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Decomposition of powders in horizontal rotary drum reactors
Powder Technology, 22 (1979) 1 - 10 0 Elsevier Sequoia S.A., Lausanne -Printed
Decomposition H. KRUGER,
of Powders in Horizontal Rotary Drum Reactors
M. HEHL,
Institut fk’rTechnische (Received
in the Netherlands
December
H. HELMRICH Chemie
and K. SCHBGERL
der Technischen
UniversitEt Hannover
(F.R.G.)
5,1977)
SUMMARY In a continuously operated laboratory rotary drum reactor 600 mm long and 250 mm in diameter, the mixing of cold and hot particles of soda was investigated and the mixing time was evaIuated_ The formal kinetics of the decomposition of sodium hydrogen carbonate to sodium carbonate (soda) was evaluated in a batch-operated drum. The distribution of residence times of the particles was measured by means of a radiotracer (PIa%) technique. The longitudinal temperature profiles and the conversion of the reaction were also measured. To describe the longitudinal temperature profile in the particle bulk without reaction, the variations of the cross-sectional area of the particle bulk and temperature of the wall must be taken into account. The heat transfer coefficients evaluated in [7] yield satisfactory results under these conditions. It is possible to calculate the longitudinal conversion and temperature profiles in the rotary drum by applying the energy and material balances for every small section of the reactor and by using reaction rates and transport coefficients estimated by separate measurements.
INTRODUCTION
Rotary kilns are used in different branches of industry. The largest units are in the cement industry. The reactors used in metallurgical and chemical industry are smaller. Most of the published papers consider the manufacture of cement; far fewer of them deal with metallurgical processes. Because of their flexibility, rotary kilns are often used also in the inorganic chemical industry for the manufacture of very different products, especially in medium-size companies. In spite of this, reaction engineer-
ing investigations of chemical reactions in rotary kilns, important for the chemical industry, are practically nonexistent_ Up to now, only one paper has been published which treats such a reaction in rotary kilns experimentally [l] _ Other papers only recommended methods of calculations without publishing experimental reaction engineering data [2,3] _ To begin with, a low-temperature reaction, the decomposition of sodium hydrogen carbonate into sodium carbonate (soda), was investigated in the temperature range up to 200 “C. Such reaction engineering investigations should be extended later to higher temperatures _
EXPERIMENTAL
Equipment
Figure 1 shows the applied horizontal rotary drum reactor, which has already been described by the authors 141. It is 60 cm long and 25 cm in diameter and at its end a ringshaped constriction with inner diameter of 21 cm influences the depth of the particle layer in the drum. Between this constriction and the flange the particles are discharged from the drum through a slit 2 cm wide. The particles are fed by a conveyor (type GAC 183-21 of Gericke Co.). The feeding rate can be varied between 0 to 12 l/h. The speed of rotation of the drum can also be varied between 0.013 and 36.36 r.p.m. Investigation of particle movement As has already been described, the particle
movements were registered photographically by means of coloured tracers. These measurements were extended in such a way that 50 g cold soda was fed to approximately 1.5 1 hot soda into the drum and the local temperature in the particle bulk was measured as a function
Fig. l_ Drum: 1 frame, 2 dust protector hood, 3 discharge slit, 4 constriction, 5 soda bulk,6 drum mantle, 13 drive for the drum, 14 anchorage of the frame. Conveyor: 7 soda supply bin, 8 speed control, 9 engine, 10 gear, 11 bulk loosener spira!, 12 conveyor screw.
20
LO
I
I
60
t lsecl
I
Fig. 3. Temperature difference A0 as a function of the time on semilogarithmic scale. c n = 2 r-p-m., o R = 6 r.p.m.,o n = 10 r.p.m.
Fig_ 2_ Measured temperature fluctuations in the particle huIk as a function of the time. n = 2 r.p.m.
of the time at the entrance of the feed near the surface of the bulk by a naked thermocouple to diminish its time constant_ Typical variations of the local temperature are shown in Fig. 2. One can recognize that at the beginning large temperature fluctuations prevail which sIowIy fade out. The maxima and/or the minima of the amplitudes of the fluctuations were connected by two lines in Fig. 2. The difference between these two lines decreases with the time and approaches a cons’tzmtvalue of about 5 “C. This constant value was subtracted from this difference and these corrected temperature differences A0 were plotted on a diagram as a function of the time (Fig- 3). This semilogarithmic plot results in straight lines. Since the heat exchange between the particles is a much slower process than the transverse mixicg [4], the transverse mixing can be presented by an exponential function of type:
Fig_ 4. Time of the half-value speed of rotation n.
AT
= AT,, exp(-t/kD)
71,~ as function
of the
(1)
The constant kD can be replaced by the time
to half-value: 71/2 = kD In 2
(2)
In fig. 4 7112 is plotted as a function of the rotational speed. The higher n, the lowerrIB, i.e. the higher the intensity of the transverse mixing. Table 1 shows 71,a and k, as a function of n and the trajectory velocity of the drum wall u.
TABLE
1
Decay constant k~ as function of the speed of rotation la (min -1 ) 1 2 4 6 8 10
Kinetic
;Im,min)
Tl’112 (set)
b (set)
0.79 1.57 3.14 4.71 6 -28
27 21.5 16 10 8
39.0 31.0 23.1 14.4 11.5
7.85
7
10.1
measurements
in
3
batch operatiorz
measurements of decomposition of sodium hydrogen carbonate into sodium carbonate: 2 NaHCOs + NasCOs + HsO + COP
3:
162
%z
n.
2
(3)
were carried out with 1.25 kg soda in the drum reactor (more about this reaction in [S] )_ This soda was heated to a given temperature. After the constant temperature of the soda had been established, 10 g cold sodium hydrogen carbonate were immediately added to the soda, equally distributed along the axis of the drum. To achieve a quick mixing of the cold and hot particles the drum was first of all rotated at maximum speed (36.36 r.p.m.) for 40 set, then the decomposition was measured at 12 r.p.m. By means of a perforated tube the gas sample was taken, equally distributed along the drum axis, and the concentration of CO* was measured in the sample by an infrared gas analyser (type URAS of Hartmann and Braun) as a function of the time. The concentration of COa and the temperature of the soda bulk were registered by a two-channel recorder. These concentration-time curves show an increasing and decreasing branch
I
.0=136=x : 5=162T
c
The
IO
IllC
1
Fig. 6. Concentration of sodium hydrogen carbonate as a function of the time on semilogarithmic plot. 08=179”C,~~=138”C,r~=162°C.
(Fig. 5). During the temperature increase the sodium hydrogen carbonate particIes were heated. After constant temperature had been achieved, the concentration of COz in the sample dropped. To avoid any error by considering the concentration-time function for non-isothermal conditions, only the part of this function which appears after the inflexion point was evaluated. The logarithmic plot of these functions results in straight lines (Fig. 6). In agreement with the measurements in fluidized beds [5], the decomposition reaction can be described by a first-order reaction. From the Arrhenius plot the apparent energy of activation EA and the constant k, were calculated to (Fig. 7): EA = 15.23 k,
min-’
Influence of the particle diameter on the rate of decomposition As a result of careless operation and/or if
tFig_ 5. Concentration-time tion of sodium hydrogen drum reactor.
kcal/mol
= 3.3 - 10’
curve of the decomposicarbonate in batch-operated
the concentration of the sodium hydrogen carbonate in the feed is too high (>30%), lumps can form which wander on the surface
4
ki Q,,,)
-1nk
K-1
Fig. 7. Rate constants
of the decomposition
reaction as a function
of the bulk of fine particles. Therefore it was important to see in which way the lump formation influences the decomposition rate. From the sodium hydrogen carbonate powder, tablets 16 mm in diameter and 7 mm thick were pressed. The tablets had a mean weight of 2.33 g, a volume of 1407 mm3, a geometrical surface area of 754 mm2, a density of 1.66 g/cm3 and a porosity E = 0.233. After the decomposition reaction the tab1et.s kept their shape. However, they had a mean weight of 1.501 g, a density of 1.07 g/cm3 and a porosity E = O-579_ The investigation of the kinetics of the reaction was identical to the kinetic measurements in batch operation. The decomposition can be described by a first-order reaction, but the rate constants k depend on the par%icIe diameter. For example, at the bulk temperature 0 = 207 “C the following rate constants were found: tablets half-tablets quarter-tablets powder (d, = 137 pm)
k k k k
= = = =
0.09 0.19 0.20 3.81
min-’ mind1 min-’ min-’
One can recognize that the decomposition rate depends on the particle size. Which transport process is the rate-deter- _ mining step was not investigated. In any event, as long as the sodium hydrogen carbonate is present as powder, the chemical reaction is the rate-determining process. This can be
of the reciprocal
temperature
proved by the high apparent tion EA = 15.23 kcal/mol.
T-l_
energy of activa-
Estimation of the conversion of the decomposition reaction in continuous operation The drum was filled with soda, it was heated up to a given temperature and a mixture of 20 wt.% dry sodium hydrogen carbonate and dry soda was fed to the reactor. After the steady state had been established, solid particle samples were taken at the outlet of the reactor and their sodium hydrogen carbonate contents were estimated by measuring the weight loss due to the decomposition of the remaining sodium hydrogen carbonate by heating the probe 24 h at 200 “C. In Table 2, not the conversion X, but (1 - X) is shown for different rotational speeds and rates and mean temperatures of the bed. However, since the bed temperature was not constant, no kinetic data could be evaluated from these measurements. _ To investigate the influence of the nonuniform temperature of the bulk on the converzion, the longitudinal temperature profiles of the bulk were measured. (The transverse temperature profiles were much smaller than the longitudinal ones.) Longitudinal temperature profiles in bulk and at the waii The longitudinal temperature profiles in the bulk were measured by shifting a thermocouple
5
TABLE3
TABLE2 (l-x)asfunctionofthespeedofrotationand rate n
FV
(r.p.m.)
(l/h)
5 5 : 5 1 1 2 10
2.5 2.5 :::5 10.2 5.1 5.1 5.1 5.1
feed
(1--xj
Fv, l/h n,r_p.m.
0.496 0.141 0.451 0.696 0.625 0.744 0.572 0.374 0.541
z
$5 368 390 388 376 374 379 382 3s3 376
Longitudinal
along the drum and measuring the temperature of the buik in constant distances of 1 cm. To evaluate the wall temperature the thermocouple was soldered to the wah. Tables 3 and 4 show typical longitudinal profiles in b-ulk as a function of the rotation speed and feed rate. At low rotation speeds the mixing between the cold feed and the hot reaction mixture occurs only slowly. Therefore the temperature in the bulk fIuctuates with a frequency according to the rotational speed of the drum. At low rotational speed (e.g. n = 1 r.p.m.) such temperature fluctuations can be fo-und up to the longitudinal position z = 0.4. The wail temperature is also not constant. From the entrance of the feed along z it increases, passes through a maximum, then decreases. This temperature profile is not only due to the fkmges, but also to the cold feed: the walI temperature at the feed entrance is lower than at the product exit. Dktributioz of residence times of the solid particles In an earIier paper [4] , the distribution of
residence times and the intensity of the longitndinai mixing of the particles in a cold drum reactor were investigated. It was necessary to investigate whether an increase in temperature influences the distribution of residence times. Therefore such measurements were carried out at a higher temperature by means of a NaS tracer. Approximately 1 g sample of soda was activated in the research reactor of the medical school in Hannover by means of a neutron flux 4. 1012/cm2sec. This sampie, with a ra-
temperature
profilesasfunctionofthe
speedofrotationn
0.15 0.2 0.3 0.4 0.5
0.6
0.7 0.8 0.9
5.1 1
5.1 2
5.1 5
5.1 10
TKj
&j
TKj
&j
340 353 367 375 379 382 383 384 381
341 353 363 377 379 385 383 383 380
343 352 365 371 375 378 384 384 383
331 343 357 373 383 391 391 390
TABLE4 Longitudinal
temperature
profiksas functionof
the
feed rateF,
F,, l/h n,r.p.m.
2.5 5
5.1 5
7.65 5
10.2 5
TKj
TKj
TK)
343 350 365 371 375 378 383 283 382
341 352 363 373 374 378 383 382 381
365 371 379 383 387 390 391 392 388
z
0.15 3.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
343 357 373 381 387 388 390 392
dioactivity of 1.7 mCi, was transported in a lead transport container to the rotary drum reactor which was separated by a plastic tent from the rest of the laboratory. 500-mg samples were given at tince to the feed and the activity of the particles at the reactor exit (after they were discharged into a measuring chamber) was measured by a scintihator counter and the data were stored on a tape. A comparison of these distribution residence times with those measured in a cold reactor with 100 g sodium hydrogen carbonate as tracer shows significant differences (Figs_ 8,9). The curves of the latter are wider than those of the former. This difference is probably due to the more pronounced deviation of 100 g sodium
Q25
0
A 0
c 5
f0
15
20
25
30
35
LO
min
50
Fig. 8. Step response cures measured in the continuousIy operated rotary drum reactor at F, = 5 I/h_ (a) With sodium hydrogen carbonate as tracer: V n = 1 r.p_m., = n = 2 r.p.m.,v n = 5 r.p.m., 0 n = 10 r.p.m. (b) With Nag4C03 as tracer: on = 5 r-p-m.
Fig. 9. Step response cures measured in the continuousIy operated rotary drum reactor at n = 5 r.p.m. (a) With sodium hydrogen carbonate as tracer: = F, = 7.65 I/%, p 5.1 I/h, o 2.55 I/h. (b) With Nag4 COa as tracer: l F,=51~,.3Ilh,o2_8I/h,x 1.51/h.
hydrogen carbonate tracer from the s-input function than that of 500 mg Nag*CO, _ According to this difference in the distribution of residence times, larger Peclet numbers were evaluated by the isotope technique than with
the -&andard technique discussed earlier [4] (Table 5). The dependence of the Peclet number on the feed rate and the rotational speed is not influenced by the applied measuring technique, only the absolute values of the Penumbers. However, for reaction engineering purpcses the difference, for example, between Pe = 100 and 200 doesnotmake anydifference.
DISCtJSSlwN Description of the Iongitudinal temperature profile in the particle Iayer without reaction
The heat transfer rate across the wall is given by eqn. (4): Gj =aF(T,
-T)
(4)
For the variation of the temperature of the particle bulk, eqn. (5) is valid: 4 = -
mc dT/dt
(5)
7 TABLE
5
Speed of rotation R, r.p.m. Feed rate F,, l/b First moment, min Dimensionless second moment Peclet number
where
a = heat
tzansfer
5 1.5 44.87 0.0045 443
coefficient
5 2.8 30.33 0.0043 464
between
particle layer and the wall of the drum, F = contact surface (heat exchange) area between particle layer and the wall of the drum, T, = wall temperature, T = temperature of the particle iayer (bulk),m = mass of the particle bulk, c = specific heat of the bulk, and t = time. The combination of eqns. (4) and (5) and the integration of the resulting equation yields eqn. (6): T,-T=(T,-To)exp(-t/H)
5 3 29.24 0.0049 407
5 5 20.48 0.0034 587
For F as function of the axial coordinate z the following relation is valid: z
s F=
sd%=
J z=o
.Ir=O
MS2
--%I
(7)
+.a*
and for the mass of particles as function of z: z m=p&=p
J r=O
Adz=
(6) = PJ
where
(~642
--A,)
+A11
03)
cb
z=o
Putting eqns. (7) and (8) into eqns. (4) and (5) and using the relations The heat transfer coefficients CCfor the heat transfer between the particle layer and the wall were evaluated for the same system [7] _ Estimation of the longitudinal temperature profiles by means of eqn. (6) with the corresponding coefficients and by assuming a constant cross-section of the particle layer and a constant wall temperature is not possibIe. There is a significant difference between the measured and calculat.ed longitudinal temperature profiles. To improve the quality of the calculated profiles, the variation of the crosssection of the particle layer was considered (Fig. 10).
s1 =a s2--sl
=
Az=g
2b
AZ-Al
=2h
yields with t = TZ eqn. (9): ar = a++-_J -s PC .=,C~
r=ro
dT TL..--T
The solution of eqn. (9) is given by eqn. (lo): -1n
T, -T
( T, -
cir
bz -+ [ h
ah-bg
xln(g+ 1.?
To 1 = F
h2
hz)
Fig. 10. Variation of the cross-sectional area of the particle bulk along the drum axis. Explanation of the symbols.
For the drum applied with the constriction at its end, the following data were estimated for F, = 2.51 l/h (Fig. 10): h, = 0.02 m - h2 = 0.0284 m S, = 0.143 A,
= 2.64
m - 10s3
m2
Ss = 0.172
m
AZ = 3-08
- 10B3 m2
(9)
r=o
’ (10)
In Fig. 11 the measured longitudinal temperature profiles and those calculated with 01 = 146 W/m2K are compared. The application of eqn. (10) yields a slight improvement in comparison to eqn. (6). However, the deviation between measured and calculated profiles is still large. To improve the model the temperature variation of the wall was also taken into account. By assuming a linear temperature profile of the wall with T,
= pK
atz=O,and
LJO
2goo
ct2
04
06
0.8
JO
2-
Fig. II_ Comparison of the longitudinal temperature profiles without reaction. (1) Calculated by eqn. (6), (2) calculated by eqn. (10). o measured_n = 5 r‘.p.x, F, = 2.5 I/h_
atzzO.5
T, = T,”
the temperature of the wall is given by eqn. (11) for 0 f 2 Q 0.5 : T, = 2(T,” -
T,o)z + T,”
(11)
By putting this value into eqns. (4) and (5), this yields eqn. (12): mc dT
2(T,m -T,O)t+T,O-TT-_ The transformation (13): -T,O)c+-T,O-T=-
2(Tz
aF
_
(12)
dt
by t = ZT yields eqn. mc
dT CYTF dz
(13)
For simplification we use: T,o)uF~
2(T,m -
mc T,” arFr mc --
(YFT mc
(14a)
= &
(14b) (14c)
Hence eqn_ (12) simphfies to eqn. (14): dT dz
-f-az+bifT=O
(14)
The solution of this differential equation yields [S] : UZ+z,
+ ” + 2,-fz (15) f P Figure 12 shows a comparison of measured and calculated IongitudinaI temperature profizes for Tz = 342 K, T! = 399 K, TO = 295 K, a = 163 W/m2 KS n = 5 r.p.m. and& = 5.1 l/h: One can recognize that eqn. (15) shows a significaat impro-cement on eqn. (6). However, T=-
-
Fv = 5.1 I/h. the agreement between calculated and measured profiles is not yet completely satisfactory. It is necessary to take into account the true temperature profile of the wall. Such calculations give satisfactory results.
Calculation of the Zongitudkzl temperature and conuersion profiles in the drum By means of the material and energy balances, the longitudinal ccnversion and temperature profiles can be calculated for small segments of the rotary drum reactor analogous to the method of Paszthory et al. [9]. The 1ongiDddinal heat transport rate is given by the transverse heat transfer rate by
f& = (YF(T,
c a
= f
Fig. 12. Comparison of the longitudinal temperature profiles without reaction. (1) Calculated by eqn. (6), (3) calculated by eqn. (15), o measured_ n = 5 r-p-m.,
-
T)
and the heat transport enthalpy by
rate due to the reaction
where C = concentration of sodium hydrogen carbonate, c = specific heat of the particle buik, F = heat trm_fer surface urea, AH =
reaction enthalpy, Q = heat fiow, R = reaction raLe, T, = mean temperature of the wall, T,, = temperature of the particle bulk at the entrance, T,, = temperature of the particle bulk at the discharge, and V, = volume of the particle bulk. In steady state the following energy balance is valid for every segment of the rotary drum reactor: oz,-&
+ddQ,+d&
(19)
Instead of the differentiai equations (19), difference equations were used for every section n: 0 = F,pcA T, + aAF,(T,
-
T,) + F,AC,(
-AH) (29)
9
where
ATi = Tn.,, - Tn.,, AC,
= en.,,
-
cn.ex
T n.en + T,.,,
T, =
2
To evaluate the c?:&version profile, the concentration difference in every section is divided by the entrance concentration C,, :
wAT,lAH
=
+ CYAF,(T, -
042.
c/i :’
r
1!
jI
j1
1
0
02
04
06
08
I
co =
Fig. 15. Longitudinal conversion and temperature profiles in tbe bulk of particles_ Calculated by the difference method. E; = 7.65 I/h, n = 5 r.p.m.
T,)/F,AH
C en (21)
where Ax, = x,-~ -x~, and AF, = the heat exchange surface area between the particle bulk and the wall in the section n. In Figs. 13 - 16 are plotted typical longitudinal conversion and temperature profiles, calculated according to this method. In Table 6 the calculated and measured conversions at the exit are compared for different feed rates. One can recognize that this simple method yields very satisfactory results.
QG6
60
OCL
60
QO2
LO
0
02
OL
06
06
1 z
Fig. 16. Longitudinal conversion and temperature profiles in rhe bulk of particles_ Calculated by the difference method_ Fv = 10.2 I/h, n = 5 r.p.m.
TABLE
6
Comparison of calculated and measured conversion a function of the feed rate
(:.p.m. 5 5 5 5
QO2
0
Q2
0-L
06
0.8
1
z
Fig. 13. Longitudinal conversion and temperature profiles in the bulk of particles_ Calculated by the difference method. F” = 2.5 i/h, n = 5 r.p.m. WC:
&ix
j
x
x
%hj
(meas.)
(caic.)
2.5 5.1 7.65 10.2
0.46 0.55 0.31 0.37
0.47 0.58 0.38 0.36
ACKNOWLEDGEMENTS
The authors gratefully acknowledge the financial support of DECHEMA and AIF.
006
120
LIST OF SYMBOLS
QOL
80
A
LO
c C
0.02
42 0
0 L
0.6
0.6
1
z
Fig. 14. Longitudinal conversion and temperature profiles in the buIk of particles. Calculated by the difference method. Fv = 5.1 i/b, n = 5 r_p.m.
as
EA
F
cross-section area, see Fig. 10 specific heat of the particle bulk concentration mean particle diameter activation energy contact surface (heat exchange) area between particle Iayer and the wall of the drum
10 F, AN
h J kD k k, K m n 4 R s(t) S f
T u T& x 2 a E ; ‘112 5
feed rate reaction enthdpy depth of the hed (see Fig. 10) integration constant (see eqn_ 15) temperature decay constant reaction rate constant maximal reaction rate constant cons+mt, see eqn. (6) mass rotational speed heat ffow reaction rate step response curve arcus (see Fig. 10) time temperature (K) velocity reaction volume degree of conversion dimensionless axial distance heat transfer coefficient porosity density temperature (“C) time to half-value, see eqn. (2) mean residence time
Indices 0 en ex
initial condition entrance discharge
n W
single section reactor wall
REFERENCES A. Manitius. E. Kureynsz and W. Kawecki, Mathematicai modd of the duminium oxide rotary kiln, Ind. Eng. Chem. Process Des_ Dev., 13 (1974) 132 - 142. V_ V. Jinescu and I. Jineacu, Verfahrenstechnische Berechnungsgrundlagen fiir Drehtrommelaniagen. Aufbereit. Tech., 9 (1972) 573 - 579. L. H. J. Wachters and H. Kramers, The calcining of sodium bicarbonate in a rotary kiln, 3rd Eur. Symp. Chem. React. Eng., Amsterdam, 1964, pp_ 77 - 87. M. Hehl, H. KrBger, H. Helmrich and K. Schiigerl, LongitudinaI mixing in horizontal rotary drum reactors, Powder Technol., 20 (1978) 29. M. Hehl, H. Helmrich, 3. Lehmbergand K. Schiigerl, Investigation of the thermal decomposition of powders in fluidiaed bed and rotary kiln reactors, Eur. Congr., Transfer Processes in Partide Systems, Nuremberg. 28 - 30 Mar. 1977, N2 (1977). H_ Helmrich, H. Kriiger. M. Hehl and K. Schiigerl, TransportvorgZnge und chemische Reaktion in Drehrohrreaktoren. presented on the DECHEMAJahrestagung 1977, Chem. Ing. Tech., 50 (1978) 139. J. Lehmberg, M. Hehl and K. Schiigerl, Transverse mixing and heat transfer in horizontal rotary drum reactors, Powder Technol., 18 (1978) 149 - 163_ H. KrGger, Untersuchungen zur Natriumhydrogencarbonataersetzungim Drehrohrofen. Diplomarbeit, TU Hannover, 1976. E. Paszthoqv, K. Schiigerl and M. Bakos, Vorausberechnung katalytischer StriimungsreaktionsSfen, Chem. Ing. Tech.. 31(1959) 432 - 438.
Decomposition H. KRUGER,
of Powders in Horizontal Rotary Drum Reactors
M. HEHL,
Institut fk’rTechnische (Received
in the Netherlands
December
H. HELMRICH Chemie
and K. SCHBGERL
der Technischen
UniversitEt Hannover
(F.R.G.)
5,1977)
SUMMARY In a continuously operated laboratory rotary drum reactor 600 mm long and 250 mm in diameter, the mixing of cold and hot particles of soda was investigated and the mixing time was evaIuated_ The formal kinetics of the decomposition of sodium hydrogen carbonate to sodium carbonate (soda) was evaluated in a batch-operated drum. The distribution of residence times of the particles was measured by means of a radiotracer (PIa%) technique. The longitudinal temperature profiles and the conversion of the reaction were also measured. To describe the longitudinal temperature profile in the particle bulk without reaction, the variations of the cross-sectional area of the particle bulk and temperature of the wall must be taken into account. The heat transfer coefficients evaluated in [7] yield satisfactory results under these conditions. It is possible to calculate the longitudinal conversion and temperature profiles in the rotary drum by applying the energy and material balances for every small section of the reactor and by using reaction rates and transport coefficients estimated by separate measurements.
INTRODUCTION
Rotary kilns are used in different branches of industry. The largest units are in the cement industry. The reactors used in metallurgical and chemical industry are smaller. Most of the published papers consider the manufacture of cement; far fewer of them deal with metallurgical processes. Because of their flexibility, rotary kilns are often used also in the inorganic chemical industry for the manufacture of very different products, especially in medium-size companies. In spite of this, reaction engineer-
ing investigations of chemical reactions in rotary kilns, important for the chemical industry, are practically nonexistent_ Up to now, only one paper has been published which treats such a reaction in rotary kilns experimentally [l] _ Other papers only recommended methods of calculations without publishing experimental reaction engineering data [2,3] _ To begin with, a low-temperature reaction, the decomposition of sodium hydrogen carbonate into sodium carbonate (soda), was investigated in the temperature range up to 200 “C. Such reaction engineering investigations should be extended later to higher temperatures _
EXPERIMENTAL
Equipment
Figure 1 shows the applied horizontal rotary drum reactor, which has already been described by the authors 141. It is 60 cm long and 25 cm in diameter and at its end a ringshaped constriction with inner diameter of 21 cm influences the depth of the particle layer in the drum. Between this constriction and the flange the particles are discharged from the drum through a slit 2 cm wide. The particles are fed by a conveyor (type GAC 183-21 of Gericke Co.). The feeding rate can be varied between 0 to 12 l/h. The speed of rotation of the drum can also be varied between 0.013 and 36.36 r.p.m. Investigation of particle movement As has already been described, the particle
movements were registered photographically by means of coloured tracers. These measurements were extended in such a way that 50 g cold soda was fed to approximately 1.5 1 hot soda into the drum and the local temperature in the particle bulk was measured as a function
Fig. l_ Drum: 1 frame, 2 dust protector hood, 3 discharge slit, 4 constriction, 5 soda bulk,6 drum mantle, 13 drive for the drum, 14 anchorage of the frame. Conveyor: 7 soda supply bin, 8 speed control, 9 engine, 10 gear, 11 bulk loosener spira!, 12 conveyor screw.
20
LO
I
I
60
t lsecl
I
Fig. 3. Temperature difference A0 as a function of the time on semilogarithmic scale. c n = 2 r-p-m., o R = 6 r.p.m.,o n = 10 r.p.m.
Fig_ 2_ Measured temperature fluctuations in the particle huIk as a function of the time. n = 2 r.p.m.
of the time at the entrance of the feed near the surface of the bulk by a naked thermocouple to diminish its time constant_ Typical variations of the local temperature are shown in Fig. 2. One can recognize that at the beginning large temperature fluctuations prevail which sIowIy fade out. The maxima and/or the minima of the amplitudes of the fluctuations were connected by two lines in Fig. 2. The difference between these two lines decreases with the time and approaches a cons’tzmtvalue of about 5 “C. This constant value was subtracted from this difference and these corrected temperature differences A0 were plotted on a diagram as a function of the time (Fig- 3). This semilogarithmic plot results in straight lines. Since the heat exchange between the particles is a much slower process than the transverse mixicg [4], the transverse mixing can be presented by an exponential function of type:
Fig_ 4. Time of the half-value speed of rotation n.
AT
= AT,, exp(-t/kD)
71,~ as function
of the
(1)
The constant kD can be replaced by the time
to half-value: 71/2 = kD In 2
(2)
In fig. 4 7112 is plotted as a function of the rotational speed. The higher n, the lowerrIB, i.e. the higher the intensity of the transverse mixing. Table 1 shows 71,a and k, as a function of n and the trajectory velocity of the drum wall u.
TABLE
1
Decay constant k~ as function of the speed of rotation la (min -1 ) 1 2 4 6 8 10
Kinetic
;Im,min)
Tl’112 (set)
b (set)
0.79 1.57 3.14 4.71 6 -28
27 21.5 16 10 8
39.0 31.0 23.1 14.4 11.5
7.85
7
10.1
measurements
in
3
batch operatiorz
measurements of decomposition of sodium hydrogen carbonate into sodium carbonate: 2 NaHCOs + NasCOs + HsO + COP
3:
162
%z
n.
2
(3)
were carried out with 1.25 kg soda in the drum reactor (more about this reaction in [S] )_ This soda was heated to a given temperature. After the constant temperature of the soda had been established, 10 g cold sodium hydrogen carbonate were immediately added to the soda, equally distributed along the axis of the drum. To achieve a quick mixing of the cold and hot particles the drum was first of all rotated at maximum speed (36.36 r.p.m.) for 40 set, then the decomposition was measured at 12 r.p.m. By means of a perforated tube the gas sample was taken, equally distributed along the drum axis, and the concentration of CO* was measured in the sample by an infrared gas analyser (type URAS of Hartmann and Braun) as a function of the time. The concentration of COa and the temperature of the soda bulk were registered by a two-channel recorder. These concentration-time curves show an increasing and decreasing branch
I
.0=136=x : 5=162T
c
The
IO
IllC
1
Fig. 6. Concentration of sodium hydrogen carbonate as a function of the time on semilogarithmic plot. 08=179”C,~~=138”C,r~=162°C.
(Fig. 5). During the temperature increase the sodium hydrogen carbonate particIes were heated. After constant temperature had been achieved, the concentration of COz in the sample dropped. To avoid any error by considering the concentration-time function for non-isothermal conditions, only the part of this function which appears after the inflexion point was evaluated. The logarithmic plot of these functions results in straight lines (Fig. 6). In agreement with the measurements in fluidized beds [5], the decomposition reaction can be described by a first-order reaction. From the Arrhenius plot the apparent energy of activation EA and the constant k, were calculated to (Fig. 7): EA = 15.23 k,
min-’
Influence of the particle diameter on the rate of decomposition As a result of careless operation and/or if
tFig_ 5. Concentration-time tion of sodium hydrogen drum reactor.
kcal/mol
= 3.3 - 10’
curve of the decomposicarbonate in batch-operated
the concentration of the sodium hydrogen carbonate in the feed is too high (>30%), lumps can form which wander on the surface
4
ki Q,,,)
-1nk
K-1
Fig. 7. Rate constants
of the decomposition
reaction as a function
of the bulk of fine particles. Therefore it was important to see in which way the lump formation influences the decomposition rate. From the sodium hydrogen carbonate powder, tablets 16 mm in diameter and 7 mm thick were pressed. The tablets had a mean weight of 2.33 g, a volume of 1407 mm3, a geometrical surface area of 754 mm2, a density of 1.66 g/cm3 and a porosity E = 0.233. After the decomposition reaction the tab1et.s kept their shape. However, they had a mean weight of 1.501 g, a density of 1.07 g/cm3 and a porosity E = O-579_ The investigation of the kinetics of the reaction was identical to the kinetic measurements in batch operation. The decomposition can be described by a first-order reaction, but the rate constants k depend on the par%icIe diameter. For example, at the bulk temperature 0 = 207 “C the following rate constants were found: tablets half-tablets quarter-tablets powder (d, = 137 pm)
k k k k
= = = =
0.09 0.19 0.20 3.81
min-’ mind1 min-’ min-’
One can recognize that the decomposition rate depends on the particle size. Which transport process is the rate-deter- _ mining step was not investigated. In any event, as long as the sodium hydrogen carbonate is present as powder, the chemical reaction is the rate-determining process. This can be
of the reciprocal
temperature
proved by the high apparent tion EA = 15.23 kcal/mol.
T-l_
energy of activa-
Estimation of the conversion of the decomposition reaction in continuous operation The drum was filled with soda, it was heated up to a given temperature and a mixture of 20 wt.% dry sodium hydrogen carbonate and dry soda was fed to the reactor. After the steady state had been established, solid particle samples were taken at the outlet of the reactor and their sodium hydrogen carbonate contents were estimated by measuring the weight loss due to the decomposition of the remaining sodium hydrogen carbonate by heating the probe 24 h at 200 “C. In Table 2, not the conversion X, but (1 - X) is shown for different rotational speeds and rates and mean temperatures of the bed. However, since the bed temperature was not constant, no kinetic data could be evaluated from these measurements. _ To investigate the influence of the nonuniform temperature of the bulk on the converzion, the longitudinal temperature profiles of the bulk were measured. (The transverse temperature profiles were much smaller than the longitudinal ones.) Longitudinal temperature profiles in bulk and at the waii The longitudinal temperature profiles in the bulk were measured by shifting a thermocouple
5
TABLE3
TABLE2 (l-x)asfunctionofthespeedofrotationand rate n
FV
(r.p.m.)
(l/h)
5 5 : 5 1 1 2 10
2.5 2.5 :::5 10.2 5.1 5.1 5.1 5.1
feed
(1--xj
Fv, l/h n,r_p.m.
0.496 0.141 0.451 0.696 0.625 0.744 0.572 0.374 0.541
z
$5 368 390 388 376 374 379 382 3s3 376
Longitudinal
along the drum and measuring the temperature of the buik in constant distances of 1 cm. To evaluate the wall temperature the thermocouple was soldered to the wah. Tables 3 and 4 show typical longitudinal profiles in b-ulk as a function of the rotation speed and feed rate. At low rotation speeds the mixing between the cold feed and the hot reaction mixture occurs only slowly. Therefore the temperature in the bulk fIuctuates with a frequency according to the rotational speed of the drum. At low rotational speed (e.g. n = 1 r.p.m.) such temperature fluctuations can be fo-und up to the longitudinal position z = 0.4. The wail temperature is also not constant. From the entrance of the feed along z it increases, passes through a maximum, then decreases. This temperature profile is not only due to the fkmges, but also to the cold feed: the walI temperature at the feed entrance is lower than at the product exit. Dktributioz of residence times of the solid particles In an earIier paper [4] , the distribution of
residence times and the intensity of the longitndinai mixing of the particles in a cold drum reactor were investigated. It was necessary to investigate whether an increase in temperature influences the distribution of residence times. Therefore such measurements were carried out at a higher temperature by means of a NaS tracer. Approximately 1 g sample of soda was activated in the research reactor of the medical school in Hannover by means of a neutron flux 4. 1012/cm2sec. This sampie, with a ra-
temperature
profilesasfunctionofthe
speedofrotationn
0.15 0.2 0.3 0.4 0.5
0.6
0.7 0.8 0.9
5.1 1
5.1 2
5.1 5
5.1 10
TKj
&j
TKj
&j
340 353 367 375 379 382 383 384 381
341 353 363 377 379 385 383 383 380
343 352 365 371 375 378 384 384 383
331 343 357 373 383 391 391 390
TABLE4 Longitudinal
temperature
profiksas functionof
the
feed rateF,
F,, l/h n,r.p.m.
2.5 5
5.1 5
7.65 5
10.2 5
TKj
TKj
TK)
343 350 365 371 375 378 383 283 382
341 352 363 373 374 378 383 382 381
365 371 379 383 387 390 391 392 388
z
0.15 3.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
343 357 373 381 387 388 390 392
dioactivity of 1.7 mCi, was transported in a lead transport container to the rotary drum reactor which was separated by a plastic tent from the rest of the laboratory. 500-mg samples were given at tince to the feed and the activity of the particles at the reactor exit (after they were discharged into a measuring chamber) was measured by a scintihator counter and the data were stored on a tape. A comparison of these distribution residence times with those measured in a cold reactor with 100 g sodium hydrogen carbonate as tracer shows significant differences (Figs_ 8,9). The curves of the latter are wider than those of the former. This difference is probably due to the more pronounced deviation of 100 g sodium
Q25
0
A 0
c 5
f0
15
20
25
30
35
LO
min
50
Fig. 8. Step response cures measured in the continuousIy operated rotary drum reactor at F, = 5 I/h_ (a) With sodium hydrogen carbonate as tracer: V n = 1 r.p_m., = n = 2 r.p.m.,v n = 5 r.p.m., 0 n = 10 r.p.m. (b) With Nag4C03 as tracer: on = 5 r-p-m.
Fig. 9. Step response cures measured in the continuousIy operated rotary drum reactor at n = 5 r.p.m. (a) With sodium hydrogen carbonate as tracer: = F, = 7.65 I/%, p 5.1 I/h, o 2.55 I/h. (b) With Nag4 COa as tracer: l F,=51~,.3Ilh,o2_8I/h,x 1.51/h.
hydrogen carbonate tracer from the s-input function than that of 500 mg Nag*CO, _ According to this difference in the distribution of residence times, larger Peclet numbers were evaluated by the isotope technique than with
the -&andard technique discussed earlier [4] (Table 5). The dependence of the Peclet number on the feed rate and the rotational speed is not influenced by the applied measuring technique, only the absolute values of the Penumbers. However, for reaction engineering purpcses the difference, for example, between Pe = 100 and 200 doesnotmake anydifference.
DISCtJSSlwN Description of the Iongitudinal temperature profile in the particle Iayer without reaction
The heat transfer rate across the wall is given by eqn. (4): Gj =aF(T,
-T)
(4)
For the variation of the temperature of the particle bulk, eqn. (5) is valid: 4 = -
mc dT/dt
(5)
7 TABLE
5
Speed of rotation R, r.p.m. Feed rate F,, l/b First moment, min Dimensionless second moment Peclet number
where
a = heat
tzansfer
5 1.5 44.87 0.0045 443
coefficient
5 2.8 30.33 0.0043 464
between
particle layer and the wall of the drum, F = contact surface (heat exchange) area between particle layer and the wall of the drum, T, = wall temperature, T = temperature of the particle iayer (bulk),m = mass of the particle bulk, c = specific heat of the bulk, and t = time. The combination of eqns. (4) and (5) and the integration of the resulting equation yields eqn. (6): T,-T=(T,-To)exp(-t/H)
5 3 29.24 0.0049 407
5 5 20.48 0.0034 587
For F as function of the axial coordinate z the following relation is valid: z
s F=
sd%=
J z=o
.Ir=O
MS2
--%I
(7)
+.a*
and for the mass of particles as function of z: z m=p&=p
J r=O
Adz=
(6) = PJ
where
(~642
--A,)
+A11
03)
cb
z=o
Putting eqns. (7) and (8) into eqns. (4) and (5) and using the relations The heat transfer coefficients CCfor the heat transfer between the particle layer and the wall were evaluated for the same system [7] _ Estimation of the longitudinal temperature profiles by means of eqn. (6) with the corresponding coefficients and by assuming a constant cross-section of the particle layer and a constant wall temperature is not possibIe. There is a significant difference between the measured and calculat.ed longitudinal temperature profiles. To improve the quality of the calculated profiles, the variation of the crosssection of the particle layer was considered (Fig. 10).
s1 =a s2--sl
=
Az=g
2b
AZ-Al
=2h
yields with t = TZ eqn. (9): ar = a++-_J -s PC .=,C~
r=ro
dT TL..--T
The solution of eqn. (9) is given by eqn. (lo): -1n
T, -T
( T, -
cir
bz -+ [ h
ah-bg
xln(g+ 1.?
To 1 = F
h2
hz)
Fig. 10. Variation of the cross-sectional area of the particle bulk along the drum axis. Explanation of the symbols.
For the drum applied with the constriction at its end, the following data were estimated for F, = 2.51 l/h (Fig. 10): h, = 0.02 m - h2 = 0.0284 m S, = 0.143 A,
= 2.64
m - 10s3
m2
Ss = 0.172
m
AZ = 3-08
- 10B3 m2
(9)
r=o
’ (10)
In Fig. 11 the measured longitudinal temperature profiles and those calculated with 01 = 146 W/m2K are compared. The application of eqn. (10) yields a slight improvement in comparison to eqn. (6). However, the deviation between measured and calculated profiles is still large. To improve the model the temperature variation of the wall was also taken into account. By assuming a linear temperature profile of the wall with T,
= pK
atz=O,and
LJO
2goo
ct2
04
06
0.8
JO
2-
Fig. II_ Comparison of the longitudinal temperature profiles without reaction. (1) Calculated by eqn. (6), (2) calculated by eqn. (10). o measured_n = 5 r‘.p.x, F, = 2.5 I/h_
atzzO.5
T, = T,”
the temperature of the wall is given by eqn. (11) for 0 f 2 Q 0.5 : T, = 2(T,” -
T,o)z + T,”
(11)
By putting this value into eqns. (4) and (5), this yields eqn. (12): mc dT
2(T,m -T,O)t+T,O-TT-_ The transformation (13): -T,O)c+-T,O-T=-
2(Tz
aF
_
(12)
dt
by t = ZT yields eqn. mc
dT CYTF dz
(13)
For simplification we use: T,o)uF~
2(T,m -
mc T,” arFr mc --
(YFT mc
(14a)
= &
(14b) (14c)
Hence eqn_ (12) simphfies to eqn. (14): dT dz
-f-az+bifT=O
(14)
The solution of this differential equation yields [S] : UZ+z,
+ ” + 2,-fz (15) f P Figure 12 shows a comparison of measured and calculated IongitudinaI temperature profizes for Tz = 342 K, T! = 399 K, TO = 295 K, a = 163 W/m2 KS n = 5 r.p.m. and& = 5.1 l/h: One can recognize that eqn. (15) shows a significaat impro-cement on eqn. (6). However, T=-
-
Fv = 5.1 I/h. the agreement between calculated and measured profiles is not yet completely satisfactory. It is necessary to take into account the true temperature profile of the wall. Such calculations give satisfactory results.
Calculation of the Zongitudkzl temperature and conuersion profiles in the drum By means of the material and energy balances, the longitudinal ccnversion and temperature profiles can be calculated for small segments of the rotary drum reactor analogous to the method of Paszthory et al. [9]. The 1ongiDddinal heat transport rate is given by the transverse heat transfer rate by
f& = (YF(T,
c a
= f
Fig. 12. Comparison of the longitudinal temperature profiles without reaction. (1) Calculated by eqn. (6), (3) calculated by eqn. (15), o measured_ n = 5 r-p-m.,
-
T)
and the heat transport enthalpy by
rate due to the reaction
where C = concentration of sodium hydrogen carbonate, c = specific heat of the particle buik, F = heat trm_fer surface urea, AH =
reaction enthalpy, Q = heat fiow, R = reaction raLe, T, = mean temperature of the wall, T,, = temperature of the particle bulk at the entrance, T,, = temperature of the particle bulk at the discharge, and V, = volume of the particle bulk. In steady state the following energy balance is valid for every segment of the rotary drum reactor: oz,-&
+ddQ,+d&
(19)
Instead of the differentiai equations (19), difference equations were used for every section n: 0 = F,pcA T, + aAF,(T,
-
T,) + F,AC,(
-AH) (29)
9
where
ATi = Tn.,, - Tn.,, AC,
= en.,,
-
cn.ex
T n.en + T,.,,
T, =
2
To evaluate the c?:&version profile, the concentration difference in every section is divided by the entrance concentration C,, :
wAT,lAH
=
+ CYAF,(T, -
042.
c/i :’
r
1!
jI
j1
1
0
02
04
06
08
I
co =
Fig. 15. Longitudinal conversion and temperature profiles in tbe bulk of particles_ Calculated by the difference method. E; = 7.65 I/h, n = 5 r.p.m.
T,)/F,AH
C en (21)
where Ax, = x,-~ -x~, and AF, = the heat exchange surface area between the particle bulk and the wall in the section n. In Figs. 13 - 16 are plotted typical longitudinal conversion and temperature profiles, calculated according to this method. In Table 6 the calculated and measured conversions at the exit are compared for different feed rates. One can recognize that this simple method yields very satisfactory results.
QG6
60
OCL
60
QO2
LO
0
02
OL
06
06
1 z
Fig. 16. Longitudinal conversion and temperature profiles in rhe bulk of particles_ Calculated by the difference method_ Fv = 10.2 I/h, n = 5 r.p.m.
TABLE
6
Comparison of calculated and measured conversion a function of the feed rate
(:.p.m. 5 5 5 5
QO2
0
Q2
0-L
06
0.8
1
z
Fig. 13. Longitudinal conversion and temperature profiles in the bulk of particles_ Calculated by the difference method. F” = 2.5 i/h, n = 5 r.p.m. WC:
&ix
j
x
x
%hj
(meas.)
(caic.)
2.5 5.1 7.65 10.2
0.46 0.55 0.31 0.37
0.47 0.58 0.38 0.36
ACKNOWLEDGEMENTS
The authors gratefully acknowledge the financial support of DECHEMA and AIF.
006
120
LIST OF SYMBOLS
QOL
80
A
LO
c C
0.02
42 0
0 L
0.6
0.6
1
z
Fig. 14. Longitudinal conversion and temperature profiles in the buIk of particles. Calculated by the difference method. Fv = 5.1 i/b, n = 5 r_p.m.
as
EA
F
cross-section area, see Fig. 10 specific heat of the particle bulk concentration mean particle diameter activation energy contact surface (heat exchange) area between particle Iayer and the wall of the drum
10 F, AN
h J kD k k, K m n 4 R s(t) S f
T u T& x 2 a E ; ‘112 5
feed rate reaction enthdpy depth of the hed (see Fig. 10) integration constant (see eqn_ 15) temperature decay constant reaction rate constant maximal reaction rate constant cons+mt, see eqn. (6) mass rotational speed heat ffow reaction rate step response curve arcus (see Fig. 10) time temperature (K) velocity reaction volume degree of conversion dimensionless axial distance heat transfer coefficient porosity density temperature (“C) time to half-value, see eqn. (2) mean residence time
Indices 0 en ex
initial condition entrance discharge
n W
single section reactor wall
REFERENCES A. Manitius. E. Kureynsz and W. Kawecki, Mathematicai modd of the duminium oxide rotary kiln, Ind. Eng. Chem. Process Des_ Dev., 13 (1974) 132 - 142. V_ V. Jinescu and I. Jineacu, Verfahrenstechnische Berechnungsgrundlagen fiir Drehtrommelaniagen. Aufbereit. Tech., 9 (1972) 573 - 579. L. H. J. Wachters and H. Kramers, The calcining of sodium bicarbonate in a rotary kiln, 3rd Eur. Symp. Chem. React. Eng., Amsterdam, 1964, pp_ 77 - 87. M. Hehl, H. KrBger, H. Helmrich and K. Schiigerl, LongitudinaI mixing in horizontal rotary drum reactors, Powder Technol., 20 (1978) 29. M. Hehl, H. Helmrich, 3. Lehmbergand K. Schiigerl, Investigation of the thermal decomposition of powders in fluidiaed bed and rotary kiln reactors, Eur. Congr., Transfer Processes in Partide Systems, Nuremberg. 28 - 30 Mar. 1977, N2 (1977). H_ Helmrich, H. Kriiger. M. Hehl and K. Schiigerl, TransportvorgZnge und chemische Reaktion in Drehrohrreaktoren. presented on the DECHEMAJahrestagung 1977, Chem. Ing. Tech., 50 (1978) 139. J. Lehmberg, M. Hehl and K. Schiigerl, Transverse mixing and heat transfer in horizontal rotary drum reactors, Powder Technol., 18 (1978) 149 - 163_ H. KrGger, Untersuchungen zur Natriumhydrogencarbonataersetzungim Drehrohrofen. Diplomarbeit, TU Hannover, 1976. E. Paszthoqv, K. Schiigerl and M. Bakos, Vorausberechnung katalytischer StriimungsreaktionsSfen, Chem. Ing. Tech.. 31(1959) 432 - 438.