Optimization of Solid HoldOptimization of Solid Hold--up in up in NanoparticlesNanoparticlesFluidized Bed Fluidized Bed Using Radioactive DensitometryUsing Radioactive Densitometry

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Optimization of Solid Hold

Optimization of Solid Hold--up in up in Nanoparticles Nanoparticles Fluidized Bed Fluidized Bed Using Radioactive Densitometry

Using Radioactive Densitometry

1 Solution Solution

Outline Outline

Introduction Introduction

Objective Objective Problem Problem

Experiments Experiments

Design of Experimental Plan Design of Experimental Plan

Analysis of the Obtained Experimental Data Analysis of the Obtained Experimental Data Conclusion

Conclusion

Design of Experimental Plan

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Introduction Introduction

Objective:

Objective: Optimization of solid hold-up in the fluidized bed reactor for eliminating the dead zone in reactor to maximize the convergence

Introduction : Fluidized Beds Introduction : Fluidized Beds

Uniform

Uniform Ununiform Ununiform

3 Dead Zone

Dead Zone

Nanoparticles Fluidized Bed

Nanoparticles

Fixed Bed

Introduction Introduction

ü Dead zone in the bed

ü Solid hold-up Dead zone occures

ü The location of dead zone The maximum of solid hold-up Problem

Problem

Reactor efficiency

ü Predict a model for Solid hold-up distribution in the bed üMaximizing the obtained solid hold-up

Solution

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Experiments Experiments

Design of Experimental Plan

Analysis the Obtained Experimental Data Step 1

Step 2

Response Variable Y : Solid hold-up

5 X

3

: Superficial Gas Velocity Controlable Factors

X

1

: Axial Position X

2

: Radial Position

Experimental Set

Experimental Set--up and up and Method of Measurement Method of Measurement

Radioactive Densitometry

is used to measure the solid hold-up in the bed

Fluidized Bed Fluidized Bed Radioactive Source Radioactive Source Detector

Detector

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Radioactive Densitometry Radioactive Densitometry

Radioactive Source

Radioactive Source Detector Detector Radioactive Source Radioactive Source Detector Detector

7 μ : attenuation coefficient

μ : attenuation coefficient ρ : bed density ρ : bed density

Design of Experiments Design of Experiments

Factors

Coded Level

-1 0 1

X

¹

: Axial Position (H) 3 6.5 11

X

²

: Radial Position (r) -2 0 2

Develop a quadratic model needs at least three level of factors

X

²

: Radial Position (r) -2 0 2

X

³

: Superficial Gas Velocity (U

g

) 0.27 3.18 6.64

- To have less runs than Complete Factorial Plan ( 3 ³ = 27 )

Box-Behnken Design (BBD) (15 runs)

- To have a “Quadratic Model”

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Box

Box--Behnken Behnken Design Design

3 factor Box-Behnken design, 1 block , 15 runs (Solid Hold-up.sta) Standard

Run A B C

1 2 3 4 5 6 7

-1.00000 -1.00000 0.00000 1.00000 -1.00000 0.00000 -1.00000 1.00000 0.00000 1.00000 1.00000 0.00000 -1.00000 0.00000 -1.00000

1.00000 0.00000 -1.00000 -1.00000 0.00000 1.00000

9 7

8 9 10 11 12 13 14 15

-1.00000 0.00000 1.00000 1.00000 0.00000 1.00000 0.00000 -1.00000 -1.00000 0.00000 1.00000 -1.00000 0.00000 -1.00000 1.00000 0.00000 1.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

Experimenal

Experimenal Results Results

Run No.

Factors Response

Variable

X

₁

X

₂

X

₃

Coded Actual Coded Actual Coded Actual Y

1 -1 3 -1 -2 0 3.18 0.177

2 1 10 -1 -2 0 6.64 0.032

3 -1 3 1 2 0 3.18 0.176

4 1 10 1 2 0 3.18 0.035

5 -1 3 0 0 -1 0.27 0.188

6 1 10 0 0 -1 0.27 0.038

7 -1 3 0 0 1 6.64 0.177

8 1 10 0 0 1 6.64 0.035

9 0 6.5 -1 -2 -1 0.27 0.192

10 0 6.5 1 2 -1 0.27 0.182

11 0 6.5 -1 -2 1 6.64 0.154

12 0 6.5 1 2 1 6.64 0.181

13 0 6.5 0 0 0 3.18 0.183

14 0 6.5 0 0 0 3.18 0.18

15 0 6.5 0 0 0 3.18 0.182

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Statistical Analysis Statistical Analysis

Effect Estimates; Var.:Solid Hold-up; R-sqr=.99653; Adj:.99029 (Solid Hold-up.sta) 3 3-level factors, 1 Blocks, 15 Runs; MS Residual=.000043

DV: Solid Hold-up Factor

Effect Std.Err. t(5) p -95.%

Cnf.Limt +95.%

Cnf.Limt

Coeff. Std.Err.

Coeff.

Mean/Interc.

(1)Height of the bed(L) Height of the bed(Q) (2)Radial Position(L) Radial Position(Q) (3)Superficial Gas Velocity(L) Superficial Gas Velocity(Q)

0.132046 0.003179 41.5394 0.000000 0.123875 0.140218 0.132046 0.003179 -0.141572 0.004882 -28.9979 0.000001 -0.154122 -0.129022 -0.070786 0.002441 0.070770 0.003482 20.3249 0.000005 0.061819 0.079720 0.035385 0.001741 0.002798 0.004882 0.5731 0.591403 -0.009752 0.015348 0.001399 0.002441 0.003020 0.003482 0.8672 0.425479 -0.005931 0.011970 0.001510 0.001741 -0.010328 0.008172 -1.2638 0.262007 -0.031336 0.010679 -0.005164 0.004086 -0.001474 0.006906 -0.2135 0.839381 -0.019227 0.016279 -0.000737 0.003453

üEffect Estimates

11

Superficial Gas Velocity(Q) 1L by 2L

1L by 3L 2L by 3L

-0.001474 0.006906 -0.2135 0.839381 -0.019227 0.016279 -0.000737 0.003453 -0.003273 0.007341 -0.4458 0.674376 -0.022143 0.015598 -0.001636 0.003670 0.006762 0.006364 1.0625 0.336593 -0.009597 0.023121 0.003381 0.003182 0.015848 0.006364 2.4903 0.055143 -0.000511 0.032207 0.007924 0.003182

üAnalysis of Variance (ANOVA)

ANOVA; Var.:Solid Hold-up; R-sqr=.99653; Adj:.99029 (Solid Hold-up.sta) 3 3-level factors, 1 Blocks, 15 Runs; MS Residual=.000043

DV: Solid Hold-up

Factor SS df MS F p

(1)Height of the bed L+Q (2)Radial Position L+Q (3)Superficial Gas Velocity L+Q 1*2

1*3 2*3 Error Total SS

0.050988 2 0.025494 592.9787 0.000001 0.000044 2 0.000022 0.5116 0.627850 0.000289 2 0.000144 3.3578 0.118990 0.000009 1 0.000009 0.1987 0.674376 0.000049 1 0.000049 1.1290 0.336593 0.000267 1 0.000267 6.2015 0.055143 0.000215 5 0.000043

0.062004 14

Pareto Chart of Standardized Effects; Variable: Solid Hold-up 3 3-level factors, 1 Blocks, 15 Runs; MS Residual=.000043

DV: Solid Hold-up

1.06254 -1.26384

2.490272

20.3249

-28.9979

1Lby3L (3)Superficial Gas Velocity(L) 2Lby3L Height of the bed(Q) (1)Height of the bed(L)

.8672129 1.06254 -1.26384

2.490272

üPareto Plot

-.213485 -.44581 .5730751

.8672129

p=.05

Standardized Effect Estimate (Absolute Value) Superficial Gas Velocity(Q)

1Lby2L (2)Radial Position(L)

Radial Position(Q)

-.44581 .5730751

.8672129

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Probability Plot; Var.:Solid Hold-up; R-sqr=.99653; Adj:.99029 3 3-level factors, 1 Blocks, 15 Runs; MS Residual=.000043

DV: Solid Hold-up

2Lby3L

Height of the bed(Q)

(1)Height of the bed(L) 1.5

2.0 2.5 3.0

Expected Half-Normal Values (Half-Normal Plot)

.75 .85 .95 .99

2Lby3L

Height of the bed(Q)

(1)Height of the bed(L)

üProbability Plot

13

Superficial Gas Velocity(Q) 1Lby2L (2)Radial Position(L)

Radial Position(Q) 1Lby3L (3)Superficial Gas Velocity(L)

2Lby3L

-5 0 5 10 15 20 25 30 35

- Interactions - Main effects and other effects Standardized Effects (t-values) (Absolute Values) 0.0

0.5 1.0

Expected Half-Normal Values (Half-Normal Plot)

.05 .25 .45 .65 .75

Superficial Gas Velocity(Q) 1Lby2L (2)Radial Position(L)

Radial Position(Q) 1Lby3L (3)Superficial Gas Velocity(L)

2Lby3L

Significant Effects are X X

₁₁

and X X

₁₁

X X

₁₁

Solid Hold

Solid Hold--up Distribution up Distribution

Quadratic Model with consideraing 2-way interactions (Linear-Linear)

&

Non significant effects are ignored To achieve this general quadratic model:

Model:

Regr. Coefficients; Var.:Solid Hold-up; R-sqr=.98471; Adj:.98217 (Solid Hold-up.sta) 3 3-level factors, 1 Blocks, 15 Runs; MS Residual=.000079

DV: Solid Hold-up Factor

Regressn Coeff.

Std.Err. t(12) p -95.%

Cnf.Limt

+95.%

Cnf.Limt Mean/Interc.

(1)Height of the bed(L) Height of the bed(Q)

0.065364 0.014805 4.4151 0.000843 0.033108 0.097621 0.055652 0.004963 11.2128 0.000000 0.044838 0.066466 -0.005869 0.000375 -15.6298 0.000000 -0.006687 -0.005051

ü The obtained “prediction Model Coefficients”

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Normal Prob. Plot; Raw Residuals 3 3-level factors, 1 Blocks, 15 Runs; MS Residual=.000079

DV: Solid Hold-up

-0.03 -0.02 -0.01 0.00 0.01 0.02

Residual -3.0

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Expected Normal Value

.01 .05 .15 .35 .55 .75 .95 .99

Response Desirability Profiling Response Desirability Profiling

Optimization Optimization

15

Observed vs. Predicted Values 3 3-level factors, 1 Blocks, 15 Runs; MS Residual=.000043

DV: Solid Hold-up

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22

Observed Values 0.00

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22

Predicted Values

Profiles for Predicted Values and Desirability

Height of the bed

-.0200 .19729 .24000

Radial Position Superficial Gas Velocity Desirability

0.

.5

1.

.03200.11200.19200 Solid Hold-up 0.

.5

1.

0.

.5

1.

1.0000

Desirability

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Troubleshooting Troubleshooting

17 h=4.75 cm

Conclusion Conclusion

ü The existance of dead zones in fluidized bed decrease its efficiency ü The dead zone occurs where the solid hold-up is maximum

üMethodology: Proposing a model for solid hold-up in the bed and maximizing it üThe experiments were designed by Box-Behnken Design (BBD)

üObjective: finding a position of maximum solid hold-up

üThe experiments were designed by Box-Behnken Design (BBD) ü The prediction model:

ü By using “response desirability profiling”, the maximum

solid hold-up is obtained in h=4.75 cm

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Optimization of Solid HoldOptimization of Solid Hold--up in up in NanoparticlesNanoparticlesFluidized Bed Fluidized Bed Using Radioactive DensitometryUsing Radioactive Densitometry