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Hydrodynamic Simulation of Horizontal Slurry Pipeline Flow Using ANSYS-CFX

Kalekudithi Ekambara, R. Sean Sanders, K. Nandakumar, , * and Jacob H. Masliyah

Department of Chemical and Materials Engineering, Uni Versity of Alberta, Edmonton, AB, Canada, T6G 2G6

The behavior of horizontal solid - liquid (slurry) pipeline ows was predicted using a transient three-dimensional(3D) hydrodynamic model based on the kinetic theory of granular ows. Computational uid dynamics (CFD)simulation results, obtained using a commercial CFD software package, ANSYS-CFX, were compared witha number of experimental data sets available in the literature. The simulations were carried out to investigatethe effect of in situ solids volume concentration (8 to 45%), particle size (90 to 500 m), mixture velocity(1.5 to 5.5 m/s), and pipe diameter (50 to 500 mm) on local, time-averaged solids concentration proles,particle and liquid velocity proles, and frictional pressure loss. Excellent agreement between the modelpredictions and the experimental data was obtained. The experimental and simulated results indicate that theparticles are asymmetrically distributed in the vertical plane with the degree of asymmetry increasing withincreasing particle size. Once the particles are sufciently large, concentration proles are dependent only onthe in situ solids volume fraction. The present CFD model requires no experimentally determined slurrypipeline ow data for parameter tuning, and thus can be considered to be superior to commonly used,

correlation-based empirical models.1. Introduction

Solid- liquid (slurry) transport has been used for decades inthe long-distance transport of materials like coal, mineral oreconcentrates, and tailings. Over the past 20 years, the oil sandsindustry of northern Alberta has become one of the worlds mostintensive users of slurry transport. Dense, coarse particle slurriesof oil sand ore are transported by pipeline from mining sites toextraction facilities. Pipeline transport is also used to carry wastetailings to the nal disposal site. In most cases, slurry pipelinesare more energy efcient and have lower operating andmaintenance costs than any other bulk material handling

methods. Additionally, operations involving slurry ow play asignicant role in many other industries, including pharmaceuti-cal manufacturing, nanofabrication, and oil rening.

Most engineering models of slurry ow have focused on theability to predict frictional pressure loss and minimum operatingvelocity (or deposition velocity) for coarse-particle, settlingslurries. Many models of this type exist and have varyingdegrees of success in predicting the aforementioned parameters.As noted in the following section, many of these models arephenomenological, meaning that some empirically derivedparameters or relationships are required. Additionally, thesemodels tend to provide macroscopic parameters only, forexample, frictional pressure drop, deposition velocity, anddelivered solids volume fraction for a narrowly sized slurry.Many industrial slurries, however, contain a range of differentparticle sizes. The location and velocity of these particles atdifferent positions in the ow will drastically affect the pipelineoperation. Knowledge of the variation of these parameters withpipe position is crucial if the understanding of mesoscopicprocesses (e.g., pipeline wear, particle attrition, or agglomera-tion) is to be advanced. Additionally, analysis of more complexthree- or four-phase ows will require models that provide localvalues of particle concentration and velocity. Finally, accuratepredictions of concentration and velocity distributions in morecomplicated geometries (pumps, hydrocyclones, mixing tanks)

will require the development and validation of mechanisticcomputational models.

With the advent of increased computational capabilities,computational uid dynamics (CFD) is emerging as a verypromising new tool in modeling hydrodynamics. While it is nowa standard tool for single-phase ows, it is at the developmentstage for multiphase systems. Work is required to make CFDsuitable for slurry pipeline modeling and scale-up. In view of the current status on this subject, the application to horizontalslurry pipeline ow of a comprehensive three-dimensionalcomputational uid dynamics (CFD) model based on the kinetictheory of granular ow has been undertaken. The kinetic theorycomponent of this model is critical because it accounts for theeffects of the interactions between particles and betweenparticles and the suspending liquid phase. Simulations have beencarried out to investigate the effect of solids volume fraction,particle size, mixture velocity, and pipe diameter on spatialvariations of particle concentration and liquid velocity, as wellas frictional pressure losses. The model predictions werecompared with existing experimental data over a wide range of

* To whom correspondence should be addressed. E-mail:[email protected]. Tel.: + 972 2 607 5418. Fax: 780-492-2881.

GASCO Chair Professor, The Petroleum Institute, P.O. Box. 2533Abu Dhabi, U.A.E. Figure 1. Grid structure for the horizontal slurry pipeline simulations.

Ind. Eng. Chem. Res. 2009, 48, 81598171 8159

10.1021/ie801505z CCC: $40.75 2009 American Chemical SocietyPublished on Web 05/29/2009

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pipeline operating conditions: that is, average solids concentra-tions of 8 to 45% (by volume), uniform particle sizes of 90 to500 m, mixture velocities of 1.5 to 5.5 m/s, and pipe diametersof 50 to 500 mm. Before the computational method andsimulation results are discussed, a brief review of previous work in this area is presented below.

2. Previous Work

Durand 1 published a pioneering work on the empiricalprediction of hydraulic gradients for coarse particle slurry ows.Wasp et al. 2 improved the calculation method and applied it tocommercial slurry pipeline design. Shook and Daniel 3 used the pseudohomogeneous approach to model slurry ow. The uniqueaspect of this technique is that it allows description of the owusing a single set of conservation equations (as for single-phaseow). The dispersed solids phase is assumed to augment thecarrier uids density and viscosity by amounts related to the

in situ solids volume fraction. Clearly, this technique is of limited value as it, by denition, assumes the slurry has nodeposition velocity. It provides reasonable predictions of frictionlosses only for relatively ne particles, low solids volumefractions, and for a narrow range of operating velocities. Shook and Daniel 4 improved on the pseudohomogeneous approach byconsidering the slurry as a pseudo single-phase uid withvariable density. However, because of the boundary conditionsadopted in their approach, it is difcult to apply their model toactual ow situations.

Oroskar and Turian 5 used a constructive energy approachto calculate the deposition velocity. In their model, they assumedthat the kinetic energy of turbulent uctuations is transferredto discrete particles, which suspends them in the ow. Despitethe fact that this model was oversimplied and not intendedfor dense slurries, predicted deposition velocities comparedfavorably with the experimental data over a wide range of solidsvolume fractions.

Wilson 6 developed a one-dimensional two-layer modelwherein coarse-particle slurry ow is considered to comprisetwo separate layers. Each layer has a uniform concentration andvelocity. Because Wilson assumed the particles were verycoarse, they were contained in the lower layer (with the upperlayer solids concentration being zero). Momentum transferoccurs between the layers through interfacial shear forces. Thetwo-layermodelhasbeenextendedby anumberof researchers. 7 - 13

Doron et al. 7 developed a two-layer model for the predictionof ow patterns and pressure drops in slurry pipelines. Thismodel is very similar to that proposed by Wilson, 6 except thatthe lower layer may also be assumed to be stationary. However,the model did not predict the existence of a stationary bed at

Table 1. Experimental Data Sets Modeled with Hydrodynamic Simulations

measurement technique

source

pipediameter

(mm)particle size

( m)solids volume

concentration (%)particle specic

gravity ( - )mixture

velocity (m/s)pressure

dropparticle

concentration velocity

Roco andShook 27

50.7 165 -ray absorption magnetic uxow meter

51.5 480 6 - 35 2.65 1.5- 4.5263 520495 1300

Schaan et al. 45 50 85 15- 45 2.65 0.8- 5.0 pressure transducers -ray absorption magnetic uxow meter

150 90100

Gillies andShook 12

105 420 26 - 47 2.65 1.8- 5.8 pressure transducers -ray absorption magnetic uxow meter

264 420495

Gillies et al. 13 103 90 10 - 45 2.65 2.0- 8.0 pressure transducers -ray absorption electrical resistivity probe,magnetic ux ow meter

270

Kaushal andTomita 24 54.9 125 5 - 50 2.47 1.0- 5.0 pressure transducers -ray absorption,sampling probe440

Figure 2. Particle concentration prole sensitivity analysis (A) effect of

forces: (O ) exptl, (- - - ) CFD-k- model with kinetic theory and dragforce; (---) CFD- k- model with kinetic theory, drag force, and turbulentdispersion force; ( s ) CFD-k- model with kinetic theory, drag, lift, turbulentdispersion, and wall lubrication force. (B) radial distribution function andkinetic solids viscosity models of Gidaspow 35 and Lun and Savage. 37

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low ow rates, which also reduced the reliability of the pressuredrop predictions. Wilson and Pugh 8 developed a dispersive-force model of heterogeneous slurry ow, which extended theapplicability of the original Wilson layer model because itaccounted for particles suspended by uid turbulence as wellas those providing contact-load (Coulombic) friction. The modelwas used to predict particle concentration and velocity prolesthat were in good agreement with experimental measurements.

Nassehi and Khan 9 developed a numerical method for thedetermination of slip characteristics between the layers of a two-layer slurry ow, but no comparisons between experimentalresults and their numerical solutions were reported.

Undoubtedly, the most commonly used version of the two-layer model is the SRC model developed by Gillies andco-workers. 10 - 13 The SRC two-layer model provides predictionsof pressure gradient and deposition velocity as a function of

particle diameter, pipe diameter, solids volume fraction, andmixture velocity. This model is semimechanistic in that theeffect of pipe diameter on pipeline friction loss is speciedmechanistically (i.e., does not depend on any empiricallydetermined coefcients). The semiempirical coefcients itcontains are based on thousands of controlled experiments doneat the Saskatchewan Research Council Pipe Flow TechnologyCentre. Since the optimum pipeline velocity is usually close tothe deposition velocity ( V c), most of the data that wereincorporated in the model were obtained at mixture velocitiesthat are just greater than the deposition velocity ( V c e V e1.3V c).

Doron and Barnea 14 extended the two-layer modeling ap-proach to a three-layer model of slurry ow in horizontalpipelines. Their model considered the existence of a dispersivelayer, which is sandwiched between the suspended layer and a

Figure 3.Comparison of predicted and experimentally determined

13

concentration proles for d p ) 270 m and V ) 5.4 m/s: (A) Rj s ) 0.10, (B) Rj s ) 0.20,(C) Rj s ) 0.30, (D) Rj s ) 0.35, (E) Rj s ) 0.40, and (F) Rj s ) 0.45.

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bed. The dispersive layer was considered to have a higherconcentration gradient than the suspended layer. A no-slipcondition between the solid particles and the uid was assumed,which is reasonable when the ow is in horizontal or near-horizontal congurations. The model predictions showed sat-isfactory agreement with experimental data. Doron and Barnea 21

also used a three-layer model to draw ow pattern maps, whichcan be used to indicate the ow pattern (essentially, the degreeof ow heterogeneity). They determined the transition linesbetween the so-called ow patterns and compared these resultswith experimental data. Ramadan et al. 16 also developed a three-layer solid model and applied to simulate slurry transport ininclined channels. The model predictions were compared with

experiments, which clearly demonstrated the limitations of thismodel.A separate (but related) approach to slurry ow modeling

also exists, where the one-dimensional Schmidt - Rouse equa-tion11 (or equivalent; see Hunt 17 ) is used to relate the rate of particle sedimentation to the rate of turbulent exchange, asrepresented by a solids eddy diffusivity, s:

where Rs is the local, time-averaged solids volume fraction, uis the terminal particle settling velocity and y is a verticalposition in the pipe. Karabelas 18 developed an empirical modelto predict the particle concentration proles based on thisformulation. Kaushal and co-workers 19 - 24 developed a diffusionmodel based on the work of Karabelas, 18 where they proposeda modication for the solids diffusivity for coarse particle slurry

ow. They constructed an empirical correlation determining theratio of the solids diffusivity to the liquid eddy diffusivity. Theirfunction shows that the solids diffusivity increases with increas-ing solids concentration. However, it does not take into accounta signicant dependence of the solids diffusivity on both particlesize and pipe Reynolds number. 25 They also compared theirpressure drop data with the modied Wasp model, 26 consideringthe effect of efux concentration on dimensionless solidsdiffusivity, 20 and found good agreement at higher ow veloci-ties; however, deviations were signicant at ow velocities nearthe deposition velocity.

Roco and Shook 27 - 29 developed a similar model for denseslurry pipeline ows. They considered the slurry to be aNewtonian uid characterized using the mixture density andviscosity. They accounted for turbulent properties of the owby introducing in the Navier - Stokes equation, an empirical termcharacterizing the turbulent viscosity. The particle concentrationprole was determined using a semiempirical diffusion equationsimilar to that described above. Model predictions werecompared with experimental data for solids volume fractionsless than 35%. This model was not reliable at higher solidsvolume concentrations. Over the years, Roco and co-workers 30,31

modied the turbulence model and used higher-order correla-tions to obtain a better estimate of eddy viscosity. Roco andMahadevan 31 used a one-equation kinetic energy model forturbulent viscosity. The model provides good predictions;however, it contains many empirical parameters.

Gillies and Shook 11 showed the most signicant limitationof this type of model. It is not applicable when the particle sizeis large enough that the particles cannot be supported by uid

Figure 4. Comparison of predicted and experimentally determined 13 concentration proles for d p ) 90 m and V ) 3.0 m/s: (A) Rj s ) 0.19, (B) Rj s ) 0.24,(C) Rj s ) 0.29, and (D) Rj s) 0.33.

Rsu - sdRsd y

) 0 (1)


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drag force F D, the lift force F L, the virtual mass force F VM, thewall lubrication force F WL and the turbulent dispersion force F T D). The liquid-phase stress tensor, l, can be represented as

The solids phase momentum balance is given by

The solids stress tensor, s, can be expressed in terms of thesolids pressure, P s, bulk solids viscosity, s, and shear solidsviscosity, s:

3.2. Kinetic Theory of Granular Flow. This is, strictlyspeaking, a class of models based on the kinetic theory of gases,generalized to take account of inelastic particle collisions. Inthese models, the constitutive elements of the solids stress arefunctions of the solids phase granular temperature, s, dened

to be proportional to the mean square uctuating particle velocityresulting from interparticle collisions: s ) u s2 /3, where u s isthe solids uctuating velocity. In most kinetic theory models,the granular temperature is determined from a transport equation.The conservation of the solids uctuating energy balance 36 canbe written as

The left-hand side of this equation represents the net change of uctuating energy. The rst term on the right-hand side representsthe uctuating energy due to solids pressure and viscous forces.The second term is the diffusion of uctuating energy in the solidsphase. The third term, s, represents the dissipation of uctuatingenergy and ls is the exchange of uctuating energy between theliquid and solids phase. Although eq 7 can be solved for thegranular temperature, the procedure is complex and the boundaryconditions are not well understood. The procedure is also compu-tationally expensive. A simpler and computationally cheapermethod is to use an algebraic expression, where local equilibriumof generation and dissipation of uctuating energy is assumed.Boemer et al. 36 simplied eq 7 to

Figure 6. Contour plots for (A) particle concentration and (B) liquid velocity taken at regularly spaced axial positions over the 10 m control volume.Obtained from numerical simulations of the following conditions: d p ) 90 m, V ) 3.0 m/s, and Rj s ) 0.19.

l ) l[u l + (u l)T ] - 23

l(u l) I (4)

t (FsRsu s) + (FsRsu su s) ) -R s p + F sRsg + s + F km

(5)

s ) (- P s + su s) I + s{[u s + (u s)T ] - 23(u s) I }(6)

32[

t (RsFss) + (RsFsu ss)]) s:u s + (k s ) - s +

ls (7)


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The dissipation uctuating energy is 35

where e is the coefcient of restitution for particle collisions, d p isthe particle diameter, and g0 is the radial distribution function atcontact. The restitution coefcient, which quanties the elasticityof particle collisions (one for fully elastic and zero for the fullyinelastic), was taken as 0.9. The radial distribution function, g0,can be seen as a measure of the probability of interparticle contact.

Popular models for the radial distribution function are given byGidaspow: 35

and Lun and Savage: 37

where Rsm is the volume fraction of a settled bed of solids. The g 0function becomes innite when the in situ solids volume fractionapproaches Rsm. A value of Rsm ) 0.64 is often assumed for arandom packing of monosize spheres. In practice, though, the valueof the settled bed volume fraction should be measured, as it dependsprimarily on particle sphericity and particle size distribution. 38

Figure 7. Predicted liquid velocity proles for (A) d p ) 90 m, V ) 3.0 m/s and Rj s ) 0.19; (B) d p ) 270 m, V ) 5.4 m/s and Rj s ) 0.20; (C) d p ) 480 m, V ) 3.44 m/s and Rj s ) 0.203. Measurements of local particle velocity shown in panel A from Gillies et al. 13

production ) dissipation sij U i x j

) s (8)

s ) 3(1 - e2

)Rs2

Fsg0

s

(4d p(

s

- diVU )) (9)

g0(Rs) ) 0.6(1 - (Rs / Rsm)1/3)- 1 (10)

g0(Rs) ) (1 - (Rs / Rsm))- 2.5Rsm (11)


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The solids pressure represents the solids phase normal forcescaused by particle - particle interactions. In the kinetic theoryof granular ow, both the kinetic and the collisional contribu-tions are considered. The particle pressure consists of a kineticterm corresponding to the momentum transport caused byparticle velocity uctuations and a second term due to particlecollisions: 35

In eq 6, the solids bulk viscosity accounts for the resistance of the granular particles to compression and expansion and hasthe form 39

The solids shear viscosity contains terms arising from particlemomentum exchange due to collision and translation. The solidsshear viscosity is expressed as a sum of the kinetic and

collisional contributions:

The collisional component of the solids viscosity is modeledas

and the kinetic component is determined based on 35

and Lun and Savage 37

where ) 1 / 2(1 + e)3.3. Interfacial Forces. The interphase momentum transfer

between solids and liquid due to drag force is given by

The drag coefcient C D has been modeled using the Gidaspowmodel, 35 which employs the Wen and Yu model when Rs > 0.2and employs the Ergun model when Rs e 0.2.

The lift force can be modeled in terms of the slip velocityand the curl of the liquid phase velocity 40,41 as

The lift coefcient has been assigned a value of 0.1 in thepresent simulation. This value is within the range suggested inthe literature. 41

The wall lubrication force, which is in the normal directionaway from the wall and decays with distance from the wall, is

expressed as42

Here, u r ) u l - u s is the relative velocity between phases, d p isthe mean particle diameter, yw is the distance to the nearest wall,and nw is the unit normal pointing away from the wall. Thewall lubrication constants C 1 and C2, as suggested by Antal etal.42 are - 0.01 and 0.05, respectively. The turbulent dispersionforce is modeled based on the Favre average of the interphasedrag force using 43

Here, tc is the turbulent Schmidt number for continuous phasevolume fraction, taken here to be tc ) 0.9.

3.4. Turbulence Equations. The turbulence model used forthe liquid phase is a variant of the two-equation k - model,which is given in standard form as:

In these equations, G represents the generation of turbulentkinetic energy due to the mean velocity gradient. For the liquidphase, a k - model is applied with its standard constants: C 1) 1.44, C 2 ) 1.92, C ) 0.09, k ) 1.0, ) 1.3. Noturbulence model is applied to the solids phase but the inuenceof the dispersed phase on the turbulence of the continuous phaseis taken into account with Satos additional term. 44

3.5. Boundary Conditions. At the inlet, velocities andconcentrations of both phases are specied. At the outlet, thepressure is specied (atmospheric). At the wall, the liquidvelocities were set to zero (no- slip condition). The velocity of the particles was also set at zero. To initiate the numericalsolution, the average solids volume fraction and a parabolicvelocity prole are specied as initial conditions.

4. Numerical Solution

The system of equations, with the aforementioned boundaryconditions, was solved using the commercial ow simulation

software ANSYS CFX 10.0. Mass and momentum equationswere solved using a second-order implicit method for space anda rst-order implicit method for time discretization. Theconservation equations were discretized using the control volumetechnique. The discretization of the three-dimensional domainresulted in 386 340 cells and the grid structure shown in Figure1. The SIMPLE algorithm was employed to solve the pressure-velocity coupling in the momentum equations. The highresolution discretization scheme was used for the convectiveterms. Initial simulations were carried out with a coarse meshto obtain rapid convergence and an indication of the positionswhere a high mesh density was needed. Grid independence wasexamined, but further grid renement did not result in signicantchanges to the simulations results. Three dimensional transientsimulations were performed. In these simulations, a constanttime step of 0.001 s and pipe length of 10.0 m were used. Time-averaged distributions of ow variables are computed over aperiod of 100 s.

P s ) F sRss + 2FsRs2

s(1 + e)g0 (12)

s )43

Rs2Fsd pg0(1 + e) (13)

s ) s,col + s,kin (14)

s,col )45

Rs2Fsd pg0(1 + e) (15)

s,kin )5 48

Fsd p(1 + e)g0(1 +

45

(1 + e)g0Rs)2 (16)

s,kin )5 96

Fsd p( 1g0 +85

Rs)(1 +85

(3 - 2)g0Rs

2 - )(17)

F D )34

C DRsFl1d p

|u l - u s|(u l - u s) (18)

F L ) C LRsFl(u s - u l) u l (19)

F WL ) -R sFl(u r - (u rnw)nw)

d pmax[C 1 + C 2 d p yw , 0] (20)

F TD )34

C Dd p

tc tc

RdFc(u d - u c)(RdRd -RcRc ) (21)

t (FlRlk ) +

x i(FlRlu lk ) )

x i(Rl( + l,tur

k ) k x i)+Rl(G - R l) (22)

t (FlRl) +

x i(FlRlu l) )

x i(Rl( + l,tur

) x i)+Rl

k

(C 1G - C 2Rl) (23)


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5. Results and Discussion

The CFD simulations were carried out to match the experi-mental conditions of Roco and Shook, 27 Schaan et al., 45 Gilliesand Shook, 12 Gillies et al., 13 and Kaushal and Tomita. 24 Table1 summarizes the experimental conditions and measurementtechniques employed to measure pressure drop, particle con-centration proles, and mixture velocity. Each data set describedin Table 1 was simulated using the model described in theprevious sections. The local, time-averaged particle concentra-tion proles, particle and liquid velocities, and frictional pressuredrop were obtained using the model and then were compared(where possible) with the existing experimental data. A widerange of particle size (90 - 500 m), solids volume concentration(8- 45%), mixture velocity (1.5 - 5.5 m/s), and pipe diameter(50- 500 mm) were considered. In the gures discussed here,

y/D is the dimensionless position along the pipes vertical axis,where y is the distance from the pipe bottom, the local particleconcentration is Rs, the liquid velocity is ul, and the frictionalpressure drop is p / L.

5.1. Sensitivity Analysis. Initially, numerical simulationswere conducted for three cases to demonstrate the effects thatthe inclusion of different forces had on the quality of thepredictions. In the rst case, the simulations were carried outwith the k - model based on the kinetic theory of granularow and drag force only . The model predictions are shown inFigure 2A, where the predicted particle concentration proleshows a peak near the bottom of the pipe. The local solidsvolume fraction rapidly approaches zero at a vertical positionof y / D 0.85. The second simulation included drag force andthe turbulent dispersion force. The predicted result is in good

Figure 8. Effect of particle size on concentration prole: (A) d p ) 90 m, V ) 3.0 m/s, Rj s ) 0.19, and D ) 103 mm; (B) d p ) 125 m, V ) 3.0 m/s, Rj s

) 0.20, andD

) 54.9 mm; (C)d

p ) 165 m,V

) 4.17 m/s, Rj s ) 0.189, andD

) 51.5 mm. (D)d

p ) 270 m,V

) 5.4 m/s, Rj s ) 0.20, andD

) 103 mm.(E) d p ) 440 m, V ) 3.0 m/s, Rj s ) 0.20, and D ) 54.9 mm. (F) d p ) 480 m, V ) 3.44 m/s, Rj s ) 0.203, and D ) 51.5 mm.


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agreement with the experimental data. In the third case, whenall the forces (drag, turbulent dispersion, lift, and wall lubricationforce) were included, the results showed no signicantimprovement.

Additionally, two radial distribution function and kineticsolids viscosity models 35,37 were tested. Essentially, there is nodifference between the two, as shown in Figure 2B. On the basisof these observations, all subsequent simulations were conductedusing (i) k - turbulence model with the kinetic theory of granular ow; (ii) drag and turbulent dispersion forces; and (iii)the Gidaspow radial distribution function/kinetic solids viscositymodel. 35

Lift and wall lubrication forces were neglected in thesesimulations.

5.2. Solids Concentration Proles. Because concentrationproles depend on many parameters, including mixture velocity,

mixture density, pipe diameter, particle size, and particle density,it is important to test the ability of a model to predict theseproles. Additionally, the knowledge of solids distribution acrossthe pipe cross-section is essential in the evaluation or predictionof pipeline wear. 46 Figure 3 shows the experimental andpredicted concentration proles for 270 m sand slurries owingat a constant mixture velocity (5.4 m/s) in a 100 mm pipeline.In situ solids volume concentrations of 10 to 45% were tested(and simulated). The experimental data were initially reportedby Gillies et al. 13 Generally, the numerical predictions showreasonable agreement with the experimental results. It can beobserved from the gures that for a given velocity, increasingthe in situ solids concentration reduces the asymmetry of theconcentration proles because of increased particle interactions.For these slurries, uid turbulence is not completely effectivein suspending the particles; instead, suspension results partly

Figure 9. Effect of pipe diameter on concentration prole, d p ) 165 m: (A) D ) 51.5 mm, Rj s ) 0.0918, and V ) 3.78 m/s; (B) D ) 51.5 mm, Rj s ) 0.286,

and V ) 4.33 m/s; (C) D ) 263 mm, Rj s ) 0.0995, and V ) 3.5 m/s; (D) D ) 263 mm, Rj s ) 0.268, and V ) 3.5 m/s; (E) D ) 495 mm, Rj s ) 0.104, andV ) 3.16 m/s; (F) D ) 495 mm, Rj s ) 0.273, and V ) 3.16 m/s.


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from particle - particle interactions. 13 This is a good test of themodels ability to predict the combined importance of uidturbulence and shear-dependent (Bagnold-like) particle - particleinteractions. Overall, the results are encouraging.

In Figure 3F, the experimentally determined concentrationprole exhibits a reversal in local concentration near the pipeinvert. This reversal is not predicted in our simulations and maybe related to the existence of near-wall forces describedpreviously.

Figures 4 and 5 show experimental data and numericalpredictions for 90 m sand slurries owing in 100 and 154 mmpipelines, respectively. The particles in these slurries areeffectively suspended by uid turbulence, as the relativelyuniform concentration proles at low in situ volume fractionsattest. These concentration proles can be accurately predictedusing a Schmidt-Rouse 1D turbulent diffusion model. 11,19 - 23

They also provide a good test of the numerical models abilityto predict the importance of the turbulent dispersion forces.Overall, the agreement between the numerical predictions andexperimental results is good.

Contour plots of particle concentration and liquid velocity alongthe pipe cross section at axial positions separated by 1.25 mintervals are shown in Figure 6. Signicant differences in particleconcentration and liquid velocity can be observed between the rstand fourth axial positions. The contour plots shown for axialpositions 5 through 8 are nearly identical, indicating that thenumerical simulations are providing results for fully developed

ow.5.3. Velocity Proles. Velocity proles in horizontal slurry

ow are directly linked to the concentration prole; as such, theyare also dependent upon particle size, in situ solids concentration,

Figure 10. Effect of pipe diameter on concentration prole for slurries of ne particles, V ) 3.0 m/s: (A) D ) 54.9 mm, d p ) 125 m, Rj s ) 0.30; (B) D) 54.9 mm, d p ) 125 m, Rj s ) 0.40; (C) D ) 103 mm, d p ) 90 m, Rj s ) 0.29; (D) D ) 103 mm, d p ) 90 m, Rj s ) 0.33; (E) D ) 150 mm, d p ) 90 m, Rj s ) 0.32; (F) D ) 150 mm, d p ) 90 m, Rj s ) 0.39.


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and mixture velocity. Figure 7 shows three pairs of illustrations.The left-hand gure shows a traditional velocity prole, where thelocal time-averaged liquid velocity along the pipes vertical axisis plotted. The corresponding contour plot is the type that is readilyattainable from CFD simulations. Figure 7A compares a measuredparticle velocity prole 13 with predictions for a 90 m sand slurry(Rj s ) 0.19, V ) 3.0 m/s). Recall that the corresponding concentra-tion prole, which is shown in Figure 4A, is nearly symmetric.Note also the agreement between the measured particle Velocityand the predicted uid Velocity is excellent, conrming that thelocal, time-averaged slip velocity approaches zero for slurries of this type. Figure 7 panels B and C show predicted liquid velocityproles for slurries containing coarser particles (270 and 480 m,respectively). It can be seen that the velocity proles becomeincreasingly asymmetrical with increasing particle size. Themaximum local velocity is found in the upper portion of the pipeand not at the centerline. This phenomenon has been demonstratedexperimentally. 13,27 Note also from the contour plots that thevelocity distribution in a horizontal plane is symmetrical about thepipe axis.

5.4. Effect of Particle Diameter. Figure 8 shows the mea-sured and predicted concentration proles for four different slurries,each with a different particle size (90, 125, 165, 270, 440, and480 m). In situ solids volume fractions are comparable for theseslurries (Rj s 0.2). The experimental data shown in these guresrepresent a broad spectrum of uid turbulence effects on particle

suspension, from highly effective (Figure 8A) to completelyineffective (Figure 8F). Concentration proles of the type shownin Figure 8F, for very coarse particles, depend primarily on in situsolids volume fraction, with only minimal dependence on mixturevelocity or pipe diameter. Thus, the measured concentration proleof Figure 8F can be considered to be typical of one that would befound for any coarse particle slurry ( d p > 300 m). In all cases,the agreement between measured and predicted proles isencouraging.

In Figure 8E,F, a distinct reversal in the concentration prolecan be seen near the pipe invert ( y / D < 0.2). This is related to thenear-wall lift force described previously, 24,32 which occurs whenthe particle is large relative to the viscous sublayer thickness. Thecurrent version of the CFD model is unable to reproduce thisconcentration reversal.

5.5. Effect of Pipe Diameter. To investigate the effect of pipediameter on the performance of the numerical model developedhere, the ow of a number of slurries in pipes of different diameter

was considered. Figure 9 shows both experimental and predictedconcentration proles for a 165 m sand slurry owing in pipesthat are 51.5, 103, 150, 263, and 495 mm in diameter. Themeasured concentration proles were taken from Roco andShook. 27 This particular particle size was chosen for two reasons:data had been collected from experiments conducted with a widerange of pipe diameters and this sand size exhibits strong pipediameter-dependent concentration proles. The relative importanceof uid turbulence vis-a-vis particle - particle interactions indetermining the shape of the concentration proles with increasingpipe diameter is clearly shown in Figure 9. The predictions are ingood agreement with the experimental data for all pipe diameters.

Figure 10 provides similar ndings for experimental measure-ments made with smaller particles of differing size and shape. Themixture velocity is the same for each panel ( V ) 3.0 m/s). Figure10 panels A and B show the experimental measurements made byKaushal and Tomita 24 for slurries of 125 m glass spheres in waterowing in a 54.9 mm pipeline loop. Figure 10 panels C - F showresults and predictions for narrowly sized 90 m sand slurriesowing in 100 and 150 mm pipelines. No noticeable effect of pipe

diameter is observed for these concentration proles, because theparticles are relatively ne and the mixture velocity in each caseis signicantly greater than the deposition velocity. Again, theconcentration prole reversal seen in Figure 10 panels A and B isnot accurately reproduced with the current model. Otherwise, themodels performance is satisfactory.

5.6. Pressure Drop. Pipeline pressure drop is one of the mostimportant parameters in slurry pipeline design and operation.To validate the numerical results obtained with the CFD model,the simulation results were compared with the experimental dataof Schaan et al., 45 Gillies and Shook, 12 Gillies et al. 13 andKaushal and Tomita. 24 As the information presented in Table1 indicates, these experimental data were collected for a widerange of particle size, mixture velocity, in situ solids volumefraction, and pipe diameter. The comparison of measured andpredicted frictional pressure drop results is shown in Figure 11.The predicted pressure drop is in good agreement with theexperimental measurements for the wide range of slurry owconditions represented by the data sets to which the numericalsimulations were compared.

6. Conclusions

A transient three-dimensional (3D) hydrodynamic model basedon the kinetic theory of granular ow has been developed forhorizontal slurry pipelines. Frictional pressure gradients and local,time-averaged solids concentration and liquid/particle velocities

were obtained. A detailed comparison between the CFD simulationresults and an expansive experimental data set (reported by Rocoand Shook, 27 Schaan et al., 45 Gillies and Shook, 12 Gillies et al. 13

and Kaushal and Tomita 24 ) was presented. Only slurries containingnarrowly sized particles were simulated in this study. Generally,excellent agreement between the predicted and the experimentaldata was obtained for a wide range of in situ solids volumefractions, particle diameters, mixture velocities, and pipe diameters.The degree of asymmetry in the concentration proles dependsprimarily upon the particle diameter, the mixture velocity, and thein situ solids volume fraction. The CFD model described here iscapable of predicting particle concentration proles for ne particleslurries where uid turbulence is effective at suspending theparticles. It also performs satisfactorily when the particles are coarseand concentration proles are primarily dependent upon the in situsolids volume fraction. In experimental data sets where the near-wall lift force was of sufcient magnitude to cause a reversal inthe concentration prole near the pipe invert, the current CFD

Figure 11. Parity plot for frictional pressure gradient (experimental data:(O ) Schaan et al.; 45 ( ) Gillies and Shook; 12 (] ) Gillies et al.; 13 and (0 )Kaushal and Tomita 24 ).


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model wasnot able to reproduce this behavior. Themodel describedhere, including the associated boundary conditions, is complete inthe sense that no experimentally determined ow measurementsare required as input data. In this sense, the present model can beconsidered to be superior to existing correlation-based, semiem-pirical models.

Acknowledgment

The authors gratefully acknowledge the nancial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) and Syncrude Canada Ltd.

Literature Cited

(1) Durand, R. Basic Relationships of the Transportation of Solids inPipes: Experimental Research. Proceedings of the 5th Congress, InternationalAssociation of Hydraulic Research, Minneapolis, Minnesota, 1953.

(2) Wasp, E. J., Aude, T. C., Kenny, J. P., Seiter, R. H., Jacques, R. B.Deposition Velocities, Transition Velocities and Spatial Distribution of Solids in Slurry Pipelines. Proceedings of the 1st International Conferenceon the Hydraulic Transport of Solids in Pipes (Hydrotransport 1), BHRA

Fluid Engineering: Craneld, U.K., Paper H4, 1970; pp 53 - 76.(3) Shook, C. A.; Daniel, S. M. Flow of Suspensions of Solids inPipelines, Part 2: Two Mechanisms of Particle Suspension. Can. J. Chem. Eng. 1968 , 46 , 238244.

(4) Shook, C. A.; Daniel, S. M. A Variable Density Model of the PipelineFlow of Suspensions. Can. J. Chem. Eng. 1969 , 47 , 196.

(5) Oroskar, A. R.; Turian, R. M. The Critical Velocity in Pipeline Flowof Slurries. AIChE J. 1980 , 26 , 551558.

(6) Wilson, K. C. A Unied Physical-based Analysis of Solid-LiquidPipeline Flow. Proceedings of the 4th International Conference of HydraulicTransport of Solids in pipes (Hydrotransport 4), BHRA Fluid Engineering:Craneld, U.K., Paper A1, 1976; 1 - 16.

(7) Doron, P.; Granica, D.; Barnea, D. Slurry Flow in Horizontal Pipes-Experimental and Modeling. Int. J. Multiphase Flow 1987 , 13 , 535547.

(8) Wilson, K. C.; Pugh, F. J. Dispersive-Force Modeling of TurbulentSuspension in Heterogeneous Slurry Flow. Can. J. Chem. Eng. 1988 , 66 , 721727.

(9) Nassehi, V.; Khan, A. R. A Numerical Method for the Determinationof Slip Characteristics between the Layers of a Two-Layer Slurry Flow. Int. J. Numer. Method Fluids 1992 , 14 , 167173.

(10) Gillies, R. G.; Shook, C. A.; Wilson, K. C. An Improved Two-layer Model for Horizontal Slurry Pipeline Flow. Can. J. Chem. Eng. 1991 ,69 , 173178.

(11) Gillies, R. G.; Shook, C. A. Concentration Distribution of SandSlurries in Horizontal Pipe Flow. Part. Sci. Technol 1994 , 12 , 4569.

(12) Gillies, R. G.; Shook, C. A. Modelling High Concentration SlurryFlows. Can. J. Chem. Eng. 2000 , 78 , 709716.

(13) Gillies, R. G.; Shook, C. A.; Xu, J. Modelling Heterogeneous SlurryFlows at High Velocities. Can. J. Chem. Eng. 2004 , 82 , 10601065.

(14) Doron, P.; Barnea, D. A Three-Layer Model for Solid - Liquid Flowin Horizontal Pipes. Int. J. Multiphase Flow 1993 , 19 , 10291043.

(15) Doron, P.; Barnea, D. Flow Pattern Maps for Solid - Liquid Flowin Pipes. Int. J. Multiphase Flow 1996 , 22 , 273283.

(16) Ramadan, A.; Shalle, P.; Saasen, A. Application of a Three-LayerModeling Approach for Solids Transport in Horizontal and InclinedChannels. Chem. Eng. Sci. 2005 , 60 , 25572570.

(17) Hunt, J. N. The Turbulent Transport of Suspended Sediment inOpen Channels. R. Soc. London, Proc., Ser. A 1954 , 224 , 322335.

(18) Karabelas, A. J. Vertical Distribution of Dilute Suspensions inTurbulent Pipe Flow. AIChE J. 1977 , 23 , 426434.

(19) Kaushal, D. R.; Tomita, Y. Solids Concentration Proles andPressure Drop in Pipeline Flow of Multi-Sized Particulate Slurries. Int. J. Multiphase Flow 2002 , 28 , 16971717.

(20) Kaushal, D. R.; Tomita, Y.; Dighade, R. R. Concentration at thePipe Bottom at Deposition Velocity for Transportation of CommercialSlurries through Pipeline. Powder Technol 2002 , 125 , 89101.

(21) Kaushal, D. R.; Tomita, Y. Comparative Study of Pressure Dropin Multisized Particulate Slurry Flow through Pipe and Rectangular Duct. Int. J. Multiphase Flow 2003 , 29 , 14731487.

(22) Kaushal, D. R.; Sato, K.; Toyota, T.; Funatsu, K.; Tomita, Y. Effectof Particle Size Distribution on Pressure Drop and Concentration Prole inPipeline Flow of Highly Concentrated Slurry. Int. J. Multiphase Flow 2005 ,31 , 809823.

(23) Seshadri, V.; Singh, S. N.; Kaushal, D. R. A Model for thePrediction of Concentration and Particle Size Distribution for the Flow of Multisized Particulate Suspensions through Closed Ducts and Open Chan-nels. Part. Sci. Technol 2006 , 24 , 239258.

(24) Kaushal, D. R.; Tomita, Y. Experimental Investigation of Near-Wall Lift of Coarser Particles in Slurry Pipeline Using Gamma-rayDensitometer. Powder Technol 2007 , 172 , 177187.

(25) Walton, I. C. Eddy Diffusivity of Solid Particles in a TurbulentLiquid Flow in a Horizontal Pipe. AIChE J. 1995 , 41 , 18151820.

(26) Wasp, E. J., Kenny, J. P., Gandhi, R. L. Solid Liquid Flow SlurryPipeline Transportation , 1st ed.; Trans. Tech. Publications: Clausthal,Germany, 1977.

(27) Roco, M. C.; Shook, C. A. Modeling of Slurry Flow: The Effectof Particle Size. Can. J. Chem. Eng. 1983 , 61 , 494503.

(28) Roco, M. C.; Shook, C. A. A Model for Turbulent Slurry Flow. J.Pipelines 1984 , 4, 313.

(29) Roco, M. C.; Shook, C. A. Computational Method for Coal SlurryPipelines with Heterogeneous Size Distribution. Powd. Technol. 1984 , 39 , 159176.

(30) Roco, M. C.; Balakrishnan, N. Modeling Slurry Flow, The Effect

of Particle Size. J. Rheol. 1983 , 29 (4), 431456.(31) Roco, M. C.; Mahadevan, S. Modeling Slurry Flow, Part 1,Turbulent Modeling. J. Energy Res. Technol. 1986 , 108 , 269277.

(32) Wilson, K. C.; Sellgren, A. Interaction of Particles and Near-wallLift in Slurry Pipelines. J. Hydraulic Eng. 2003 , 129 , 7376.

(33) Wilson, K. C.; Clift, R.; Sellgren, A. Operating Points for PipelinesCarrying Concentrated Heterogeneous Slurries. Powder Technol. 2002 , 123 ,1924.

(34) Campbell, C. S.; Francisco, A. S.; Liu, Z. Preliminary Observationsof a Particle Lift Force in Horizontal Slurry Flow. Int. J. Multiphase Flow2004 , 30 , 199216.

(35) Gidaspow, D. Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions ; Academic Press: New York, 1994.

(36) Boemer, A.; Qi, H.; Renz, U.; Vasqyez, S.; Boysan, F. EulerianComputation of Fluidized Bed Hydrodynamics s A Comparison of PhysicalModels. Fluid. Bed Combust., ASME 1995 , 2, 775787.

(37) Lun, C. K. K.; Savage, S. B. The Effects of an Impact VelocityDependent Coefcient of Restitution on Stresses Developed by ShearedGranular Materials. Acta Mech. 1986 , 63 , 1544.

(38) Shook, C. A.; McKibben, M. J.; Small, M. Investigation of SomeHydrodynamical Factors Affecting Slurry Pipeline Wall Erosion. Can. J. Chem. Eng. 1990 , 68 , 1723.

(39) Lun,C.K. K.; Savage, S. B.; Jeffrey, D. J.; Chepurnity, N. Kinetic TheoryforGranular Flow: InelasticParticles inCouette Flow andSlightly InelasticParticlesin a General Flow Field. J. Fluid Mech. 1984 , 140 , 223235.

(40) Zun, I. The Transverse Migration of Bubbles Inuenced by Wallsin Vertical Bubbly Flow. Int. J. Multiphase Flow 1980 , 6 , 583588.

(41) Tomiyama, A. Drag, Lift and Virtual Mass Forces Acting on a SingleBubble. 3rd Int. Symp. Two-Phase Flow Modell. Expt. (Pisa) 2004 , 2224.

(42) Antal, S.; Lahey, R.; Flaherty, J. Analysis of Phase Distribution inFully-developed Laminar Bubbly Two Phase Flow. Int. J. Multiphase Flow1991 , 7 , 635.

(43) Burns, A. D. B., Frank, T., Hamill, I., Shi, J.-M. Drag Model forTurbulent Dispersion in Eulerian Multiphase Flows. 5th InternationalConference on Multiphase Flow, ICMF, Yokohama, Japan, 2004.

(44) Sato, Y.; Sekoguchi, K. Liquid Velocity Distribution in Two-PhaseBubbly Flow. Int. J. Multiphase Flow 1975 , 2, 7995.

(45) Schaan, J.; Sumner, R. J.; Gillies, R. G.; Shook, C. A. The Effectof Particle Shape on Pipeline Friction for Newtonian Slurries of FineParticles. Can. J. Chem. Eng. 2000 , 78 , 717725.

(46) Hoffman, A. C.; Finkers, H. J. A Relation for the Void Fraction of Randomly Packed Particle Beds. Powder Technol. 1995 , 82 , 197203.

Recei Ved for re View October 6, 2008 ReVised manuscript recei Ved March 8, 2009

Accepted March 11, 2009

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Hydrodynamic Simulation of Horizontal Slurry Pipeline Flow Using ANSYS-CFX

Kalekudithi Ekambara, R. Sean Sanders, K. Nandakumar, , * and Jacob H. Masliyah

Department of Chemical and Materials Engineering, Uni Versity of Alberta, Edmonton, AB, Canada, T6G 2G6

The behavior of horizontal solid - liquid (slurry) pipeline ows was predicted using a transient three-dimensional(3D) hydrodynamic model based on the kinetic theory of granular ows. Computational uid dynamics (CFD)simulation results, obtained using a commercial CFD software package, ANSYS-CFX, were compared witha number of experimental data sets available in the literature. The simulations were carried out to investigatethe effect of in situ solids volume concentration (8 to 45%), particle size (90 to 500 m), mixture velocity(1.5 to 5.5 m/s), and pipe diameter (50 to 500 mm) on local, time-averaged solids concentration proles,particle and liquid velocity proles, and frictional pressure loss. Excellent agreement between the modelpredictions and the experimental data was obtained. The experimental and simulated results indicate that theparticles are asymmetrically distributed in the vertical plane with the degree of asymmetry increasing withincreasing particle size. Once the particles are sufciently large, concentration proles are dependent only onthe in situ solids volume fraction. The present CFD model requires no experimentally determined slurrypipeline ow data for parameter tuning, and thus can be considered to be superior to commonly used,correlation-based empirical models.

1. Introduction

Solid- liquid (slurry) transport has been used for decades inthe long-distance transport of materials like coal, mineral oreconcentrates, and tailings. Over the past 20 years, the oil sandsindustry of northern Alberta has become one of the worlds mostintensive users of slurry transport. Dense, coarse particle slurriesof oil sand ore are transported by pipeline from mining sites toextraction facilities. Pipeline transport is also used to carry wastetailings to the nal disposal site. In most cases, slurry pipelinesare more energy efcient and have lower operating andmaintenance costs than any other bulk material handling

methods. Additionally, operations involving slurry ow play asignicant role in many other industries, including pharmaceuti-cal manufacturing, nanofabrication, and oil rening.

Most engineering models of slurry ow have focused on theability to predict frictional pressure loss and minimum operatingvelocity (or deposition velocity) for coarse-particle, settlingslurries. Many models of this type exist and have varyingdegrees of success in predicting the aforementioned parameters.As noted in the following section, many of these models arephenomenological, meaning that some empirically derivedparameters or relationships are required. Additionally, thesemodels tend to provide macroscopic parameters only, forexample, frictional pressure drop, deposition velocity, anddelivered solids volume fraction for a narrowly sized slurry.Many industrial slurries, however, contain a range of differentparticle sizes. The location and velocity of these particles atdifferent positions in the ow will drastically affect the pipelineoperation. Knowledge of the variation of these parameters withpipe position is crucial if the understanding of mesoscopicprocesses (e.g., pipeline wear, particle attrition, or agglomera-tion) is to be advanced. Additionally, analysis of more complexthree- or four-phase ows will require models that provide localvalues of particle concentration and velocity. Finally, accuratepredictions of concentration and velocity distributions in morecomplicated geometries (pumps, hydrocyclones, mixing tanks)

will require the development and validation of mechanisticcomputational models.

With the advent of increased computational capabilities,computational uid dynamics (CFD) is emerging as a verypromising new tool in modeling hydrodynamics. While it is nowa standard tool for single-phase ows, it is at the developmentstage for multiphase systems. Work is required to make CFDsuitable for slurry pipeline modeling and scale-up. In view of the current status on this subject, the application to horizontalslurry pipeline ow of a comprehensive three-dimensionalcomputational uid dynamics (CFD) model based on the kinetictheory of granular ow has been undertaken. The kinetic theorycomponent of this model is critical because it accounts for theeffects of the interactions between particles and betweenparticles and the suspending liquid phase. Simulations have beencarried out to investigate the effect of solids volume fraction,particle size, mixture velocity, and pipe diameter on spatialvariations of particle concentration and liquid velocity, as wellas frictional pressure losses. The model predictions werecompared with existing experimental data over a wide range of

* To whom correspondence should be addressed. E-mail:[email protected]. Tel.: + 972 2 607 5418. Fax: 780-492-2881.

GASCO Chair Professor, The Petroleum Institute, P.O. Box. 2533Abu Dhabi, U.A.E. Figure 1. Grid structure for the horizontal slurry pipeline simulations.

Ind. Eng. Chem. Res. 2009, 48, 81598171 8159

10.1021/ie801505z CCC: $40.75 2009 American Chemical SocietyPublished on Web 05/29/2009

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pipeline operating conditions: that is, average solids concentra-tions of 8 to 45% (by volume), uniform particle sizes of 90 to500 m, mixture velocities of 1.5 to 5.5 m/s, and pipe diametersof 50 to 500 mm. Before the computational method andsimulation results are discussed, a brief review of previous work in this area is presented below.

2. Previous Work

Durand 1 published a pioneering work on the empiricalprediction of hydraulic gradients for coarse particle slurry ows.Wasp et al. 2 improved the calculation method and applied it tocommercial slurry pipeline design. Shook and Daniel 3 used the pseudohomogeneous approach to model slurry ow. The uniqueaspect of this technique is that it allows description of the owusing a single set of conservation equations (as for single-phaseow). The dispersed solids phase is assumed to augment thecarrier uids density and viscosity by amounts related to the

in situ solids volume fraction. Clearly, this technique is of limited value as it, by denition, assumes the slurry has nodeposition velocity. It provides reasonable predictions of frictionlosses only for relatively ne particles, low solids volumefractions, and for a narrow range of operating velocities. Shook and Daniel 4 improved on the pseudohomogeneous approach byconsidering the slurry as a pseudo single-phase uid withvariable density. However, because of the boundary conditionsadopted in their approach, it is difcult to apply their model toactual ow situations.

Oroskar and Turian 5 used a constructive energy approachto calculate the deposition velocity. In their model, they assumedthat the kinetic energy of turbulent uctuations is transferredto discrete particles, which suspends them in the ow. Despitethe fact that this model was oversimplied and not intendedfor dense slurries, predicted deposition velocities comparedfavorably with the experimental data over a wide range of solidsvolume fractions.

Wilson 6 developed a one-dimensional two-layer modelwherein coarse-particle slurry ow is considered to comprisetwo separate layers. Each layer has a uniform concentration andvelocity. Because Wilson assumed the particles were verycoarse, they were contained in the lower layer (with the upperlayer solids concentration being zero). Momentum transferoccurs between the layers through interfacial shear forces. Thetwo-layermodelhasbeenextendedby anumberof researchers. 7 - 13

Doron et al. 7 developed a two-layer model for the predictionof ow patterns and pressure drops in slurry pipelines. Thismodel is very similar to that proposed by Wilson, 6 except thatthe lower layer may also be assumed to be stationary. However,the model did not predict the existence of a stationary bed at

Table 1. Experimental Data Sets Modeled with Hydrodynamic Simulations

measurement technique

source

pipediameter

(mm)particle size

( m)solids volume

concentration (%)particle specic

gravity ( - )mixture

velocity (m/s)pressure

dropparticle

concentration velocity

Roco andShook 27

50.7 165 -ray absorption magnetic uxow meter

51.5 480 6 - 35 2.65 1.5- 4.5263 520495 1300

Schaan et al. 45 50 85 15- 45 2.65 0.8- 5.0 pressure transducers -ray absorption magnetic uxow meter

150 90100

Gillies andShook 12

105 420 26 - 47 2.65 1.8- 5.8 pressure transducers -ray absorption magnetic uxow meter

264 420495

Gillies et al. 13 103 90 10 - 45 2.65 2.0- 8.0 pressure transducers -ray absorption electrical resistivity probe,magnetic ux ow meter

270

Kaushal andTomita 24 54.9 125 5 - 50 2.47 1.0- 5.0 pressure transducers -ray absorption,sampling probe440

Figure 2. Particle concentration prole sensitivity analysis (A) effect of

forces: (O ) exptl, (- - - ) CFD-k- model with kinetic theory and dragforce; (---) CFD- k- model with kinetic theory, drag force, and turbulentdispersion force; ( s ) CFD-k- model with kinetic theory, drag, lift, turbulentdispersion, and wall lubrication force. (B) radial distribution function andkinetic solids viscosity models of Gidaspow 35 and Lun and Savage. 37


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low ow rates, which also reduced the reliability of the pressuredrop predictions. Wilson and Pugh 8 developed a dispersive-force model of heterogeneous slurry ow, which extended theapplicability of the original Wilson layer model because itaccounted for particles suspended by uid turbulence as wellas those providing contact-load (Coulombic) friction. The modelwas used to predict particle concentration and velocity prolesthat were in good agreement with experimental measurements.

Nassehi and Khan 9 developed a numerical method for thedetermination of slip characteristics between the layers of a two-layer slurry ow, but no comparisons between experimentalresults and their numerical solutions were reported.

Undoubtedly, the most commonly used version of the two-layer model is the SRC model developed by Gillies andco-workers. 10 - 13 The SRC two-layer model provides predictionsof pressure gradient and deposition velocity as a function of

particle diameter, pipe diameter, solids volume fraction, andmixture velocity. This model is semimechanistic in that theeffect of pipe diameter on pipeline friction loss is speciedmechanistically (i.e., does not depend on any empiricallydetermined coefcients). The semiempirical coefcients itcontains are based on thousands of controlled experiments doneat the Saskatchewan Research Council Pipe Flow TechnologyCentre. Since the optimum pipeline velocity is usually close tothe deposition velocity ( V c), most of the data that wereincorporated in the model were obtained at mixture velocitiesthat are just greater than the deposition velocity ( V c e V e1.3V c).

Doron and Barnea 14 extended the two-layer modeling ap-proach to a three-layer model of slurry ow in horizontalpipelines. Their model considered the existence of a dispersivelayer, which is sandwiched between the suspended layer and a

Figure 3.Comparison of predicted and experimentally determined

13

concentration proles for d p ) 270 m and V ) 5.4 m/s: (A) Rj s ) 0.10, (B) Rj s ) 0.20,(C) Rj s ) 0.30, (D) Rj s ) 0.35, (E) Rj s ) 0.40, and (F) Rj s ) 0.45.


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bed. The dispersive layer was considered to have a higherconcentration gradient than the suspended layer. A no-slipcondition between the solid particles and the uid was assumed,which is reasonable when the ow is in horizontal or near-horizontal congurations. The model predictions showed sat-isfactory agreement with experimental data. Doron and Barnea 21

also used a three-layer model to draw ow pattern maps, whichcan be used to indicate the ow pattern (essentially, the degreeof ow heterogeneity). They determined the transition linesbetween the so-called ow patterns and compared these resultswith experimental data. Ramadan et al. 16 also developed a three-layer solid model and applied to simulate slurry transport ininclined channels. The model predictions were compared with

experiments, which clearly demonstrated the limitations of thismodel.A separate (but related) approach to slurry ow modeling

also exists, where the one-dimensional Schmidt - Rouse equa-tion11 (or equivalent; see Hunt 17 ) is used to relate the rate of particle sedimentation to the rate of turbulent exchange, asrepresented by a solids eddy diffusivity, s:

where Rs is the local, time-averaged solids volume fraction, uis the terminal particle settling velocity and y is a verticalposition in the pipe. Karabelas 18 developed an empirical modelto predict the particle concentration proles based on thisformulation. Kaushal and co-workers 19 - 24 developed a diffusionmodel based on the work of Karabelas, 18 where they proposeda modication for the solids diffusivity for coarse particle slurry

ow. They constructed an empirical correlation determining theratio of the solids diffusivity to the liquid eddy diffusivity. Theirfunction shows that the solids diffusivity increases with increas-ing solids concentration. However, it does not take into accounta signicant dependence of the solids diffusivity on both particlesize and pipe Reynolds number. 25 They also compared theirpressure drop data with the modied Wasp model, 26 consideringthe effect of efux concentration on dimensionless solidsdiffusivity, 20 and found good agreement at higher ow veloci-ties; however, deviations were signicant at ow velocities nearthe deposition velocity.

Roco and Shook 27 - 29 developed a similar model for denseslurry pipeline ows. They considered the slurry to be aNewtonian uid characterized using the mixture density andviscosity. They accounted for turbulent properties of the owby introducing in the Navier - Stokes equation, an empirical termcharacterizing the turbulent viscosity. The particle concentrationprole was determined using a semiempirical diffusion equationsimilar to that described above. Model predictions werecompared with experimental data for solids volume fractionsless than 35%. This model was not reliable at higher solidsvolume concentrations. Over the years, Roco and co-workers 30,31

modied the turbulence model and used higher-order correla-tions to obtain a better estimate of eddy viscosity. Roco andMahadevan 31 used a one-equation kinetic energy model forturbulent viscosity. The model provides good predictions;however, it contains many empirical parameters.

Gillies and Shook 11 showed the most signicant limitationof this type of model. It is not applicable when the particle sizeis large enough that the particles cannot be supported by uid

Figure 4. Comparison of predicted and experimentally determined 13 concentration proles for d p ) 90 m and V ) 3.0 m/s: (A) Rj s ) 0.19, (B) Rj s ) 0.24,(C) Rj s ) 0.29, and (D) Rj s) 0.33.

Rsu - sdRsd y

) 0 (1)


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turbulence, which occurs approximately when u / u* 0.78,where u* is the friction velocity ( u* ) ( w / F)1/2). As the particlediameter (and u) increases, concentration proles take anoticeably different shape, becoming largely dependent on localconcentration and exhibiting almost no dependence on mixturevelocity (or uid turbulence levels).

Numerous observations of a local maximum in particleconcentration up from the bottom of the pipe have been madewhen the particle diameter is relatively large and the mixturevelocity is high. 3,11,24,32,33 Wilson and Sellgren 32,33 demonstratedthat this effect is the result of a near-wall lift force that occursin certain coarse-particle slurry ows. Recently, Kaushal and

Tomita 24 conducted experiments with two slurries of narrowlysized glass beads (0.125 and 0.44 mm) owing in a 55 mmpipeline loop. These results clearly demonstrated the importanceof the near-wall lift force on concentration proles and onfrictional pressure gradient for slurries containing the coarseparticles. These researchers conrmed many of the ndings of Wilson and Sellgren: most notably, that the smaller particlesare fully encapsulated in the viscous sublayer and thus are notsubjected to a near-wall force. Also, Campbell et al. 34 reportedexperimental observations of an unexpected lift-like interactionforce at the center of channel containing a owing solids - liquidmixture. This force has no apparent analog for single particlesin innite uids and appeared to be a result of multiparticleinteractions. The magnitude of this force was found to be asignicant fraction (e.g., 40%) of the total weight of particlesin the channel and thus may play a role in offsetting theCoulombic (contact load) friction in coarse particle slurry ows.

As described above, many papers have been published in thepast 50 years on the subject of horizontal slurry pipeline ow. Fromthese publications, the following observations can be made:

(i) Most of the investigations were conducted using smallpipeline loops ( D e 55 mm) to determine pressure gradientsand deposition velocities.

(ii) Many of the earlier studies considered only moderatesolids volume concentrations (say up to 26%).

(iii) The purpose of many of the models that have beendeveloped is to predict frictional pressure drop and/or minimumoperating velocity (i.e., deposition velocity).

(iv) Many of the models are 1D or 2D semiempirical models,meaning that they are limited in their ability to describe suchcharacteristics as uid turbulence, interfacial forces, or the radialvariation of particle velocity or concentration.

(v) While the SRC two-layer model provides accuratepredictions of frictional pressure drop and deposition velocityover a wide range of pipe diameter, particle size, particleconcentration, and mixture velocity, it does not provide infor-mation about uid turbulence, local particle velocities, or local

particle concentrations. It is also limited in application to straightruns of pipeline having a circular cross-sectional area; in otherwords, it is not suitable for more complex geometries that areof great interest in many mineral processing industries.

In view of these limitations, an attempt has been made todevelop a comprehensive computational model to describe thehydrodynamics of horizontal slurry ow based on the kinetictheory of granular ow and using a commercially available CFDpackage (ANSYS-CFX 10.0).

3. Mathematical Modeling

The CFD model used in this work is based on the extendedtwo-uid model, which uses granular kinetic theory to describe

particle - particle interactions. Particles are considered to besmooth, spherical, inelastic, and to undergo binary collisions.The fundamental equations of mass, momentum, and energyconservation are then solved for each phase. Appropriateconstitutive equations have to be specied in order to describethe physical and/or rheological properties of each phase and toclose the conservation equations. The solids viscosity andpressure are computed as a function of granular temperature atany time and position. A more complete discussion of theextended two-uid model, including the implementation of granular kinetic theory, can be found in Gidaspow. 35

3.1. Continuity and Momentum Equation. Each phase isdescribed using volume-averaged, incompressible, transientNavier - Stokes equations. The volume-averaged continuityequation is given by ( i ) liquid, solids):

where R is the concentration of each phase, u is the velocityvector, and F is the density. Mass exchange between the phases,for instance, due to reaction or combustion, is not considered.

The momentum balance for the liquid phase is given by theNavier - Stokes equation, modied to include an interphasemomentum transfer term:

where g is the acceleration of gravity, p is the thermodynamicpressure, F km is the sum of the interfacial forces (including the

Figure 5. Comparison of predicted and experimentally determined 45

concentration proles for d p ) 90 m and Rj s ) 0.15: (A) V ) 1.5 m/s, (B)V ) 3.0 m/s.

t (FiRi) + (FiRiu i) ) 0 (2)

t (FlRlu l) + (FlRlu lu l) ) -R l p + F lRlg + l + F km

(3)


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drag force F D, the lift force F L, the virtual mass force F VM, thewall lubrication force F WL and the turbulent dispersion force F T D). The liquid-phase stress tensor, l, can be represented as

The solids phase momentum balance is given by

The solids stress tensor, s, can be expressed in terms of thesolids pressure, P s, bulk solids viscosity, s, and shear solidsviscosity, s:

3.2. Kinetic Theory of Granular Flow. This is, strictlyspeaking, a class of models based on the kinetic theory of gases,generalized to take account of inelastic particle collisions. Inthese models, the constitutive elements of the solids stress arefunctions of the solids phase granular temperature, s, dened

to be proportional to the mean square uctuating particle velocityresulting from interparticle collisions: s ) u s2 /3, where u s isthe solids uctuating velocity. In most kinetic theory models,the granular temperature is determined from a transport equation.The conservation of the solids uctuating energy balance 36 canbe written as

The left-hand side of this equation represents the net change of uctuating energy. The rst term on the right-hand side representsthe uctuating energy due to solids pressure and viscous forces.The second term is the diffusion of uctuating energy in the solidsphase. The third term, s, represents the dissipation of uctuatingenergy and ls is the exchange of uctuating energy between theliquid and solids phase. Although eq 7 can be solved for thegranular temperature, the procedure is complex and the boundaryconditions are not well understood. The procedure is also compu-tationally expensive. A simpler and computationally cheapermethod is to use an algebraic expression, where local equilibriumof generation and dissipation of uctuating energy is assumed.Boemer et al. 36 simplied eq 7 to

Figure 6. Contour plots for (A) particle concentration and (B) liquid velocity taken at regularly spaced axial positions over the 10 m control volume.Obtained from numerical simulations of the following conditions: d p ) 90 m, V ) 3.0 m/s, and Rj s ) 0.19.

l ) l[u l + (u l)T ] - 23

l(u l) I (4)

t (FsRsu s) + (FsRsu su s) ) -R s p + F sRsg + s + F km

(5)

s ) (- P s + su s) I + s{[u s + (u s)T ] - 23(u s) I }(6)

32[

t (RsFss) + (RsFsu ss)]) s:u s + (k s ) - s +

ls (7)


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The dissipation uctuating energy is 35

where e is the coefcient of restitution for particle collisions, d p isthe particle diameter, and g0 is the radial distribution function atcontact. The restitution coefcient, which quanties the elasticityof particle collisions (one for fully elastic and zero for the fullyinelastic), was taken as 0.9. The radial distribution function, g0,can be seen as a measure of the probability of interparticle contact.

Popular models for the radial distribution function are given byGidaspow: 35

and Lun and Savage: 37

where Rsm is the volume fraction of a settled bed of solids. The g 0function becomes innite when the in situ solids volume fractionapproaches Rsm. A value of Rsm ) 0.64 is often assumed for arandom packing of monosize spheres. In practice, though, the valueof the settled bed volume fraction should be measured, as it dependsprimarily on particle sphericity and particle size distribution. 38

Figure 7. Predicted liquid velocity proles for (A) d p ) 90 m, V ) 3.0 m/s and Rj s ) 0.19; (B) d p ) 270 m, V ) 5.4 m/s and Rj s ) 0.20; (C) d p ) 480 m, V ) 3.44 m/s and Rj s ) 0.203. Measurements of local particle velocity shown in panel A from Gillies et al. 13

production ) dissipation sij U i x j

) s (8)

s ) 3(1 - e2

)Rs2

Fsg0

s

(4d p(

s

- diVU )) (9)

g0(Rs) ) 0.6(1 - (Rs / Rsm)1/3)- 1 (10)

g0(Rs) ) (1 - (Rs / Rsm))- 2.5Rsm (11)


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The solids pressure represents the solids phase normal forcescaused by particle - particle interactions. In the kinetic theoryof granular ow, both the kinetic and the collisional contribu-tions are considered. The particle pressure consists of a kineticterm corresponding to the momentum transport caused byparticle velocity uctuations and a second term due to particlecollisions: 35

In eq 6, the solids bulk viscosity accounts for the resistance of the granular particles to compression and expansion and hasthe form 39

The solids shear viscosity contains terms arising from particlemomentum exchange due to collision and translation. The solidsshear viscosity is expressed as a sum of the kinetic and

collisional contributions:

The collisional component of the solids viscosity is modeledas

and the kinetic component is determined based on 35

and Lun and Savage 37

where ) 1 / 2(1 + e)3.3. Interfacial Forces. The interphase momentum transfer

between solids and liquid due to drag force is given by

The drag coefcient C D has been modeled using the Gidaspowmodel, 35 which employs the Wen and Yu model when Rs > 0.2and employs the Ergun model when Rs e 0.2.

The lift force can be modeled in terms of the slip velocityand the curl of the liquid phase velocity 40,41 as

The lift coefcient has been assigned a value of 0.1 in thepresent simulation. This value is within the range suggested inthe literature. 41

The wall lubrication force, which is in the normal directionaway from the wall and decays with distance from the wall, is

expressed as42

Here, u r ) u l - u s is the relative velocity between phases, d p isthe mean particle diameter, yw is the distance to the nearest wall,and nw is the unit normal pointing away from the wall. Thewall lubrication constants C 1 and C2, as suggested by Antal etal.42 are - 0.01 and 0.05, respectively. The turbulent dispersionforce is modeled based on the Favre average of the interphasedrag force using 43

Here, tc is the turbulent Schmidt number for continuous phasevolume fraction, taken here to be tc ) 0.9.

3.4. Turbulence Equations. The turbulence model used forthe liquid phase is a variant of the two-equation k - model,which is given in standard form as:

In these equations, G represents the generation of turbulentkinetic energy due to the mean velocity gradient. For the liquidphase, a k - model is applied with its standard constants: C 1) 1.44, C 2 ) 1.92, C ) 0.09, k ) 1.0, ) 1.3. Noturbulence model is applied to the solids phase but the inuenceof the dispersed phase on the turbulence of the continuous phaseis taken into account with Satos additional term. 44

3.5. Boundary Conditions. At the inlet, velocities andconcentrations of both phases are specied. At the outlet, thepressure is specied (atmospheric). At the wall, the liquidvelocities were set to zero (no- slip condition). The velocity of the particles was also set at zero. To initiate the numericalsolution, the average solids volume fraction and a parabolicvelocity prole are specied as initial conditions.

4. Numerical Solution

The system of equations, with the aforementioned boundaryconditions, was solved using the commercial ow simulation

software ANSYS CFX 10.0. Mass and momentum equationswere solved using a second-order implicit method for space anda rst-order implicit method for time discretization. Theconservation equations were discretized using the control volumetechnique. The discretization of the three-dimensional domainresulted in 386 340 cells and the grid structure shown in Figure1. The SIMPLE algorithm was employed to solve the pressure-velocity coupling in the momentum equations. The highresolution discretization scheme was used for the convectiveterms. Initial simulations were carried out with a coarse meshto obtain rapid convergence and an indication of the positionswhere a high mesh density was needed. Grid independence wasexamined, but further grid renement did not result in signicantchanges to the simulations results. Three dimensional transientsimulations were performed. In these simulations, a constanttime step of 0.001 s and pipe length of 10.0 m were used. Time-averaged distributions of ow variables are computed over aperiod of 100 s.

P s ) F sRss + 2FsRs2

s(1 + e)g0 (12)

s )43

Rs2Fsd pg0(1 + e) (13)

s ) s,col + s,kin (14)

s,col )45

Rs2Fsd pg0(1 + e) (15)

s,kin )5 48

Fsd p(1 + e)g0(1 +

45

(1 + e)g0Rs)2 (16)

s,kin )5 96

Fsd p( 1g0 +85

Rs)(1 +85

(3 - 2)g0Rs

2 - )(17)

F D )34

C DRsFl1d p

|u l - u s|(u l - u s) (18)

F L ) C LRsFl(u s - u l) u l (19)

F WL ) -R sFl(u r - (u rnw)nw)

d pmax[C 1 + C 2 d p yw , 0] (20)

F TD )34

C Dd p

tc tc

RdFc(u d - u c)(RdRd -RcRc ) (21)

t (FlRlk ) +

x i(FlRlu lk ) )

x i(Rl( + l,tur

k ) k x i)+Rl(G - R l) (22)

t (FlRl) +

x i(FlRlu l) )

x i(Rl( + l,tur

) x i)+Rl

k

(C 1G - C 2Rl) (23)


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5. Results and Discussion

The CFD simulations were carried out to match the experi-mental conditions of Roco and Shook, 27 Schaan et al., 45 Gilliesand Shook, 12 Gillies et al., 13 and Kaushal and Tomita. 24 Table1 summarizes the experimental conditions and measurementtechniques employed to measure pressure drop, particle con-centration proles, and mixture velocity. Each data set describedin Table 1 was simulated using the model described in theprevious sections. The local, time-averaged particle concentra-tion proles, particle and liquid velocities, and frictional pressuredrop were obtained using the model and then were compared(where possible) with the existing experimental data. A widerange of particle size (90 - 500 m), solids volume concentration(8- 45%), mixture velocity (1.5 - 5.5 m/s), and pipe diameter(50- 500 mm) were considered. In the gures discussed here,

y/D is the dimensionless position along the pipes vertical axis,where y is the distance from the pipe bottom, the local particleconcentration is Rs, the liquid velocity is ul, and the frictionalpressure drop is p / L.

5.1. Sensitivity Analysis. Initially, numerical simulationswere conducted for three cases to demonstrate the effects thatthe inclusion of different forces had on the quality of thepredictions. In the rst case, the simulations were carried outwith the k - model based on the kinetic theory of granularow and drag force only . The model predictions are shown inFigure 2A, where the predicted particle concentration proleshows a peak near the bottom of the pipe. The local solidsvolume fraction rapidly approaches zero at a vertical positionof y / D 0.85. The second simulation included drag force andthe turbulent dispersion force. The predicted result is in good

Figure 8. Effect of particle size on concentration prole: (A) d p ) 90 m, V ) 3.0 m/s, Rj s ) 0.19, and D ) 103 mm; (B) d p ) 125 m, V ) 3.0 m/s, Rj s

) 0.20, andD

) 54.9 mm; (C)d

p ) 165 m,V

) 4.17 m/s, Rj s ) 0.189, andD

) 51.5 mm. (D)d

p ) 270 m,V

) 5.4 m/s, Rj s ) 0.20, andD

) 103 mm.(E) d p ) 440 m, V ) 3.0 m/s, Rj s ) 0.20, and D ) 54.9 mm. (F) d p ) 480 m, V ) 3.44 m/s, Rj s ) 0.203, and D ) 51.5 mm.


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agreement with the experimental data. In the third case, whenall the forces (drag, turbulent dispersion, lift, and wall lubricationforce) were included, the results showed no signicantimprovement.

Additionally, two radial distribution function and kineticsolids viscosity models 35,37 were tested. Essentially, there is nodifference between the two, as shown in Figure 2B. On the basisof these observations, all subsequent simulations were conductedusing (i) k - turbulence model with the kinetic theory of granular ow; (ii) drag and turbulent dispersion forces; and (iii)the Gidaspow radial distribution function/kinetic solids viscositymodel. 35

Lift and wall lubrication forces were neglected in thesesimulations.

5.2. Solids Concentration Proles. Because concentrationproles depend on many parameters, including mixture velocity,

mixture density, pipe diameter, particle size, and particle density,it is important to test the ability of a model to predict theseproles. Additionally, the knowledge of solids distribution acrossthe pipe cross-section is essential in the evaluation or predictionof pipeline wear. 46 Figure 3 shows the experimental andpredicted concentration proles for 270 m sand slurries owingat a constant mixture velocity (5.4 m/s) in a 100 mm pipeline.In situ solids volume concentrations of 10 to 45% were tested(and simulated). The experimental data were initially reportedby Gillies et al. 13 Generally, the numerical predictions showreasonable agreement with the experimental results. It can beobserved from the gures that for a given velocity, increasingthe in situ solids concentration reduces the asymmetry of theconcentration proles because of increased particle interactions.For these slurries, uid turbulence is not completely effectivein suspending the particles; instead, suspension results partly

Figure 9. Effect of pipe diameter on concentration prole, d p ) 165 m: (A) D ) 51.5 mm, Rj s ) 0.0918, and V ) 3.78 m/s; (B) D ) 51.5 mm, Rj s ) 0.286,

and V ) 4.33 m/s; (C) D ) 263 mm, Rj s ) 0.0995, and V ) 3.5 m/s; (D) D ) 263 mm, Rj s ) 0.268, and V ) 3.5 m/s; (E) D ) 495 mm, Rj s ) 0.104, andV ) 3.16 m/s; (F) D ) 495 mm, Rj s ) 0.273, and V ) 3.16 m/s.


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from particle - particle interactions. 13 This is a good test of themodels ability to predict the combined importance of uidturbulence and shear-dependent (Bagnold-like) particle - particleinteractions. Overall, the results are encouraging.

In Figure 3F, the experimentally determined concentrationprole exhibits a reversal in local concentration near the pipeinvert. This reversal is not predicted in our simulations and maybe related to the existence of near-wall forces describedpreviously.

Figures 4 and 5 show experimental data and numericalpredictions for 90 m sand slurries owing in 100 and 154 mmpipelines, respectively. The particles in these slurries areeffectively suspended by uid turbulence, as the relativelyuniform concentration proles at low in situ volume fractionsattest. These concentration proles can be accurately predictedusing a Schmidt-Rouse 1D turbulent diffusion model. 11,19 - 23

They also provide a good test of the numerical models abilityto predict the importance of the turbulent dispersion forces.Overall, the agreement between the numerical predictions andexperimental results is good.

Contour plots of particle concentration and liquid velocity alongthe pipe cross section at axial positions separated by 1.25 mintervals are shown in Figure 6. Signicant differences in particleconcentration and liquid velocity can be observed between the rstand fourth axial positions. The contour plots shown for axialpositions 5 through 8 are nearly identical, indicating that thenumerical simulations are providing results for fully developed

ow.5.3. Velocity Proles. Velocity proles in horizontal slurry

ow are directly linked to the concentration prole; as such, theyare also dependent upon particle size, in situ solids concentration,

Figure 10. Effect of pipe diameter on concentration prole for slurries of ne particles, V ) 3.0 m/s: (A) D ) 54.9 mm, d p ) 125 m, Rj s ) 0.30; (B) D) 54.9 mm, d p ) 125 m, Rj s ) 0.40; (C) D ) 103 mm, d p ) 90 m, Rj s ) 0.29; (D) D ) 103 mm, d p ) 90 m, Rj s ) 0.33; (E) D ) 150 mm, d p ) 90 m, Rj s ) 0.32; (F) D ) 150 mm, d p ) 90 m, Rj s ) 0.39.


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and mixture velocity. Figure 7 shows three pairs of illustrations.The left-hand gure shows a traditional velocity prole, where thelocal time-averaged liquid velocity along the pipes vertical axisis plotted. The corresponding contour plot is the type that is readilyattainable from CFD simulations. Figure 7A compares a measuredparticle velocity prole 13 with predictions for a 90 m sand slurry(Rj s ) 0.19, V ) 3.0 m/s). Recall that the corresponding concentra-tion prole, which is shown in Figure 4A, is nearly symmetric.Note also the agreement between the measured particle Velocityand the predicted uid Velocity is excellent, conrming that thelocal, time-averaged slip velocity approaches zero for slurries of this type. Figure 7 panels B and C show predicted liquid velocityproles for slurries containing coarser particles (270 and 480 m,respectively). It can be seen that the velocity proles becomeincreasingly asymmetrical with increasing particle size. Themaximum local velocity is found in the upper portion of the pipeand not at the centerline. This phenomenon has been demonstratedexperimentally. 13,27 Note also from the contour plots that thevelocity distribution in a horizontal plane is symmetrical about thepipe axis.

5.4. Effect of Particle Diameter. Figure 8 shows the mea-sured and predicted concentration proles for four different slurries,each with a different particle size (90, 125, 165, 270, 440, and480 m). In situ solids volume fractions are comparable for theseslurries (Rj s 0.2). The experimental data shown in these guresrepresent a broad spectrum of uid turbulence effects on particle

suspension, from highly effective (Figure 8A) to completelyineffective (Figure 8F). Concentration proles of the type shownin Figure 8F, for very coarse particles, depend primarily on in situsolids volume fraction, with only minimal dependence on mixturevelocity or pipe diameter. Thus, the measured concentration proleof Figure 8F can be considered to be typical of one that would befound for any coarse particle slurry ( d p > 300 m). In all cases,the agreement between measured and predicted proles isencouraging.

In Figure 8E,F, a distinct reversal in the concentration prolecan be seen near the pipe invert ( y / D < 0.2). This is related to thenear-wall lift force described previously, 24,32 which occurs whenthe particle is large relative to the viscous sublayer thickness. Thecurrent version of the CFD model is unable to reproduce thisconcentration reversal.

5.5. Effect of Pipe Diameter. To investigate the effect of pipediameter on the performance of the numerical model developedhere, the ow of a number of slurries in pipes of different diameter

was considered. Figure 9 shows both experimental and predictedconcentration proles for a 165 m sand slurry owing in pipesthat are 51.5, 103, 150, 263, and 495 mm in diameter. Themeasured concentration proles were taken from Roco andShook. 27 This particular particle size was chosen for two reasons:data had been collected from experiments conducted with a widerange of pipe diameters and this sand size exhibits strong pipediameter-dependent concentration proles. The relative importanceof uid turbulence vis-a-vis particle - particle interactions indetermining the shape of the concentration proles with increasingpipe diameter is clearly shown in Figure 9. The predictions are ingood agreement with the experimental data for all pipe diameters.

Figure 10 provides similar ndings for experimental measure-ments made with smaller particles of differing size and shape. Themixture velocity is the same for each panel ( V ) 3.0 m/s). Figure10 panels A and B show the experimental measurements made byKaushal and Tomita 24 for slurries of 125 m glass spheres in waterowing in a 54.9 mm pipeline loop. Figure 10 panels C - F showresults and predictions for narrowly sized 90 m sand slurriesowing in 100 and 150 mm pipelines. No noticeable effect of pipe

diameter is observed for these concentration proles, because theparticles are relatively ne and the mixture velocity in each caseis signicantly greater than the deposition velocity. Again, theconcentration prole reversal seen in Figure 10 panels A and B isnot accurately reproduced with the current model. Otherwise, themodels performance is satisfactory.

5.6. Pressure Drop. Pipeline pressure drop is one of the mostimportant parameters in slurry pipeline design and operation.To validate the numerical results obtained with the CFD model,the simulation results were compared with the experimental dataof Schaan et al., 45 Gillies and Shook, 12 Gillies et al. 13 andKaushal and Tomita. 24 As the information presented in Table1 indicates, these experimental data were collected for a widerange of particle size, mixture velocity, in situ solids volumefraction, and pipe diameter. The comparison of measured andpredicted frictional pressure drop results is shown in Figure 11.The predicted pressure drop is in good agreement wit

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