thesis_presentation_ver3
TRANSCRIPT
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
80Introduction Model Setup Spouted Bed Fracturing SummaryDrag Model Time-Averaging Validation Swirling
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
80Introduction Model Setup Spouted Bed Fracturing SummaryDrag Model Time-Averaging Validation Swirling
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
80Introduction Model Setup Spouted Bed Fracturing SummaryDrag Model Time-Averaging Validation Swirling
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
80Introduction Model Setup Spouted Bed Fracturing SummaryDrag Model Time-Averaging Validation Swirling
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
swirling ratio = 0.57
ess = 0.95αs,max = 0.61
swirling ratio = 1.0
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
80Introduction Model Setup Spouted Bed Fracturing SummaryDrag Model Time-Averaging Validation Swirling
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
80Introduction Model Setup Spouted Bed Fracturing SummaryIntroduction Validation Input Parameters Contour Plot Mixing Zone
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
80Introduction Model Setup Spouted Bed Fracturing SummaryIntroduction Validation Input Parameters Contour Plot Mixing Zone
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
80Introduction Model Setup Spouted Bed Fracturing SummaryIntroduction Validation Input Parameters Contour Plot Mixing Zone
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
80Introduction Model Setup Spouted Bed Fracturing SummaryIntroduction Validation Input Parameters Contour Plot Mixing Zone
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
80Introduction Model Setup Spouted Bed Fracturing SummaryIntroduction Validation Input Parameters Contour Plot Mixing Zone
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
80Introduction Model Setup Spouted Bed Fracturing Summary
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
80Introduction Model Setup Spouted Bed Fracturing Summary
0 1 2 3 4 5 6 7 8 9 10t,s
0.8
0.9
1
1.1
1.2
1.3
<U
g>
, 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
<U
s>, 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
80Introduction Model Setup Spouted Bed Fracturing Summary
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
80Introduction Model Setup Spouted Bed Fracturing Summary
0 0.0065 0.013 0.0195r, m
0
1
2
3
4
<U
>, 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
<U
>, 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
80Introduction Model Setup Spouted Bed Fracturing Summary
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
80Introduction Model Setup Spouted Bed Fracturing Summary
0 2 4 6 8 10 12 14t,s
0.8
1
1.2
1.4
<U
g>
, 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
<U
s>, 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
<U
g>
, m
/s
ess
= 0.97
ess
= 0.99
0 2 4 6 8 10 12t,s
0.1
0.2
0.3
0.4
<U
s>, 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
80Introduction Model Setup Spouted Bed Fracturing Summary
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
80Introduction Model Setup Spouted Bed Fracturing Summary
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
80Introduction Model Setup Spouted Bed Fracturing Summary
0 2 4 6 8 10t,s
0.7
0.8
0.9
1
1.1
1.2
1.3
<U
g>
, m
/s
vθ = 0.568
vθ = 0.136
vθ = 1
0 2 4 6 8 10t,s
0
0.5
1
<U
s>,
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
80Introduction Model Setup Spouted Bed Fracturing Summary
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
80Introduction Model Setup Spouted Bed Fracturing Summary
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
80Introduction Model Setup Spouted Bed Fracturing Summary
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