Descripción de la Instalación Experimental

The mechanism of contact-sorption drying is very complex because mois-ture transfer takes place in heterogeneous and multicomponent systems and is accompanied by thermal effects. The idealized scheme of

Stage 1 Stage 2 Stage 3

Driving force

Mass transfer between material particle and

sorbent particle

Mass transfer inside sorbent particle and inside material particle

Mass transfer between sorbent−sorbent particles and between material−material particles

Microscale Microscale

Macroscale

Moisture content difference

Gradient of moisture concentration

Moisture content difference

Penetration

+ diffusion Diffusion Penetration

+ diffusion MechanismMass transfer ScaleConfiguration

Material

Sorbent Material−sorbent

contact

Material−material contact

Sorbent−sorbent contact

FIGURE 12.1

General mechanism of contact-sorption drying in a dynamic particulate system.

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dry casein powder in 1:1.2 mass ratio, and dried in a fluidized bed at a

sorption drying shown in Figure 12.1 reflects the phenomena taking place in a dynamic system (e.g., mixing or fluidization), where the interaction

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172 Advanced Drying Technologies

between the sorbent and material, the material and material, and the sorbent and sorbent is likely to occur.

When the wet material is brought into contact with a capillary-porous dry sorbent, the surface layer of the sorbent starts to adsorb liquid depends greatly on the contact area. Because the amount of liquid mois-ture at the material surface decreases gradually, the suction potential at the material surface equals, at a certain point, the suction potential at the sorbent surface. This stops the moisture transfer through the interface between both media. However, the concentration gradient that developed in the sorbent and material particles causes moisture from the surface to diffuse throughout the sorbent volume as well as the moisture from the material core to migrate to the contact surface. When contact time is suf-and the material particle can be expected. Because at this moment the mass exchange is maximal, the sorbent could be separated and regener-ated, whereas the material being dried could be contacted again with a dry (or regenerated) sorbent for deeper drying. In practice, the contact time is much shorter than that required to attain equilibrium conditions, and therefore the diffusion of moisture proceeds when sorbent and mate-rial particles are no longer in contact. In case of random motion, which there is a possibility of sorbent–sorbent and material–material contact that may lead to further moisture transfer at the microscopic level. Then the sorbent particle can again contact temporarily more wet material, and as the process continues, a dynamic equilibrium between the material being dried and the wet–dry sorbent mixture is attained at a lower level from the previous one.

Although contact-sorption drying was a subject of numerous stud-ies, mostly in Russia, the mechanism of the process and the respective mathematical models are not well established. According to Tutova (1988), mass transfer during contact-sorption drying is determined by a dynamic nature of the sorption process. Therefore, to analyze the

pro-Before physical contact, the initial moisture concentration in the material being dried (material moisture content) is C^m_i , and the initial concentra-tion of moisture in dry sorbent is C^s_i = 0. At the contact time (t = 0), mois-ture from the material surface is assumed to be transferred instantly to the sorbent surface. Thus, the sorption front with the moisture content being in equilibrium with the material moisture content is established at the sorbent surface. At the same instant, moisture from the sorbent

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ficiently long, equilibrium between the moisture content in the sorbent

cess of mass transfer, she proposed a model configuration in which a semi-infinite plate of a bone dry sorbent is suddenly contacted with a semi-infinite slab of the wet material of uniform moisture distribution.

face begins to diffuse into the sorbent core. Assuming definite velocity of ture by ordinary capillary flow, and therefore the rate of mass transfer

is the characteristic of fluid beds, vibrated fluid beds, and spouted beds,

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a progressing sorption front u, the time needed for the sorption front to travel a distance x is given by

t x

u

d⫽ (12.1)

cess of moisture sorption starts at the k-th layer of a sorbent located at the distance x. The net time of sorption (t_k) at the k-th layer is then equal to

t t t t x

k⫽ ⫺ ⫽ ⫺kd uk (12.2)

lished in the sorbent volume. In due time, the moisture concentration at any point of a sorbent attains the equilibrium value C^s_f^s_ff, which is

consid-Accounting for the time-delay effect, the equation for moisture concen-tration in the sorbent can be written as

C t x^s( , )⫽HC^m(t⫺t x_k, ) for tⱖt_k (12.3)

Finally, the following expression can be obtained by combining Equations 12.3, 12.5, and 12.6:

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and it quantifies the time delay (relaxation time) after which the

pro-Because of the time delay, a certain moisture concentration profile is

estab-ered as the final moisture content of the sorbent.

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174 Advanced Drying Technologies

k

to the ordinary equation of sorption kinetics as

C t x^s( , )⫽HC^m( , )t x (12.8) Analyzing the preceding mathematical model for the dynamics of the contact-sorption drying, one can conclude that

An increase in the velocity of a sorption front and a decrease in

•

the delay time accelerate the moisture transfer rate.

Larger contact areas create favorable conditions for adsorption

•

rather than for much slower sorption, which is limited by diffu-sion in the sorbent volume.

Because of opposite processes of mass transfer in the sorbent

•

and the material being dried, the maximum transfer rate can be attained at an optimum contact time.

time and the variation of dimensionless sorption capacity with time in contact-sorption freeze-drying (F-D) of water-saturated ceramics by a

1

Reduced drying efficiency Sorption capacity

3´

Drying and sorption curves for contact-sorption F-D for different thicknesses of the zeolite layer: 1, 1′—10 mm; 2, 2′—20 mm; 3, 3′—30 mm.

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Figure 12.2 illustrates the variation of reduced drying efficiency with

granulated zeolite-type CaA (Tutova, 1988). The reduced drying efficiency η is defined here as the ratio of the moisture content drop during F-D When the delay time is very short (t>> t ), the general equation simplifies

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with the assistance of a sorbent to that in pure F-D taken as a reference process:

 

⫽X

X₀ (12.9)

whereas the dimensionless sorption capacity a* relates the current sorp-tion capacity of the sorbent to its initial sorpsorp-tion capacity:

a a

a_i

*⫽ (12.10)

maximum at the moment of contact with a solid sorbent and drops with time, reaching η= 1 when the sorption capacity approaches zero. Because the maximum sorption capacity is at the beginning of the process when the sorbent is dry, and it reduces dramatically when the sorbent is close to saturation, it is reasonable to interrupt the contact of the material with the sorbent after a certain time. Based on numerous experiments, the follow-ing relationship was proposed for determinfollow-ing the optimum contact time (Tutova, 1988; Tutova and Kuts, 1987):

t_c⫽

(

0 3. ⫺0 5.

)

t_s ^(12.11) where t_sis the time for sorbent saturation according to the kinetic sorption curve.

Once the contact time is chosen, the partially saturated sorbent may be removed and replaced with the new charge of a dry sorbent; renewal of the sorbent can then increase the rate of contact-sorption drying even by severalfold (Tutova and Kuts, 1987). Having the contact time established, the rate of sorbent renewal can be expressed by the number of renewals per batch (run) and determined from the ratio of the total amount of mois-ture to be removed to the amount of moismois-ture absorbed during the contact time as follows:

n m

m

H O H O tc

⫽ ²

2 ,

(12.12)

In practice, renewal of the partially wet sorbent can be accomplished by complete separation of the sorbent from the material being dried, by

various technologies can be found elsewhere (Kudra and Strumillo, 1998;

Tutova and Kuts, 1987; Tutova, 1988).

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It is clear that the efficiency of contact-sorption drying attains its

a counterflow of sorbent–material layers, or by continuous replacement of a fraction of the sorbent as it is in contact-sorption drying in a fluid-ized bed. These methods are briefly described in Section 12.4. Details of

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176 Advanced Drying Technologies

Another approach to mathematical modeling of contact-sorption drying that was used to simulate drying of corn by mixing with zeolite particles differential equations for heat and mass transfer (Luikov, 1966; Luikov and Mikhailov, 1961):

Considering grain as a spherical particle surrounded by a layer of powdery sorbent (Figure 12.3) and neglecting the second term in Equation 12.13 particular equations for corn and sorbent, respectively:

N

Nomenclature for the mathematical model of contact-sorption drying.

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(Alikhani, 1990) is based on the following simplified system of Luikov’s

as insignificant, Equations 12.13 and 12.14 turn into the following set of

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for t > 0 and 0 ≤ R ≤ R1, and

The parameter R in Equations 12.15 through 12.18 is the radial coordi-nate, ∆H is the heat of sorption, and the subscripts C and S refer to corn assumed a priori to be 0.5 for corn and 1.0 for zeolite, and these were then The initial conditions at t = 0 for the system shown in Figure 12.3 are as follows:

Equations 12.15 through 12.18, together with the initial and boundary conditions, were solved numerically using differential systems simulator DSS/2 and source code for the computer programs written in FORTRAN 77 (Alikhani, 1990). Figures 12.4 and 12.5 present typical variations in tem-perature and moisture content of the corn–zeolite mixture as a function of time and the spatial coordinate. Figure 12.6 shows the temporal variation

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and sorbent, respectively. The values of the phase change coefficient were confirmed during process simulation (Alikhani, 1990).

The boundary conditions for an adiabatic process are defined by the

fol-where h is the heat-transfer coefficient between a granular material and a

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178 Advanced Drying Technologies

ticulate medium for contact heating and drying of corn, Ph.D. Thesis, McGill University, Montreal, 1990.)

ticulate medium for contact heating and drying of corn, Ph.D. Thesis, McGill University, Montreal, 1990.)

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Temperature profile of corn–zeolite mixture. (Extracted from Alikhani, Z., Zeolite as

Moisture profile of corn–zeolite mixture. (Extracted from Alikhani, Z., Zeolite as

par-© 2009 by Taylor & Francis Group, LLC

of an experimentally determined average moisture content of corn kernels and the one calculated from the mathematical model. The relatively small quacy of the mathematical model for the contact-sorption drying of corn kernels. Details of the experiments, model solution, and validation can be found in the source literature (Alikhani, 1990; Alikhani and Raghavan, 1991; Alikhani et al., 1992).

In document DESARROLLODE UN MODELO NUMÉRICO Y EXPERIMENTALPARA EL ANÁLISIS TÉRMICO Y ECONÓMICODE UN SISTEMA DE CLIMATIZACIÓNBASADO EN UNA BOMBA DE CALOR GEOTÉRMICAY SUELO RADIANTE (página 77-89)