Epstein N., Grace J.R. Spouted and Spout-Fluid Beds: Fundamentals and Applications

Подождите немного. Документ загружается.

Catalytic reactors and their modeling 307

and

(

)

(

−C

)

+ k

(

1 − ε

)

= 0. (19.2)

The modeling predicted the reactor overall conversion with varying k, D, U, d

, and H.

Excluding the last parameter, which surprisingly generated a maximum conversion for

a bed depth lower than H

(caused by simplifying assumptions and a combination of

hydrodynamic features), all other results were in line with expectations. The predicted

conversion was compared with those for ﬁxed and ﬂuidized beds. The drawback of

spouted beds was shown to be gas bypassing through the spout. The use of a spouted

bed as a catalytic reactor appeared to be conﬁned to relatively fast reactions, where the

reaction rate is unaffected by the particle size. It was strongly recommended that studies

be conducted to conﬁrm the theoretical conclusions.

Some modiﬁcations to the ﬁrst theoretical account were introduced

to describe the

performance of spouted beds (SBs) and spout-ﬂuid beds (SFBs). After assuming that

is identical for the two conﬁgurations, the spout voidage was assumed to be linearly

proportional to z. The velocity ﬁeld in the SB annulus was modiﬁed to compensate for

overestimation. As a result, the reactor conversion no longer showed its maximum value

at H < H

for fast reactions. The overall conversion generated by the SFB is usually

greater than for the SB because of greater ﬂow of gas in the annulus.

Experimental results were later presented, together with modeling improvements.

Diffusional mass transfer between spout and annulus was added to the earlier two-

region model. In addition, a novel representation of the annulus was proposed, the

so-called streamtube model (see Figure 19.2): it is represented by a variable number of

concentric annular pathlines of increasing length, radiating outward, each collecting gas

crossﬂowing from the spout into the annulus; the integral of the ascending gas ﬂowrate is

consistent with the Mamuro and Hattori

velocity proﬁle. The experiments were carried

out in a 0.155-m ID vessel, adding ozone to the spouting air and decomposing it on an

alumina-supported iron oxide catalyst, crushed to particle fractions in the 0.82 to 2.00

mm range. The agreement between the calculated and measured annulus and overall

concentrations was good.

This project was continued

by scaling up the unit t o 0.22 m ID and by reﬁning

the scrutiny scale of measurement at the top of the annulus. Sampling from the spout

was accomplished by online ozone measurement. Because of the characteristics of the

catalyst granules, it was possible to operate with spherical particles decreasing from

4.4 to 2.6 mm in diameter by progressive milling during the tests, while maintaining

their original internal porosity and catalytic activity. The reaction rate constant k was

varied from 1.5 to 63 s

−1

by varying the temperature from 290 to 335 K. Within the

ranges of the operating parameters explored, detailed investigation of the larger column

shed light on the concentration proﬁles along the annulus radial coordinate. Figure 19.3

compares the predictions of both the one-dimensional and streamtube models with

the experimental results; the experimental proﬁle, which is intermediate between the

predictions of the two models, suggests that the one-dimensional two-region description

is oversimpliﬁed, whereas the streamtube representation requires some radial dispersion

308 Giorgio Rovero and Norberto Piccinini

tot

exit

tot

+ dC

aiH

Spout

Annulus

i = 2

Figure 19.2. Section through spouted bed showing streamlines, concentrations, and ﬂows used in

streamtube model.

100

020406080

annulus

spout

one-dimensional model

) × 100

experimental

profile

streamtube model

prediction

100

r (mm)

Figure 19.3. Dimensionless exit concentration proﬁles for 0.22 m column,

k = 1.53 s

−1

.Overall

: experimental outlet value = 0.95, experimental integrated average = 0.90, predicted =

0.89.

Catalytic reactors and their modeling 309

between the streamtubes to make its prediction less steep radially. An alternative could

be offered by a modiﬁed Mamuro and Hattori axial velocity proﬁle in the annulus to

account for gas recirculation at the bottom of spouted beds; such a modiﬁcation could

be described by a well-mixed region ahead of the streamlines, changing their respective

lengths and receiving gas of more uniform concentration.

The mass balances for the reactant, written in dimensionless form, together with

all the equations needed to evaluate the required quantities, led to a new complete

theoretical model

for a ﬁrst-order isothermal catalytic SB reactor. This model can apply

to coarse spherical particles. Its outputs were compared to predictions from the earlier

one-dimensional and streamtube models. Owing to a more favorable spout–annulus gas

distribution, the new model predicts slightly higher conversion. However, the average

deviation (11%, instead of 5% for the other models) was approximately double with

respect to the experimental data in the 0.15-m unit.

The ﬁrst nonisothermal model

considered an adiabatic spouted bed catalytic unit for

the dehydrogenation of ethylbenzene, an endothermic ﬁrst-order irreversible reaction.

Separate energy balances were required for the spout and annulus, interacting across

their interface by bulk ﬂows of gas and particles. For these conditions, axial and radial

diffusional resistances within the phases were of negligible importance. Within the

individual phases, no mass and heat transfer resistances were considered between the

catalyst particles and gas. The model was developed by an a priori approach including

all equations that provide the annulus–spout gas distribution, U

, U

, H

, D

, ε

and a

simpliﬁed description of the particle circulation velocities. Dynamic material balances

were written for the spout and the annulus, respectively, as:

∂C

∂t

=−u

∂C

∂z

− k

(

1 − ε

)

ex p(−E/R

(19.3)

and

∂C

∂t

=−u

∂C

∂z

∂u

∂z

− C

) − k

(1 − ε

)ex p(−E/R

. (19.4)

Analogously the energy balances for the spout and annulus were written in the form:

∂T

∂t

=−



(ρC

)

+ (ρC

)



∂T

∂z

+ (ρC

)

∂v

∂z

− T

)

+(−H)k

(1 − ε

)ex p



−E/R



(19.5)

and

∂T

∂t



(ρC

)

− (ρC

)



∂T

∂z

+ (ρC

)

∂u

∂z

− T

)

(

−H

)

(

1 − ε

)

ex p(−E/R

. (19.6)

As a ﬁrst step, steady state was studied, erasing the transient terms and resulting in ordi-

nary differential equations. Two cases, a ﬂat-bottomed and a conical-bottomed vessel,

were described, giving the same functional form to the annulus velocity and a cone-

function of z to the cross-sectional area. The fractional exit conversion was evaluated as

310 Giorgio Rovero and Norberto Piccinini

a function of D, H, θ , d

, and U/U

. The sensitivity analysis of the last variable demon-

strated that, by moderately increasing the gas velocity, additional solids circulation was

obtained with more convective heat transfer to the annulus and an improved reaction

rate, sufﬁcient to compensate for increased gas bypassing in the spout.

A dynamic analysis

with 10 percent changes in temperature and inlet concentration

demonstrated different responses for the spout and annulus, because of their different

thermal capacity and particle/ﬂuid interaction. New steady states were obtained after a

20- to 30-min transition. A moderate ﬂow rate increase at the inlet initially caused an

inverse response, followed by overall similar dynamics. The operability goals deﬁned

the control system design: the output concentration was selected as the control variable,

with the inlet concentration as the main disturbance and the temperature or inlet ﬂow

rate as manipulated variables. Several control schemes were simulated and compared.

In a concise communication,

it was demonstrated that the “one-dimensional model”

and “streamtube model” do not provide different overall conversions when a ﬁrst-order

reaction is considered, provided that the same hydrodynamic representations and the

same mass transfer assumptions are included in both models. Based on general reactor

engineering considerations, it was proved that the one-dimensional model predicts higher

overall conversions for reactions of order less than unity, whereas the streamtube model

generates higher conversions for reaction orders greater than one. It was noted that if the

problem were tackled by a detailed experimental program, radial concentration proﬁles

at different depths in the annulus would be helpful in discriminating between the models.

A fur ther simple model was based on a phenomenological evaluation of the gas

hydrodynamics, with the spout having well-deﬁned plug ﬂow, whereas some mixing

was inferred in the annulus. This description

was deﬁned as “semicompartmental,” as

the annulus was represented by two perfectly mixed regions in series. By assuming an

annulus gas velocity proﬁle as given by the Mamuro and Hattori equation,

evaluated at

the dimensionless bed heights, z/H, of 0.25 and 0.75, the description of the two stages was

straightforward. The predicted overall gas conversion was a function of d

, k, U/U

, and

a spout–annulus mass transfer coefﬁcient. No maximum conversion was predicted with

increasing bed depth, unlike the original model.

The experimental results available at

that time were in s atisfactory ag r eement, although the semicompartmental representation

makes no allowance for radial variations in the reacting species concentration.

19.2 Applied studies

An exothermic reaction, CO oxidation over a Co

/α-Al

catalyst, was used to

demonstrate the validity of a reactor model

for an adiabatic spouted bed. The theoretical

description was based a priori on the deﬁnition of all variables acting in a spouted bed

reactor. Considering a ﬂat-based vessel, the model refers to an inlet region in which the

gas expands before generating the actual spout, the peripheral annulus, a fountain core

as an extension of the spout, and an axisymmetric downﬂowing fountain. The model

predicted that the fountain contributed signiﬁcantly to the reaction. Heat generated on

the catalyst particles was then transferred to the gas by convection, as in a slowly moving

Catalytic reactors and their modeling 311

1.0

0.8

0.6

(K)

473

498

523

Feed wt. %CO

0.6 1.0 1.3

0.4

0.2

0.0

0.0 0.2 0.4 0.6 0.8 1.0

Experimental Conversion

Predicted Conversion

Figure 19.4. Comparison of experimental data with model predictions of overall reactor

conversion.

Operating conditions: D = 0.1 m, H = 0.17 m, D

= 16 mm. Reprinted with

permission of John Wiley & Sons, Inc.

packed bed. These two conditions apply speciﬁcally to fast reactions and combustion.

Separate energy balances were written for the solids and gaseous phases. All regions

required voidage proﬁles and circulation rates, including a detailed description of the

fountain, which had previously been neglected in spouted bed reactor models. The motion

of particles in the annulus strictly followed streamlines, to satisfy both continuity with

the spout loading and energy balances. The recursive numerical solution of the equation

system required a sequence of steps:

(1) Read the input data.

(2) Calculate the hydrodynamic parameters.

(3) Calculate t he annulus ﬂuid ﬂow ﬁeld.

(4) Calculate t he mass ﬂow rate proﬁles and annulus particle velocity ﬁeld.

(5) Calculate t he annulus particle velocity balance.

(6) Calculate t he spout mass and energy balance.

(7) Calculate t he annulus particle energy balance.

(8) Calculate the annulus ﬂuid mass and energy balance.

(9) Calculate t he fountain mass and energy balances.

(10) Verify step 6.

The convergence criterion was a negligible change in temperature in the annulus, as

this region provides a critical contribution to the overall reactant conversion. Model

predictions were compared with the experimental data in a unit with D = 0.11 m, H =

0.17 m, d

= 3 mm, and D

= 16 mm, operating at 200

◦

C to 250

◦

C and about 210 kPa

absolute pressure. It is seen in Figure 19.4 that the experimental results agree well with

model predictions.

The catalytic disproportionation of propylene to ethylene and butylene under quasi-

isothermal conditions was also investigated

in a small spouted bed (D = 0.05 m, H =

0.12 m, D

= 0.002 m), operated with a ﬁne WO

-on-SiO

catalyst (d

= 0.14 mm and

= 740 kg/m

). Radial and axial conversions were measured at 673 K and 201 kPa

312 Giorgio Rovero and Norberto Piccinini

Product

(x,y,z) or (r,θ,z)

Fluid cell

Mass transfer coefficient k

Reactant

Δr

Δz

Δr

Figure 19.5. Axisymmetric representation of a spouted bed in cylindrical coordinates with

ﬂuid-particle ﬂow ﬁeld for a two-dimensional model cell.

for gas ﬂowrates covering an unusually broad range for spouted beds (1.21 < U/U

3.21). The reactant and product concentrations were measured by gas chromatography

on samples from the spout, in the middle of the annulus, and at the wall; positive

radial conversion gradients were conﬁrmed. Because gas velocity in the annulus was

not inﬂuenced by the overall gas ﬂowrate, the experimental results suggest that the

contacting efﬁciency between catalyst and gas could be improved by increasing the

system turbulence. However, the conversion measured at the annulus top was always

much lower than expected from the experimental proﬁles or calculated from the simple

“one-dimensional,” “streamtube,” or “one-dimensional with axial dispersion” models.

In the last case, the experimental and calculated axial proﬁles were compared, with the

Peclet number, Pe

(z), varied from 0.1 to 1.0. Optimizing reactor models for spouted

bed reactors should include axial and radial velocity proﬁles, solids mixing, and spout–

annulus mass transfer, to consider mixing in the conical bottom and plug ﬂow with some

axial dispersion in the cylindrical part.

A computational ﬂuid dynamic model based on equations of particle motion, gas

motion, and mass conservation was developed

to predict the s patial par ticle distribution

and the unconverted reactant distribution. The motion of particles was evaluated by a

force balance that included the effects of gravitational, contact and drag forces. The

model was based on the discrete element method (DEM) (see Chapter 4). Figure 19.5

shows the spouted bed unit, the axisymmetric geometry, and a model cell. A ﬁrst-

order irreversible reaction (catalyzed ozone decomposition) was chosen for the mass

Catalytic reactors and their modeling 313

0.5

t = 0.00 s t = 0.08 s t = 0.16 s t = 0.50 s

Bed height (m)

0.4

0.3

0.2

0.1

Dimensionless radial position

–1 –1 –1 –1 –1 –1 –1 –10

Dimensionless ozone concentration in solid phase (C

A,S

)

Dimensionless ozone concentration in gas phase (C

)

0.0 0.01-0.50 0.51-0.60 0.61-0.70 0.71-0.80 0.81-0.90

0.6 0.7 0.8 0.9 1.0

0.91-1.00

000 000011 1 11111

Figure 19.6. Predicted

particle distribution (left member of each pair) and unconverted ozone

mole fraction (right member of each pair) distributions in gas and particle phases as functions of

time with U = 2.28 m/s.

conservation equations of the unconverted reactant in the gas phase and within the

porous particles. Three types of equations were solved simultaneously to give proﬁles of

particle velocity and void fraction, gas ﬂow ﬁeld, and the conversion of the reactant in the

system. The operating conditions reported in a previous experimental study

were ﬁtted

into the model to predict the ozone concentration and particle motion starting from a

static initial condition. The system was predicted to reach steady state in about 0.5 s (see

Figure 19.6). The predictions are compared with experimental results in Figure 19.7,

demonstrating reasonably good agreement with the calculated proﬁle at z/H = 1, but

the earlier streamtube model

gives a somewhat better overall representation.

19.3 Conical spouted bed reactors

The features of a conical spouted bed (CcSB) reactor operating in a jet mode were studied

by Olazar et al.

The reaction (polymerization of benzyl alcohol) was characterized by

product sticking (because of temperature) and particle size heterogeneity (caused by

growth of a polymer coating on the ﬁne catalyst). An important feature of this kind of

reactor, with respect to conventional spouted and bubbling ﬂuidized beds, is that highly

exothermic reactions can be carried out isothermally, without signiﬁcant segregation in

the solids phase.

Several aspects of CcSBs were investigated: (1) critical geometric

factors, (2) design hydrodynamic correlations, (3) hydrodynamic model of the reactor,

and (4) experimental model validation. An optimal cone angle in the range from 20

◦

to 45

◦

guarantees operability in terms of cyclic solid motion and gas residence time

distribution. The D

ratio inﬂuences the pressure drop and dead zone formation.

314 Giorgio Rovero and Norberto Piccinini

0.9

0.8

0.7

0.6

0 0.2

0.2

0.3

0.4

1.0

Experimental

0.4 0.6 0.8

Dimensionless Radial Position (r/R)

Gas

Solidz/Z

Figure 19.7. Radial proﬁles of unconverted ozone fraction at different heights for t = 4 s in gas

and porous particle phases.

Comparison with the experiments

for d

= 4.4 mm, catalyst

loading: 3.93 kg (40,000 particles); U = 2.44 m/s.

sets an operable reactor voidage. Previously proposed correlations for U

, P

and P

were veriﬁed. The reactor was divided into a number of conical streamtubes,

each described by a one-dimensional unsteady-state mass conservation equation in plug

ﬂow, with longitudinal dispersion coefﬁcient, D

, obtained by ﬁtting all the streamtubes

for the gas phase with helium as tracer, for a range of experimental conditions. The

polymer productivity was obtained by continuously running an automated laboratory

reactor, changing the mean residence time of the catalyst and the par tial pressure of

benzyl alcohol.

In a subsequent paper,

the calculation steps for a CcSB simulation were presented

after extending the governing mass conservation equation for an elemental volume

of a streamtube to the reaction term. The polymerization rate derived from the liter-

ature also contained an expression for catalyst deactivation.

In principle, this sim-

ulation can apply to systems with catalyst circulation or other reactions. The calcu-

lation routine predicts the distribution activity of the catalyst, particle size distribu-

tion, ﬂow rates of the gas phase and of the reactant, dispersion coefﬁcient, radial and

longitudinal proﬁles of gas velocity, reactant concentration proﬁle, catalyst ﬂow rate,

and polymer production. Thanks to the simpliﬁed hydrodynamics, reactor scaleup is

straightforward.

Continuous in situ pyrolysis of sawdust

20,21

was carried out for a CcSB, in which

a small amount (10 g with d

= 0.7 to 1.35 mm) of HZSM-5 zeolite catalyst was

ﬂuidized in a dilute mode. The biomass alone was treated thermally to obtain the yield

and composition of the products. A conical spouted bed seems to offer an optimal

geometric conﬁguration in terms of handling heterogeneous materials, mixing of the

various bed solids components (biomass and catalyst), and a very short gas residence

Catalytic reactors and their modeling 315

Gaseous product

Char extraction

Char quenching

Vent

Flowmeter

Cyclon

Sawdust

Hopper

Reactor

Preheater

Mass flowmeter

Condensers

Centrifuge

filter

Organic

liquid fraction

Aqueous

liquid fraction

ice

Figure 19.8. Schematic of continuous pyrolysis experimental unit.

20, 21

C

2000

American Institute of Chemical Engineers (AIChE). Used with permission.

time. The geometric structure of t he experimental unit (see Figure 19.8) had a total

height of 0.34 m, D = 0.12 m, H

= 0.21 m, D

= 0.02 m, D

= 0.01 m, and a cone

included angle of 28

◦

. The CcSB was operated at 400

◦

C, 450

◦

C, and 500

◦

C with 10

to 14 L/min of nitrogen for as long as 5 h with pneumatic char extraction from the

top. The bed was spouted at U/U

= 1.2 with a gas residence time of 50 ms in the

bed and 20 ms in the spout. Typical results are shown in Figure 19.9: gaseous products

reached higher yields at higher temperature owing to the catalytic effect. In addition,

the catalyst modiﬁed the liquid phase, with the organic fraction converted to aqueous

soluble products because of reduction reactions, leading to a more stable and less

corrosive fuel.

In a related study, catalytic pyrolysis of biomass was carried out batchwise in a

conical spouted bed

and compared with ther mal pyrolysis: the kinetic scheme, kinetic

constants, and yields of products in the gaseous, light liquid, and heavy liquid fractions

were obtained. The goal of the process was to maximize the gas yield at the expense

of the liquid products, which had limitations as bio-oils. The unit was the same as

described in the previous work.

It operated at 673 K; 2 g of pine sawdust were dropped

into 26 g of a sand/catalyst mixture, varying the active solids mass fraction from 0 to

100 percent. The sawdust was in a size range of 0.8 to 2 mm, and the catalyst was

zeolite/bentonite/alumina in a 25/30/45 percent blend. The gas yields increased with

a larger fraction of catalyst, with the ultimate effect of transforming heavy liquids into

316 Giorgio Rovero and Norberto Piccinini

without catalyst

with catalyst

gas

liquid

char

yield (wt %)

375 400 425 450 475 500 525

T (°C)

Figure 19.9. Effect of catalyst on distribution of products in pyrolysis of sawdust at different

temperatures.

20, 21

C

2000 American Institute of Chemical Engineers (AIChE). Used

with permission.

gases, water, and less oxygenated liquid matter, which may undergo downstream steam

reforming to generate syngas.

To obtain value from plastics residues, pyrolysis is one of the most practiced processes

in ﬂuidization studies, as well as being promising for implementation on a large scale.

The use of acid catalysts offers advantages in shifting the process toward increased

selectivity of products at lower temperatures. In this situation, conical spouted bed reac-

tors are favorable because they operate in a diluted and well-mixed mode, efﬁciently

preventing sticking and lump formation. An account

appeared in which a previously

described

20,21

reactor was applied to HDPE pyrolysis (3 g of chips per batch) in 100 g

of HZSM-5 zeolite catalyst. The operating temperature was set at 450

◦

C and 500

◦

with N

as the spouting gas at a velocity 20 percent in excess of the minimum spouting

value. Polymer decomposition was completed in 150 s and 120 s, with peak rates at

80 s and 50 s. About 55 percent of light oleﬁns, 15 percent of light alkanes, 29

percent of gasoline fraction, and minimal heavy compounds and char residue were

generated.

The catalytic partial oxidation of methane to syngas was investigated

inaCcSB

with D = 0.05 m operated at 900

◦

C to 1000

◦

CusingaNi/La/Al

catalyst (d

150–200 μm and 600 μm). Experimental limitations, as well as process considerations,

suggested particles signiﬁcantly ﬁner than those typically employed in spouted beds.

Because of the lack of data, spouting was veriﬁed for hydrodynamic conditions simulat-

ing the actual process. The motion in the reactor appeared to be particularly favorable to

preserve the catalytic activity over time, thanks to oxidation and reduction cycles while

spouting with reaction. The hydrodynamics of the CcSB permitted a catalyst formulation

(Ni concentration) more effective than that required by dense systems, leading to high

conversions and high selectivity to syngas.