Upload
rmm
View
117
Download
9
Tags:
Embed Size (px)
DESCRIPTION
Study on Slurry Flow Modelling in Pipeline (Eth) [LAHIRI, Sandir Kumar] [Nat. Inst. of Techn. Durgapur; 2009] {329s}
Citation preview
From the SelectedWorks of Dr. Sandip KumarLahiri
March 2010
My PhD thesis : Study on slurry flow modelling inpipeline
ContactAuthor
Start Your OwnSelectedWorks
Notify Meof New Work
Available at: http://works.bepress.com/sandip_lahiri/23
i
SSTTUUDDYYOONNSSLLUURRRRYYFFLLOOWWMMOODDEELLIINNGGIINNPPIIPPEELLIINNEE
SSaannddiipp KKuummaarr LLaahhiirrii
ii
SSTTUUDDYYOONNSSLLUURRRRYYFFLLOOWWMMOODDEELLIINNGGIINNPPIIPPEELLIINNEE
THESIS
Submittedinpartialfulfillmentofthe
Requirementsforthedegreeof
DOCTOR OF PHILOSOPHY
By
SANDIP KUMAR LAHIRI
UndertheSupervisionof
DR. K.C.GHANTA
Professor,DepartmentofChemicalEngineering
NATIONALINSTITUTEOFTECHNOLOGY,DURGAPUR
DEPARTMENTOFCHEMICALENGINEERING
DURGAPUR713209,INDIA
2009
iii
DEDICATED
TO
MY PARENTS
&
MY WIFE
iv
NATIONAL INSTITUTE OF TECHNOLOGY
DURGAPUR
DEPARTMENT OF CHEMICAL ENGINEERING
CERTIFICATE
This is to certify that the thesis entitled Study on slurry flow modeling in
pipeline submitted by Sandip Kumar Lahiri in fulfillment of the requirement
of the Degree of Doctor of Philosophy is a record of bonafide research work
carried out by him, in the Department of Chemical Engineering, National
Institute of Technology, Durgapur, under my guidance and supervision. In my
opinion, the thesis has reached the standard fulfilling the requirements of the
Ph. D. degree as prescribed in the regulations of this institute.
(Dr. K.C. Ghanta) Department of Chemical Engineering National Institute of Technology Durgapur, 713209 India
v
Acknowledgement
Finally, a successful end to the long episode of my PhD study is reached. My journey towards the PhD degree could not have been better than this. I appreciate the support provided by many people, which made this journey more exciting and delightful.
I am highly grateful to my supervisor Prof. K.C. Ghanta, who helped me in shaping up the research work presented in this thesis. Sir, thank you for all the help inside and outside the campus you have provided to enable me to reach the target. Your simplicity and attitude of life long learning always kept me motivated and encouraged me to learn the different aspects of science and technology.
I would like to express my deepest gratitude to the authority of NIT, Durgapur, IPCL, Nagothane and Sabic , Saudi Arabia to allow me to pursue my dream and helping me to see this day. I wish to thank to my colleagues Mr Nadeem Khalfe and Mr. Chnimaya Lenka for their continuous support and encouragement.
I wish to extend the deepest sense of respect to my parents who always inspired and motivated me to go for the best, in spite of many testing times at their end. Heartiest thanks to my wife , whose patience, understanding and constant encouragement enabled me to complete this work.
Sandip Kumar Lahiri
vi
Paper published based on present thesis
Regime identification
1. Lahiri, Sandip K. and Ghanta, Kartik Chandra ,Development of a Hybrid Artificial
Neural Network and Genetic Algorithm Model for Regime Identification of Slurry
Transport in Pipelines, Chemical Product and Process Modeling: Vol. 4 : Iss. 1,
Article 22. (2009)
2. Lahiri S.K and Ghanta K.C , Development of a Support Vector Classification Method
For Regime Identification of Slurry Transport in Pipelines , Hydrocarbon
Processing, To be published in Sept issue ,(2009)
Critical velocity
3. Lahiri S.K and Ghanta K.C , The support vector regression with the parameter
tunning assisted by a differential evolution technique: Study of the critical velocity of
a slurry flow in a pipeline, Chemical Industry & Chemical Engineering Quarterly 14
(3) ,191203 (2008)
4. Lahiri S.K and Ghanta K.C , Minimize power consumption in slurry transport,
Hydrocarbon Processing,December issue(2008)
5. Lahiri, Sandip K. and Ghanta, Kartik Chandra ,Hybrid Support Vector Regression
and Genetic Algorithm Technique A Novel Approach in Process Modeling,
Chemical Product and Process Modeling: Vol. 4 : Iss. 1, Article 4. (2009)
Hold up 6. Lahiri S.K and Ghanta K.C , Development of an artificial neural network correlation
for prediction of hold-up of slurry transport in pipelines, Chemical Engineering
Science 63 ,1497 1509 (2008)
vii
7. Lahiri S.K and Ghanta K.C ,Artificial neural network model with the parameter
tunning assisted by a differential evolution technique: The study of hold up of the
slurry flow in a pipeline, Chemical Industry & Chemical Engineering Quarterly 15
(2009)
8. Lahiri S.K and Ghanta K.C , Genetic algorithm tuning improves artificial neural
network models , Hydrocarbon Processing, January issue(2009)
Pressure drop 9. Lahiri S.K and Ghanta K.C, Development of an artificial neural network correlation
for prediction of pressure drop of slurry transport in pipelines, International J. of
Math. Sci. & Engineering Applications, Vol 2,No 1,1-21(2008)
10. Lahiri S.K and Ghanta K.C , Prediction of Pressure drop of Slurry Flow in Pipeline
by Hybrid Support Vector Regression and Genetic Algorithm Model, Chinese Journal
of Chemical Engineering, 16(6) ,(2008)
11. Lahiri, S.K. and Ghanta, Kartik Chandra, Artificial Neural Network Model with
Parameter Tuning Assisted by Differential Evolution Technique: Study of Pressure
Drop of Slurry Flow in Pipeline, Chemical Product and Process Modeling: Vol.
3 : Iss. 1, Article 54. (2008)
12. Lahiri S.K and Ghanta K.C , Support vector regression with parameter
tuning assisted by differential evolution technique: Study on pressure drop of
slurry flow in pipeline, paper accepted for publication(schedule october09
issue), Korean journal of chemical engineering(2009)
CFD 13. Lahiri S.K and Ghanta K.C , Computational Fluid Dynamics Simulation of the Solid
liquid slurry flow in a pipeline, Hydrocarbon Processing, may issue ,(2009)
viii
14. Lahiri S.K and Ghanta K.C, Computational technique to predict the velocity and
concentration profile for solid-liquid slurry flow in pipelines. Hydro transport 17, The
17th International Conference on the hydraulic transport of solids. The Southern
African Institute of Mining and metallurgy and the BHR Group, 2007, 149-175
(August 2007)
Commercial application 15. Lahiri, S.K. and Khalfe N , Process modeling and optimization of industrial ethylene
oxide reactor by integrating support vector regression and genetic algorithm, The
Canadian Journal of Chemical Engineering, Volume 87, Issue 1, Pages 118-128,
(February 2009)
16. Lahiri S.K , Khalfe N and Garawi M , Process modeling and optimization strategies
integrating neural networks and differential evolution, Hydrocarbon Processing, Oct
issue ,35-50(2008)
17. Lahiri S.K and Khalfe N , Novel approach for process plant monitoring,
Hydrocarbon Processing, march issue ,(2008)
18. Lahiri, Sandip Kumar and Khalfe, Nadeem) ,Process Modeling and Optimization
Strategies Integrating Support Vector Regression and Differential Evolution: A Study
of Industrial Ethylene Oxide Reactor, Chemical Product and Process Modeling:
Vol. 3 : Iss. 1, Article 57. (2008)
Paper under review
19. Lahiri S.K and Ghanta K.C , Critical velocity of slurry flow, under review, Asia
pacific journal of chemical engineering(2009)
ix
20. Lahiri S.K and Ghanta K.C , Prediction of pressure drop and concentration
profile by semi empirical correlations--modification of Wasp model, under
review, Chemical engineering progress(2009)
21. Lahiri S.K and Ghanta K.C , Prediction of hold up of Slurry Flow in Pipeline
by Hybrid Support Vector Regression and differential evolution Model,
under review, Powder technology(2009)
x
List of Contents Contents Page
1. Introduction 1.1 Introduction 2
1.2 Typical flow regime 5
1.3 Critical velocity 5
1.4 Hold up 6
1.5 Pressure drop 6
1.6 Concentration and velocity profile 6
1.7 Motivation of present work 7
1.8 Scope of present work
1.8.1 Advanced numerical modeling 9
1.8.2 Semi empirical modeling 9
1.8.3 Multiphase computational fluid dynamics (CFD) based 9
modeling
1.9 Thesis purview 10
2. Mathematical tools 2.1 Introduction 13
2.2 Artificial neural network 14
2.2.1 Background works 14
2.2.2 Overview of classification neural networks 15
2.2.3 Overview of prediction neural networks 16
2.2.4 Strengths of ANN 17
2.2.5 Limitations of neural networks 19
2.3 Comparison of neural networks to empirical modeling 20
2.4 Artificial neural network (ANN) based modeling 21
2.4.1 Network Architecture 21
2.4.2 Training 22
2.4.3 Back propagation algorithm (BPA) 22
2.4.3.1 Different back propagation algorithm 25
xi
2.4.4 Performance measures of ANN model 25
2.4.5 Generalizability 27
2.4.6 Step-wise Procedure for Developing an Optimal MLP Model 27
2.5 Tuning parameters of ANN 28
2.6 Optimization of ANN model 30
2.7 Genetic algorithm 32
2.7.1 Literature survey of genetic algorithm 33
2.7.2 Techniques used in GA 33
2.8 GA-based Optimization of ANN Models 36
2.9 Differential evolution 39
2.9.1 Literature survey of Differential evolution 39
2.9.2 Steps performed in DE 40
2.10 DE-based Optimization of ANN Models 41
2.11 Support Vector Machines 44
2.12 Background works 45
2.13 The basic idea behind SVM modeling 46
2.13.1 Support vector machine for classifications 46
2.13.2 Mathematics behind SVM algorithm for classification 48
2.13.3 Training, testing and Generalizability 51
2.13.4 Mathematics behind SVM algorithm for regression 52
2.14 Tuning parameters of SVR 55
2.15 Optimization of SVM model 58
2.16 GA-Based Optimization of SVR Models 60
2.17 DE based optimization of SVR model 61
2.18 Conclusion 64
3. Regime identification of slurry transport in pipelines 3.1 Introduction 82
3.2 Background work 83
3.2.1 Flow regimes in slurry flow 85
3.2.2 Head loss correlations for separate flow regimes 87
3.2.3 Flow regime boundaries (Turian and Yuans approach) 88
3.3 Performance check of Turian Yuans approach 91
xii
3.3.1 Data Collection 91
3.3.2 Regime identification 92
3.4 Scope of present work 92
3.5. Development of the artificial neural network (ANN) based correlation
3.5.1. Input selection and data collection 96
3.5.2 Prediction performance of hybrid ANN-DE model 96
3.5.3 Prediction performance of hybrid ANN-GA model 99
3.5.4 Comparison of hybrid ANN-DE model with ANN model 100
3.6 Development of the support vector machine (SVM) based correlation
3.6.1. Input selection and data collection 101
3.6.2 Prediction performance of hybrid SVM-DE model 101
3.7. Conclusion 102
4. Critical velocity of slurry flow in pipeline 4.1 Introduction 107
4.2 Background works 110
4.3 Development of the artificial neural network (ANN) and support
vector regression (SVR) based correlation 120
4.3.1 Collection of data 120
4.3.2 Identification of input parameters 120
4.4 Results and discussion
4.4.1 Prediction performance of hybrid ANN-DE model 123
4.4.2 Comparison of hybrid ANN-DE model with ANN model: 125
4.4.3 Prediction performance of hybrid SVR-GA model prediction 126
4.5 Dependence of critical velocity with model input parameters 128
4.6 Comparison with other published correlations 132
4.7. Conclusion 132
5. Hold up in slurry flow in pipeline 5.1 Introduction 138
5.2 Background works 139
5.3. Development of the artificial neural network (ANN) and support
vector regression (SVR) based correlation 141
xiii
5.3.1 Collection of data 141
5.3.2 Identification of input parameters 142
5.4. Results and discussion 144
5.4.1 Prediction performance of hybrid ANN-DE model 144
5.4.2 Comparison of hybrid ANN-DE model with ANN model 146
5.4.3. Prediction performance of hybrid SVR-DE model 147
5.5 Conclusion 148
6. Pressure drop of slurry flow in pipeline 6.1 Introduction 152
6.2 Background works 154
6.2.1 Methods Based on the Drag Coefficient of Particles 157
6.2.2 Models Based on Terminal Velocity 159
6.2.3 Friction losses for compound mixture in horizontal
heterogeneous flows 159
6.2.4 Stratified flows 161
6.2.5 Two layer mode 163
6.2.6 Modified Wasp model 165
6.2.7 Summary of literature survey 166
6.3. Development of the artificial neural network (ANN) and
support vector regression (SVR) based correlation 167
6.3.1 Collection of data 168
6.3.2 Identification of input parameters 169
6.4 Results and discussion 169
6.4.1 Prediction performance of hybrid ANN-DE model 169
6.4.2 Prediction performance of hybrid ANN-GA model 171
6.4.3 Comparison of hybrid ANN-GA model with ANN model 173
6.4.4 Prediction performance of hybrid SVR-DE model 173
6.4.5 Comparison with other published correlations 175
6.5 Conclusion 176
xiv
7. Semi-empirical method for pressure drop and concentration profile
7.1 Introduction 183
7.2 Background work 184
7.3 Wasp et al. (1977) model 187
7.4 Comparison of pressure drop prediction by Wasp model with
experimental data 189
7.5 Modified Wasp model
7.5.1 Modifications incorporated in Wasp model 192
7.5.2 Steps to implement modified Wasp model 193
7.6 Results and discussions 196
7.7 Conclusion 205
8. Computational Fluid Dynamics modeling of the Solid liquid slurry flow in a pipeline
8.1 Introduction 212
8.2 Background works 214
8.2.1 Multiphase modeling 215
8.2.2 Approaches to Multiphase Modeling 216
8.2.2.1 The Euler-Lagrange Approach 216
8.2.2.2 The Euler-Euler Approach 217
8.2.2.2.1 The VOF Model 217
8.2.2.2.2 The Mixture Model 218
8.2.2.2.3 The Eulerian Model 218
8.2.3 Choosing a Multiphase Model 218
8.2.4 Effect of Particulate Loading 218
8.2.5 Significance of the Stokes Number 220
8.2.6 Guidelines for choosing appropriate model 220
8.3 Formulation of multiphase CFD model 221
8.3.1 Eulerian Model 222
8.3.1.1 Continuity Equation 222
8.3.1.2 Momentum Equations 223
8.3.1.3 Fluid-solid momentum equations 223
xv
8.3.1.4 Interphase exchange co-efficient 224
8.3.1.5 Fluid-Solid Exchange Coefficient 224
8.3.1.6 Lift Forces 227
8.3.1.7 Solid pressure 228
8.3.1.8 Radial Distribution Function 228
8.3.1.9 Solids Shear Stresses 229
8.3.2 Turbulent model 231
8.4 Description of CFD simulation 232
8.4.1 Two dimensional simulation 232
8.4.2 Validation of CFD simulation 236
8.4.3 Comparison between measured and predicted
concentration profiles based on Syamlal-O'Brien model model,
Wen and Yu model and Gidaspow model 236
8.4.4 Description of modified model 237
8.4.5 Comparison between measured and predicted
concentration profiles based on modified model 238
8.4.6 Three dimensional simulation 239
8.4.7 Results and discussion of 3D simulation 241
8.4.7.1 Concentration profile 241
8.4.7.2 Velocity profile 242
8.4.7.3 Pressure drop 242
8.4.7.4 Contours of solid concentration and velocity 243
8.5 Conclusion 286
9. Contribution of present thesis and future scope 9.1 Contribution of present thesis 293
9.2 Future scope 298
xvi
List of tables
Table 2.1: Different activation function 29
Table 2.2: Different Kernel type 59
Table 2.3: Different Loss function 60
Table 3.1: System and parameter studied 93
Table 3.2: Some of the input and output data for ANN & SVM training 94
Table 3.3: Regime identification by Turian and Yuan (1977) approach 95
Table 3.4: Prediction error by hybrid ANN-DE based model 98
Table 3.5: Set of equations and fitting parameters for neural network
correlations (i=7, j=7, k=1) 99
Table 3.6: Comparison of performance of ANN-DE hybrid model Vs ANN
Model 100
Table 3.7: Prediction error by hybrid SVM-DE based model 102
Table 4.1: Performance of different correlations to predict critical velocity 119
Table 4.2: System and parameter studied 121
Table 4.3: Typical input and output data for ANN or SVR training 122
Table 4.4: Prediction error by hybrid ANN-DE based model 124
Table 4.5: Set of equations and fitting parameters for neural network
correlations(i=7,j=8,k=1) 125
Table 4.6: Comparison of performance of ANN-DE hybrid model Vs ANN
Model 126
Table 4.7: Prediction error by hybrid SVR-GA based model 127
Table 4.8: Optimum parameters obtained by hybrid SVR- GA algorithm 127
Table 5.1: System and parameter studied 142
Table 5.2: Typical input and output data for ANN & SVR training 143
Table 5.3: Prediction error by the hybrid ANN-DE based model 144
Table 5.4: Set of equations and fitting parameters for neural network
correlations (i=7, j=8,k=1) 145
Table 5.5: Comparison of performance of ANN-DE hybrid model Vs ANN
Model 146
Table 5.6: Prediction error by hybrid SVR-DE based model 147
Table 5.7: Optimum parameters obtained by hybrid SVR- DE algorithm 148
xvii
Table 5.8: Comparison of performance of SVR-DE hybrid model Vs SVR
model 148
Table 6.1: System and parameter studied 168
Table 6.2: Typical input and output data for ANN training 170
Table 6.3: Prediction error by hybrid ANN-DE based model 171
Table 6.4: Set of equations and fitting parameters for neural network
correlations (i=7, j=8, k=1) 172
Table 6.5: Comparison of performance of ANN-DE hybrid model Vs ANN
Model 173
Table 6.6: Prediction error by SVR based model 174
Table 6.7: Optimum parameters obtained by hybrid SVR- DE algorithm 175
Table 6.8: Comparison of performance of SVR-DE hybrid model Vs SVR model 175
Table 6.9: Performance of different correlations to predict pressure drop 176
Table 7.1: Drag relationships 188
Table 7.2: System and parameter studied collected from the literature 190
Table 7.3: Coal water slurry data collected from Roco & Shook (1984) 190
Table 7.4: Comparison of pressure drop and concentration profile prediction 197
Table 7.5: Comparison of correlation co-efficient (R) for concentration profile
prediction by Wasp model and modified Wasp model. 205
Table 8.1: Experimental data used in the present study 233
Table 8.2: Different inputs for simulation in FLUENT 234
Table 8.3: Data used in 3D CFD simulation 241
xviii
List of figures
Figure 2.1: Different application of ANN 15
Figure 2.2: Strength and characteristics of ANN 19
Figure 2.3: Architecture of feed forward network with one hidden layer 23
Figure 2.4: Different ANN algorithms published in various literatures 26
Figure 2.5: Structure of different activation function 29
Figure 2.6: Schematic for hybrid ANN-GA algorithm implementation 38
Figure 2.7: Schematic for hybrid ANN-DE algorithm implementation 43
Figure 2.8: Separation of two classes by SVM 47
Figure 2.9: Non-linear transformation from input to a higher-dimensional feature
space 51
Figure 2.10: A schematic diagram of support vector regression using -sensitive loss
function 53
Figure 2.11: Schematic for hybrid SVR-GA algorithm implementation 62
Figure 2.12: Schematic for hybrid SVR-DE algorithm implementation 63
Figure 2.13: A simplified three layer feed forward perceptron network 65
Figure 3.1: Heterogeneous flow regimes in terms of speed versus volumetric
concentration. 84
Figure 3.2: Flow regimes of heterogeneous flows in terms of particle size versus
mean velocity 84
Figure 3.3: Four regimes of flow of settling slurries in horizontal pipeline 86
Figure 3.4: Decision tree for establishing flow regimes 90
Figure 3.5: Experimental Vs predicted flow regime for BFGS algorithm 97
Figure 4.1: Plot of transitional mixture velocity with pressure drop 108
Figure 4.2: Schematic representation of the boundaries between the flow regimes
for settling slurries in horizontal pipelines 109
Figure 4.3: Simplified concept of particle distribution in a pipe as a function of
volumetric concentration and velocity 110
Figure 4.4: Major critical velocity correlations available in literatures 113
Figure 4.5: Experimental Vs predicted critical velocity for Marquard Levenburg
algorithm 124
Figure 4.6: Variation of critical velocity with density ratio 129
xix
Figure 4.7: Variation of critical velocity with pipe diameter 130
Figure 4.8: Variation of critical velocity with particle diameter 130
Figure 4.9: Variation of critical velocity with solid concentration 131
Figure 4.10: Variation of critical velocity with dimensionless group 131
Figure 5.1: Experimental Vs predicted hold up for FletcherReeves update
algorithm 145
Figure 6.1: Major correlations for pressure drop published in literature 154
Figure 6.2: Transfer of momentum between the fluid and the wall during slurry
flows through a pipe 155
Fig 6.3: Experimental Vs predicted pressure drop by Marquard Levenburg
algorithm 172
Figure 7.1: Pressure drop prediction by Wasp model and modified Wasp model
based on typical Roco & Shook (1984) data 191
Figure 7.2: Experimental and calculated concentration profile using modified
Wasp model for some typical data of Roco and Shook (1983).
a)Run A1:Vm= 1.66 m/s, Cvf=8.37%,D=0.0515 m ,
b)Run A2:Vm= 3.78 m/s, Cvf=9.2%, D=0.0515m , c)Run A3:
Vm= 1.66 m/s, Cvf=18.7%, D=0.0515 m 198
Figure 7.3: Experimental and calculated concentration profile using modified
Wasp model for some typical data of Roco and Shook (1983). a)Run
A4:Vm= 4.17 m/s, Cvf=18.9%,D=0.0515 m , b)Run A5:Vm= 1.66 m/s,
Cvf=28%, D=0.0515m , c)Run A6: Vm= 4.33 m/s, Cvf=28.6%,
D=0.0515 m 199
Figure 7.4: Experimental and calculated concentration profile using modified
Wasp model for some typical data of Roco and Shook (1983).
a)Run A7:Vm= 2.9 m/s, Cvf=10.3%,D=0.263m b)Run A8:Vm= 3.5 m/s,
Cvf=10%, D=0.263m, c)Run A9: Vm= 2.9 m/s, Cvf=19 %,
D=0.263m 200
Figure 7.5: Experimental and calculated concentration profile using modified
Wasp model for some typical data of Roco and Shook (1983).
a)Run A10:Vm= 3.5 m/s, Cvf=18.4%,D=0.263m b)Run A11:
Vm= 2.9 m/s, Cvf=27%, D=0.263m, c)Run A12: Vm= 3.5 m/s,
Cvf=26.8 %, D=0.263m 201
xx
Figure 7.6: Experimental and calculated concentration profile using modified
Wasp model for some typical data of Roco and Shook (1983).
a)Run A13:Vm= 2.9 m/s, Cvf=34.1%,D=0.263m b)Run A14:
Vm= 3.5 m/s, Cvf=33.8%, D=0.263m, c)Run A15: Vm= 3.16 m/s,
Cvf=10.4 %, D=0.495 m 202
Figure 7.7: Experimental and calculated concentration profile using modified
Wasp model for some typical data of Roco and Shook (1983).
a)Run A16:Vm= 3.76 m/s, Cvf=10.0 %,D=0.495 m b)Run A17:
Vm= 3.07 m/s, Cvf=18.7%, D=0.495 m, c)Run A18: Vm= 3.76 m/s,
Cvf=18.4 %, D=0.495 m 203
Figure 7.8: Experimental and calculated concentration profile using modified
Wasp model for some typical data of Roco and Shook (1983).
a)Run A19:Vm= 3.16 m/s, Cvf=27.3 %,D=0.495 m b)Run A20:
Vm= 3.76 m/s, Cvf=26.9%, D=0.495 m 204
Figure 8.1: Different approaches to multiphase modeling 217
Figure 8.2: Guidelines for choosing multiphase model 219
Figure 8.3: Measured (by Kaushal) and predicted (by present model, Syamlal
model Gidaspow model and Wen and Yu model) concentration
profiles at different efflux concentrations and flow velocity for the
flow of zinc tailing slurry through a 105-mm-diameter pipe. 239
Figure 8.4: Measured (by Mukhtar) and predicted (by present model)
concentration profiles at different efflux concentrations and flow
velocity for the flow of zinc tailing slurry through a
105-mm-diameter pipe. 240
Figure 8.5: Measured (by Kaushal) and predicted (by present model) concentration
profiles at different efflux concentrations and flow velocity for the
flow of zinc tailing slurry through a 105-mm-diameter pipe with a
velocity of 2.75 m/s. 241
Figure 8.6A: Comparison of experimental and calculated vertical concentration
profile for flow of 125 micron glass beads in 54.9 mm diameter pipe
at different efflux concentration and flow velocity 245
Figure 8.6B: Comparison of experimental and calculated vertical concentration
profile for flow of 125 micron glass beads in 54.9 mm diameter pipe
at different efflux concentration and flow velocity 246
xxi
Figure 8.7A: Comparison of experimental and calculated vertical concentration
profile for flow of 125 micron glass beads in 54.9 mm diameter pipe
at different efflux concentration and flow velocity 247
Figure 8.7B: Comparison of experimental and calculated vertical concentration
profile for flow of 125 micron glass beads in 54.9 mm diameter pipe
at different efflux concentration and flow velocity 248
Figure 8.8A: Comparison of experimental and calculated vertical concentration
profile for flow of 125 micron glass beads in 54.9 mm diameter pipe
at different efflux concentration and flow velocity 249
Figure 8.8B: Comparison of experimental and calculated vertical concentration
profile for flow of 125 micron glass beads in 54.9 mm diameter pipe
at different efflux concentration and flow velocity 250
Figure 8.9: Experimental and calculated vertical concentration profile for flow
of 125 micron glass beads in 54.9 mm diameter pipe 251
Figure 8.10A: Experimental and calculated vertical concentration profile for flow
of 440 micron glass beads in 54.9 mm diameter pipe 252
Figure 8.10B: Experimental and calculated vertical concentration profile for flow
of 440 micron glass beads in 54.9 mm diameter pipe 253
Figure 8.11A: Experimental and calculated vertical concentration profile for flow
of 440 micron glass beads in 54.9 mm diameter pipe 254
Figure 8.11B: Experimental and calculated vertical concentration profile for flow
of 440 micron glass beads in 54.9 mm diameter pipe 255
Figure 8.12A: Experimental and calculated vertical concentration profile for flow
of 440 micron glass beads in 54.9 mm diameter pipe 256
Figure 8.12B: Experimental and calculated vertical concentration profile for flow
of 440 micron glass beads in 54.9 mm diameter pipe 257
Figure 8.13: Concentration profiles in the vertical plane for slurry of 125 micron
particle size 258
Figure 8.14: Concentration profiles in the vertical plane for slurry of 440 micron
particle size 259
Figure 8.15A: CFD predicted solid phase vertical velocity profile for flow of 125
micron glass beads in 54.9 mm diameter pipe at different efflux
concentration and flow velocity 260
xxii
Figure 8.15B: CFD predicted solid phase vertical velocity profile for flow of 125
micron glass beads in 54.9 mm diameter pipe at different efflux
concentration and flow velocity 261
Figure 8.16A: CFD predicted solid phase vertical velocity profile for flow of 125
micron glass beads in 54.9 mm diameter pipe at different efflux
concentration and flow velocity. 262
Figure 8.16B: CFD predicted solid phase vertical velocity profile for flow of 125
micron glass beads in 54.9 mm diameter pipe at different efflux
concentration and flow velocity. 263
Figure 8.17A: CFD predicted solid phase vertical velocity profile for flow of 125
micron glass beads in 54.9 mm diameter pipe at different efflux
concentration and flow velocity 264
Figure 8.17B: CFD predicted solid phase vertical velocity profile for flow of 125
micron glass beads in 54.9 mm diameter pipe at different efflux
concentration and flow velocity 265
Figure 8.18: CFD predicted solid phase vertical velocity profile for flow of 125
micron glass beads in 54.9 mm diameter pipe 266
Figure 8.19: CFD predicted solid phase vertical velocity profile for flow of 440
micron glass beads in 54.9 mm diameter pipe 267
Figure 8.20: Comparison of vertical velocity profile at a) 1 m/s, b) 3 m/s and
c) 5 m/s for different efflux concentration 268
Figure 8.21: Parity plot of predicted Vs experimental pressure drop for slurry flow
at different overall area-average concentrations and flow velocities 269
Figure 8.22: Pressure drop for slurry of 125 m particle size at different overall
area-average concentrations and flow velocities 270
Figure 8.23: Pressure drop for slurry of 440 m particle size at different overall
area-verage concentrations and flow velocities 270
Figure 8.24: Contours of volume fraction of solid [Cvf- 9.4 %, Vm-1 m/s, d-125
micron] 271
Figure 8.25: Contours of solid velocity magnitude (m/s) [Cvf- 9.4 %, Vm-1 m/s,
d-125 micron] 271
Figure 8.26: Contours of volume fraction of solid [Cvf- 10.41 %, Vm-3 m/s,
d-125 micron] 272
xxiii
Figure 8.27: Contours of solid velocity magnitude (m/s) [Cvf- 10.41 %,
Vm-3 m/s, d-125 micron] 272
Figure 8.28: Contours of volume fraction of solid [Cvf- 10.93 %, Vm-5 m/s,
d-125 micron] 273
Figure 8.29: Contours of solid velocity magnitude (m/s) [Cvf- 10.93 %,
Vm-5 m/s, d-125 micron] 273
Figure 8.30: Contours of volume fraction of solid [Cvf- 20.4 %, Vm-3 m/s,
d-125 micron] 274
Figure 8.31: Contours of volume fraction of liquid [Cvf- 20.4 %, Vm-3 m/s,
d-125 micron] 274
Figure 8.32: Contours of solid velocity magnitude (m/s) [Cvf- 20.4 %,
Vm-3 m/s, d-125 micron] 275
Figure 8.33: Contours of volume fraction of solid [Cvf- 20.45 %,
Vm-5 m/s, d-125 micron] 275
Figure 8.34: Contours of solid velocity magnitude (m/s) [Cvf- 20.45 %,
Vm-5 m/s, d-125 micron] 276
Figure 8.35: Contours of volume fraction of solid [Cvf- 30.3 %,
Vm-1 m/s, d-125 micron] 276
Figure 8.36: Contours of solid velocity magnitude (m/s) [Cvf- 30.3 %,
Vm-1 m/s, d-125 micron] 277
Figure 8.37: Contours of volume fraction of solid [Cvf- 31.19 %,
Vm-3 m/s, d-125 micron] 277
Figure 8.38: Contours of solid velocity magnitude (m/s) [Cvf- 31.19 %,
Vm-3 m/s, d-125 micron] 278
Figure 8.39: Contours of volume fraction of solid [Cvf- 30.24 %,
Vm-5 m/s, d-125 micron] 278
Figure 8.40: Contours of solid velocity magnitude (m/s) [Cvf- 30.24 %,
Vm-5 m/s, d-125 micron] 279
Figure 8.41: Contours of volume fraction of solid [Cvf- 41.1 %,
Vm-2 m/s] , d-125 micron] 279
Figure 8.42: Contours of solid velocity magnitude (m/s) [Cvf- 41.1 %,
Vm-2 m/s, d-125 micron] 280
Figure 8.43: Contours of volume fraction of solid [Cvf- 39.56 %,
Vm-5 m/s, d-125 micron] 280
xxiv
Figure 8.44: Contours of solid velocity magnitude (m/s) [Cvf- 39.56 %,
Vm-5 m/s, d-125 micron] 281
Figure 8.45: Contours of volume fraction of solid [Cvf- 49.24 %,
Vm-3 m/s, d-125 micron] 281
Figure 8.46: Contours of solid velocity magnitude (m/s) [Cvf- 49.24 %,
Vm-3 m/s, d-125 micron] 282
Figure 8.47: Contours of volume fraction of solid [Cvf- 48.56 %,
Vm-4 m/s, d-125 micron] 282
Figure 8.48: Contours of solid velocity magnitude (m/s) [Cvf- 48.56 %,
Vm-4 m/s, d-125 micron] 283
Figure 8.49: Contours of volume fraction of solid [Cvf- 48.96 %,
Vm-5 m/s, d-125 micron] 283
Figure 8.50: Contours of solid velocity magnitude (m/s) [Cvf- 48.96 %,
Vm-5 m/s, d-125 micron] 284
Figure 8.51: Contours of volume fraction of solid [Cvf- 9.77 %,
Vm-1 m/s, d-440 micron] 284
Figure 8.52: Contours of solid velocity magnitude (m/s) [Cvf- 9.77 %,
Vm-1 m/s, d-440 micron] 285
Figure 8.53: Contours of volume fraction of solid [Cvf- 8.62 %, Vm-5 m/s,
d-440 micron] 285
Figure 9.1: Contribution of present thesis 294
xxv
Abstract
Many large slurry pipelines were built and operating around the world. Pipeline transport is
considered economical and environment friendly as compared to rail and road transport. To
design the pipelines and its associated facilities (pumps etc) designers need accurate
information regarding pressure drop, hold up, critical velocity, flow regimes etc at the early
design phase. Also the operating engineers need to know accurately the critical velocity so that he can adjust the slurry flow to have a minimum pressure drop to ensure minimum
operating cost. Such flows are complex and presently very little known about the two-phase
interaction of solid liquid behavior inside pipeline. The correlations presently available in open
literatures for the above mentioned parameters have a prediction error of 25-35%. This much
of error in design and slurry operation has serious cost implication and is totally unacceptable
in present day competitive business scenario. This study was performed in order to develop
model for flow of slurries through pipelines so that the error % can be reduced. This thesis can
be considered as a step forward for better understanding of flow behavior in slurry pipelines.
Attempt has been made in this thesis to utilize the computational capability of two recent
advanced numerical technique namely artificial neural network (ANN) and support vector
regression (SVR) in slurry flow modeling. This thesis has build some simple and superior
correlations of pressure drop, hold up, critical velocity, flow regimes which can be readily
used by design engineers to design slurry pipelines and pumps.
There are some model parameters both in ANN and SVR that are to be tuned by the expert
user during model building time. A new approach was developed in this thesis to tune these
parameters automatically using differential evolution (DE) and genetic algorithm (GA). The
method employs a hybrid approach for minimizing the generalization error. The proposed
hybrid technique relieves the non-expert users to choose the meta parameters of ANN or SVR
algorithm for the used case study and find out the optimum value of these meta parameters on
its own.
In the present study existing Wasp model (1977) for pressure drop has been modified by
alleviating some of the restrictive assumptions used in that model. A new method was also
developed to calculate concentration profile using Wasp model as a starting point. The
concentration profile and pressure drop data predicted by modified model were compared with
the experimental one collected from literature.
xxvi
In this study the capability of computational fluid dynamics (CFD) is explored to model
complex solid liquid slurry flow in pipeline. A comprehensive CFD model was developed to
gain deeper insight of the solid liquid slurry flow in pipelines. The theoretical model
developed in this work represents the synthesis of hydrodynamic and interparticle interaction
effects within the framework of equation of conservation of momentum and mass. Two and
three-dimensional model problems are developed using CFD to understand the influence of the
particle drag coefficient on solid concentration profile. It is found that the commercial CFD
software is capable to successfully model the solid liquid interactions in slurry flow and the
predicted concentration profiles show reasonably good agreement with the experimental data.
Chapter1
1
CHAPTER 1
Introduction Abstract Slurry transport through pipeline is a widely practiced field in mining and allied industries.
Background of slurry flow modeling, its evolution over the years and limitations of our current
knowledge in this field is presented in this introductory note. Designers need accurate
information regarding pressure drop, hold up, critical velocity, flow regimes etc. at the early
stage of designing the pipelines and its associated facilities (pumps etc). The meaning and
implications of these design parameters in slurry flow modeling, motivation and the scope of
present thesis are described in this chapter with little details. At the end a road map is given
regarding how to read this thesis.
Keywords: Artificial neural network (ANN); Differential evolution (DE); Slurry flow regime,
Slurry critical velocity
Introduction
2
1.1 Introduction
Pipeline transport has been a progressive technology for conveying a large quantity of bulk
materials. This includes long distance hauling of coal, minerals, ore and solid commodities,
dredging and filling, collection and disposal of solid waste and material processing. It is
possible in the present day technology to incorporate sequences of processing operations into
the overall slurry transport operation, thereby leading to elimination of processing steps and
savings in capital investment; for example, integrating microbial desulfurization into the long
distance coal slurry pipeline transport operation. Compared to a mechanical transport, the use
of a pipeline ensures a dust free environment, demands substantially less space, makes
possible full automation and requires a minimum number of operating staff. On the other hand,
it needs higher operational pressures and demands considerably high quality pumping
equipment and control system.
The behavior of solids and liquids flowing through pipelines has been the subject of
continuing investigation since the turn of the century. In the 1950s significant technical
progress was made in several countries through a strong research effort. In United Kingdom,
experimental work was conducted particularly on the handling of coarse coal slurries. This
work was mainly carried out by worldwide well known British Hydraulic Research
Association (BHRA) in conjunction with the National Coal Board,UK. In France, Durand and
Condolios (1952) carried out a large amount of work on the hydraulic transport of aggregates.
During 1960s several countries became involved in developing hydraulic transport for mining
and a number of coal mine haulage systems were installed. Rigby (1982) took a wide historical
view concerning slurry transport, referring to its early development in the American gold rush
of the mid-nineteenth century. Since then, the Ohio Cadiz coal line, built in 1957 pioneered the
large scale (147 km long254 mm diameter) transport of material at high throughputs (1.5
Mtpa). It was later overtaken by the Black Mesa, 439 km457 mm5 Mtpa, supplying coal to
the Mohave power station in southern Nevada. The first iron ore concentrate line (Savage
River) was built in Tasmania (1967), with conservative slope specifications to cope with the
solids specific gravity. It too has been overtaken in scale by the Brazilian Samarco line,
carrying 7 Mtpa of iron ore concentrate over 400 km. Other materials have included limestone
(UK), gold slime (Australia, South Africa), phosphate (Canada, South Africa), copper
concentrate (Papua New Guinea), copper tailings (Chile), and zinc sulphites (Japan), to name
but a few. Requirements are now placed on public utilities and mining companies to
Chapter1
3
incorporate effective means of waste disposal into their future plans. Slurry systems are used
in flue gas desulphurization and in waste material transport. Hydraulic transport of waste
material, such as bauxite residue, coal mine tailings and sewage, is also a widely accepted and
practiced application.
At the present time there are many organizations throughout the world carrying out research
and development in the field of slurry transport. It is understood that the greatest interest is
been shown in these major lines because of their huge capital investment and substantial
engineering content. It must be noted, however, that there are many small slurry pipelines
being designed and built particularly in the mining, chemical and food processing industries,
for which the details remain unpublished.
A basic understanding of the underlying phenomena is vital to the control of slurry transport
system. Literature survey reveals that studies concerned with solid-liquid mixture flows have
followed one of these three major approaches: 1) the empirical approach 2) the rheological
based continuum approach and 3) the multiphase flow modeling approach. The empirical
approach seems to have received the most attention, perhaps as a concession to the complexity
of slurry flows. Because of its long history a large body of empirical studies dealing with
slurry transport has accumulated the correlations for prediction of pressure drop and for
delineation of flow regimes which constitute two major elements of this body of empirical
work. The rheological approach has emerged in a major way in the mid fifties. It is, however,
strictly applicable to slurries of ultra fine non-colloidal particles, capable of meaningful
rheological characteristics. The multiphase flow modeling approach, which accounts for
liquid, particle and boundary interaction effects, provides the most rational framework for
describing such heterogeneous solid-liquid mixture flows. It requires basic information
regarding the effects of the particle on the structure of the turbulent flow, the particle-particle
and the particle-boundary interactions and other effects, and this approach commonly entails
substantial computational effort.
All of the above methods have their own limitations generating out of inherent complexity and
poor understanding of two-phase flow systems. Despite of extensive research in slurry
technology, our present knowledge of the fundamentals of solid-liquid flow does not satisfy
engineering needs. The need to control processes involving solid-liquid slurry and to design
pipelines, pumps has resulted in the accumulation of a great deal of experimental data. In turn
these data have help developed the body of empirical relations and practical guidelines. But it
is difficult to integrate this body of knowledge into a framework leading to the design
correlation. A predictive model with sound understanding of the fundamentals of particle laden
Introduction
4
turbulent flow, including all significant interactions and the ability to integrate these
quantitatively is not so successful till today as seen from various literatures.
Some of the limitations of this body of published work include:
The slurries investigated and the problems addressed are so specific as to cover a very limited range of the variables involved.
The particle size distribution (PSD) considered in the experiment is very narrow, whereas the PSD is very broad in industrial scenario.
Most of the experiments were carried out in very low solid concentration (less than 10%) and correlations developed from such experiments failed to produce reasonable
results at higher solid concentrations (above 25%).
The average error for pressure drop prediction was 35% during Wasp (1977) and now reduced to 20% with maturity in slurry modeling. This 20% error is not even
acceptable in todays scenario as the slurry transport is very energy extensive
operation and whole economics of the transportation depends on pressure drop.
The slurry systems are not well defined with respect to, say, solids shape and particle size distributions.
The published works contain incomplete data, which are often impossible to retrieve and reconstruct from the published versions.
The body of published empirical correlations on slurry pressure drop and critical velocity is extensive but largely conflicts with each other.
There is limited range of applicability and validity. As for example the correlations developed for coal-water slurry are found not fit for sand-water slurry.
Because of the resulting uncertainties, extensive pilot pipeline tests are conducted for major
projects around the world. But even then the knowledge of the detailed in situ conditions is
often beyond reach. Because of the complexity of the process, mathematical solution to the
general hydrodynamic problem of slurry flows in pipeline has been a forbidden task for many
decades. Advances in our understanding of turbulent flows and their modeling in recent years
have provided the basic framework for development of mathematical models of slurry flow.
Furthermore, emergence of powerful numerical technique like artificial neural network,
support vector regression, computational fluid dynamics etc. along with the accessibility of
powerful computers has made possible to test such models and to carry out investigations of
the basic phenomena using computer simulation.
Chapter1
5
1.2 Typical flow regime
In slurry transport different patterns of solids movements are observed, depending upon the
nature of the slurry and the prevailing flow condition. In horizontal pipes these may
conveniently be classified according to the following four regimes:
Homogeneous flow: This regime is also named as symmetric flow characterizing uniform
distribution of solids about the horizontal axis of the pipe, although not necessarily exactly
uniform. In this regime, turbulent and other lifting forces are capable of overcoming the net
body forces as well as the viscous resistance of the particles.
Heterogeneous flow: With decrease in the slurry velocity, intensity of turbulence and lift
forces are decreased. As a result there is distortion of the concentration profile of the particles,
with more of the solids, particularly the larger particles, being contained in the lower part of
the pipe. Thus there is a concentration gradient across the pipe cross section with a larger
concentration of solids at the bottom. This flow is also called asymmetric flow.
Saltation flow: This type of flow takes place at low velocities and is one in which solid
particles tend to accumulate on the bottom of the pipe, first in the form of separated dunes
and then as a continuous moving bed.
Stationary bed flow: As the slurry velocity is further reduced, the lowermost particles of the
bed become nearly stationary, the bed thickens and bed motion is limited to the uppermost
particles tumbling over one another (saltation). Eventually, with continued reduction in the
mixture velocity and build up of the bed, pressure gradient increases very rapidly to maintain
the flow and in the absence of an abnormally high applied pressure, blockage of pipe occurs.
1.3 Critical velocity
The critical velocity is defined as the minimum velocity demarcating flows in which the solids
form a bed at the bottom of the pipe from fully suspended flows. It is the transition velocity
between heterogeneous flow and saltation flow. The critical velocity is one of the important parameter that must be accurately known for the optimized design of a slurry transportation
pipeline. The significance of this velocity is that it represents the lowest speed at which slurry
pipelines can operate and corresponds to lowest pressure drop in slurry transport.
Introduction
6
1.4 Hold up
In solid liquid slurry flow in pipelines different layers of solids move with different speeds.
Hold-ups are due to velocity slip of layers of particles of larger sizes, particularly in the
moving bed flow pattern. Due to this slip in velocity, in-situ concentrations are not same as the
concentrations in which the phases are introduced or removed from the system. The variation
of in-situ concentrations from the supply concentrations is referred to as hold up phenomenon.
Very few correlations with limited applicability are available in literatures to predict hold up
ratio in solid liquid slurry flow. Obviously hold up plays an important role in the failure of
many empirical correlations for predicting head loss in flow regimes involving bed formation.
1.5 Pressure drop
The design of a slurry pipeline entails predicting the power requirement per unit mass of solids
delivered over a unit distance. It is vital in this context to be able to relate head gradient to the
independent design parameters. Power consumption and subsequently the whole economics of
the hydro-transport depend on it. There are large number of empirical and semi empirical
correlations available in literatures to predict pressure drop. Most of these equations have been
developed based on limited data comprising of uniform or narrow size-range particles with
very low to moderate concentrations. These correlations are prone to great uncertainty as one
departs from the limited database that supports them. When all the major correlations are
exposed to the large experimental data bank collected from open literature (800 measurements
covering a wide range of pipe dimensions, operating conditions and physical properties), the
average prediction error is found in the range of 25 to 50%. This is definitely not acceptable in
todays scenario.
1.6 Concentration and velocity profile
Wear is a very important consideration in the design and operation of slurry systems, as it
affects both the initial capital costs and the life of components. It may be defined as the
progressive volume loss of material from a surface, due to erosion, abrasion or other causes.
Kawashima et al. (1978) indicated that wear is proportional to volume concentration,
Chapter1
7
(C v) 0.822.0 and velocity, (V) 0.85-4.5 from the review of various laboratory test results. It is
reasonable to assume that wear will depend on the number of particle impacts on the surface,
which in turn depends on the concentration and velocity. Thus to understand the wear
phenomena it is very important to know the detailed in-situ velocity profiles and concentration
profiles of solid, liquid and mixture. Such information is basic to a fundamental understanding
of the mechanisms of dense slurry transport.
1.7 Motivation of present work
Large number of long slurry pipelines was already built around the world and lot more still to
come up. Designers need accurate information regarding pressure drop, hold up, critical
velocity, flow regimes etc. at the early stage to design the pipelines and its associated facilities
(pumps etc). Despite of significant research efforts, prediction of pressure drop, hold up, critical velocity and other design parameters to ensure optimum pipeline design is still an open
problem for design engineers. The major empirical equations regarding pressure drop, hold up,
critical velocity and flow regime identification when tested with experimental data of different
systems collected from open literatures, it was found that prediction error ranges above 25%
on an average. The capital investments for a slurry pipeline are tremendously high and
naturally 25% error in design or a few per cent error in operating conditions may have critical
cost implications. Even though the error for pressure drop has come down to 20% from 35%
during Wasp(1977), the same is not acceptable in todays business scenario as the slurry
transport is very energy extensive operation and whole economics of the transportation
depends on pressure drop. With this background, the motivation of the present work is to
develop more generalized correlations of pressure drop, hold up, critical velocity having
reasonably low prediction error over a wide range of study. Therefore, this work explores the
possibility of application of two recent advance computational techniques namely artificial
neural network (ANN) methodology and support vector machine (SVM) methodology in
slurry flow modeling. ANN and SVM have emerged as two attractive tools for nonlinear
modeling especially in situations where the development of phenomenological or conventional
regression models becomes impractical or cumbersome. The sole objective is to quickly build
the simple and superior correlations which can be readily used by design engineers to design
slurry pipelines and pumps.
Introduction
8
The second motivation is how the limited range of applicability and validity of existing
correlations can be overcome. Presently the need of the industry is to transport slurry at
maximum concentration as possible (above 30%) to reduce the water consumption and make
the transport economically more viable. Obviously, objective of the present work is to push
this concentration envelop upto 50% and to develop a generalized correlation applicable to
any slurry systems.
The third motivation is to explore the possibility of improving some existing correlations
available in literature. Among various pressure drop models available in literature Wasp model
was found most promising and versatile and can be applied with suitable modification over a
wide range of slurry system. The method developed by Wasp et al. (1977) has been used very
successfully over the last 25 years for Newtonian slurries and large number of long distance
pipelines across the world has been designed using this model. In the present study Wasp
model for pressure drop has been modified by alleviating some of the restrictive assumptions
used in the model.
The fourth motivation is to find the applicability of Computational Fluid Dynamics (CFD) in
slurry flow modeling. The limitations of empirical equations or ANN/ SVM based correlations
are that they do not provide deeper insight of complex phenomena of slurry flow. In recent
years, CFD becomes a powerful tool for predicting fluid flow, heat/mass transfer, chemical
reactions and related phenomena by solving mathematical equations that govern these
processes using a numerical algorithm on a computer. A brief review of recent literature shows
little progress in simulating flow for a slurry pipeline using computational fluid dynamics
(CFD). For solid liquid multiphase flows, the complexity of modeling increases considerably
and this remains as an area for further research and development. Due to the inherent
complexity of multiphase flows, from a physical as well as a numerical point of view,
general applicable codes of computational fluid dynamics (CFD) are non-existent.
Considering the limitations in the published studies, the present work has been concentrated on
a systematic development of a CFD based model to predict the solid concentration profile,
velocity profile and pressure drop in slurry pipeline. The objective is to gain insight of
complex solid-liquid slurry flow.
Chapter1
9
1.8 Scope of present work
The problem considered in this thesis is the formulation of a theory for the flow of dense, non-
colloidal, settling slurries through horizontal pipelines and the development of appropriate
numerical scheme to carry out computer simulations of these flows based on the theoretical
model.
In the present thesis all the three approaches namely advance numerical modeling (artificial
neural networks (ANNs) and support vector regression (SVR)), semi-empirical modeling and
detailed phenomenological i.e. multiphase CFD modeling have been developed to predict
pressure drop, concentration profile, velocity profile, hold up, critical velocity and flow regime
for slurry flow in pipeline.
1.8.1 Advanced numerical modeling In the present study, two advanced techniques namely ANN and SVR are applied for slurry
flow modeling. There are some model parameters both in ANN and SVR that are to be tuned
by the expert user during model building time. A new approach was developed in this thesis
to tune these parameters automatically using differential evolution (DE) and genetic algorithm
(GA). The method employs a hybrid approach for minimizing the generalization error. The
proposed hybrid technique also relieves the non-expert users to choose the meta parameters of
ANN or SVR algorithm for the used case study and find out the optimum value of these meta
parameters on its own.
1.8.2 Semi empirical modeling In the present study Wasp model (1977) for pressure drop has been modified by alleviating
some of the restrictive assumptions used in the model. A new method was also developed to
calculate concentration profile using Wasp model as a starting point. The concentration profile
and pressure drop data predicted by modified model were compared with the experimental one
collected from literature.
1.8.3 Multiphase computational fluid dynamics (CFD) based modeling A comprehensive computational fluid dynamics (CFD) model was developed in the present
study to gain deeper insight of the solid liquid slurry flow in pipelines. The theoretical model
developed in this work represents the synthesis of hydrodynamic and interparticle interaction
Introduction
10
effects within the framework of equation of conservation of momentum and mass. Two and
three-dimensional model problems were developed using CFD to understand the influence of
the particle drag coefficient on solid concentration profile.
1.9 Thesis purview Chapter 2 of the thesis contains an overview of different mathematical tools used in this
work. Initially the basic model building steps using ANN and SVR methodology was
discussed. Thereafter automatic tuning of various model parameters of both ANN and SVR by
hybrid techniques was discussed. The thesis has developed four new hybrid modeling
technique namely 1)hybrid SVR-DE technique 2)hybrid SVR-GA technique 3)hybrid ANN-
DE technique 4)hybrid ANN-GA technique to minimize the generalization error. The detail
steps for hybrid model building and tuning of model parameters have been presented in this
section while the application of models and their performance were discussed in subsequent
chapters.
Chapter 3 describes the application of ANN and SVM model to identify regimes in slurry
flow in pipelines. Initially, different flow regimes in solid-liquid flow are discussed. The
method of Turian and Yuan correlations to classify different regimes were summarized and
performance of this correlation assessed. Later on, the classification capability of ANN and
SVM model were explored to identify different regimes of slurry flow based on experimental
data collected from open literature.
Chapter 4 discussed on different critical velocity correlations available in literatures and
significance of the critical velocity in slurry transport. The prediction performance of ANN
and SVR based correlations for critical velocity was presented and comparison was made with
other major correlations available in literature. The parametric study of critical velocity against
its model input parameters was discussed at the end of the chapter.
Chapter 5 presents emergence of hold up phenomena in slurry flow and capability of ANN
and SVR techniques to predict this phenomenon.
Chapter 6 contains an overview of historical pressure drop correlations in slurry transport.
The application of hybrid ANN and SVR models to develop pressure drop correlations is
discussed in this chapter. The superiority of ANN and SVR model over the major historic
correlations are shown at the end.
Chapter1
11
Chapter 7 describes the Wasp model for pressure drop prediction and its performance on
large database. The chapter presents how Wasp model for pressure drop has been modified by
alleviating some of the restrictive assumptions. A comparative study on concentration profile
and pressure drop predicted by modified model is shown in the chapter.
Chapter 8 explores the applicability of CFD technique to predict the concentration profile,
velocity profile and pressure drop for slurry flow in pipeline. Initially different approaches of
multiphase modeling and detail steps of Eulerian model building are discussed. Later on, how
2D and 3D CFD models perform against experimental data was shown in this chapter.
Chapter 9 summarizes the contribution of the present work. The chapter ends with the future
directions and scopes of the studies in slurry flow modeling.
References
1. Durand, R. and Condolios, G., The hydraulic transport of coal and solids in pipes, Colloquium on Hydraulic Transport , National Coal Board, London. (1952)
2. Kawashima, T. et al. ,Wear of pipes for hydraulic transport of solids.Proc. Hydro transport 5 Conf. , Paper E3, BHRA, Cranfield. (1978)
3. Rigby, G.R. Slurry pipelines for the transportation of solids, Mechanical Engineering Transactions , Paper M1173, pp. 1819, I.E. Aust. (1982)
4. Wasp, E.J., Kenny, J.P., Gandhi, R.L., Solid Liquid Flow Slurry Pipeline Transportation, Trans.Tech. Publications, Clausthal, Germany. (1977).
Mathematical Tools
12
Chapter 2
Mathematical tools Abstracts This section describes two recent computational techniques namely artificial neural network
(ANN) and support vector regression (SVR) which have emerged as attractive tools for
nonlinear modeling especially in situations where the development of phenomenological or
conventional regression models becomes impractical or cumbersome. In the present study,
these two advanced numerical techniques are applied for slurry flow modeling and detail steps
for model building were discussed. The sole objective is to build up quick, simple and superior
correlations which can be readily used by design engineers to design slurry pipelines and
pumps.
There are some model parameters both in ANN and SVR model that has to be tuned by the
expert user during model building time. The model prediction performance greatly depends
on the optimum tuning of these parameters. Most of the earlier approaches use trial and error
procedures for tuning the ANN or SVR parameters while trying to minimize the training and
test errors. Such an approach apart from consuming enormous time may not really obtain the
best possible performance. A new approach was developed in this thesis to tune these
parameters automatically using differential evolution (DE) and genetic algorithm (GA). This
thesis has developed four new hybrid modeling technique namely 1)hybrid SVR-DE technique
2)hybrid SVR-GA technique 3)hybrid ANN-DE technique 4)hybrid ANN-GA technique and
applied them for minimizing the generalization error. The detail steps for hybrid model
building were presented in this section whereas the application of models and their
performance were discussed in subsequent chapters. The proposed hybrid techniques relieve
the non-expert users to choose the meta parameters of ANN or SVR algorithm for the case
study and find out optimum value of these meta parameters on its own.
Keywords: Artificial neural network (ANN), support vector regression (SVR), support vector
machine (SVM), differential evolution (DE), genetic algorithm (GA).
Chapter2
13
2.1 Introduction Conventionally, two approaches namely phenomenological (first principles) and empirical, are
employed for slurry flow modeling. In phenomenological modeling, the detailed knowledge of
the solid liquid interaction and associated heat, momentum and mass transport phenomena are
required to represent mass, momentum, and energy balances. The advantages of a
phenomenological model are: (i) since it represents physico-chemical phenomenon underlying
the process explicitly, it provides a valuable insight into the process behavior, and (ii) it
possesses extrapolation ability. Owing to the complex nature of many multiphase slurry
processes, the underlying physico-chemical phenomenon is seldom fully understood. Also,
collection of the requisite phenomenological information is costly, time-consuming and
tedious, and therefore development of phenomenological process models poses considerable
practical difficulties. Moreover, nonlinear behavior being common in multiphase slurry
processes, it leads to complex nonlinear models, which in most cases are not amenable to
analytical solutions; thus, computationally intensive numerical methods must be utilized for
obtaining solutions. Difficulties associated with the construction and solution of
phenomenological models necessitate exploration of alternative modeling formalisms.
Modeling using empirical (regression) methods is one such alternative. In conventional
empirical modeling, appropriate linear or nonlinear models are constructed exclusively from
the process input-output data without invoking the process phenomenology. A fundamental
deficiency of the conventional empirical modeling approach is that the structure (functional
form) of the data-fitting model must be specified a priori. Satisfying this requirement,
especially for nonlinearly behaving processes is a cumbersome task since it involves selecting
heuristically an appropriate nonlinear model structure from numerous alternatives.
In the last decade, artificial neural networks (ANNs) and more recently support vector
regression (SVR) have emerged as two attractive tools for nonlinear modeling especially in
situations where the development of phenomenological or conventional regression models
becomes impractical or cumbersome. In the present study, these two advanced techniques are
applied for slurry flow modeling. The sole objective is to build the quick, simple and superior
correlations which can be readily used by design engineers to design slurry pipelines and
pumps.
Mathematical Tools
14
2.2 Artificial neural network Over the past decade, neural networks have received a great deal of attention among the
scientists and engineers and they are being touted as one of the greatest computational tools
ever developed. Much of this excitement is due to the apparent ability of neural network to
emulate the brains ability to learn by examples, which in turn enables the networks to make
decisions and draw conclusions when presented with complex, noisy, and/or incomplete
information. ANN is a computer modeling approach that learns from examples through
iterations without requiring a prior knowledge of the relationships of process parameters and,
is consequently, capable of adapting to a changing environment. It is also capable of dealing
with uncertainties, noisy data, and non-linear relationships. ANN modeling have been known
as effortless computation and readily used extensively due to their model-free approximation
capabilities of complex decision-making processes. The advantages of an ANN-based model
are: (i) it can be constructed solely from the historic process input-output data (example set),
(ii) detailed knowledge of the process phenomenology is unnecessary for the model
development, (iii) a properly trained model possesses excellent generalization ability owing to
which it can accurately predict outputs for a new input data set, and (iv)even multiple input-
multiple output (MIMO) nonlinear relationships can be approximated simultaneously and
easily.
The goal of a neural network is to map a set of input patterns onto a corresponding set of
output patterns. The network accomplishes this mapping by first learning from a series of past
examples defining sets of input and output corresponding to the given system. Based on this
learning, the network then applies to a new input pattern to predict the appropriate output.
2.2.1 Background works
Application of neural networks to chemical engineering has increased significantly since 1988.
One of the first application papers was by Hoskins and Himmelblau (1988), who applied a
neural network to the fault diagnosis of chemical reactor system. Since then, the number of
research publications and network applications in bio processing and chemical engineering has
increased significantly. Baugmann and Liu (1995) provide a good overview of potential
application of neural network, as listed below:
Fr
ap
Co
to
Be
pr
2.
A
en
rom literature
pplications to
ompared to em
o noise and inco
ecause of the f
rediction, the a
.2.2 Overview
Applications of
ngineering fall
Classi
Pred
Assoc
Filt
Optim
Concept
Figu
survey it is ev
chemical engi
mpirical and cu
omplete inform
fact that in this
applications in t
w of classific
f neural netwo
l into two m
fication
diction
ciation
ering
mization
tualization
Ch
ure 2.1: Differ
vident that neu
ineering probl
urve-fitting mo
mation and can
s work we are
these two area
cation neural
orks to classifi
ajor areas: (1
useinputvandlabora
useinputvtemperaturate.
learnassocdatathatcrecognizen
smoothan
determinetravellings
Analyzedawithmanyn
hapter2
ent applicatio
ural networks
lems that are
odels, neural n
thus deal with
going to use n
s are explored
l networks
ication problem
) identificatio
valuestopredictatoryresults,deter
valuestopredictare,humidityandw
ciationsoferrorfrontainserror;e.g.noisyinputpattern
inputsignale.g.,s
optimalvaluee.gsalesperson.
taanddetermineattributessothat
on of ANN
hold much pr
complex, non
networks are re
h problems with
neural network
in detail from
ms in bio proc
on of process
categoricaloutpurminethemostlik
noutputvalues;ewindvelocity,pred
reeoridealdata,t.,learnfiveidealpnsasoneoffivep
smoothanoisyele
.,determineminim
conceptualrelatiotgroupingrelation
romise for sig
nlinear and un
elatively less s
h noisy data.
ks in classificat
literatures.
cessing and ch
faults based
ut;e.g.,givensympkelydisease.
e.g.,givendicttheevaporatio
henclassifyassocpatternsandthenatterns.
ectocardiosignal
mumlengthtripo
onshipe.g.,clustenshipscanbeinfer
15
nificant
ncertain.
ensitive
tion and
hemical
on the
ptoms
on
iate
fa
rdatarred.
Mathematical Tools
16
operating conditions of a given process and (2) prediction of the most likely categorical group
for a given input pattern, for example, identification of cell growh phase categorizing
(induction phase, growth phase, stationary phase, death phase) fermentation processes.
A partial list of various reported application includes:
Fault diagnosis on a CSTR (Venkatasubramanian, 1990) Fault diagnosis on a chemical reactor catalytically converting heptanes to toluene
(Hoskins and Himmenblau, 1990)
Classification networks produce Boolean output responses .i.e., zero indicates that the input
patterns are not within the specific class and one indicates that it is. The actual output from the
neural network is a numerical value between 0 and 1, and can represent the probability that
the input pattern corresponds to a specific class. Classification networks used for feature
categorization activate only one output response for any input pattern and select that category
based on which output response has the highest value. In comparison, fault diagnosis networks
allow multiple faults to occur for a given set of operating conditions and can therefore activate
multiple output responses for a given input pattern. From literature survey, the radial-bias-
function network is the most frequently used network architecture for classification problems.
Radial-bias-function networks outperform back propagation networks for most of the case
studies found in literatures.
2.2.3 Overview of prediction neural networks
There is lot of literatures where neural networks are applied to predict the values of process
performance variables from independent operating variables based on laboratory or plant data
in bio processing and chemical engineering. A partial list of various reported application
includes:
Prediction of remote temperature measurements in aluminium manufacturing (Wizzard & Fehrman,1991)
Estimation of mass transfer co-efficient in electrochemical refining of metals ( Reisner et al.,1993)
Prediction of the silicon contents in the pig iron from blast furnace data (Bulsari & Saxen,1991)
Prediction of complex kinetics in metallurgical and mineral processing (Reuter et al.,1993)
Chapter2
17
Prediction of overall gas holdup in bubble column reactors (Ashfaq Shaikh, Muthanna Al-Dahhan , 2003)
Calculation of the friction factor in pipeline flow of Bingham plastic fluids (Sablania, S.S. , Walid H.S & Kacimovc, A.,2003)
Prediction performance of a drying system ( Huang & Mujumdar,1993) From literatures it is evident that neural networks have been very effective in predicting and
optimizing performance data from processes and analytical instrumentation that are complex
and ill defined by first principles.
2.2.4 Strengths of ANN
ANN has a number of properties that give them advantages over other computational
techniques as described below and shown in figure 2.2.
Information is distributed over a field of nodes. This distribution provides greater flexibility than one finds in symbolic processing, where information is held in one
fixed location.
Neural networks have the ability to learn Neural networks allow extensive knowledge indexing: Knowledge indexing is the
ability to store a large amount of information and access it easily. ANN can easily
recall, for example, diverse amounts of information associated with a chemical name,
a process, or a set of process conditions. The network stores and retains knowledge in
two forms: a) the connections between nodes and b) the weight factors of these
connections. Because it has so many interconnections, the network can index and
house large amounts of information corresponding to the interrelations between
variables.
ANN is better suited for processing noisy, incomplete or inconsistent data: No single node within a neural network is directly responsible for associating a certain input
with a certain output. Instead, each node encodes a micro feature of the input-output
pattern. The concept of micro feature implies that each node affects the input-output
pattern only slightly, thus minimizing the effects of noisy or incomplete data in any
given node. Only when we assemble all the nodes together into a single coordinated
network, these micro features map the macroscopic input-output pattern. Other
Mathematical Tools
18
computational techniques do not include this micro feature concept. In empirical
modeling, for instance, each variable used has a significant impact in most models.
Consequently, if the value of one variable is off, the model will most likely yield
inaccurate results. In ANN, however, if the value of one variable is off, the model
will not be affected substantially.
ANN mimics human learning processes: Most human learning and problem solving occurs by trial and error. For example, if a piece of equipment is not operating
correctly we observe its symptoms and recommend corrective actions. Based on the
results of those actions, we recommend additional corrections. ANN functions in
same fashion. We can train them by iteratively adjusting the strength of the
connections between the nodes. After numerous iterative adjustments, the network
can properly predict the cause and effect relationships.
Automated abstraction: ANN can determine the essentials of input-output relationships automatically. We do not need a domain expert, that is, an expert in a
particular problem solving domain (e.g. Slurry specialist) to develop the knowledge
base that expert systems require. Through training with direct (and sometimes
imprecise) numerical data, the network can automatically determine cause-and-effect
relations and develop its own knowledge base.
Potential for online use: ANN may take a very long time to train, but once trained, they can calculate results from a given input very quickly. Since a trained network
may take less than a second to calculate results, it has the potential to be used online
in a control system.
2. W
of
.2.5 Limitatio
While neural ne
f neural networ
Long trimpract
network
technol
Large process
such da
but all
small t
essentia
f
p
Figure 2
ons of neural
etworks have m
rks as follows:
training times:
tical. Most sim
k and comple
logy of powerf
amount of tra
s, we may rec
ata. In addition
the training d
training data s
al.
Potentialforonline
use
mimicshumanlearningprocesses
Ch
2.2: Strength a
l networks
many advantage
Training can
mple problem
ex problems c
ful PC, this lim
aining data: I
onsider the us
n, we may also
data are very s
sets. Thus, a b
AN
abilitylearn
processnoisyd
hapter2
and character
es, they are no
n take long en
ms require at l
can require up
mitations getting
f little input-o
se of neural ne
o have a situat
similar, causin
broad based
N
yton
Aa
singdata
ristics of ANN
ot a cure-all. So
nough to make
least 1000 tim
pto 75000. Ho
g wiped out da
output data ex
etworks, since
tion where ther
ng the same pr
data set or ex
extensiveknowledgeindexing
Automatedabstraction
ome of the lim
e the neural n
me steps to tr
owever with th
ay by day.
xist on a prob
they rely hea
re is a large da
roblems as in
xperimental de
19
mitations
network
rain the
he new
blem or
avily on
atabase,
having
esign is
Mathematical Tools
20
No guarantee of optimal results: Most training techniques are capable of tunning the network, but they do not guarantee that the network will operate properly. The
training may bias the network, making it accurate in some operating regions, but
inaccurate in others. In addition, one may in advertently get trapped in local
minima during training.
No guarantee of 100% reliability: While this applies to all computational applications, this point is particularly true for neural networks with training data.
Good set of input variables: Selection of input variables that give the proper output mapping is often difficult. It is not always obvious which input variables of those
variables (e.g. Log, inverse etc) obtain the best results. Some trial and error in
selecting input variables is often required.
2.3 Comparison of neural networks to empirical modeling Consider the multilayer ANN shown in figure 2.3 where each layer (input, hidden and output)
has three nodes. This network has a total of eighteen connections and eighteen weight factors
to adjust during train the network. An engineer may say, Hold on here! If you give me
eighteen variables, I can curve fit almost anything. This neural network is nothing but
empirical modeling, which has been around for more than fifty years. You are just doing some
fancy curve-fitting. There is truth in that claim (Mah, 1991). A neural network is an
empirical modeling tool and it does operate by curve fitting. However some notable
differences exist between neural networks and typical empirical models. As a result, ANN
offer distinct advantages in some areas, as explained above, but have limitations in other areas.
First, ANN has a better filtering capacity than empirical models because of the micro feature
concept as discussed earlier. Because each node encodes only a micro feature of the overall
input output pattern, it affects the input-output pattern slightly. Moreover, neural networks
are also massively parallel, so that each node operates independently. We can view each node
as a processor in its own right and these processors all operate in parallel. As a result, the
network does not depend on a single node as heavily as, for instance; an empirical model
depends on an independent variable. Because of this parallelism, ANN has a better filtering
capacity and generally performs better than empirical models with noisy or incomplete data.
Second, neural network are more adaptive than empirical models. ANN has specified training
algorithms, where we adjust weight factors between nodes until we achieve the desired input-
Chapter2
21
output pattern. If conditions change such that the network performance is inadequate, we can
train the neural network further under these new conditions to correct its performance. In
addition, we can design the network to periodically update its input-output performance,
resulting in a continuous, online, self correcting model. Typical empirical models do not have
this ability.Third, ANN is truly multi input and multi output (MIMO) systems. Most empirical
modeling tools map one, or at most two or three dependent variables. Neural networks can
map many independent variables with many dependent variables as needed.
2.4 Artificial neural network (ANN) based modeling Neural networks are computer algorithms inspired by the way information is processed in the
nervous system. An ANN is a massively parallel-distributed processor that has a natural
propensity for storing experimental knowledge and making it available. An important
difference between neural networks and standard Information Technology (IT) solutions is
their ability to learn. This learning property has yielded a new generation of algorithms. An
ANN paradigm is composed of a large number of highly interconnected processing elements,