875 2.000 1.90 9 to 12

SPE 24594 4.750 1.750 3.000 2.00 1.77 30 8.33

" " 4.750 2.000 2.750 3.20 2.95 8.33

SPE 29491 5.000 1.900 3.100 2.38 1.90

" " 5.000 1.900 3.100 4.76 3.81

SPE 35128 3.750 2.375 1.375 10 to 70 9.16

SPE 35544 3.500 2.875 0.625 7 to 25

SPE 37074 2.875 75 to 200

SPE 38397 4.750 2.375 2.375 3 to 50

SPE 50405 3.750 2.375 1.375 40 to 50 12,5

SPE 54496 3.750 2.000 1.750 1.50 2.56 9.16

SPE 54502 6.125 2.375 3.750 2.50 1.35 20 9.16

SPE 57459 4.750 2.375 2.375

SPE 62744 2.750 2.000 20

SPE 67824 2.750 12 to 21

" " 4.125 12 to 21

SPE 68436 5.000 1.900 3.100 1.25 1.00 9.16

" " 5.000 1.900 3.100 6.23 4.99 9.16




a. SUSPENDED SYMMETRIC b. SUSPENDED ASYMMETRIC

c. MOVING BED d. STATIONARY - MOVING BED

TABLE 2: Comparison of field conditions with experimental set up

Parameter Field Conditions Experimental Conditions

dhole (in) 2.75 – 3.75 – 4.75 2.75

di (in) 2 – 2.375 – 2.875 1.575

di / do 0.40 – 0.53 – 0.63 – 0.82 0.57

(do – di) / do 0.37 – 0.47 – 0.50 – 0.61 0.43

Q (bpm) 1.5 - 3.0 0.13 – 4.4U (ft/s) 1.0 – 4.9 1.0 – 14.5

(ppg) 8.33 – 9.5 8.33 – 8.75

ρp (ppg) 20.8 20.8

dp (in) 0.04 to 0.275 0.04 - 0.08 - 0.16

C (% by volume) 0.8 to 4 0.8 to 4

µ water & polymers CMC – water solutions

wγ Ν (= 12U/d o-d i ) (s-1

) 60 – 180 50 - 1800

Figure 1. Flow patterns for solid liquid flow in horizontal concentric annulus Figure 2. Schematic for the two layer model

Figure 3. Schematic of the three layer model




0

0,2

0,4

0,6

0,8

1

0 0,2 0,4 0,6 0,8 1C / CB

y

/ d o

Pe = 3 Pe = 1 Pe = 5

Figure 4. Schematic of annulus flow loop: 1 – annulus section, 2 – measuring section, 3 – tank, 4 – agitator, 5 – pump,

6 – Coriolis flow meter, 7 – pressure transducer, 8 – P/C for data acquisition

a. Two layers b. Three layersFigure. 5: Photos of the layer patterns

Figure B-1: Schematic for deriving diffusion equation Figure B-2: Solid distribution for h/do=0.1

minimum transport velocity

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