Drying Technology
An International Journal
ISSN: 0737-3937 (Print) 1532-2300 (Online) Journal homepage: http://www.tandfonline.com/loi/ldrt20
One-dimensional phosphate flash dryer model for
design application
Zhor El Hallaoui, S. Vaudreuil, T. Moudakkar & T. Bounahmidi
To cite this article: Zhor El Hallaoui, S. Vaudreuil, T. Moudakkar & T. Bounahmidi (2018):
One-dimensional phosphate flash dryer model for design application, Drying Technology, DOI:
10.1080/07373937.2018.1441867
To link to this article: https://doi.org/10.1080/07373937.2018.1441867
Published online: 07 Mar 2018.
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DRYING TECHNOLOGY
https://doi.org/10.1080/07373937.2018.1441867
none defined
One-dimensional phosphate flash dryer model for design application
Zhor El Hallaouia,b, S. Vaudreuilb, T. Moudakkara,b, and T. Bounahmidia,b
a
Laboratoire d’Analyse et Synthèse des Procédés Industriels, Ecole Mohammadia d’Ingénieurs, Université Mohamed V, Rabat, Morocco;
Euromed Research Institute, Euro-Mediterranean University of Fes, Fes, Morocco
b
ABSTRACT
ARTICLE HISTORY
The present paper studies the design of a bench scale flash dryer for phosphate particles using a
one-dimensional steady-state model. The model was based on the two-fluid theory considering
momentum, heat, and mass transfer between the solid and gas phases for a dilute gas–solid
suspension flow and for which solid interactions were neglected. The set of coupled nonlinear
differential equations of the model was solved using a Runge–Kutta method. A sensitivity analysis
for inlet air and solid velocity, air temperature and pressure, air and solid moisture content, and for
tube diameter and length was performed to design phosphate bench scale flash dryer to reduce
the solid moisture content from 18 to 2%. An analysis of the results enabled choosing the
appropriate conditions for experiments of phosphate drying for a hot air stream inlet of 200°C, in a
flash dryer of 1.7 m length and 0.2 m internal diameter.
Received 28 August 2017
Accepted 13 February 2018
1. Introduction
Among the major producing countries of “natural
phosphate,” Morocco is in the most advantageous
position with more than half of the global phosphate
reserves.[1] “Natural phosphates” (NP) mean products
that are outcoming from mining and subsequent
beneficiation processing of phosphorous-containing
minerals. NP undergoes various enrichment operations,
thus increasing its moisture content to more than 15%.
This level, considered too high, impacts transportation
costs while exceeding customer requirement of about
2% moisture content. Drying of NP thus becomes a
mandatory operation prior to exportation.
To achieve the product final moisture content and
have a significant production in less time, pneumatic
dryer, also known as “flash dryer,” is the most suitable
technology for this purpose.[2] It is referred to the
process where simultaneous pneumatic conveying and
heat and mass transfer occur along the dryer tube. Flash
dryer is characterized by a rapid drying rate[3] and
suitability for heat-sensitive materials due to the very
short residence time.
The technology consists of a cylindrical tube in
which the product is introduced at its lower part and
transported in cocurrent through the hot air stream
previously heated at the required process temperature.
The solid/air mixture exits from the upper part of the
KEYWORDS
Design; mathematical
modeling; phosphate
particles; pneumatic drying
tube where it is then separated by a cyclone enabling
the recovery of the dried product. The exiting humid
air passes through a filter before release.
To simulate the coupled phenomena mentioned
above, many mathematical models have been
developed, most of them considering a steady-state
one-dimensional flow for a dilute transport.[4–8] 2D
models were later developed considering an axial and
radial variations of the variables.[9–11] Experimental tests
have proved the hypothesis of radial variations, thus
explaining the differences perceived between 1D simulations and experimental results. 3D models using CFD
were covered later, showing better accuracy of the
model and illustrating facts previously untreated in
the other models.[12–15] These simulations however
require a longer time and more developed tools to
perform.
The present work aims to use a 1D model for the
design of a bench scale flash dryer for phosphate drying.
For this purpose, the complexity of 2D model and the
time consuming/cost of 3D simulations are not worthy.
To the best of our knowledge, no published works have
investigated modeling of a phosphate flash dryer.
In this study, a one-dimensional model for the
pneumatic drying of phosphate particles was solved in
MATLAB along with a sensitivity analysis of the
model parameters on the product moisture content.
CONTACT Zhor El Hallaoui
zhor.hallaoui@gmail.com
Euromed Research Institute, Euro-Mediterranean University of Fes, Eco-Campus,
Route Meknes, Route de Moulay Yacoub, BP51, Fes principale, Morocco.
Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/ldrt.
© 2018 Taylor & Francis
2
Z. E. HALLAOUI ET AL.
This model will enable the choice of design parameters
for a bench scale flash dryer. Future work will focus on
the experimental testing required for the development
of 2D and 3D modeling, something which could permit
the choice of adequate model for phosphate flash drying
monitoring and control.
The pressure drop measured in the dryer consists of
acceleration, static, and frictional terms as[17]:
2. One-dimensional model equations
Where the acceleration term could be neglected in
dilute phase flow[18]
The volume fraction of particles is expressed by:
The 1D model for flash drying, presented below, is a transport phenomena model based on Tanaka et al.[6] model for
rice drying and Bhattarai et al.[8] model developed for
sawdust drying. In this model, the drying medium and
the solid phase are flowing cocurrently along the dryer
tube. It was adapted in the present work to simulate the
phosphate particle flash drying using adequate estimation
methods for physical properties of phosphate.
The model is based on the two-fluid theory to describe
the gas–solid flow at dilute conditions, considering the
two phases as pseudocontinuous phases in interactions.
The model considers macroscopic balances of mass, heat,
and momentum, while particle–particle interactions are
usually neglected in the dilute phase flow.[16]
2.1. Governing equations
The momentum, heat, and mass balances in a control
volume of a flash dryer are presented in Figure 1. Based
on the above assumptions the drying process can be
described by the following balance equations.
2.2.1. Gas phase
a. Momentum balance
The momentum equation is given by:
�
�
dVa
1 dP 3 1 e
q
¼
Cd a ðVa Vp Þ2
Va
qp
dz
qa dz 4dp
e
ð1Þ
� �2 � �
�
�
�
Va
1
6w 1 e
g 4f
Va Vp
2
D
qa dp
e
dP �
¼ eqa þ ð1
dz
þ 2fp ð1
e
1
e
¼
�
V2
eÞqp g þ 2f qa a
D
Vp2
eÞqp
D
q a V a G p ð1 þ M Þ
qp Vp Ga ð1 þ HÞ
ð2Þ
ð3Þ
b. Energy balance
Va
dTa
¼
dz
�
�
�
6h
1 e
Ta Tp
dp Ca qa
e
�
�
�
6wCv 1 e
Q
Ta Tp
dp Ca qa
e
Ga Ca ð1 þ HÞ
ð4Þ
the terms in the right-hand side of the Eq. (4) represent the energy loss by air due to convection
between air and particles, energy flux due to mass
transfer, and heat losses through the pipe walls,
respectively.
c. Mass balance
A water mass balance is applied to the control volume between the solid and gas phases, where the
fraction of water evaporated from the solid is transferred to the gas. This lets to express the air
humidity variation as function of solid and gas mass
flow rate and the variation of solid moisture content.
Thus, the mass balance equation for the air
humidity could be expressed as:
� �� �
Gp
dH
dX
¼
ð5Þ
Ga
dz
dz
2.2.2. Solid phase
a. Momentum balance
The momentum equation is given by:
Vp
Figure 1. Control volume of a flash dryer.
dVp
3
q
Cd a ðVa
¼
dz
4dp qp
!
qa
g
1
qp
Vp Þ2
� �2 � �
Vp
1
fp
D
2
ð6Þ
The terms in the right-hand side represent the
drag force, gravitational and frictional force,
respectively.
DRYING TECHNOLOGY
b. Energy balance
Vp
dTp
6
h Ta
¼
dz
dp Cp qp
Tp
�
wLv M; Tp
��
ð7Þ
c. Mass balance
The mass balance equation for moisture on particle
is expressed by:
dX
¼
dz
6wð1 þ XÞ
dp Vp qp
where ri and di represent the weight fraction and the
mean diameter of the ith size fraction, respectively.
The phosphate sample has an initial moisture content
and temperature of 18% and 15°C, respectively. As first
approximation, some phosphate properties (density,
diameter, and the heat capacity) are assumed to be
constant throughout the drying process. The physical
properties of phosphate particles are grouped in Table 2.
ð8Þ
2.3. Model parameter estimation
The model parameters will be presented in this section.
Some of these parameters are geometrical, physicochemical properties of the two phases, and others of correlations for the drag coefficient and transport properties.
2.3.1. Gas properties
A literature review revealed many correlations for
the estimation of physical properties of the gas
stream,[3,6,8,19–21] all relying mainly on the temperature
range of the drying air. The selected correlations hence
satisfy the drying air temperature margin of the present
work and compared to results obtained through the
thermodynamic properties implemented in the
Engineering Equation Solver software.
Physical properties of air, namely, the density,
viscosity, heat capacity, and diffusion coefficient of
water vapor are given in Table 1.
2.3.2. Solid properties
The solid particles used in this study are phosphate
grains with size distribution ranging from 20 to
200 µm, with a D50 of 100 µm as established by a sieve
analysis. In this D50 analysis, the mean diameter of
phosphate was calculated and considered constant
during drying using Eq. (9)
P ri
i d2
dm ¼ P rii
i d3i
Table 1.
ð9Þ
2.3.3. Drag coefficient
As phosphate particles are supposed to be spherical, the
drag coefficient can be written as[8]:
�
24 �
1 þ 0:15Rep0:687 ; Rep � 1000
Cd ¼
Rep
Cd ¼ 0:44
Rep > 1000
jvp va jdp qa
where Rep ¼
g
a
2.3.4. Friction factors
. Assuming a smooth wall surface for the dryer tube,
the frictional factor between the air and wall is[22]:
16
Re
0:079
f ¼ 0:25
Re
f ¼
Re � 2300
Re > 2300
. The frictional factor for the wall–solid interaction[24]
is given by: fp ¼ 0:048Tp 1:22
2.3.5. Heat and mass transfer coefficients
. Convective
heat
transfer
coefficient[25]:
�
�
1
1
h ¼ Dk � 2 þ 0:6 � Pr3 � Re2
. Mass transfer coefficient[6]: km ¼ C ð1þHh Þ a 2
ðDv Þ3
a
k
.
where a ¼ q�C
a
2.3.6. Drying rate
Mass
loss
due
�
�
aw Psat ðTp Þ
w ¼ km 0:622 P a P T
H .
w sat ð p Þ
to
drying[23]:
Properties of hot air.
Density[5]
H
Pv ¼ P 0:622þH
�
3:4396097�10 3 T
Zc ¼ 1 þ PPv 1:007840
1 3:4299543�10 3 T
[5]
Heat capacity
q ¼ Z1 ðP Pv ÞMRTda þPv Mv
�
Ca ¼ 1 PPv ð1:0653697 � 103
3
Cv ¼ ð6:564117 � 10
Diffusion of water
vapor[18]
Viscosity[19]
Dv ¼ 22 � 10
3
1
�
4:4730851 � 10 1 T þ 9:8719042 � 10 4 T 2
2 2
2:6905819 � 10T þ 5:1820718 � 10 T
6 T 1:81 101320
273
H
7 3
4:6376809�� 10
� T
Pv
5 3
3:2682964 � 10 T Þ
P
l ¼ ð6:0453459 þ 0:042489943T Þ þ ð 6:8323022 þ 0:0059284286T Þ
H
H þ 0:622
�
�2
H
ð0:67799257 þ 0:011338714T Þ
H þ 0:622
4
Z. E. HALLAOUI ET AL.
Table 2.
Properties of phosphate particles.[18]
Property
Value
Mean diameter (µm)
Density (kg/m3)
Specific heat (J/kg · K)
Water activity
Latent heat of vaporization (J/kg)
300
1430
771
0.1
2501 − 2.65 * Tp
It is supposed that the drying rate is controlled by
convection at the outer layer of the particle–air film.
3. Simulation results and discussion
A MATLAB program was performed for the simulation,
using a fourth-order Runge–Kutta method with variable
value of integration step. The base case drying condition
Table 3. A base case for drying conditions of the bench scale
flash dryer simulation.
Variables
Gp
M0
Ta0
Va0
Dpipe
L
Value
50 kg/h of wet solid
0.18 kg water/kg dry solid
180°C
7.4 m/s
200 mm
1.7 m
used for the simulation is listed in Table 3. Figure 2
shows the changes in air and solid particle properties
along the dryer. The air pressure dropped by 21 Pa,
from 101,365 kPa at the inlet to 101,343 kPa at the outlet of the dryer (Figure 2a). From simulations, the air
temperature decreases from 180 to 68°C due to the mass
and heat transfer from the discrete phase, while the particle temperature increased from 15 to 60°C during the
0.1 s retention time in the drying tube (Figure 2b). The
simulated moisture content of the product decreases
while the air humidity raises due to mass transfer
(Figure 2c). The air velocity decreases while the solid
velocity increases and tends to reach the air velocity at
the dryer outlet (Figure 2d).
As the inlet air velocity is higher at least by three
times the solid’s sedimentation velocity, the particles
are accelerated in the entrance region. In this stage,
the particle moisture content diminishes considerably
while the air humidity rises and the air temperature
decreases. During the final drying stage, the solid
moisture content decreases slowly until it reaches equilibrium with the surrounding air, where humidity
becomes constant. The solid velocity at the dryer outlet
tends to reach the air velocity.
Figure 2. 1-D Simulation results. a:Air pressure; b: Air temperature profile; c: air and solid humidity; d: Air and solid velocity.
DRYING TECHNOLOGY
The trend of the curves obtained by the modeling
was compared with the results of the research of other
products dried in a flash dryer, having relatively close
properties in terms not only of density, moisture
content but also of geometrical properties of the dryers.
In this sense, the simulation results of sawdust
particles[8] have a similar trend. The hot air temperature
was reduced along the dryer while the solid temperature
increased until reaching equilibrium. The vapor fraction
of the air stream increased due to heat and mass transfer
from the solid phase. As resulted in food drying,[3] the
velocity profile for the solid phase shows a gain in
acceleration after the entrance region, and the curve
runs almost parallel to the air velocity curve.
4. Sensitivity analysis and design
The sensitivity analysis enables to study the effect of
various parameters on simulation results. This
sensitivity study will test theoretically the model and
will help perform the design of the bench scale dryer
for the target conditions.
4.1. Effect of inlet air temperature on the dryer
length
The impact of inlet air temperature with dryer length
is shown in Figure 3 for a constant solid feed rate of
50 kg/h, air velocity of 7 m/s, and dryer tube diameter
of 200 mm. The final moisture content to be achieved
was set at 2%.
Inlet air temperature was varied between 180 and
310°C. Figure 3 illustrates clearly that raising the inlet
air temperature leads to the shortening of the dryer tube
length, all other parameters being the same. This results
from the increased energy transfer by higher air temperature, enabling the particle to attain the required
moisture content more rapidly.
Figure 3. Inlet air temperature variation with the dryer length,
varied from 180 to 310°C.
5
Pelegrina and Crapiste[3] presented the response surface
for the effect of air velocity and temperature on the dryer
length required to reach a specified final moisture content
of the solid. They confirmed in their work that a high inlet
gas temperature leads to a shorter dryer, due to the high
driving forces for the heat and mass transfer.
4.2. Effect of air mass flow rate on the product
final moisture content
The impact of process air flow rate was evaluated by two
manners, first by changing the inlet air velocity for the
same dryer tube section and then by changing the dryer
tube section for the same inlet air velocity. These simulations were performed for a dryer having a process air
inlet temperature of 200°C and a feed rate of 50 kg/h of
wet phosphate (18% humidity, 15°C).
Figure 4 shows the variation of inlet air velocity on
the product moisture content along the dryer. Velocities
of 5, 7, and 8 m/s were tested for a pipe diameter of
200 mm, yielding rough flow rates of 0.09, 0.12, and
0.14 kg/s. As shown, increasing air velocity by 60%
results in a 25% additional moisture removal for the
same dryer length, even if the particle residence time
is reduced. This can be explained by the increased heat
and mass transfers between air and particles. However,
the analysis of air temperature profile at different air
velocities (Figure 5) shows that this increase results in
an increase in the dryer energy requirement. As
example, an increase in 60% in air velocity leads to a
52% increase in dryer energy requirement.
The effect of inlet air velocity on the product moisture content with variation of solid feed rate was studied
by Rajan et al.[26] For the same solid feed rate, increasing air velocity at constant dryer diameter leads to an
increase in the heat transfer coefficient, thus a decrease
Figure 4. Variation of the solid moisture content along the
dryer for different inlet velocities.
6
Z. E. HALLAOUI ET AL.
Figure 6. Variation of the solid moisture content along the
dryer with different pipe diameters.
Figure 5. Variation of the air temperature along the dryer for
different inlet velocities.
in the solid moisture content is perceived at the dryer
outlet. The same trend was observed by Narimatsu
et al.[27] for alumina drying where the heat transfer coefficient was plotted against air velocity. The transfer
coefficient raises with increasing velocity until reaching
a maximum value characterizing the maximum moisture removal at the entrance region, and a decrease
in the coefficient where the solid reaches equilibrium
with the surrounding air. It should be mentioned however that raising the velocity beyond a limit leads to a
faster transport of the solid, reducing the residence time
which means that the particles dry less. This effect was
discussed by Kaensup et al.[28] where they investigated
the variation of final moisture content with drying air
temperature for different air velocities, for rice particles
drying in a vertical column (75 mm ID � 8 m high). At
constant air temperature, the raise in air velocity implies
a higher air flow, which greatly enhance the heat and
mass transfer coefficients but likely to decrease the
residence time. Thus, the choice of air velocity is a
key parameter to be considered in a flash dryer.
The effects of changes in air flow rate from increasing
pipe diameter were also studied on product moisture
content without changing the residence time of the particles. Diameters of 180, 200, and 220 mm were tested
for an air velocity of 7 m/s, yielding flow rate of 0.10,
0.13, and 0.17 kg/s. As shown in Figure 6, the final
moisture content decreases with increasing pipe
diameter. It can be seen that a 22% variation of pipe
diameter, corresponding to a 70% increase in air flow
rate, provides an additional 26% in moisture removal.
In fact, when increasing the air mass flow rate, the
ratio of air to solid flow rate increases. Thus, a higher
convective transport of heat and mass results, yielding
to a decrease of the solid moisture content.
To study the effect of dryer diameter on the solid
final moisture content along the dryer length, Bhattarai
et al.[8] modified the pilot scale dryer using a buffer to
increase the internal surface of the dryer. Simulation
results—for the same conditions without the buffer—
show that increasing the buffer diameter by two times
enables to reduce the solid moisture content from 19
to 13.3%. This is due to the fact that the raise in the
diameter meant to reduce the solid velocity, thus
increasing the residence time which consequently
enabled more drying with the gas.
4.3. Effect of inlet air temperature on the
product moisture content
The effect of inlet air temperature on product moisture
content as a function of dryer length is plotted for
different air temperatures (150, 180, and 220°C). Dryer
conditions were set at a constant air velocity of 7 m/s
with a 200-mm pipe diameter (Figure 7). As expected,
increasing inlet air temperature at constant flow rate
leads to a lower phosphate moisture content at the dryer
outlet. This can be explained by the increased energy
transfer between the two phases.
Figure 7. Variation of the solid moisture content for three inlet
air temperatures.
DRYING TECHNOLOGY
In fact, raising the inlet air temperature by 46% yields
a 27% increase in moisture removal. This, however,
results in a 50% increase in dryer energy requirement
(Figure 8).
Xia et al.[29] discussed the effect of inlet air temperature on oil shale moisture content in a pneumatic
conveying dryer (48 mm ID, 1.8 m high). The air temperature influences the heat and mass exchanges where
an increased inlet air temperature leads to a significant
water removal from the solid. They also raised the issue
of drying efficiency, where it decreased after a specified
temperature due to the decrease in the air density with
increasing temperature. El Behery et al.[11] studied the
effect of inlet gas temperature on the solid water content
along the dryer length in a pilot-scale dryer (81 mm
ID � 4.5 m high), where the mathematical model used
was numerically solved by the four-way coupling
Eulerian–Lagrangian approach. Raising the gas inlet
temperature increases the solid temperature and gas
water content with a decrease in solid moisture content
and gas temperature. This is explained by the fact that
the raise in air temperature leads to an increase in the
driving forces of heat and mass transfers, leading to
an additional water removal from the solid.
7
Figure 9. Phosphate moisture content along the axial position
for different feed rates.
The impact of solid feed rate on the product moisture
content along the dryer length is shown in Figure 9.
The flash drying model was solved for three different
feed rates of 40, 50, and 60 kg/h for the conditions of
Ta ¼ 180°C, Va ¼ 7.4 m/s, and D ¼ 200 mm.
Figure 9 reveals that the final moisture content
decreases with decreasing solid feed rate. At 40 kg/h
feed rate, the 2% moisture target is reached with a
shorter dryer duct. The model’s results show that a
50% decrease in feed rate leads to an additional 25%
removal in moisture content. This can be explained by
the fact that when less particles are introduced into
the dryer, the dryer surface to particles ratio is greater,
allowing better mass and energy transfer between the
hot gas and particles. This greater transfer thus yields
reduced moisture content in the solid at the outlet.
The model also shows that increasing by 50% the feed
rate of the solid in the dryer only requires an additional
12% of energy (Figure 10).
Kaensup et al.[28] discussed the variation of final
moisture content of paddy grain with inlet air temperature for different solid feed rates. As expected, for the
same air temperature, the final moisture content
decreases with decreasing feed rate for high air temperature, while no effect was perceived at low air temperatures. In this work, they also plotted the variation of
evaporation rate against solid feed rate. It is clearly
shown that a low feed rate is characterized by an important evaporation rate at fixed air temperature, explaining the variation of decrease in final moisture content
with decreasing feed rate. Xia et al.[29] also discussed
the effect of oil shale mass flow rate on the moisture
Figure 8. Variation of the air temperature for three inlet
temperatures.
Figure 10. Air temperature along the axial position for
different feed rates.
4.4. Effect of phosphate feed rate on the final
moisture content
8
Z. E. HALLAOUI ET AL.
content along the dryer. A 10 times decrease in the solid
feed rate involves 24% in addition of water removal. The
raise of feed rate implies an increase in the amount of
water introduced to the dryer for the same conditions
of air flow and temperature, which results in higher
moisture content at the dryer outlet.
4.5. Effect of phosphate inlet moisture content
on the dryer length
Figure 11. Effect of the solid’s initial moisture content on the
dryer length for (Ta = 220°C, Va = 7 m/s, D = 200 mm).
Figure 12. Schematic diagram of a flash dryer.
Figure 13. Sizing possibilities from the sensitivity analysis.
Figure 11 illustrates the impact of solid inlet moisture
content on the required dryer length to achieve a 2%
moisture content in solid. The simulations were performed on a 200-mm internal diameter dryer for the
conditions (Ta ¼ 220°C; Va ¼ 7 m/s). Simulation results
show that a diminution of the solid’s inlet moisture content can decrease considerably the dryer length needed.
Pelegrina and Crapiste[3] discussed the effect of initial
moisture content on the required dryer length to
achieve a constant final moisture content for the same
conditions (Ta ¼ 180°C, Va ¼ 12 m/s) as function of
the particle size. For the same particle diameter, increasing the inlet moisture content results in a longer dryer
required. Results from the sensitivity analysis were used
to size the bench scale flash dryer (Figure 12) for phosphate particles. For the base case conditions previously
defined, the analysis enabled to determine the optimized
physical dimensions of the dryer, along with the process
parameters. Figure 13 represents the sizing possibilities
where a final moisture content of 2% can be achieved,
varying the inlet air temperature, its velocity as well as
the dimensions of the dryer, namely, its length and its
diameter. It should be highlighted that the dimensions
of the dryer must allow testing different configurations
of the phosphate drying in terms of air temperature and
mass flow rate. Hence, the larger dryer will be selected
with adapting the operation variables according to the
DRYING TECHNOLOGY
Table 4.
Design parameters of the bench scale flash dryer.
Design parameters
Physical dimensions of the dryer
Dryer length
Dryer diameter
Process air stream
Air velocity
Air flow rate
IN: air temperature
IN: air humidity
OUT: air temperature
OUT: air humidity
OUT: relative humidity
Phosphate stream
IN: flow rate
IN: moisture content
IN: temperature
OUT: moisture content
OUT: temperature
Performances
Drying energy requirement
1.7 m
200 mm
7.4 m/s
0.1433 kg/s
180°C
0.007 kg water/kg air
68°C
0.019 kg water/kg air
10.54%
0.014 kg/s
0.18 kg water/kg phosphate
15°C
0.02 kg water/kg phosphate
60°C
18.29 KW
9
capacity, and inlet moisture content and temperature
of the phosphates. Because of construction and energy
constraints, a dryer tube of 200 mm internal diameter
and 1.7 m length was chosen to dry phosphate with an
initial moisture content of 18%. The best drying results
seem to be obtained with a stream of hot air of 180°C at
a flow of 0.14 kg/s, this to achieve a final phosphate
moisture content of 2%. This design will be used to
set up the bench scale dryer to perform experiments,
which will be used for further development of flash drying process modeling and optimization. Results from
the present bench scale will then serve as the basis for
the development of a two-dimensional model. The final
stage of the study will be an integration of a solar plant
as a principal source of energy supply, to decrease the
fuel consumption.
Funding
This work was supported by IRESEN—Institut de Recherche
en Energie Solaire et Energies Nouvelles.
Nomenclature
Figure 14. Configurations of flow rate and temperature for the
design.
sensitivity analysis results presented above. However,
some limitations were considered: the maximum values
of tube length and inlet air temperature are 3 m and
370°C, respectively. As a result, the dryer consists of a
200-mm internal diameter tube with a length of 1.7 m
(Table 4). Figure 14 illustrates the range of temperature
and flow rate to be tested for the drying air. A properly
sized air heater will allow for temperature to range
between 150 and 370°C, while the fan should deliver a
flow rate between 0.007 and 0.18 kg/s.
5. Conclusion
A one-dimensional mathematical model for phosphate
drying was used to design a laboratory-scale flash dryer.
A sensitivity analysis was performed on tube diameter
and length, air temperature and flow rate, solid feed
aw
C
Cd
f
dp
D
Dv
g
G
H
h
km
L
Lv
M
Nu
P
Pr
Re
Rep
T
V
X
W
Z
ε
α
µ
λ
ρ
water activity (–)
heat capacity (J/kg)
drag coefficient (–)
frictional coefficient (–)
solid diameter (m)
dryer diameter (m)
coefficient of water vapor diffusion (m2/s)
gravity acceleration (m/s2)
mass flow rate (kg/s)
air humidity (kg/kg)
convective heat transfer coefficient (W/m2 · K)
mass transfer coefficient (m/s)
dryer length (m)
latent heat of vaporization (J/kg)
molecular weight (g/mol)
Nusselt number (–)
pressure (Pa)
Prandlt number (–)
Reynolds number based on the duct
diameter (–)
Reynolds number around the particle (–)
temperature (K)
velocity (m/s)
solid moisture content (kg/kg dry solid)
drying rate (kg/m2 · s)
axial position in the dryer (m)
volume fraction (–)
thermal diffusivity (m2/s)
viscosity (kg/m · s)
thermal conductivity (W/m · K)
density (kg/m3)
Subscripts
a
da
air
dry air
10
Z. E. HALLAOUI ET AL.
P
sat
V
particle
surrounding air
vapor
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