Convective drying of porous material containing a partially miscible mixture

Chemical Engineering and Processing 38 (1999) 487 – 502 www.elsevier.com/locate/cep

Convective drying of porous material containing a partially miscible mixture M.J. Steinbeck * Institut fu¨r Thermische Verfahrenstechnik, Uni6ersita¨t Karlsruhe (TH), D-76128 Karlsruhe, Germany Received 1 April 1999; accepted 12 April 1999

Abstract Non-hygroscopic capillary porous bodies were dried by convection to investigate the influence of a two-phase moisture on the drying characteristics. The samples were wetted with the ternary liquid mixture 2-propanol/water/1-butanol. This system forms two liquid phases at low propanol concentrations. The drying rate is not significantly influenced by a two-phase moisture. Selectivity is influenced by the drying conditions as well as the characteristics of the capillary porous body. In the two-phase region selectivity can be shifted most effectively by the temperature of the drying air and by the pore size of the porous body. Selectivity can even inverted if the initial moisture composition is close to the boundary line. In the porous body a moisture profile, as well as a concentration profile, was measured. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Convective drying; Selectivity; Miscibility gap; Drying rate; Porous material

1. Introduction Drying is not known as the key unit operation in most process lines. However, in a wide range of applications it is used in production or processing, from wheat to white picments, from alfa alfa to zeolithes. Dryers are operated in the food industry, chemical industry and pharmaceutical industry. In many cases, the moisture to be evaporated is not a pure liquid but a mixture of two or more components. In the production of pharmaceuticals, for example, the active agent is often dissolved in a mixture of water and ethanol. Foodstuffs are dried in order to preserve them and to make transportation easier. The moisture in foodstuff, for example, is not only water but also volatiles and flavouring. Thijssen was one of the first who reported the selectivity of drying [1 – 3]. He studied aroma retention

 Dedicated to Professor Em. Dr-Ing. Dr h.c. mult. E.-U. Schlu¨nder on the occasion of his 70th birthday. * Present address: ZT-TE, Bayer AG, Leverkusen, 51368 Leverkusen, Germany. Tel.: +49-214-3055870; fax: + 49-2143050262. E-mail address: [email protected] (M.J. Steinbeck)

during the drying of foodstuff and spray dried a solution of water, alcohol and sugar. The sugar builds a membrane like coating on the surface of the droplets. The small but less volatile water molecules can pass this coating much faster than the more volatile, but larger, alcohol molecules. Thus the evaporation is selective. The less volatile water evaporates preferentially because of the difference in the effective diffusion coefficient in the coating. Thijssen called this phenomenon selective diffusion. Schlu¨nder and Thurner [4–6] thoroughly studied the drying characteristics of porous material wetted with a binary liquid mixture. They demonstrated the dependence of selectivity and drying rate on the drying conditions and the properties of the porous material. The gas-side mass transfer, the liquid-side mass transfer and the vapor–liquid equilibrium govern the selectivity of drying. The drying behavior of material wetted with a ternary mixture was studied by Martinez and co-authors [7–9]. They modeled the evaporation of a ternary, miscible liquid mixture and studied it experimentally. The influence of the transport of gas and liquid in the pores of the material and of the properties of the material itself was not investigated. Pakowski gave an overview of the research on drying of products containing a multicomponent moisture [10].

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M.J. Steinbeck / Chemical Engineering and Processing 38 (1999) 487–502

Aicher et al. studied the evaporation of a ternary liquid mixture, which forms two liquid phases, with respect to drying [11]. Steinbeck and Schlu¨nder continued this work. They first investigated, experimentally and theoretically, the evaporation of a ternary partially miscible liquid mixture [12,13]. The selectivity of the process is controlled by the vapor – liquid equilibrium and the gas-side mass transfer. They carried on the work with studies on the influence of a liquid moisture which forms two liquid phases during the drying process. The present publication continues this work. In order to study the drying of a ternary only partially miscible moisture experiments of convective drying were performed. Bodies of capillary porous material were used for this study. Since not only the moisture content and moisture composition of the remaining moisture is of interest but also the local distribution of the moisture and its composition, such data were obtained by drying, dividing into single layers and analyzing the different layers of a bed of glass beads. The ternary mixture 2-propanol/water/1-butanol was chosen as model moisture. This mixture has a miscibility gap at a low propanol concentration. The component water is a very typical moisture in pharmaceutical industry, food industry and chemical industry. As well as alcohols, which are a typical solvent in pharmaceutical products and foodstuff.

2. Experimental Fig. 1 shows a phase diagram of the ternary system. Depicted are the binodal curves at 293.15 and 333.15 K as well as three tie-lines at 333.15 K. The vapor – liquid equilibrium of the binary systems 2-propanol/water and 2-propanol/1-butanol is also plotted in Fig. 1. To calculate the vapor–liquid – liquid equilibrium the UNIQUAC-equation was chosen. Only the parameters of

the binary mixtures as in [14] were used. This correlation gave reasonable good results in comparison to experimental data [15]. A fitting of the UNIQUAC parameter on the results of evaporation experiments of the ternary mixture was not used. Such a fitting does not improve the vapor–liquid equilibrium if a homogeneous liquid mixture is evaporated. Besides there are in general no such experimental data available in the industrial practice. Since for an industrial application one will only have access to the published data these were used in this study. All further property data were taken as in [16–19]. As porous bodies spheres, cylinders and plates of a porous silicate ceramic (Schumacher Umwelttechnik, Aerolith5) were used. This material is not hygroscopic and has a mean pore size of 20 mm. In order to study the influence of the mean pore size on selectivity plates of porous glass were used. All these plates had a different mean pore size but the same size. Table 1 gives a list of the used samples. A bed of glass beads was used to study the moisture profile and the concentration profile in a porous body. Monodisperse glass beads of a mean diameter of 225 mm were employed to form the bed. To study the drying characteristics for a ternary and partially miscible liquid mixture, single porous bodies were dried by convection in a laboratory scale drying channel. Fig. 2 presents the principle of the measurement. During the course of drying the weight of the sample was measured. Evaluation of the readout of the balance gives the drying rate curve, i.e. the drying rate m; as a function of the relative moisture saturation X/X0. By means of infrared gas analysis the composition of the exhaust of the drying channel was measured yielding the composition curve. This is the composition of the moisture xi as a function of the relative moisture saturation X/X0. The composition of the moisture can also be displayed as a trajectory in a phase diagram.

Fig. 1. Equilibrium of the ternary system 2-propanol/water/1-butanol at 333.15 K, phase diagram at 105 Pa, binodal curves at 293.15 and 333.15 K.

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Table 1 Properties of the samples Material

Form

Diameter (mm)

Length/thickness (mm)

Mean pore diameter (mm)

Porosity

Aerolith Aerolith Aerolith Glass Glass Glass Glass

Sphere Cylinder Plate Plate Plate Plate Plate

63.2 20, 40 70 70 70 70 70

– 100 2, 20 5 5 5 5

20 20 20 130 70 13 1.3

0.37 0.37 0.37 0.29 0.34 0.43 0.44

This form of representation allows us easily to determine if the overall composition of the moisture in the porous body is within the two-phase region. All experiments were performed in a convective drying channel having a cross section of 0.15 × 0.15 m. A schematic diagram of the set-up is illustrated in Fig. 3. As a drying agent ambient air is used. The filter F1 and the adsorber K remove dust and moisture, respectively. Thus, the water content of the air is reduced below 100 ppm volume. The adsorber K1 and K2, which consist of a bed of molecular sieves, are operated alternatively. To regenerate an adsorber air at 550 K is passed through it at countercurrent flow. After the air passes filter F2, which retains fines of the molecular sieve, the air flow rate is adjusted by valve V and measured by an orifice plate flow meter OP. The air is heated to the desired temperature by an electrical resistance heater WH3. In the horizontal drying channel DC the air passes the sample, which is attached to an electrical precision balance B (Sartorius, LC 1200S). Therefore, the weight of the sample can be monitored continuously. The drying agent and the evaporated moisture are mixed thoroughly by a static mixer M at the outlet of the drying channel. A bypass stream of the exhaust is withdrawn and analyzed by an infrared gas analyzer IR (Perkin Elmer, MCS100). This spectrometer measures the concentrations of the components 2-propanol, water and 1-butanol. In order to adjust the concentration of component i y˜i,b in the drying air vapor of component i is injected in the air before it enters the drying channel. All data taken by the balance, the thermocouples and the infrared gas analyzer are recorded by a personal computer. If the drying of a single porous body was performed, the sample was dried in an oven at 400 K for 20 h before starting the drying experiment. Next it was cooled to 300 K in a desiccator. The dry sample was wetted with a liquid mixture at vacuum and heated to wet-bulb temperature. Then the sample was introduced in the drying channel, operating at constant temperature Tb, constant air velocity ub, and constant preloading of the air y˜i,b. Since it is nearly impossible to wet a capillary porous material with a two-phase liquid in a reproducible way, all samples were wetted with an

initial composition just outside the two-phase region. The sample were dried until no change in mass could be observed anymore in the drying channel. The analysis of the data characterizes the drying process completely.

Fig. 2. Principle of measurement.

Fig. 3. Schematic drawing of the drying channel OP orifice plate; F1, F2 filter; F3, F4 flame filter; G1, G2 blower; IR infrared gas analyzer; K1, K2 adsorber; M static mixer; MP membrane pump; DC drying channel; V valve; B balance; WH1, WH2, WH3 heater.

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is a multicomponent mixture, the composition of the moisture, which remains in the product at the end of the drying process, is an imported factor of the product quality. The change of the composition of the moisture is given by the selectivity Si (1)

Si = r; i − x˜i with r; i =

n; i n

% n; j

n

: % r; j = 1

(2)

j=1

j=1

Fig. 4. Drying and shearing device for experiments with a bed of glass beads.

To study the local moisture content and local moisture composition in a porous body, a bed of glass beads was dried. Fig. 4 depicts the container, which was used to hold the bed. The inner cylinder is put together out of five rings. These rings are used to separate the bed in different slices more easily and are held by the outer cylinder. The bottom of the outer cylinder can be moved up and down. Before a drying experiment is started the glass beads are dried in an oven at 400 K for 20 h and cooled in a desiccator afterwards. Next the bed of beads was wetted with a liquid mixture. Always a miscible liquid mixture was chosen. The wetted bed was filled in the rings, which were hold by the cylinder. This set-up was put in an insulating container. In this way the heat flux, which is not directed through the surface of the bed, could be minimized. The probe was placed in the drying channel operating at constant conditions. The drying was interrupted after a set period of time. The cylinder holding the glass beads were taken out of the drying channel. Immediately the bottom of the cylinder was lifted up in five steps. After each step one layer of the bed, defined by all beads in one ring, was sheared from the bed and filled in a glass tube. All five samples were dried by desorption. During the desorption process all liquid evaporated out of the sample was collected in a cold trap at 70 K. Thus, the moisture content and moisture composition of each layer could be analyzed. The desorption procedure is described in detail elsewhere [4,20,21]. By drying a bed at identical conditions for different periods of time and analyzing the moisture content and the moisture composition one will get the drying characteristics of the different layers. Thus, information of the moisture distribution and its local composition is available.

3. Theory If the moisture of a product, which has to be dried,

where the relative molar flux r; i is the quotient of the molar flux n; i of component i versus the sum of all molar fluxes at the gas–liquid interface. If the process is not selective the selectivity is equal to zero. For Si \0 component i evaporates preferentially. The concentration of component i raises in the remaining moisture in case of Si \ 0. By analyzing the drying characteristics of many products different periods can be observed during the course of drying. At high moisture content a period of constant drying rate takes place. This period is called the constant-rate period. Not only the drying rate but also the temperature is constant. The porous body takes up the so called wet-bulb temperature. During this period the mass transport from the surface of the wet porous body is equivalent to the evaporation rate of a free liquid surface of the same geometry and the same drying conditions. The capillaries of the porous material transport as many moisture to the surface of the porous body as can be evaporated. The evaporation rate is determined by the kinetic of the heat and mass transfer and the thermodynamic of the liquid. This drying period was studied intensively in case of a pure moisture. However, a constant rate period is also observed for a multicomponent moisture if drying takes place not selectively. If the capillaries can not anymore transport as many liquid to the surface as could be evaporated based on heat and mass transfer, the wet core in the porous body will shrink. The shrinking wet core has a distinct interface called the drying front. Now the heat and mass transport resistance increases, since the heat as well as the vapor must be transported through the outer dry shell of the porous body. This period is characterized by a decreasing mass transfer rate. The drying rate falls. The period is called falling rate period.

3.1. Wet-bulb temperature The wet-bulb temperature not only exists for a product wetted with a pure liquid but also for a product wetted with a liquid mixture in case of a nonselective drying. In the following outline the analogy of heat and mass transfer is applied and the kinetic

M.J. Steinbeck / Chemical Engineering and Processing 38 (1999) 487–502

of the mass transfer is expressed as a logarithmic function. A more general form are the Maxwell – Stefan equations [22]. However, our studies did show that there is not major difference in the results. Furthermore the necessary self-diffusion coefficients and cross-diffuison coefficients of a multicomponent liquid mixture are not available for the most systems used in the industrial production process. For the calculation of the wet-bulb temperature it was assumed that “ the evaporation rate is much smaller than the mass flow rate of the drying agent. Thus, neither the temperature nor the composition of the drying air changes. “ drying is not selective. “ the liquid-side concentration profile is fully developed. “ there is no change in temperature and no gradient of temperature in the sample. “ thermodynamic equilibrium at the gas –liquid interface. “ the analogy of heat and mass transfer is valid. “ always as many moisture is transported to the body surface as is evaporated. The energy balance of a sample gives q; = % n; j Dh0 v, j.

(3)

j=1

The specific heat flux is expressed as q; = (ac Ka+ ar)(Tb −Twb)

(4)

where ac is the heat transfer coefficient of convection and ar the heat transfer coefficient of radiation. The Ackermann-correction Ka takes into account the energy which is required to head up the evaporated vapor from wet-bulb temperature Twb to the bulk temperature Tb. In case the surface of the sample is much smaller than the surface of the surrounding drying channel, which it can see, ar can be written as (T 4b −T 4wb) (Tb −Twb)

The Ackerman-correction Ka Ka =



(5)



Dh0 v(T wb) c˜ 1 ln 1 + p(T m) (Tb −Twb) 0 c˜p(T m) Dhv(T wb) (Tb −Twb) (6)

is calculated using the mean temperature Tm, the molar heat capacity c˜p and the molar heat of vaporization Dh0 v Tm =

Simplifying the general Maxwell–Stefan equations leads to



n; i = r˜ gbg,ir; i ln



r; i − y˜i, . r; i − y˜i,ph

(10)

This equation describes the gas-side mass transfer rate exact in case one component passes the gas–liquid interface. However, if the diffusion coefficients do not differ in order of magnitude and the concentrations in the gas phase are low, this equation describes the mass transfer rate reasonably well. The composition of the gas phase at the gas–liquid interface is defined by the vapor–liquid equilibrium [14,17] and expressed as: y˜i,ph = gix˜i

p*i p

(11)

Since we assume that drying is not selective, it is (12)

r; i = x˜i

Substituting Eqs. (4), (10) and (12) into Eq. (3) and rearranging yields



r˜ gbg,i ln



x˜i − y˜i,b Dh0 v = (ac Ka+ ar)(Tb − Twb). x˜i − y˜i,ph

(13)

Applying the analogy of heat and mass transfer

3

ar = s o

491

Tb + Twb 2

(7)

ac = r˜ g c˜p,gLe1i4− n bg,i

(14)

with the Lewis-Number Lei,4 Lei4 =



lg k = r˜ gc˜p,gdg,i4 dg,i4



(15)



permits Eq. (13) to be rewritten as Dh0 vln



x˜i − y˜i,b a = c˜p,gLe1i4− n Ka+ r (Tb − Twb) x˜i − y˜i,ph ac (16)

The exponent n results from the Nusselt- and Sherwood correlation. For laminar flow it is equal to 1/3, for turbulent flow n is equal to 0.42 [23,24]. Taking into account that the sum of the molar fraction x˜i of the three components in the liquid mixture is equal to one enables us to solve Eq. (16) for all three components. The solution gives the wet-bulb temperature Twb as well as the composition of the liquid mixture at the gas–liquid interface x˜i,ph. For the bed of glass beads the wet-bulb temperature can be calculated in the same way taking into account the correct kinetic. Since the cylinder is not entire adiabatic, the heat transfer through the isolated walls of the cylinder has to be taken into account in order to calculate the wet-bulb temperature right.

3

c˜p = % r; j c˜pg, j

(8)

Dh0 v = % r; j Dh0 v, j.

(9)

j = 13

j=1

3.2. Constant rate period During the first drying period the sample takes up

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492

the wet-bulb temperature. It is assumed that drying is not selective. Thus, we can fall back on the results of Section 3.1 for the calculation of the drying rate m; . In addition, it is not necessary to calculate the composition of the remaining moisture since it does not change. Substitution of the mass flux m; and Eq. (4) into Eq. (3) yields for the drying rate during the constant rate period m; =

ac Ka+ ar 3

(Tb −Twb)

(17)

% xj Dhv, j

where R is the radius of the porous body and r* the radius of the drying front. It is assumed that an ideal moisture profile is developed inside the porous body. Not only the mass flux has to overcome the transport resistance of the dry shell but also the heat flux. Thus, during the falling rate period the heat flux is expressed as

Bi=

3.3. Falling rate period As soon as the capillaries of the porous material can not any longer transport as many moisture as evaporates during the constant rate period the drying rate decreases. The falling rate period of the drying process has started. The moisture content at the begin of the falling rate period is called the critical moisture content Xcr. Krischer developed the so-called shrinking core model to explain the drying characteristics during the falling rate period [23]. This model was improved by Schlu¨nder [25]. Krischer assumes that the wet core is surrounded by an entire dry shell during the falling rate period and that the wet core always has the critical moisture content. The evaporation takes place at the interface of the wet core and the dry shell. This zone is called the drying front. During the drying process the wet core shrinks and the drying front pulls back to the inner center of the porous body. Thus, the evaporated moisture diffuses from the drying front to the surface of the body and from the surface of the sample to the bulk flow. This extra diffusion resistance has to be taken into account for the calculation of the falling rate period. Consider the series connection of the transport resistances the drying rate can be expressed as



M0 i r˜ g bg,i r; −y˜i,b ln i 1+Bi% f(r*/R) r; i −y˜i,ph



(18)

The Biot number Bi% Bi% =

bg,i R m dg,i4 c

(19)

relates the mass transfer resistance of the dry shell to the mass transfer resistance of the boundary layer of the body. The function f expresses the extent of the dry shell. It is related to the location of the drying front. For a spherical body f is written as R − 1. r* In case of a cylindrical body f is written as

f(r*/R)

sphere

f(r*/R)

cylinder

=

= ln

(22)

with the Biot-number Bi

j=1

m; =

a (Tb − Tph) 1+ Bi f(r*/R)

q; =

 R r*

(20)

(21)

aR ls

(23)

which relates the inner to the outer heat transfer resistance. To calculate the drying rate of the falling rate period, one needs not only the equations of heat and mass transfer but also a model of the composition of the evaporating moisture and a model of the motion of the drying front. Schlu¨nder lined out that Eqs. (20) and (21) model the location of the drying front only in case of an ideal moisture profile in the porous body [25]. To express the drying characteristics right a correction function has to be introduced. Schwarzbach [26] has picked up this idea and suggested for a spherical body r* = R

' 3



X (1−(X/Xkr))nˆ exp 3nˆ Xcr



(24)

A analogous equation can be written for cylindrical bodies. The correlation expresses the mass transport as a series and parallel connection of transport resistances. In Eq. (24) the parameter nˆ describes the velocity of the drying front. For nˆ = 0 the drying front is static. The evaporation takes place exclusively at the surface of the body. No falling rate period is observed. In case of nˆ “ the velocity of the drying front reaches its maximum. During the falling rate period no capillary transport takes place. Drying of a multicomponent moisture is selective during the falling rate period. The diffusion in the liquid-side boundary layer, the diffusion of the gas phase in the dry pores, the diffusion at the surface of the sample and the vapor–liquid equilibrium govern the selectivity of the drying process. If the moisture consists of a not miscible mixture and forms two liquid phases, the different wettabilities of the two liquid phases inside the porous material as well as the time, in which the liquid–liquid equilibrium is developed, are of interest. An exact model of the combination of all those mechanism is not yet available. Data of diffusion coefficients of multicomponent liquid mixture are rare, especially near the binodal curve, not of the necessary accuracy or in most cases even not available. To characterize the porous material there is a lack on data on porosity, wettability inside the porous and permeability.

M.J. Steinbeck / Chemical Engineering and Processing 38 (1999) 487–502

This is the case in particular for all products in industry. A simple model of the drying behavior can reach good results as long as the selectivity is not dominated by the two-phase characteristics. The following assumptions are made: “ Vapor–liquid equilibrium at the gas – liquid interface. “ Liquid–liquid equilibrium at the liquid – liquid interface. “ An effective diffuison coefficient is applied for the diffusion inside the porous. “ No gradient of temperature in the wet core. Solving of the material balance at the vapor –liquid interface for all components and for component i gives dNl dx˜i = . Nl r; i − x˜i

(25)





The liquid-side mass transfer is expressed as r; −x˜i,ph n; i = r˜ l bl,ir; i ln i r; i − x˜i

Since the inert component of the gas phase is dominant, the gas-side mass transfer is written as (27)

Application of Eqs. (2) and (11) and rearranging Eqs. (26) and (27) yields

r; 1 =



r; 2 =





         



r˜ bg,i4Aph N: g

(32)

The gas-side mass transfer coefficient describes the different diffusion velocities of the components i and j in the gas phase. NTU is the number of transfer units in the gas phase. The vapor-liquid equilibrium at the gas–liquid interface is expressed as aij =

gi(x˜ ph)p*i y˜i,ph x˜j,ph = gj(x˜ ph)p*j y˜j,ph x˜i,ph

(33)

For further details of the selectivity of a evaporation process see [13,19,21,28]

To guarantee that the moisture distribution and the local composition of the moisture is equal for all experiments, the porous bodies were wetted with a completely miscible liquid mixture. Since drying is selective this approach enables to study the drying of a moisture, which forms two liquid phases. Fig. 5 depicts the

(29)





6l n; = exp − bl,i r˜ l bl,i



=

r; i −x˜i r; i −x˜i,ph

(30)

is the liquid-side mass transfer coefficient. For Kl,i = 1 the liquid-side mass transfer resistance is negligible. No liquid-side concentration profile is developed. For Kl,i “0 the evaporation is not selective. The gas-side mass transfer is written as Kg,ij =

NTUg,i4 =

Kl,2 −1 Kg,23 1 r; 2 + x˜2 Kl,2 Kl,2 a23 Kl,1 −1 a23 Kl,2 − 1 1 1 r; 1 + x˜1 + −1 r; 2 + x˜ + 1 Kl,1 Kl,1 Kl,2 Kl,2 2 Kg,23



This set of two equations allows us to calculate the relative molar flux r; i and the selectivity of the process. Substitution of Eqs. (28) and (29) into Eq. (27) gives the molar flux of the selective drying process. In Eqs. (28) and (29) Kl,i =exp −

with

(28)



a13 −1 Kg,13

(31)

Kl,1 −1 1 Kg,13 r; + x˜ a13 Kl,1 1 Kl,1 1 Kl,1 −1 1 a23 Kl,2 − 1 1 r; 1 + x˜ + −1 r; 2 + x˜ + 1 Kl,1 1 Kg,23 Kl,2 2 Kl,1 Kl,2



a13 −1 Kg,13

NTUg,i4 + 1 NTUg, j 4 NTUg,i4 NTUg, j 4 + 1

4. Results (26)

n; i = r˜ g bg,i (y˜i,ph −y˜i,b).

=

493

y˜i,ph −y˜i,in y˜j,out −y˜j,in y˜i,out −y˜i,in y˜j,ph −y˜j,in





trajectories of drying experiments at six different initial compositions in a phase diagram. The trajectories of the initial compositions A and B pass by the two-phase region on the right. The trajectory of the initial composition F passes by the two-phase region on the left. However, the two-phase region is crossed by the trajectories of drying of initial compositions C, D and E. During the course of drying the overall composition of the moisture is within the two-phase region. Two liquid phases will be formed if the moisture is a free liquid. Thus, this experimental procedure is suitable to study the drying characteristics of a two-phase moisture. Those experiments were performed by drying porous spheres of a diameter of 63 mm at 333 K and an air velocity of 0.2 m s − 1. Analyzing the course of the trajectories one observes that the trajectories show two different main directions. The trajectories of the experi-

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M.J. Steinbeck / Chemical Engineering and Processing 38 (1999) 487–502

Fig. 5. Trajectories of drying for 6 different initial compositions A-F at Tb =333 K, ub =0.2 m s − 1, spheres of Aerolith, dp =63 mm.

ments with a high initial butanol content end in the butanol corner. However, the trajectories of drying started with a high initial water content end in the water corner. A boundary line separates the phase diagram into two areas and crosses the two-phase region. The course of the boundary line depends on the drying conditions. It is close to initial composition D for the drying conditions of the experiments depicted in Fig. 5.

4.1. Influence of temperature The drying rate depends strong on the temperature of the drying agent, see Eq. (17), during the constant rate period as well as the falling rate period. Thus, increasing the air temperature results in an increasing drying rate during the entire drying process. This is shown in Fig. 6, which depicts the drying rate curves of three experiments. Spheres of 63 mm in diameter were dried at different temperatures, 333, 353 and 373 K (ub = 0.2 m s − 1). After an initial period the drying rate is constant. The constant rate period ends at a relative moisture content of 0.5, the critical moisture content of this drying process. During the following falling rate period the drying rate decreases more and more. For a spherical body, as used for these experiments, the drying rate reaches zero if the moisture content tends towards zero. As it is predicted by theory the drying rate increases with raising air temperature during the constant rate period as well as the falling rate period. Increasing the air temperature by 40 K from 333 to 373 nearly doubles the drying rate. Not only the drying rate depends on the air temperature but also the selectivity of the drying process. The gas-phase concentration of the evaporating moisture at the gas–liquid interface is governed for a multicomponent liquid mixture not only by the composition of the moisture but also by the temperature. The influence of temperature on selectivity is expressed by Eq. (33),

which considers the saturation pressure p*i and the activity coefficient gi. The influence of temperature is particularly strong in the two-phase region near the boundary line. Fig. 7 presents the influence of temperature on selectivity. Depicted are the trajectories of drying experiments in a phase diagram. The experiments (spheres, dp = 63 mm, ub = 0.2 m s − 1) were performed with two initial compositions, A and D, at different temperatures, 333, 353 and 373 K. The temperature not influences the selectivity significantly, if the trajectories not cross the two-phase region near the boundary line. See initial composition A. The trajectories, which cross the two-phase region near the boundary line, depend on the air temperature. See initial composition D. At low temperature (333 K) the middle-boiling solvent water is evaporated preferentially. The trajectory ends in the butanol corner. With rising temperature the selectivity is more and more shifted towards a preferential evaporation of the high-boiling solvent 1-butanol. The selectivity is inverted with increasing temperature. The trajectories end in the water corner at high air temperature (353 and 373 K). Therefore, it is possible to control

Fig. 6. Influence of air temperature Tb on drying rate, spheres of Aerolith dp =63 mm, x1,0 =0.21, x2,0 =0.51 (D), ub =0.2 m s − 1.

M.J. Steinbeck / Chemical Engineering and Processing 38 (1999) 487–502

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Fig. 7. Influence of air temperature Tb on trajectories of drying, spheres of Aerolith, dp =63 mm, x1,0 =0.21, x2,0 =0.51 (D), x1,0 = 0.21, x2,0 =0.30 (A), ub =0.2 m s − 1.

Fig. 8. Influence of air temperature Tb on trajectories of drying, spheres of Aerolith, dp =63 mm, x1,0 =0.21, x2,0 =0.51 (D), ub =0.2 m s − 1, experiments: symbols, calculation: bold lines.

the composition of the moisture, which remains in the product at the end of the drying process, by changing the temperature of the drying agent in case the composition of the moisture is within the two-phase region near the boundary line. This behavior is correctly described by the model presented in Section 3.3. Fig. 8 depicts the results of the experiments of initial composition D. Furthermore, calculated trajectories are depicted. The effective diffusion coefficients were fitted to the experimental results at 333 K. This model is capable of describing the temperature dependence of the selectivity of the drying process reasonably well. However, the trajectories for drying are not only dependent on the vapor–liquid equilibrium but also the liquid-side and gas-side mass transfer resistance. This follows from comparson of Fig. 8 and Fig. 9. The later one presents trajectories calculated for the evaporation of a free

liquid surface. Liquid-side mass transfer resistance is negligible, and the number of transfer units is set to infinity. That means, the evaporation process is governed by thermodynamic and not by gas-side kinetic. The trajectories for the thermodynamically governed evaporation also depend on temperature. However, the course is quite different from that of the drying processes, which are governed not only by thermodynamics, but also by kinetics.

4.2. Influence of air 6elocity A rising air velocity results in an increasing heat and mass transfer from the surface of the sample to the bulk flow and vice versa. Since the drying rate is governed by these transport mechanisms during the constant rate period, it enhances with rising air velocity. As soon as

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Fig. 9. Influence of temperature Tb on trajectories of evaporation at different temperatures, Tb =298, 333, 373 K, calculation at NTU “ .

the drying front pulls back from the surface to the center of the sample, the heat and mass transfer resistance of the outer dry shell influences the drying char-acteristics as well and increases with the drying front pulling back. Thus, the overall heat and mass transfer is more and more determined by the resistance of the dry shell. An increasing air velocity does not improve the transfer in the dry shell significant. Therefore, the influence of the air velocity on the drying rate diminishes with decreasing moisture content. The drying rate curves, plotted for different air velocities, are equal at low moisture content. The drying rate is independent of the air velocity at the end of the falling rate period. Fig. 10 shows the drying rate curves at three different air velocities, 0.1, 0.2 and 1 m s − 1 (spheres, dp =63 mm, Tb =333 K). During the constant rate period the drying rate increases with rising air velocity, The difference in the drying rate decreases with decreasing moisture content during the falling rate period. All three curves are identical and independent of the air velocity at low moisture. Since the trajectories of initial composition D cross the two-phase region at low moisture content and the one of initial composition B does not and the drying rates of all three experiments are equal at low moisture content, it follows that the two-phase liquid moisture has no significant influence on the drying rate for the applied conditions. The selectivity of the drying process is slightly influenced by the air velocity as well. Fig. 11 shows the experimental results as well as the calculated trajectories for initial composition D and B at different air velocities. If the moisture not separates into two phases (initial composition B) no significant influence of the air velocity on selectivity was observed. However, a slightly influence of the air velocity on selectivity is obtained for the drying of samples, of those the trajectories of the drying process cross the two-phase region and are in the vicinity of the boundary line (initial composition D).

Most of the moisture is removed without a significant difference in selectivity. Finally, 1-butanol is retained preferentially at low air velocity. Water is retained preferentially at high air velocity at low moisture content (X/X0 B 0.05). Those experimental results are described by the model by only fitting the parameter to one experiment.

4.3. Influence of preloaded drying agent The study of the influence of a moisture component, which is injected as vapor in the drying air, is done on the premiss that the dew point of the drying agent is always above the wet-bulb temperature of the sample. Hence, the concentration of the moisture component in the drying agent is so low that condensation never occurs. Drying rate as well as selectivity are a function of the composition of the drying agent (see Eq. (16) and Eq. (27)). If the drying agent is not a pure inert gas but an inert gas loaded with a component of the moisture of the

Fig. 10. Influence of air velocity ub on drying rate, spheres of Aerolith, dp =63 mm, x1,0 =0.21, x2,0 =0.51 (D), x1,0 =0.21, x2,0 = 0.40 (B), Tb =333 K.

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Fig. 11. Influence of air velocity ub on trajectories of drying, spheres of Aerolith, dp =63 mm, x1,0 =0.21, x2,0 =0.51 (D), x1,0 =0.21, x2,0 = 0.40 (B), Tb = 333 K, experiment: symbols and light lines, calculation: bold lines.

sample, the concentration gradient of this component at the gas–liquid interface in the gas phase is reduced. Hence, the mass transfer of this component in the gas phase is reduced. This leads to a reduced drying rate. Also selectivity is influenced. The component of the moisture, which is present in the drying agent, is retained in the sample. In a phase diagram, the trajectories are shifted towards the component, which is present in the drying agent. This occurs for trajectories crossing the two-phase region as well as for those passing by this region. However, selectivity can be inverted by adding a component to the drying agent for those compositions, of those the trajectories cross the two-phase region and are in the vicinity of the boundary line. Fig. 12 depicts the composition curves for two drying experiments, one using inert air as drying agent, one using air preloaded with water (y˜2,b =0.03, cylinders, dp = 20 mm, Tb =333 K, ub =0.2 m s − 1, initial composition C). The composition curve depicts the concentration of the component i in the moisture versus the relative moisture content. Drying is nearly not selective until 70% of the moisture is removed. The 1-propanol content of these experiments is not significantly dependent on the preloading of the drying agent. The water content of the remaining moisture is increased slightly and the butanol content is reduced slightly during drying with preloaded air until 90% of the moisture is evaporated. At low moisture content the concentration of the evaporating components at the surface of the porous body is reduced due to the increased transport resistance. Thus, the concentration gradient, which is already reduced due to the preloaded air, decreases further. The selectivity is shifted towards a preferential evaporation of the component, which is not present in the drying agent. In case of a moisture composition within the two-phase region in the vicinity of the boundary line, as it is in Fig. 12, the selectivity is

inverted at low moisture content. This shift of selectivity can be increased by rising the concentration of the component, which is present in the drying air.

4.4. Moisture distribution in porous material Analyzing the moisture distribution of a wetted bed of glass beads after different periods of drying allows to study the local moisture content and composition. The drying characteristics of the bed is comparable to the one of a single porous body. After a starting period the bed dries at constant drying rate until 80% of the moisture is removed (X/X0 = 0.2). During the following falling rate period the drying rate decreases. See Fig. 13, which depicts the drying rate curve of a bed (dp = 225 mm, Tb = 333 K, ub = 0.2 m s − 1, initial composition D). The matching moisture content of the five layers of the bed is displayed in Fig. 14 at different time periods. The five layers are plotted on the ordinate in form of the depth of the bed measured from its upper

Fig. 12. Influence of preloading of drying air on composition curve, cylinders of Aerolith, dp =20 mm, x1,0 = 0.21, x2,0 =0.46 (C), Tb = 333 K, ub =0.2 m s − 1.

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Fig. 13. Drying rate curve for a bed of glass bead, Tb = 333 K, ub = 0.2 m s − 1, x1,0 =0.21, x2,0 = 0.51 (D), dp = 225 mm.

Fig. 14. Moisture distribution in a bed of glass beads, depth 0 is the gas–solid surface, Tb = 333 K, ub = 0.2 m s − 1, x1,0 = 0.21, x2,0 = 0.51 (D), dp =225 mm, time of drying: ( ) 15 min; ( ) 45 min; () 90 min; (") 135 min.

surface. This is the surface in contact with the gas phase, where heat and mass transfer takes place. In the upper layers the moisture content is reduced much

Fig. 16. Local composition in a bed of glass beads, depth 0 is the gas – solid surface, Tb =333 K, ub =0.2 m s − 1, x1,0 =0.21, x1,0 = 0.51 (D), dp =225 mm, time of drying: all-clear symbols: water: () 0 min; () 15 min; ( ) 90 min; all-dark symbols: 2-propanol () 0 min; ( ) 15 min; ( ) 90 min.

faster than in the lower layers. A moisture profile is developed in the bed. However, the capillaries still transport as many moisture to the surface of the bed as can be evaporated there based on heat and mass transfer. Thus, the constant rate period continues while the moisture content is reduced significantly. A comparison of Figs. 13 and 14 shows that a relative moisture content of 0.2 in the upper layer is sufficient to maintain a constant drying rate. This mechanism was theoretically analyzed by Schlu¨nder [27]. In Fig. 15 the trajectories of different initial compositions are plotted in a phase diagram. The symbols represent the composition of different layers at different drying times. Plotted are the result of the infrared gas-analysis (bold line) as well for initial composition D. No significant difference in the compositions of the individual layers is observed for a one-phase moisture. If the moisture forms two phases, the composition of

Fig. 15. Trajectories of drying for a bed of glass beads, Tb = 333 K, ub = 0.2 m s − 1, x1,0 =0.21, x2,0 =0.51 (D), x1,0 =0.21, x2,0 = 0.30 (A), dp =225 mm, IR-analysis: bold line, desorption of single layers: symbols.

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Fig. 17. Influence of large body size on composition curve, cylinders of Aerolith, dp =20, 40 mm, x1,0 = 0.21, x2,0 = 0.51 (D), Tb =333 K, ub =0.2 m s − 1.

Fig. 18. Influence of large body size on the composition curve, plates of Aerolith dp =2, 20 mm, x1 = 0.21, x2 = 0.51 (D), Tb = 333 K, ub =0.2 m s − 1.

the top layer is quite different to those of the other layers. The composition of the different layers is presented in Fig. 16. The depth is plotted versus the mass fraction for two components of the moisture at three different time periods. The solid – gas interface at the surface of the bed corresponds to penetration depth of zero. During the starting period 2-propanol evaporates preferentially, the water content keeps constant, the 1-butanol content increases slightly. A concentration profile is developed. At low moisture content (X/X0 = 0.4, t= 90 min) the composition is nearly identical in the deeper layers. Since most of the moisture remains in those layers they determine the overall moisture composition. Thus, the trajectory of the overall composition matches nearly those of the deeper layers (layer: 3–5, depth: 4–10 mm)

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the penetration depth of the concentration profile in the moisture to the characteristic length of the body. If the penetration depth of the concentration profile in the liquid phase is smaller than the characteristic length of the porous body by an order of magnitude, the body size has no influence on the drying characteristics. A constant concentration profile is formed in the liquid phase during the constant rate period. Drying is not selective for this period. Due to different body sizes the heating-up is different while the body dries in the falling rate period. This results in a slightly different selectivity since it depends on the vapor–liquid equilibrium, which depends on temperature. Fig. 17 shows the composition curves of two experiments performed at identical conditions (Tb = 333 K, ub = 0.2 m s − 1, initial composition D). Cylinders of a diameter of 20 and 40 mm were dried. Within experimental accuracy no difference in selectivity was observed. If the penetration depth of the concentration profile in the liquid phase and the characteristic length of the porous body are in the same order of magnitude or if even the later one is the smaller, the body size governs selectivity. In this case no constant concentration profile is formed. No constant rate period occurs. Drying is selective right from the beginning. Thermodynamic and kinetic of the gas-side mass transfer determine the selectivity. In some cases the selectivity can be inverted by choosing the characteristic length of the sample. Fig. 18 depicts the composition curves of a sample with a large characteristic length (plate of 20 mm thickness) and of a sample of a small characteristic length (plate of 2 mm thickness). Both samples were dried at the same conditions (Tb = 333 K, ub =0.2 m s − 1, initial composition D). The drying characteristics of the thick plate show a constant rate period. The moisture is evaporated non selectively until 60 per cent of the moisture is evaporated (X/X0 = 0.4). Finally propanol and water are evaporated preferentially. For this experiment the moisture composition is within the two-phase region from a relative moisture content of 0.2. The thin plate shows an opposite characteristic. No constant rate period occurs. It dries selectively right from the beginning. The moisture forms two phases already at a relative moisture content of X/X0 =0.8. During the entire drying process 2-propanol and 1-butanol evaporate preferentially. Water remains in the sample most. Selectivity is inverted compared to the thick plate for this initial composition D, of whose the trajectory crosses the two-phase region, due to the different characteristic length.

4.6. Influence of pore size 4.5. Influence of body size Selectivity of a drying process of a non hygroscopic capillary porous body depends strongly on the ratio of

In case of a one-phase liquid mixture the pore size has no significant influence on selectivity. The gas-side heat mass transfer is not influenced by the pore size.

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Fig. 19. Influence of pore size on the trajectories of drying, plates of porous glass, dp =70 mm, sp =5 mm, x1,0 =0.21, x2,0 =0.51 (D), x1,0 = 0.21, x2,0 =0.30 (A), Tb = 333 K.

The liquid-side mass transfer resistances is not as well. However, if the moisture in the capillaries of the porous body forms two liquid phases, the pore size has a significant influence on selectivity. The liquid phases are different in their density and wettability. If the two liquid phases are not in liquid – liquid-equilibrium, the compositions of the gas phases at the vapor – liquid interfaces depend on which of the two liquid phases forms the vapor–liquid interface. Most important are the pore structure and the wettability. Thus, selectivity can be controlled by choosing the pore size and the wettability in the pores of the material. The influence of the pore size on selectivity is presented in Fig. 19 displaying the trajectories of drying in a phase diagram. Different plate of porous glass were dried at identical conditions (Tb =333 K, ub =0.2 m s − 1, initial composition A and D). The size of the plates is the same but they differ in the mean pore size (see Table 1). For initial composition A no difference in the trajectories was observed. These trajectories do not cross the two-phase region. The pore size does not influence selectivity. The trajectories of initial composition D cross the two-phase region. The liquid forms two liquid phases. Selectivity depends strong on the pore size of the sample. Striking is the dividing of the trajectories into two distinct classes. The trajectories of drying of the samples with a small mean pore diameter are equal. 2-propanol and water evaporate preferentially. Thus, the phase, which is rich in water, evaporates preferentially. The samples with a large mean diameter dry nearly with no change in the ratio of water to 1-butanol. The component 2-propanol evaporates preferentially. Thus, if the moisture forms to liquid phases, selectivity and,thus, the composition of the remaining moisture can be controlled by the mean pore size.

5. Conclusion Convective drying of porous body wetted with a ternary and partially miscible mixture was investigated. The ternary system 2-propanol/water/1-butanol was used as moisture. If the moisture of a product, which has to be dried, forms two liquid phases during the drying process the two-phase moisture does not significantly influence the drying rate. Raising temperature as well as air velocity increases the drying rate during the constant rate period. During the falling rate period only increasing the temperature raises the drying rate. A relative moisture content of 0.2 at the surface of the porous material is enough to transport so many liquid to the body surface as is necessary to maintain a constant drying rate. Two liquid phases have a strong impact on selectivity of drying. Selectivity can be controlled effectively by air temperature and preloading of the air. The body size influences selectivity if the characteristic length of the porous body is smaller as the penetration depth of the concentration profile in the liquid phase. For a composition of the moisture outside the two-phase region the pore size has no influence on selectivity. In case of a two-phase moisture selectivity and, thus, the composition of the remaining moisture depend on the characteristic of the porous material and can be controlled, for example, by the mean pore size. If the moisture forms to liquid phases, several parameters of the drying process can be adjusted to control selectivity and, thus, the quality of the product. 6. Nomenclature aij A

thermodynamic separation factor area (m2)

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c˜p d f Dh0 v m; N n; N: g p pi q; r R r; i s Si t T u xi x˜i X y˜i

molar specific heat (J mol−1 K−1) diameter (m) function molar heat of vaporization (J g−1) mass flux, drying rate (g m−2 s−1) molar quantity (mol) molar flux per unit area (mol m−2 s−1) molar flow rate of the inert gas (mol s−1) total pressure (Pa) partial pressure (Pa) specific heat flux (J m−2 s−1) radius (m) radius of the outer diameter (m) relative molar flux of component i thickness (m) selectivity (-) time (s) temperature (K) velocity (m s−1) mass fraction of component i in the liquid phase mol fraction of component i in liquid phase moisture content (kg moisture/kg dry material) mol fraction of component i in gas phase (-)

Greek letters a heat transfer coefficient (W m−2 K−1) b mass transfer coefficient (m s−1) g activity coefficient dg,i4 diffusion coefficient in gas phase (m2 s−1) o emissivity k thermal diffusivity (m2 s−1) l thermal conductivity (W m−1 K−1) m tortuosity molar density (mol m−3) r˜ s Stefan–Boltzmann constant (W m−2 K−4) c porosity Subscripts 0 1 2 3 4 b c cr g

initial 2-propanol water 1-butanol air bulk convection critical gas

in l m out p ph r s wb

inlet liquid mean outlet particle, pore interface radiation solid wet bulb

Superscripts * n nˆ

saturation, drying front exponent exponent

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Dimensionsless numbers Bi Biot number of heat transfer Bi% Biot% number of mass transfer Le Lewis number Kg gas-side kinetic coefficient Kl liquid-side kinetic coefficient Ka Ackermann correction NTU Number of transfer units

Acknowledgements This publication is part of a research project supported by the Forschungsvereinigung fu¨r Luft- und Trocknungstechnik (FLT), sponsored by the Bundesministerium fu¨r Wirtschaft (AIF-Nr. 11360N/1).

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