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Modeling of vacuum contact drying of crystalline powders packed beds
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Chemical Engineering and Processing 47 (2008) 722–730
Modeling of vacuum contact drying of crystalline powders packed beds A. Michaud, R. Peczalski ∗ , J. Andrieu Universit´e de Lyon, Universit´e Lyon 1, ESCPE Lyon, CNRS, UMR 5007, Laboratoire d’Automatique et de G´enie des Proc´ed´es -LAGEP, Villeurbanne F-69616, France Received 31 October 2006; received in revised form 18 December 2006; accepted 18 December 2006 Available online 23 December 2006
Abstract Vacuum contact drying of monohydrate lactose and potassium chloride packed beds were experimentally investigated and numerically simulated. The classical “vaporization front” model was improved to correctly represent the experimental drying rate data. The main model modification consisted of introducing linear variation in solvent content at the vaporization front as opposed to classical modeling where this parameter was assumed constant. The new model, as applied to the falling rate drying period, involved only one fitting parameter. The validation experiments were conducted with a laboratory vacuum contact dryer. © 2006 Elsevier B.V. All rights reserved. Keywords: Vacuum contact drying; Modeling; “Vaporization front”; Packed bed; Powder
1. Introduction Contact heating in a vacuum is widely used in the pharmaceutical industry to dry granular products, which are sensitive to oxygen and temperature and are often toxic and explosive. The major challenge in thermosensible powder drying is the preservation of the initial grain size and shape during the process. The agglomeration and attrition phenomena, which depend primarily on the stirring mode (rate, periodicity) and geometrical parameters (stirrer, vessel), must be prevented. To succeed, the easiest solution is to alternate periods of stirring and no stirring, a process called contact drying under intermittent stirring. With this drying protocol, the study and analysis of stirred (agitated period) and packed bed (static period) drying phenomena are equally important. Whereas the contact drying of powder and grains in stirred bed has been investigated in detail by Schl¨under and Mollekopf [1], Tsotsas and Schl¨under [2,3] and Farges et al. [4], little experimental data on packed bed drying kinetics in vacuum have been published. ∗ Corresponding author at: University Lyon 1 – LAGEP – La Doua Campus – 3 rue Victor Grignard, Villeurbanne F-69616, France. Tel.: +33 4 72 43 18 70; fax: +33 4 72 43 16 99. E-mail address: [email protected] (R. Peczalski).
0255-2701/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2006.12.009
To our knowledge, the most detailed experimental study on packed bed vacuum contact drying was conducted by Moyne [5]. This author conducted some experiments with pure water and 200 m non-porous glass beads. According to Moyne, the experimental drying rate curves presented four distinct periods: • a short initial period during which both the bed temperature and drying rate increased; • a classical constant rate period during which the bed at the heating wall remained saturated with solvent; • a first falling rate period, starting from a critical moisture practically independent of operating conditions; • a second falling rate period during which the slope of the drying rate curve decreased to a greater extent. Baillon [6] studied the experimental temperature profile during vacuum contact drying of pharmaceutical granular packed beds. He observed that during the falling rate period, the temperature profiles inside the bed corresponded to two zones: a dried zone near the heating wall, where the temperature gradient was high and a wet zone where the temperature gradient was much lower. Tsotsas [7] conducted several experiments of vacuum contact drying of hygroscopic packed beds. Contrary to Moyne, this author did not observe a constant rate period and the falling rate
A. Michaud et al. / Chemical Engineering and Processing 47 (2008) 722–730
period started as soon as the drying began. During Tsotsas’s experiments, all moisture was located in the particles (since the particles were porous) and consequently, the liquid water transfer was not possible from the bulk to the heating wall. Thus, in this particular case, Tsotsas [7] succeeded in simulating the experiment by using a classical quasi-stationary “vaporization front” model. The most recent data were published by Kohout et al. [8,9]. These authors developed two models in order to simulate the drying rates of non-porous glass beads packed in a vessel of cylindrical geometry: a general dynamic model and a specific steady state model. The second was valid in the case where the mass transfer of the liquid phase to the heating wall by capillary flow was faster than the water vapour mass transfer from the wall during the constant rate period. According to their second model, during the constant rate period, the evaporation phenomena occurred essentially in a thin zone near the heating wall and the drying rates were governed both by heat transfer at this heating wall and by water vapour mass transfer through the bulk of the granular bed. The average moisture content decreased from its initial value to the percolation threshold value when redistribution of the liquid by capillary flow stopped and the falling rate period started. Then, a sharp drying front moved from the heating wall to the bulk of the bed which was divided into two zones: a drying zone between the heated wall and the drying front and a wet zone between the drying front and the free surface of the bed. In the wet zone, the solvent content was supposed to be uniform and equal to the percolation threshold as in a classical “vaporization front” drying model. Whereas Kohout et al. [9] observed good agreement between the experimental and simulated overall drying times, the simulated drying curves did not represent the falling rate period of their experimental drying kinetics well. Nastaj [10] used a similar “vaporization front” model in order to simulate the falling rate period during the vacuum contact drying in packed beds of selected biotechnology products. A good agreement between simulations and experiments was only observed in the case where the bed depth was small (2 mm). According to our results, the classical “vaporization front” model did not adequately represent the vacuum contact drying data of monohydrate lactose and potassium chloride in packed beds during the falling rate period. As a result, modification of the classical model was proposed resulting in a satisfactory representation of our experimental data. 2. Materials and methods 2.1. Apparatus The experiments were conducted with a vacuum contact dryer designed and set up in our laboratory as schematized in Fig. 1. The main part (1) of the apparatus was constituted by an 8 liters jacketed cylindrical vessel heated from the bottom by thermo fluid circulation (silicon oil). The fluid temperature was controlled by a thermostat (2) in the range between 30 and 90 ◦ C. The pressure inside the vessel was controlled by means of a piezoelectric pressure probe, a vacuum pump (3) and an electro valve (4) in the range of 1500–10,000 Pa.
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Fig. 1. Laboratory vacuum contact dryer.
The vessel was 200 mm wide and 300 mm high. The bottom plate of this vessel was made of stainless steel and supported a temperature probe in contact with the first layer of powders. The vessel side wall was made of glass. The vessel cover was made of stainless steel and supported a pressure probe and a temperature probe in contact with the bulk of the powder bed. The solvent vapour evaporated in the vessel was condensed by means of a cooling fluid (methanol) circulating through the condenser (5). The residual solvent vapour was condensed inside a trap cooled with liquid nitrogen (6). The total mass of the condensate, the inlet and outlet jacket temperatures and the bulk and bottom product temperatures were continuously recorded throughout the duration of the experiments. 2.2. Materials Two testing powdered materials, namely potassium chloride and monohydrate lactose were selected, according to the following criteria: • morphology close to that of industrial pharmaceutical powders; • weakly hygroscopic; • well known physical properties; • no major chemical and physical transformations during drying; Their properties are gathered in Table 1. The solvent chosen was ethanol. Its properties are presented in Table 2. 2.3. Drying experiments protocol The initial and final (after drying) product solvent content values were determined by weighing three samples before and
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Table 1 Physical properties of potassium chloride and monohydrate lactose Physical properties
Potassium chloride
Monohydrate lactose
Particle mean diameter, dpa (m) Thermal conductivity of dry layer, λd (W m−1 K−1 ) Density of dry layer, ρd (kg m−3 ) Porosity of dry layer, ψd
467 × 10−6
47 × 10−6 0.056 (aerated), 0.074 (tapped) 695 (aerated), 864 (tapped) 0.55 (aerated), 0.44 (tapped)
0.169 1086 0.45
Table 2 Physical properties of ethanol at 25 ◦ C
3. Modeling
Physical properties
Ethanol
Specific heat of liquid, Cpl (J kg−1 K−1 ) Specific heat of vapour, Cpv (J kg−1 K−1 ) Latent heat of evaporation, Hvap (J kg−1 ) Absolute viscosity of vapour, ηv (kg m−1 s−1 ) Thermal conductivity of vapour, v (W m−1 K−1 ) Surface tension: σ (N m−1 ) Density of liquid, ρl (kg m−3 )
2840 1424 9.186 × 10−5 8.6 × 10−6 0.0145 0.0224 790
Table 3 Operating conditions of drying runs with monohydrate lactose Operating conditions (◦ C)
Temperature of hot fluid, Tf Operating total pressure, Pvessel (Pa) Initial solvent content, Xini (%)
Trial 1
Trial 2
Trial 3
56.3 7000 48
57.2 7000 17
57.2 7000 15
after complete dehydratation in an oven at 110 ◦ C during 1 day for potassium chloride runs and at 80 ◦ C during 1 day for monohydrate lactose runs. The drying rate curve was obtained by derivating the solvent content versus time curve smoothed by a five points running average. The last one was determined from the condensate mass recording. The heat transfer coefficient of the jacketed vessel (hf ) was experimentally determined by evaporating experiments of pure water inside the dryer. During water boiling, the vapour flow rate (which represents the heat flux), the hot fluid temperature and the internal vessel surface temperature were recorded and their steady state values were used for calculating the hf coefficient values (hf = 200 W m−2 K−1 ). For monohydrate lactose, three experiments were conducted. During one of these experiments, several samples were removed from the upper part of the bed at different drying times. The operating conditions of these are given in Table 3. For potassium chloride, three experiments were realized. The operating conditions of these trials are given in Table 4.
Table 4 Operating conditions of drying runs with potassium chloride Operating conditions
Trial 4
Trial 5
Trial 6
Temperature of hot fluid, Tf (◦ C) Operating total pressure, Pvessel (Pa) Initial solvent content, Xini (%)
55.6 7000 34
56.9 7000 10
67.6 7000 33
3.1. The classical “vaporization front” model The steady state model proposed by Kohout et al. [8] was used to simulate both the constant rate and the falling rate periods. 3.1.1. The constant rate period During this period, the evaporation was supposed to occur at the heating wall and the drying rate was determined by the simultaneous solution of steady state heat and mass transfer equations. The vapour flux from the wall to the bed surface was described by Darcy’s law which was given by the relationship expressed with the formula: Kv ρv Pvessel − Psat,wall (Tsat,wall ) m ˙ =− (1) ηv zmax where Kv represents the packed bed permeability of vapour, ρv the density of vapour, zmax the depth of the bed, Psat,wall the saturation pressure at the heating wall and Tsat,wall is the saturation temperature at the heating wall. The heat flux at the heating wall was expressed by the classical relationship: q˙ ws = hf (Tf − Tsat,wall )
(2)
In steady state conditions, the heat flux was entirely consumed by water vaporization: m ˙ =
q˙ ws Hvap
(3)
The saturation pressure and temperature are related by the following equilibrium equation (Antoine’s equation): Psat = 103 e−5.09 log(Tsat )−(6.61×10
3 /T )+53.17+5.95×10−7 T 2 sat sat
(4)
By combining the four above equations, we could calculate the saturation temperature at the heating wall and the solvent vapour or the heat flux. The average solvent content decreased from the initial conditions to a critical solvent content (Xcr ) at which the falling rate period begins. The evolution of mean solvent content of the powder, noted X, with time was given by the relationship: dX mA ˙ = dt md
(5)
where A represents the heating wall area and md is the dry product mass.
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The bed permeability of the solvent vapour and the critical solvent content were obtained by fitting the calculated curves to the experimental ones.
By combining Eqs. (7) and (8), the vapour flux could be calculated by the following expression: m ˙ =
3.1.2. The falling rate period During this period a drying front moved from the heating wall to the bulk of the bed. In the dry layer, the heat conduction mechanism was mainly by conduction. In the wet layer, the solvent vapour mass transfer was supposed to take place by permeation. During the entire falling rate period, the solvent content at the front (Xfront ) was supposed to be equal to the critical solvent content. Except for the mass transfer equation, the model presented below proceeds from the well known phase change front approach developed by Plank (Grigull and Sandner [11] and other ‘Heat Conduction’ textbooks). The scheme of temperature and solvent content profiles through the bed during this period is presented in Fig. 2. The vapour flux in the wet zone above the drying front was expressed by the following Darcy’s law: m ˙ =−
Kv ρv ηv
Pvessel − Psat,front (Tsat, front ) zmax − zfront
(6)
where Psat,front represents the saturation pressure at the vaporization front, Tsat,front the saturation temperature at the vaporization front and zfront is the distance from the heating wall to the vaporization front. Moreover, the heat flux at the vaporization front was given by q˙ front =
Tf − Tsat,front (1/ hf ) + (zfront /λd )
q˙ front Hvap
Tf − Tsat,front Hvap ((1/ hf ) + (zfront /λd ))
(9)
The saturation pressure and temperature were still related by the classical Antoine’s Eq. (4). As well, the solvent balance at the vaporization front was expressed by m ˙ = ρd Xfront
dzfront dt
(10)
where Xfront represents the solvent content in the wet zone near the vaporization front. The evolution of solvent content with time was still described by Eq. (5). By combining Eqs. (9) and (10), the vaporization front rate could be calculated by the following equation: dzfront (Tf − Tsat,front ) = (11) dt ρd × Xfront ×Hvap × (1/ hf + zfront /λd ) Furthermore, by combining Eqs. (4), (6), (9) and (11), we could calculate the saturation temperature and the solvent vapour or the heat flux at the vaporization front. During this period, as soon as the vaporization front penetrated just a few millimetres through the bed, the drying rate was mainly controlled by the heat conduction into the dry layer and the solvent vapour permeation through the wet zone could be neglected. Thus, Eq. (6) could be removed and Eqs. (7)–(11) could be used by replacing Tsat,front by Tsat,vessel (Pvessel ).
(7)
The thermal energy balance at the vaporization front was expressed by the following steady state relationship: m ˙ =
725
(8)
Fig. 2. Scheme of temperature and solvent content profiles through the bed during the falling rate period of the classical model.
3.2. The new “vaporization front with a varying solvent supply” model 3.2.1. The constant rate period To simulate this period, Eqs. (1)–(5) of the classical model were used. During this period, the average solvent content decreased from the initial conditions to the first critical solvent content, noted Xcr1 . The permeability of the bed and first critical solvent content values were obtained by fitting the simulated curves to the experimental data. 3.2.2. The “transition” period This period corresponded to the transition between the constant rate period and the starting of the vaporization front progression. During this period, the amount of liquid at the heating wall decreased but the vaporization still occurred only in a thin zone near the heating wall. As a result, the equations corresponding to the constant rate period were used. Nevertheless, for bed solvent contents ranging from the first critical solvent content to the second critical value, noted Xcr2 , the heat transfer coefficient between the hot fluid and the first layer of particles, noted hg,tran , was supposed to vary linearly with the average solvent content as expressed by the following relationships: hf − h g hg,tran = (X − Xcr2 ) + hg (12) Xcr1 − Xcr2
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with: hg =
1 1 + hf hws
−1 (13)
The contact heat transfer coefficient (hws ) was calculated by the method proposed by Schl¨under [12] and Mollekopf and Martin [13] and described in details by Schl¨under and Mollekopf [1]. The values of the parameters necessary to apply this correlation can be found in Tsotsas [7]. Besides, the q˙ ws , m ˙ and dX/dt values were calculated in the same manner than during the constant rate period by replacing the parameter hf by the hg,tran expression given by Eq. (12). The second critical solvent content was also obtained by fitting the simulated curves to the experimental data. 3.2.3. The falling rate period During this period, a drying front was supposed to move from the heating wall to the bulk of the bed. The previously described classical model was modified by introducing a linear variation of the solvent content at the vaporization front with the bed average solvent content. Thus, at the beginning of the falling rate period, the solvent content at the vaporization front was higher than the second critical solvent content so that the drying rate was increased. In the same way, at the end of the falling rate period, the solvent content at the vaporization front was lower than the second critical solvent content so that the drying rate was decreased. The scheme of temperature and solvent content profiles through the bed during this period is presented in Fig. 3. Then, Eqs. (6)–(11) were applied by replacing hf by hg . A new fitting parameter, called the solvent supply parameter, noted a, was used to express the vaporization front solvent content at follows: Xfront = aX + b
(14)
In this last equation, the parameter b is an empirical parameter which enabled to have a solvent content equal to zero when the drying front reached the surface of the bed. Next the b value was
Fig. 3. Scheme of temperature and solvent content profiles through the bed during the falling rate period of the new model.
determined from the following equation: Xfin Zmax dX = Aρd (Xfront − Xfin ) dz −md Xcr2
(15)
0
where Xfin represents the final solvent content and which led after integrating to the relationship: (aXcr2 − Xfin + b) e−a − ((a − 1)Xfin + b) = 0
(16)
As for the classical “vaporization front” model, from the early stage of the falling rate period, the drying rate was controlled by the heat flux through the dry layer. It is worth noting that the key parameters of this last period modeling were the dry layer thermal conductivity and the variation of the solvent content at the vaporization front expressed by Eq. (14). If the drying period started at an initial solvent content lower than Xcr2 , which is generally the case when the drying was operated after a filtration step, then, in this case, only the solvent supply parameter (a) was fitted instead of the four fitting parameters (a, Kv , Xcr1 and Xcr2 ) for the general case. 4. Results and discussion 4.1. Simulations with the classical “vaporization front” model The simulated (with the classical model) curves corresponding to experimental conditions of runs 1 and 4 (see Tables 3 and 4) are presented in Figs. 4 and 5 and range over the constant rate and the falling drying rate periods. During trial 1, the bed was much more compact than for trial 2 due to the much higher initial solvent content and consequently, the “tapped” thermophysical properties (see Table 1) of monohydrate lactose were used to simulate the trial 1. For trial 2, the “aerated” thermophysical properties (see Table 1) of monohydrate lactose were used. The simulated (with the classical model) curves corresponding to experimental conditions of runs 2 and 5 (see Tables 3 and 4) are presented in Figs. 4 and 5 and range only over the falling rate period. In the case of potassium chloride, the bed had practically the same (“aerated”) density whatever was
Fig. 4. Measured and simulated (with the classical model) drying rate curves: monohydrate lactose (trials 1 and 2).
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Fig. 5. Measured and simulated (with the classical model) drying rate curves: potassium chloride (trials 4 and 5).
Fig. 6. Solvent content as a function of time measured by sampling the upper part of the bed and by “condensate” mass recording during trial 3.
the initial solvent content. Identified values of vapour permabilities and critical solvent contents for each trial are provided in Table 5. The small disturbance on the drying rate curve for trial 1 (see Fig. 1) at a solvent content of about 8% was due to an experimental malfunction. Concerning the constant rate period of trials 1 and 4, the only drying rate controlling parameter is the packed bed permeability of vapour (Kv ). This parameter was adjusted so a necessarily good agreement between measured and simulated drying rate curves was obtained. Concerning the falling rate period, the drying rate curves simulated with the classical model merged one to another shortly after the critical solvent content. The experimental curves of trials 1 and 4, starting at high initial solvent contents, are located, respectively, above the experimental curves of trials 2 and 5, starting at low solvent contents. Moreover, the simulated curves for trials 2 and 5 are significantly located below the experimental ones so that the classical model underestimates the experiments. Furthermore, the solvent content evolutions as a function of time measured by sampling the upper part of the bed and by “condensate” mass recording during trial 3 are presented in Fig. 6. The initial solvent content of this trial corresponded to the beginning of the falling rate period. The solvent content of the samples extracted from the upper part of the bed decreased as soon as the drying started. This observation is inconsistent with the classical “vaporization front” model hypothesis, in which the solvent content of the wet zone above the vaporization front should be constant during the entire duration of the falling rate period. Nevertheless, the solvent content in the upper part of the bed decreased more slowly than the average solvent content measured by condensate which seemed to indicate that a vaporization
front exists inside the bed since its lower part dried more quickly than its upper part. From the above observations, we can conclude the classical model did not precisely predict the drying curves during the falling rate period of vacuum contact drying of crystalline powder packed beds. As a matter of fact, Moyne [5] showed that the first falling rate period can be represented by the classical model but not the second one since at the end of the drying, a drying rate not equal to zero was obtained despite the fact that the solvent content in the wet zone remained constant. Moreover, Schl¨under [14] criticized the classical “vaporization front” model generally used to describe the falling rate period of porous material during convective drying. According to this author, application of this model resulted in considerable temperature gradients within the dry zone which actually did not exist during convective drying. Then, Schl¨under developed a new model called “wet surface model” based on the assumption that the dry and wet zones are arranged in “parallel” and not in “series”, with the solvent being transported to the heating surface by capillary flow. In the case of vacuum contact drying, strong temperature gradients were experimentally observed near the heating wall by Moyne [5] and Baillon [6] which indicates that a vaporization front exists and moves through the bed. Nevertheless, we believe that Schl¨under’s approach [14] is really interesting as it introduced a liquid water transport to the vaporization front even during the falling rate period. Consequently, the basic hypothesis of our new modeling was to suppose that the vaporization front was supplied with solvent by gravitational permeation or capillary diffusion during the falling rate period. In the frame of a ‘vaporization front’ model, this assumption implied an artificial front solvent content
Table 5 Identified parameters of drying runs (classical “vaporization front” model) Identified parameters Packed bed permeability of vapour, Kv Critical solvent content, Xcr
Trial 1 (m2 )
4.3 × 10−13 15.0%
Trial 2 4.3 × 10−13 –
Trial 4 1.2 × 10−12 10.0%
Trial 5 1.2 × 10−12 –
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Table 6 Identified parameters of drying runs (new “vaporization front with a varying solvent supply” model) Identified parameters Packed bed permeability of vapour, Kv First critical solvent content, Xcr1 Second critical solvent content, Xcr2 Solvent supply parameters, a
Trial 1 (m2 )
Trial 2
4.3 × 10−13 21.0% 17.5% 10
– – 1.7
higher than the second critical solvent content and thus resulted in enhanced drying rates. It must be emphasized that the empirical ‘solvent supply parameter’ (a) was intended to represent a liquid solvent flux arriving at the front and that the resulting front solvent content increase was an artefact of the simple ‘front’ approach. In reality, there was no a sharp line delimiting the wet and dry zone and there was a continuous liquid solvent content gradient from a maximum at the top and the minimum at the bottom of the bed. In our approach, the artificial front solvent content overshoot corresponded to the solvent that moved from the wet to the dry zone and was vaporized in the dry zone. In order to discriminate between gravitational and capillary flow within the wet zone (directed toward the vaporization front) the Bond number was calculated. This dimensionless number is the ratio of gravitational potential to capillary potential and is expressed by Bo =
ρl g σ/r 2
Trial 4
4.3 × 10−13
1.2 × 10−12 16.0% 11.0% 3.5
Trial 5 1.2 × 10−12 – – 1
Fig. 7. Experimental and simulated (with the new model) drying rates: monohydrate lactose (trials 1 and 2).
(17)
where ρl is the density of liquid solvent, g the acceleration due to gravity, σ the surface tension and r is the mean void radius of the bed. This radius was considered equal to the mean crystal radius in our calculation (see Table 2). The Bo value of 1.9 × 10−4 was obtained for the fine grained lactose monohydrate and 1.9 × 10−2 for the coarse grained potassium chloride. Both values indicated that the capillarity dominated strongly over gravity. 4.2. Simulations with the new “vaporization front with a varying solvent supply” model The simulated (with the new model) curves corresponding to experimental conditions of runs 1 and 4 (see Tables 3 and 4) with the new model are presented in Figs. 7 and 8 and range over the constant rate and falling drying rate periods. The simulated (with the new model) curves corresponding to experimental conditions of runs 2 and 5 (see Tables 3 and 4) are presented in Figs. 7 and 8 and range only over the falling rate period. For trial 1, the “tapped” thermophysical properties (see Table 1) of monohydrate lactose were used whereas for trial 2 the “aerated” thermophysical properties (see Table 1) were used. For trials 4 and 5, the “aerated” density of potassium chloride was used. Identified values of vapour permeabilities, the first and second critical solvent contents and solvent supply parameters for each trial are provided in Table 6. As shown in Figs. 7 and 8, a very good agreement between experimental and simulated (with the new model) curves was obtained over the entire duration of the drying process. More-
Fig. 8. Experimental and simulated (with the new model) drying rates: potassium chloride (trials 4 and 5).
over, the data of Table 7 showed that the overall drying times needed to achieve a fixed final solvent content equal to 0.5% were also well predicted by this new model. One might observe that the difference between the experimental drying curves of trials 1 and 2 corresponding to Table 7 Predicted and experimental drying times for final solvent content equal to 0.5% (trials 1, 2, 4 and 5) Trials
Predicted drying times (min)
Experimental drying times (min)
1 2 4 5
161.3 (from 25%) 470.0 (from 16%) 99.6 (from 25%) 96.7 (from 8%)
171.2 (from 25%) 471.6 (from 16%) 101.4 (from 25%) 101.7 (from 8%)
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Fig. 9. Experimental and simulated (with the new model) drying rates: potassium chloride (trial 6).
monohydrate lactose was much higher than the difference between the experimental drying curves of trials 4 and 5 corresponding to potassium chloride. Concerning the simulations, this effect turned into an identified ‘solvent supply parameter’ (representing the mobility of the solvent) much lower for potassium chloride than for lactose monohydrate. These results corroborated with the Bond number values indicating that the mobility of ethanol by capillary flow within the powder bed is much higher for monohydrate lactose (Bo = 1.9 × 10−4 ) than for potassium chloride (Bo = 1.9 × 10−2 ). Another explanation for the difference between the drying trials was that the liquid solvent flux at the vaporization front depended on the solvent content of the wet zone and thus that the “solvent supply parameter” (a) was probably a function of the second critical solvent content (Xcr2 ). According to Table 6, these two parameters appear effectively correlated. 4.3. Validation of the new “vaporization front with a varying solvent supply” model Moreover, our new model was validated by conducting one experiment and the corresponding simulation with other operating conditions that the ones used for identification of the parameters optimal values. The simulated drying rate data corresponding to trial 6 presented in Fig. 9 have been obtained by using the same values of the identified parameters (Kv , Xcr1 , Xcr2 and a) than the ones optimised with the data for trial 4. The experimental and simulated drying times needed to obtain a final solvent content equal to 0.5% starting from 23% are equal to 71.5 and 67.9 min, respectively. Consequently, as shown in Fig. 9, good agreement between simulated and experimental drying rates was obtained and the overall drying time was also accurately predicted, with our new model. 5. Conclusions It was confirmed that the vacuum contact drying model of packed beds based on the classical “vaporization front” approach
729
for the falling rate period did not precisely represent the experimental drying rates. Consequently, a new “vaporization front with a varying solvent supply” model was developed. Primary model improvement consisted of assuming linear variation of the solvent content at the vaporization front, contrary to classical modeling for which this parameter was assumed constant. This new model required only one fitting parameter if the drying process started at such a low solvent content that the falling rate period had already begun. To validate this new model, experiments were conducted with a laboratory vacuum contact dryer. Drying rates of monohydrate lactose and potassium chloride for different heating wall temperatures were measured. Good agreement between the simulated and experimental curves was observed and the experimental drying times were accurately predicted. Moreover, the final objective of this study was to simulate the drying rates during vacuum contact drying with intermittent stirring using the new model developed in this work to simulate the period without stirring. With this new approach, we will be able to determine, on a more scientific basis than the usual “trial and error” method, the optimal intermittent stirring sequence parameters (duration, frequency) which correspond to the best compromise between the drying times and attrition defects that usually affects the quality of dried powder. Acknowledgements This work was financially supported by the French Agency for Environment and Energy Management ‘ADEME’ and the pharmaceutical group ‘SANOFI-AVENTIS’. Appendix A. Nomenclature
a A b Bo Cp dpa g hf hg hws H K m ˙ md P Pvessel q˙ front q˙ ws r
solvent supply parameter heating wall area (m2 ) empirical parameter (Eqs. (14) and (16)) Bond number specific heat (J kg−1 K−1 ) particle mean diameter (m) acceleration due to gravity (m2 s−1 ) fluid-wall heat transfer coefficient (W m−2 K−1 ) overall heat transfer coefficient (W m−2 K−1 ) contact heat transfer coefficient (W m−2 K−1 ) latent heat (J kg−1 ) packed bed permeability (m2 ) drying rate (kg m−2 s−1 ) dry product mass (kg) pressure (Pa) operating total pressure (Pa) heat flux at the vaporization front (W m−2 ) heat flux at the heating wall (W m−2 ) mean void radius of the bed (m)
730
t T X Xcr1 Xcr2 z zmax
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time (s) temperature (K) solvent content (kg solvent kg−1 dry product) first critical mean solvent content (kg solvent kg−1 dry product) second critical mean solvent content (kg solvent kg−1 dry product) distance from the heating wall (m) depth of the bed (m)
Greek letters η absolute viscosity (kg m−1 s−1 ) λ thermal conductivity (W m−1 K−1 ) ρ density (kg m−3 ) σ surface tension (N m−1 ) ψ porosity Subscripts b bulk cr critical d dry f hot fluid fin final front vaporization front ini initial l liquid sat saturation tran transition period v vapour vap evaporation wall heating wall
References [1] E.U. Schl¨under, N. Mollekopf, Vacuum contact drying of free flowing mechanically agitated particulate material, Chem. Eng. Process. 18 (1984) 93–111. [2] E. Tsotsas, E.U. Schl¨under, Vacuum contact drying of free flowing mechanically agitated particulate multigranular packing, Chem. Eng. Process. 20 (1986) 339–349. [3] E. Tsotsas, E.U. Schl¨under, Vacuum contact drying of mechanically agitated beds: the influence of hygroscopic behaviour on the drying rate curve, Chem. Eng. Process. 21 (1987) 199–208. [4] D. Farges, M. Hemati, C. Lagu´erie, F. Vachet, P. Rousseaux, A new approach to contact drying modeling, Dry. Technol. 13 (1995) 1317–1329. [5] C. Moyne, Transferts couples chaleur—masse lors du s´echage: prise en compte du mouvement de la phase gazeuse, Th`ese, Institut National Polytechnique de Lorraine, 1987. [6] B. Baillon, S´echage sous vide micro-ondes combin´e de granul´es pharmaceutiques, Th`ese, Universit´e de Pau et des Pays de l’Adour, 1996. ¨ [7] E. Tsotsas, Uber den Einfluß der Dispersit¨at und der Hygroskopizit¨at auf den Trocknungsverlauf bei der Vakuum-Kontakttrocknung rieself¨ahiger Trocknungsg¨uter, Dissertation, Universit¨at Karlsruhe, 1985. [8] M. Kohout, A.P. Collier, F. Stepanek, Mathematical modelling of solvent drying from a static particle bed, Chem. Eng. Sci. 61 (2006) 3674–3685. [9] M. Kohout, A.P. Collier, F. Stepanek, Multi-scale analysis of vacuum contact drying, in: Proceedings of the IDS 2006 B, 2006, pp. 1087–1094. [10] J.F. Nastaj, Vacuum contact drying of selected biotechnology products, Dry. Technol. 12 (1994) 1145–1166. [11] U. Grigull, H. Sandner, in: B. Munz Brienza (Ed.), Heat Conduction, Hemisphere Publishing Corporation, United States of America, 1984. [12] E.U. Schl¨under, W¨arme¨ubergang an bewegte Kugelsh¨uttungen bei kurfristigem Kontakt, Chem.-Ing.-Technol. 43 (1971) 651–654. [13] N. Mollekopf, H. Martin, Zur Theorie des W¨arme¨ubergangs an bewegte Kugelsch¨uttungen bei kurzfristigem Kontakt, VT-Verfahrenstechnik 16 (1982) 701–706. [14] E.U. Schl¨under, Drying of porous material during the constant and the falling rate period: a critical review of existing hypotheses, Dry. Technol. 22 (2004) 1517–1532.
Chemical Engineering and Processing 47 (2008) 722–730
Modeling of vacuum contact drying of crystalline powders packed beds A. Michaud, R. Peczalski ∗ , J. Andrieu Universit´e de Lyon, Universit´e Lyon 1, ESCPE Lyon, CNRS, UMR 5007, Laboratoire d’Automatique et de G´enie des Proc´ed´es -LAGEP, Villeurbanne F-69616, France Received 31 October 2006; received in revised form 18 December 2006; accepted 18 December 2006 Available online 23 December 2006
Abstract Vacuum contact drying of monohydrate lactose and potassium chloride packed beds were experimentally investigated and numerically simulated. The classical “vaporization front” model was improved to correctly represent the experimental drying rate data. The main model modification consisted of introducing linear variation in solvent content at the vaporization front as opposed to classical modeling where this parameter was assumed constant. The new model, as applied to the falling rate drying period, involved only one fitting parameter. The validation experiments were conducted with a laboratory vacuum contact dryer. © 2006 Elsevier B.V. All rights reserved. Keywords: Vacuum contact drying; Modeling; “Vaporization front”; Packed bed; Powder
1. Introduction Contact heating in a vacuum is widely used in the pharmaceutical industry to dry granular products, which are sensitive to oxygen and temperature and are often toxic and explosive. The major challenge in thermosensible powder drying is the preservation of the initial grain size and shape during the process. The agglomeration and attrition phenomena, which depend primarily on the stirring mode (rate, periodicity) and geometrical parameters (stirrer, vessel), must be prevented. To succeed, the easiest solution is to alternate periods of stirring and no stirring, a process called contact drying under intermittent stirring. With this drying protocol, the study and analysis of stirred (agitated period) and packed bed (static period) drying phenomena are equally important. Whereas the contact drying of powder and grains in stirred bed has been investigated in detail by Schl¨under and Mollekopf [1], Tsotsas and Schl¨under [2,3] and Farges et al. [4], little experimental data on packed bed drying kinetics in vacuum have been published. ∗ Corresponding author at: University Lyon 1 – LAGEP – La Doua Campus – 3 rue Victor Grignard, Villeurbanne F-69616, France. Tel.: +33 4 72 43 18 70; fax: +33 4 72 43 16 99. E-mail address: [email protected] (R. Peczalski).
0255-2701/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2006.12.009
To our knowledge, the most detailed experimental study on packed bed vacuum contact drying was conducted by Moyne [5]. This author conducted some experiments with pure water and 200 m non-porous glass beads. According to Moyne, the experimental drying rate curves presented four distinct periods: • a short initial period during which both the bed temperature and drying rate increased; • a classical constant rate period during which the bed at the heating wall remained saturated with solvent; • a first falling rate period, starting from a critical moisture practically independent of operating conditions; • a second falling rate period during which the slope of the drying rate curve decreased to a greater extent. Baillon [6] studied the experimental temperature profile during vacuum contact drying of pharmaceutical granular packed beds. He observed that during the falling rate period, the temperature profiles inside the bed corresponded to two zones: a dried zone near the heating wall, where the temperature gradient was high and a wet zone where the temperature gradient was much lower. Tsotsas [7] conducted several experiments of vacuum contact drying of hygroscopic packed beds. Contrary to Moyne, this author did not observe a constant rate period and the falling rate
A. Michaud et al. / Chemical Engineering and Processing 47 (2008) 722–730
period started as soon as the drying began. During Tsotsas’s experiments, all moisture was located in the particles (since the particles were porous) and consequently, the liquid water transfer was not possible from the bulk to the heating wall. Thus, in this particular case, Tsotsas [7] succeeded in simulating the experiment by using a classical quasi-stationary “vaporization front” model. The most recent data were published by Kohout et al. [8,9]. These authors developed two models in order to simulate the drying rates of non-porous glass beads packed in a vessel of cylindrical geometry: a general dynamic model and a specific steady state model. The second was valid in the case where the mass transfer of the liquid phase to the heating wall by capillary flow was faster than the water vapour mass transfer from the wall during the constant rate period. According to their second model, during the constant rate period, the evaporation phenomena occurred essentially in a thin zone near the heating wall and the drying rates were governed both by heat transfer at this heating wall and by water vapour mass transfer through the bulk of the granular bed. The average moisture content decreased from its initial value to the percolation threshold value when redistribution of the liquid by capillary flow stopped and the falling rate period started. Then, a sharp drying front moved from the heating wall to the bulk of the bed which was divided into two zones: a drying zone between the heated wall and the drying front and a wet zone between the drying front and the free surface of the bed. In the wet zone, the solvent content was supposed to be uniform and equal to the percolation threshold as in a classical “vaporization front” drying model. Whereas Kohout et al. [9] observed good agreement between the experimental and simulated overall drying times, the simulated drying curves did not represent the falling rate period of their experimental drying kinetics well. Nastaj [10] used a similar “vaporization front” model in order to simulate the falling rate period during the vacuum contact drying in packed beds of selected biotechnology products. A good agreement between simulations and experiments was only observed in the case where the bed depth was small (2 mm). According to our results, the classical “vaporization front” model did not adequately represent the vacuum contact drying data of monohydrate lactose and potassium chloride in packed beds during the falling rate period. As a result, modification of the classical model was proposed resulting in a satisfactory representation of our experimental data. 2. Materials and methods 2.1. Apparatus The experiments were conducted with a vacuum contact dryer designed and set up in our laboratory as schematized in Fig. 1. The main part (1) of the apparatus was constituted by an 8 liters jacketed cylindrical vessel heated from the bottom by thermo fluid circulation (silicon oil). The fluid temperature was controlled by a thermostat (2) in the range between 30 and 90 ◦ C. The pressure inside the vessel was controlled by means of a piezoelectric pressure probe, a vacuum pump (3) and an electro valve (4) in the range of 1500–10,000 Pa.
723
Fig. 1. Laboratory vacuum contact dryer.
The vessel was 200 mm wide and 300 mm high. The bottom plate of this vessel was made of stainless steel and supported a temperature probe in contact with the first layer of powders. The vessel side wall was made of glass. The vessel cover was made of stainless steel and supported a pressure probe and a temperature probe in contact with the bulk of the powder bed. The solvent vapour evaporated in the vessel was condensed by means of a cooling fluid (methanol) circulating through the condenser (5). The residual solvent vapour was condensed inside a trap cooled with liquid nitrogen (6). The total mass of the condensate, the inlet and outlet jacket temperatures and the bulk and bottom product temperatures were continuously recorded throughout the duration of the experiments. 2.2. Materials Two testing powdered materials, namely potassium chloride and monohydrate lactose were selected, according to the following criteria: • morphology close to that of industrial pharmaceutical powders; • weakly hygroscopic; • well known physical properties; • no major chemical and physical transformations during drying; Their properties are gathered in Table 1. The solvent chosen was ethanol. Its properties are presented in Table 2. 2.3. Drying experiments protocol The initial and final (after drying) product solvent content values were determined by weighing three samples before and
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Table 1 Physical properties of potassium chloride and monohydrate lactose Physical properties
Potassium chloride
Monohydrate lactose
Particle mean diameter, dpa (m) Thermal conductivity of dry layer, λd (W m−1 K−1 ) Density of dry layer, ρd (kg m−3 ) Porosity of dry layer, ψd
467 × 10−6
47 × 10−6 0.056 (aerated), 0.074 (tapped) 695 (aerated), 864 (tapped) 0.55 (aerated), 0.44 (tapped)
0.169 1086 0.45
Table 2 Physical properties of ethanol at 25 ◦ C
3. Modeling
Physical properties
Ethanol
Specific heat of liquid, Cpl (J kg−1 K−1 ) Specific heat of vapour, Cpv (J kg−1 K−1 ) Latent heat of evaporation, Hvap (J kg−1 ) Absolute viscosity of vapour, ηv (kg m−1 s−1 ) Thermal conductivity of vapour, v (W m−1 K−1 ) Surface tension: σ (N m−1 ) Density of liquid, ρl (kg m−3 )
2840 1424 9.186 × 10−5 8.6 × 10−6 0.0145 0.0224 790
Table 3 Operating conditions of drying runs with monohydrate lactose Operating conditions (◦ C)
Temperature of hot fluid, Tf Operating total pressure, Pvessel (Pa) Initial solvent content, Xini (%)
Trial 1
Trial 2
Trial 3
56.3 7000 48
57.2 7000 17
57.2 7000 15
after complete dehydratation in an oven at 110 ◦ C during 1 day for potassium chloride runs and at 80 ◦ C during 1 day for monohydrate lactose runs. The drying rate curve was obtained by derivating the solvent content versus time curve smoothed by a five points running average. The last one was determined from the condensate mass recording. The heat transfer coefficient of the jacketed vessel (hf ) was experimentally determined by evaporating experiments of pure water inside the dryer. During water boiling, the vapour flow rate (which represents the heat flux), the hot fluid temperature and the internal vessel surface temperature were recorded and their steady state values were used for calculating the hf coefficient values (hf = 200 W m−2 K−1 ). For monohydrate lactose, three experiments were conducted. During one of these experiments, several samples were removed from the upper part of the bed at different drying times. The operating conditions of these are given in Table 3. For potassium chloride, three experiments were realized. The operating conditions of these trials are given in Table 4.
Table 4 Operating conditions of drying runs with potassium chloride Operating conditions
Trial 4
Trial 5
Trial 6
Temperature of hot fluid, Tf (◦ C) Operating total pressure, Pvessel (Pa) Initial solvent content, Xini (%)
55.6 7000 34
56.9 7000 10
67.6 7000 33
3.1. The classical “vaporization front” model The steady state model proposed by Kohout et al. [8] was used to simulate both the constant rate and the falling rate periods. 3.1.1. The constant rate period During this period, the evaporation was supposed to occur at the heating wall and the drying rate was determined by the simultaneous solution of steady state heat and mass transfer equations. The vapour flux from the wall to the bed surface was described by Darcy’s law which was given by the relationship expressed with the formula: Kv ρv Pvessel − Psat,wall (Tsat,wall ) m ˙ =− (1) ηv zmax where Kv represents the packed bed permeability of vapour, ρv the density of vapour, zmax the depth of the bed, Psat,wall the saturation pressure at the heating wall and Tsat,wall is the saturation temperature at the heating wall. The heat flux at the heating wall was expressed by the classical relationship: q˙ ws = hf (Tf − Tsat,wall )
(2)
In steady state conditions, the heat flux was entirely consumed by water vaporization: m ˙ =
q˙ ws Hvap
(3)
The saturation pressure and temperature are related by the following equilibrium equation (Antoine’s equation): Psat = 103 e−5.09 log(Tsat )−(6.61×10
3 /T )+53.17+5.95×10−7 T 2 sat sat
(4)
By combining the four above equations, we could calculate the saturation temperature at the heating wall and the solvent vapour or the heat flux. The average solvent content decreased from the initial conditions to a critical solvent content (Xcr ) at which the falling rate period begins. The evolution of mean solvent content of the powder, noted X, with time was given by the relationship: dX mA ˙ = dt md
(5)
where A represents the heating wall area and md is the dry product mass.
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The bed permeability of the solvent vapour and the critical solvent content were obtained by fitting the calculated curves to the experimental ones.
By combining Eqs. (7) and (8), the vapour flux could be calculated by the following expression: m ˙ =
3.1.2. The falling rate period During this period a drying front moved from the heating wall to the bulk of the bed. In the dry layer, the heat conduction mechanism was mainly by conduction. In the wet layer, the solvent vapour mass transfer was supposed to take place by permeation. During the entire falling rate period, the solvent content at the front (Xfront ) was supposed to be equal to the critical solvent content. Except for the mass transfer equation, the model presented below proceeds from the well known phase change front approach developed by Plank (Grigull and Sandner [11] and other ‘Heat Conduction’ textbooks). The scheme of temperature and solvent content profiles through the bed during this period is presented in Fig. 2. The vapour flux in the wet zone above the drying front was expressed by the following Darcy’s law: m ˙ =−
Kv ρv ηv
Pvessel − Psat,front (Tsat, front ) zmax − zfront
(6)
where Psat,front represents the saturation pressure at the vaporization front, Tsat,front the saturation temperature at the vaporization front and zfront is the distance from the heating wall to the vaporization front. Moreover, the heat flux at the vaporization front was given by q˙ front =
Tf − Tsat,front (1/ hf ) + (zfront /λd )
q˙ front Hvap
Tf − Tsat,front Hvap ((1/ hf ) + (zfront /λd ))
(9)
The saturation pressure and temperature were still related by the classical Antoine’s Eq. (4). As well, the solvent balance at the vaporization front was expressed by m ˙ = ρd Xfront
dzfront dt
(10)
where Xfront represents the solvent content in the wet zone near the vaporization front. The evolution of solvent content with time was still described by Eq. (5). By combining Eqs. (9) and (10), the vaporization front rate could be calculated by the following equation: dzfront (Tf − Tsat,front ) = (11) dt ρd × Xfront ×Hvap × (1/ hf + zfront /λd ) Furthermore, by combining Eqs. (4), (6), (9) and (11), we could calculate the saturation temperature and the solvent vapour or the heat flux at the vaporization front. During this period, as soon as the vaporization front penetrated just a few millimetres through the bed, the drying rate was mainly controlled by the heat conduction into the dry layer and the solvent vapour permeation through the wet zone could be neglected. Thus, Eq. (6) could be removed and Eqs. (7)–(11) could be used by replacing Tsat,front by Tsat,vessel (Pvessel ).
(7)
The thermal energy balance at the vaporization front was expressed by the following steady state relationship: m ˙ =
725
(8)
Fig. 2. Scheme of temperature and solvent content profiles through the bed during the falling rate period of the classical model.
3.2. The new “vaporization front with a varying solvent supply” model 3.2.1. The constant rate period To simulate this period, Eqs. (1)–(5) of the classical model were used. During this period, the average solvent content decreased from the initial conditions to the first critical solvent content, noted Xcr1 . The permeability of the bed and first critical solvent content values were obtained by fitting the simulated curves to the experimental data. 3.2.2. The “transition” period This period corresponded to the transition between the constant rate period and the starting of the vaporization front progression. During this period, the amount of liquid at the heating wall decreased but the vaporization still occurred only in a thin zone near the heating wall. As a result, the equations corresponding to the constant rate period were used. Nevertheless, for bed solvent contents ranging from the first critical solvent content to the second critical value, noted Xcr2 , the heat transfer coefficient between the hot fluid and the first layer of particles, noted hg,tran , was supposed to vary linearly with the average solvent content as expressed by the following relationships: hf − h g hg,tran = (X − Xcr2 ) + hg (12) Xcr1 − Xcr2
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with: hg =
1 1 + hf hws
−1 (13)
The contact heat transfer coefficient (hws ) was calculated by the method proposed by Schl¨under [12] and Mollekopf and Martin [13] and described in details by Schl¨under and Mollekopf [1]. The values of the parameters necessary to apply this correlation can be found in Tsotsas [7]. Besides, the q˙ ws , m ˙ and dX/dt values were calculated in the same manner than during the constant rate period by replacing the parameter hf by the hg,tran expression given by Eq. (12). The second critical solvent content was also obtained by fitting the simulated curves to the experimental data. 3.2.3. The falling rate period During this period, a drying front was supposed to move from the heating wall to the bulk of the bed. The previously described classical model was modified by introducing a linear variation of the solvent content at the vaporization front with the bed average solvent content. Thus, at the beginning of the falling rate period, the solvent content at the vaporization front was higher than the second critical solvent content so that the drying rate was increased. In the same way, at the end of the falling rate period, the solvent content at the vaporization front was lower than the second critical solvent content so that the drying rate was decreased. The scheme of temperature and solvent content profiles through the bed during this period is presented in Fig. 3. Then, Eqs. (6)–(11) were applied by replacing hf by hg . A new fitting parameter, called the solvent supply parameter, noted a, was used to express the vaporization front solvent content at follows: Xfront = aX + b
(14)
In this last equation, the parameter b is an empirical parameter which enabled to have a solvent content equal to zero when the drying front reached the surface of the bed. Next the b value was
Fig. 3. Scheme of temperature and solvent content profiles through the bed during the falling rate period of the new model.
determined from the following equation: Xfin Zmax dX = Aρd (Xfront − Xfin ) dz −md Xcr2
(15)
0
where Xfin represents the final solvent content and which led after integrating to the relationship: (aXcr2 − Xfin + b) e−a − ((a − 1)Xfin + b) = 0
(16)
As for the classical “vaporization front” model, from the early stage of the falling rate period, the drying rate was controlled by the heat flux through the dry layer. It is worth noting that the key parameters of this last period modeling were the dry layer thermal conductivity and the variation of the solvent content at the vaporization front expressed by Eq. (14). If the drying period started at an initial solvent content lower than Xcr2 , which is generally the case when the drying was operated after a filtration step, then, in this case, only the solvent supply parameter (a) was fitted instead of the four fitting parameters (a, Kv , Xcr1 and Xcr2 ) for the general case. 4. Results and discussion 4.1. Simulations with the classical “vaporization front” model The simulated (with the classical model) curves corresponding to experimental conditions of runs 1 and 4 (see Tables 3 and 4) are presented in Figs. 4 and 5 and range over the constant rate and the falling drying rate periods. During trial 1, the bed was much more compact than for trial 2 due to the much higher initial solvent content and consequently, the “tapped” thermophysical properties (see Table 1) of monohydrate lactose were used to simulate the trial 1. For trial 2, the “aerated” thermophysical properties (see Table 1) of monohydrate lactose were used. The simulated (with the classical model) curves corresponding to experimental conditions of runs 2 and 5 (see Tables 3 and 4) are presented in Figs. 4 and 5 and range only over the falling rate period. In the case of potassium chloride, the bed had practically the same (“aerated”) density whatever was
Fig. 4. Measured and simulated (with the classical model) drying rate curves: monohydrate lactose (trials 1 and 2).
A. Michaud et al. / Chemical Engineering and Processing 47 (2008) 722–730
727
Fig. 5. Measured and simulated (with the classical model) drying rate curves: potassium chloride (trials 4 and 5).
Fig. 6. Solvent content as a function of time measured by sampling the upper part of the bed and by “condensate” mass recording during trial 3.
the initial solvent content. Identified values of vapour permabilities and critical solvent contents for each trial are provided in Table 5. The small disturbance on the drying rate curve for trial 1 (see Fig. 1) at a solvent content of about 8% was due to an experimental malfunction. Concerning the constant rate period of trials 1 and 4, the only drying rate controlling parameter is the packed bed permeability of vapour (Kv ). This parameter was adjusted so a necessarily good agreement between measured and simulated drying rate curves was obtained. Concerning the falling rate period, the drying rate curves simulated with the classical model merged one to another shortly after the critical solvent content. The experimental curves of trials 1 and 4, starting at high initial solvent contents, are located, respectively, above the experimental curves of trials 2 and 5, starting at low solvent contents. Moreover, the simulated curves for trials 2 and 5 are significantly located below the experimental ones so that the classical model underestimates the experiments. Furthermore, the solvent content evolutions as a function of time measured by sampling the upper part of the bed and by “condensate” mass recording during trial 3 are presented in Fig. 6. The initial solvent content of this trial corresponded to the beginning of the falling rate period. The solvent content of the samples extracted from the upper part of the bed decreased as soon as the drying started. This observation is inconsistent with the classical “vaporization front” model hypothesis, in which the solvent content of the wet zone above the vaporization front should be constant during the entire duration of the falling rate period. Nevertheless, the solvent content in the upper part of the bed decreased more slowly than the average solvent content measured by condensate which seemed to indicate that a vaporization
front exists inside the bed since its lower part dried more quickly than its upper part. From the above observations, we can conclude the classical model did not precisely predict the drying curves during the falling rate period of vacuum contact drying of crystalline powder packed beds. As a matter of fact, Moyne [5] showed that the first falling rate period can be represented by the classical model but not the second one since at the end of the drying, a drying rate not equal to zero was obtained despite the fact that the solvent content in the wet zone remained constant. Moreover, Schl¨under [14] criticized the classical “vaporization front” model generally used to describe the falling rate period of porous material during convective drying. According to this author, application of this model resulted in considerable temperature gradients within the dry zone which actually did not exist during convective drying. Then, Schl¨under developed a new model called “wet surface model” based on the assumption that the dry and wet zones are arranged in “parallel” and not in “series”, with the solvent being transported to the heating surface by capillary flow. In the case of vacuum contact drying, strong temperature gradients were experimentally observed near the heating wall by Moyne [5] and Baillon [6] which indicates that a vaporization front exists and moves through the bed. Nevertheless, we believe that Schl¨under’s approach [14] is really interesting as it introduced a liquid water transport to the vaporization front even during the falling rate period. Consequently, the basic hypothesis of our new modeling was to suppose that the vaporization front was supplied with solvent by gravitational permeation or capillary diffusion during the falling rate period. In the frame of a ‘vaporization front’ model, this assumption implied an artificial front solvent content
Table 5 Identified parameters of drying runs (classical “vaporization front” model) Identified parameters Packed bed permeability of vapour, Kv Critical solvent content, Xcr
Trial 1 (m2 )
4.3 × 10−13 15.0%
Trial 2 4.3 × 10−13 –
Trial 4 1.2 × 10−12 10.0%
Trial 5 1.2 × 10−12 –
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Table 6 Identified parameters of drying runs (new “vaporization front with a varying solvent supply” model) Identified parameters Packed bed permeability of vapour, Kv First critical solvent content, Xcr1 Second critical solvent content, Xcr2 Solvent supply parameters, a
Trial 1 (m2 )
Trial 2
4.3 × 10−13 21.0% 17.5% 10
– – 1.7
higher than the second critical solvent content and thus resulted in enhanced drying rates. It must be emphasized that the empirical ‘solvent supply parameter’ (a) was intended to represent a liquid solvent flux arriving at the front and that the resulting front solvent content increase was an artefact of the simple ‘front’ approach. In reality, there was no a sharp line delimiting the wet and dry zone and there was a continuous liquid solvent content gradient from a maximum at the top and the minimum at the bottom of the bed. In our approach, the artificial front solvent content overshoot corresponded to the solvent that moved from the wet to the dry zone and was vaporized in the dry zone. In order to discriminate between gravitational and capillary flow within the wet zone (directed toward the vaporization front) the Bond number was calculated. This dimensionless number is the ratio of gravitational potential to capillary potential and is expressed by Bo =
ρl g σ/r 2
Trial 4
4.3 × 10−13
1.2 × 10−12 16.0% 11.0% 3.5
Trial 5 1.2 × 10−12 – – 1
Fig. 7. Experimental and simulated (with the new model) drying rates: monohydrate lactose (trials 1 and 2).
(17)
where ρl is the density of liquid solvent, g the acceleration due to gravity, σ the surface tension and r is the mean void radius of the bed. This radius was considered equal to the mean crystal radius in our calculation (see Table 2). The Bo value of 1.9 × 10−4 was obtained for the fine grained lactose monohydrate and 1.9 × 10−2 for the coarse grained potassium chloride. Both values indicated that the capillarity dominated strongly over gravity. 4.2. Simulations with the new “vaporization front with a varying solvent supply” model The simulated (with the new model) curves corresponding to experimental conditions of runs 1 and 4 (see Tables 3 and 4) with the new model are presented in Figs. 7 and 8 and range over the constant rate and falling drying rate periods. The simulated (with the new model) curves corresponding to experimental conditions of runs 2 and 5 (see Tables 3 and 4) are presented in Figs. 7 and 8 and range only over the falling rate period. For trial 1, the “tapped” thermophysical properties (see Table 1) of monohydrate lactose were used whereas for trial 2 the “aerated” thermophysical properties (see Table 1) were used. For trials 4 and 5, the “aerated” density of potassium chloride was used. Identified values of vapour permeabilities, the first and second critical solvent contents and solvent supply parameters for each trial are provided in Table 6. As shown in Figs. 7 and 8, a very good agreement between experimental and simulated (with the new model) curves was obtained over the entire duration of the drying process. More-
Fig. 8. Experimental and simulated (with the new model) drying rates: potassium chloride (trials 4 and 5).
over, the data of Table 7 showed that the overall drying times needed to achieve a fixed final solvent content equal to 0.5% were also well predicted by this new model. One might observe that the difference between the experimental drying curves of trials 1 and 2 corresponding to Table 7 Predicted and experimental drying times for final solvent content equal to 0.5% (trials 1, 2, 4 and 5) Trials
Predicted drying times (min)
Experimental drying times (min)
1 2 4 5
161.3 (from 25%) 470.0 (from 16%) 99.6 (from 25%) 96.7 (from 8%)
171.2 (from 25%) 471.6 (from 16%) 101.4 (from 25%) 101.7 (from 8%)
A. Michaud et al. / Chemical Engineering and Processing 47 (2008) 722–730
Fig. 9. Experimental and simulated (with the new model) drying rates: potassium chloride (trial 6).
monohydrate lactose was much higher than the difference between the experimental drying curves of trials 4 and 5 corresponding to potassium chloride. Concerning the simulations, this effect turned into an identified ‘solvent supply parameter’ (representing the mobility of the solvent) much lower for potassium chloride than for lactose monohydrate. These results corroborated with the Bond number values indicating that the mobility of ethanol by capillary flow within the powder bed is much higher for monohydrate lactose (Bo = 1.9 × 10−4 ) than for potassium chloride (Bo = 1.9 × 10−2 ). Another explanation for the difference between the drying trials was that the liquid solvent flux at the vaporization front depended on the solvent content of the wet zone and thus that the “solvent supply parameter” (a) was probably a function of the second critical solvent content (Xcr2 ). According to Table 6, these two parameters appear effectively correlated. 4.3. Validation of the new “vaporization front with a varying solvent supply” model Moreover, our new model was validated by conducting one experiment and the corresponding simulation with other operating conditions that the ones used for identification of the parameters optimal values. The simulated drying rate data corresponding to trial 6 presented in Fig. 9 have been obtained by using the same values of the identified parameters (Kv , Xcr1 , Xcr2 and a) than the ones optimised with the data for trial 4. The experimental and simulated drying times needed to obtain a final solvent content equal to 0.5% starting from 23% are equal to 71.5 and 67.9 min, respectively. Consequently, as shown in Fig. 9, good agreement between simulated and experimental drying rates was obtained and the overall drying time was also accurately predicted, with our new model. 5. Conclusions It was confirmed that the vacuum contact drying model of packed beds based on the classical “vaporization front” approach
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for the falling rate period did not precisely represent the experimental drying rates. Consequently, a new “vaporization front with a varying solvent supply” model was developed. Primary model improvement consisted of assuming linear variation of the solvent content at the vaporization front, contrary to classical modeling for which this parameter was assumed constant. This new model required only one fitting parameter if the drying process started at such a low solvent content that the falling rate period had already begun. To validate this new model, experiments were conducted with a laboratory vacuum contact dryer. Drying rates of monohydrate lactose and potassium chloride for different heating wall temperatures were measured. Good agreement between the simulated and experimental curves was observed and the experimental drying times were accurately predicted. Moreover, the final objective of this study was to simulate the drying rates during vacuum contact drying with intermittent stirring using the new model developed in this work to simulate the period without stirring. With this new approach, we will be able to determine, on a more scientific basis than the usual “trial and error” method, the optimal intermittent stirring sequence parameters (duration, frequency) which correspond to the best compromise between the drying times and attrition defects that usually affects the quality of dried powder. Acknowledgements This work was financially supported by the French Agency for Environment and Energy Management ‘ADEME’ and the pharmaceutical group ‘SANOFI-AVENTIS’. Appendix A. Nomenclature
a A b Bo Cp dpa g hf hg hws H K m ˙ md P Pvessel q˙ front q˙ ws r
solvent supply parameter heating wall area (m2 ) empirical parameter (Eqs. (14) and (16)) Bond number specific heat (J kg−1 K−1 ) particle mean diameter (m) acceleration due to gravity (m2 s−1 ) fluid-wall heat transfer coefficient (W m−2 K−1 ) overall heat transfer coefficient (W m−2 K−1 ) contact heat transfer coefficient (W m−2 K−1 ) latent heat (J kg−1 ) packed bed permeability (m2 ) drying rate (kg m−2 s−1 ) dry product mass (kg) pressure (Pa) operating total pressure (Pa) heat flux at the vaporization front (W m−2 ) heat flux at the heating wall (W m−2 ) mean void radius of the bed (m)
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t T X Xcr1 Xcr2 z zmax
A. Michaud et al. / Chemical Engineering and Processing 47 (2008) 722–730
time (s) temperature (K) solvent content (kg solvent kg−1 dry product) first critical mean solvent content (kg solvent kg−1 dry product) second critical mean solvent content (kg solvent kg−1 dry product) distance from the heating wall (m) depth of the bed (m)
Greek letters η absolute viscosity (kg m−1 s−1 ) λ thermal conductivity (W m−1 K−1 ) ρ density (kg m−3 ) σ surface tension (N m−1 ) ψ porosity Subscripts b bulk cr critical d dry f hot fluid fin final front vaporization front ini initial l liquid sat saturation tran transition period v vapour vap evaporation wall heating wall
References [1] E.U. Schl¨under, N. Mollekopf, Vacuum contact drying of free flowing mechanically agitated particulate material, Chem. Eng. Process. 18 (1984) 93–111. [2] E. Tsotsas, E.U. Schl¨under, Vacuum contact drying of free flowing mechanically agitated particulate multigranular packing, Chem. Eng. Process. 20 (1986) 339–349. [3] E. Tsotsas, E.U. Schl¨under, Vacuum contact drying of mechanically agitated beds: the influence of hygroscopic behaviour on the drying rate curve, Chem. Eng. Process. 21 (1987) 199–208. [4] D. Farges, M. Hemati, C. Lagu´erie, F. Vachet, P. Rousseaux, A new approach to contact drying modeling, Dry. Technol. 13 (1995) 1317–1329. [5] C. Moyne, Transferts couples chaleur—masse lors du s´echage: prise en compte du mouvement de la phase gazeuse, Th`ese, Institut National Polytechnique de Lorraine, 1987. [6] B. Baillon, S´echage sous vide micro-ondes combin´e de granul´es pharmaceutiques, Th`ese, Universit´e de Pau et des Pays de l’Adour, 1996. ¨ [7] E. Tsotsas, Uber den Einfluß der Dispersit¨at und der Hygroskopizit¨at auf den Trocknungsverlauf bei der Vakuum-Kontakttrocknung rieself¨ahiger Trocknungsg¨uter, Dissertation, Universit¨at Karlsruhe, 1985. [8] M. Kohout, A.P. Collier, F. Stepanek, Mathematical modelling of solvent drying from a static particle bed, Chem. Eng. Sci. 61 (2006) 3674–3685. [9] M. Kohout, A.P. Collier, F. Stepanek, Multi-scale analysis of vacuum contact drying, in: Proceedings of the IDS 2006 B, 2006, pp. 1087–1094. [10] J.F. Nastaj, Vacuum contact drying of selected biotechnology products, Dry. Technol. 12 (1994) 1145–1166. [11] U. Grigull, H. Sandner, in: B. Munz Brienza (Ed.), Heat Conduction, Hemisphere Publishing Corporation, United States of America, 1984. [12] E.U. Schl¨under, W¨arme¨ubergang an bewegte Kugelsh¨uttungen bei kurfristigem Kontakt, Chem.-Ing.-Technol. 43 (1971) 651–654. [13] N. Mollekopf, H. Martin, Zur Theorie des W¨arme¨ubergangs an bewegte Kugelsch¨uttungen bei kurzfristigem Kontakt, VT-Verfahrenstechnik 16 (1982) 701–706. [14] E.U. Schl¨under, Drying of porous material during the constant and the falling rate period: a critical review of existing hypotheses, Dry. Technol. 22 (2004) 1517–1532.