SB Fountain Dry Sand

7/23/2019 SB Fountain Dry Sand

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chemical engineering research and design 8 9 ( 2 0 1 1 ) 20542062

Contents lists available atScienceDirect

Chemical Engineering Research and Design

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c h e r d

Modelling batch drying of sand in a draft-tube conical

spouted bed

Martin Olazar, Gartzen Lopez, Haritz Altzibar, Javier Bilbao

Univ. of the Basque Country, Dept. Chemical Engineering, P.O. Box 644-E48080, Bilbao, Spain

a b s t r a c t

A model has been built to predict the evolution of sand drying in a conical spouted bed with a non-porous draft

tube. Three regions have been considered in the model, i.e., spout, annulus and fountain, and unsteady-state mass

balances have been written for water in the solid and gaseous phases. The model has been validated by comparing

its results with the experimental ones obtained in a previous study and it allows predicting the moisture content

evolution of both the air and the sand during the drying process.

2011 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Keywords: Spouted bed; Drying; Draft tube; Simulation

1. Introduction

Although rotary dryers dominate the market, fluidised orspouted bed dryers could be an alternative, since they are

characterised by an efficient external heat and mass transfer

leading to short residence times andcompactdesign (Vanecek

et al., 1965). Moreover, reported mean residence times (Kamke

and Wilson, 1985)range from 10 to 20 min when drying saw-

dust in a rotary dryer to 10 times lower in fluid bed dryers

(Jensen, 1995). Spouted beds/dilute spouted beds are able

to lower these times and with the advantage of processing

unscreened materials (Berghel, 2005; Olazar et al., 1994a).

The applicability of the spouted bed technique lies in its

ability to treat coarse particles (Mathur and Epstein, 1974)

and granular products of irregular texture, fine particles and

those with a wide size distribution and sticky solids, whichare difficult to treat using other gassolid contact regimes

(Olazar et al., 1992).Thus, the spouted bed regime is an alter-

native contact method that is especially interesting when

conventional regimes have limitations imposed by the phys-

ical characteristics of the solid and by gas residence time

(Olazar et al., 1992). Conical spouted beds allow attaining

low gas residence times and this parameter can be varied

from few seconds operating in conventional spouting condi-

tions to values of milliseconds in dilute conditions (Olazar

et al., 1993).The good performance of conical spouted beds

Corresponding author. Tel.: +34 94 601 2527; fax: +34 94 601 3500.E-mail addresses: [email protected] (M. Olazar), [email protected] (G. Lopez), [email protected] (H. Altzibar),

[email protected](J. Bilbao).Received2 November 2010; Receivedin revisedform 22 December 2010; Accepted13 January2011

has been proven in the combustion of bituminous coals

(Tsuji et al., 1989), catalytic polymerizations (Olazar et al.,

1994b), pyrolysis of waste materials (Arabiourrutia et al.,2008; Elordi et al., 2009) and drying (Oliveira and Passos,

1997).

A crucial parameter that limits the scaling-up of spouted

beds is theratiobetweenthe inlet diameter andparticle diam-

eter. In fact, the inlet diameter should be up to 2030 times

the average particle diameter in order to achieve spouting

status. The use of a draft tube is the usual solution to this

problem (Swasdisevi et al., 2005).In fact, an internal device is

the key for stable operation in a large-scale spouted bed and,

moreover, it allows increasing the spoutable bed height and

reducing bed pressure drop (Luo et al., 2004; Swasdisevi et al.,

2004; Swasdisevi et al., 2005).Nevertheless, solid circulation,

particle cycle time, gas distribution and so on are governedby the space between the bottom of the bed and the draft

tube (Altzibar et al., 2009; Cunha et al., 2009; Ishikura et al.,

2003; Kalwar andRaghavan,1992;Neto et al., 2008; Wang et al.,

2010a,b;Zhaoetal.,2008). Moreover, minimumspoutingveloc-

ity and operating pressure drop are also functions of the type

of draft tube used. The use of different types of draft tubes

improves the versatility of the conical spouted bed in terms of

gas flowrate, gas residence time, solid circulation, materials

to be handled and so forth. Moreover, the draft tube is easy to

build and install.

0263-8762/$ see front matter 2011 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.doi:10.1016/j.cherd.2011.01.012
http://www.sciencedirect.com/science/journal/02638762mailto:[email protected]:[email protected]:[email protected]:[email protected]://localhost/var/www/apps/conversion/tmp/scratch_3/dx.doi.org/10.1016/j.cherd.2011.01.012http://localhost/var/www/apps/conversion/tmp/scratch_3/dx.doi.org/10.1016/j.cherd.2011.01.012mailto:[email protected]:[email protected]:[email protected]:[email protected]://www.sciencedirect.com/science/journal/02638762


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chemical engineering research and design 8 9 ( 2 0 1 1 ) 20542062 2055

Nomenclature

aan wet surface area of the sand in an elementnin

the annulus, m2 kg1

af wet surface area of the sand in the fountain,

m2 kg1

asn wet surface area of the sand in an elementninthe spout, m2 kg1

dp particle diameter, mm

dp average particle diameter, mm

Cd drag coefficient

Dv diffusivity of steam into air, m2 s1

f fraction of the inlet gas flow rate that crosses

the annulus.

g acceleration of gravity m s2

G inlet air mass flow rate, kg s1

Ka overall masstransfer coefficient in the annulus,

m s1

Kf overall mass transfer coefficient in the foun-

tain, m s1Ks overall mass transfer coefficient in the spout,

m s1

Ms mass of sand, kg

Re Reynolds number

Sc Schmidt number

Sh Sherwood number

t time, s

u velocity of the gas, m s1

v velocity of the particles, m s1

Van volume of an elementnin the annulus, m3

Vf volume of the fountain, m3

Vsn volume of an elementnin the spout, m3

W sand mass flowrate, kg s1xi mass fraction of particles of sizedpiXan moisture content of sand in an element n in the

annulus, kg water kg1 sand

Xc critical moisture content, kg water kg1 sand

Xf moisture content of sand in the fountain,

kgwaterkg1 sand

Xsn moisture content of sand in an element n in the

spout, kgwater kg1 sand

Yan moisture content of air in an elementn in the

annulus, kg water kg1 air

Yf moisture content of air in the fountain,

kgwaterkg1 air

Ysn moisture content of air in an elementn in thespout, kgwater kg1 air

Ysat moisture content corresponding to the adia-

batic saturation at the operating temperature,

kgwaterkg1 air

z vertical position of the particle, m

Greek letters

a bed voidage in the annulus

f bed voidage in the fountain

s bed voidage in the spout

g density of the air, kg m3

s density of the sand, kg m3

A way of improving our understanding of the hydrody-

namic behaviour of spouted beds involves Computational

Fluid Dynamics (CFD). This technique has been applied to

conventional (Wu and Mujumdar, 2008),conical (Wang et al.,

2010c; Duarte et al., 2009)and two-dimensional spouted beds

(Hosseini et al., 2010).Recently CFD studies have been applied

to spouted beds provided with draft tubes (Hosseini et al.,

2009, Szafran and Kmiec,2004;Szafran et al., 2005; Wanget al.,2010a,b). These models provide accuratepredictions,but com-

plexity is their main disadvantage.

The advantage of the spouted bed technique for drying lies

in its the capacity for handling granular products that are too

coarse to be readily fluidized and where good heat and mass-

transferand favourablegas solidcontacting are important (Cui

and Grace, 2008; Olazar et al., 1993).Moreover spouted beds

are suitable for operating with heat sensitive materials due to

their good heat transfer and isothermicity (Freitas and Freire,

2001).The spouted bed has been successfully applied to the

drying of different solid materials such as sawdust (Berghel

et al., 2008),grain (Markowski et al., 2007),seeds (Ando et al.,

2002)and inert materials (Altzibar et al., 2008).The spoutedbed with inert particles has been commonly used for the dry-

ing of pastes, suspensions and solutions (Correa et al., 2004;

Jumah et al., 2007; Marmo, 2007; Passos et al., 2004; Taruna and

Jindal, 2002).

This paper models the batch drying of construction sand

whose average particle size is 0.415 mm. The specification is

that the sand should be dried to approximately 0.0005 kg of

water per kg of dried solid for subsequent use. This solid is

usually dried in rotary driers where mass transfer and effi-

ciency are low (Couper et al., 2010).The conical spouted bed is

an interesting alternative since it is characterised by efficient

heat and mass transfer resulting in higher drying rates and a

compact and simple design. However, in other drying devices,such as rotatory dryers,the gassolid contact is poorerand hot

air must be used to increase drying rates, which means higher

operatingcosts.In thisstudy, theperformance of a non-porous

draft tube conical spouted bed has been addressed in order to

verify its performance for the drying of fine solids. A theoret-

ical model has been developed and its predictions have been

compared with experimental results to check its suitability.

2. Experimental

2.1. Equipment

Based on the knowledge acquiredin previousstudies about the

hydrodynamics of conical spouted beds (Altzibar et al., 2009;

Olazar et al., 1992)and the application of this technology to

other processes, such as polymerization (Olazar et al., 1994b)

or pyrolysis (Arabiourrutia et al., 2008),a new pilot plant dryer

has been designed and built,Fig. 1.This pilot plant is made

of 304-L stainless steel, and consists of a blower, a solid feed-

ing system, the contactor and a fabric filter for fine particle

retention.

The blower supplies a maximum air flowrate of

300Nm3 h1 at a pressure of 1500mm of water column.

The flowrate is measured by two computer-controlled mass

flow-meters in the ranges 50300 m3 h1 and 0100m3 h1.

The blower supplies a constant flowrate, and the first mass

flow-meter controls the air flowing into the contactor (in

the range 50300m3 h1) by operating on a motor valve that

reroutes the remaining air to the outside. When the flow


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2056 chemical engineering research and design 8 9 ( 2 0 1 1 ) 20542062

Fig. 1 Diagramme of the dryer unit fitted with the spouted

bed contactor.

required is lower than 50m3 h1, it passes through the first

mass flow-meter, being regulated by the second one placed in

series, which also operates another motor valve that adjusts

thedesired flowrate. The accuracy of this control is 0.5% of the

measured flowrate. The solid feeder is made up of a hopper

and a vibrating device. The solid flowrate into the dryer is

controlled by the vibration level.

The measurement of bed pressure drop (040 kPa range)

is relayed to a differential pressure transducer (Siemens

Teleperm), which quantifies these measurements within the

0100% range with an accuracy of 1%. The transducer sends

the 420 mA signal to a data logger (Alhborn Almeno 2290-8),

which is connected to a computer where the data are regis-

tered and processed by AMR-Control software. This software

also registers and processes the air velocity data, providing

continuous curves of pressure drop vs. air velocity.

Two thermocouples located at the bed inlet and outlet,

respectively, measure the temperatures of the air supplied

by the blower before entering the contactor and at the

exit. In addition, there are thermal conductivity detectors

(Alhborn MT8636-HR6) for measuring air moisture content

(00.01kgwaterkg1 air range) at both inlet and outlet with

and accuracy of 1%. Temperature and moisture contents are

also stored in the Alhborn Almeno 2290-8 data logger, which

allows monitoring their evolution over time. The gas stream

leavesthe dryerand passesthrougha fabric filter forremoving

any entrained matter.

The pilot plant main component is the contactor which

has a conical geometry. The dimensions of the contactor, are:

diameter of the upper cylindrical section, Dc, 0.35 m, conical

section height,Hc, 0.51 m, included angle of the cone,/2, 36,

inlet diameter,Do, 0.04 m and base diameter,Di, 0.068m. The

total height of the contactor (conical plus cylindrical section)

is 1.16 m. In addition to the stainless steel contactor, an exact

poly-methylmethacrylate replica has also been constructed

for observing the bed whilst conducting hydrodynamic stud-

ies.

A Schiltknecht C-59875 anemometer has been used for

measuring the gas velocity at different positions on the bed

surface and thereby estimating the gas distribution on the

upper surface and across the bed. The anemometer has been

inserted in the upper end of a 20 mm diameter tube of 80 cm

lengthand thelower endis protected by a grill to stop particles

entering the tube and possibly damaging the anemometer.

The experimentation used for the validation of the model

has been carried out using a non-porous draft tube. It is part

of a more extensive experimental work including the effect of

different draft tubes, the evolution of pressure dropwith mois-

ture content and air velocity, amongst others (Altzibar et al.,

2008).The dimensions of the non-porous draft tube are: thediameter of all the tubes,DT, is the same as the inlet, 0.04m,

the length is 0.27 m and the height of the entrainment zone,

LH(distance between the gas inlet nozzle and bottom of draft

tube), is 0.07 m.

2.2. Material

The material used for drying is construction sand. The ini-

tial moisture content (as received) is between 7 and 10%, and

the specification is that it should be dried to approximately

0.0005kg of water per kg of dried solid forsubsequentuse. The

particle size distribution of this material has been reported in

a previous paper (Altzibar et al., 2008)and the average size

(reciprocal mean diameter) has been calculated by the expres-

sion:

dp =1

[

(xi/dpi )] (1)

The average size of the sand obtained using Eq. (1) is

0.415mm.

The sands real or chemical density and surface area, mea-

sured in a Micromeritics ASAP 2010, are 2358kg m3 and

65 m2 kg1, respectively. The porous structure of the sand has

been analysed by a Micromeritics AUTOPORE 9220. The pore

volume is 0.005 mlg1 of sand, which indicates that it is of lowporosity. In addition, the analysis shows that the prevailing

pores are those between 10 and 100m.

Runs have been carried out in a batch mode using air

at 23 C (saturation moisture content 0.02 kg water kg1 air).

Thus, 0.5 kg of wet sand (7% moisture) have been added to

a bed containing 7kg of dry sand (stagnant bed height, 27cm)

and the gaseous outlet stream has been monitored through-

out the drying process. The air flowrate used in the drying has

been 40m3 h1. The evolution of the air moisture content at

the outlet of the dryer is compared with the calculated one

using the model.

3. Process modelling

A model has been developed for the simulation of the drying

process in conical spouted beds provided with a non-porous

draft tube. The modelling of this type of draft tube is sim-

pler than the porous draft tube because gas transfer between

the annulus and spout takes place only at the lower part of

the contactor, whereas in the case of the porous one the gas

transfer between the spout and annulus region occurs along

the entire tube surface. The model is based on unsteady state

mass balances applied to the solid and gaseous phases in the

different regions of the spouted bed dryer: spout, annulus and

fountain.

Fig. 2shows the volume elements defined for establishing

the mass balances in the model. The spout and the annulus

regions have been divided intofour different volume elements

of the same height, the first being in both cases the upper

one in contact with the fountain and the fourth the lower one


4/9


Fig. 2 Scheme of the spouted bed dryer showing the

volume elements in the different zones and the gas and

solid flows.

at the bottom of the contactor. In the case of the fountain,thewhole volume hasbeen considered a perfect mix element.

Given that thevolume elements in both thespout andannulus

are all of the same height, those at the bottom of the annu-

lus have smaller volume than the upper ones. This is by no

means a problem for the simulation, but rather an advantage,

given that as the gas rises through the annulus the gradient

for the mass transfer decreases due to the progressive satu-

ration of the gas. Consequently, a similar mass transfer rate

is achieved in each volume element by using this type of vol-

ume elements. The fountainis assumed to have a paraboloidal

shape,Fig. 2.Its base is the upper surface of the bed and its

height has been calculated experimentally and theoretically

according to a procedure based on a force balance, which willbe described below.

The mass balances for water in the gaseous phase volume

elements defined in the annular region are:

VanagdYan

dt = Gf(Ya(n+1) Yan)+ Kaaan(Ysat Yan)

(1 a)Vansg (2)

where Van is the volume of the element (m3), a the poros-

ity, g and s the densities of the gas and solid (kg m3), Yathe moisture content (kg water kg1 drygas), Ysatthe equilib-

rium concentrationat the particle surface, G the gaseous mass

flowrate (kg s1), f the fraction of the total gas flowrate that

crosses the bed through the annulus, Ka is the overall mass

transfer coefficient (ms1) based on the unit surface area of

the particles, andaanis the interphase surface area (m2 kg1),

i.e., thecontactsurfacebetweenthe gaseous andsolidphases.

With all the bed particles at the sametemperature, namely, the

adiabatic saturation temperature, the value ofYsatwill remain

constant throughout the bed.

In thefourth element, theair enters from thespout andnot

from the lower volume element,Fig. 2,but the inlet flowrate

is the same as in any other element, Gf.

Similarly, in the case of the sand, the mass balance for

water in any element in the annulus is as follows:

Van(1 a)sdXan

dt = W(Xa(n1) Xan) Kaaan(Ysat Yan)

(1 a)Vansg (3)

where Xanis the moisture content of the solid (kg water per kg

of dry solid) and Wis the solid mass flowrate (kg s1). In the

first volume element, the inlet solid flow rate is that coming

from the fountain,W.

Likewise, themass balances for water in thegaseous phase

volume elements defined in the spout region are:

VsnsgdYsdt = G(1 f)(Ys(n+1) Ys) + Ksasn(Ysat Ysn)

(1 s)Vsnsg (4)

For the fourth element, the inlet flow rate is that fed into

the contactor,G.

For the solid phase, the mass balance in an element of the

spout region is as follows:

Vsn(1 s)sdXsn

dt = W(Xs(n+1) Xsn) Ksasn(Ysat Ysn)

(1 s)Vsnsg (5)

In the fourth element, the solid flow enters from the cor-

responding annular element, but its rate is the same as that

crossing the whole annulus,W.

The gaseous streams leaving the upper elements of the

annulus and spout enter the fountain. Both gaseous streams

become mixed in this region and then leave the dryer. The

mass balance for water in the gaseous phase in the fountain

is:

VFFgdYF

dt

= GfYa1 + G(1 f)Ys1 GfYF + KFaF(Ysat YF)

(1 F)VFsg (6)

The solid flowrate leaving the upper element in the spout

enters the fountain and, after remaining for a given time, it

fallsback ontothe upper surface of theannularregion.Accord-

ingly, the mass balance for water in the solid phase of the

fountain is as follows:

VF(1 F)sdXFdt = W(Xs1 XF) KFaF(Ysat YF)(1 F)VFsg(7)

Solving the mass balances for all the volume elements given

by Eqs. (2)(7) provides the evolution of moisture content

throughout the bed for both the gaseous and solid phases.

At the start of the simulation, the moisture content in the

solid in the different regions of the contactor is the same and

equal to the initial moisture content of the sand. Regarding


5/9


gas moisture content, the air moisture content att = 0 is that

corresponding to ambient conditions, 0.005 kg water kg1 air.

An essential parameterof this model is theinterphase area

or wet area. This area depends on the solid moisture. When

the sand has a high moisture content this area is the full sur-

face area of the particle. During the drying process this area

decreases as the sand moisture content falls. Critical moisture

content can be defined as the lower value that maintains thewhole surface wet. The decrease in the wet surface brings the

constant rate period to an end. Consequently, the mass trans-

fer rate to the gaseous phase decreases and the falling rate

period starts. Drying in the constant rate period is controlled

by the mass transfer from the sand surface to the air, whereas

the drying controlling mechanism in the falling rate period is

the internal diffusion of water inside the particle. The value

of critical moisture content has been experimentally obtained

by monitoring the evolution of both air and sand moisture

content during the drying process. Thus, when we observed

the start of the falling rate period by monitoring air moisture

evolution at the outlet, we extracted samples of sand from

the bed and determined the average moisture content of thesolid at this time. This value is referred to as the sands critical

moisture content. For the material used it is around 0.0023kg

water per kg of dry solid. A linear dependence of wet surface

area with moisture content has been assumed.Whenthe sand

moisture content is higher than the critical value the wet sur-

face area is the total area but when the moisture content is

lower than the critical value, the surface area decreases pro-

portionally to water content until zero value is reached when

thesandhasbeenfullydried.The evolution ofwet surfacearea

withthe solidmoisture content is obtainedusing the following

empirical equation:

X > Xc, a = 65 m2 kg1

X < Xc, a = 65X/Xcm2 kg1 (8)

A further parameter of this model is the fraction of the

gas flow rate, f, that crosses the bed from the spout into the

annulus region. The gas distribution in spouted beds can be

modified by inserting an internal device. The use of a non-

porous draft tube limits the gas cross-flow from the spout

into the annulus through the entrainment zone (bottom of

the contactor). Consequently, the gas distribution between the

annulus and the spout is constant along the contactor. The

value of the parameterfdepends on the operating conditions,

especially bed height, solid particle diameter and height of

the entrainment zone in the draft tube (Cunha et al., 2009;

Ishikura et al., 2003; Nagashima et al., 2009; Neto et al., 2008;

Wang et al., 2010a).These variables have a major influence on

pressure drop in the annulus, which is the controlling hydro-

dynamic parameter for gas cross-flow from the spout into the

annulus.

The anemometer allows obtaining the gas velocity at the

upper surface of the bed, especially on the annulus surface,

although it may also give a good indication of the velocity in

the spout zone. Accordingly, the gas distribution at the bottom

of the bed and, consequently, the fraction of the gas ascend-

ing through the annulus and spout may be estimated. For the

experimental conditions used for drying, approximately 20%

of the total air flowrate crosses the bed from the spout into

the annulus. The anemometer has also been used to estimate

the gas velocity in the fountain. We have observed that up

to a height of 0.7 m over the bed surface the gas velocity is

not uniform in the cross section of the contactor. In fact, a

non-porous draft tube gives way to a high gas velocity in the

core of the fountain and, consequently, the particles reach

high positions in the fountain, whereas the gas velocity in

the peripheral region of the fountain is low and the particles

are draw back onto the annulus by gravity. The behaviour of

the conical spouted bed without a draft tube or fitted with

an open-sided draft tube (Altzibar et al., 2008, 2009)is signifi-cantly different, given that thegas distribution in the fountain

is highly uniform from lower heights over the bed surface.

These considerations are essential for predicting the fountain

height and particle trajectories in the fountain.

The mass transfer coefficients are estimated by two differ-

ent equations. For the annulus, with its low particle Reynolds

numbers (below 1000), the packed bed equation of Thoenes

and Kramers (1958) is appropriate, given that it is used for

both gas and liquid flow over Reynolds numbers between 10

and 1000:

Sh = (1.81 0.18)Sc1/3 Re1/2 (9)

where Sh is the Sherwood number, Sc the Schmidt number

and Re the Reynolds number.

For the assessment of the mass transfer coefficient in the

spout and fountain regions, which are dilute regions with a

higher gas velocity than the annulus, an appropriate equation

is that ofRowe and Claxton (1965),commonly used for fluid

beds:

Sh =Kdp

Dv=A + B Sc1/3 Re0.55 (10)

where K is the mass transfer coefficient, dp is the particle

diameter, andDv is the diffusivity of steam into air. A and Bparameters depend on bedvoidage andare definedas follows:

A =2

[1 (1 )1/3](11)

B =2

3 (12)

Accordingto Mathur and Epstein (1974), Eqs. (9)and (10) can

be simplified because the Schmidt number takes the value 0.6

for airwater vapour systems in the spout and annulus.

Bed voidage in the annulus has been assumed to be that

of the loose bed (0.35), and for the spout and fountain regions

it have been determined based, on the one hand, on the fact

that at steady state the amount of solid that rises through

the spout is equal to that falling through the annular region,

and on the other, on the knowledge of the solid flow rate and

particle residence times in these zones. Thus, the solid mass

flow rate hasbeen determined from total bedweight andaver-

age cycle time, which has been experimentally measured by

monitoring a traced particle in the fountain. The cycle time

obtained experimentally for a bed mass of 7.5 kg is 20 s and,

consequently, the solid mass flowrate is 0.375kg s1.

The first step is to ascertain the residence times of the

solid in thespout andfountain core,which arecalculatedfrom

the velocity of particles in these regions. The annulus parti-

cles enter the spout at the bottom of the spout and so their

vertical component is zero. They are then entrained by the

gas in the spout and their velocity increases. When the par-

ticles reach the fountain their velocity decreases due to the

lower gas velocity as fountain level is higher. Consequently,


6/9


the main force acting on the particle at the top of the fountain

is gravitational. In addition, the particles leave the fountain

core and enter the periphery of the fountain, where gas veloc-

ity is lower, being drawn back onto the annulus surface by

gravity.

Particle velocity in the spout and fountain is calculated by

means of a balance of forces acting on a single particle. The

expressions of this balance as a function of height and timeare:

vdv

dz =

3

4

Cdg(u v)2

dps

g(s g)

s(13)

dv

dt =

3

4

Cdg(u v)2

dps

g(s g)

s(14)

The drag coefficient is calculated by the expression:

Cd =24

Re(1 + 0.15Re0.687) (15)

Eq. (13) is integratedfrom thebottom of thespout to itstop,

which is the bed surface located at 0.27m from the bottom.

The velocity of the gas in the spout is constant due to the

use of a solid draft tube.Fig. 3shows the evolution of particle

velocity across the spout region. As observed, peak velocity is

obtained at the outlet of the spout, 1.4 m s1. The residence

time of the solid in the spout is obtained by integrating Eq.

(13),so the time for which velocity reaches a value 1.4 m s1 is

the time the particle remains in the spout, 0.32 s.

Gas velocity has been measured at different levels in the

fountain by means of the anemometer described above. This

velocity peaks at the bottom centre of the fountain and

decreases as the particle rises. The values obtained using theanemometer show that gas velocity over the bed surface is

uniform at a height of approximately 0.7 m. According to this

observation, a linearly decreasing profile has been assumed

for the gas in the fountain axis, from the maximum value at

the outlet of the spout to the minimum one (cross-sectional

superficial velocity) at a height of 0.7m. Once the gas veloc-

ityprofile is known,the evolution of particle velocity along the

fountain axis is obtained bysolving Eqs. (13)(15) withthis pro-

file. The height of the fountain is that corresponding to zero

particle velocity, which is 0.37 m for the stagnant bed height

Fig. 3 Evolution of particle velocity across the spout

region.

of 0.27 m. This value is consistent with the value measured

experimentally (approximately 0.40 m). The particle velocity

in thefountain downward zone or fountain periphery is deter-

mined by assuming that only gravitational forces are relevant

in this region of low gas velocity.

Once the particle velocity profile is known in the fountain

core and periphery, particle residence time can be calculated

in this region.Fig. 4shows the velocity of the particle and itslongitudinal position with time. The residence time estimated

for the particles in the fountain is 0.68 s.

The amount of sand in thespout andfountain at any time is

obtained by multiplying the residence time in the correspond-

ingzone by themass flow rate. Once these amounts have been

determined, the overall bed voidage in each zone is calculated

as:

= 1MsVs

(16)

Fig. 4 Particle velocity and its longitudinal position with time in the fountain.


7/9


Fig. 5 Comparison of the experimental values of gas

moisture at the outlet of the contactor with those calculated

using the model.

where Ms is the mass of sand in the zone (spout or foun-

tain) andVthe volume of the corresponding zone. The values

estimated are 0.85 for the spout and 0.98 for the fountain.

The voidage for the fountain is rather high but this is con-

sistent with the experimental observation that fine particles

like those used in this study produce very high and narrow

fountains.

4. Results of the model

A program written in Matlab 7.0 has been used to solve the

model. The subroutine Ode23 has been applied to solve the

differential equations (Eqs. (2)(7)). The results provided by the

model are those concerning the evolution throughout time

of the moisture content of gaseous and solid phases in the

different regions of the conical spouted bed dryer.

Fig. 5 compares the experimental results obtained in a

previous paper (Altzibar et al., 2008) and the values calcu-

lated for the evolution of the outlet gas stream moisture

content with time. According to the model, the calculated

moisture content is that corresponding to the fountain

region.

As observed, the fitting is satisfactory, especially during the

constant rate period, although a longer period than the exper-

imental one is predicted by the model. It is noteworthy that

the model is able to accurately predict the end of the dry-

ing period, which is essential information in a batch drying

process.

Fig. 6ashows the evolution of air moisture content pre-

dicted by the model in the four elements of the annulus. As

observed, moisture content in the annulus air increases with

bed level, i.e., from the lower element to the upper one. Thus,

there is hardly any mass transfer from the sand into the air

in the upper element of the annulus, which is because the

gaseous stream is very close to saturation. The situation is

different in the spout region,Fig. 6b. In this case, moisture

content reaches lower values than in the annulus, and it is

far from equilibrium moisture content even in the upper ele-

ment in the spout. The cause of that difference is the shorter

Fig. 6 Evolution of gas moisture content with drying time

in the four volume elements defined in the annulus, (a) and

in the spout, (b).

residence time in the spout compared to the annulus. Thus,

80% of the gas crosses the bed through the spout region but

the volume of this region is much smaller than that of the

annulus.The moisture content in the fountain is intermediate

between the annulus and the fountain (Fig. 5). In fact, the

gaseous streams from the spout and annulus mix in the foun-

tain and, moreover, there is also a significant mass transfer in

this region.

Fig. 7shows the experimental and simulated data corre-

spondingto the evolution of sand moisture content during the

drying process. Only the values corresponding to the fountain

are shown because there is no significant difference between

the evolution of sand moisture in the different regions in the

spouted bed dryer. This has been experimentally proven and

is explained bytwo facts: (i) the sand drys in 20min and so the

change in sand moisture content is slow, (ii) thesandis contin-uously circulating in the bed, which also helps to temper the

differences in moisture content between the different dryer

zones. Consequently, the sand moisture content at a given

time is almost the same at all positions in the bed.


8/9


Fig. 7 Experimental and simulated moisture contents of

the solid in the fountain throughout the drying process.

5. Conclusions

Conical spouted beds fitted with a draft tube perform well

when drying fine solids, and are an interesting alternative to

standard but more expensive and less efficient rotary dryers.

A model based on mass balances has been built to predict the

performance of the conical spouted bed with a non-porous

draft tube in the process of drying building sand. The model

predicts the evolution of moisture content in both gaseous and

solid phases with time. It is noteworthy that it accurately pre-

dicts the end of the drying period. The air leaving the annulus

is close to saturation, but that leaving the spout is not. Nev-

ertheless, the high fountains of fine particles contribute to

saturating the air leaving the spout. The moisture content in

the solid at a given time is similar in the three zones, which

indicates that the solid is well mixed.

Acknowledgements

This research was carried outwith the financial support of the

University of the Basque Country (Project GICO7/24-IT-220-07)

and of the Ministry of Science and Education of the Spanish

Government (Project CTQ2007-61167).

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