cQ3wm9183 13.w + .a, Pergmon Press Ltd.

DRYING OF POROUS GRANULAR MATERIALS

ANDERS HALLSTRoM* and ROLAND WIMMERSTEDT Department of Chemical engineering, Lund University, Lund, Sweden

(Received 25 January 1983; accepted 9 February 1983)

Abstract-Drying characteristics have been measured for two types of granular compound fertilizer and for granular mono calcium phosphate. Au was forced through a fixed bed, and the humidity of the air leaving the bed was analysed by means of an infrared photometer.

All results confirm the assumption of vapour diffusion as the rate determining mechanism. Experiments with varying temperature and air humidity show that the dependence of the drying rate on those parameters may be calculated from the sorption isotherms. These were measured for all three materials. Experiments also show that the drying rate is inversely proportional to the granule radius squared.

A shrinking core model was successfully used for predicting the drying behaviour of two of the materials. FOI the third material the drying rate fell rapidly, and the shrinking core model was used with a correction function

lNTROOtlCTlON

The purpose of this contribution is to clarify the drying process for three types of porous granular bulk materi-

als. They are all industrially dried with low thermal efficiency in rotary driers. The low moisture content and the significant hygroscopicity of the materials make process optimization difficult.

Most reports on drying experiments describe fun- damental work on uniform, inert and we!l-defined materials. In this article we present an example of work on more complicated materials. It has still been possible to obtain adequate drying data, and to correlate them to a simple mathematical model. We have used a shrinking core model based on a vapour pressure driving force.

The drying rate data presented in the article will be used for process optimization, as indicated in Ref. [l]. The objective is to lower the energy demand of industrial dryers.

MATIUZMATICAL MODEL

The shrinking core or receding front model is well- known in different chemical engineering applications. It assumes that the processed material consists of a shell of converted matter, and a core, as yet unaffected by the process. Applied to drying, the moisture concentration in the core is maintained at the initial value, X0. The shell concentration, X,*, is taken to be in equilibrium with the bulk air humidity. For a sphere, the average concen- tration may be calculated from

x-x* 1 A=7 x0-x0* i

in which 5 is the ratio between the sphere radius and the radius of the core. The drying rate per surface area is calculated as the pseudo stationary diffusive vapour flux to the surface from the receding interface between the zones:

*Author to whom correspondence should be addressed.

Ap, = P ln((P - p,)/(P - p z,)) is the driving force. p *, is the equilibrium vapour pressure in the core, and p,,.” is the partial pressure of water vapour in the air bulk. By means of a mass balance f may be eliminated, and eqns (1) and (2) combine to give

dX 3M _=__w dt

(3)

In eqn (3) external mass transfer resistance is neglected. This is an undisputable approximation for the materials in question in any convective drying operation. Fur- thermore, for the relatively dry materials investigated in

this work, temperature gradients may be neglected within the granules.

Shrinking core drying models have been used in the literature in a number of cases. Garside et nl. 121 employed an integrated version of eqn (3) for evaluating diffusivities. Werling [3] used the model for adsorption on molecular sieves. Schliinder et al. [4-71 included external film transfer resistance as well as heat flow from the air bulk to the core. They also multiplied the non- dimensional concentration term on the r.h.s. of eqn (3) by a correction function, which varied with the non- dimensional concentration. The shrinking core concept has also been used for freeze drying [B].

Even though the shrinking core model may seem very crude, it has a sound theoretical foundation. Garside showed that the important transport mechanism in a material very similar to those investigated here, is vapour phase diffusion [2]. If the material can be treated as a

homogeneous continuum, the following equation applies for a sphere.

M, ap_ ax M, 1 a E~~+P~-~=N,T&T;~;~; [

r2-apw P W-PJ ar 1 ’

(4)

The first term may be neglected. The equation is soluble if local equilibrium is assumed. Then the sorption iso therms determine the relationship between X and pw.

1507

1508 A. HALLSTIC& and R. WIMMERSTKIT

Figure 1 shows moisture profiles in a spherical granule after 15 minutes of drying for three different sorption isotherms, obtained by numerical solution of eqn (4). Temperature has been assumed to be constant. Typical values of parameters for a compound fertilizer at 95°C have been used. A steep profile is generated by sorption isotherm u, which is characterized by a’X/apW2 > 0. This isotherm is favourable for desorption. The drying process may, in this case, be well described by the shrinking core model. However, if an effective diffusivity were to be evaluated from a drying curve, the shrinking core model would not yield the same result as the exact eqn (4) solution. This is partly due to deviation from rectangular profiles, partly because the transient terms are neglected in the shrinking core model. The dis- crepancy has been found to be around ten per cent for the materials in question.

For a linear isotherm, eqn (4) can approximately be rewritten as Fick’s second law, so the isotherm b solu- tion resembles the solution of the “ordinary” diffusion equation. Isotherm c gives a flattened moisture profile. This isotherm is favourable for adsorption, and makes it possible to use the shrinking core model for that process.

DIBCRIPTION OF MATERIALS

Some data on the investigated materials are shown in Table 1. All three materials are dried industrially in rotary driers, in granulation-drying plants with recir- culation of solids. Samples to be dried in the experimen- tal equipment were taken out wet from the process, i.e. before the material entered the drying drums. The granules were screened after having cooled down to about 10°C. Experiments were carried out on material that was between four day and two weeks old.

EQUILIBRIUM DATA

Sorption isotherms were measured for all three materials. Small samples were placed in desiccators, and the weights of the samples were monitored as the water vapour pressure in the desiccators was varied. The pres- sure was controlled by saturated salt solutions. To decrease equilibration time, the air was evacuated from the desiccators. Five isotherms were measured between 30 and 90°C.

Special attention was focused on the high moisture content region. A V&ala HMI-HMP 14 instrument was used to register relative humidity over moist material between 25 and 80°C. A small container with about 5grams of granules was screwed directly onto the measuring probe and placed in a heating chamber.

The resulting curves for the fertilizer NPK 167-13 are shown in Fig. 2. The isotherms have the same ap- pearance for all three materials, although the isotherms for mono calcium phosphate (MCP) are even more favourable for desorption than those of the fertilizers. In general there was good agreement between adsorption and desorption. However, both fertilizer types showed considerable hysteresis at 60°C and above. This was attributed to irreversible changes in the materials, caus- ing loss of ammonia and water.

Despite complicating factors such as the apparent hysteresis, the general form of the curves is clear. The equilibrium relative humidity at the plateau is known with an accuracy between -C 2 and * 5% RH. It should be noted, that it is the plateau which determines the over-all driving force for vapour diffusion. Furthermore, the temperature dependence of the moisture content in the low RH region, as shown in the figure, is qualitatively ascertained, although the exact values are difficult to establish.

usl 05 1.0 1.5

RADIUS, m m

Fig. 1. Moisture profiles in a granule during drying. The profiles were calculated from eqn (4) employing a computer program presented in ref. [3]. Three different sorption equilibria were used, corresponding to those in the

sorption isotherm diagram. A first order boundary condition was used: X = 0.00015, r = R.

Drying of porous granular materials 1509

Mater1 a1 Table 1.

MCP l4onr.l calcium Full compound Full cowound phosphate fertilizer fert~llzer Ca Oi*P0*)2.1 Ii20 NPK 12-g-16 NPK M-7-13

technical

Provided by Boliden Ken1 AB supra AB Supra AB ;:;;;;gborg Landskrona Landskrona

Sweden Sweden

Granule diameter Of product fraction. awn l-2 2-4 2-4

Typical nwlsture content before and after industrial 0.08, 0.04 0.02. 0.01 0.015. 0.005 drying, kg/kg

Granule density, kg/m' 2000 1600 1600

Granule porosity 1) 0.12 0.10-0.14

Average pore 1j 300 1000 diameter, nm

1) Fran mercury porasimetry measurements.

The heat of sorption was calculated applying the tween 2100 and 600 kJ/kg H20. Mono calcium phosphate Clausius-Clapeyron equation to the high moisture con- generates an equilibrium relative humidity that is lar- tent region. For the fertilizers, the heat of sorption was ger-around 80%--and much less temperature dependent found to vary between 300 and 1700kJ/kg HzO. The first than those of the fertilizers. Thus the heat of sorption is value is valid at 30°C. the second one at 90°C. This much smaller, and may be neglected in practical cal- corresponds to an effective heat of vaporization of be- culations.

1, I I I

42 Q.1 a6 96 RELATIVE HUM1 DITY

Fig. 2. Sorption isotherms for fertilizer NPK l&7-13.

15 10 A. HALLSTR~Y and R. WIMMERSTEDT

ROTAMETER

DETECTOR IR CELL

INFRARED

PHOTOMETER

\ ,c I& ,_~$I~TIONED

Fig. 3. The experimental equipment.

DEW-POINT

METER

L

DRYING RATE EXPRRIMRNTS

In the experimental equipment shown in Fig. 3, air with controlled temperature and humidity was forced through a fixed bed of granules. The diameter of the bed was 1OOmm and the weight of the sample was lO& 150grams. By varying the superficial velocity from normal 0.1 m/s, it could be concluded that the bed could be treated as differential. The air leaving the bed entered a Wilks Miran infrared transmission photometer after it had been brought to constant temperature. The air left the equipment through a rotameter.

The IR photometer had a cell length of 0.5 m and measured absorbance by water vapour at a wavelength of 2.6 or 2.67 Wm. It provided an accurate and selective method of air humidity analysis. The total time of res- ponse from bed to signal was less than 3 seconds. An EG t G cooled mirror dew-point meter was used for cali- bration.

Only isothermal runs were performed. The sample holder was placed in an isothermal chamber. The tem- perature above the bed was measured and found to remain at essentially the same level throughout each experiment. Before drying, the samples were heated for 8 minutes in a sealed vessel and in that way reached the desired temperature.

During the drying process, the IR absorbance was registered. Knowing the air humidity increase over the bed, the drying rate was given by a mass balance. Numerical integration of the drying rate gave the mois- ture content of the sample-The IR absorbance method was particularly useful, as a conventional weighing method would have registered not only the water drying rate but also loss of ammonia.

Moisture content analysis was performed by equili- bration at 45°C in evacuated desiccators with saturated lithium chloride solution.

Drying of porous granular materials 1511

RESULTS measured dependence on granule radius is within the The shrinking core model was found to describe the limits of experimental accuracy. It also seems possible to

drying behaviour accurately for two of the materials. The predict the temperature dependence between 65 and estimated diffusivities at 65-75°C are as follows. 75°C. Extrapolating to higher temperatures introduces an

error of about 30%, but the drying curve retains the same NPK 12-9-16 &/Do = 1.7 x lo-’ shape.

The drying behaviour of NPK 12-9-16 could also be MCP D,,/D,, = 0.37 x lo-‘. described by the shrinking core model (Fig. 5). Only a

narrow temperature range was investigated, but within Figure 4 shows the results of eight experimental runs that range the model seems to follow the experimental with MCP. The curves represent the shrinking core drying curves and the dependence on granule size. model with the diffusivity relationship mentioned above For the second fertilizer material, NPK S-7-13, the and the driving force calculated from sorption equili- drying curves do not follow the typical shrinking core S brium data. The difference between predicted and shape. Yet for the larger particles all drying curves have

0 A cl

I I

RADIUS, mm

0.47

a8

Fig. 4. Experimental and calculated drying rates for mono calcium phosphate. XO = 0.053 kg/kg, X,* = 0.000 kg/kg, P wn = 100 Pa.

1512 A. HALLSTROM and R. WMMERSTEDT

Fig. 5. Experimental and calculated drying rates for fertilizer NPK 12-9-16. Temperature 6%7l”C, XO = O.O14Okg/kg, X.* = 0.0005 kg/kg, pvm = 150 Pa.

approximately the same form. For the smaller particles a slightly different shape was observed, but this shape is in turn maintained through all temperatures.

Despite the deviating shape of the drying curve, the shrinking core model was used as a basis for describing the drying of NPK M-7-13 mathematically. The drying rate, according to eqn (3), was multiplied by a correction function, which varied with the nondimensional moisture

content (Fig. 6). A better fit to the curves could have been achieved if some other function had been used, but the one shown in Fig. 6 was chosen for its simplicity. It is worth emphasizing that the correction only affects the shape of the standard drying curve. The dependence on particle size and process parameters is still calculated from basic data.

The predicted temperature dependence agreed

Fig. 6. Drying rate correction function for fertilizer NPK 167-13.

Drying of porous gram&u materials 1513

0 86-89 % A 77 -70 l c El 67 ‘C

54- 55 ‘c

L3-&5 ‘G

4 RADIUS c 0.71 mm

I- RADIUS

127 mm

I

I RADIUS 1.53 mm

I

92 Qb 0.6 0.0

(Z -x,“, I (X0-X,“, Fig. 7. Experimental and calculated drying rates for fertilizer NPK E-7-13. X0 = 0.0160 kg/kg, pW = 700 Pa. X.*

varied between 0.0001 k&kg and 0.0050 kg/kg.

1514 A. HALLSTRC~M and R. WIMMERSTEM

Fig. 8. Experimental and calculated drying rates for fertilizer NPK 16-7-13. Temperature 6768°C. granule radius 1.27 mm, X0 = 0.0160 kg/kg. X,* varied between 0.0022 kg/kg and 0.0034 kg/kg.

reasonably well with experimental data in the whole examined region, 4%90°C. The temperature dependence is shown in Fig. 7 for all three size fractions. All curves are drawn using the same correction function and the same diffusivity value. The latter, now without any phy- sical significance, is l&f = 1.25 X 10m7 m’/s.

The moisture content of the drying air was varied between t 3 and t 30°C dew-point. This is equivalent to a variation of the calculated driving force of about 2: 1. The agreement with the predicted behaviour was good, which can be seen in Fig. 8.

The discrepancy between predicted and experimental curves is somewhat bigger for small granules than it is for large ones. This may be due to the fact that in the granulation process small and large granules are probably formed by different mechanisms. It should also be noted, that the size difference between fractions is quite large. The smaller granules are recirculated in the industrial process, and do not form part of the product fraction. They are therefore also of minor practical importance.

Furthermore, the sorption equilibrium data are quan- titatively somewhat uncertain. This is partly due to vari- ations in the product composition. The equilibrium data give the temperature and humidity dependence of the

drying rate as well as the conversion from dimensional to nondimensional moisture content. Considering these circumstances, the agreement between theoretical. and experimental values is satisfactory.

CONCLUSIONS

With a few exceptions, good agreement has been observed between predicted and experimental drying curves for all three materials. It should be noted that the materials are technical products, of complicated chem- ical and physical nature. It is plausible, that the assump- tion of vapour diffusion as the rate determining mechanism of drying would be successful for many similar hygroscopic materials with relatively low mois- ture content.

From a practical point of view it is important that the temperature and size dependence on the drying process has been predicted from basic data alone. In principle, it would thus be possible to optimize a process on the basis of one drying experiment. The drying curve, plotted as logarithmic drying rate versus nondimensional moisture content, will maintain its form when extrapolated to different parameter values, for instance temperature

Drying of porous granular materials

O!tVN q ATk

X MCP + NPK 12-9-16

LITERATURE DATA

00O ::: 0

0

. . . ::::::. ,.:.:.>:.:.>:.:.:.: . . . . . . . . . . . . . . . . . . . . . . .;..............:: .,.,._.. ; _. . .

.., ..:.:.: .:.:.:_: + 0 .I:.:.:. y:::::.

.

X

I I 1

0.1 Q2

POROSITY

QS 1.0

Fig. 9. Relative diffusivity of water vapour in air in porous media.

levels. From a fundamental point of view some intriguing questions remain unanswered.

For the two materials which follow the shrinking core model, it may be debated whether the model physically describes the process or is just a mathematical tool. The correlation of data to the predicted dependence on size indicates a macro diffusion process. Furthermore, the agreement with the predicted temperature and humidity dependence points towards vapour phase diffusion.

The estimated effective diffusivities are very small. However, the magnitude does not seem unrealistic when compared with other drying data. Figure 9 shows some literature data on observed diffusivities in porous media. All data are for adsorption or desorption of water vapour at normal atmospheric pressure. The materials include brick and lightweight concrete as well as molecular sieves and alumina. The data by Garside et al. [Z] are for granulated compound fertilizer.

The reduction in the diffusivity in comparison with the binary diffusivity in air, Do, is conventionally written as the porosity divided by a tortuosity factor. In the lit- erature on diffusion in catalysts, tortuosity factors are

usually smaller than the inverse of the porosity. From an analysis of Fig. 9, it is evident that most data represent larger tortuosity factors than those found in the literature on catalysis. The scattering in Fig. 9 is considerable, which is only natural as many different kinds of material are involved_ Nevertheless, Fig. 9 may serve as a rough indication of the drying rates one can expect for a porous material.

If the physical aspect of the model is accepted, the deviating form of the drying curves for the third material must still be explained. One possibility could be that the granules are heterogeneous. In one case the porosity has been found to vary slightly with granule size. It is generally assumed that large granules are built on small, recirculated granules in the granulation process. Another possible explanation is that physical changes take place in the material during drying.

NOTATION

D iz

effective ditfusivity, m21s binary diffusivity of water vapour in air, m2/s

M, molecular weight of water, kg/kmole

A. HALLSTRCM and R. WIMMERSTEDT

gas constant, Jlkmole K vapour flux, kg/m* s total pressure, Pa partial pressure of water vapour, Pa radius of sphere, m radius coordinate, m temperature, K time, s local moisture content, kg/kg dry matter average moisture content of sphere, kg/kg dry

matter

Greek symbols

hPW vapour pressure driving force, Pa c porosity 5 ratio between radius of sphere and radius of core

pi density, kg dry material/m3

Subscripts a air bulk c core 0 initial state

Superscript * equilibrium value

REFERENCES

[l] Hallstriim A., Drying ‘82 (Edited by Mujumdar A. S.). New York 1982.

121 Garside J.. Lord L. and Reagan R., Chem. Engng. Sci. 1970 25 1133.

[3] Werling K., Ph.D. Thesis, University of Lund 1980. I41 Giines S., Schliinder E. U. and Gnielinski V., Verfahren-

stechnik 1980 14 31. (51 Haertling M., Ph.D. Thesis, University of Karlsruhe 1978. [6] Schliinder E. U., Chem. Ing. Technik 1976 48 190. [7] Zabeschek G., Ph.D. Thesis, University of Karlsruhe 1977. 181 King C. J.. Freeze-Dvina of Foods. Cleveland 1971. j9j Jo&h F.‘and Kast ti.,“vi>r-Berichre 1975 No. 232 113.

IlO] Krischer, 0. and Mahler. K., VDI-Forschungsheft 1959 B25 No. 473.

[II] Krischer O., W&man W. and Kast W., Ges.-lng. 1958 79 129.

[I21 Marcussen, L., Chem. Engng Sci. 1974 29 2061. [13] Sommer, E., Ph.D. Thesis, University of Darmstadt 1971.