Antecedentes, actualidad y características distintivas
4.1 Argentina: el Monotributo y sus regímenes complementarios
4.1.3 Algunos efectos y resultados derivados del funcionamiento del régimen
Contact–sorption drying integrates two drying techniques: (a) classical contact drying, where the moisture is evaporated using heat conducted from a heated solid surface; and (b) sorption drying (also termed ‘‘desiccant drying’’ or ‘‘ad- sorption drying’’), where moisture transfer is driven by a mass concentration gradient between the material being dried and the adsorbent material it is con- tacted with.
A very general scheme of contact–sorption drying comprises mixing a solid sorbent with the material being dried followed by separation of these two media once the desired mass transfer has taken place. The solid sorbent is then regenerated and returned to the process. Clearly, the technical justifica- tion for the contact–sorption drying depends on whether the sorbent can be easily regenerated and recycled.
The sorbent may be passive (inert) or active depending on whether it is used only for moisture removal and then separated from the dried material or it becomes an integral part of the dry product. Typical inert sorbents are molecular sieves, zeolite, chabazite, activated carbon, bentonite, or silica gel.
The group of active sorbents comprises starch, peat, bran, straw, cellulose, wheat bran, corn meal, potato starch, sugar beet pulp, fruits and oil plants, cut green parts of plants such as hay, and many others. Often the already dry product is regarded as an active sorbent since it can be mixed with the wet feed prior to drying. An example of such a process is simultaneous drying and granulation of biomaterials in a fluidized bed (Dencs and Ormos, 1989). The alternative term for active sorbent is a ‘‘carrier’’ or a ‘‘filler’’ as the materials being dried are usually solutions or suspensions that are either spread over the surface of inert particles or absorbed within the porous structure of the solid material (Kudra and Strumillo, 1998; Tutova and Kuts, 1987).
In contrast with drying on inert sorbents, which has found application in drying leather and agricultural products (Piper and Alimpic, 1993; Lapczyn- ska and Zaremba, 1988; Kudra and Mujumdar, 1996; Ciborowski and Kopec, 1979; Anon., 1980; Ghate and Chhinnan, 1983; Alikhani, 1990; Sotocinal et. al., 1997), contact–sorption drying on active sorbents has been proven to be especially suitable for drying biomaterials and products of biosynthesis as it turns the process of drying of liquid droplets into drying of capillary-porous materials wetted with the same liquid. This makes it possible to take certain advantages of convective drying of solids such as drying at the wet bulb tem- perature. In such a case, it is possible to maintain biological activity of heat- sensitive products at a much higher level than with most other drying tech- niques (Kudra and Strumillo, 1998; Tutova and Kuts, 1987; Adamiec et al., 1990; Pan et al., 1994; Pan et al., 1995). Also, the end product can be a ready- to-use mixture of a sorbent-carrier with other additives such as vitamins, anti- biotics, amino acids, flavor enhancers, pesticides, bacteria concentrates, etc. This eliminates otherwise necessary downstream operations as grinding, siev- ing, or blending. Because the majority of applied research was done using a sorbent carrier, the commonly used term ‘‘contact–sorption drying’’ is synon- ymous with drying on active sorbents.
A typical fermentation culture is an aqueous mixture of microorganisms or biopolymers, unreacted residues of nutrients, byproducts, process-control- ling additives, and other components, with solid content amounting to only several percent. Thus, the solid sorbent used in contact–sorption drying per- forms two basic functions:
It absorbs a great fraction of moisture from the highly diluted suspension of biomaterials subject to drying. This alters the heat and mass transfer characteristics as the moisture is to be evaporated from a capillary- porous solid instead of from a liquid spray.
Although both functions are inseparable, the first one dominates when the suspension to be dried is contacted with the solid sorbent simultaneously with the process of moisture sorption and partial evaporation. A typical example is drying the fermentation broth that is sprayed onto a fluidized bed of the sorbent particles or atomized within the spray cone of a dispersed sorbent as it is in the spray dryer with a solid–liquid feed. The second function of the sorbent-filler plays the key role when the suspension and the sorbent get into contact prior to the drying in a separate device installed outside the drying chamber. This is the case of drying a preformed feed in a rotary, band, tunnel, and compartment dryer as well as in a classical fluid-bed dryer which accept particulate materials of high moisture content. Mixing of the suspension to be dried with a sorbent-filler in the mixer with subsequent granulation that pre- cedes drying is an example of such a variant of the contact–sorption drying (Kudra and Strumillo, 1998; Tutova and Kuts, 1987).
12.2
MECHANISM OF CONTACT–SORPTION
DRYING
The mechanism of contact–sorption drying is very complex because moisture transfer takes place in heterogeneous and multicomponent systems and is ac- companied by thermal effects. The idealized scheme of contact–sorption dry- ing shown in Figure 12.1 reflects phenomena taking place in a dynamic system (e.g., mixing or fluidization), where interaction between the sorbent–material, material–material, and sorbent–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 moisture by ordinary capillary flow so the rate of mass transfer depends greatly on the contact area. Because the amount of liquid moisture 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 mois- ture transfer through the interface between both media. However, the concen- tration 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 sufficiently long, equilibrium between moisture content in the
FIGURE12.1 General mechanism of contact–sorption drying in a dynamic particu- late system.
sorbent and the material particle can be expected. Because at this moment the mass exchange is maximal, the sorbent could be separated and regenerated while the material being dried could be contacted again with a dry (or regener- ated) sorbent for deeper drying. In practice, the contact time is much shorter than that required to attain equilibrium conditions so diffusion of moisture proceeds when sorbent and material particles are no longer in contact. In case of random motion that is characteristic of fluid beds, vibrated fluid beds, or spouted beds, there is a possibility of sorbent–sorbent and material–material contact, which 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
mostly in Russia, the mechanism of the process and the respective mathemati- cal models are not well established. According to Tutova (1988), mass transfer during contact–sorption drying is determined by a dynamic nature of the sorp- tion process. Therefore, to analyze the process 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. Prior to physical contact, the initial moisture concentra- tion in the material being dried (material moisture content) is Cm
i, and initial
concentration of moisture in dry sorbent is Cs
i ⫽ 0. At the contact time (t ⫽
0), moisture 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 surface begins to dif- fuse into the sorbent core. Assuming definite velocity of a progressing sorption front u, the time needed for the sorption front to travel a distance x is given by
td⫽ x
u (12.1)
and it quantifies the time delay (relaxation time) after which the process of moisture sorption starts at the kth layer of a sorbent located at the distance x. The net time of sorption (tk) in a kth layer is then equal to
tk⫽ t ⫺ tdk⫽ t ⫺
xk
u (12.2)
Because of time delay, a certain moisture concentration profile is estab- lished in the sorbent volume. In due time, the moisture concentration at any point of a sorbent attains the equilibrium value Cs
f that is considered as the
final moisture content of the sorbent.
Accounting for the time-delay effect, the equation for moisture concen- tration in the sorbent can be written as
Cs(t, x)⫽ HCm(t⫺ t
k, x) for tⱖ tk (12.3)
and
Cs ⫽ 0 for t⬍ t
where H is the Henry’s constant H⫽ Cs
f/Cmi. The function Cm(t⫺ tk, x) can
be expanded into a Taylor series with the argument t:
Cm(t⫺ t k, x)⫽ C(t, x) ⫺
冢
∂C m ∂t冣
t⫽0 t⫹ . . . (12.5) Then, at tk⫽ 0 dCs dt ⫽ H dCm dt (12.6) and dCs dt ⫽ l tk (HCm⫺ Cs) (12.7)When the delay time is very short (t⬎⬎ tk), the general equation simplifies
to the ordinary equation of a sorption kinetics
Cs(t, x)⫽ HCm(t, x) (12.8)
Analyzing the above 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 moisture transfer rate.
Larger contact areas create favorable conditions for adsorption rather than for much slower sorption, which is limited by diffusion 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 optimum contact time.
Figure 12.2 illustrates the variation of a reduced drying efficiency with time, and the variation of a dimensionless sorption capacity with time in contact– sorption freeze-drying of water-saturated ceramics by a granulated zeolite type
CaA (Tutova, 1988). The reduced drying efficiencyη is defined here as the
ratio of the moisture content drop during freeze-drying with the assistance of a sorbent to that in pure freeze-drying taken as a reference process:
η ⫽ ∆X
∆X0
FIGURE12.2 Drying and sorption curves for contact–sorption freeze-drying for dif-
ferent thicknesses of the zeolite layer: 1, 1′—10 mm; 2, 2′—20 mm; 3, 3′—30 mm.
while the dimensionless sorption capacity a* relates the current sorption ca- pacity of the sorbent to its initial sorption capacity:
a*⫽ a ai
(12.10) It is clear that the efficiency of contact–sorption drying attains its maxi- mum at the moment of contact with solid sorbent and drops with time reaching η ⫽ 1 when the sorption capacity approaches zero. Because the sorption capacity is maximum at the beginning of the process when the sorbent is dry, and reduces dramatically when the sorbent is close to saturation, it is reason- able to interrupt the contact of the material with the sorbent after a certain time. Based on numerous experiments the following relationship was proposed for determination of the optimum contact time (Tutova, 1988; Tutova and Kuts, 1987):
tc⫽ (0.3 ⫺ 0.5)ts (12.11)
where ts is the time for sorbent saturation according to the kinetic sorption
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 several- fold (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 moisture to be removed to the amount of moisture absorbed during a contact time:
n⫽ mH2O mH2O,tc
(12.12) In practice, renewal of the partially wet sorbent can be accomplished either by complete separation of the sorbent from the material being dried, by 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 fluidized bed. These methods are briefly described in Section 12.4 of this chapter. Details of various technologies can be found elsewhere (Kudra and Strumillo, 1998; Tutova and Kuts, 1987; Tutova, 1988).
Another approach to mathematical modeling of contact–sorption drying that was used to simulate drying of corn by mixing with zeolite particles (Alighani, 1990) is based on the following simplified system of Luikov’s dif- ferential equations for heat and mass transfer (Luikov, 1966; Luikov and Mi- khailov, 1961): ∂C ∂t ⫽ D䉮 2C⫹ αδ䉮2T (12.13) ∂T ∂t ⫽ α䉮 2T⫹ ε∆H c ∂C ∂T (12.14)
Considering grain as a spherical particle surrounded by a layer of powdery sorbent (Figure 12.3) and neglecting the second term in Eq. (12.13) as insig- nificant, Eqs. (12.13) and (12.14) turn into the following set of particular equa- tions for corn and sorbent, respectively:
∂CC ∂t ⫽ DC
冢
2 R ∂CC ∂R ⫹ ∂2C C ∂R2冣
(12.15) ∂TC ∂t ⫽ αC冢
2 R ∂TC ∂R ⫹ ∂2T C ∂R2冣
⫹ 0.5∆HC cC ∂CC ∂t (12.16)FIGURE12.3 Nomenclature for the mathematical model of contact–sorption drying. ∂CS ∂t ⫽ DS
冢
2 R ∂CS ∂R ⫹ ∂2C S ∂R2冣
(12.17) ∂TS ∂t ⫽ αS冢
2 R ∂TS ∂R ⫹ ∂2T S ∂R2冣
⫹ 1.0∆HS cS ∂CS ∂t (12.18) for t⬎ 0 and R1ⱕ R ⱕ R2.The parameter R in Eqs. (12.15) through (12.18) is the radial coordinate, ∆H is the heat of sorption, and the subscripts C and S refer to corn and sorbent, respectively. The values of the phase change coefficient were assumed a priori to be 0.5 for corn and 1.0 for the zeolite, and these were then confirmed during process simulation (Alighani, 1990).
The initial conditions at t⫽ 0 for the system shown in Figure 12.3 are as follows:
CC⫽ CCi and TC⫽ TCi for 0ⱕ R ⱕ R1 (12.19a)
CS⫽ CSi and TS⫽ TSi for R1ⱕ R ⱕ R2 (12.19b)
The boundary conditions for an adiabatic process are defined by the following equations: R⫽ 0 ∂CC ∂R ⫽ 0 ∂TC ∂R ⫽ 0 (12.20a) R⫽ R2 ∂CS ∂R ⫽ 0 ∂TS ∂R ⫽ 0 (12.20b)
FIGURE 12.4 Temperature profile in the corn–zeolite mixture. (From Alighani, 1990.)
R⫽ R1 CC⫽ CS ⫺ kC
∂TC
∂R ⫽ h(TC⫺ TS) (12.20c)
where h is the heat transfer coefficient between a granular material and a particulate sorbent.
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 (Ali- khani, 1990). Figures 12.4 and 12.5 present typical variations in temperature and moisture content of a corn–zeolite mixture as a function of time and the spatial coordinate. Figure 12.6 shows the temporal variation of an experimen- tally determined average moisture content of corn kernels and the one calcu- lated from the mathematical model. The relatively small difference between experimental and simulated data confirms the adequacy of the mathematical model for the contact–sorption drying of corn kernels. Details of the experi-
FIGURE12.6 Temporal variation of an average corn moisture content. (From Ali- ghani, 1990.)
ments, model solution, and validation can be found in the source literature (Alikhani, 1990; Alikhani and Raghavan, 1991; Alikhani et al., 1992).