thesis_presentation_ver3

CFD-Based Modeling of Multiphase Flows: From

Spout Beds to Hydraulic Fracturing

MSc Thesis Oral Presentation, UofA, CME, Edmonton, 21 April, 2015

Md. Omar Reza

1

80Introduction Model Setup Spouted Bed Fracturing SummaryMultiphase Flows Modeling Concepts

Multiphase �ow are important in many industrialprocess: �uidized bed reactors, scrubbers, dryersetc.

CFD modeling of multiphase �ow has becomewidely accepted because of its broad range ofapplication

CFD simulation also enables the researchers toinvestigate the processes those are impossible tomeasure

But the bottle-neck of this processes is thevlaidation of software and model against reliablesource of data

Example of a spout bed

2

80Introduction Model Setup Spouted Bed Fracturing SummaryMultiphase Flows Modeling Concepts

Euler-Lagrange method is suitable for disperse �ows where individual

particles are tracked using the Lagrangian system of coordinates. A

bulk �ow is modeled using the Eulerian system of coordinates.

In this method, Naviar-Stokes equations are used to model bulk�ow and the Newton's equations of motion are utilized fortracking of individual particle.

Euler - Euler approach uses N-S equations averaged for each phase.

In this way, Euler-Euler method is computationally cheaper, butneeds intensive modeling e�ort.

There are many software that can simulate multiphase �ow system i.e. ANSYS-FLUENT, ANSYS-CFX, COMSOL Multiphysics, MFix etc.

At this point, software validation is necessary to represent real life �owsystem in an adequate way.

In this work, Euler-Euler method is utilized to conduct research on�spouted bed" and �hydraulic fracturing" to solve some of the`unknown' behaviors which still exist in the present systems.

φ = 0.57

(a) E-L model

φ = 0.57

(b) E- E model

3

80Introduction Model Setup Spouted Bed Fracturing SummaryGeometry Model Parameters

Geometry

(Y. He et al. Can. J. Chem. Eng. ,72:229�234, 1994.)

Cylinder enclosure height: 1.4 m

Inside diameter: d =0.152 m

Initial bed height: 0.325 m

Inlet ori�ce diameter: din =0.019 m

Mean particle diameter: dp =1.41mm

Conical base angle: 60 o

Inlet gas velocity: uin =44 m/s, =⇒U

Ums= 1.3, Ums = 0.54 m/s

Gas density: ρg =1.225 kg/m3

Particle density: ρs =2503 kg/m3 Figure: Schematicdiagram of spout bed

4

80Introduction Model Setup Spouted Bed Fracturing SummaryGeometry Model Parameters

Model Input Parameters

Multiphase �ow model: Unsteady Laminar Euler-Euler

Drag model: Syamlal-O'Brien

Granular viscosity: Syamlal-O'Brien

Frictional viscosity: Johnson et. al.

Solid pressure: Syamlal-O'Brien

Restitution coe�cient, ess = 0.90, 0.95, 0.97, 0.99

Maximum packing limit, αmax = 0.55, 0.58, 0.61

Numerics

Grid size: 14x103 control volumes

Time step: 10−4 sec

Iteration per time step: 40

Maximum normalized residual per time step: 10−5

Discretization of convective term: QUICK scheme

modi�ed HRIC scheme is used for convective terms in eqs.of the volume fraction of gas/solid.

r, m

z, m

0 0.050

0.4

Figure: Computationalaxisymmetric domain and

grid (zoomed view)

5

80Introduction Model Setup Spouted Bed Fracturing SummaryDrag Model Time-Averaging Validation Swirling

Syamlal-O'Briendrag model

ess = 0.95, αs,max = 0.61

Gidaspowdrag model

ess = 0.95, αs,max = 0.61

Wen-Yudrag model

ess = 0.95, αs,max = 0.61

Figure: Contour plot of time-average volume fraction of solid particle calculated usingdi�erent drag model. Here ess = restitution coe�cient and αs,max = maximum

packing limit6


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8z, m

0

1

2

3

4

5

6

7

u, m

/s

experimentDu et al. (S-B model)Du et al. (Gidaspow model)

simulation, S-B model simulation, Gidaspow model

Simulation, Yu model

Figure: Axial pro�les of the time-averaged velocity of particles for di�erent drag model.Here 'experiment He' data correspond to the work He et al. 1

'simulation Du et al.' corresponds to the work Du et al., 2 'S-B' denotesSyamlal-O'Brien drag model.

1Y. He, C. Lim, J. R. Grace, and J. Zhu. Can. Jo. Chem. Eng.,72:229�234, 1994.

2W. Du, X. Bao, J. Xu, and W. Wei.' Chem. Eng. Sci., 61:4558-4570, 2006. 7


ess = 0.99αs,max = 0.61

ess = 0.97αs,max = 0.61

ess = 0.95αs,max = 0.61

ess = 0.90αs,max = 0.61

Elastic �� Inelastic

Figure: The impact of restitution coe�cient,

here αs,max= maximum packing limit, and ess= coe�cient of restitution

8


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8z, m

0

1

2

3

4

5

6

7u, m

/sexperimentDu et al. (S-B model)Du et al. (Gidaspow model)

simulation, ess

=0.90

simulation, ess

=0.95

simulation, ess

=0.97

simulation, ess

=0.99

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9z, m

0

1

2

3

4

5

6

7

u, m

/s

experiment

Du et al. (S-B model)Du et al. (Gidaspow model)

simulation, αs,max

=0.55

simulation, αs,max

=0.58

simulation, αs, max

=0.61

(a) In�uence of restitution coe�cient (b) In�uence of maximum packing limit

Figure: Axial pro�les of the time-averaged velocity of the solid phase.Here 'experiment He' data correspond to the work He et al. 3

'simulation Du et al.' corresponds to the work Du et al., 4 'S-B' denotesSyamlal-O'Brien drag model.

3Y. He, C. Lim, J. R. Grace, and J. Zhu. Can. Jo. Chem. Eng.,72:229�234, 1994.

4W. Du, X. Bao, J. Xu, and W. Wei.' Chem. Eng. Sci., 61:4558-4570, 2006. 9


ess = 0.95αs,max = 0.61

swirling ratio = 0

ess = 0.95αs,max = 0.61

swirling ratio = 0.136

ess = 0.95αs,max = 0.61


ess = 0.95αs,max = 0.61


Swirling Ratio = 0 ��-�� Swirling Ratio =1

Figure: Contour plots of the time average volume fraction of solid phase - (from left

to right) swirling ratio, vθ = 0, 0.136, 0.57, 1.0. Here, swirling ratio =Vswirling

Vinlet10


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8z, m

0

1

2

3

4

5

u, m

/s

simulation, without swirl

simulation, vθ

= 0.136

simulation, vθ = 0.568

simulation, vθ = 1

Figure: Axial pro�les of the time-averaged velocity of the solid phase. Here `simulation- without swirl' corresponds to the simulation work where ess = 0.95 and

αs,max = 0.61 and vθ represents swirling ratio

11

80Introduction Model Setup Spouted Bed Fracturing SummaryIntroduction Validation Input Parameters Contour Plot Mixing Zone

In this work, the CFD analysis of slurry �ow through ahydraulic fracturing using Euler-Euler model is also studied.

The main objective consists in gaining understanding of thebehavior of slurry (water+sand) pumped into a fracture.

Following cases were considered:

- 2D straight shaped fracture

- 2D zikzak shaped fracture with di�erent viscous ratio

- 3D zikzak shaped fracture with di�erent viscous ratio

Euler-Euler model was validated with Euler-Lagrange modelfor particle sedimentation 5 .

Mixing zone for straight shaped and zikzak shaped fracturewere successfully calculated.

5F. Dierich, P.A. Nikrityuk, and S.Ananiev. 2d modeling of moving particles with phase-change

e�ect. Chem. Eng. Sci., 66:5459�5473, 2011. 12


Fig: Snapshots of the volume fraction of particles predicted using di�erent models:(top) with Euler-Lagrange model 6 at (left to right) t= 0.02, 0.62, 1.09, 1.62, 3.42 sec;(bottom) with Euler-Euler model at (left to right) t= 0.05, 0.55, 1.0, 2.0, 4.0 sec.

6F. Dierich, P.A. Nikrityuk, and S.Ananiev. 2d modeling of moving particles with phase-change

e�ect. Chem. Eng. Sci., 66:5459�5473, 2011. 13


General sim. con�guration:- Particle diameter: 0.6 mm- Particle density: 999 kg/m3

- Water density: 999 kgm3

- In�ow velocity: 0.3 m/s- In�ow VOF of particles: 0.3

Straight shaped fracture:

- Reynoldsparticle =179.28- Reynoldswater =2988

Zikzak shaped fracture:

* For viscous ratio : 1- Reynoldsparticle =179.28- Reynoldswater =2988

* For viscous ratio : 5- Reynoldsparticle =35- Reynoldswater =597.6

* For viscous ratio : 30- Reynoldsparticle =5.98- Reynoldswater =99.6

14


Figure: Contour plots of straight shaped fracture with slurry �ow, ess =0.90 at time, t= 2.25 sec

Figure: Contour plots of zikzak shaped fracture with slurry �ow, ess =0.90 at time, t= 11.50 sec

15


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

z*

0.2

0.25

0.3

0.35

0.4

φs

Rµ = 1

Rµ = 5

Rµ = 30

(a) (b)

Figure: (a) Contour plots of zikzak shaped fracture with slurry �ow for viscosity ratio=1, (b) pro�le of volume fraction of particles in z-direction for di�erent viscous ratio attime t= 1.13-1.5 sec, location x = 0.45m and y = 0.0125m. Here, Rµ = viscous ratio

16


The mixing zone is the distance between the slurry front and aplace where sand detaches the wall.

0 2 4 6 8 10t, sec

0

0.5

1

1.5

2L

mix

, m

Rµ= 5

Rµ= 1

Rµ = 30

Figure: Time history of the mixing length predicted for zikzak shaped fracture withdi�erent viscosity ratio of water

17

80Introduction Model Setup Spouted Bed Fracturing Summary

Spouted Bed

Unsteady laminar Euler-Euler simulation result shows verygood agreement with the experimental work of He at. el.

The decrease in restitution coe�cient ess up to 0.90 leads toincrease in the fountain height up to 30%.

Syamlal-O'Brein drag model provided better agreement withexperiment in compared to Gidaspow and Yu model.

Hydraulic Fracturing

Volume fraction of particles pro�le shows an `M' shapedstructure for straight fracture, but doesn't appear in zikzak.

Instability appears in Z-direction for lower viscous ratio inzikzak shaped fracture.

Mixing length for lower viscosity ratio (i. e. Rµ = 1.0) gives avery low increment rate of mixing length with time.

18


Acknowledgments

We thank Schlumberger Canada for its support.

Financial support by NSERC is gratefully acknowledged.

Natural Sciences and Engineering Research Council of

Canada

http://www.nserc-crsng.gc.ca

19

http://www.nserc-crsng.gc.ca


0 1 2 3 4 5 6 7 8 9 10t,s

0.8

0.9

1

1.1

1.2

1.3



, m

/s

Gidspow modelYu modelS-B model

0 1 2 3 4 5 6 7 8 9 10t,s

0

0.1

0.2

0.3

0.4

0.5

, m

/s

Gidspow modelYu modelS-B model

Figure : Time history of (left �gure) gas and (right �gure) solid phase areshown for di�erent drag model

20


0.005 0.01 0.015 0.02 0.025r, m

0

0.1

0.2

0.3

z, m

experiment, Hesim. e

ss =0.90

sim. ess

=0.95

sim. ess

=0.97

sim. ess

=0.99

Figure: Spout boundary.Here 'experiment He' data

correspond to the work He etal. where ess=coe�cient of

restitution

0.005 0.01 0.015 0.02 0.025r, m

0

0.1

0.2

0.3

z, m

experiment, Hesim. α

s,max=0.55

sim. αs,max

= 0.58

sim. αs,max

=0.61

Figure: Spout boundary.Here 'experiment He' data

correspond to the work He etal. where αs,max=maximum

packing limit.

Figure: Spout boundary foress = 0.90 and αs,max = 0.58

21


0 0.0065 0.013 0.0195r, m

0

1

2

3

4

, m

/s

experiment, He

simulation ess

=0.90

simulation ess

=0.95

simulation ess

=0.97

simulation ess

=0.99

0 0.02 0.04 0.06 0.08r, m

-2

-1

0

1

2

3

4

, m

/s

experiment, He

simulation ess

=0.90

simulation ess

=0.95

simulation ess

=0.97

simulation ess

=0.99

Figure: Radial pro�les of the time-averaged velocity of the solid phase in the bedregion, z = 0.268m (left �gure) and fountain region z = 0.045m. Here 'experiment'

data correspond to the work He et al. 7 where ess=coe�cient of restitution andαs,max=frictional packing limit=0.61.

7Y. He, C. Lim, J. R. Grace, and J. Zhu. Can. Jo. Chem. Eng.,72:229�234, 1994. 22


0 0.005 0.01 0.015 0.02 0.025r, m

0.4

0.5

0.6

0.7

0.8

0.9

1

ε g

experiment, He

simulation, ess

=0.90

simulation, ess

=0.95

simulation, ess

=0.97

simulation, ess

=0.99

0 0.005 0.01 0.015 0.02 0.025r, m

0.4

0.5

0.6

0.7

0.8

0.9

εg

experiment, He

simulation, ess

=0.90

simulation, ess

=0.95

simulation, ess

=0.97

simulation, ess

=0.99

Figure: Radial pro�les of the time-averaged volume fraction of gas phase (voidage) indi�erent height, z=0.053 m (left �gure), z=0.218 m (right �gure). Here 'experiment'

data correspond to the work He et al. 8 where ess=coe�cient of restitution andαs,max=frictional packing limit=0.61.

8Y. He, C. Lim, J. R. Grace, and J. Zhu. Can. Jo. Chem. Eng.,72:229�234, 1994. 23


0 2 4 6 8 10 12 14t,s

0.8

1

1.2

1.4



, m

/s

ess

= 0.90

ess

=0. 95

0 2 4 6 8 10 12 14t,s

0

0.2

0.4

0.6

0.8

, m

/s

ess

= 0.90

ess

=0. 95

(a) gas (b) solid

0 2 4 6 8 10 12 14t,s

0.9

1

1.1

1.2



, m

/s

ess

= 0.97

ess

= 0.99

0 2 4 6 8 10 12t,s

0.1

0.2

0.3

0.4

, m

/s

ess

= 0.97

ess

= 0.99

(c) gas (d) solid

Figure: Time histories of the volume-averaged velocities of the gas and solid phasespredicted numerically for di�erent values of the restitution coe�cient ess

24


0.244 s 0.906 s 1.201 s 1.348 s 2.157 s 2.378 s 8.999 s.

Figure: Snapshots of the volume fraction of the solid phase predicted numerically forthe restitution coe�cient of ess = 0.95 and packing limit αs,max = 0.61.

25


0.158 s 0.92 s 1.634 s 2.062 s 2.372 s 2.467 s 11.54 s

Figure: Snapshots of the volume fraction of the solid phase predcited numerically forthe restitution coe�cient of ess = 0.90 and packing limit αs,max = 0.58.

26


0 2 4 6 8 10t,s

0.7

0.8

0.9

1

1.1

1.2

1.3



, m

/s

vθ = 0.568

vθ = 0.136

vθ = 1

0 2 4 6 8 10t,s

0

0.5

1

,

m/s V

θ = 0.136

Vθ = 0.568

Vθ = 1

Figure: Time history of (left to right) gas phase and solid phase for swirling usingess = 0.95 and αs,max = 0.61

27


2.81 s 2.875 s 3.74 s s 3.88 s 7.345 s

Figure: Snapshots of the volume fraction of the solid phase predicted numerically forthe restitution coe�cient of ess = 0.95 and packing limit αs,max = 0.61 for swirling

ratio of 0.136

28


0 0.2 0.4 0.6 0.8 1

d*

0

0.1

0.2

0.3

0.4

0.5

φs

x = 0.25 m

x = 0.50 m

x = 0. 75 m

x = 0.80 m

0 0.2 0.4 0.6 0.8

x*

0

0.1

0.2

0.3

0.4

φs

t = 2.14 sec

Figure: Volume fraction of particles for straight shaped fracture, ess at time t= 2.14sec (left) in radial direction at di�erent axial location (right) in axial direction at

center line

29


0 0.2 0.4 0.6 0.8 1

d*

0.15

0.2

0.25

0.3

0.35

φs

x = 0.69m

0 0.2 0.4 0.6 0.8 1

d*

0

0.1

0.2

0.3

0.4

0.5

φs

x = 1.33 m

x = 2.54 m

x = 3.65 m

x = 4.78 m

Figure: Volume fraction of particles for ess =0.90 at time (left) t=0.5 sec (right) t=11.50 sec in radial direction at di�erent axial location

30

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