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: diegohschaves@outlook.com

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.

2

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.

4

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.

5

Mechanisms of powder formation

6

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

7

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)

8

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

9

Sorption isotherm of milk powder

10

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

11

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.

12

𝑋𝑜 = 𝑋𝑝𝑎𝑟𝑡𝑖𝑐𝑢𝑙𝑎

∞

0

× 𝐸 𝜏 𝑑𝜏 𝐸 𝑡 =1

𝜏𝑒−

𝑡𝜏

Milk drying curve

𝑋𝑐𝑟 = 0,5249

13

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

14

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.

15

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.

16

Thank you!

Questions?

Diego Chaves

diegohschaves@outlook.com