Estimation of the mean moisture content of a population of milk powder particles with different residence times in a spray dryer
Chaves D.H.S.1, Campos E.C.2, Birchal M.A.S.3, Costa Jr E.F.1,2 and Birchal V.S.2
1 Mechanical Engineering Department, Federal University of Minas Gerais. Av. Pres. Antônio Carlos, 6627, Belo Horizonte, Minas Gerais, Brazil, 31270-901
2 Chemical Engineering Department, Federal University of Minas Gerais. Av. Pres. Antônio Carlos, 6627, Belo Horizonte, Minas Gerais, Brazil, 31270-901
3 Control and Automation Engineering Department, PUC Minas. Av. Dom José Gaspar, 500, Belo Horizonte, Minas Gerais, Brazil, 30535-901
Contact e-mail: [email protected]
Rio de Janeiro, May 21th, 2019.
Spray Drying Technique
the most common industrial powder manufacturing technology;
attends different sectors: food industry, agrochemical, biotechnology and pharmaceutical sectors among others;
unique technique to produce:
almost spherical and usually hollow particles;
a relatively narrow size distribution.
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Principles Air G, Tg0, Yi
Tp, Wp
Product (spherical particles)
atomizer
gas + steam
Great superficial area for drying
G, Tg, Y
drops
• Main steps:
I) atomizing of the liquid feed into
droplets;
II) mixing of these droplets with the hot
drying gas;
III) evaporating of solvent (commonly
water);
IV) separating of powder product from
exhaust gas.
suspension
F, Tp0, W0
Short drying period leads to less deterioration! 3
Efforts to identify mechanisms
manipulate powder
properties
desirable characteristics
with improvement of the
final product quality
Current market requires:
a high powder product quality;
reduced environment impacts;
low costs;
low energy consumption.
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Process production optimization
Objective
The objective of this work is to propose and simulate a model that can satisfactorily describe the spray drying process in order to obtain an estimative of the powdered product moisture content using a distribution function to consider the entire population of particles present in the drying chamber.
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Mechanisms of powder formation
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FIRST PERIOD
temperature of the particle changes until it
reaches the wet bulb temperature;
water (solvent) evaporates and the particle
shrinks;
particle moisture decreases dissolved solids
begin to settle on the surface of the particle,
forming a porous crust on the particle.
Mechanisms of powder formation
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SECOND PERIOD
the crust increases the thickness into the
particle;
reduction in drying rate: porous crust restricts
the mass transfer of steam from the core to the
outside of the particle;
temperature increases and tends to achieve
thermal equilibrium with the gas.
Kinetics of particle drying
Mass transfer rate:
𝑚𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 =𝑃 ∙ 𝑀𝑤𝑎𝑡𝑒𝑟
𝑅𝑇𝑜 + 𝑇𝑠𝑖
2
∙2𝐷𝑒𝑓𝑓
𝐷𝑝 𝑓 +2𝐷𝑒𝑓𝑓
𝑘𝑚𝑎𝑠𝑠 ∙ 𝐷𝑝
∙ 𝑙𝑛𝑃 − 𝑃𝑣
𝑃 − 𝑃𝑠𝑎𝑡(𝑇𝑠𝑖)
𝑓 = 0
se 𝑋𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 > 𝑋𝑐𝑟 (1st period)
𝑓 =𝑋𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 − 𝑋𝑒𝑞
𝑋𝑐𝑟 − 𝑋𝑒𝑞
−1/3
− 1
se 𝑋𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 ≤ 𝑋𝑐𝑟 (2nd period)
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Kinetics of particle drying
Particle diameter:
𝐷𝑝 = 𝐷𝑝 𝑖𝑛𝑖𝑡𝑖𝑎𝑙3 −
6 ∙ 𝑀𝑠(𝑋𝑖 − 𝑋𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒)
𝜋 ∙ 𝜌𝑤𝑎𝑡𝑒𝑟
1/3
se 𝑋𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 > 𝑋𝑐𝑟 (1st period)
𝐷𝑝 = 𝐷𝑝 𝑖𝑛𝑖𝑡𝑖𝑎𝑙3 −
6 ∙ 𝑀𝑠(𝑋𝑖 − 𝑋𝑐𝑟)
𝜋 ∙ 𝜌𝑤𝑎𝑡𝑒𝑟
1/3
se 𝑋𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 ≤ 𝑋𝑐𝑟 (2nd period)
Mass rate transferred from the particle surface to the gaseous phase:
𝑀𝑠
𝑑𝑋𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒
𝑑𝑡= −𝜋 ∙ 𝐷𝑝
2 ∙ 𝑚𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟
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Sorption isotherm of milk powder
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𝑋𝑒𝑞 =0,04277 ∙ 𝐶 ∙ 𝐾 ∙ 𝑎𝑤
1 − 𝐾 ∙ 𝑎𝑤 1 − 𝐾 ∙ 𝑎𝑤 + 𝐶 ∙ 𝐾 ∙ 𝑎𝑤
𝐶 = 0,1925 ∙ 𝑒𝑥𝑝 1261,13𝑇
𝐾 = 2,960 ∙ 𝑒𝑥𝑝 −386,70𝑇
Sorption eq.
Birchal (2003)
Eq
uil
ibri
um
hu
mid
ity (
d.b
.)
Water activity
Sorption isotherm of milk powder
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𝑋𝑒𝑞 =0,04277 ∙ 𝐶 ∙ 𝐾 ∙ 𝑎𝑤
1 − 𝐾 ∙ 𝑎𝑤 1 − 𝐾 ∙ 𝑎𝑤 + 𝐶 ∙ 𝐾 ∙ 𝑎𝑤
𝐶 = 0,1925 ∙ 𝑒𝑥𝑝 1261,13𝑇
𝐾 = 2,960 ∙ 𝑒𝑥𝑝 −386,70𝑇
Eq
uil
ibri
um
hu
mid
ity (
d.b
.)
Water activity
Temperature
Population of particles
After a time 𝑡 after the start-up, a portion of the population of particles comes directly from the feed while another part comes from particles that have entered in previous instants and are already partially dry;
The distribution of moisture depends on the type of flow within the drying chamber.
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𝑋𝑜 = 𝑋𝑝𝑎𝑟𝑡𝑖𝑐𝑢𝑙𝑎
∞
0
× 𝐸 𝜏 𝑑𝜏 𝐸 𝑡 =1
𝜏𝑒−
𝑡𝜏
Milk drying curve
𝑋𝑐𝑟 = 0,5249
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Temperature (ºC) Critical (d.b.)
time (s)
mo
istu
re c
on
tent
(d.b
.)
Single droplet drying
(BIRCHAL, 2003)
𝑋𝑜 = 0,072
𝑋 = 0,021
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Variable Value
mo
istu
re c
on
tent
(d.b
.)
time (s)
Conclusions
The model satisfactorily represents the drying of a single particle and presents a good estimative of the mean moisture content of a population of particles in spray dryers.
Several simplifications in the model can justify the difference between the results obtained;
Since the model is valid for all drying phases (constant rate and decreasing rate) and there is a large number of particles , it is necessary to re-evaluate: • if 𝐷𝑒𝑓𝑓 remains constant throughout the process; • 𝑘𝑚𝑎𝑠𝑠, since the water vapor pressure at the surface of the particle tends to vary with the
increase in the distance traveled by the particle in the drying chamber.
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References
Birchal, V.S., Huang, L., Mujumdar, A.S., Passos, M. L.,2006. Spray dryers: modeling and simulation. Drying Technology, 24 (3), 359–371.
Clement, K.H., Hallström, A., Dich, H.C., Le, C.M., Mortensen, J., Thomsen, H. A., 1991. On the dynamic behavior of spray dryers. Chemical Engineering Research & Design, 69 (3), 245–252.
Lin, S. X. Q., Chen, X. D., Pearce, D. L., 2005. Desorption isotherm of milk powders at elevated temperatures and over a wide range of relative humidity. Journal of Food Engineering, 68 (2), 257–264.
Mezhericher, M., Levy, A., Borde, I., 2007. Theoretical drying model of single droplets containing insoluble or dissolved solids. Drying Technology, 25 (6), 1035–1042.
Viswanathan, K., 1986. Model for continuous drying of solids in fluidized/spouted beds. The Canadian Journal of Chemical Engineering, 64 (1), 87–95.
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