multiobjective optimization of a spouted bed reactor

Proceedings of International Conference on Engineering and Information Technology

Sep. 17-19, 2012, Toronto, Canada

*Corresponding Author

MULTI-OBJECTIVE OPTIMIZATION OF A SPOUTED BED REACTOR

Ghanim M. Alwan1,*

, Stoyan Nedeltchev2, Shreekanta Aradhya

3 and Muthanna Al-Dahhan

2, 3

(1) Chemical Engineering Department, University of Technology, Baghdad, Iraq.

(2) Department of Chemical and Biological Engineering, Missouri University of Science and Technology,

Rolla, MO, USA.

(3) Nuclear Engineering Department, Missouri University of Science and Technology, Rolla, MO., USA.

Abstract

Gas-solid spouted beds are either cylindrical bed with cone base or the whole bed is in a cone shape where the gas

enters as a jet. The gas forms a spout region that carries the solids upward in a diluted phase, which forms a fountain at

the top of the bed where the solids fall down and move downward in the annular region. The performance of the gas-solid

spouted bed benefit from solids uniformity structure (UI) with lower pressure drop (PD) across the bed reactor.

Optimization search is a powerful tool could select best set of operating conditions, which could enhance performance of

the bed .This would guide the experimental work by reducing the risk of experimental runs and cost would be consumed

for design and operation.

Therefore, the focus of this work is to maximize UI of the solid particles and to minimize the PD along the bed.

Hence, UI and PD are to be considered as the objectives. Four selected decision variables affecting the objectives that

are gas velocity, pressure, particle's density and particle's diameter.

Steady-state solids concentration measurements were carried out in a narrow (0.076 m ID) cylindrical spouted bed

made of Plexiglas that used 60° spouted conical shape. Radial concentrations of particles (glass and steel beads) at

various bed heights under different flow patterns were measured by sophistical optical probe. The spouted bed has found

highly interactive nonlinear hybrid process. Genetic Algorithm (GA) has been found suitable stochastic search for the bed.

Reliability of optimization process can be enhanced by adaptation GA's operators. Maximum UI was obtained with high-

density steel beads, while minimum PD was observed with low- density glass beads. The optimum values of UI are; 0.447

to 0.755 while, values of PD is ranged between 0.895 to 1.672 at experimental operating conditions. Reasonable

agreements have been found when compared the optimization results with the experimental data by using sophisticated

optical probe and high accuracy pressure transducers.

Keywords: Genetic algorithm; Optimization; Pressure drop; Spouted bed; Uniformity index.

Nomenclature

C Cavg

Cmin

Cmax

Relative concentration of solid particles Average solid concentration Minimum solid concentration Maximum solid concentration

dp Diameter of solid particle, [mm] P Pressure into spouted bed, [Kpa] PD Pressure drop across the bed, [Kpa] UI Uniformity index of solid particles Vg Superficial velocity of gas, m/s Greek Symbols ρs Density of solid particles, Kg/m

3

€ Porosity of bed, [-] Ø Sphersity of the solid particle

1. Introduction

A spouted bed is a special case of fluidization. It is

an effective means of contacting gas with coarse solid

particles. There is increasing a application of spouted as

reactors such as; coating, desulfurization, CO2 capture,

combustion and gasification of coal and biomass [1].The

spouted bed is a kind of high performance reactor for

fluid-solid particles reaction, also it is a hybrid fluid-solid

contacting system [2].

Conversion and coating of particle nuclear fuel is

performed in spouted bed reactor, in order to achieve

uniform particle coating and prevent agglomeration of the

particle bed. Spouted bed reactors are specialized

fluidized bed reactors with unique fluidization

characteristics and particle handling advantages [3].

Uniformity index of solid particles enhances the

conversion of reactants and coating of particles and

reducing of the pressure drop across the bed is dropped

the risk of dissipated pumping energy.

Most studies, concerning solid behavior and

hydrodynamic correlations of bed reactors, have been

done at ambient temperature. The lack of studies at

higher temperatures is due difficulties associated with

measuring techniques under these conditions. In

extrapolating hydrodynamic parameters derived at

ambient temperature to higher temperatures, only the

physical property changes of gas and solid phases, such

as density and viscosity are taken into consideration [4].

2. Content

2.1. Scope of the Work

The mimicking with the spouted bed nuclear

particles coating reactor: Chemical Vapor Deposition

(CVD) for producing the tri-structural isotropic (TRISO)

particle coating was studied. The steel and glass beads

are used as the solid particles and the air as the spouted

gas at ambient temperature. The performance of the

spouted bed reactor benefit from solids uniformity

structure with lower pressure drop. Therefore, the

objective is to select best operating conditions could

maximize UI of solid particles and minimize PD across

the bed.Multi-objective stochastic GA is implemented to

solve the conflicted optimization problem of the system.

2.2. Experimental set-up

The experimental set-up was designed and constructed in the best way to collect the data as explained in Figure1.The cylindrical spouted bed is made of Plexiglas was employed in this study which was the major part of the experimental set-up. The bed is (3 inches in diameter and 36 inches in height).At the bottom of the bed, there is a 60° cone-shaped distributor (3 inches in height), on which 20 holes (0.5 inch in diameter) are perforated horizontally. .At the bottom of the bed, there is a 60° cone-shaped base (3 inches in height).The spouting orifice is made of Pyrex with 0.25 inch in diameter locates in the center of the conical base.

The spouted gas is air supplied from the air

compressor.The airflow rate is measured by the

rotameter (Figure 1). The solid particles used are steel

and glass beads with different average diameters and

properties (Table 1).

Holes are drilled at vertical intervals of (1.86 inch)

along the column wall in which the optical probe is placed

at different radial positions: 1.5, 1.25, 1.0, 0.75, 0.5, and

0.25 inch. The spouted bed divided into three positions:

position 1 with head of 7.5 inch while positions 2 and 3

have head of 5.5 and 3.5 inches above the conical base.

The newly optical probe (manufactured by the

Institute of Chemical Metallurgy, Chinese, and Academy

of Sciences) is used to measure both solids'

concentration and solids' velocity and their fluctuation.

The optical probe is adapted to the Particle Analyzer

(PV6) which manufactured by the ‘Institute of Chemical

Metallurgy, Chinese, Academy of Science’) .It consists

of; photoelectric converter and amplifying circuits, signal

pre-processing circuits, high-speed A/D interface card

and its software PV6, is adapted to the optical probes

The pressure drop across the bed is measured by the

pressure transducer (Type: PX309-002G5V) with the

range of (0-2.0 psig) manufactured by omega company.

The pressure into the spouted bed is adjusting within the

desired values by using the inverted circular stabilizer; 60

mm in diameter is installed at the top of the bed column.

This prevents the spout fountain from swaying. Samples

of on-line optical probe signals in the spouted bed are

shown in Figure 6.

2.3. Optimization Technique

The multi-objective genetic algorithm (GA) is

implemented to obtain the optimum operating conditions

of the process.GA is a global search algorithm based on

mechanics of natural selection and natural genetics.GA

is based on Darwin's theory of ‘survival of the fittest’.

There are several genetic operators. Such as; selection,

crossover and mutation…etc..Each chromosome

represents a possible solution to the problem being

optimized, and each bit (or group of bits) represents a

value of variable of the problem (gene).A population of

chromosomes represents a set of possible solution.

These solutions are classified by an evaluation function,

giving better values, or fitness, to better solution [5].

2.4. Result and Discussion

2.4.1 Uniformity index

In the present work, the uniformity index equation

was developed depended on the Nedeltchev and Zhang

correlations 6 and 7.For steady state conditions, the

equation can be written as in Equation 1.

Figure 2a illustrates the effect of the air velocities

on the uniformity index (UI) with the steel and glass

beads. The UI decreased with increasing the air velocity

(Vg) because of increasing the desperation of the solid

particles due the kinetic energy of the solid particles is

increased. In addition, two regions are appeared in these

curves, which represent the transition region from the

packed bed flow regime at Vg of 0.74 m/s to the stable

spouting flow regime at Vg of 0.95 and 1.0 m/s. The axial

mixing is more vigorous than the radial mixing with the

increase of spouting air velocity [7 & 8].

The static bed height has important effect on the

uniformity of the final mixtures with increasing the static

bed height; the degree of mixing axially decreased then

increased, but in the lateral direction decreased [9]. Also

with the increasing in the spouting gas velocity the

coating thickness linearly decreased [10]. UI of the steel

beads is higher than that of glass beads (Figure 2a) due

to high scattering occurred with the particles of low

density. Low concentrations of solid particles were

obtained for all positions with the glass beads system

that affected directly on the values of UI.Figure 2b

explains the effect of the spouted bed pressure on UI.As

the pressure increased the stochastic motion and the

scattering of particles will be increased, then the

uniformity of solid particles decreased. The density of the

solid particles has the positive effect on UI of the spouted

bed (Figure 3a).Since the increasing of the particles'

density tends to get the bed more strength and

resistance to the motion and dispersion against the

vortex of the fountain. Therefore, it gives the solid

particles more stability and uniformity.

The denser material is continued to spout in the

central region while the less dense particle formed

atorriodal vortex around the central spout. The solid

beads diameter has negative effect on the UI of the solid

particles as shown in Figure 3b.As the diameter of the

particles decreased, the free area (mean free path) into

the bed increased. Then the particles of small size are

helpful to raise the mixing speed [9].This provides the

smaller particles more uniformity in the radial distribution.

However, UI is a good indication for improve the mass,

heat and the conversion of reactants into the spouted

bed reactor.

2.4.2. Pressure drop

Figures 4 and 5 explain the effect of the process

variables (air velocity, bed pressure, density and

diameter of solid particles) on the pressure drop across

the reactor bed. PD will be increased with increasing the

velocity of air for both steel & glass beads due to

increasing the kinetic energy and the interaction of the

solid particles [11].

In the case of steel beads PD is higher than with

glass beads because of high strength and friction with

steel beads (Figure 4a).The effect of the spouted bed

pressure on PD across the bed is very low. Then the

pressure drop increased slightly with increasing the inlet

pressure of the air to the spouted bed (Figure 4b).The

dense particles (steel) create more resistance and friction

against the air flow and then tend to raise the pressure

drop across the bed (Figure 5a).The porosity of the bed

increased with the large particles diameter, so that the

strength of the solids to the air flow then reduced. These

tend to reduce PD across the spouted bed (Figure

5b).These conclusions also confirmed by [12]. Figure 6

explains sample of optical signal for non-uniformity

region at high-pressure drop.

2.4.3. Optimization Problem

In the present work, the objectives (UI and PD)

were empirically formulated with the decision variables.

The selected decision variables are air velocity, bed

pressure, density and diameter of particles. The objective

of optimization search is to maximize UI and minimize

PD. Two advanced nonlinear regression optimization

algorithms were used as: Newton-Quasi and Hook-Jeevs

pattern moves to formulate the developed nonlinear

objective functions with the aid of the computer program

(Statistica version10). The empirical correlations are

shown in Equations 2, 3 and 4.From Equations 2 and 3;

one can conclude that the spouted bed is highly

nonlinear interacted process. Equation 2 confirms that

the air velocity, reactor pressure and particle diameter

have the negative effect on UI, while the density of solids

has the positive effect as described in the previous

section. From Equation 3, one can observe that the air

velocity, reactor pressure and density of the solid

particles have positive effect on PD across the bed, while

the diameter of particles has negative effect. The density

of solid particles also is the more effective variable. In

extrapolating hydrodynamic parameters derived at

ambient temperature to higher temperatures, only the

physical property changes of gas and solid phases, such

as density and viscosity are taken into consideration.

2.4.4. Multi-objective optimization

In this technique, the two conflicted objective

functions (equations 2 and 3) are process together to

obtain the global optimization results. The operators of

GA were adapted as shown in Table 2 to attain the best

solution. Since the objective functions are conflicted, so

that 26 chromosomes were created as shown in Figure

7.Each chromosome represents the possible solution to

the optimization problem, and each bit represents the

value of the variables of the problem. The optimization

results have 26 sets of new operating conditions.

Optimum results can reduce the risk of experimental runs

and the cost consumed for design and operation. In

addition, it will modify the performance of the spouted

bed reactor. Figure 8 illustrates the solution/operators of

the GA. The compromise values of UI

0.755) while, for PD within (0.895-1.672

Table 3.

The optimum results obtained by multi-objective search

are stay the limits of the operating conditions of the

process (equation 4).The optimal values confirmed by

the experimental results using sophisticated

and high-accuracy pressure transducers .However, the

optimization technique can guide the experimental work

for selecting the best operating conditions(high UI with

low PD) that could improve the performance of spouted

bed (Figure 9).

Maximum UI could be obtained by the steel beads and minimum PD was observed by the glass beads. of optimization search depends on; best formulationobjectives with decision variables and selection of the proper optimization algorithm [13].

2.6. Illustrates

Figure. 1. Experimental Set-up.

values of UI are (0.447 to

1.672) as shown in

objective search

are stay the limits of the operating conditions of the

The optimal values confirmed by

sticated optical probe

accuracy pressure transducers .However, the

experimental work

operating conditions(high UI with

low PD) that could improve the performance of spouted

by the steel beads and by the glass beads. Success

best formulation of objectives with decision variables and selection of the

2.5. Equations, Formulas, Symbols, Units

Ui = (Cavg-CMin)/(CMax-Cmin)

Maximize UI=0.184Vg-0.214

Minimize PD=0.037Vg0.381

P

� 0.74 � � � 1.0101.0 � � � 312.02400.0 � �� 74001.09 � �� 2.18 �

PV

Optical

Equations, Formulas, Symbols, Units

(1) 0.214

P-0.301

ρs0.316

dp-0.267

(2)

P0.05ρs

0.407dp

-0.221 (3)

� (4)

PV6 system

Probe Optical

(a) (b)

Figure 2 .Uniformity index with;(a)gas velocity,(b) bed pressure.

(a) (b)

Figure 3.Uniformity index with;(a)solid density,(b) solid diameter.

0.7 0.75 0.8 0.85 0.9 0.95 10.4

0.42

0.44

0.46

0.48

0.5

0.52

0.54

0.56

Gas velocity,(m/s)

un

ifo

mity

in

de

x

steel beads

glass beads

100 150 200 250 300 3500.544

0.546

0.548

0.55

0.552

0.554

0.556

0.558

0.56

0.562

0.564

Pressure (Kpa)

Unif

orm

ity I

ndex

Gas velocity 1.0 m/s

2000 3000 4000 5000 6000 7000 80000.44

0.46

0.48

0.5

0.52

0.54

0.56

Solid density(Kg/m3)

Un

ifo

rmit

y I

nd

ex


1 1.2 1.4 1.6 1.8 2 2.2 2.40.45

0.455

0.46

0.465

0.47

0.475

0.48

0.485

0.49

0.495

0.5

Solid beads diameter(mm)

Un

ifo

rmit

y I

nd

ex


100 150 200 250 300 3500.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Pressure,(kpa) P

res

sure

dro

p,(

kp

a)

(a) (b)

Fig.4.Pressure drop with;(a)gas velocity,(b)bed pressure.

.

(b) (a)

Figure 5. Pressure drop with;(a)solid density,(b)solid diameter.

2000 3000 4000 5000 6000 7000 80000.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Solid density,(Kg/m3)

Pre

ss

ure

dro

p,(

kp

a)

1 1.2 1.4 1.6 1.8 2 2.2 2.40.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Solid beads diameter,(mm)

Pre

ss

ure

dro

p,(

kp

a)

0.7 0.75 0.8 0.85 0.9 0.95 10.5

1

1.5

2

Gas velocity,vg(m/s)

Pre

ssure

dro

p,(

kpa)

Steel beads

Glass beads

Figure 6.Sample of optical signal explains

Figure 7. Pareto results of multi-objective GA

-0.75 -0.7 -0.65 -0.6 -0.550.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Objective 1

Obje

ctive 2

Pareto front

Sample of optical signal explains the non- uniformity of solids at high

GA search.

-0.5 -0.45 -0.4 -1 00

20

40Score Histogram

Score (range)

Pareto front

fun1 [-0.755327

fun2 [0.895935

high-pressure zone.

1 2

Score Histogram

Score (range)

Pareto front

0.755327 -0.44754]

0.895935 1.67226]

Figure 8.Stochastic solution of multi-objective GA .

1 2 3 4 5 60

20

40Rank histogram

RankNu

mb

er

of

ind

ivid

ua

ls200 400 600 800

0

2000

4000

Generation

Av

erg

ae

Dis

tan

ce Average Distance Between Individuals

0 20 40 60 800

10

20Selection Function

Individual

Nu

mb

er

of

ch

ildre

n

0 20 40 60 800

0.1

0.2Distance of individuals

Individuals

Dis

tan

ce

Nu

mb

er

of

ind

ivid

ua

ls

Figure 9. Enhancement of operating of the bed at best optimal operating conditions. 2.7.Tables Table 1. Properties of the particulate materials. Table 3.Results of GA search.

Material Dp

(mm) �s

(Kg/m^3) € Ø

Steel beads

1.09 7400.0 0.42 1.0

Glass beads

1.09 2450.0 0.42 1.0

Glass beads

2.18 2400.0 0.41 1.0

Decision variables Max. Min.

Gas velocity(m/s) 0.89 0.8

Bed pressure(Kpa) 312 101

Density of solid(Kg/m3) 7400 2400

Diameter of particle(mm) 1.09 2.18

Optimum results UI = 0.44 – 0.75 PD = 0.89 – 1.67

Table 2. Adapted operators of GA.

3. Conclusions

Multi-objective GA has been found suitable search of highly interacted nonlinear hybrid spouted bed. Density of solid particles is effective variable on uniformity index of solids and pressure drop across the bed. Maximum UI could be obtained with high-density beads (steel), while minimum PD was observed with low-density glass particles. The optimum values of UI are; 0.447 to 0.755, while corresponding values of PD are ranged between 0.895 to 1.672.Reasonable agreement has been found when compared the selected optimal values with the experimental results. Optimization search could guide the experimental work by reducing the risk of experimental runs and cost of design by selecting best operating conditions. Reliability of GA search can be enhanced by adaptation of algorithm operators.

Acknowledgments

We thank all the participants to Chemical and Biological Department-Missouri University of S & T, Rolla, Missouri (USA). References

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multiobjective optimization of a spouted bed reactor

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