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By
Dr. Bikram Jit Singh
Professor
MMDU Mullana
OPTIMIZATION OF SLURRY CONTENT
ALONG WITH PIPE DIAMETER AND VELOCITY
FOR MINIMUM PRESSURE DROP
THROUGH MIXTURE DESIGN OF EXPERIMENTS
A B C D P1 P2
Levels Bottom Ash Fly Ash Additive Water Velocity Pipe Diameter
Lower 4% 6% 1.50% 40% 25m/s 350mm
Upper 40% 50% 3% 70% 40m/s 450mm
Factors with Levels
Linear Constraint
A + B ≤ 55%
COMPUTATIONAL SIMULATION OF PIPELINE
 Computational Fluid Dynamic [CFD] is the analysis of system
involving fluid flow by means of computer based simulation.
 Computers are used to perform the calculations required to
simulate the interaction of liquids with surfaces defined by
boundary conditions.
ASSUMPTIONS FOR SIMULATION
• Steady state condition
• Incompressible fluid flow
• Constant fluid properties
Model of Straight 100 meter Pipe
MESHED 100 METER STRAIGHT PIPE
METHODOLOGY
SOLUTION PARAMETERS
• Three-dimensional meshing with double-precision (3-ddp) solver is
extremely useful when dealing with very sensitive analysis like
aerodynamic drag prediction, multiphase flow systems. Meshing is
an important factor to obtain the better results.
• Standard K- € model is selected for pipeline flow simulation. This
model gives very useful results for turbulent flow.
• A convergence criterion in the simulation is 10-3. Advance
computers are required to increase the criteria of convergence for
simulation of fluid flow.
• Second-order scheme with limiters is one of the more popular
numerical schemes because of its combination of accuracy and
stability.
• In computational fluid dynamics (CFD), simple algorithm is a
widely used numerical procedure to solve the Navier-Stokes
equations. Since then it has been extensively used by many
researchers to solve different kinds of fluid flow and heat transfer
problems.
BOUNDARY CONDITIONS
• Velocity inlet: It is applied on inlet face of pipeline.
• Pressure outlet: It is applied on outlet face of delivery pipeline.
• Slurry is added in material list by giving soot conditions
density and molar mass. For bottom ash density and molar
mass is taken 2250 kg/m3 and 36.281g/mol. In case of fly ash
density is taken 1950kg/m3and 28.12 g/mol.
• Bottom ash specified diameter is taken as 162 micron and for
fly ash 57 micron.
• Simulations are done on 25 and 40m/s.
Differentconcentrations are taken for fly and bottom ash.
• 4 % turbulence intensity and turbulence viscosity ratio of 10 is
taken for inlet condition.
• 4% backflow turbulence intensity and backflow turbulence
viscosity ratio of 10 is taken for outlet condition.
PRESSURE DROP IN STRAIGHT PIPE
Runs Bottom Ash Fly Ash Additive Water Velocity Pipe Diameter Pressure Drop (KPa)
1 0.04 0.23 0.03 0.70 40 350 4243.8
2 0.05 0.50 0.02 0.44 25 350 4243.8
3 0.23 0.06 0.02 0.70 40 450 2912.3
4 0.04 0.50 0.02 0.45 25 450 1426.8
5 0.21 0.16 0.02 0.62 25 450 1084.4
6 0.30 0.16 0.02 0.53 25 350 4243.8
7 0.30 0.20 0.03 0.48 25 350 2845.9
8 0.40 0.15 0.03 0.42 25 450 1477.1
9 0.40 0.06 0.02 0.53 40 350 4243.8
10 0.04 0.25 0.02 0.70 25 450 1193.2
11 0.04 0.50 0.03 0.43 25 450 1425.1
12 0.21 0.06 0.03 0.70 40 350 4243.8
13 0.40 0.06 0.02 0.53 25 350 4243.8
14 0.04 0.23 0.03 0.70 25 450 1185.2
15 0.05 0.50 0.02 0.44 40 350 4243.8
16 0.12 0.38 0.02 0.49 40 350 4243.8
17 0.12 0.24 0.03 0.62 25 350 4243.8
18 0.12 0.38 0.03 0.48 40 450 297.5
19 0.21 0.06 0.03 0.70 25 350 2103.6
20 0.19 0.25 0.02 0.54 40 450 3196.7
21 0.05 0.50 0.02 0.44 25 450 1211.8
22 0.04 0.50 0.03 0.43 40 450 3482.6
23 0.04 0.50 0.02 0.45 40 450 3105.0
24 0.12 0.24 0.03 0.62 40 450 3196.2
25 0.30 0.16 0.02 0.53 40 350 4243.8
26 0.30 0.16 0.03 0.52 40 450 3488.4
27 0.30 0.16 0.03 0.52 25 350 4243.8
28 0.12 0.38 0.02 0.49 25 350 2489.3
29 0.40 0.06 0.03 0.51 40 450 2995.5
30 0.40 0.06 0.02 0.53 40 450 3808.6
31 0.04 0.23 0.03 0.70 25 350 42473.8
32 0.05 0.50 0.03 0.42 25 450 1424.8
33 0.40 0.15 0.03 0.42 40 350 4243.8
34 0.12 0.25 0.02 0.62 25 450 1018.0
35 0.20 0.16 0.03 0.62 40 450 2674.7
36 0.12 0.38 0.03 0.48 40 350 4243.8
37 0.30 0.20 0.02 0.49 25 350 4243.8
38 0.30 0.20 0.03 0.48 25 450 1502.5
39 0.12 0.38 0.02 0.49 25 350 4243.8
40 0.19 0.25 0.02 0.54 25 350 4243.8
41 0.21 0.06 0.03 0.70 25 450 1446.5
42 0.05 0.50 0.02 0.44 40 450 3132.7
43 0.12 0.25 0.02 0.62 25 350 4243.8
44 0.30 0.20 0.02 0.49 25 450 1450.5
45 0.21 0.06 0.03 0.70 40 450 2926.5
46 0.05 0.50 0.03 0.42 40 450 2973.0
47 0.04 0.25 0.02 0.70 25 350 4243.8
48 0.30 0.16 0.02 0.53 25 450 3214.7
49 0.30 0.20 0.02 0.49 40 450 3597.5
50 0.12 0.25 0.02 0.62 40 450 2987.3
Designed Experiments of Slurry
51 0.12 0.24 0.03 0.62 25 450 994.2
52 0.20 0.16 0.03 0.62 25 350 4243.8
53 0.21 0.16 0.02 0.62 40 350 4243.8
54 0.40 0.06 0.03 0.51 25 350 4243.8
55 0.21 0.16 0.02 0.62 25 350 2961.5
56 0.21 0.16 0.02 0.62 40 450 2977.3
57 0.12 0.38 0.03 0.48 40 350 4243.8
58 0.04 0.25 0.02 0.70 40 350 4243.8
59 0.23 0.06 0.02 0.70 40 350 4243.8
60 0.12 0.38 0.03 0.48 25 450 1238.8
61 0.12 0.38 0.02 0.49 40 450 2777.1
62 0.12 0.24 0.03 0.62 40 350 4243.8
63 0.30 0.16 0.03 0.52 25 450 3317.5
64 0.12 0.38 0.02 0.49 25 450 1221.6
65 0.40 0.15 0.02 0.44 40 350 4243.8
66 0.04 0.25 0.02 0.70 40 450 30557.1
67 0.04 0.50 0.03 0.43 40 350 4243.8
68 0.12 0.38 0.02 0.49 40 450 2777.1
69 0.19 0.25 0.02 0.54 40 350 4243.8
70 0.20 0.16 0.03 0.62 25 450 1301.8
71 0.12 0.38 0.03 0.48 25 350 3149.8
72 0.40 0.15 0.02 0.44 25 350 4243.8
73 0.04 0.50 0.02 0.45 25 350 3092.4
74 0.12 0.38 0.02 0.49 25 450 1221.6
75 0.40 0.06 0.03 0.51 40 350 4243.8
76 0.30 0.20 0.02 0.49 40 350 4243.8
77 0.20 0.16 0.03 0.62 40 350 4243.8
78 0.19 0.25 0.02 0.54 25 450 1447.8
79 0.04 0.50 0.02 0.45 40 350 4243.8
80 0.12 0.25 0.02 0.62 40 350 4243.8
81 0.23 0.06 0.02 0.70 25 450 1091.5
82 0.40 0.15 0.03 0.42 25 350 3144.3
83 0.12 0.38 0.02 0.49 40 350 4243.8
84 0.40 0.06 0.02 0.53 25 450 1382.1
85 0.30 0.16 0.03 0.52 40 350 4243.8
86 0.40 0.06 0.03 0.51 25 450 1293.1
87 0.30 0.20 0.03 0.48 40 350 4243.8
88 0.30 0.20 0.03 0.48 40 450 3308.8
89 0.12 0.38 0.03 0.48 25 450 1238.8
90 0.04 0.50 0.03 0.43 25 350 2900.4
91 0.40 0.15 0.02 0.44 25 450 1486.6
92 0.30 0.16 0.02 0.53 40 450 3066.6
93 0.12 0.38 0.03 0.48 25 350 3149.8
94 0.23 0.06 0.02 0.70 25 350 4243.8
95 0.05 0.50 0.03 0.42 40 350 4243.8
96 0.04 0.23 0.03 0.70 40 450 2622.3
97 0.12 0.38 0.03 0.48 40 450 3344.5
98 0.40 0.15 0.02 0.44 40 450 3943.0
99 0.05 0.50 0.03 0.42 25 350 3164.3
100 0.40 0.15 0.03 0.42 40 450 4296.2
Extreme Vertices Design
Components: 4 Design points: 100
Process variables: 2 Design degree: 1
Mixture total: 1.00000
Number of Boundaries for Each Dimension
Point Type 1 2 3 0
Dimension 0 1 2 3
Number 12 18 8 1
Number of Design Points for Each Type
Point Type 1 2 3 4 0 -1
Distinct 48 0 0 0 4 48
Replicates 1 0 0 0 1 1
Total number 48 0 0 0 4 48
Bounds of Mixture Components
Amount Proportion Pseudo component
Comp Lower Upper Lower Upper Lower Upper
A 0.040000 0.400000 0.040000 0.400000 0.000000 0.774194
B 0.060000 0.500000 0.060000 0.500000 0.000000 0.946237
C 0.015000 0.030000 0.015000 0.030000 0.000000 0.032258
D 0.420000 0.700000 0.420000 0.700000 0.000000 0.602151
* NOTE * Bounds were adjusted to accommodate specified constraints.
Linear Constraints of Mixture Components
Constraint Lower A B C D Upper
1 1.000000 1.000000 0.000000 0.000000 0.550000
20000100000-10000
99.9
99
90
50
10
1
0.1
Residual
Percent
20000150001000050000
20000
10000
0
-10000
Fitted Value
Residual
180001200060000-6000
60
45
30
15
0
Residual
Frequency
1009080706050403020101
20000
10000
0
-10000
Observation Order
Residual
Normal Probability Plot Versus Fits
Histogram Versus Order
Residual Plots for Pressure Drop
Stepwise for Mixtures: Pressure Drop Versus Mixture Constituents & Process Parameters
Stepwise model selection
Response: Pressure Drop
Number of terms considered = 117 Number of cases used = 100
Alpha-to-Enter = 0.1500 Alpha-to-Remove = 0.1500
Forced terms: Bottom Ash Fly Ash Additive Water
Step 1 2 3 4
Bottom A -5975 -9197 -9197 -9197
T-Value * * * *
P-Value * * * *
Fly Ash -1976 -10918 -10918 -10918
T-Value * * * *
P-Value * * * *
Additive 16077 6008 6008 6008
T-Value * * * *
P-Value * * * *
Water 9448 22605 22605 22605
T-Value * * * *
P-Value * * * *
Bottom A*Water*(-) 142848 142848 142848
T-Value 3.69 3.84 3.90
P-Value 0.000 0.000 0.000
Additive*Water*(-)2*Pi -318619 -730580
T-Value -2.98 -3.18
P-Value 0.004 0.002
Bottom A*Water*(-)2*Pi 133896
T-Value 2.01
P-Value 0.047
S 4835 4545 4368 4298
R-sq 6.44 18.16 25.23 28.35
R-sq(adj) 3.52 14.72 21.25 23.73
PRESS 2566162117 2535017408 2531433725 2666661873
R-Sq(pred) 0.00 0.00 0.00 0.00
Forced terms: Bottom Ash Fly Ash Additive Water
Step 5 6 7
Bottom A -9197 -9197 -9197
T-Value * * *
P-Value * * *
Fly Ash -10918 -10918 -10918
T-Value * * *
P-Value * * *
Additive 6008 6008 6008
T-Value * * *
P-Value * * *
Water 22605 22605 22605
T-Value * * *
P-Value * * *
Bottom A*Water*(-) 142848 142848 142848
T-Value 3.93 4.01 4.10
P-Value 0.000 0.000 0.000
Additive*Water*(-)2*Pi -730580 -730580 -730580
T-Value -3.20 -3.26 -3.34
P-Value 0.002 0.002 0.001
Bottom A*Water*(-)2*Pi 133896 133896 133896
T-Value 2.03 2.07 2.12
P-Value 0.046 0.042 0.037
1/Additive*Velocity 12.747 39.635 -119.367
T-Value 1.48 2.66 -1.69
P-Value 0.144 0.009 0.094
Additive*Water*(-)*Vel 232170 1362719
T-Value 2.19 2.72
P-Value 0.031 0.008
Water*Velocity 27694
T-Value 2.30
P-Value 0.024
S 4272 4186 4090
R-sq 30.01 33.52 37.22
R-sq(adj) 24.68 27.67 30.94
PRESS 2692139756 2788090995 2806387601
R-Sq(pred) 0.00 0.00 0.00
Regression for Mixtures: Pressure Drop versus Mixture Constituents &
Process Parameters
Estimated Regression Coefficients for Pressure Drop (component proportions)
Term Coef SE Coef T P VIF
Bottom Ash -9197 3811 * * 4.508
Fly Ash -10918 3772 * * 7.133
Additive 6008 68868 * * 15.309
Water 22605 4121 * * 29.948
Bottom Ash*Water*(-) 142848 34848 4.10 0.000 8.100
Water*Velocity 27694 12018 2.30 0.024 254.675
Additive*Water*(-)*Velocity 1362719 501408 2.72 0.008 72.720
1/Additive*Velocity -119 71 -1.69 0.094 72.633
Bottom Ash*Water*(-)2*Pipe Diameter 133896 63273 2.12 0.037 4.783
Additive*Water*(-)2*Pipe Diameter -730580 218899 -3.34 0.001 4.783
* NOTE * Coefficients are calculated for coded process variables.
S = 4090.14 PRESS = 2806387601
R-Sq = 37.22% R-Sq(pred) = 0.00% R-Sq(adj) = 30.94%
Analysis of Variance for Pressure Drop (component proportions)
Source DF Seq SS Adj SS Adj MS
Regression 9 892733445 892733445 99192605
Component Only
Linear 3 154468287 423716329 141238776
Full Cubic 1 281112490 281112490 281112490
Bottom A*Water*(-) 1 281112490 281112490 281112490
Component* Velocity
Linear 1 14967245 88835039 88835039
Water*Velocity 1 14967245 88835039 88835039
Full Cubic 1 149818160 123568498 123568498
Additive*Water*(-)*Velocity 1 149818160 123568498 123568498
Inverse 1 47930436 47930436 47930436
1/Additive*Velocity 1 47930436 47930436 47930436
Component* Pipe Diameter
Full Quartic1 2 244436827 244436827 122218413
Bottom A*Water*(-)2*Pipe Diameter 1 58088163 74915126 74915126
Additive*Water*(-)2*Pipe Diameter 1 186348664 186348664 186348664
Residual Error 90 1505634238 1505634238 16729269
Total 99 2398367683
Source F P
Regression 5.93 0.000
Component Only
Linear 8.44 0.000
Full Cubic 16.80 0.000
Bottom A*Water*(-) 16.80 0.000
Component* Velocity
Linear 5.31 0.024
Water*Velocity 5.31 0.024
Full Cubic 7.39 0.008
Additive*Water*(-)*Velocity 7.39 0.008
Inverse 2.87 0.094
1/Additive*Velocity 2.87 0.094
Component* Pipe Diameter
Full Quartic1 7.31 0.001
Bottom A*Water*(-)2*Pipe Diameter 4.48 0.037
Additive*Water*(-)2*Pipe Diameter 11.14 0.001
Pressure Drop = -9197 Bottom Ash – 10918 Fly Ash + 6008
Additive + 22605 Water + 142848 (Bottom
ash X Water) + 27694 (Water X Velocity) +
1362719 (Additive X Water X (-) Velocity)–
119 (1/Additive X Velocity) + 133896
Bottom Ash X Water X (-)2 X Pipe Diameter)
– 730580 (Additive X Water X (-) 2 X Pipe
Diameter)
Statistical Model
4025
5000
4500
4000
3500
3000
450350
Velocity
Mean
Pipe Diameter
Main Effects Plot for Pressure Drop
Data Means
450350
5000
4000
3000
2000
1000
4025
5000
4000
3000
2000
1000
Velocity
Pipe Diameter
25
40
Velocity
350
450
Diameter
Pipe
Interaction Plot for Pressure Drop
Data Means
450
350
4025
Pipe Diameter
Velocity
4177.79
4243.825235.54
1451.85
Cube Plot (data means) for Pressure Drop
Velocity
PipeDiameter
40.037.535.032.530.027.525.0
450
425
400
375
350
Bottom Ash 0.04
Fly Ash 0.23
Additive 0.03
Water 0.7
Hold Values
>
–
–
–
–
–
–
–
< 2000
2000 4500
4500 7000
7000 9500
9500 12000
12000 14500
14500 17000
17000 19500
19500
Pressure Drop
Mixture Contour Plot of Pressure Drop
0.30.20.10.0-0.1-0.2
12000
10000
8000
6000
4000
2000
0
deviation from reference blend in proportion
FittedPressureDrop
Velocity: 25
Pipe Diameter: 350 Bottom Ash 0.1925
Fly Ash 0.2525
Additive 0.0225
Water 0.5325
Comp:RefBlend
Cox Response Trace Plot
(1)
Bottom A sh
0.040
0.505
Fly A sh
0.525
0.060
A dditive
0.480
0.015
(2)
Bottom A sh
0.040
0.505
Fly A sh
0.525
0.060
A dditive
0.480
0.015
(3)
Bottom A sh
0.040
0.505
Fly A sh
0.525
0.060
A dditive
0.480
0.015
(4)
Bottom A sh
0.040
0.505
Fly A sh
0.525
0.060
A dditive
0.480
0.015
Water 0.42
Velocity 25
Pipe Diameter 450
Velocity 40
Pipe Diameter 450
Velocity 25
Pipe Diameter 350
Velocity 40
Pipe Diameter 350
(1)
(2)
(3)
(4)
Hold Values
>
–
–
–
–
–
< 0
0 2000
2000 4000
4000 6000
6000 8000
8000 10000
10000
Pressure Drop
Multiple Mixture Contour Plot for Pressure Drop
(component amounts)
(1)
Fly A sh
0.060
0.525
A dditive
0.480
0.015
Water
0.885
0.420
(2)
Fly A sh
0.060
0.525
A dditive
0.480
0.015
Water
0.885
0.420
(3)
Fly A sh
0.060
0.525
A dditive
0.480
0.015
Water
0.885
0.420
(4)
Fly A sh
0.060
0.525
A dditive
0.480
0.015
Water
0.885
0.420
Bottom Ash 0.04
Velocity 25
Pipe Diameter 450
Velocity 40
Pipe Diameter 450
Velocity 25
Pipe Diameter 350
Velocity 40
Pipe Diameter 350
(1)
(2)
(3)
(4)
Hold Values
>
–
–
–
–
–
< -10000
-10000 0
0 10000
10000 20000
20000 30000
30000 40000
40000
Pressure Drop
Multiple Mixture Contour Plot for Pressure Drop
(component amounts)
(1)
Additive
0.015
0.480
Water
0.885
0.420
Bottom Ash
0.505
0.040
(2)
Additive
0.015
0.480
Water
0.885
0.420
Bottom Ash
0.505
0.040
(3)
Additive
0.015
0.480
Water
0.885
0.420
Bottom Ash
0.505
0.040
(4)
Additive
0.015
0.480
Water
0.885
0.420
Bottom Ash
0.505
0.040
Fly Ash 0.06
Velocity 25
Pipe Diameter 450
Velocity 40
Pipe Diameter 450
Velocity 25
Pipe Diameter 350
Velocity 40
Pipe Diameter 350
(1)
(2)
(3)
(4)
Hold Values
>
–
–
–
–
–
< -10000
-10000 0
0 10000
10000 20000
20000 30000
30000 40000
40000
Pressure Drop
Multiple Mixture Contour Plot for Pressure Drop
(component amounts)
(1)
Water
0.420
0.885
Bottom Ash
0.505
0.040
Fly Ash
0.525
0.060
(2)
Water
0.420
0.885
Bottom Ash
0.505
0.040
Fly Ash
0.525
0.060
(3)
Water
0.420
0.885
Bottom Ash
0.505
0.040
Fly Ash
0.525
0.060
(4)
Water
0.420
0.885
Bottom Ash
0.505
0.040
Fly Ash
0.525
0.060
Additive 0.015
Velocity 25
Pipe Diameter 450
Velocity 40
Pipe Diameter 450
Velocity 25
Pipe Diameter 350
Velocity 40
Pipe Diameter 350
(1)
(2)
(3)
(4)
Hold Values
>
–
–
–
–
–
< 3000
3000 6000
6000 9000
9000 12000
12000 15000
15000 18000
18000
Pressure Drop
Multiple Mixture Contour Plot for Pressure Drop
(component amounts)
Water
0.420
0.878
Bottom Ash
0.498
0.040
Fly Ash
0.518
0.060
Velocity 40
Pipe Diameter 450
Additive 0.0225
Hold Values
900
2500
Drop
Pressure
(component amounts)
Overlaid Contour Plot of Pressure Drop
Bottom Ash
0.040
0.365
Fly Ash
0.385
0.060
Additive
0.340
0.015
Velocity 40
Pipe Diameter 450
Water 0.56
Hold Values
900
2500
Drop
Pressure
(component amounts)
Overlaid Contour Plot of Pressure Drop
Fly Ash
0.060
0.345
Additive
0.300
0.015
Water
0.705
0.420
Velocity 40
Pipe Diameter 450
Bottom Ash 0.22
Hold Values
900
2500
Drop
Pressure
(component amounts)
Overlaid Contour Plot of Pressure Drop
Additive
0.015
0.260
Water
0.665
0.420
Bottom Ash
0.285
0.040
Velocity 40
Pipe Diameter 450
Fly Ash 0.28
Hold Values
900
2500
Drop
Pressure
(component amounts)
Overlaid Contour Plot of Pressure Drop
Bottom A sh
0.040
0.365
Fly A sh
0.385
0.060
A dditive
0.340
0.015
Bottom A sh
0.040
0.497
Fly A sh
0.517
0.060
Water
0.877
0.420
Bottom A sh
0.040
0.285
A dditive
0.260
0.015
Water
0.665
0.420
Fly A sh
0.060
0.345
A dditive
0.300
0.015
Water
0.705
0.420
Bottom Ash 0.22
Fly Ash 0.28
Additive 0.0225
Water 0.56
Velocity 40
Pipe Diameter 450
Hold Values
>
–
–
–
–
–
< -5000
-5000 -2500
-2500 0
0 2500
2500 5000
5000 7500
7500
Pressure Drop
(component amounts)
Matrix of Closed Mixture Contour Plots for Pressure Drop
Response Optimization
Parameters
Goal Lower Target Upper Weight Import
Pressure Drop Minimum 1000 1000 4473 1 1
Starting Point
Components
Bottom Ash = 0.04
Fly Ash = 0.06
Additive = 0.015
Water = 0.40
Process Variables
Velocity = 25
Pipe Diameter = 350
Global Solution
Components
Bottom Ash = 0.2199
Fly Ash = 0.320
Additive = 0.0178
Water = 0.4423
Process Variables
Velocity = 34
Pipe Diameter = 440
Predicted Responses
Pressure Drop = 1185.7543 ,
Desirability = 0.94651
Cur
High
Low0.94651
D
New
d = 0.94651
Minimum
Pressure
y = 1185.7543
0.94651
Desirability
Composite
350.0
450.0
25.0
40.0
0.420
0.70
0.0150
0.030
0.1148
0.50
0.040
0.40
[ ]:Fly Ash [ ]:Additive [ ]:Water Velocity Pipe Dia[ ]:Bottom A
[0.2199] [0.320] [0.0178] [0.4423] [34.0] [440.0]
Synergizing mixture do e with cfd for ash slurry optimization

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Synergizing mixture do e with cfd for ash slurry optimization

  • 1. By Dr. Bikram Jit Singh Professor MMDU Mullana OPTIMIZATION OF SLURRY CONTENT ALONG WITH PIPE DIAMETER AND VELOCITY FOR MINIMUM PRESSURE DROP THROUGH MIXTURE DESIGN OF EXPERIMENTS
  • 2. A B C D P1 P2 Levels Bottom Ash Fly Ash Additive Water Velocity Pipe Diameter Lower 4% 6% 1.50% 40% 25m/s 350mm Upper 40% 50% 3% 70% 40m/s 450mm Factors with Levels Linear Constraint A + B ≤ 55%
  • 3. COMPUTATIONAL SIMULATION OF PIPELINE  Computational Fluid Dynamic [CFD] is the analysis of system involving fluid flow by means of computer based simulation.  Computers are used to perform the calculations required to simulate the interaction of liquids with surfaces defined by boundary conditions.
  • 4. ASSUMPTIONS FOR SIMULATION • Steady state condition • Incompressible fluid flow • Constant fluid properties
  • 5. Model of Straight 100 meter Pipe
  • 6. MESHED 100 METER STRAIGHT PIPE
  • 8. SOLUTION PARAMETERS • Three-dimensional meshing with double-precision (3-ddp) solver is extremely useful when dealing with very sensitive analysis like aerodynamic drag prediction, multiphase flow systems. Meshing is an important factor to obtain the better results. • Standard K- € model is selected for pipeline flow simulation. This model gives very useful results for turbulent flow. • A convergence criterion in the simulation is 10-3. Advance computers are required to increase the criteria of convergence for simulation of fluid flow. • Second-order scheme with limiters is one of the more popular numerical schemes because of its combination of accuracy and stability. • In computational fluid dynamics (CFD), simple algorithm is a widely used numerical procedure to solve the Navier-Stokes equations. Since then it has been extensively used by many researchers to solve different kinds of fluid flow and heat transfer problems.
  • 9. BOUNDARY CONDITIONS • Velocity inlet: It is applied on inlet face of pipeline. • Pressure outlet: It is applied on outlet face of delivery pipeline. • Slurry is added in material list by giving soot conditions density and molar mass. For bottom ash density and molar mass is taken 2250 kg/m3 and 36.281g/mol. In case of fly ash density is taken 1950kg/m3and 28.12 g/mol. • Bottom ash specified diameter is taken as 162 micron and for fly ash 57 micron. • Simulations are done on 25 and 40m/s. Differentconcentrations are taken for fly and bottom ash. • 4 % turbulence intensity and turbulence viscosity ratio of 10 is taken for inlet condition. • 4% backflow turbulence intensity and backflow turbulence viscosity ratio of 10 is taken for outlet condition.
  • 10. PRESSURE DROP IN STRAIGHT PIPE
  • 11. Runs Bottom Ash Fly Ash Additive Water Velocity Pipe Diameter Pressure Drop (KPa) 1 0.04 0.23 0.03 0.70 40 350 4243.8 2 0.05 0.50 0.02 0.44 25 350 4243.8 3 0.23 0.06 0.02 0.70 40 450 2912.3 4 0.04 0.50 0.02 0.45 25 450 1426.8 5 0.21 0.16 0.02 0.62 25 450 1084.4 6 0.30 0.16 0.02 0.53 25 350 4243.8 7 0.30 0.20 0.03 0.48 25 350 2845.9 8 0.40 0.15 0.03 0.42 25 450 1477.1 9 0.40 0.06 0.02 0.53 40 350 4243.8 10 0.04 0.25 0.02 0.70 25 450 1193.2 11 0.04 0.50 0.03 0.43 25 450 1425.1 12 0.21 0.06 0.03 0.70 40 350 4243.8 13 0.40 0.06 0.02 0.53 25 350 4243.8 14 0.04 0.23 0.03 0.70 25 450 1185.2 15 0.05 0.50 0.02 0.44 40 350 4243.8 16 0.12 0.38 0.02 0.49 40 350 4243.8 17 0.12 0.24 0.03 0.62 25 350 4243.8 18 0.12 0.38 0.03 0.48 40 450 297.5 19 0.21 0.06 0.03 0.70 25 350 2103.6 20 0.19 0.25 0.02 0.54 40 450 3196.7 21 0.05 0.50 0.02 0.44 25 450 1211.8 22 0.04 0.50 0.03 0.43 40 450 3482.6 23 0.04 0.50 0.02 0.45 40 450 3105.0 24 0.12 0.24 0.03 0.62 40 450 3196.2 25 0.30 0.16 0.02 0.53 40 350 4243.8 26 0.30 0.16 0.03 0.52 40 450 3488.4 27 0.30 0.16 0.03 0.52 25 350 4243.8 28 0.12 0.38 0.02 0.49 25 350 2489.3 29 0.40 0.06 0.03 0.51 40 450 2995.5 30 0.40 0.06 0.02 0.53 40 450 3808.6 31 0.04 0.23 0.03 0.70 25 350 42473.8 32 0.05 0.50 0.03 0.42 25 450 1424.8 33 0.40 0.15 0.03 0.42 40 350 4243.8 34 0.12 0.25 0.02 0.62 25 450 1018.0 35 0.20 0.16 0.03 0.62 40 450 2674.7 36 0.12 0.38 0.03 0.48 40 350 4243.8 37 0.30 0.20 0.02 0.49 25 350 4243.8 38 0.30 0.20 0.03 0.48 25 450 1502.5 39 0.12 0.38 0.02 0.49 25 350 4243.8 40 0.19 0.25 0.02 0.54 25 350 4243.8 41 0.21 0.06 0.03 0.70 25 450 1446.5 42 0.05 0.50 0.02 0.44 40 450 3132.7 43 0.12 0.25 0.02 0.62 25 350 4243.8 44 0.30 0.20 0.02 0.49 25 450 1450.5 45 0.21 0.06 0.03 0.70 40 450 2926.5 46 0.05 0.50 0.03 0.42 40 450 2973.0 47 0.04 0.25 0.02 0.70 25 350 4243.8 48 0.30 0.16 0.02 0.53 25 450 3214.7 49 0.30 0.20 0.02 0.49 40 450 3597.5 50 0.12 0.25 0.02 0.62 40 450 2987.3 Designed Experiments of Slurry
  • 12. 51 0.12 0.24 0.03 0.62 25 450 994.2 52 0.20 0.16 0.03 0.62 25 350 4243.8 53 0.21 0.16 0.02 0.62 40 350 4243.8 54 0.40 0.06 0.03 0.51 25 350 4243.8 55 0.21 0.16 0.02 0.62 25 350 2961.5 56 0.21 0.16 0.02 0.62 40 450 2977.3 57 0.12 0.38 0.03 0.48 40 350 4243.8 58 0.04 0.25 0.02 0.70 40 350 4243.8 59 0.23 0.06 0.02 0.70 40 350 4243.8 60 0.12 0.38 0.03 0.48 25 450 1238.8 61 0.12 0.38 0.02 0.49 40 450 2777.1 62 0.12 0.24 0.03 0.62 40 350 4243.8 63 0.30 0.16 0.03 0.52 25 450 3317.5 64 0.12 0.38 0.02 0.49 25 450 1221.6 65 0.40 0.15 0.02 0.44 40 350 4243.8 66 0.04 0.25 0.02 0.70 40 450 30557.1 67 0.04 0.50 0.03 0.43 40 350 4243.8 68 0.12 0.38 0.02 0.49 40 450 2777.1 69 0.19 0.25 0.02 0.54 40 350 4243.8 70 0.20 0.16 0.03 0.62 25 450 1301.8 71 0.12 0.38 0.03 0.48 25 350 3149.8 72 0.40 0.15 0.02 0.44 25 350 4243.8 73 0.04 0.50 0.02 0.45 25 350 3092.4 74 0.12 0.38 0.02 0.49 25 450 1221.6 75 0.40 0.06 0.03 0.51 40 350 4243.8 76 0.30 0.20 0.02 0.49 40 350 4243.8 77 0.20 0.16 0.03 0.62 40 350 4243.8 78 0.19 0.25 0.02 0.54 25 450 1447.8 79 0.04 0.50 0.02 0.45 40 350 4243.8 80 0.12 0.25 0.02 0.62 40 350 4243.8 81 0.23 0.06 0.02 0.70 25 450 1091.5 82 0.40 0.15 0.03 0.42 25 350 3144.3 83 0.12 0.38 0.02 0.49 40 350 4243.8 84 0.40 0.06 0.02 0.53 25 450 1382.1 85 0.30 0.16 0.03 0.52 40 350 4243.8 86 0.40 0.06 0.03 0.51 25 450 1293.1 87 0.30 0.20 0.03 0.48 40 350 4243.8 88 0.30 0.20 0.03 0.48 40 450 3308.8 89 0.12 0.38 0.03 0.48 25 450 1238.8 90 0.04 0.50 0.03 0.43 25 350 2900.4 91 0.40 0.15 0.02 0.44 25 450 1486.6 92 0.30 0.16 0.02 0.53 40 450 3066.6 93 0.12 0.38 0.03 0.48 25 350 3149.8 94 0.23 0.06 0.02 0.70 25 350 4243.8 95 0.05 0.50 0.03 0.42 40 350 4243.8 96 0.04 0.23 0.03 0.70 40 450 2622.3 97 0.12 0.38 0.03 0.48 40 450 3344.5 98 0.40 0.15 0.02 0.44 40 450 3943.0 99 0.05 0.50 0.03 0.42 25 350 3164.3 100 0.40 0.15 0.03 0.42 40 450 4296.2
  • 13. Extreme Vertices Design Components: 4 Design points: 100 Process variables: 2 Design degree: 1 Mixture total: 1.00000 Number of Boundaries for Each Dimension Point Type 1 2 3 0 Dimension 0 1 2 3 Number 12 18 8 1 Number of Design Points for Each Type Point Type 1 2 3 4 0 -1 Distinct 48 0 0 0 4 48 Replicates 1 0 0 0 1 1 Total number 48 0 0 0 4 48 Bounds of Mixture Components Amount Proportion Pseudo component Comp Lower Upper Lower Upper Lower Upper A 0.040000 0.400000 0.040000 0.400000 0.000000 0.774194 B 0.060000 0.500000 0.060000 0.500000 0.000000 0.946237 C 0.015000 0.030000 0.015000 0.030000 0.000000 0.032258 D 0.420000 0.700000 0.420000 0.700000 0.000000 0.602151 * NOTE * Bounds were adjusted to accommodate specified constraints. Linear Constraints of Mixture Components Constraint Lower A B C D Upper 1 1.000000 1.000000 0.000000 0.000000 0.550000
  • 15. Stepwise for Mixtures: Pressure Drop Versus Mixture Constituents & Process Parameters Stepwise model selection Response: Pressure Drop Number of terms considered = 117 Number of cases used = 100 Alpha-to-Enter = 0.1500 Alpha-to-Remove = 0.1500 Forced terms: Bottom Ash Fly Ash Additive Water Step 1 2 3 4 Bottom A -5975 -9197 -9197 -9197 T-Value * * * * P-Value * * * * Fly Ash -1976 -10918 -10918 -10918 T-Value * * * * P-Value * * * * Additive 16077 6008 6008 6008 T-Value * * * * P-Value * * * * Water 9448 22605 22605 22605 T-Value * * * * P-Value * * * * Bottom A*Water*(-) 142848 142848 142848 T-Value 3.69 3.84 3.90 P-Value 0.000 0.000 0.000 Additive*Water*(-)2*Pi -318619 -730580 T-Value -2.98 -3.18 P-Value 0.004 0.002 Bottom A*Water*(-)2*Pi 133896 T-Value 2.01 P-Value 0.047 S 4835 4545 4368 4298 R-sq 6.44 18.16 25.23 28.35 R-sq(adj) 3.52 14.72 21.25 23.73 PRESS 2566162117 2535017408 2531433725 2666661873 R-Sq(pred) 0.00 0.00 0.00 0.00
  • 16. Forced terms: Bottom Ash Fly Ash Additive Water Step 5 6 7 Bottom A -9197 -9197 -9197 T-Value * * * P-Value * * * Fly Ash -10918 -10918 -10918 T-Value * * * P-Value * * * Additive 6008 6008 6008 T-Value * * * P-Value * * * Water 22605 22605 22605 T-Value * * * P-Value * * * Bottom A*Water*(-) 142848 142848 142848 T-Value 3.93 4.01 4.10 P-Value 0.000 0.000 0.000 Additive*Water*(-)2*Pi -730580 -730580 -730580 T-Value -3.20 -3.26 -3.34 P-Value 0.002 0.002 0.001 Bottom A*Water*(-)2*Pi 133896 133896 133896 T-Value 2.03 2.07 2.12 P-Value 0.046 0.042 0.037 1/Additive*Velocity 12.747 39.635 -119.367 T-Value 1.48 2.66 -1.69 P-Value 0.144 0.009 0.094 Additive*Water*(-)*Vel 232170 1362719 T-Value 2.19 2.72 P-Value 0.031 0.008 Water*Velocity 27694 T-Value 2.30 P-Value 0.024 S 4272 4186 4090 R-sq 30.01 33.52 37.22 R-sq(adj) 24.68 27.67 30.94 PRESS 2692139756 2788090995 2806387601 R-Sq(pred) 0.00 0.00 0.00
  • 17. Regression for Mixtures: Pressure Drop versus Mixture Constituents & Process Parameters Estimated Regression Coefficients for Pressure Drop (component proportions) Term Coef SE Coef T P VIF Bottom Ash -9197 3811 * * 4.508 Fly Ash -10918 3772 * * 7.133 Additive 6008 68868 * * 15.309 Water 22605 4121 * * 29.948 Bottom Ash*Water*(-) 142848 34848 4.10 0.000 8.100 Water*Velocity 27694 12018 2.30 0.024 254.675 Additive*Water*(-)*Velocity 1362719 501408 2.72 0.008 72.720 1/Additive*Velocity -119 71 -1.69 0.094 72.633 Bottom Ash*Water*(-)2*Pipe Diameter 133896 63273 2.12 0.037 4.783 Additive*Water*(-)2*Pipe Diameter -730580 218899 -3.34 0.001 4.783 * NOTE * Coefficients are calculated for coded process variables. S = 4090.14 PRESS = 2806387601 R-Sq = 37.22% R-Sq(pred) = 0.00% R-Sq(adj) = 30.94%
  • 18. Analysis of Variance for Pressure Drop (component proportions) Source DF Seq SS Adj SS Adj MS Regression 9 892733445 892733445 99192605 Component Only Linear 3 154468287 423716329 141238776 Full Cubic 1 281112490 281112490 281112490 Bottom A*Water*(-) 1 281112490 281112490 281112490 Component* Velocity Linear 1 14967245 88835039 88835039 Water*Velocity 1 14967245 88835039 88835039 Full Cubic 1 149818160 123568498 123568498 Additive*Water*(-)*Velocity 1 149818160 123568498 123568498 Inverse 1 47930436 47930436 47930436 1/Additive*Velocity 1 47930436 47930436 47930436 Component* Pipe Diameter Full Quartic1 2 244436827 244436827 122218413 Bottom A*Water*(-)2*Pipe Diameter 1 58088163 74915126 74915126 Additive*Water*(-)2*Pipe Diameter 1 186348664 186348664 186348664 Residual Error 90 1505634238 1505634238 16729269 Total 99 2398367683 Source F P Regression 5.93 0.000 Component Only Linear 8.44 0.000 Full Cubic 16.80 0.000 Bottom A*Water*(-) 16.80 0.000 Component* Velocity Linear 5.31 0.024 Water*Velocity 5.31 0.024 Full Cubic 7.39 0.008 Additive*Water*(-)*Velocity 7.39 0.008 Inverse 2.87 0.094 1/Additive*Velocity 2.87 0.094 Component* Pipe Diameter Full Quartic1 7.31 0.001 Bottom A*Water*(-)2*Pipe Diameter 4.48 0.037 Additive*Water*(-)2*Pipe Diameter 11.14 0.001
  • 19. Pressure Drop = -9197 Bottom Ash – 10918 Fly Ash + 6008 Additive + 22605 Water + 142848 (Bottom ash X Water) + 27694 (Water X Velocity) + 1362719 (Additive X Water X (-) Velocity)– 119 (1/Additive X Velocity) + 133896 Bottom Ash X Water X (-)2 X Pipe Diameter) – 730580 (Additive X Water X (-) 2 X Pipe Diameter) Statistical Model
  • 23. Velocity PipeDiameter 40.037.535.032.530.027.525.0 450 425 400 375 350 Bottom Ash 0.04 Fly Ash 0.23 Additive 0.03 Water 0.7 Hold Values > – – – – – – – < 2000 2000 4500 4500 7000 7000 9500 9500 12000 12000 14500 14500 17000 17000 19500 19500 Pressure Drop Mixture Contour Plot of Pressure Drop
  • 24. 0.30.20.10.0-0.1-0.2 12000 10000 8000 6000 4000 2000 0 deviation from reference blend in proportion FittedPressureDrop Velocity: 25 Pipe Diameter: 350 Bottom Ash 0.1925 Fly Ash 0.2525 Additive 0.0225 Water 0.5325 Comp:RefBlend Cox Response Trace Plot
  • 25. (1) Bottom A sh 0.040 0.505 Fly A sh 0.525 0.060 A dditive 0.480 0.015 (2) Bottom A sh 0.040 0.505 Fly A sh 0.525 0.060 A dditive 0.480 0.015 (3) Bottom A sh 0.040 0.505 Fly A sh 0.525 0.060 A dditive 0.480 0.015 (4) Bottom A sh 0.040 0.505 Fly A sh 0.525 0.060 A dditive 0.480 0.015 Water 0.42 Velocity 25 Pipe Diameter 450 Velocity 40 Pipe Diameter 450 Velocity 25 Pipe Diameter 350 Velocity 40 Pipe Diameter 350 (1) (2) (3) (4) Hold Values > – – – – – < 0 0 2000 2000 4000 4000 6000 6000 8000 8000 10000 10000 Pressure Drop Multiple Mixture Contour Plot for Pressure Drop (component amounts)
  • 26. (1) Fly A sh 0.060 0.525 A dditive 0.480 0.015 Water 0.885 0.420 (2) Fly A sh 0.060 0.525 A dditive 0.480 0.015 Water 0.885 0.420 (3) Fly A sh 0.060 0.525 A dditive 0.480 0.015 Water 0.885 0.420 (4) Fly A sh 0.060 0.525 A dditive 0.480 0.015 Water 0.885 0.420 Bottom Ash 0.04 Velocity 25 Pipe Diameter 450 Velocity 40 Pipe Diameter 450 Velocity 25 Pipe Diameter 350 Velocity 40 Pipe Diameter 350 (1) (2) (3) (4) Hold Values > – – – – – < -10000 -10000 0 0 10000 10000 20000 20000 30000 30000 40000 40000 Pressure Drop Multiple Mixture Contour Plot for Pressure Drop (component amounts)
  • 27. (1) Additive 0.015 0.480 Water 0.885 0.420 Bottom Ash 0.505 0.040 (2) Additive 0.015 0.480 Water 0.885 0.420 Bottom Ash 0.505 0.040 (3) Additive 0.015 0.480 Water 0.885 0.420 Bottom Ash 0.505 0.040 (4) Additive 0.015 0.480 Water 0.885 0.420 Bottom Ash 0.505 0.040 Fly Ash 0.06 Velocity 25 Pipe Diameter 450 Velocity 40 Pipe Diameter 450 Velocity 25 Pipe Diameter 350 Velocity 40 Pipe Diameter 350 (1) (2) (3) (4) Hold Values > – – – – – < -10000 -10000 0 0 10000 10000 20000 20000 30000 30000 40000 40000 Pressure Drop Multiple Mixture Contour Plot for Pressure Drop (component amounts)
  • 28. (1) Water 0.420 0.885 Bottom Ash 0.505 0.040 Fly Ash 0.525 0.060 (2) Water 0.420 0.885 Bottom Ash 0.505 0.040 Fly Ash 0.525 0.060 (3) Water 0.420 0.885 Bottom Ash 0.505 0.040 Fly Ash 0.525 0.060 (4) Water 0.420 0.885 Bottom Ash 0.505 0.040 Fly Ash 0.525 0.060 Additive 0.015 Velocity 25 Pipe Diameter 450 Velocity 40 Pipe Diameter 450 Velocity 25 Pipe Diameter 350 Velocity 40 Pipe Diameter 350 (1) (2) (3) (4) Hold Values > – – – – – < 3000 3000 6000 6000 9000 9000 12000 12000 15000 15000 18000 18000 Pressure Drop Multiple Mixture Contour Plot for Pressure Drop (component amounts)
  • 29. Water 0.420 0.878 Bottom Ash 0.498 0.040 Fly Ash 0.518 0.060 Velocity 40 Pipe Diameter 450 Additive 0.0225 Hold Values 900 2500 Drop Pressure (component amounts) Overlaid Contour Plot of Pressure Drop
  • 30. Bottom Ash 0.040 0.365 Fly Ash 0.385 0.060 Additive 0.340 0.015 Velocity 40 Pipe Diameter 450 Water 0.56 Hold Values 900 2500 Drop Pressure (component amounts) Overlaid Contour Plot of Pressure Drop
  • 31. Fly Ash 0.060 0.345 Additive 0.300 0.015 Water 0.705 0.420 Velocity 40 Pipe Diameter 450 Bottom Ash 0.22 Hold Values 900 2500 Drop Pressure (component amounts) Overlaid Contour Plot of Pressure Drop
  • 32. Additive 0.015 0.260 Water 0.665 0.420 Bottom Ash 0.285 0.040 Velocity 40 Pipe Diameter 450 Fly Ash 0.28 Hold Values 900 2500 Drop Pressure (component amounts) Overlaid Contour Plot of Pressure Drop
  • 33. Bottom A sh 0.040 0.365 Fly A sh 0.385 0.060 A dditive 0.340 0.015 Bottom A sh 0.040 0.497 Fly A sh 0.517 0.060 Water 0.877 0.420 Bottom A sh 0.040 0.285 A dditive 0.260 0.015 Water 0.665 0.420 Fly A sh 0.060 0.345 A dditive 0.300 0.015 Water 0.705 0.420 Bottom Ash 0.22 Fly Ash 0.28 Additive 0.0225 Water 0.56 Velocity 40 Pipe Diameter 450 Hold Values > – – – – – < -5000 -5000 -2500 -2500 0 0 2500 2500 5000 5000 7500 7500 Pressure Drop (component amounts) Matrix of Closed Mixture Contour Plots for Pressure Drop
  • 34. Response Optimization Parameters Goal Lower Target Upper Weight Import Pressure Drop Minimum 1000 1000 4473 1 1 Starting Point Components Bottom Ash = 0.04 Fly Ash = 0.06 Additive = 0.015 Water = 0.40 Process Variables Velocity = 25 Pipe Diameter = 350 Global Solution Components Bottom Ash = 0.2199 Fly Ash = 0.320 Additive = 0.0178 Water = 0.4423 Process Variables Velocity = 34 Pipe Diameter = 440 Predicted Responses Pressure Drop = 1185.7543 , Desirability = 0.94651
  • 35. Cur High Low0.94651 D New d = 0.94651 Minimum Pressure y = 1185.7543 0.94651 Desirability Composite 350.0 450.0 25.0 40.0 0.420 0.70 0.0150 0.030 0.1148 0.50 0.040 0.40 [ ]:Fly Ash [ ]:Additive [ ]:Water Velocity Pipe Dia[ ]:Bottom A [0.2199] [0.320] [0.0178] [0.4423] [34.0] [440.0]